{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 3, 0, 0, -6],\n [-1, 5, 1, -5, -3],\n [-4, -4, -1, -5, 1],\n [-6, 0, -6, 1, 2],\n [-3, -4, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 0, -3, 3, -5],\n [-4, 4, -5, -1, 5],\n [0, 5, 6, 5, 3],\n [2, -2, -2, 6, -2],\n [-3, 6, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 5, 0, 6, -6],\n [-5, 2, 3, -1, 2],\n [6, 6, 0, -1, 4],\n [0, -1, 4, -1, 6],\n [2, 1, 0, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 6, -4, -3, 6],\n [4, 5, 4, -6, 0],\n [-4, 4, 0, 6, 4],\n [-6, 6, 4, 2, 5],\n [0, 1, -4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -2, -2, 4, 1],\n [-2, 5, -5, 3, 1],\n [-5, 1, 3, 2, 3],\n [0, -1, -2, 2, -5],\n [-2, 2, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 0, 3, -6, -1],\n [-3, -3, -3, 1, 3],\n [3, -3, 4, 2, -2],\n [2, -4, 4, 3, -3],\n [-5, -1, -6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, -1, -1, 3],\n [5, -1, 3, -5, -5],\n [1, -3, 5, 3, 0],\n [-4, -1, 2, 5, -2],\n [-1, 3, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 5, 2, 6, 2],\n [-2, -2, -3, 2, -2],\n [-3, 5, -2, -4, 0],\n [-4, 3, -1, -3, -6],\n [-3, 3, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -6, 6, -4, -3],\n [-3, -5, -5, -1, 2],\n [3, 0, 1, 6, 5],\n [-3, 0, 3, -6, 1],\n [3, 6, -2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -4, -2, 3, -2],\n [3, -3, -3, -1, 6],\n [-1, 4, 1, -6, -5],\n [0, -5, 1, 2, 4],\n [-6, -4, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -5, -4, -5, 6],\n [6, -6, -2, -1, 0],\n [-5, -1, -2, 0, -4],\n [1, -2, 2, -2, 1],\n [-5, 2, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -5, -6, -2, 0],\n [0, 3, -5, 0, 4],\n [6, 3, 4, 4, 0],\n [-1, -5, 1, -4, -2],\n [5, 1, -1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 2, -2, 5, -3],\n [-6, 5, 5, 1, 0],\n [2, 3, -4, -5, 5],\n [-5, 0, -1, -4, 5],\n [6, -1, 1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, -4, -2, -1],\n [2, -2, -4, 0, -6],\n [3, -2, 1, 0, -1],\n [-4, 6, 2, -6, -1],\n [5, 5, 3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, 5, -1, -6],\n [2, -1, -6, 6, 1],\n [-6, 6, -6, -3, 0],\n [-3, 5, -6, 2, 5],\n [-6, -6, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, 3, -5, -2],\n [1, 6, -6, 6, -2],\n [-3, 1, -4, -2, 4],\n [5, 1, 4, 3, 3],\n [6, 6, -3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, -6, -3, -2],\n [-6, 6, -3, 0, -1],\n [6, 3, 1, -4, 0],\n [1, 4, 2, -6, 0],\n [2, 5, 6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 6, 5, 0, 5],\n [5, 3, 3, -4, -5],\n [2, -2, -1, -3, -3],\n [-2, -1, 3, 0, 5],\n [1, -2, 2, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -5, -6, 2, -1],\n [2, -1, -6, 4, 2],\n [-1, -6, 5, 6, -5],\n [3, -1, 1, -4, -6],\n [4, 3, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 2, -6, 0, 1],\n [4, 6, -2, 3, -6],\n [5, -3, -3, -5, 0],\n [-1, -3, -2, -1, -3],\n [2, -3, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -1, 3, -2, -5],\n [5, -6, -6, 1, -5],\n [0, -2, 4, 5, -5],\n [6, 1, -3, 4, -1],\n [6, 5, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -6, 1, 1, 2],\n [-5, 5, -4, 1, -6],\n [-5, 5, -3, -2, -6],\n [-5, -2, 1, 5, -1],\n [3, 2, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 2, 1, 1, 1],\n [3, 3, -1, -5, 4],\n [-6, -1, -3, 0, -3],\n [1, 0, 2, -5, 2],\n [-4, -5, -5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 6, -2, 3, 2],\n [6, -1, 1, -3, -3],\n [4, 2, 5, -6, -3],\n [4, 6, 0, 4, 1],\n [2, 2, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 2, 4, 2, 3],\n [-5, 5, -4, -4, -5],\n [1, 1, -4, -2, 6],\n [3, -1, -3, 0, 0],\n [-3, -2, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 1, 2, -1, 3],\n [4, 5, -4, 5, 4],\n [-5, -6, -4, 1, -5],\n [-5, -4, 0, 4, -6],\n [-1, 1, 0, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -6, -5, 2, 5],\n [3, -5, 3, -6, -3],\n [-5, 0, -4, -4, -3],\n [2, 3, -4, 3, -1],\n [6, 1, 4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -6, 0, 5, -1],\n [-6, 0, -6, -5, 1],\n [-5, -4, 2, 4, 4],\n [0, -1, -1, -6, -1],\n [5, -5, -3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, 6, 0, 6],\n [1, 2, 2, 2, -3],\n [5, 1, -3, 1, 5],\n [3, 1, -3, -5, -4],\n [-2, -3, 2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 1, 2, -2, -1],\n [3, 4, 6, -3, 1],\n [0, 3, 0, -4, 4],\n [1, 3, -4, -2, 4],\n [0, -3, 1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 3, -3, -1, 3],\n [-6, 4, -2, 0, -2],\n [-6, -5, 5, -2, -5],\n [0, -5, -3, -1, 1],\n [1, -2, 6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 6, 2, -1, 4],\n [-3, -6, 3, -5, -1],\n [-3, 2, -4, 5, 0],\n [2, -1, -1, -2, -3],\n [5, 2, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 4, -4, -6, 5],\n [-1, 4, 1, 1, 0],\n [5, 0, -6, 2, 6],\n [3, 6, 0, -5, 6],\n [2, -3, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 5, 3, 1, 2],\n [3, 5, 6, -5, 2],\n [-6, 1, 2, 6, -5],\n [2, 5, -3, -5, -1],\n [-4, -3, 1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, 3, 0, -2],\n [-1, -4, 5, -4, 3],\n [5, -1, -2, -5, 3],\n [-5, 2, -2, -6, 0],\n [3, -6, -6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 6, -6, 4, -1],\n [6, 1, 3, 4, -5],\n [0, 0, -5, -6, 3],\n [1, 0, -2, 4, -4],\n [-3, -1, 0, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 6, -3, -3, -3],\n [6, 3, 4, 6, -3],\n [-2, 4, -2, 0, -4],\n [4, 2, -5, -2, 6],\n [2, -4, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 5, 2, -6, 4],\n [-5, 0, -6, 3, 0],\n [-1, -5, -2, 1, -2],\n [0, -1, 6, 1, 5],\n [-5, -2, 5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 5, 1, 5, -3],\n [4, 0, 0, -3, -3],\n [6, 2, -6, 4, 3],\n [-3, -1, -1, -5, -5],\n [6, -2, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 1, -2, -6, 0],\n [6, -5, 6, -4, 2],\n [4, -2, 3, -1, -6],\n [5, -6, 1, 0, -5],\n [-1, 1, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 3, -1, 1, -2],\n [1, -3, 3, 5, -1],\n [-1, -4, 5, -5, -3],\n [-3, 1, 0, 6, 1],\n [-4, -1, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 2, -5, -5, 5],\n [2, -6, -1, 2, 5],\n [4, -4, -4, -4, 0],\n [-2, -3, -2, 4, 4],\n [-1, 1, 2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 3, -6, -1, 5],\n [3, 1, -2, 5, 5],\n [-5, -1, 1, 4, 0],\n [-4, -3, 1, 6, 3],\n [-5, -5, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 1, -5, 3, 0],\n [1, -1, 3, -2, 3],\n [2, 1, -2, 3, -5],\n [1, -2, 2, -5, 1],\n [1, 1, -1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -4, 3, 3, 3],\n [5, 2, 0, 2, -5],\n [0, 1, -3, -1, -6],\n [3, -4, 6, -1, 6],\n [-1, -1, 0, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 0, -2, 1, -3],\n [4, 2, -1, 6, 4],\n [4, -1, 3, 0, -1],\n [4, -3, -5, -5, 0],\n [-5, -4, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, -6, 6, -5],\n [2, 6, -1, 5, -3],\n [-3, 2, 6, -4, -4],\n [4, -6, 0, 0, -4],\n [-6, 6, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -6, -1, 1, -6],\n [2, 1, 6, -2, -5],\n [0, 5, -5, 6, -1],\n [0, 5, -1, -2, -4],\n [6, -3, 3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, -1, 3, -1],\n [6, -6, -6, -6, 2],\n [3, -3, -2, -4, 2],\n [-1, 3, 6, -3, -3],\n [1, -5, 4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, 1, 1, -4],\n [-2, 3, -5, 2, 6],\n [-6, 1, 1, 0, 0],\n [3, -1, -1, 3, -5],\n [-1, -6, 2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 1, -2, 0, -1],\n [-3, 3, 3, -5, 1],\n [6, 1, -1, -6, 1],\n [-4, 4, 6, 4, -2],\n [-1, 2, -5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 5, 6, -3, -2],\n [-3, 1, 2, -4, 4],\n [-3, 3, 3, 5, -2],\n [-4, 5, 2, 2, -1],\n [-6, -1, 5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 1, -4, -2, -3],\n [-4, -1, -4, -6, 1],\n [-3, -1, -6, -4, 5],\n [0, 3, -4, 1, 5],\n [6, 4, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 0, -5, -2, 5],\n [-4, 4, 4, -3, 2],\n [-5, 2, 3, -5, -1],\n [-2, 4, 2, 5, 3],\n [4, -5, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 0, 3, -2, -6],\n [3, 2, 3, 5, 0],\n [0, 5, -5, -4, -3],\n [-1, -4, -6, -6, 5],\n [-3, -6, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -4, -1, 1, -1],\n [-3, 1, -6, -5, 3],\n [-6, -3, -6, -5, 4],\n [6, -5, 2, 6, -6],\n [4, 5, -3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -6, 0, -4, 0],\n [-6, 1, 3, -3, 1],\n [-2, 1, 4, 6, 4],\n [-1, -3, 6, -6, -6],\n [2, 5, 1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -3, -1, 3, -5],\n [-3, -2, 0, 0, 4],\n [-1, -1, 6, 5, -5],\n [0, 5, 0, 2, 3],\n [0, 3, 5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, -6, -5, 5],\n [-6, 3, 6, -1, 6],\n [-4, 6, -4, 2, -3],\n [-2, 5, -5, -5, 1],\n [5, 3, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 5, 3, -1, -4],\n [0, 4, 3, 4, 3],\n [6, 1, -4, 4, 3],\n [-5, -5, -2, -2, -6],\n [3, 0, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 5, -6, 1, -1],\n [-3, -3, -6, 5, 0],\n [-3, 0, 4, -3, 4],\n [1, -5, 5, 2, -1],\n [6, -3, 3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -2, -6, 4, 1],\n [5, -2, -6, -5, -3],\n [-5, 3, 1, 4, 6],\n [5, 4, 6, -6, -4],\n [-4, 4, 2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -2, -5, -2, 0],\n [6, 1, 0, 6, 6],\n [5, -6, 2, 4, -5],\n [2, 6, -3, -4, -6],\n [-4, 2, -2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -3, -2, -1, -2],\n [0, -6, 3, -4, 5],\n [-3, 4, -6, 6, 3],\n [-6, 4, -6, 0, -4],\n [-3, 3, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -1, 5, 1, 1],\n [-3, -4, -5, 4, -3],\n [2, 0, 6, 2, -4],\n [0, -4, 2, -6, 6],\n [0, 0, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -3, -3, -6, -6],\n [6, -4, -2, 5, -1],\n [5, -2, -4, -6, 1],\n [-2, 0, -3, 6, -2],\n [5, 0, 4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 3, -4, -3, 5],\n [-1, -1, 6, -6, -3],\n [-1, 1, -3, 3, 5],\n [4, 6, -1, -5, -6],\n [1, 3, -5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -6, 1, 6, 1],\n [-5, -4, -5, -1, 4],\n [-3, -2, -5, -5, 3],\n [-2, 5, -1, 6, 0],\n [1, -3, -5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, 1, 1, 6],\n [-2, 2, -1, 4, -3],\n [-4, 0, -5, -3, -4],\n [-4, 4, 3, 0, 2],\n [3, 4, 2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 1, -2, -6, 2],\n [6, -6, 2, 5, 3],\n [3, -3, 2, 5, -6],\n [-1, 4, 2, 1, -5],\n [-1, 2, 5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 0, -1, -3, 6],\n [-6, 3, 6, -4, -2],\n [-5, 5, 3, -4, 2],\n [2, -6, -5, 2, -5],\n [3, -6, -6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 2, 2, 6, 4],\n [-1, 3, 0, -5, 6],\n [6, -1, 5, -3, 3],\n [4, 6, 0, 4, -1],\n [-6, -2, 4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 4, -1, 4, -6],\n [2, 6, 5, -6, -2],\n [0, 0, -2, 2, -2],\n [5, -2, -4, -3, -2],\n [5, 2, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, -6, 6, 6],\n [2, 4, 5, 2, 3],\n [4, -1, -6, -2, 0],\n [-6, -5, -5, 1, 1],\n [4, 3, 2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 0, 1, 2, 5],\n [-3, 3, -5, 5, 3],\n [0, -5, 5, 2, -4],\n [6, -6, 1, 3, 4],\n [3, -5, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 2, 6, -3, 3],\n [-1, -2, 3, 6, -5],\n [-4, 2, -1, 6, -5],\n [-4, 4, 3, 2, 3],\n [4, 0, -5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 0, 4, -2, -5],\n [-5, -3, 0, -6, 0],\n [4, 5, 3, -2, 6],\n [-6, 6, -2, -1, -1],\n [-1, -3, 1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -4, 3, 0, 2],\n [-1, 1, 2, -3, 1],\n [0, -5, 0, -5, -3],\n [-2, 5, 6, 4, -5],\n [-6, -2, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, -4, -5, -2],\n [2, 6, -1, -5, 4],\n [5, -5, 6, -3, 5],\n [1, -2, 6, -6, -2],\n [-2, -4, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, 6, 4, -4],\n [6, -6, 5, 0, -3],\n [-6, -5, 3, 5, 3],\n [-1, 3, 3, 3, 2],\n [1, 2, 0, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -3, -5, 0, -5],\n [-4, 2, -3, 5, 0],\n [6, -4, 6, 2, 0],\n [2, 1, -5, 3, -6],\n [-6, -6, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 6, 1, 2, 5],\n [-4, -4, -4, -6, 5],\n [-4, -4, 3, 2, 2],\n [4, -4, 6, 2, 6],\n [5, 5, 0, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 3, -1, -3, 5],\n [1, 4, 1, -2, -6],\n [-5, 1, -4, 2, 3],\n [-2, -2, 0, -2, 0],\n [-5, -6, -5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, 1, 2, 5],\n [6, 1, -6, 2, 4],\n [6, 2, -4, 2, 5],\n [-2, 4, -3, 0, -2],\n [6, 4, -6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 5, 1, -3, 6],\n [-5, 4, 1, 1, 4],\n [4, 3, 0, 0, 2],\n [4, 5, 1, 5, 3],\n [-5, -3, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -4, 3, 6, -2],\n [-6, -3, 2, -4, 2],\n [-3, 5, -2, -5, -3],\n [-2, 6, -2, 4, -3],\n [-1, -1, 4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -3, -3, 1, 3],\n [-3, -1, -4, 3, -6],\n [2, 1, -4, 5, -2],\n [-4, 0, 0, 5, 4],\n [0, -1, -4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, 5, 1, -6],\n [-5, 2, -2, -4, 0],\n [5, -4, -6, -4, -4],\n [-1, 2, 4, 3, -5],\n [6, 5, 5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, 3, -2, 6],\n [0, -2, 4, 3, -3],\n [6, -4, 1, -6, -6],\n [3, -6, 4, -5, -4],\n [3, 6, 4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, -2, -4, 0],\n [3, 2, 6, 2, 0],\n [1, 6, 4, 3, -4],\n [0, -3, 3, -3, 0],\n [3, 6, -6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 3, -5, -3, 1],\n [6, 0, 1, 4, -5],\n [2, 1, 4, 6, 3],\n [2, -2, 0, -6, 1],\n [-3, -6, -1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 1, 2, 6, -1],\n [0, 0, 3, 5, 4],\n [5, 5, 6, 3, -2],\n [6, -6, 5, -4, 3],\n [6, -1, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 1, 0, -3, -2],\n [-1, 0, -1, 1, -3],\n [-1, -5, 0, -6, -4],\n [1, -1, 5, 1, 6],\n [-6, -5, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -2, 4, 4, 1],\n [-4, 6, -6, 5, 4],\n [-6, 1, -4, 5, 5],\n [2, -5, -6, 6, -6],\n [0, 3, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, -5, 5, 6],\n [-3, 3, 2, 4, -6],\n [-3, 5, -6, 1, 2],\n [1, 2, 2, 5, -5],\n [2, 2, -6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, -4, 5, 2],\n [4, 0, 4, -2, 4],\n [2, -6, 4, -6, -5],\n [2, 1, 3, -1, 2],\n [-1, 3, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 1, -5, 1, -6],\n [6, 5, -2, 2, -3],\n [2, -4, 5, 0, 1],\n [0, 0, 2, 2, -2],\n [1, 2, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -4, -1, -3, 4],\n [3, 0, 0, 1, -3],\n [6, 4, -2, 0, 2],\n [-2, 0, -1, 3, -6],\n [2, 3, 4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 4, -1, 3, 5],\n [-1, 3, -3, 2, -6],\n [-5, 3, -6, -2, 1],\n [-1, -2, -3, 2, 3],\n [2, -6, 3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 3, 5, -4, -2],\n [-2, 1, 4, 5, -2],\n [3, -5, -2, -1, -2],\n [-6, -4, 2, 5, 0],\n [6, 6, 3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, 3, 4, 6],\n [-6, 2, -1, -1, -2],\n [-2, -3, 4, -3, 1],\n [4, 4, -4, -5, -3],\n [-1, -2, 4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 1, 1, -6, -3],\n [0, -2, -3, 1, -3],\n [-5, 0, -6, -3, 3],\n [-6, 6, 5, 6, -1],\n [-2, 5, -3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 0, 0, -4, -5],\n [-3, 1, -3, 1, 0],\n [6, 0, -5, 6, 6],\n [2, -5, -1, 4, 4],\n [-4, -6, -4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 5, -3, -5, -3],\n [-4, -5, -1, 5, 5],\n [2, -5, -4, -1, -1],\n [2, -2, 2, 2, 0],\n [3, 0, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 2, 1, 6, 5],\n [-4, 5, 4, 0, -6],\n [1, -2, -5, 6, 3],\n [5, 3, 6, -6, 4],\n [-4, 5, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, 5, 3, 2],\n [-1, 6, -3, -6, -3],\n [4, 6, 0, 6, 3],\n [5, 5, 1, -2, -2],\n [-6, 6, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 1, -6, 6, -5],\n [0, -2, 1, -2, 4],\n [1, 2, -6, 5, -2],\n [1, 4, 5, 0, -5],\n [2, -4, 6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -5, 4, -2, 3],\n [3, -6, -3, 6, -2],\n [-6, 5, 0, 4, 3],\n [6, 4, -4, 1, -6],\n [6, 5, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 0, 0, -1, 6],\n [-1, 6, 3, 2, 1],\n [-1, 4, 5, 2, 4],\n [-2, 0, 0, 2, 4],\n [5, -6, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -3, -1, -4, -6],\n [3, -3, 1, -3, -5],\n [6, 5, 4, -6, 6],\n [-5, 6, 4, 0, -1],\n [4, 6, -6, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -4, 1, 0, 5],\n [5, 0, 2, 0, -6],\n [-5, -3, 1, 1, 4],\n [6, 6, -3, 1, 4],\n [-3, -5, 0, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 5, 2, -3, -3],\n [-6, 0, 2, 0, 4],\n [-5, -1, -6, 2, -5],\n [6, 2, 4, -6, -5],\n [6, -4, -6, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 0, 4, 4, -6],\n [-3, -6, -2, 0, -5],\n [5, -6, -3, -1, -2],\n [4, 3, -6, 1, -3],\n [2, -3, 3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 5, 1, -6, 3],\n [5, 6, 4, -1, -1],\n [4, -1, 4, -1, -2],\n [-3, -4, -4, 2, -2],\n [-4, 6, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, 2, 4, 1],\n [-2, -2, -4, -6, 5],\n [4, -4, 4, -5, 4],\n [2, -2, 3, -5, 3],\n [1, 0, -5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 3, -3, -3, 0],\n [4, -3, -4, -2, 0],\n [-3, 3, 1, 0, -2],\n [5, -1, -3, -3, -1],\n [6, 0, -5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 4, -2, 3, 0],\n [-1, 2, 3, 2, -2],\n [5, 6, 1, 5, -3],\n [4, 4, -5, -1, 3],\n [0, -2, 5, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -4, 1, -2, -2],\n [-5, -6, 4, -3, -5],\n [2, 0, 4, 1, -1],\n [6, 2, 1, -5, -1],\n [5, -4, -1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, -4, -3, -4],\n [-1, 4, -5, 3, -3],\n [5, 2, -3, -4, 4],\n [2, 3, 4, 4, 0],\n [6, 5, -1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -1, 5, 6, 1],\n [4, 2, 6, -2, 2],\n [2, 6, -3, -1, 3],\n [5, 3, 0, 4, 5],\n [5, 3, 0, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -2, 5, 1, -1],\n [5, 1, -1, 5, 3],\n [-3, 1, -2, -2, -4],\n [1, -3, -1, 0, 2],\n [6, 3, -3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 2, -3, 0, 0],\n [0, 0, -5, -1, -6],\n [-5, 2, 0, 3, 3],\n [-5, -1, -1, -2, 0],\n [-5, 3, 2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -5, -4, 5, -1],\n [5, -2, -3, -4, 5],\n [4, 5, 6, -6, 4],\n [0, -1, 1, 3, 6],\n [2, -6, 2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -2, -2, -5, 1],\n [3, -4, 0, 4, -1],\n [-2, 2, 1, 1, 5],\n [-6, 0, -2, -1, 1],\n [-5, -1, 3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -1, 6, -4, -2],\n [-2, -6, 4, -3, -5],\n [-1, 4, -6, -1, 5],\n [-4, -2, -1, 4, 6],\n [6, 5, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 6, 6, 5, 0],\n [-6, -2, 6, -5, -3],\n [3, 6, 6, 2, 4],\n [-2, -5, 6, -4, -6],\n [-3, -1, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -3, 6, -3, -6],\n [6, 3, -2, -4, -5],\n [-3, -4, -1, -2, -1],\n [0, 5, 5, 2, 2],\n [-2, -6, 0, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 6, 6, 0, -2],\n [4, 4, 0, 6, -2],\n [6, -2, -4, -2, -3],\n [-2, 2, 4, 3, 4],\n [-2, 6, 1, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -3, -3, 5, 0],\n [-3, -3, 4, -6, -6],\n [-1, 6, -6, 6, 4],\n [-6, -4, -2, 2, -2],\n [-5, -4, -2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 5, -2, -1, 1],\n [-1, 4, -1, -2, -1],\n [-2, 5, 5, 6, 2],\n [2, 6, 0, -6, 3],\n [-1, -4, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -4, -1, -2, -6],\n [0, 5, 5, 4, -6],\n [1, -2, -5, -5, 1],\n [-6, 1, -3, 1, -2],\n [6, 0, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 6, 4, 3, -4],\n [4, -3, 3, 4, 2],\n [-3, -1, 3, -2, 3],\n [0, -2, 2, -1, 4],\n [-4, -6, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 1, 5, -4, -2],\n [1, 5, 3, 6, 3],\n [-5, -3, 6, -1, 0],\n [6, -6, -1, 5, -2],\n [-3, 1, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 2, 4, 3, 5],\n [-4, -1, 0, 2, 1],\n [3, 6, 3, 4, 5],\n [1, 0, -4, 6, 4],\n [1, 4, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -3, -5, 5, 3],\n [-6, -4, 4, -5, 6],\n [-3, 2, 4, 2, 0],\n [6, 0, 5, 0, 1],\n [-2, -5, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 2, -5, -1, 5],\n [3, -5, -5, 3, 6],\n [-3, 2, -1, 6, 5],\n [-3, -5, -1, -3, -3],\n [1, 4, 1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, -4, -3, -6],\n [-5, 1, -6, 1, -1],\n [-4, -3, -1, -5, 2],\n [-4, -1, -5, -2, 1],\n [-4, 2, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 1, -3, -6, 6],\n [3, 1, -2, 3, 5],\n [3, 1, 0, -4, -2],\n [-6, 4, 3, -1, 2],\n [1, -3, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 1, 2, 1, -6],\n [-2, 5, 1, -3, 4],\n [-4, 6, -5, -2, -4],\n [5, -2, 3, 4, -3],\n [-1, 1, 1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 3, 1, 6, 0],\n [-4, -4, -5, -2, 0],\n [-3, -6, 5, -5, 5],\n [0, -6, -3, -2, 0],\n [6, -4, -1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 1, -5, 6, -3],\n [-6, 6, -5, -6, -1],\n [-4, -1, 4, -5, 2],\n [1, 1, -4, 2, 2],\n [5, -5, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 0, -1, 2, -2],\n [-5, 4, -1, -4, 2],\n [1, -4, -3, -1, -5],\n [-5, 1, -2, 5, 4],\n [0, -3, 5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 6, 3, 5, 6],\n [1, 0, -4, -5, 0],\n [3, 2, 0, -4, 4],\n [5, 2, -5, 0, -3],\n [2, 3, 4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 5, 5, 5, 2],\n [-6, 1, -5, -1, -6],\n [3, -3, 4, -6, 5],\n [-1, -6, 1, -6, 2],\n [2, -4, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -4, 1, -2, -4],\n [2, -5, -3, 6, -6],\n [-2, -3, -4, 6, -4],\n [-3, -3, -1, 1, 0],\n [-4, -6, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, 3, -5, 2],\n [3, 1, -2, 6, 0],\n [-6, 6, -5, 0, -4],\n [6, -1, -2, -3, -2],\n [3, 5, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 5, 6, -4, 2],\n [-2, -5, 6, -3, 1],\n [-3, 4, -1, -4, 3],\n [0, -2, -3, 5, 4],\n [-1, -2, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 6, -3, 0, -3],\n [5, -5, 0, 2, -5],\n [-2, -4, -5, -2, -1],\n [0, 4, 3, 3, -1],\n [4, -3, -2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -5, -2, -4, 3],\n [4, -3, 6, -1, -5],\n [5, 3, -1, 5, 0],\n [2, 3, 1, 3, -2],\n [1, -3, -6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 2, 3, -3, 6],\n [-5, -2, -5, 0, 3],\n [3, -1, -3, 4, -6],\n [-1, 1, 5, 0, 2],\n [-3, 6, 3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -6, 2, -5, 5],\n [2, 5, 1, 1, -5],\n [-3, -2, -3, -6, 3],\n [3, 4, -2, -1, 5],\n [-6, 6, 4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -1, 3, 3, 6],\n [-3, 1, -6, -3, 2],\n [0, -5, 2, -3, 5],\n [6, 3, 0, -4, 3],\n [3, -6, 3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -4, 0, 1, -2],\n [5, 4, -2, -6, -1],\n [3, 1, -4, -1, 6],\n [3, -4, -5, -5, 2],\n [1, -5, 5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, 6, -2, 6],\n [3, 5, 0, -3, -4],\n [-6, -5, 2, -1, 1],\n [0, 1, -1, 5, 0],\n [-2, 4, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -3, -4, -4, 6],\n [-1, 5, -3, -1, -2],\n [-5, -5, 0, 5, 2],\n [-1, -5, 6, 6, -4],\n [-5, 2, 5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, 3, -4, 6],\n [2, 3, -3, -4, -1],\n [3, 6, 0, 3, -4],\n [-1, 6, -3, 0, -4],\n [1, -5, 5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -3, 4, -1, 1],\n [-3, -1, 4, 5, 4],\n [2, 3, 2, 0, 0],\n [2, 4, 4, -6, 6],\n [-4, -6, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -3, 5, -3, -1],\n [-5, -4, 2, 5, 5],\n [-5, -2, -3, -6, -4],\n [-4, -5, 2, -2, -6],\n [6, -4, -4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 0, 3, -5, -6],\n [-2, -4, -1, -3, -6],\n [-6, 6, -2, -2, -4],\n [1, -5, -5, -5, -4],\n [-6, -3, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -1, -5, 0, -2],\n [1, 5, 6, -5, 2],\n [2, 3, -2, 3, -5],\n [3, -5, 5, 6, 2],\n [6, 6, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -4, -6, 0, 5],\n [0, 1, 2, 5, 4],\n [2, 0, -6, -2, -4],\n [-2, 6, -1, -6, 2],\n [-6, 5, 1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 2, 3, -5, 5],\n [1, -1, 0, -1, -1],\n [1, -3, 6, 2, 0],\n [4, -5, -3, 1, -1],\n [4, -1, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, 5, 1, 2],\n [4, -1, 1, 2, 5],\n [0, -4, 2, 0, -3],\n [-4, 6, -2, -1, -6],\n [0, 4, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 2, 0, -3, -3],\n [-4, 6, 0, -1, -5],\n [1, 4, -6, -1, 6],\n [-1, -5, -1, -6, 5],\n [-1, -5, 0, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 2, -4, -1, 2],\n [-6, -1, -5, -5, 1],\n [-6, 2, 0, -2, -1],\n [2, -1, -4, 6, -1],\n [-6, -6, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -4, -4, 6, -1],\n [2, -2, 4, -6, 4],\n [-2, 3, -2, -1, -3],\n [2, -5, -2, -3, -2],\n [-6, 4, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -5, 1, -5, -6],\n [3, 4, 5, -2, 4],\n [-5, 2, -2, 1, 5],\n [2, -5, -3, 0, 2],\n [-1, -6, 4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 1, -6, 4, 5],\n [3, -4, 2, 0, 2],\n [-4, 4, 5, 6, -3],\n [-1, -6, 4, -2, 4],\n [-4, 6, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 0, -4, 6, 6],\n [3, -4, 4, -4, -5],\n [-2, -2, -2, 3, 1],\n [2, -2, -4, -3, 0],\n [-2, -3, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -2, 4, 5, -5],\n [1, 4, 4, -2, 6],\n [2, 0, 2, -4, 3],\n [1, -6, -1, 2, 3],\n [-1, 5, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 6, 1, 1, 5],\n [-2, -1, -5, -5, 4],\n [1, -2, 5, 4, 0],\n [2, -1, -4, 1, 1],\n [2, 6, 5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 4, 2, -6, -6],\n [-4, -2, -4, -4, 1],\n [6, -1, -3, -4, -4],\n [5, -2, 6, 4, 4],\n [-1, 1, 3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -6, 1, -4, 4],\n [-2, 3, -6, 6, 5],\n [-5, 4, 1, -4, -1],\n [1, -5, 4, -5, -3],\n [-6, 4, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, -1, 3, -4],\n [-4, 2, -4, 3, -3],\n [2, -3, 3, 5, 4],\n [4, 6, 5, -4, 1],\n [4, 1, -3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 6, 3, 4, 0],\n [-4, -1, 3, -4, 0],\n [2, -4, -5, 3, 2],\n [-6, -2, -6, -3, 6],\n [3, 6, 1, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 6, -1, -4, 1],\n [-3, -4, -2, -1, -1],\n [2, -5, -1, -6, 3],\n [4, -1, 6, -4, 5],\n [-1, 1, 6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 0, -5, 1, 5],\n [0, 0, -2, 1, 0],\n [0, 0, 1, -4, -2],\n [0, -4, 6, -4, -2],\n [-6, -1, 6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, 3, -3, 4],\n [0, -6, 1, -6, -1],\n [-5, -1, 5, 5, -1],\n [-4, 2, -5, 5, 3],\n [-2, -4, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 6, -6, -6, -5],\n [0, 5, -6, -4, 2],\n [4, -1, 4, 1, -6],\n [2, 4, 4, -5, 0],\n [-5, 1, 6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 6, 6, 0, 2],\n [3, -6, 0, -3, -2],\n [-6, 2, 0, 3, -3],\n [6, -2, 3, -6, 1],\n [-1, 4, -6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 6, 1, 2, 1],\n [2, 5, -3, -1, 6],\n [-6, 5, -6, 2, -3],\n [0, -4, -1, 0, 4],\n [-6, 6, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, -3, -2, 0],\n [-4, -5, 6, -5, 0],\n [6, 0, 5, -3, -4],\n [-5, 6, -2, 4, 1],\n [-3, -3, 5, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -4, 6, -2, -5],\n [-4, -3, 1, -1, 2],\n [-3, -5, 0, -1, -5],\n [0, -5, -3, 5, 3],\n [6, 1, -2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 3, -5, -6, -3],\n [-6, -4, 2, -5, -3],\n [-3, -6, -4, -5, 4],\n [-2, 5, 5, 3, 4],\n [2, 6, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -4, 1, 3],\n [4, -3, -6, -2, -3],\n [2, 3, 2, -4, -4],\n [4, -3, -3, 6, -4],\n [-5, 1, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -2, -1, 4, 5],\n [-3, -6, 5, -1, 1],\n [6, 4, 3, -2, -1],\n [-4, -4, 5, 0, -6],\n [-3, -6, 1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, -5, 4, 3],\n [-6, 6, 4, -3, -2],\n [6, 3, -6, -6, -3],\n [4, -4, -1, 0, 0],\n [-4, -4, -1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -2, -1, 4, -1],\n [-2, -3, 6, -1, -3],\n [6, -1, -1, 1, -6],\n [-5, -1, 1, -6, -1],\n [6, -1, -4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 5, -5, 3, 0],\n [6, -4, 2, 6, 5],\n [-4, 5, -3, 0, -3],\n [-4, -5, -6, 6, 0],\n [-5, -2, -3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -4, 0, 2, -5],\n [-5, 4, -4, 5, 3],\n [0, -2, -1, 3, 0],\n [-3, 5, 1, 5, 5],\n [6, -5, -6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 2, 0, 2, 0],\n [-4, 5, 1, 4, -4],\n [-2, 6, -5, -6, 3],\n [5, 5, 5, -2, 2],\n [6, 2, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, 6, -2, -5],\n [2, -1, 5, 4, -5],\n [6, 5, 6, 3, -1],\n [6, 3, -4, -6, -1],\n [-1, 4, -3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -2, -6, 2, -2],\n [3, 3, -4, -6, 1],\n [-6, -6, -5, 2, 1],\n [5, 5, -5, -2, 6],\n [6, 1, -2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 3, 0, 5, 1],\n [5, -2, -1, 3, 0],\n [-4, 3, 4, -2, -4],\n [3, -1, -6, 6, 3],\n [4, 4, -1, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 6, -6, -6, 4],\n [-4, -4, 0, 6, 4],\n [4, 5, 3, 1, -6],\n [2, 0, -5, 5, -3],\n [-4, -3, 6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 0, -1, -4, 6],\n [-3, 3, -5, 3, 0],\n [1, 2, 6, 0, 0],\n [3, -2, -3, 6, 0],\n [-1, 0, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 3, 6, 4, -2],\n [-6, 2, -5, 1, 5],\n [1, 1, -5, -6, 2],\n [-2, -6, -3, 3, 1],\n [-1, -6, 3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 4, 0, 6, -2],\n [-2, -6, 0, 3, -6],\n [-3, -5, -2, -5, 2],\n [-3, -4, 6, -1, -5],\n [6, -3, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 2, -1, 1, 3],\n [3, -1, -5, 2, -3],\n [1, -4, 1, -2, -6],\n [-3, -1, 1, 5, -3],\n [6, -1, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 1, -4, -2, -3],\n [-3, -1, -5, 2, -1],\n [0, -2, 2, 4, 2],\n [-4, -3, 5, 4, 4],\n [0, -1, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 4, 6, -2, -5],\n [-3, -2, -5, -5, 5],\n [4, -5, -4, 0, -5],\n [-1, -6, 0, -5, -5],\n [-6, -3, 6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 1, -3, 5, -3],\n [6, 3, 5, 6, 1],\n [-1, -1, -1, -5, -4],\n [-5, 1, 2, 3, 4],\n [5, 0, 3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -3, -6, 1, -4],\n [-2, -5, 6, 6, -6],\n [4, -2, -3, -4, -6],\n [-6, -5, 5, 5, 4],\n [0, -1, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -5, -3, -6, -5],\n [5, -4, 3, 5, 3],\n [0, 6, -2, -5, 0],\n [-1, -4, 4, 0, 0],\n [1, -3, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -2, -3, 0, 2],\n [3, 5, -6, 0, -4],\n [3, 0, 4, -3, -4],\n [1, -5, -5, 4, -2],\n [-1, 5, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -1, 1, -3, 5],\n [2, -3, 6, -3, -2],\n [0, 0, 5, 1, -2],\n [1, 3, -5, 2, 6],\n [3, 5, 1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -1, 5, 6, -4],\n [-4, 5, 4, 4, -4],\n [1, -4, -4, 0, 6],\n [6, -3, 1, 2, 5],\n [3, 3, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 0, -3, 4, 4],\n [0, 5, -6, -6, 2],\n [2, -5, -5, -2, -5],\n [3, 4, 6, 5, -3],\n [5, 6, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -3, -3, 2, -6],\n [-5, -3, 4, 4, -1],\n [5, 0, 1, 4, 2],\n [-1, 2, -3, 3, -2],\n [3, -6, 4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 4, 4, 3, 0],\n [2, 3, 2, 1, 2],\n [-5, -3, -4, -1, -1],\n [5, -4, -4, -6, 2],\n [-3, -5, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, -1, 0, 1],\n [1, 3, 5, 1, 0],\n [-2, 5, 2, 4, -1],\n [-5, -5, 2, -2, -3],\n [-1, 4, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 3, 0, 4, -3],\n [-3, 1, -2, -5, -5],\n [-4, 3, -4, -6, 4],\n [3, -5, 5, 0, -1],\n [-5, -1, -4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -2, 0, -3, -2],\n [-6, -2, 6, -4, 2],\n [-2, -4, 2, 0, 2],\n [0, 6, -3, 2, -5],\n [2, 6, -5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -1, 5, 5, -5],\n [3, -5, -6, -1, 0],\n [-3, 5, 0, 5, 5],\n [6, 0, 3, 3, 0],\n [0, 5, -5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -5, 3, 5, 0],\n [2, -4, -2, -3, 6],\n [4, 4, 6, 6, -2],\n [-5, 2, -5, -3, 1],\n [6, 0, 4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 6, -3, 3, 3],\n [-5, -2, -4, -5, 4],\n [1, -6, -5, 6, -4],\n [-3, -6, 2, 4, 4],\n [-2, 0, 1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -6, 3, 5, 5],\n [-1, -5, -6, -5, 3],\n [3, -4, 0, 2, -3],\n [3, -6, -4, 0, 5],\n [-1, -5, 6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 4, 3, -4, 1],\n [-4, -1, 1, -3, 3],\n [6, 3, 1, 4, 3],\n [2, -6, 5, 3, 0],\n [-5, 5, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -1, 3, -5, -1],\n [-6, 6, -1, -2, 6],\n [6, 3, 4, 5, 2],\n [-4, -5, 3, 2, -3],\n [-5, 3, 5, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 1, 6, -6, 6],\n [-4, -2, -4, 1, -3],\n [-5, 3, 5, 2, 4],\n [-2, 6, -6, -5, 3],\n [6, -4, -5, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 6, 3, -3, 3],\n [-6, -6, -6, 3, -3],\n [0, 6, -6, 6, -3],\n [0, 1, -3, 6, -3],\n [-1, -2, 6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 3, 4, 0, 0],\n [-1, 6, 6, 1, 0],\n [4, 1, -2, 6, 1],\n [5, -5, -3, 1, -1],\n [-3, 6, -4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -6, 3, 6, -5],\n [2, 4, -1, -1, -1],\n [-6, -1, -5, 0, -4],\n [-3, -3, -4, 4, -4],\n [3, -3, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 0, 6, -6, -1],\n [-2, 6, -2, -1, -3],\n [-4, -1, 4, 4, -5],\n [1, -6, -3, 0, -1],\n [-5, -5, -2, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -3, 5, 1, -1],\n [6, -3, -2, 4, -4],\n [4, -4, -3, 1, 5],\n [-2, 2, 0, 2, -6],\n [6, 0, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, -4, 0, -6],\n [-5, -3, 1, -2, 5],\n [-3, 2, -2, -3, -4],\n [-5, -4, -5, 3, -4],\n [5, -3, -5, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -4, 4, -4, -2],\n [1, 2, 5, 6, 0],\n [5, -3, -6, 5, 0],\n [-5, 1, -6, -3, 0],\n [6, -3, -2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 1, -2, -1, -3],\n [0, -6, 6, -5, 6],\n [-3, 2, 1, 5, 5],\n [2, -3, 0, 0, 2],\n [3, 4, -6, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 5, -2, 6, -2],\n [-6, 0, 6, 3, 5],\n [5, -4, 1, -3, 3],\n [3, 5, -4, 0, 0],\n [3, -6, 4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 0, 2, 4, -3],\n [-1, 6, -4, 2, 6],\n [-4, 4, -4, 0, -1],\n [-4, 4, -2, 6, -1],\n [-3, -1, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 2, 2, 6, -2],\n [-6, -1, 5, -5, -4],\n [-3, -2, 1, 4, 6],\n [-4, 2, -6, -2, 4],\n [-2, 2, 1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 6, -5, 0, 4],\n [-5, -1, -6, -1, 2],\n [5, -5, -1, -1, -5],\n [-2, -6, -6, -3, 4],\n [6, 4, -5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -6, -1, 6, 5],\n [-5, 2, 6, -6, 6],\n [2, -3, -3, -4, -4],\n [-6, 0, 0, 2, -6],\n [6, 5, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -4, 2, -2, -5],\n [6, 2, 5, -4, -4],\n [0, -5, 4, -5, -6],\n [-6, 6, 3, -2, 6],\n [3, 4, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -3, 6, -4, -1],\n [6, -5, -4, -4, -3],\n [1, 4, 0, -6, 5],\n [-4, -3, 5, -1, -1],\n [3, 1, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 3, -1, -4, 2],\n [1, 6, 2, -2, 3],\n [-5, 5, -5, -1, -4],\n [6, 6, -4, -6, 4],\n [-6, -3, -1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 3, -4, -1, -4],\n [-3, 6, 2, -6, -1],\n [-6, -4, 0, -6, -1],\n [-6, 5, 3, -3, -5],\n [0, 1, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -6, 2, -4, 4],\n [5, 2, -6, 0, -5],\n [4, 3, 4, 0, 3],\n [2, -3, -6, -1, 3],\n [5, -3, 6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -5, 4, 2, -1],\n [1, -6, -1, 0, -1],\n [0, -1, -5, -4, 4],\n [6, -2, -3, 1, -4],\n [-3, -2, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 6, -4, 6, -3],\n [0, -2, -3, -3, -2],\n [6, -4, 2, -5, 3],\n [1, -3, 0, -6, 2],\n [-1, 6, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 1, 5, -2, -6],\n [-3, -1, 0, 1, 5],\n [-1, 3, -4, 0, -3],\n [-4, 3, 1, -5, 1],\n [-4, 5, 4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, 1, -1, -3],\n [2, -5, 3, 2, -3],\n [-2, 1, -5, 4, 5],\n [3, 3, 0, -1, 4],\n [-2, -2, 1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -6, 6, -2, 3],\n [2, -3, -5, 5, 5],\n [-6, 6, -6, 0, 5],\n [-4, 1, 5, 4, -2],\n [5, 1, -3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -6, -4, -4, 0],\n [3, 6, 0, -6, 3],\n [-5, -3, 0, 1, -4],\n [-1, 3, 6, -3, -6],\n [5, -3, -5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -6, -2, 3, 6],\n [-5, 1, -6, -3, 0],\n [-5, -4, -6, -5, 5],\n [5, 4, 1, 5, 0],\n [-2, -5, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 2, 1, 6, 1],\n [-5, 1, -5, 1, -4],\n [1, 5, 1, 2, 1],\n [3, 6, -5, -4, 5],\n [2, 3, -1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -1, -2, 1, 6],\n [6, 0, -2, 2, -3],\n [-6, 5, -2, -1, 6],\n [5, 2, -1, -2, -3],\n [3, 1, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 0, -4, -4, 3],\n [-3, -6, -4, -3, 4],\n [1, -4, -6, -6, 3],\n [-2, -1, -4, 2, -1],\n [-4, 3, -5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 6, -2, 0, -5],\n [-4, -3, 6, 0, -5],\n [-3, -2, -3, -4, -5],\n [0, -1, 3, 5, -6],\n [5, -3, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -3, 0, 0, 4],\n [-2, 1, 3, -1, -5],\n [-2, -1, 3, -4, -1],\n [-6, 4, -2, -1, -6],\n [2, -6, 5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 5, 2, 3, -3],\n [5, 4, 3, 2, 5],\n [4, 4, 1, -1, 6],\n [6, -2, -5, 2, -5],\n [2, 5, 2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, -2, 6, -3],\n [-2, -1, 0, 4, 0],\n [-1, -1, 2, -4, 4],\n [-3, -1, 1, 0, 1],\n [5, -3, -5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 0, -4, 3, -4],\n [4, 1, 3, 3, 6],\n [1, -1, -1, -1, -2],\n [2, 0, 0, 1, 2],\n [3, -1, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -4, -2, -3, 4],\n [5, 1, 4, -1, 1],\n [0, -5, -2, -3, 2],\n [2, -1, -4, -4, 2],\n [6, 0, 5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, -6, -1, 1],\n [5, 1, -5, 2, -5],\n [3, -2, -2, -1, -6],\n [-4, 6, 1, -3, -3],\n [2, 0, -2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -4, -4, 2, 2],\n [-2, 4, 6, 2, 5],\n [1, 1, 3, 4, -2],\n [3, 5, -5, 3, 4],\n [5, -2, 1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -6, -1, 2, 3],\n [-3, 4, 5, -2, 6],\n [1, 1, 0, 3, -2],\n [-3, -1, 3, -6, 5],\n [-4, -1, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 2, 6, 3, -1],\n [-3, -1, -6, 5, -5],\n [-5, 0, -6, -3, 1],\n [-1, -1, 0, -5, -2],\n [3, 6, -3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 1, 0, -4, 1],\n [4, -4, 6, -4, 4],\n [4, -1, -2, -5, -3],\n [0, -6, 4, 1, -6],\n [-5, -6, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -6, -1, -4, -5],\n [1, 2, 5, 3, -6],\n [-3, 6, 0, -4, 6],\n [-3, 4, -2, -1, -2],\n [0, -5, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -3, 6, -1, -1],\n [-1, -3, -4, -5, 1],\n [-3, 0, 0, 4, -6],\n [0, -3, 4, -4, -5],\n [-1, -6, -2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, -1, 4, 1],\n [-3, 2, -6, 3, -5],\n [6, 5, -6, -3, -4],\n [2, 2, -6, -5, 1],\n [-3, 0, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -3, 0, -6, -5],\n [-2, 0, -1, 3, 1],\n [3, 6, 3, -2, 3],\n [0, -4, -1, 0, -3],\n [-3, -1, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 5, -6, -6, 3],\n [-5, -2, -4, 4, -3],\n [-5, -4, 6, -3, 4],\n [5, 2, 3, 4, 4],\n [-5, -1, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -4, -1, 3, -2],\n [4, -3, 4, 2, -1],\n [-4, -5, 1, 4, 0],\n [-1, -6, -6, 4, 1],\n [3, -4, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -2, -5, -2, 3],\n [-5, 2, 5, 3, 3],\n [-4, 5, -4, 3, 3],\n [-3, 5, -2, 6, -4],\n [3, -2, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -2, -6, 0, -5],\n [5, 6, 6, 6, -4],\n [-4, 6, 4, -3, 3],\n [-6, 2, -5, -3, 3],\n [0, 2, -1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 0, 4, -2, 4],\n [-4, -1, -1, 2, 1],\n [4, -1, 0, 0, 6],\n [3, -3, -4, 0, 6],\n [-1, 1, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -3, -1, -3, 0],\n [-2, -2, -2, 1, -2],\n [3, 6, 0, -2, -5],\n [-2, -6, -6, -5, 4],\n [-4, 2, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -6, 6, 4, 1],\n [6, -1, 3, 5, -3],\n [-1, -3, 6, -2, -1],\n [4, 6, 3, -5, -6],\n [3, 4, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 5, -2, -4, -6],\n [2, 4, -3, 5, -2],\n [3, 4, -2, -6, -3],\n [3, 6, -2, -5, 0],\n [2, 0, 6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 5, -6, -2, -1],\n [-2, 6, 1, 1, -1],\n [2, -2, -3, 1, -3],\n [0, 3, 1, 0, -5],\n [-2, 4, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 5, 2, 6, 2],\n [5, 4, 6, -3, -6],\n [4, 3, -1, -2, -4],\n [4, 0, 1, 1, -2],\n [4, 3, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -3, 6, 2, 6],\n [0, 3, -2, -6, -4],\n [1, 0, 4, -3, -5],\n [6, 4, 0, 0, -1],\n [-5, 0, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 2, 6, 0, -4],\n [2, -5, 5, 4, -3],\n [5, 2, -5, -6, -5],\n [0, 6, -2, -2, 6],\n [2, 3, -1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 0, 2, -5, -3],\n [0, -5, 0, -4, 1],\n [4, -6, -5, 6, 5],\n [-2, -2, -5, 6, -4],\n [5, -3, -1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -2, 5, -3, -3],\n [6, -4, 2, 4, 1],\n [5, 3, 4, -3, -6],\n [-1, -4, 1, 2, -2],\n [-2, 3, 3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, 5, -2, -6],\n [5, 0, 2, 2, 1],\n [0, -2, -3, -1, -6],\n [3, -2, -1, 5, -2],\n [3, -4, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 6, -5, 2, -1],\n [0, -5, 6, -2, -2],\n [-3, 6, -1, 0, -1],\n [-3, 6, -5, 3, -1],\n [-2, 5, 3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -2, 6, 5, 0],\n [-1, -2, -5, 4, 1],\n [2, 6, 0, 3, 6],\n [6, -1, 5, -6, -1],\n [-5, -2, -2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, 1, -5, 5],\n [-6, -3, -4, -4, 2],\n [6, 1, 6, 2, 3],\n [3, 0, 3, -1, -5],\n [-5, -5, 3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 1, -5, -3, -1],\n [0, 6, 6, 5, -1],\n [4, 3, 2, -3, -4],\n [-1, -1, 0, 0, -2],\n [1, 0, -5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 3, 1, -6, 4],\n [-2, -3, -4, 0, -6],\n [6, -2, -6, 1, 4],\n [-6, 5, -4, 5, 4],\n [0, -3, 3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, 2, -6, -6],\n [0, 2, 3, 4, 4],\n [-4, -6, 4, 6, -5],\n [-3, -6, 6, -2, 0],\n [4, 4, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 0, 3, 3, 3],\n [1, 4, -6, 3, 2],\n [-5, 2, -4, -6, -6],\n [6, -3, 5, 1, -6],\n [3, -3, -2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -6, -6, -5, -3],\n [-2, 2, -3, -1, -3],\n [3, -4, -4, 5, -6],\n [6, 1, 3, 5, 2],\n [-1, 1, 1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -1, 1, -2, 5],\n [-6, -3, -4, 4, 6],\n [4, 1, -1, 5, -2],\n [6, -1, 3, -3, -4],\n [-1, 4, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -2, 4, -2, 5],\n [5, -4, -2, -1, -5],\n [2, -6, -4, -2, 5],\n [-6, -3, -4, 6, -6],\n [-3, -4, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 3, 6, -3, 5],\n [5, -6, 6, 5, -1],\n [-1, -2, -3, 0, -5],\n [-6, 3, 5, 6, 3],\n [-3, 0, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -5, -5, 0, -5],\n [6, -2, 0, 3, 5],\n [6, 2, 1, -2, 6],\n [-4, 1, -6, -6, -4],\n [-1, 6, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, -1, 2, -5],\n [-1, -3, 4, -5, 3],\n [4, 5, -1, 5, -6],\n [5, -3, -2, 0, 4],\n [6, 5, 5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 6, 1, 2, 4],\n [1, -2, -1, 4, -3],\n [6, 4, -3, 5, -5],\n [-1, 4, 4, -2, -2],\n [3, -3, 2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 3, -4, -5, 0],\n [1, 0, -2, 0, -4],\n [4, -4, 2, 0, -1],\n [6, -5, -6, 1, 3],\n [4, -3, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 6, 1, -6, -3],\n [-6, 6, 5, 4, 3],\n [-1, 0, 5, -4, 5],\n [-2, 0, 2, 0, -1],\n [2, -4, 4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 1, 1, -4, 0],\n [1, 1, 1, -3, -1],\n [2, 0, -5, 1, 3],\n [-3, -1, 5, -2, 1],\n [-1, 3, 2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 0, -6, 2, -5],\n [0, 2, 3, -1, 2],\n [-1, -6, -2, 4, 5],\n [0, -4, 2, 6, 6],\n [-3, 0, 0, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -4, -3, 0, 5],\n [3, 4, -3, -5, 5],\n [-3, -6, 4, -6, -3],\n [-4, 6, 0, 6, 5],\n [-1, -6, -1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 0, -4, 2, 3],\n [-1, -5, 4, 2, -4],\n [3, 0, 6, -6, 1],\n [6, -6, 5, -6, -1],\n [-4, -5, -6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -6, 0, 6, -2],\n [1, 4, 2, 2, -6],\n [6, 6, 5, 2, -6],\n [-5, -4, -3, 1, 0],\n [-2, 3, 5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -5, -6, 3, 6],\n [-4, 4, -4, -2, 1],\n [-5, -2, 3, -4, 0],\n [-1, -6, 3, 5, 1],\n [1, 1, -4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -4, 5, 6, 6],\n [-5, 0, -6, 5, 1],\n [2, 2, 1, 1, -1],\n [-3, -2, -1, -1, 2],\n [-5, -6, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 1, -5, 6, -5],\n [6, 6, -6, 2, -3],\n [2, -5, -3, 3, 3],\n [-3, 2, -4, 3, 1],\n [3, 4, -5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, -6, -5, 3],\n [-1, 6, 2, -5, 5],\n [-5, -1, -3, -1, -6],\n [5, 4, 1, 1, 2],\n [-4, -5, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, -2, 4, -3],\n [-1, 6, -3, -3, -1],\n [-5, -2, 2, -1, 1],\n [-4, 2, -5, -1, -4],\n [-1, 2, 6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -3, 0, -5, 3],\n [4, 4, 0, 6, -3],\n [-2, 3, 3, -5, -3],\n [-3, -2, 3, -1, -4],\n [2, -6, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, -2, -4, 5],\n [6, -6, -5, -5, 4],\n [-3, -3, 6, 2, -4],\n [-2, 4, 2, 3, 2],\n [3, 2, -4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, -5, 3, -6],\n [2, -1, 2, 5, 3],\n [1, -3, -2, 0, -1],\n [-1, 0, 2, 1, -3],\n [-1, -2, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 0, 1, -3, 2],\n [-5, -6, 3, 3, -4],\n [-4, -5, 4, -3, 0],\n [6, -6, -6, -6, -6],\n [-1, 5, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -6, 5, -2, -1],\n [4, -1, -5, -6, -3],\n [1, -1, 3, 6, 3],\n [2, -1, -4, 4, 0],\n [3, -3, 3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 6, 5, -1, 5],\n [4, 4, -1, 4, 2],\n [1, -2, -1, 3, -4],\n [-1, 6, 0, -6, 5],\n [3, -1, -2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 1, -3, 0, 6],\n [4, 3, -1, -3, 6],\n [-4, -6, 0, -5, 2],\n [5, -6, 1, -4, -2],\n [-2, 1, -4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -5, -5, -1, 6],\n [-3, 2, 3, -1, 3],\n [2, -4, 5, 4, 6],\n [6, -3, 6, -1, 1],\n [-1, 5, -3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -4, -5, -5, -3],\n [-6, -5, -6, -5, 6],\n [-1, -3, 0, 3, -4],\n [0, 3, -5, -1, 6],\n [-4, 1, 6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -2, -3, -5, 5],\n [0, -4, 0, -5, -6],\n [6, -4, 0, -2, 1],\n [0, -4, 2, 4, 0],\n [-6, -5, -4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 6, 2, 5, -1],\n [-3, 1, 4, 3, -2],\n [5, 1, 5, -6, 0],\n [0, 2, 5, -4, -1],\n [1, -4, 5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 5, 4, 0, -5],\n [-5, -5, 1, 1, 2],\n [1, -6, -1, -5, -4],\n [5, 1, -3, -2, 4],\n [-1, 0, 1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 5, -5, 6, 4],\n [3, -4, 5, 3, 5],\n [-1, -2, 4, -3, -6],\n [-1, 6, -6, 1, -6],\n [-3, 1, -1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 4, -2, 4, 4],\n [-6, -5, -5, -2, -2],\n [-5, 5, -5, 1, 6],\n [-3, 4, -4, 1, -6],\n [-3, 0, -4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -1, -3, -4, -2],\n [0, 6, 4, 2, 0],\n [0, 3, -1, -1, 3],\n [2, -4, -2, -1, -3],\n [-6, -6, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -4, -5, 3, 2],\n [5, 0, 0, 5, -3],\n [0, -3, -2, -3, 4],\n [1, -6, -1, 1, 3],\n [2, 0, 4, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 6, 0, -6, 3],\n [4, -3, 2, 4, -5],\n [-2, -4, -4, 6, 2],\n [-6, -2, 4, 2, 0],\n [-3, 6, -3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, 5, -4, -6],\n [2, 2, -2, 2, 4],\n [3, -4, 0, 0, 6],\n [-3, -3, -4, 6, -6],\n [6, 4, -3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -5, -4, -4, 4],\n [6, 4, -4, 3, -2],\n [-3, -5, -1, -4, 4],\n [-5, 1, -3, -2, 3],\n [4, -2, 1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -4, 6, -3, -5],\n [2, 1, 1, -2, 5],\n [-6, -4, -4, 0, -3],\n [-1, 6, 5, 0, 2],\n [-2, 3, 4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 2, 2, -3, 5],\n [4, -2, 6, -2, 5],\n [-5, 3, -1, -2, -2],\n [6, -1, -4, -1, -4],\n [1, 0, -5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 0, -2, 1, -5],\n [4, 4, 2, 3, 4],\n [4, 2, -2, -6, 0],\n [-4, 6, 6, -6, 3],\n [3, -5, 6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 3, 4, -5, 3],\n [6, 5, -6, 5, -5],\n [1, -1, -1, 6, 1],\n [-5, 2, 5, 2, -2],\n [0, -3, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 6, 6, 4, -6],\n [-2, 0, 2, 2, 6],\n [0, 4, 4, 0, 2],\n [6, 0, -3, -1, 4],\n [0, 0, -3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -6, -5, 2, -2],\n [-3, -5, -1, -6, -1],\n [-1, -5, 1, -2, -3],\n [4, 2, -4, 5, 3],\n [-6, -4, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -4, -6, 1, 2],\n [6, -6, -2, -2, 0],\n [-2, -1, 5, -4, -3],\n [-4, 3, 0, -6, 5],\n [-1, 6, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -4, -3, 4, 1],\n [1, 3, 6, -5, 6],\n [3, -4, 1, 5, -5],\n [-5, -5, 3, 2, 2],\n [3, -6, -1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, 0, 3, 3],\n [3, 3, 4, 2, 1],\n [6, 2, 1, -5, 3],\n [5, -4, 4, 6, -4],\n [-4, 1, 2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 0, -3, -3, 5],\n [-3, 2, -6, 6, 1],\n [-4, 0, -3, -4, 2],\n [-6, -3, -3, -5, 0],\n [-4, -3, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -4, -3, 0, -2],\n [5, -2, -1, -4, -3],\n [-3, 1, 2, 6, 6],\n [4, 0, 3, -2, -1],\n [4, 2, 0, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, -2, 4, 3],\n [5, 3, 2, 3, 4],\n [-5, 2, 1, -6, -4],\n [3, -5, 5, 6, 1],\n [-6, 1, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, -3, 3, -2],\n [0, 2, -4, 5, 2],\n [5, -3, 2, -3, 5],\n [-1, 3, 3, 0, 6],\n [6, -6, 5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 1, -4, 4, -5],\n [-1, 3, -6, -5, -1],\n [4, -3, 2, -4, -6],\n [-3, -4, 4, 1, -4],\n [6, 2, -6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -4, -5, 6, 4],\n [5, 5, 3, -6, 3],\n [0, 6, -4, -5, -2],\n [3, 0, -1, -2, 5],\n [-4, 0, -5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 1, 1, -6, 0],\n [2, -1, 0, -4, -2],\n [4, -6, -1, -5, -4],\n [2, -3, -5, 6, -5],\n [4, 3, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 0, 2, -5, -3],\n [0, -4, 6, -3, -1],\n [1, 5, 0, 3, 1],\n [4, 5, 3, 2, 2],\n [6, -2, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -3, 4, 4, 5],\n [3, 5, -1, -5, -6],\n [-4, 0, 4, -2, 0],\n [-3, 4, 3, 4, 5],\n [1, 2, 1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -6, 0, -2, 1],\n [1, -6, 6, -4, 2],\n [-3, 6, -3, 4, 3],\n [6, 6, 2, -2, 4],\n [2, 1, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 4, 0, -6, -3],\n [2, -4, -3, 3, 2],\n [0, 6, 3, 5, -4],\n [-6, 1, -4, -4, -1],\n [5, -4, -2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -2, 3, -2, 0],\n [-3, 1, -4, 1, 4],\n [-4, 3, 3, -6, 1],\n [5, -2, -1, 4, 2],\n [-3, 3, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 3, -4, -4, 4],\n [1, 1, 4, -2, 1],\n [-3, 1, -2, -3, 1],\n [-3, 2, 1, -3, -4],\n [2, -5, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -4, -2, -4, -6],\n [5, 2, -6, 1, 0],\n [2, 2, -5, 6, -4],\n [-3, 5, 0, -3, -6],\n [6, 6, 5, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, 3, -5, 0],\n [-3, 4, -1, -2, -6],\n [6, 3, -5, -1, -4],\n [-1, -4, -6, -5, -6],\n [3, 6, -1, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -4, -5, -1, -4],\n [-1, 0, 2, -6, -4],\n [1, -5, -4, 2, -5],\n [5, -3, -3, 2, 4],\n [-5, 1, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -2, 5, 4, 4],\n [5, -5, -5, 5, -6],\n [2, -1, 2, -4, 5],\n [3, -6, -3, -2, 1],\n [1, 1, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 1, 6, 1, 6],\n [-4, -5, 5, 5, 1],\n [-3, 2, 0, 2, -6],\n [-6, -1, -4, -6, 1],\n [-1, 3, -6, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 2, -4, -2, -3],\n [-3, -3, 1, -4, -4],\n [-2, 4, -1, -5, 4],\n [4, -3, 0, -3, -3],\n [2, -2, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -3, 5, -4, -6],\n [4, 5, 3, -2, 4],\n [3, 0, 6, -2, -6],\n [0, 6, 4, 0, 1],\n [-2, 4, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -3, 5, -6, -4],\n [1, -3, 0, -6, -6],\n [4, -1, -4, 2, -2],\n [4, 5, -2, 0, -1],\n [1, -5, 6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -2, 6, -3, 4],\n [-4, 4, 5, -2, 4],\n [-4, -4, -6, 6, 3],\n [-5, 1, 0, -4, -1],\n [-3, 6, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 1, 6, 4, -2],\n [1, 3, 1, 3, 1],\n [5, 0, 5, -4, 0],\n [1, 1, -5, -5, -5],\n [-2, -2, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -6, -2, -5, 2],\n [-3, -6, -3, -4, 5],\n [3, 5, 4, 2, -3],\n [-6, -4, -4, -5, 0],\n [2, 6, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 6, -6, -2, 3],\n [-1, 3, 4, 2, -5],\n [0, 5, -1, 2, 0],\n [-2, 4, -4, -3, -1],\n [6, -5, -5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, -4, -2, 5],\n [0, 5, 3, 2, -3],\n [-6, -2, 6, 6, 6],\n [-2, 5, -4, -5, -6],\n [-2, -2, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 1, 5, -6, -1],\n [-5, 0, -6, 1, 5],\n [-2, 2, 1, -3, -3],\n [1, 2, 2, -2, 5],\n [0, 3, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, 2, -1, -4],\n [4, 1, 3, -1, 4],\n [3, -6, -4, 6, 1],\n [3, 4, 5, -2, 5],\n [5, -1, -6, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -3, 1, -1, 0],\n [2, -5, 6, 6, -5],\n [-4, -6, -1, 0, 2],\n [-4, 4, 6, -1, -3],\n [2, 2, -1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 5, 5, 0, -6],\n [-3, 0, 1, -2, -5],\n [2, 3, -1, -4, 0],\n [-2, -3, -1, 4, -3],\n [-1, -1, -5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 1, -3, 1, -2],\n [-2, 4, -4, 3, -1],\n [-2, 6, 6, -4, 3],\n [3, 6, -5, -1, -6],\n [0, -2, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -6, 4, 2, 1],\n [3, -4, 0, -1, 0],\n [6, -2, -6, 6, 4],\n [-3, 6, 3, 6, 0],\n [4, -4, 4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 6, -5, -4, -1],\n [5, -4, 1, 6, 5],\n [2, -4, 1, 4, 6],\n [-5, 4, 3, 4, 4],\n [5, -6, 1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 2, 3, 0, 1],\n [5, 4, -1, -1, 1],\n [-3, 5, -3, 6, 1],\n [3, 3, 2, 1, -2],\n [1, 4, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 0, 0, -2, 3],\n [-4, 3, -4, -4, 0],\n [-2, 3, 1, -3, 4],\n [-2, 1, -6, -4, -6],\n [2, -5, -5, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 2, 5, -4, 0],\n [-3, -4, 2, -2, -4],\n [-1, 2, -4, 4, -6],\n [2, -5, -4, -2, -2],\n [6, -1, -2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -1, -5, 1, -4],\n [-6, 5, 6, -5, 3],\n [-5, 3, 5, -4, 4],\n [0, 6, -1, 2, 0],\n [0, -5, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -6, -5, -5, 5],\n [2, 4, -1, -2, -2],\n [5, 6, 4, -1, 4],\n [3, 4, -3, -1, 4],\n [-2, -6, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 5, 5, 1, 4],\n [0, 6, 2, 6, -3],\n [3, 6, -4, 0, 3],\n [3, 0, -1, 2, 1],\n [6, -3, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 6, -2, -1],\n [-5, -5, -5, -2, -2],\n [-4, 1, -3, -2, 0],\n [-3, 1, -1, 0, 2],\n [-4, -6, 5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 3, -6, 1, -6],\n [-4, -4, -1, 1, -2],\n [-3, 2, -3, 4, -5],\n [-4, 2, -6, 5, 0],\n [3, -6, 0, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, 2, -2, 1],\n [3, -5, -3, 3, 2],\n [-3, 4, 6, -5, 0],\n [5, -4, -6, -2, -4],\n [-2, 0, -6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -1, -3, -4, 5],\n [-5, -3, -4, 6, 2],\n [5, -1, 0, -3, -4],\n [-4, -4, -5, 4, -3],\n [-3, 0, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -4, 3, 5, 3],\n [4, 6, 1, -4, -4],\n [-1, 1, -6, -5, 0],\n [6, 6, -1, -4, 2],\n [-4, -3, -5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, 5, 1, -6],\n [5, 1, -4, 2, 0],\n [-4, 0, -5, 6, -5],\n [-1, 2, -6, -2, 0],\n [3, -5, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 4, 1, -4, -4],\n [2, -3, 5, 6, -6],\n [-2, -6, -1, 5, 1],\n [2, -5, 3, -3, 6],\n [-4, 3, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 3, -4, 5, -4],\n [-6, -1, 3, 3, -1],\n [-5, 1, -1, -3, 3],\n [2, 0, 6, -4, 6],\n [-5, 3, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 5, 2, 4, 0],\n [2, 3, 0, -3, -2],\n [4, 3, 6, 2, 1],\n [1, 6, -6, -1, 1],\n [-5, 2, 1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 4, -6, -1, -2],\n [5, -6, -5, 4, 0],\n [-2, 5, 2, 2, 4],\n [6, -1, -3, -3, -5],\n [0, 4, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 3, 3, -4, 5],\n [2, 2, 4, 2, 5],\n [1, -1, -4, 1, -6],\n [-3, -5, 1, 5, 3],\n [0, -4, 5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -6, 2, -3, -2],\n [-1, 6, -2, 1, -1],\n [3, -4, 6, -2, -4],\n [6, 4, 0, 3, -1],\n [-5, 2, -3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 3, 5, 2, 6],\n [-1, -2, -3, -5, 6],\n [2, 1, 2, 5, -1],\n [4, 4, -6, 3, 2],\n [6, -1, 4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 6, 1, 3, -3],\n [1, 0, -1, 1, -2],\n [6, 5, 0, 2, 3],\n [-1, 5, 1, -5, -2],\n [1, 6, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -4, -2, -4, -5],\n [2, -1, 4, 1, 2],\n [0, 5, 0, 5, 1],\n [-5, -3, 2, -2, 3],\n [-5, 5, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, -6, 3, -3],\n [-5, 2, -1, -5, -4],\n [6, 6, -2, -5, -5],\n [-5, 1, -6, 3, 6],\n [0, 6, -3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 1, -4, 1, -6],\n [3, -2, -2, -1, -3],\n [-3, -5, -1, 4, 2],\n [-1, 4, -3, 1, -3],\n [-6, 1, -2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 6, 3, -6, -2],\n [1, -2, 2, 5, 4],\n [3, -5, 0, -4, -5],\n [5, -4, 5, -1, 0],\n [-1, -5, -5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -5, -6, -2, -3],\n [-6, 5, 6, -6, -4],\n [6, -4, -5, 0, 0],\n [-1, -1, 4, 5, 3],\n [2, 2, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -1, -4, 3, 4],\n [1, -5, -2, -2, -5],\n [-2, -4, 0, 4, 5],\n [-4, 6, -2, 0, -1],\n [3, -6, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -5, 4, -4, 5],\n [3, -4, 0, -6, -6],\n [6, 6, -5, -5, -6],\n [3, -3, -6, -4, 2],\n [2, 0, -3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -3, -4, -3],\n [-3, -6, -1, -1, -4],\n [1, 0, 5, 6, -4],\n [-2, -5, -4, -3, -4],\n [0, -3, -1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 4, -2, 6, 3],\n [4, -5, -6, -3, -1],\n [4, -2, 6, -6, -2],\n [3, 4, 5, 1, -4],\n [-4, 0, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, 0, 4, -3],\n [2, -3, 4, -6, -3],\n [-6, 1, -6, 5, 1],\n [-4, 1, -5, -5, -6],\n [-6, -4, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -3, -6, 6, -1],\n [-4, 1, 6, 3, -6],\n [-4, 5, -1, 2, 5],\n [6, 0, -6, 5, 1],\n [-4, 0, 4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -1, 2, 0, 6],\n [0, 5, 3, 6, 6],\n [-3, 5, -3, -1, 0],\n [0, 6, 1, -6, 6],\n [0, 2, 1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -2, -3, 3, -1],\n [-3, 1, -6, 5, -6],\n [0, 4, 2, -4, -3],\n [-5, 4, 4, -2, 2],\n [3, -5, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -5, 1, -3, -5],\n [6, -3, 2, -3, -4],\n [-3, 2, 6, -2, -2],\n [-6, -5, 2, -2, 6],\n [3, 2, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 6, -1, -2, 2],\n [-5, 1, 1, 4, 3],\n [1, 1, 0, -4, -2],\n [-5, -6, -3, -3, -6],\n [-2, -4, -6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, 1, 0, 5],\n [1, 3, 6, -4, -6],\n [-2, 3, -2, -1, 6],\n [-4, 6, 2, 6, 3],\n [4, 6, -3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 0, 1, -4, 1],\n [6, -4, -5, -6, 1],\n [-2, 1, 3, 2, -4],\n [3, 2, 1, 3, 4],\n [2, 0, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 1, 6, 3, -1],\n [-5, -3, 4, 6, -1],\n [-2, -3, 2, 5, 5],\n [-5, 4, -2, -3, 5],\n [1, 5, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, 1, -4, 0],\n [1, 1, 2, -3, 5],\n [1, 3, -4, 0, 2],\n [6, 5, -3, 6, 5],\n [-5, -6, -6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -6, 1, 2, -2],\n [6, -3, 4, 6, -4],\n [-4, 0, 3, -2, 0],\n [-5, -2, -6, 3, 1],\n [-4, 0, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 2, -3, 6, -3],\n [5, 0, -3, 4, -4],\n [-1, 4, 6, 0, -3],\n [-3, 6, 4, 2, 1],\n [-2, 0, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -1, -2, 4, -4],\n [4, -2, 2, 4, 6],\n [6, 3, -2, 2, 1],\n [0, 0, -2, 3, -3],\n [-6, 0, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 0, -4, -6, -5],\n [0, 6, -6, -6, -1],\n [4, -6, 0, -3, 3],\n [-2, 0, -2, -6, -6],\n [-1, 3, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 2, -6, 1, -1],\n [4, -5, -5, -5, 0],\n [3, 3, 5, 1, 2],\n [-4, -6, 4, 1, -1],\n [0, -6, -1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 1, -1, -3, -2],\n [0, -6, 5, -2, 5],\n [3, -2, 2, 1, -2],\n [3, -4, -4, 2, 1],\n [-5, 2, -3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 0, 4, -5, -1],\n [-5, -5, -6, -5, -4],\n [5, 6, 4, 2, 3],\n [-1, -1, -5, -3, 2],\n [-1, -6, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -1, 0, -6, -4],\n [-4, 2, -2, -5, 0],\n [3, -5, 1, 3, 0],\n [-1, -4, -6, 1, -5],\n [-4, -4, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 2, 3, -3, 0],\n [0, -1, 2, -2, -6],\n [2, 1, 6, 0, 4],\n [-1, 4, 2, -6, 0],\n [0, -4, 5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 2, -3, 5, 4],\n [3, -4, -6, 6, 4],\n [2, -5, 3, -4, -2],\n [1, -3, 4, -5, 0],\n [4, 0, 5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 5, -4, -5, -5],\n [-5, -4, -4, 2, 5],\n [0, 4, 1, 0, 1],\n [0, -2, 6, 2, 0],\n [-1, -1, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 0, 3, -1, -5],\n [0, -6, 5, 0, -2],\n [4, -1, 1, 3, 3],\n [-6, 1, 1, 6, -5],\n [-6, 3, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -3, -3, -6, 5],\n [-6, 6, -2, -2, -2],\n [-2, -2, -5, 1, 1],\n [-1, -6, 5, -3, -3],\n [-3, 5, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 4, -6, -5, 1],\n [4, 2, 1, -1, 1],\n [3, 6, -3, 3, 5],\n [0, 1, -4, -6, 6],\n [3, -1, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, 1, 5, -5],\n [-2, 0, -1, 4, 3],\n [4, 0, -1, -6, -3],\n [5, 1, 5, -6, -2],\n [6, 4, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -4, -2, -4, 2],\n [-2, -6, 2, -3, -3],\n [-3, -2, -4, 1, -2],\n [3, -5, 1, 1, -5],\n [-2, -3, 5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 2, 2, 3, 2],\n [1, 6, 0, 1, 1],\n [-6, 0, 3, 6, 5],\n [2, -2, 1, 1, 1],\n [-5, -5, -3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -2, 4, -5, -4],\n [3, 1, -6, -2, 5],\n [-6, 5, 4, 2, -2],\n [-4, -4, -5, -2, -5],\n [-1, -1, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 6, 4, 2, 2],\n [6, -4, 0, 4, -2],\n [-2, 2, -3, -6, 3],\n [5, 0, 0, 2, 5],\n [0, 6, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 0, -6, 5, 4],\n [0, 6, -3, 4, -4],\n [-5, -4, -1, -3, 1],\n [4, 0, -4, -4, -5],\n [0, 5, -4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 6, -6, 6, -6],\n [-2, -6, 3, 6, 6],\n [-4, -2, -5, 3, 4],\n [3, -1, 5, -1, 3],\n [0, 4, -6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 2, -5, -3, 4],\n [6, 4, 5, -3, 3],\n [0, -3, -6, 3, -5],\n [-6, -1, 5, -2, 5],\n [-5, 0, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, -4, -5, -2],\n [1, 6, -5, 1, 4],\n [-4, 1, 2, 2, 2],\n [3, 4, 3, 1, -5],\n [-5, 1, 4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -3, -4, 4, -6],\n [0, 2, 1, -6, 3],\n [-2, 4, -1, 4, 3],\n [1, 5, 6, -2, -5],\n [4, 3, 2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 2, 0, -1, 5],\n [-4, -6, 2, -1, -3],\n [5, 6, 0, 2, 4],\n [6, 2, 6, -6, 1],\n [0, -6, -4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 4, 2, -2, 3],\n [3, -3, -4, -5, 3],\n [-3, 6, -6, 3, 0],\n [3, 4, 1, 0, 0],\n [6, 4, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 6, -1, 1, 4],\n [-3, 3, 5, 3, -2],\n [-6, -4, 6, 3, -1],\n [4, 4, -5, 6, 3],\n [4, -3, 1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -4, 2, 5, -5],\n [5, 3, 4, -6, 2],\n [4, 6, 5, -3, 5],\n [-5, 3, 1, -3, -1],\n [2, 1, -2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 5, 0, 6],\n [-6, 2, -2, -2, -3],\n [1, -2, 3, -5, 0],\n [6, -4, 3, -3, 2],\n [3, 0, -6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 5, -1, 3, 5],\n [4, 1, 1, 0, 3],\n [6, -3, -6, -2, 1],\n [-4, 0, 5, 0, -3],\n [6, 1, -1, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, -5, -4, 3],\n [-2, 0, -2, 4, 4],\n [5, -2, 5, -2, 3],\n [-3, 1, 3, 3, -2],\n [0, -4, 6, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -4, -1, 5, 6],\n [6, 0, -6, 4, -6],\n [5, -1, -6, 5, 1],\n [3, -5, 6, 5, -3],\n [-3, -5, 4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -4, -3, -4, -6],\n [5, -4, -3, -3, -2],\n [4, -4, -1, 0, 4],\n [2, -3, 3, -1, -2],\n [3, -1, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -6, 5, 1, 2],\n [-6, -1, -1, -4, 1],\n [6, -1, 0, 0, 1],\n [-6, 5, -3, 6, 5],\n [-3, -5, -5, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 2, -6, 0, -4],\n [5, -1, -4, 4, 0],\n [4, 1, -3, -4, 2],\n [-2, -6, 4, 2, -1],\n [3, -4, -3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, -4, 0, 2],\n [-4, 0, -2, 5, -5],\n [5, -3, 5, -6, 3],\n [4, 4, 1, -4, -1],\n [-5, -2, -2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -6, -3, 5, -3],\n [-5, -5, -2, -5, 2],\n [0, 3, 4, -3, -2],\n [-5, 4, -3, -4, 3],\n [6, -3, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, -5, 1, 5],\n [-3, -5, 5, -3, 1],\n [4, 2, 5, -5, 5],\n [5, 0, -6, -5, 6],\n [1, 3, 6, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 6, 1, -4, 4],\n [0, -1, -1, 5, -6],\n [6, -5, 2, -6, 6],\n [-5, -3, -1, 5, 4],\n [-4, -1, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, 0, 2, -1],\n [-4, 1, -2, -5, 6],\n [0, -1, 2, 5, 2],\n [-6, -5, 4, 5, -6],\n [-4, 4, -2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 5, -5, 2, 1],\n [-1, 4, 1, -3, -1],\n [-5, -5, 2, -5, -5],\n [5, -6, 0, -3, -5],\n [-6, -4, -1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -1, 1, -4, -2],\n [4, 1, 6, 6, -5],\n [6, 1, 6, -4, 1],\n [3, 6, -4, -1, 0],\n [-4, 2, 6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 5, -6, 3, -5],\n [4, 4, -6, 1, 4],\n [-5, -1, 0, -5, 0],\n [-2, -5, 2, -6, 4],\n [5, 3, -6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -5, -4, -6, 2],\n [-6, 2, 5, 6, -4],\n [1, -6, 6, -1, -4],\n [-2, -2, 1, 4, 4],\n [3, -3, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -5, -4, -4, -2],\n [-3, -1, -3, 4, 2],\n [-1, 0, 2, 2, 4],\n [5, 5, 6, -4, 2],\n [-4, 0, 1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 0, 6, -1, -2],\n [4, -3, -2, 0, -4],\n [-2, -3, 4, -1, -1],\n [-2, -4, -3, 0, 2],\n [-1, -3, -3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -5, 0, 1, -3],\n [4, 0, 0, -6, -3],\n [-5, 0, 2, 3, 3],\n [-2, -5, 4, 1, 5],\n [4, 0, -6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 5, -2, 6, -3],\n [3, -3, 6, 2, 4],\n [2, -1, 3, 2, 3],\n [-1, -6, 4, -1, 4],\n [-3, 4, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 1, 1, 1, 3],\n [5, -3, 5, -5, -2],\n [2, -2, 1, -5, 1],\n [-4, -5, -2, 1, -5],\n [-2, -6, 1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, 0, 5, -5],\n [0, 6, 6, 1, -5],\n [-4, -3, 0, 4, 1],\n [3, 1, -5, 0, 4],\n [-1, -6, 1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, 3, 5, -2],\n [-2, -2, 4, -1, 5],\n [3, -2, 5, 5, 4],\n [2, -3, 6, 2, -3],\n [4, -5, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 6, 1, -5, -2],\n [4, 3, -3, -4, 0],\n [1, -4, -4, 1, -2],\n [-2, 2, -4, 5, 2],\n [-4, 6, -2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 4, -2, -2, 6],\n [4, -4, 0, 1, -5],\n [6, -1, -2, -5, 2],\n [5, -6, -1, 4, 4],\n [-4, -6, -1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 1, 0, -5, -5],\n [2, 3, 2, 3, -5],\n [6, 0, -1, 5, 1],\n [-3, -5, 5, -6, -4],\n [1, 4, -5, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 6, 3, -4, 1],\n [5, 4, -5, 6, -5],\n [4, -5, -3, 4, 5],\n [1, -5, 1, 5, 0],\n [3, -6, -6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -3, 2, 3, -3],\n [-3, -3, -3, -6, 0],\n [1, 6, 5, 0, 2],\n [-1, 0, -4, -6, -1],\n [-5, 5, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 0, -1, 1, -4],\n [6, 2, 5, 6, 2],\n [-2, 1, -1, 0, 4],\n [-2, 4, -2, -2, -6],\n [-4, -2, -2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -3, -5, -2, -5],\n [-2, 1, 5, 3, 3],\n [1, -3, 0, -2, -4],\n [-5, 6, -6, 1, 3],\n [2, 6, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -4, -1, 4, -5],\n [-3, -4, -6, 4, 4],\n [-1, 6, -4, 6, -4],\n [-3, 5, 3, 2, -4],\n [1, 5, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -1, 6, -4, -3],\n [-3, -5, -5, 4, -6],\n [5, 1, -2, 0, 4],\n [-3, -2, -4, 3, 5],\n [-2, 5, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 3, 3, 2, 1],\n [5, -4, 2, -5, -1],\n [-6, -3, 0, 0, 3],\n [-2, 5, 5, 0, -4],\n [3, 4, 3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -4, 6, 2, -5],\n [-5, 2, -2, -1, 0],\n [-6, 0, -5, -2, -4],\n [-4, 5, 6, 5, -2],\n [2, 5, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, 1, -1, -5],\n [1, 3, -2, -5, -6],\n [5, 3, -5, 6, 1],\n [4, -4, 0, -6, -4],\n [3, 2, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 4, 4, 6, -5],\n [0, 5, 4, 6, -4],\n [-2, 6, -5, 4, 2],\n [-4, -4, 4, -5, -4],\n [5, -3, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 0, 4, 2, -4],\n [-5, 6, 5, 5, 6],\n [-3, 1, -2, 6, 5],\n [0, 4, -1, 1, -1],\n [-1, -6, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -3, -4, 5, 6],\n [4, -1, 4, 0, -4],\n [-5, -5, -1, -6, -5],\n [3, 2, -1, 3, -3],\n [1, -3, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -6, -1, 6, 3],\n [2, 3, -1, -4, -2],\n [-4, 3, 3, 1, 2],\n [-3, 3, -6, 3, -4],\n [2, -5, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 4, 6, -1, 4],\n [-5, 1, -1, 3, 4],\n [-6, 0, -4, -1, -2],\n [5, -6, 5, 4, -5],\n [-4, -3, 4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 6, -4, 4, -5],\n [4, 1, 1, 5, 5],\n [4, -5, -2, 6, -4],\n [3, 4, -2, -1, -2],\n [1, -2, 3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 2, -3, 6, 4],\n [3, 5, -5, -3, 0],\n [3, 5, 4, 1, -6],\n [-2, -3, 5, 1, -3],\n [-3, -1, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -5, 6, -2, -5],\n [-1, -6, -2, 0, 2],\n [-4, 6, 5, -5, 5],\n [-6, -3, -1, 5, 4],\n [6, -2, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -6, -3, -6, 6],\n [-4, 1, 2, -6, -4],\n [-5, 1, 2, 0, 5],\n [0, -6, -1, -1, -4],\n [3, 6, -6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 0, 5, -6, -1],\n [-4, -3, -3, 1, 1],\n [5, 1, 1, -2, -6],\n [-5, -4, 3, 5, -5],\n [0, -5, -3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 1, 3, 4, 3],\n [3, -5, 6, -2, -5],\n [3, -3, -4, -5, -4],\n [-5, 2, 6, 6, 3],\n [5, -1, 2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -4, 2, -5, -5],\n [-6, -4, -3, 6, 0],\n [-3, 4, 4, 0, 1],\n [-3, 1, 0, 5, 1],\n [-2, -3, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 3, 1, -5, -4],\n [2, -6, 0, -4, 1],\n [-4, 6, -2, 3, -5],\n [1, 5, -1, -2, -4],\n [1, 3, -2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 2, 3, -1, -3],\n [2, -3, -2, -4, -6],\n [6, -4, 3, 4, 5],\n [-4, 6, 0, 0, 5],\n [2, 1, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 5, 1, -3, 6],\n [-6, -6, 4, 0, 2],\n [-3, 4, -6, -3, -5],\n [3, 1, 5, -5, -6],\n [-1, -2, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -4, 4, 0, 5],\n [-2, -6, -2, 2, 0],\n [-4, 6, -2, 4, 5],\n [4, 0, 5, 4, 0],\n [6, 1, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, -5, -3, -4],\n [0, 0, 1, 4, 4],\n [-2, 2, -3, 5, 1],\n [-1, 3, -2, 2, 0],\n [-6, -6, -4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 3, -4, 0, -2],\n [-4, -1, 1, -3, -1],\n [0, -4, 4, 2, -6],\n [-4, 5, 4, -3, -6],\n [4, 0, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, 5, -4, -1],\n [-4, 1, -6, 4, -5],\n [-2, -4, -3, 1, 5],\n [0, 5, 4, 2, -5],\n [0, 2, 3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, 2, -3, -1],\n [1, -4, -2, -2, 1],\n [-6, 3, -1, -6, -1],\n [1, 0, -3, -5, -5],\n [-4, -6, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 4, -3, 0, 1],\n [-1, 5, -4, -3, -1],\n [1, 0, -6, -3, 0],\n [5, 1, 6, -6, 5],\n [-5, 6, -5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 3, 5, -1, 0],\n [0, 2, -6, 2, 2],\n [6, 3, 2, 4, -6],\n [3, -1, 6, -4, 1],\n [-1, -6, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 5, 3, -3, -3],\n [4, 1, 0, 6, -1],\n [6, 0, -6, 3, 6],\n [-6, 1, 0, -4, 0],\n [4, 0, -3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, 3, 3, 5],\n [-3, 4, 6, 1, 5],\n [-6, -2, 2, 0, -3],\n [0, 3, 2, 2, 1],\n [-1, 5, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, 1, 2, -5],\n [-4, -4, 2, 2, -1],\n [-3, 0, 3, 2, -2],\n [-3, 2, -6, 1, 6],\n [2, 1, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 6, 1, 0, -2],\n [6, 4, -1, 5, 2],\n [-3, -1, 5, 6, -4],\n [6, -5, 5, 3, 6],\n [-2, 0, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -1, 5, -6, -4],\n [3, -6, -6, 2, 4],\n [5, -4, 3, 5, -3],\n [-1, -5, -3, -3, 0],\n [3, 5, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 6, -4, -2, 1],\n [-6, -4, -3, -4, -4],\n [0, 0, 5, -1, -2],\n [-2, 3, 4, 6, -6],\n [-3, 1, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -2, 4, 3, 3],\n [-4, -5, 5, -5, 6],\n [-6, -3, 4, 3, -3],\n [-5, -3, 5, -5, 5],\n [4, -2, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, -2, 4, 4],\n [0, 4, 0, -4, -5],\n [6, -2, -3, 0, 4],\n [-1, 5, -4, 4, 6],\n [-5, 0, 3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -5, -3, 5, -1],\n [4, -5, 5, -2, -1],\n [1, -1, -2, -3, -1],\n [5, 2, 2, -1, -3],\n [-3, -1, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 4, 6, -2, 5],\n [-2, -1, 4, -1, -5],\n [3, 0, -3, -3, -6],\n [5, -4, 4, 3, 5],\n [-5, 0, 3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 0, -6, -2, -3],\n [-2, 1, -1, 1, 0],\n [4, 2, 0, -6, -4],\n [-1, -2, -2, 4, 6],\n [1, 5, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 3, 2, -5, 5],\n [0, 5, 5, 1, -5],\n [-5, 5, 5, -4, 1],\n [-1, 0, 2, 1, -1],\n [1, -5, -4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 3, 5, -5, -6],\n [-3, 2, -1, 5, -4],\n [-1, 3, 6, 6, -3],\n [2, 6, -3, 4, 4],\n [2, -4, 6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 2, -3, 2, 5],\n [1, 6, -5, -2, 4],\n [1, -2, -3, 5, -2],\n [3, -2, 4, 3, -5],\n [-1, -6, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -5, 1, 4, 2],\n [-3, 2, -5, 0, 5],\n [3, 2, -4, 5, -5],\n [5, -2, 5, 1, 1],\n [0, -2, -6, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 3, -6, 1, 3],\n [-5, 5, 5, -5, -6],\n [-1, 2, 6, -6, -1],\n [-6, 6, -1, -3, 2],\n [0, 2, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 4, -6, -1, 2],\n [0, -2, 3, 6, 0],\n [5, 5, -2, -4, 4],\n [2, 5, -6, -6, 6],\n [3, -3, 1, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, 6, -6, -4],\n [-2, 1, 2, -4, -6],\n [6, -3, -2, 0, 1],\n [6, 3, 3, 4, 0],\n [-4, -5, 2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 5, -4, -3, -6],\n [-5, 1, -6, 6, 6],\n [2, 1, -5, 3, -4],\n [2, -3, -1, 4, -1],\n [-1, 0, 0, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 0, 2, 0, 0],\n [-3, 4, 4, 6, 6],\n [-1, -3, 3, -5, 5],\n [1, -5, 1, -5, 6],\n [3, 0, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 2, 4, -5, 1],\n [5, 0, -6, 2, 2],\n [6, 3, 5, 2, 2],\n [1, 6, 2, 6, 2],\n [5, -5, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 1, 1, -3, -3],\n [-6, 3, -4, 5, 3],\n [-6, -6, -3, -3, 0],\n [-4, -3, 1, -3, -3],\n [6, 5, 6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 6, -1, -6, 4],\n [1, 1, 3, -5, 2],\n [-4, -6, 0, -4, 1],\n [2, -5, 0, -1, -6],\n [3, -6, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 0, 5, 5, 0],\n [-3, 4, 3, -3, 1],\n [-5, -4, 4, -2, 0],\n [5, -3, -2, -6, 2],\n [-1, -5, 5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 6, -5, 1, 5],\n [4, 1, 0, -4, 3],\n [-5, -3, 5, -4, 3],\n [-1, -4, -2, -1, -5],\n [-6, 3, -5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -6, 0, 5, 0],\n [-6, 4, 3, 2, -3],\n [-4, -2, 4, 4, 5],\n [-6, -5, -1, -6, -3],\n [0, -4, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 1, 0, 5, 4],\n [-3, -1, 1, 0, -1],\n [-6, -2, -4, 5, -4],\n [3, 4, 4, 2, 5],\n [-2, 4, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 2, 6, 2, 4],\n [3, 6, 6, -6, -4],\n [-6, 4, 3, 6, 5],\n [0, 5, 0, 0, 0],\n [4, 5, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 3, 0, -3, -2],\n [-2, 3, -3, -1, 4],\n [-6, 0, -5, -4, -6],\n [1, 1, -6, -3, -2],\n [0, 6, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -3, -2, 3, 3],\n [-5, -4, 5, 0, 6],\n [-6, 3, 0, 3, 0],\n [2, -4, 6, -1, -6],\n [4, -2, 6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -4, -2, -5, -6],\n [-4, 2, -3, 4, -3],\n [-1, 6, -4, -5, 0],\n [-4, 2, 6, 1, 0],\n [4, -4, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -5, -4, -5, 4],\n [-4, -1, -4, -6, 1],\n [-3, 6, -5, 2, -5],\n [6, -3, 5, 4, 6],\n [-4, 3, -5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, -5, -6, 3],\n [-5, -5, -2, 2, 0],\n [0, -6, 6, 5, 4],\n [-3, 3, -5, 1, 6],\n [-5, 1, 3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 0, -6, -6, -1],\n [5, 4, 6, -3, -6],\n [-4, -2, 1, 2, 6],\n [3, -5, 4, 0, -1],\n [2, -3, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 0, -5, -2, 1],\n [4, 3, 4, -4, -1],\n [6, 1, -5, -5, 6],\n [-4, 4, 4, 6, 0],\n [-6, 0, 0, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -5, -1, -5, -6],\n [3, 4, -5, -4, 3],\n [-2, -4, -3, -2, -5],\n [-6, 1, 3, -4, -2],\n [2, 2, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -2, -3, -2, 2],\n [-1, 1, 1, -5, 2],\n [0, 1, -3, 6, 5],\n [2, 3, -3, 3, 0],\n [-2, 6, 2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -3, -5, -2, -4],\n [-2, 5, 5, 0, 6],\n [1, 0, 1, -6, -3],\n [-4, -1, 5, -2, -2],\n [-5, 3, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 0, -1, -3, -5],\n [3, -5, -5, 4, -2],\n [3, 2, -2, -3, 0],\n [-3, -1, -5, -4, -4],\n [-1, 0, 5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -6, -3, -4, 1],\n [-4, 0, 0, -3, 2],\n [-4, 6, 3, -1, -3],\n [0, 4, -3, -4, -6],\n [3, 6, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -3, 5, -5, -5],\n [2, -5, 5, -2, -3],\n [2, 1, 4, 0, -5],\n [-3, -3, -1, -3, 5],\n [4, 0, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -3, 5, 1, 5],\n [3, -1, -3, 0, -4],\n [3, 5, -6, -5, 3],\n [1, 1, 3, 4, -3],\n [-6, -2, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 0, 6, 0, 5],\n [-3, 6, 3, -3, 3],\n [-3, -5, 3, -3, -5],\n [4, -2, 6, 0, -4],\n [-3, 5, -2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -5, 5, -3, -1],\n [2, 4, 2, -4, 2],\n [5, -5, 6, -4, -6],\n [-1, -6, 3, -5, -4],\n [-5, 6, 5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -3, 5, 6, 0],\n [0, -2, -2, -5, -6],\n [0, 6, 4, 4, 4],\n [3, -2, 0, 3, 4],\n [-2, 0, -3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 0, 6, -5, 0],\n [-5, 0, 2, 1, -5],\n [5, 6, -5, -5, 0],\n [1, -1, 0, 4, 6],\n [1, 3, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, -4, -5, 0],\n [-2, 5, 6, 6, -4],\n [-1, 2, -5, 5, 1],\n [4, 6, -5, -2, 1],\n [-1, 1, -4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 5, 3, 6, -1],\n [4, -3, 4, -6, -4],\n [-6, -1, -6, -1, 1],\n [6, 2, 5, 6, -6],\n [3, -2, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 5, 5, 5, 6],\n [-1, 5, 0, -4, -2],\n [-4, -2, -6, 5, 1],\n [-2, 4, 0, 2, -3],\n [-6, 2, 6, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 4, 1, 6, -5],\n [-4, -1, 3, 4, -1],\n [4, 2, 2, -5, 0],\n [3, -3, -6, 3, -2],\n [0, 1, 2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -5, -3, 3, 1],\n [4, 4, 3, -3, 5],\n [-4, 4, 1, 1, -1],\n [-1, -5, 5, -5, 1],\n [5, 1, 4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -2, -5, 2, 0],\n [3, 6, -3, -1, 2],\n [5, 5, 2, -3, -2],\n [-1, 0, 6, 5, -2],\n [-3, 4, -5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -5, 4, -6, 0],\n [-5, 3, -2, -5, -3],\n [4, -5, -4, -4, -2],\n [0, -2, -1, 3, 1],\n [3, 0, 3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -3, 2, -2, -1],\n [0, 0, 1, -6, 5],\n [2, 1, 5, -4, -2],\n [3, -4, 5, 5, -5],\n [-1, 0, -2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 3, 0, -6, 4],\n [6, -4, -6, -3, 4],\n [-6, 0, -5, -5, -1],\n [-2, -4, -3, 5, 5],\n [3, 2, 5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 5, 3, 6, -2],\n [-4, 0, 1, -1, 6],\n [3, 6, -5, 0, 4],\n [-2, 4, 4, -6, 3],\n [0, -6, -6, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 3, -3, 0, 6],\n [0, -1, 3, -2, -2],\n [1, 2, -5, 0, -6],\n [-4, 1, 2, -6, 6],\n [2, 2, -3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -6, 3, 3, 4],\n [-1, -6, 0, 6, 5],\n [6, 4, 0, 4, 0],\n [0, 1, -1, -1, -2],\n [1, -4, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -3, -3, 1, 2],\n [0, -2, 1, 1, -5],\n [-3, -2, -4, 1, -2],\n [-1, -5, 3, 3, 0],\n [-2, -5, 6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -6, 1, 3, -1],\n [2, -5, -4, 4, 0],\n [-5, 0, 6, -1, 0],\n [0, 2, 2, 4, -6],\n [-6, -5, -2, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 4, -1, -6, 1],\n [1, -2, -5, -5, -2],\n [3, 4, -4, -6, -3],\n [1, -4, -3, -1, 0],\n [-1, -3, 3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 1, 4, 3, 1],\n [-1, 0, -3, 6, 3],\n [6, -4, 6, -1, -3],\n [2, 2, 3, -5, -5],\n [-5, 0, 6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 2, 1, 0, -6],\n [6, -6, -1, -1, 5],\n [-4, 5, 3, 1, -3],\n [-5, 0, -6, 0, 2],\n [-2, -4, -6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 2, -2, 6, -5],\n [-1, 0, 2, 1, 2],\n [2, -1, 3, -6, 3],\n [5, 1, -1, -3, -5],\n [3, 3, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 4, -4, 6, 4],\n [6, -1, -6, 1, -3],\n [5, -1, 1, 4, 0],\n [0, 3, -2, -3, -4],\n [-3, 0, -3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -3, 1, 4, 1],\n [-5, 5, 3, -4, 2],\n [-3, 0, 2, 5, -4],\n [3, -4, 3, 2, 4],\n [4, -2, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -3, 5, 1, -3],\n [6, -6, 0, 4, 3],\n [3, 6, -2, -1, 2],\n [4, -5, -5, -3, -5],\n [-4, 1, -5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -3, 4, 4, 4],\n [6, 1, 2, 3, 3],\n [6, -4, 4, -6, -4],\n [-3, -1, 3, 6, 0],\n [-4, 1, -2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, 3, 1, 3],\n [-2, 0, 0, 4, 6],\n [5, 0, -5, 1, -2],\n [6, -1, -1, -1, 5],\n [-3, -1, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 2, -4, -5, -6],\n [-5, 1, -4, -2, -2],\n [2, -4, 1, 5, 4],\n [1, -1, -3, 2, -6],\n [5, 4, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 1, 5, -1, 3],\n [0, 4, 2, 2, -3],\n [-4, -6, -5, -5, -1],\n [6, 3, 4, 4, 1],\n [4, -5, -6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 1, -3, -3, 1],\n [-4, -3, 2, 4, 3],\n [0, 0, -6, 2, -2],\n [3, -1, -6, -2, 4],\n [-1, 6, -2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, 6, -6, -5],\n [1, -5, -5, 1, -6],\n [-3, -3, 4, 1, -4],\n [2, -5, -2, -1, 2],\n [1, 0, 0, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 5, 4, 3, -6],\n [5, 1, -2, 5, -6],\n [6, -6, -2, 5, -3],\n [-5, 5, -1, -4, -2],\n [-3, 3, 2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 1, 6, -6, 2],\n [2, 1, -1, -5, 4],\n [-1, -6, 0, 5, -6],\n [4, 2, -6, 3, 5],\n [-4, 1, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 3, 1, 2, -3],\n [-5, 6, -5, 2, -1],\n [-2, 2, 5, 3, -6],\n [3, 5, -6, -6, -4],\n [2, 3, -1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -6, -1, 1, 2],\n [-5, -4, -1, -3, 1],\n [2, 6, 1, -1, 0],\n [-3, -5, 1, -1, -3],\n [5, 4, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 6, 1, -1, -4],\n [5, 4, 1, 0, 2],\n [3, -4, 6, -5, -1],\n [3, 2, -4, 3, 5],\n [-1, -6, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -2, -5, 0, -1],\n [4, -5, 2, 4, 0],\n [4, -4, -1, -2, 5],\n [3, 0, 6, 3, 1],\n [-1, -3, -6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 1, 1, -2, 0],\n [-6, -2, 5, -1, 5],\n [0, 3, -5, 2, -6],\n [-4, 6, 1, 2, 4],\n [2, -1, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 1, -5, 4, -1],\n [-3, 2, 2, 2, 4],\n [-1, -1, 3, 6, 5],\n [6, 4, 5, 1, -3],\n [-6, 1, -2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -2, -3, 4, -3],\n [0, 6, -4, 3, 2],\n [-1, 1, -5, 0, 2],\n [6, 0, 3, 4, -5],\n [1, -4, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 4, 4, 2, 1],\n [-1, 5, 0, 2, 0],\n [-2, 6, 0, 6, 6],\n [6, 0, 5, 3, -4],\n [1, 3, 2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, 3, 5, 0],\n [5, 4, 1, -3, -1],\n [4, -4, 1, -4, -4],\n [-3, -4, -5, -4, -3],\n [1, -4, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -2, 3, 1, 6],\n [-6, 3, 1, -3, 1],\n [-5, 6, -5, 0, 1],\n [-1, 0, -4, 6, -2],\n [3, 0, 3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 2, -2, 4, -2],\n [4, 6, -4, 6, 0],\n [3, 1, -2, 3, -1],\n [-6, 6, 1, -2, 3],\n [0, -4, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, -1, 3, 4],\n [-3, 6, 0, 5, 5],\n [5, 0, 6, -2, 2],\n [2, -2, 6, -1, 3],\n [4, -1, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -5, -4, -2, -4],\n [-5, 4, -3, 5, -1],\n [-5, 0, -3, 2, 2],\n [-5, 5, -1, 6, 0],\n [0, 0, 0, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 6, 2, -3, -3],\n [-4, 2, -4, 4, -1],\n [4, 5, 4, -2, 4],\n [3, -2, 0, 1, 5],\n [2, 5, -5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -1, -3, 5, 4],\n [-4, -2, -6, -2, 1],\n [-3, 3, 4, -3, -2],\n [4, -6, -1, 4, 2],\n [2, 2, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -3, 2, -6, -4],\n [-6, -2, -6, 3, -1],\n [-1, 0, -6, -6, 3],\n [-6, -5, 5, 3, 2],\n [-4, 5, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -5, -6, 2, -4],\n [1, -6, -3, -6, 1],\n [-3, -6, -3, 4, 5],\n [-3, 0, 3, -3, -3],\n [-5, 0, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -4, 2, -1, 0],\n [4, -5, -5, -2, 1],\n [3, -6, 3, 2, -2],\n [-4, -1, 2, 5, -6],\n [-1, 5, -3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, -5, -4, -3],\n [4, 2, 6, 3, 5],\n [-1, 3, 2, 3, 5],\n [5, -1, -2, 3, -5],\n [-4, -6, -4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, 6, -5, 1],\n [-5, -4, -5, 3, 4],\n [4, -1, -2, -4, 6],\n [-3, 6, 3, 4, -1],\n [5, -3, 4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 5, 1, -2, 1],\n [-4, 1, -4, 3, -5],\n [2, -1, 2, 4, 4],\n [-2, -6, 3, -3, -1],\n [-2, 6, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 5, 6, -2, 6],\n [5, 3, 2, 3, -3],\n [5, -2, -4, 3, -1],\n [0, -1, -1, -2, 0],\n [0, 2, 6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 6, -5, 0, -5],\n [-4, -6, -5, 0, 6],\n [4, 1, 4, 0, -6],\n [0, -3, -4, -5, -6],\n [6, -6, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -2, 0, 0, 3],\n [-1, 1, -6, 1, -3],\n [-4, 6, -4, 3, 1],\n [6, 3, 0, 3, -4],\n [-4, -5, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 5, 5, 2, 2],\n [4, 0, 2, 0, 5],\n [-3, -2, 2, 0, 2],\n [-4, -1, 0, 3, -5],\n [4, 1, -3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -2, -1, -4, 0],\n [5, 3, -3, -4, 1],\n [4, 4, -2, -1, -1],\n [6, 1, 3, -4, -5],\n [5, -5, -1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -5, 2, -3, 4],\n [-3, -1, 3, -1, 0],\n [1, -6, -2, -1, -6],\n [1, 2, 2, 3, 5],\n [0, -4, 5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -3, -6, 6, -4],\n [2, -2, 2, 6, -2],\n [-5, 1, -4, 1, 6],\n [1, -3, 3, 5, 6],\n [5, 0, -6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 4, -2, -4, -1],\n [-6, 0, -1, -2, 5],\n [-5, -6, -1, 5, 1],\n [6, -6, 5, 5, 2],\n [-3, 1, -5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 1, -5, 4, -2],\n [-3, -1, -5, 5, -3],\n [5, -3, 6, -6, 5],\n [2, 5, 4, 2, -5],\n [3, 5, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -3, 0, 3, 2],\n [4, 6, -3, 2, 3],\n [-6, 2, -6, 3, 2],\n [6, -3, 3, -1, 6],\n [6, -1, 1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 4, 2, 4, 2],\n [4, -3, 3, -1, 2],\n [5, 4, -6, -3, -5],\n [-3, 1, 2, -3, 0],\n [-5, 0, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 3, 5, 2, 3],\n [-5, -6, -3, -4, -5],\n [5, -4, 4, -3, -2],\n [4, -1, 1, 1, 2],\n [6, 2, 3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 2, 1, 6, 5],\n [2, 1, 5, 3, -1],\n [3, 5, 3, -3, -1],\n [-2, -5, -2, -3, 5],\n [0, -3, 3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -4, -4, -5, 6],\n [-5, 6, -1, -6, 1],\n [3, 1, -4, 5, 2],\n [5, -6, 5, 3, 4],\n [-6, 1, 6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 1, -1, -2, 2],\n [-2, 6, 6, -2, 1],\n [0, -1, 4, -6, 4],\n [-1, 1, 4, 1, -6],\n [-4, 6, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -4, -1, 5, -6],\n [6, -4, -2, -3, 3],\n [5, 3, -1, 2, 5],\n [5, 2, 4, -2, 0],\n [2, 2, -6, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 6, 1, -1, -1],\n [2, 1, 3, 6, -4],\n [5, 0, -2, -1, 3],\n [5, 5, -6, 4, -6],\n [1, 5, -2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -3, 1, -3, -3],\n [-1, -3, -5, -3, 6],\n [5, 0, 1, 1, 6],\n [4, -4, -5, -2, 3],\n [-3, 5, -2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -4, -3, 4, 3],\n [-6, -3, 3, -1, 2],\n [-1, 0, -5, -3, 3],\n [4, -2, 3, -4, -4],\n [-5, 5, -6, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -4, -6, 3, 6],\n [3, 2, 3, -2, -6],\n [-3, -4, 1, -6, 4],\n [6, -4, -5, -1, 5],\n [1, 6, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -6, 5, 5, 6],\n [6, 5, -6, -6, 1],\n [-5, -5, 0, 2, 4],\n [4, 6, 0, -2, -6],\n [1, 0, -3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -5, 6, 3, 3],\n [-6, 5, 1, -3, 0],\n [4, -4, -6, 1, -5],\n [1, -6, 4, -3, -6],\n [-3, 1, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -5, -3, -6, 0],\n [-3, -2, 4, -1, 5],\n [5, -5, 3, 4, 0],\n [-6, -3, 0, -2, -1],\n [-1, 2, -2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -5, 4, 5, 6],\n [3, 4, 6, 2, 3],\n [1, 5, 3, 6, 1],\n [5, 5, -6, -5, 6],\n [-3, 5, -5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 4, -6, 2, 6],\n [3, -6, -1, 1, -6],\n [-5, 3, 0, 0, -3],\n [-6, -1, -5, 5, -6],\n [-6, 3, 5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 1, 0, -4, -4],\n [6, 0, -1, -2, 1],\n [6, 2, 5, 0, 0],\n [1, 1, -2, 5, 1],\n [-5, -6, 6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -6, -6, 4, 1],\n [-3, 5, -4, 5, 5],\n [-4, 6, 4, 0, -1],\n [-4, -1, -1, 6, 6],\n [-6, -1, 6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -5, 1, -2, -2],\n [-1, 2, -3, 5, 4],\n [4, 1, -1, 6, 0],\n [3, 3, -3, 4, -5],\n [1, 4, -1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 3, -5, -5],\n [-4, 0, -4, 6, 6],\n [3, -5, -5, 6, -2],\n [5, -1, -6, 6, 6],\n [-1, -1, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -5, -1, 1, 4],\n [-1, 6, 3, -2, 4],\n [0, -2, -6, 3, -2],\n [-1, 0, 2, -4, -6],\n [-5, -2, 5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 3, 5, 6, 4],\n [-3, 2, 6, -3, -5],\n [-6, 3, 3, 1, 2],\n [3, 6, -3, 1, 4],\n [-3, -5, -1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 5, 1, 1, -5],\n [5, -2, -3, -2, -2],\n [-1, 5, 1, 6, 1],\n [-6, 1, 3, 6, -6],\n [3, 5, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -4, -6, -1, -6],\n [-4, 3, 5, 6, -2],\n [-2, -5, 0, -5, 5],\n [-3, 1, 1, 4, -4],\n [6, 4, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -1, -3, 1, -4],\n [-4, -5, -3, 1, -5],\n [1, -3, -2, 4, -1],\n [2, -5, 4, 4, -3],\n [-3, 5, -6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 5, -2, -4, -1],\n [2, 5, 0, 5, -6],\n [3, 5, 4, -5, -2],\n [1, 2, 1, -5, 5],\n [-4, 5, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -4, 5, 5, -6],\n [5, 4, 6, 0, -2],\n [3, 0, 4, 5, -5],\n [-6, -3, -2, -6, 3],\n [-5, 0, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -2, -4, 0, -1],\n [2, -1, 6, -6, 1],\n [-3, 1, 6, 4, 6],\n [4, -3, -3, -2, -4],\n [4, -4, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, -6, 3, -2],\n [1, -3, 0, 3, -6],\n [3, 1, -4, 5, 1],\n [-2, 0, 5, -3, 5],\n [1, -3, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -2, -4, 3, -6],\n [-1, 0, 4, -5, 4],\n [-6, -1, 0, 0, 3],\n [-5, 2, -2, -3, 2],\n [0, 4, -4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, -6, 4, -3],\n [-4, 5, 2, -6, -4],\n [-1, 3, -6, 5, 6],\n [2, 3, -5, 2, 0],\n [-5, -6, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 4, -6, -6, 0],\n [-5, -5, -3, -5, 6],\n [-4, 4, 2, 1, -4],\n [0, 4, 3, -6, 2],\n [4, -3, 5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -4, 3, 4, 2],\n [-2, -3, 0, 1, -4],\n [-6, 3, -3, 5, -2],\n [3, 5, 6, -6, 3],\n [0, 4, 6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -4, 3, -5, 2],\n [-5, 4, -1, -2, -4],\n [-4, -5, 1, 6, 3],\n [-3, -5, -5, -1, 4],\n [-6, -2, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 1, 4, 4, -4],\n [5, -6, -2, 1, -3],\n [-2, 1, -1, 1, 5],\n [0, 3, 3, -3, -6],\n [0, 2, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -4, -4, -4, -1],\n [-1, -3, -2, -1, 5],\n [-4, 4, -3, 3, 3],\n [-5, 3, 3, 3, -2],\n [4, 4, 5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -4, -2, 6, -4],\n [-6, 3, 3, -6, 1],\n [3, -2, -4, 0, 6],\n [1, -4, 1, 2, 5],\n [1, 1, -5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, -4, 5, 2],\n [-3, 4, -1, 1, -4],\n [2, -2, -6, 3, -5],\n [5, 0, -3, -1, -4],\n [-4, -3, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, 1, 5, 3],\n [-2, 3, 5, 2, 0],\n [-3, 6, 1, 3, 1],\n [-1, -1, 6, -6, -6],\n [-5, 3, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 4, 0, -1, -4],\n [-1, -1, -6, -2, 1],\n [-1, -4, -3, -1, 2],\n [-6, -6, -6, -2, 1],\n [-6, -3, 2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -6, -2, 3, 3],\n [6, -1, 1, -4, 0],\n [1, -4, -5, -6, 2],\n [0, -5, 4, -2, 0],\n [-5, -5, -5, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -5, -1, 3, -5],\n [6, 5, 6, 3, 4],\n [4, 6, 4, -2, 5],\n [2, -6, 5, -2, 1],\n [0, 4, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 5, -4, -5, -4],\n [-2, 4, 1, 0, -1],\n [0, 5, 0, -5, -2],\n [-3, -3, 1, 6, -2],\n [-2, -3, 3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -1, -1, -1, -1],\n [5, -1, 3, 3, 0],\n [-6, 4, -2, 3, 1],\n [3, -2, 3, -1, 6],\n [5, 5, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 3, 6, 3, 3],\n [-1, -3, -2, 6, 6],\n [-5, -3, 0, -5, -3],\n [6, -1, 6, -6, 0],\n [-6, -5, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -1, 1, -6, 4],\n [5, 2, -5, 3, 3],\n [5, 6, 2, -3, 5],\n [3, -3, -4, 3, 4],\n [6, -6, 3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, 6, 4, -1],\n [-4, 0, -6, -5, -1],\n [-4, 4, 2, -3, 4],\n [1, 3, 2, 5, -5],\n [4, 2, 3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 5, -5, -3, -4],\n [6, -2, 0, -5, -5],\n [1, -5, -2, 0, 2],\n [6, 4, -4, -2, 4],\n [-6, -1, 2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -4, -5, 6, -1],\n [-5, 4, -1, -6, 0],\n [5, -2, -3, 1, 2],\n [5, 0, 6, -6, -4],\n [1, -1, -1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 5, 0, -6, 2],\n [-6, -6, 6, 2, 0],\n [2, -3, 5, -1, 4],\n [-4, 3, 2, -1, 6],\n [-5, 3, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, 6, 1, 2],\n [2, -6, 2, 3, 3],\n [6, 2, -6, 1, -2],\n [3, 4, -2, -5, -2],\n [-4, 4, -4, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 2, -4, 3, 5],\n [1, -5, -3, 2, 5],\n [-2, -2, 3, 2, -2],\n [1, 6, -6, 6, 2],\n [0, 2, -6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, 3, 1, -4],\n [6, -4, -3, 6, -3],\n [1, -2, -1, 4, 4],\n [5, 2, 3, -2, -5],\n [1, -1, 5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 3, 2, -1, -4],\n [6, 5, 6, 3, 4],\n [-1, -2, -1, 4, -1],\n [2, -3, -3, -2, -2],\n [-6, -5, -6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 1, -2, 2, -3],\n [6, -6, -4, 1, 1],\n [-6, -6, 3, 1, 2],\n [-3, 6, 5, 0, 3],\n [1, 3, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 6, 4, -1, 4],\n [-3, 4, -3, 4, 3],\n [-1, -3, 6, 1, 0],\n [3, 2, 5, 5, -6],\n [-2, -6, 5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 2, -5, 2, 3],\n [6, -1, 1, 1, 0],\n [-4, -5, -2, -4, 4],\n [6, -3, -4, 4, 0],\n [-4, 5, -6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 6, 0, -5, 1],\n [0, -5, 3, 1, 1],\n [1, 3, 5, -6, 2],\n [-1, -1, 1, 0, -2],\n [4, -5, 3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -6, 1, 2, -6],\n [-6, -5, 0, 5, -6],\n [6, -4, 3, -6, -2],\n [-6, -1, -6, 3, 5],\n [-6, -3, 4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 1, -6, 3, 5],\n [2, 0, 0, -3, 5],\n [1, 0, 4, 0, 6],\n [-4, -2, -3, -6, 2],\n [-1, 1, -6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -2, -4, 1, -2],\n [-1, 5, -5, 0, 0],\n [5, 6, 1, -6, -4],\n [3, -6, -1, -3, 2],\n [-1, -6, -5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 5, 1, -5, -2],\n [4, 6, 1, -5, 5],\n [-1, -4, -5, 5, 5],\n [0, -4, 5, -4, 4],\n [3, -3, -6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, 2, -5, -2],\n [-2, 5, -5, 1, 4],\n [-5, -6, 6, 3, 1],\n [1, 6, 6, -6, -3],\n [1, 1, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -2, 3, 3, 2],\n [-6, -1, -5, -3, -4],\n [-3, -1, -5, -3, -5],\n [5, -4, -3, -4, 5],\n [-6, -5, 4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 4, 3, 2, -3],\n [5, 0, 3, 5, 2],\n [3, 6, 2, 1, -5],\n [4, -3, -2, -6, -3],\n [6, 5, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -3, -4, 3, 0],\n [4, -1, 5, 2, 4],\n [-6, -4, 5, 2, -4],\n [5, 0, -6, 1, 2],\n [0, -4, -2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -3, -6, -5, 0],\n [6, 5, 6, 0, 0],\n [2, -5, -2, -2, -5],\n [-5, 5, 1, 6, -4],\n [2, 1, 2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -2, 5, -5, -5],\n [0, 4, 4, -1, 1],\n [4, 4, 0, 2, 0],\n [-3, -2, 6, 2, -2],\n [3, 2, 4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, 0, -3, 6],\n [-3, -4, 0, 6, -1],\n [4, -3, 6, -2, -6],\n [-6, 3, -5, -5, 6],\n [-4, 1, -3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -2, 5, -6, 2],\n [-2, 1, 1, 2, -6],\n [-3, -5, 5, -6, 0],\n [-5, -1, -5, -1, 2],\n [-6, 6, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -4, 4, -5, 1],\n [6, 0, 1, 1, -4],\n [4, -5, 0, -1, -2],\n [4, 3, -1, -5, 2],\n [0, -2, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 3, 1, 4, 5],\n [-6, 3, -3, -6, 3],\n [3, -2, -4, -1, 3],\n [-4, -6, 6, -3, 6],\n [1, 2, 6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 1, -1, 2, -2],\n [0, 5, 0, 1, 4],\n [-3, -6, 5, -4, 6],\n [-4, -1, -5, -5, -3],\n [-2, -6, 0, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 3, 5, 5, 0],\n [0, 5, 4, 2, -1],\n [-5, -5, -4, 1, -1],\n [-2, 2, 0, 2, 1],\n [3, 2, 2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 1, 0, 4, 2],\n [1, -5, 3, -1, -2],\n [5, -4, -2, 6, -2],\n [3, 4, 2, 4, 1],\n [-3, -5, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 0, 6, 5, 1],\n [4, -1, -3, -1, -6],\n [3, -3, 1, 0, -4],\n [-4, 2, -1, -5, 0],\n [1, 2, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -1, -5, -4, -1],\n [2, -5, 6, 2, 0],\n [-4, 5, 6, -4, 1],\n [4, 5, 3, 5, 3],\n [-1, -4, 2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -2, 3, 0, -3],\n [-1, 6, 2, 1, 5],\n [0, 2, 6, -4, 1],\n [-5, 5, 1, 0, 1],\n [-5, 4, 3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 4, -1, 2, 6],\n [0, 5, -6, -6, 6],\n [-5, 3, -1, 3, 4],\n [-4, 0, 6, 0, 0],\n [0, 0, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -1, -3, 3, 4],\n [4, 5, -1, -5, -6],\n [0, -6, 0, 3, 1],\n [-2, -3, 3, -3, 4],\n [3, -4, -3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -6, 3, 0, 0],\n [5, 4, 0, -5, -2],\n [-1, 1, -3, 0, 4],\n [-3, -6, -6, 1, 6],\n [4, 0, -5, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 5, 4, 1, 5],\n [4, 1, -4, 2, -6],\n [-5, -6, 0, -4, -4],\n [-3, 2, 1, 1, 2],\n [-1, -4, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 3, 0, -4, -4],\n [-5, 6, -5, 5, 6],\n [2, 2, -2, -4, 4],\n [6, 3, -5, 1, 3],\n [2, 5, -5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 3, 2, 6, 5],\n [-5, -1, 2, 4, -6],\n [-1, -2, -1, 0, -6],\n [-5, -1, 3, -5, 3],\n [3, -6, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 2, -2, -2, 6],\n [2, -5, -1, -4, -5],\n [-2, 4, 4, 5, -5],\n [-2, -3, 0, 3, 0],\n [2, 6, -2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 1, 3, 2, 0],\n [2, -6, 1, 6, -4],\n [-1, 4, -2, 4, 5],\n [5, 0, 2, -4, 6],\n [3, -3, 2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -4, 1, 1, 0],\n [-3, 5, 3, 0, 1],\n [1, 2, 4, -6, -5],\n [0, -5, 5, 6, 2],\n [4, -6, 2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -1, 3, 0, -5],\n [3, 2, 3, -1, -4],\n [-6, 3, -6, 6, 3],\n [-2, -1, 0, 0, -5],\n [-4, -4, 1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 6, -3, 1, -1],\n [0, -5, -2, 3, -2],\n [-5, 4, 6, -5, -1],\n [-3, 3, 0, 3, -4],\n [6, 3, 3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -5, -1, 2, -3],\n [5, -5, 3, 6, -4],\n [4, 5, 5, 4, 2],\n [-3, 5, 1, 2, -6],\n [-6, -5, -2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 5, 3, -3, 2],\n [-5, -6, -4, -3, 1],\n [3, -6, 0, -5, -4],\n [6, -5, -6, 6, 0],\n [3, 0, 6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -3, -5, 0, -6],\n [1, 0, 2, 2, 5],\n [5, -6, -6, 2, -4],\n [-2, -5, -6, 6, -2],\n [1, 6, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, 1, -3, 2],\n [-2, 3, 4, -6, -3],\n [-2, -3, 4, 0, -1],\n [3, 1, 1, -1, -4],\n [2, 6, 0, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -5, 5, 3, 4],\n [-2, 2, 5, -6, -4],\n [-6, -1, -6, 4, 6],\n [0, 1, -5, -5, 4],\n [-3, 5, -2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 2, 4, 5, 1],\n [4, 1, 2, 0, -2],\n [-4, -6, 5, -3, 0],\n [-5, -4, 5, -3, -3],\n [-3, 2, -5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 1, -3, -6, -6],\n [2, -1, 1, -4, 2],\n [-6, -1, 4, 1, 4],\n [0, -4, 3, -4, 3],\n [-1, -4, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 1, -6, 6, 4],\n [-2, -4, -5, -6, -2],\n [5, 3, -5, -6, 5],\n [-5, 4, -3, -2, 6],\n [0, 5, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -6, 0, -2, -5],\n [-4, -4, 2, 5, -3],\n [3, -4, 6, 5, 1],\n [0, -6, 5, -5, -2],\n [-6, -3, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, -2, 6, 2],\n [4, 3, 1, 2, 2],\n [-1, -6, -3, 2, 2],\n [5, 5, -5, -2, 1],\n [4, -5, -6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, -3, 1, -3],\n [4, -3, 6, -5, 6],\n [3, 2, 3, 1, -6],\n [-5, 5, 2, -6, -1],\n [4, 4, -3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 1, 0, -3, -6],\n [2, 3, -3, 4, 2],\n [-6, -4, -6, -5, 4],\n [1, 2, 1, 2, 1],\n [1, 4, 2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 3, 4, 5, 4],\n [-6, -2, 3, -4, -2],\n [-3, 5, -6, -5, -4],\n [-1, 2, -5, -5, 5],\n [1, 4, 6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -3, 6, -5, -3],\n [1, 0, 6, 6, -5],\n [-6, 1, 5, 2, -3],\n [2, -6, 4, 5, -2],\n [-1, 3, -3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, 5, -2, -1],\n [0, -6, -2, -1, -1],\n [0, 0, -4, 3, -6],\n [-6, 5, 2, -4, -1],\n [-1, -1, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -4, -3, 5, 2],\n [-6, 3, 5, -2, -2],\n [-4, 4, 1, 0, 0],\n [-5, -6, 2, 1, 0],\n [-1, -6, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -5, 6, -5, -6],\n [-3, -6, -1, 1, 2],\n [3, -1, 5, 4, -1],\n [0, 3, -5, -3, -3],\n [1, -1, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 4, -6, -5, 0],\n [1, 6, -3, -3, 5],\n [5, -1, -6, 2, 0],\n [1, 6, -3, -5, -1],\n [6, -4, -2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -6, -5, -4, 0],\n [-2, 4, 5, 5, -1],\n [0, 5, 2, -5, -3],\n [5, 4, -4, 5, 4],\n [-5, -5, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -4, -3, 6, 4],\n [-4, 4, 6, -3, 2],\n [4, 4, -4, 1, -2],\n [-1, -2, -5, -2, 1],\n [-1, -1, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 2, -1, -4, 2],\n [2, 6, -1, 2, 2],\n [1, 5, 0, -6, 3],\n [1, 2, -1, 1, -5],\n [2, 3, 5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 4, 1, 6, 0],\n [-5, 2, -4, -2, 1],\n [6, -2, 2, 4, 6],\n [-2, 0, -6, -5, 2],\n [-2, -4, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 6, 5, -2, 4],\n [-2, -5, 6, 0, -2],\n [1, -3, -5, 3, -3],\n [0, -2, 5, 6, -2],\n [2, 6, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 1, -4, -1, -1],\n [-5, -5, 5, 0, -3],\n [2, -2, 3, 4, 1],\n [-2, -6, -4, 5, -1],\n [-1, -2, -1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -2, -5, 4, -2],\n [-5, 6, -5, -6, 1],\n [-1, 2, -5, -4, -1],\n [5, -5, 4, -6, -4],\n [-4, 4, -6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -3, 1, -1, -3],\n [6, 0, 0, 2, -6],\n [1, -1, -1, -4, 2],\n [3, 5, -2, -5, 0],\n [-4, 2, 4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 2, -1, -5, -4],\n [-4, -6, -3, -6, -3],\n [-5, -1, -4, -6, -4],\n [-2, 5, 1, 5, -2],\n [-5, 6, 1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -4, -1, 0, 6],\n [6, 1, 3, -6, 2],\n [-5, -5, 4, 6, -5],\n [-3, 1, 5, -6, 4],\n [1, 4, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 4, -2, -2, -1],\n [3, -5, -5, -2, -4],\n [6, 4, -5, 4, 1],\n [3, -4, -6, -5, 1],\n [4, 1, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 0, -1, 5, -2],\n [1, -2, -2, 0, 4],\n [-2, 3, 0, -1, 4],\n [-5, -3, 6, -6, -1],\n [5, 6, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -4, 3, -6, 2],\n [-1, -6, -6, -3, -6],\n [-6, 3, 5, 2, -5],\n [-3, 2, 6, 6, 5],\n [-2, -5, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, 6, 4, -4],\n [-3, 4, 3, -3, 5],\n [-4, -3, -6, -6, 2],\n [-6, -4, -4, 5, -5],\n [5, -6, 4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 5, -1, 2, 1],\n [-4, -4, 3, 2, -5],\n [0, 1, 6, -1, -4],\n [-4, -6, -1, -3, -2],\n [-1, -4, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -6, -4, 0, -4],\n [-5, -6, 4, -3, -2],\n [6, 3, 0, -3, -4],\n [1, -6, 0, 2, 0],\n [5, -2, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 0, -5, -1, 4],\n [0, -3, 3, 4, 0],\n [3, -2, 6, -3, 1],\n [-6, -4, 0, -1, 6],\n [4, 6, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -3, -1, -2, 5],\n [-5, 6, 1, -3, -4],\n [6, -1, 1, 5, -1],\n [-6, -3, 5, -1, -2],\n [6, -2, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, 2, -4, 3],\n [3, -4, -5, -3, -2],\n [0, 1, -5, 0, 3],\n [3, 3, -3, 5, -6],\n [-6, -4, 6, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -3, -6, 2, 5],\n [-6, -6, 6, -6, 1],\n [-3, -6, 6, 0, 0],\n [0, -3, -6, -5, 2],\n [-1, 6, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 2, 0, 4, 2],\n [3, -1, 4, -3, -3],\n [-5, -4, 4, 1, -3],\n [-6, 5, -4, -4, -4],\n [2, -4, -3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 4, 0, 2, -1],\n [3, 4, 1, -6, 3],\n [-2, -4, -4, -5, 6],\n [-3, 4, 0, 5, 6],\n [6, -5, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 1, -3, -4, -4],\n [-5, 2, -4, 5, 3],\n [6, 6, 2, 3, -1],\n [-6, -4, -2, 1, -6],\n [2, 2, -4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -1, 2, 1, 0],\n [0, 3, -2, -6, -1],\n [-3, -6, -6, -3, 0],\n [1, 6, 5, -4, 6],\n [6, 3, -6, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -2, 2, 5, 5],\n [-2, 5, -4, -4, 0],\n [5, 3, -2, 6, -2],\n [6, 5, -2, 1, 2],\n [4, 0, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 3, 6, -2, 6],\n [-1, 3, 6, 2, 3],\n [-3, 5, 5, -5, 6],\n [2, -2, 0, 6, -6],\n [6, -3, -4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -3, 6, -5, 1],\n [-2, 2, 3, 6, 1],\n [6, -2, 5, -4, -4],\n [-5, -5, -3, 5, 3],\n [2, 2, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -1, 2, 4, 6],\n [-6, 6, 2, -6, 1],\n [-5, 1, 2, 4, 2],\n [-6, 6, 4, -6, 6],\n [4, 4, -5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 0, -3, -5, 2],\n [5, -2, 4, 4, -1],\n [-1, -1, -1, -4, 5],\n [-5, 1, -3, 6, 4],\n [6, -4, -5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 2, 4, -5, 3],\n [6, -1, -5, 3, -1],\n [5, 3, 0, -2, 6],\n [1, 2, 3, 6, -4],\n [-2, -5, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 6, 6, -6, 6],\n [0, 4, 1, -4, -4],\n [1, 2, 1, -5, 0],\n [-2, -3, -6, -1, -4],\n [-2, 3, 4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, 3, 6, -5],\n [0, 5, 3, 1, 5],\n [-5, 5, 2, -2, -2],\n [2, 1, -4, 4, -6],\n [-1, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 4, 4, 5, -3],\n [5, -3, -1, -4, 5],\n [-5, -1, 6, -6, -1],\n [-6, -1, 1, 4, 1],\n [1, -2, -5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 0, -5, 3, 6],\n [-2, 3, 5, -4, 6],\n [2, -2, -1, 3, -2],\n [5, -5, 3, 5, -3],\n [6, -4, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 6, -5, -3, -4],\n [-4, -4, -6, -3, 4],\n [6, 1, 4, -6, -2],\n [2, -6, 4, -5, 4],\n [0, -1, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, -5, 4, 1],\n [-2, -2, -3, -1, -3],\n [-5, 6, 4, 4, 3],\n [4, -2, -6, -1, -5],\n [-1, 0, -5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -6, -5, -4, -5],\n [-3, 4, 2, -3, 5],\n [-1, 4, -4, -4, -4],\n [0, -4, -3, 0, -3],\n [6, -1, -6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -3, -4, 0, -6],\n [1, -6, -6, 6, -2],\n [-6, -4, -3, -6, -4],\n [-3, -3, -3, 5, -3],\n [-4, -2, 4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 2, -1, 5, 0],\n [6, -1, 3, 3, -4],\n [-4, 0, 1, -5, -1],\n [-2, -5, -2, -2, -6],\n [1, 3, -4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 2, -3, -2, 2],\n [-1, -2, -1, 5, -2],\n [0, 2, -6, 5, 5],\n [6, -3, 4, -2, -2],\n [-5, 1, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -4, 1, 5, -4],\n [1, 1, 0, 3, -1],\n [-1, -2, -3, -6, 0],\n [4, -3, -2, 4, -4],\n [1, 5, -4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, 2, 2, -3],\n [4, 1, -6, -6, -3],\n [0, 3, 4, 5, -6],\n [5, -1, 0, -6, 6],\n [2, 5, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 5, -4, -3, 6],\n [2, -3, 3, 2, 5],\n [-4, 5, -6, 2, -4],\n [-1, -3, -2, -1, -6],\n [1, 6, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 6, 1, -4, -3],\n [5, -2, -5, 1, -5],\n [5, 6, 6, -6, -1],\n [-3, -5, -6, 0, 3],\n [6, -5, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -6, -2, 0, -5],\n [-5, 4, 6, 2, 3],\n [4, 2, -4, 3, -6],\n [2, -4, 0, -3, 3],\n [-5, 1, 6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -6, -6, -4, -2],\n [-3, -5, 5, -6, -2],\n [-2, -5, -3, -3, 2],\n [0, -2, 3, 5, 1],\n [2, -1, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 2, -5, 0, -5],\n [5, 0, -2, -3, 0],\n [6, 4, -6, -5, 4],\n [-4, 1, -6, -2, -3],\n [-1, 6, -2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -3, -1, 6, -5],\n [5, 2, 2, -4, 1],\n [6, 4, 3, -3, 6],\n [-3, 3, -3, -1, -2],\n [-3, 6, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 1, 3, -6, -3],\n [1, 5, -6, 6, -5],\n [-6, 5, -6, -6, -2],\n [-1, -2, 6, -3, 2],\n [-6, -1, -3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -1, 1, 0, 6],\n [-5, 1, -5, -5, -2],\n [4, 1, 1, -6, 4],\n [6, 6, -2, 3, 4],\n [-3, -1, 0, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 6, -3, 1, 0],\n [-4, 4, -3, -4, -1],\n [1, 4, 4, 0, -5],\n [-6, -6, -6, 0, -1],\n [0, 3, 6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -2, 0, 4, 3],\n [-4, 3, 3, -4, 4],\n [-1, 2, -3, 4, -2],\n [-6, 5, 6, 3, 0],\n [3, 6, 5, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 1, -1, 1, 3],\n [3, 3, -5, 0, 4],\n [0, -4, -2, 5, -6],\n [4, -2, -1, -3, 2],\n [6, -5, 6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -2, -6, 1, -1],\n [-2, -1, 6, 3, -1],\n [2, -6, 1, 4, -2],\n [-4, 5, 2, -5, 3],\n [4, -6, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 6, 2, -1, -5],\n [3, -5, 4, 4, 3],\n [3, 5, 3, 4, 1],\n [-6, 1, 3, -2, -5],\n [6, 5, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -4, -6, 2, 3],\n [-2, 2, -1, 6, -5],\n [-3, 3, -3, 5, -6],\n [6, -2, -6, 1, -1],\n [0, -6, 4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 5, 3, 2, -5],\n [-5, 1, 1, 0, 0],\n [1, 0, 2, -2, -6],\n [2, 2, 1, 4, -4],\n [1, 3, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -6, 3, -3, -2],\n [3, 1, -5, 1, -6],\n [-3, 1, 4, 2, -1],\n [4, -5, -1, -6, 2],\n [-6, 4, 0, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 5, -1, -3, -4],\n [-3, 1, -1, -5, 1],\n [-6, -2, 5, 2, -6],\n [1, -2, -5, 5, -2],\n [3, -4, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -4, 4, 3, 4],\n [5, -1, -1, -1, 5],\n [-4, 2, 2, 0, 1],\n [-4, 0, -4, -3, -1],\n [-3, 5, -6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, -6, -4, 3],\n [-1, 6, 2, 3, 1],\n [2, 4, -4, 5, 0],\n [4, 0, 6, 5, -2],\n [3, 2, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -3, 5, 0, 3],\n [-6, -2, -3, 6, -4],\n [-4, 1, 2, -3, -2],\n [-5, 5, 3, -5, 4],\n [2, -2, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -2, -3, -4, -4],\n [-4, 0, -2, -6, 2],\n [-4, -1, 2, -3, 0],\n [4, -2, 3, 0, 3],\n [1, -4, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, -5, 1, 4],\n [-5, 4, 4, 1, 3],\n [-6, -2, -4, 3, -2],\n [-4, 2, 5, 2, 6],\n [-3, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -6, 4, -2, 0],\n [-3, 5, 2, -2, 5],\n [0, 6, 4, -2, 1],\n [-3, -2, 3, -3, -6],\n [6, 3, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, 1, -4, -5],\n [-2, 0, -3, 3, -1],\n [-6, 1, -5, 5, -1],\n [-4, -2, 4, 0, -1],\n [2, 0, -6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 3, -2, 3, -2],\n [0, 1, 3, -2, 5],\n [6, 3, -3, 6, 3],\n [-1, 5, 1, -2, -2],\n [-3, -1, -6, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -6, -3, 1, 4],\n [0, 6, 4, 2, -4],\n [-3, 3, 5, 3, -3],\n [5, 6, 0, 2, -2],\n [-4, -3, 3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, 1, -2, 0],\n [-1, -3, 3, 1, -5],\n [6, -6, 2, -1, 5],\n [-4, 2, 4, -6, -3],\n [-4, 0, 5, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -4, -4, 4, -6],\n [1, -6, 5, 6, 0],\n [4, 4, -5, -2, 0],\n [-5, 6, -3, -5, -1],\n [5, -2, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -6, 5, -5],\n [-4, -3, 2, 3, -3],\n [-4, -3, -4, -4, 0],\n [-3, 3, -5, -2, -4],\n [1, -2, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 0, 1, -3, 3],\n [1, 1, 6, 3, 6],\n [5, -1, 1, -6, -3],\n [-2, 0, 6, 5, 1],\n [-1, 3, -6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 6, 1, 3, -1],\n [4, 4, 3, -5, -4],\n [3, -1, 5, 0, -6],\n [-1, 0, 3, 6, -1],\n [-6, -2, -1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -6, -4, 4, -2],\n [-4, 5, 5, -4, -1],\n [-4, -4, 4, 4, -5],\n [-6, 5, 3, 3, 5],\n [-3, -3, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, -1, 0, 5],\n [5, 5, 1, 4, 3],\n [-5, 3, 1, 1, -1],\n [5, 6, 6, -6, 5],\n [-2, 4, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 1, -4, -2, -1],\n [-4, 2, -2, 2, 0],\n [4, 3, 4, 0, -6],\n [4, 1, 5, 5, 4],\n [4, 2, -5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 0, 2, -1, 6],\n [-5, 0, 2, 1, 4],\n [1, -5, 2, 3, 1],\n [2, -1, -6, 3, -5],\n [2, 0, 4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -4, 4, -3, -3],\n [0, -4, -4, -2, 3],\n [-4, -5, -1, -6, 3],\n [-4, -5, 3, -2, 2],\n [-1, -2, -3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 4, -5, -5, 5],\n [1, -2, 4, 5, 2],\n [0, -3, -5, 5, 2],\n [4, 3, -5, 2, 2],\n [6, 3, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 4, -4, -5, 1],\n [-5, 6, 4, 1, -4],\n [-2, 2, -2, -6, 2],\n [2, 6, -3, -3, -6],\n [-2, 0, 5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -1, -2, 2, -6],\n [-1, -3, -2, -1, 3],\n [-5, -6, 1, -3, 1],\n [-6, -1, -2, 3, 2],\n [5, 1, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 1, -4, -6, -3],\n [1, 0, 1, 6, 1],\n [-2, -4, -3, 2, -5],\n [4, -4, -4, 2, 4],\n [-2, 0, 3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -6, 3, 5, 5],\n [3, 5, 6, -3, -5],\n [2, -3, -3, 2, -4],\n [1, 6, -5, 5, -4],\n [1, -6, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -2, -6, -3, 1],\n [1, 6, -5, 5, 2],\n [0, -6, -3, -5, -6],\n [-5, -1, -5, -1, -4],\n [3, -5, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -2, -3, -2, -6],\n [3, -2, -4, -6, -2],\n [6, -5, 6, -2, -2],\n [3, 1, -4, 2, 3],\n [-5, -5, 6, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, 6, -3, -6],\n [4, -1, -3, 3, -5],\n [4, -2, -5, 1, 1],\n [0, 3, -5, -6, 6],\n [0, 5, -6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -6, 6, 3, 1],\n [0, 2, -5, -2, 4],\n [-3, 0, 2, 1, -3],\n [5, -6, 0, 6, 6],\n [-5, 0, 1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 5, -6, -3, -5],\n [-2, -4, 3, 1, 3],\n [3, 6, 4, 0, 2],\n [-5, 2, 4, -1, -3],\n [-3, -6, -2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 4, -3, 1, -2],\n [-6, -1, -5, 0, -4],\n [-4, -4, 4, 1, -2],\n [4, 4, 4, 6, -2],\n [-3, 1, -3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -1, 5, 3, 5],\n [6, -1, 0, -4, 3],\n [6, 0, -1, -4, 0],\n [-3, 6, -1, -3, -5],\n [1, 2, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 3, -3, 6, 4],\n [0, -3, -6, 6, 6],\n [5, 3, -1, -5, -1],\n [5, -1, 0, -1, 0],\n [3, 2, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -4, 0, 5, 3],\n [-3, -4, -2, -6, -1],\n [-5, 3, 2, 6, -1],\n [5, 5, -6, 3, -5],\n [6, 6, -4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 5, -4, -6, 0],\n [-1, -1, 4, -3, 5],\n [3, 6, -2, -3, -4],\n [-1, -3, -1, 5, 6],\n [6, 5, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -2, 1, 5, -4],\n [1, 5, 0, 2, 6],\n [1, -4, -2, 0, -2],\n [-4, 2, 1, 2, -6],\n [1, 6, 6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 4, -1, 1, -5],\n [5, -6, -3, 0, 3],\n [0, 1, -3, -6, 0],\n [1, -5, 6, 0, 0],\n [-4, 2, 5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 2, 6, 2, -4],\n [-1, 5, 5, -4, -4],\n [1, -5, -1, 5, 0],\n [6, -1, 2, 6, -1],\n [-3, 3, 0, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 5, 5, -2, 6],\n [4, 2, -1, 5, 3],\n [2, 3, -5, -3, -3],\n [-5, -4, 6, 0, -1],\n [-6, 6, -1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -1, -6, -5, -5],\n [-6, 0, 0, -1, -6],\n [4, -1, -3, 3, 3],\n [-2, 0, -4, 0, -4],\n [3, 3, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -1, 3, 1, 4],\n [-5, -2, -2, -5, -3],\n [-2, 6, -1, 3, -2],\n [-4, -3, -1, 5, 1],\n [-4, 4, -6, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 4, 4, 4, 3],\n [-5, 6, -2, 1, 5],\n [-5, -2, -2, -5, -3],\n [0, 6, 1, -2, -1],\n [4, -4, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 5, 4, -2, 2],\n [5, -5, 5, -6, 1],\n [-6, -1, -6, 2, -5],\n [-6, 4, 1, -3, -2],\n [0, 1, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 2, -1, -6, 2],\n [5, -5, 4, -3, 3],\n [5, 5, 6, 4, -3],\n [4, -4, 6, -4, -5],\n [-1, 4, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 6, -2, -4, -2],\n [5, -2, 4, -2, 4],\n [-2, 0, 2, 2, 5],\n [-1, -3, -6, 6, -4],\n [2, 0, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 4, 0, 4, 0],\n [6, -3, 2, 5, 5],\n [1, -3, 4, -4, -3],\n [3, 5, 5, -3, 6],\n [-2, -3, 5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -2, -1, 1, 1],\n [-4, -4, -3, 2, 6],\n [-3, -4, 6, -2, 3],\n [-6, 5, 4, -2, 6],\n [3, 5, -4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, -6, -2, 2],\n [-5, -4, -4, -3, 1],\n [-2, -5, 2, -1, 6],\n [-3, 0, 0, 3, 1],\n [-2, -4, 5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 3, 5, -2, 2],\n [-3, -5, -1, -3, 4],\n [4, 1, -2, -3, -6],\n [1, 1, -4, -4, 1],\n [6, 5, -3, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -1, 5, 0, 1],\n [-4, -3, -1, 5, 1],\n [6, -4, -1, -3, 0],\n [3, 1, -2, 0, -3],\n [1, 3, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -4, 4, -3, -4],\n [0, -5, -4, 1, 3],\n [-5, -4, 2, 6, -5],\n [0, -5, 2, 0, 3],\n [1, 5, 5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -5, 3, 1, 5],\n [-1, 4, 0, 1, 3],\n [-1, 4, 6, 0, -2],\n [-5, 6, 2, 2, -1],\n [-3, -4, -5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -5, 0, 0, 6],\n [-1, 6, 2, 0, 2],\n [2, 2, 2, 2, -3],\n [-5, 0, 4, -6, 6],\n [3, -2, -2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -4, -6, 0, -6],\n [-3, -3, 6, -4, -2],\n [0, -4, -2, -3, 6],\n [5, 3, -4, -4, 6],\n [-5, -5, 5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -5, 1, -2, 0],\n [0, 2, -5, 4, 3],\n [1, 3, -3, -3, -2],\n [3, 4, -4, -5, 4],\n [3, -4, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 4, -6, 5, 0],\n [-2, 4, 4, 5, 5],\n [2, 5, 4, -6, -3],\n [-1, -2, -6, 0, 0],\n [6, -2, -2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 3, 6, 6, 5],\n [3, -5, -4, 2, 1],\n [6, 4, 2, -2, -6],\n [0, 1, -1, 4, -3],\n [0, -2, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -3, 1, -2, 4],\n [2, 3, -1, -5, -4],\n [-6, -1, 2, -5, 4],\n [4, 0, -3, -6, 3],\n [-4, -1, 3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -1, 3, 5, -1],\n [5, -5, 4, 0, 0],\n [0, 5, 4, -1, 0],\n [-2, -5, -4, -2, 1],\n [6, 0, 2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, -3, 4, -3],\n [4, 2, 1, -1, -1],\n [2, 4, -3, -6, 4],\n [-2, -6, -6, -4, 1],\n [3, 2, -6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -6, -5, 2, -2],\n [4, 6, 6, 5, -6],\n [-4, -4, 5, 5, -4],\n [-1, 2, -6, 2, -4],\n [-1, -2, 5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 2, -2, 2, 1],\n [0, -6, 2, 5, 6],\n [-1, 5, -6, 0, 0],\n [6, -3, -5, -1, -6],\n [-6, -3, 6, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -6, -4, 0, 1],\n [-4, 0, -6, 3, 3],\n [-3, 3, 4, -5, 1],\n [-5, -2, -6, -2, 0],\n [-3, 4, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -4, -3, -2, 1],\n [-6, 2, 0, 5, 2],\n [3, -4, 3, -3, -2],\n [-5, 4, -3, 1, -1],\n [-4, 6, -2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -4, -5, -2, 0],\n [-4, 1, 3, 1, -2],\n [5, -6, -5, 6, -1],\n [-1, 0, -5, 3, 3],\n [3, -4, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -4, -4, 6, 5],\n [5, 4, -1, 3, -6],\n [-4, -5, -4, 6, -6],\n [0, -1, 1, 3, 4],\n [3, 5, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 3, 2, -6, -6],\n [-4, 4, 5, 5, -3],\n [-1, -2, -1, -6, 3],\n [-6, 3, -3, 0, 1],\n [4, 1, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -1, -2, 6, 1],\n [-5, 5, -5, 6, 6],\n [0, 5, 0, -6, 4],\n [2, 2, 6, 6, 6],\n [-4, 0, 5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 2, -6, 6, 4],\n [5, 2, 1, 1, -2],\n [-4, 5, -1, -6, -2],\n [0, -2, -2, -6, 2],\n [4, -3, 3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -3, 0, 0, 3],\n [0, -2, -2, -6, 2],\n [6, 3, 4, -2, -3],\n [-5, 4, 6, -4, -1],\n [0, 5, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 3, -1, 6, 0],\n [2, 6, 0, -5, 1],\n [2, -3, 1, -3, 2],\n [-6, 0, -4, 4, -2],\n [3, 6, 6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, 4, 5, 3],\n [0, 2, 4, -4, 1],\n [-3, 4, 4, 4, -3],\n [-2, -4, 2, 5, 2],\n [-6, 3, 5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -3, -3, 5, 6],\n [0, 3, 3, -4, 3],\n [-4, 6, 2, -6, -4],\n [3, -1, 6, 5, 2],\n [-6, -4, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, -4, -2, 5],\n [-5, 2, -3, 4, -1],\n [2, -1, 4, 1, 4],\n [2, -6, 3, -4, -5],\n [-1, -2, -6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -2, 3, 2, 1],\n [3, 0, 2, -6, 4],\n [5, 4, -3, -1, 4],\n [-3, -2, -1, 5, -1],\n [3, 3, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 6, -4, -4, 0],\n [-1, 4, -2, 3, -2],\n [6, -5, 3, -4, 5],\n [0, 5, 0, 2, -3],\n [-6, -2, -4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 6, -5, -5, -1],\n [-4, 0, 3, -2, 0],\n [6, 3, 6, -4, -1],\n [2, 0, 5, 4, 6],\n [-6, -1, 6, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 2, 0, 6, 5],\n [-5, -5, -1, 3, 6],\n [-4, 4, -3, -3, 3],\n [-4, -6, -2, 2, 2],\n [-4, -1, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -6, 0, 3, -5],\n [4, 1, -2, 3, 4],\n [6, 2, -2, 2, -4],\n [3, 3, -5, -5, 6],\n [-6, -1, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 2, 1, -3, 1],\n [1, -3, 4, -2, 0],\n [-4, 3, -5, 6, -3],\n [3, -2, -6, -6, -5],\n [4, 4, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -1, 4, -1, 4],\n [-1, 5, 1, 2, -3],\n [-5, -4, 0, 6, -3],\n [6, -2, 1, -4, -1],\n [-3, 2, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -5, -5, 6, -5],\n [3, 3, -5, 3, -1],\n [1, 5, 4, -1, 4],\n [-1, 0, 2, -1, -5],\n [-5, 2, -3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 5, -1, -5, 5],\n [6, 0, 0, -2, -6],\n [5, -6, 1, -6, -2],\n [2, 2, -4, 6, -2],\n [-6, -2, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 6, 2, -2, -3],\n [-6, 3, 1, 5, -6],\n [5, -4, -2, -1, 0],\n [6, 0, 3, -4, -6],\n [6, -5, -3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, 3, 4, 2],\n [3, -5, 1, -6, -1],\n [3, -3, 2, -4, -2],\n [5, 3, -1, -5, 3],\n [-5, 4, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 4, -3, 1, 1],\n [-1, -2, 4, 0, -3],\n [6, -5, 2, 0, 6],\n [-5, -6, -3, -6, -6],\n [2, 5, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 0, -5, 4, -2],\n [6, 0, 6, 5, -6],\n [-3, 4, 0, 1, 4],\n [-4, 0, 4, 4, 0],\n [5, -2, -5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 4, 6, -6, 3],\n [5, -6, -3, 4, -2],\n [0, 2, -1, 4, 3],\n [1, 0, -1, 4, 2],\n [2, 0, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, 6, -2, -5],\n [5, 3, 4, -5, -5],\n [-1, -6, -1, 5, 6],\n [2, -5, -2, 6, -5],\n [6, 6, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -5, -1, 6, -1],\n [-2, 0, -3, -6, 2],\n [3, -5, 6, -3, -3],\n [-3, -3, 6, -3, 6],\n [-6, 1, -3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, -6, -3, -2],\n [-1, -2, 2, -4, -4],\n [4, -6, 6, -1, -6],\n [1, 3, -5, -4, -6],\n [4, 5, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, 3, -2, 1],\n [6, 1, 0, -2, 3],\n [-4, 5, -4, 5, -3],\n [3, 2, -5, 6, 4],\n [-4, 3, -3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 1, -3, 6, -5],\n [-6, 3, -1, 4, 3],\n [2, 4, 3, 3, -1],\n [-1, -6, -3, -6, 4],\n [-2, 0, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -2, -6, -2, -3],\n [-5, 6, -1, -6, -2],\n [6, 4, 3, 4, -3],\n [2, 3, -3, -3, 0],\n [-2, 3, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 4, 1, -1, 0],\n [-3, -5, 4, -5, -6],\n [-4, -4, -1, 3, -1],\n [3, 0, 1, -6, 4],\n [-6, 0, -6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 0, 1, -6, -6],\n [1, 2, -3, 3, 3],\n [3, 2, 5, -5, 0],\n [-3, 5, 3, 1, 1],\n [-5, -6, -6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 5, 1, -4, -2],\n [-2, 3, 0, 3, -3],\n [5, -5, 4, -5, 6],\n [-3, 5, 2, 3, -6],\n [-2, 4, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 6, 1, -3, -2],\n [5, 0, 2, -6, 4],\n [1, -6, 1, -4, 2],\n [0, -4, 0, 5, -1],\n [-1, 2, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -1, 6, -4, 2],\n [-6, -5, 4, -1, -6],\n [-5, 0, -4, -3, 0],\n [4, -1, 6, -2, 1],\n [6, 4, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -3, 6, 1, 1],\n [-2, 2, 4, -1, -3],\n [-2, 3, -4, -4, -3],\n [-2, -2, -4, -2, -6],\n [4, -6, 0, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -1, 0, 3, -5],\n [6, -6, 2, 2, 4],\n [-5, 0, -5, -5, 6],\n [-6, 3, 2, 3, 0],\n [-3, 3, 4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 1, 5, -2, -6],\n [-3, 5, 4, 5, 5],\n [0, 2, 4, 6, -1],\n [1, -1, 3, 0, -2],\n [-4, -6, -6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, 3, 2, -1],\n [6, -3, 5, 4, -3],\n [2, 0, 6, -5, -5],\n [-2, 3, 6, -5, -6],\n [2, 0, 3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -3, 2, -3, -1],\n [0, -5, -3, 4, 2],\n [0, 4, -5, 3, -4],\n [-5, -4, 5, 3, -6],\n [0, -6, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -5, 3, 0, -6],\n [3, 5, -1, -6, -3],\n [-1, -2, 6, 0, 3],\n [0, -4, 0, 3, 4],\n [-2, 1, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -4, 5, 0, -1],\n [-4, 5, -4, -2, 1],\n [-6, 1, -2, -3, 0],\n [-3, -4, 5, 6, 1],\n [-3, 3, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -5, -3, 3, -3],\n [4, 3, 3, -4, 0],\n [-4, -6, 5, -1, -3],\n [-4, 4, -5, -3, 5],\n [0, -3, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -6, 4, -4, -4],\n [-1, -1, 6, -3, 5],\n [1, 3, 0, -4, 2],\n [-1, 0, 0, 2, 5],\n [2, 5, 5, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 4, -1, 2, -4],\n [-3, 0, -1, -6, 5],\n [3, -4, -4, 1, 2],\n [3, -1, -1, 5, -1],\n [-3, -1, -5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 0, -4, 3, 6],\n [0, 2, 5, -1, -4],\n [-2, -5, 4, 6, -5],\n [-2, 1, 6, 5, -2],\n [6, 3, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 3, 4, 2, 0],\n [-2, 3, -4, 4, 3],\n [-2, -6, -2, -6, 4],\n [2, 6, 6, 3, 3],\n [6, 1, -2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 3, 6, -1, 6],\n [-1, -2, 5, -3, -4],\n [0, 0, 6, -2, 1],\n [-6, 3, 5, -5, -3],\n [5, 4, -1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -1, 6, 1, -6],\n [-6, -5, -5, 2, 1],\n [4, 2, 2, -3, 4],\n [-1, -6, -6, 4, 4],\n [3, -4, 1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, 0, 1, 5],\n [-3, 4, 0, -2, 4],\n [-3, -5, 0, 5, -5],\n [-5, 5, 3, 2, 3],\n [2, -1, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 2, -6, -6, -4],\n [6, 2, -1, -1, 0],\n [-3, -4, 2, 1, -5],\n [-1, 0, 6, 1, 2],\n [-3, 3, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, 4, -6, -5],\n [-1, 0, 3, -2, -2],\n [-4, 2, 1, -3, -1],\n [0, 1, 4, -3, -6],\n [2, 3, 0, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 4, 6, -6, 5],\n [-5, 1, 4, 4, 6],\n [3, 0, 2, 3, -2],\n [2, 4, 6, 5, -4],\n [-3, 3, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 5, 0, 4, 3],\n [-1, -6, 0, -2, 1],\n [2, -1, 4, 4, 3],\n [-1, 5, -4, -2, -1],\n [6, -5, 5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 5, -6, -4, -2],\n [6, -3, 6, -3, 5],\n [1, 2, -2, 4, -3],\n [3, -3, 1, -3, -6],\n [0, 4, 3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -2, -1, -4, 5],\n [6, 2, -1, 0, -1],\n [3, 3, -4, 3, 5],\n [4, 0, -6, -1, -4],\n [-4, 0, -5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -6, 4, 6, 0],\n [-2, -2, 0, -1, 2],\n [2, 2, 0, -3, -1],\n [2, -6, -6, 0, 6],\n [0, 6, -1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 0, 5, 2, 3],\n [3, 5, -1, 6, 2],\n [2, 5, -4, -4, -5],\n [6, 2, 5, 2, -6],\n [6, 4, -6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -4, 2, 2, 6],\n [5, -3, 4, -4, -1],\n [-5, 2, 0, -3, -5],\n [5, 4, 1, -6, -5],\n [6, 6, -6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 0, 3, 5, 6],\n [6, -5, -6, -4, -1],\n [-2, 5, 4, -3, 3],\n [-1, 2, -3, -6, -1],\n [6, 5, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, 5, -4, -2],\n [0, 4, -1, 0, -6],\n [-3, -4, 5, -5, -5],\n [4, -4, -1, 0, 6],\n [-3, 2, -3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, -5, -4, 0],\n [-1, 5, -2, 6, 5],\n [-5, -1, 3, 6, -1],\n [4, -4, -4, -2, 2],\n [0, 6, -1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, 1, 3, 4],\n [-1, 1, 3, 6, -4],\n [0, 6, 1, 2, 2],\n [4, -6, 5, 2, -2],\n [-2, -5, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 4, 4, -4, -6],\n [-5, 2, 3, 1, -2],\n [4, 2, -4, 0, -2],\n [-6, 2, -1, -4, 3],\n [-2, 5, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 5, -6, 6, 1],\n [3, 5, 1, 6, 2],\n [3, 5, -2, 5, -1],\n [-2, 5, -3, 6, 2],\n [3, -6, -5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -2, 1, -5, -4],\n [1, 1, 5, -6, -2],\n [0, 0, 0, -5, 0],\n [3, 4, 4, 1, -1],\n [2, 4, -1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 6, 0, 0, -4],\n [1, -4, -1, 2, 5],\n [3, 4, -4, -6, 1],\n [-4, 4, -4, 6, 2],\n [-3, 6, -6, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -2, -6, 5, 5],\n [1, -4, -2, -3, -4],\n [-5, -2, 2, -6, 4],\n [0, 3, 5, 2, -5],\n [-5, -6, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 5, -1, 5, -4],\n [5, 3, 3, -5, -2],\n [3, 5, -4, -4, 3],\n [-6, 2, 4, -3, 6],\n [-1, -3, -5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 1, -3, -3, -1],\n [6, 0, 4, 5, 2],\n [-2, -5, -1, 0, 5],\n [3, 6, 4, -2, -1],\n [3, -6, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 6, -3, -6, 6],\n [4, 5, -3, -1, 6],\n [3, -2, -4, 4, 0],\n [5, 1, -4, 2, 1],\n [-3, 3, 3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -6, -6, -1, -2],\n [-3, 0, 2, 2, 4],\n [-6, -1, 0, -1, 6],\n [5, -4, -1, 3, 4],\n [5, -5, 4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 2, -1, 3, -5],\n [-2, 3, 6, -5, -5],\n [-3, 1, 2, -4, 6],\n [6, 6, 4, 5, 6],\n [0, 4, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 2, -5, -1, 6],\n [2, -4, 0, 2, -2],\n [0, 6, 3, -5, -4],\n [-5, 1, 4, -6, -2],\n [-6, 3, 1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, 0, 2, 1],\n [0, 4, 4, 3, -3],\n [-5, -1, 0, 1, -1],\n [5, 2, 4, -5, 5],\n [6, -5, 3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 1, -6, -2, -5],\n [-1, 3, -4, 2, -3],\n [2, -3, 0, -6, -3],\n [2, -6, -2, -3, -2],\n [-2, -3, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -4, 4, -3, 3],\n [3, 6, 4, 4, 6],\n [5, -1, -6, -1, 4],\n [-2, -4, -2, -5, -4],\n [0, 1, 2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -4, 2, 1, -3],\n [6, 6, 2, 3, -3],\n [-1, -2, -2, 6, -4],\n [1, -3, 2, 2, 1],\n [1, 2, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 0, 1, -1, -6],\n [-2, 6, -4, -1, 2],\n [-5, 0, -5, -6, 2],\n [-2, 5, -3, -1, -2],\n [3, -5, -5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -6, 2, -4, 1],\n [-5, -3, -4, 0, 6],\n [-4, -5, -3, 1, 3],\n [-1, 6, 6, 2, 1],\n [-1, -3, 0, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -5, 2, 0, -3],\n [4, 5, 2, -6, -2],\n [1, 5, 5, 3, 5],\n [-1, -2, 0, 5, 0],\n [4, 6, 4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 3, -2, -6, 3],\n [1, 4, 6, 6, 3],\n [-6, 0, 4, -5, -4],\n [-2, 5, 5, 6, -1],\n [4, 0, 1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 5, -4, -3, -4],\n [-4, -2, 2, 1, 6],\n [6, 3, 3, -2, -5],\n [3, -1, 0, 0, 6],\n [-6, -6, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 2, -3, 1, -2],\n [2, 4, -2, 4, 5],\n [-6, 0, -6, -3, 5],\n [-3, 3, 4, -1, -6],\n [5, 2, -3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -4, 5, -1, 4],\n [2, -6, 1, -5, -3],\n [-2, 1, -5, 1, -1],\n [4, 5, 2, 1, 1],\n [-1, 3, 4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, 4, 3, 5],\n [4, 3, -2, -4, 1],\n [0, -4, 2, 0, -3],\n [1, -3, 2, -4, -5],\n [2, 4, -5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -1, 1, -5, -1],\n [0, -2, 5, -2, 4],\n [-2, -3, -1, -2, 1],\n [-3, 2, -4, -1, 1],\n [0, 6, 4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -3, 0, 1, -4],\n [2, -6, -2, 5, -6],\n [1, -4, -1, -1, 4],\n [3, 5, 0, -5, -1],\n [4, 0, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 3, -4, -4, 2],\n [-6, -2, -5, 5, -2],\n [-2, -4, -1, -1, 4],\n [2, -3, -1, -5, 0],\n [2, -2, -5, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -6, -3, -6, 1],\n [-3, -4, 4, 0, 0],\n [-2, 2, 6, 6, -4],\n [6, -2, -4, 4, 4],\n [1, -6, 5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 3, 3, -4, 6],\n [3, 2, -4, 0, -6],\n [-4, 3, -1, 1, 3],\n [1, 6, -1, 2, -5],\n [0, 1, -5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 0, 6, 0, -6],\n [-1, -3, 5, -3, 2],\n [6, 6, -2, -2, 1],\n [6, -2, 0, 5, 1],\n [-2, 4, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 0, 5, 2, 2],\n [-1, 5, 0, -3, 4],\n [-6, -2, -5, 6, 5],\n [-4, -3, -3, 5, 5],\n [-6, -6, -5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, -5, 5, -5],\n [6, -5, 4, -2, 3],\n [0, -1, 2, -5, 5],\n [-2, 6, -2, -6, -4],\n [-4, 4, -3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 4, -2, 5, -2],\n [4, 2, 5, 4, 2],\n [1, -4, 3, -5, 4],\n [-4, 5, 1, 6, -1],\n [-1, -5, 6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, 0, 0, -2],\n [1, 2, 2, 3, 6],\n [-5, 4, -2, 0, -2],\n [1, -5, -2, -1, 3],\n [-3, -3, 6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 3, 6, -3, -5],\n [-3, -3, 2, 5, 0],\n [-4, -2, 6, 2, -1],\n [2, 1, -6, 6, 3],\n [3, 2, -6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 5, -3, 5, 6],\n [2, 2, -4, 6, -1],\n [1, -1, 1, 3, -5],\n [1, 4, -3, -4, 3],\n [-5, -3, -1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 2, 5, -4, 0],\n [3, 0, 2, -5, -6],\n [-6, -5, -3, -6, 5],\n [-2, 6, -2, 2, -2],\n [-4, -4, -1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -2, 2, 3, -1],\n [6, 2, -5, 5, -1],\n [4, -6, -1, 2, 5],\n [-6, -2, 6, 3, -5],\n [-4, -5, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -1, 4, 0, 5],\n [6, 5, 2, 0, 5],\n [-4, 5, -6, 5, -2],\n [0, 6, -4, -6, -6],\n [-6, -5, 4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 2, -4, 6, -3],\n [2, 3, 1, -5, 0],\n [-2, -4, 0, 0, 2],\n [1, 2, -6, 2, 1],\n [0, -1, 1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -5, 4, -1, 1],\n [0, 0, 5, 3, -5],\n [3, 1, -2, 1, -1],\n [1, -5, -2, -1, -1],\n [-6, 2, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 3, 1, 1, 2],\n [1, -5, 6, 4, -1],\n [6, -1, 2, -6, 3],\n [6, 1, 5, 3, 5],\n [-3, -4, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 6, -4, -1, 3],\n [-4, -2, -4, -4, 3],\n [-4, -5, 5, -4, 4],\n [-4, -4, -6, -1, -1],\n [0, -1, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 2, 1, -1, -6],\n [-5, 1, 5, 2, -6],\n [6, -5, -6, 4, -2],\n [-2, 2, -4, -4, 6],\n [5, 5, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 4, -5, -1, 2],\n [-6, 0, 1, 6, -6],\n [4, -2, -5, 4, 1],\n [6, -6, 3, 1, -5],\n [-6, -4, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -5, 5, 6, 4],\n [4, -5, 4, 0, -5],\n [5, 6, -3, 1, 3],\n [-5, 2, -4, 6, -2],\n [-6, -4, -4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 3, -3, 6, -6],\n [-1, 5, 6, -6, -6],\n [-1, -2, -5, 0, 5],\n [0, -4, -2, -1, 5],\n [1, -4, -2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 2, 6, -3, -1],\n [-2, 3, -5, -5, -1],\n [1, 6, 2, 4, -5],\n [4, 4, -5, 3, 4],\n [4, 3, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -2, 4, 0, 3],\n [6, 0, 2, 1, 6],\n [5, -1, 5, -4, 2],\n [4, 4, -3, -5, 6],\n [-1, 4, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 3, -6, 2, -5],\n [3, 3, 1, -6, 4],\n [-1, 5, 4, -6, -4],\n [5, -5, 6, 3, 5],\n [-1, 3, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -1, 1, -2, -2],\n [-6, 1, -5, -4, -4],\n [5, 5, -2, -5, -2],\n [0, -6, 2, -3, 2],\n [6, 2, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 4, 4, 4, 3],\n [2, 2, -2, -6, -5],\n [6, 5, 2, -1, 4],\n [3, -1, 1, -6, -2],\n [-2, -6, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 1, 3, -2, 0],\n [-1, 3, -2, -4, -1],\n [-1, 6, -4, -4, 0],\n [-6, 6, 3, 4, -4],\n [-2, -2, -6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, -4, 2, -4],\n [0, 1, -5, -6, 0],\n [2, -4, -3, -5, 3],\n [4, 5, -4, 4, -5],\n [2, 0, -6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 2, -4, -1, 0],\n [-2, 3, 0, -5, -1],\n [-6, 2, -5, -3, 1],\n [0, 3, -2, 3, 3],\n [-3, -1, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, -3, 2, -4],\n [-1, -3, -2, -2, -3],\n [-2, 3, 2, 4, 5],\n [3, -3, 2, -1, 1],\n [1, -3, 4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -3, 5, 3, -5],\n [2, -1, 5, 1, -6],\n [3, 0, -4, -4, 5],\n [-6, -2, -4, -1, -4],\n [5, -2, -5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -6, -1, 0, -6],\n [5, 4, -3, -3, 5],\n [-6, -1, -5, -3, -2],\n [-4, 6, 3, 2, -6],\n [5, -4, -6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, 1, 3, 0],\n [3, 0, 2, -5, 1],\n [4, -6, -4, -3, 4],\n [-1, -4, 4, -5, -6],\n [0, -3, 4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -4, -1, -1, -1],\n [-5, -1, 2, 6, -3],\n [-3, -6, -4, -3, -2],\n [6, 3, -5, 6, 0],\n [0, -2, -2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 3, 2, -4, -2],\n [3, -5, -3, -1, 3],\n [5, 2, -4, 4, 1],\n [-5, 1, 4, -6, 6],\n [-6, -2, 4, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, -1, 3, -3],\n [-3, -6, 4, 2, -3],\n [5, -2, 5, 0, 0],\n [4, 5, -6, 0, -3],\n [0, -6, -6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 1, 0, 0, -2],\n [6, -2, -3, 5, 1],\n [-6, 6, -2, -5, -6],\n [-2, 0, 3, 1, -4],\n [2, 2, 5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -5, -3, -4, 3],\n [1, 0, -2, 0, 1],\n [0, -6, -3, 2, -3],\n [-6, 3, -2, 5, -1],\n [-1, -3, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -5, -5, 2, -6],\n [-1, -5, 0, -1, -3],\n [-2, 2, 4, 2, -1],\n [-5, 0, 6, -5, -3],\n [-1, 5, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 4, -2, -4, 4],\n [6, -3, 6, -6, -3],\n [-5, 5, 1, -3, -2],\n [-4, 6, -6, 0, 1],\n [5, -2, 0, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, 0, 5, 4],\n [2, 6, -2, -1, -6],\n [5, -5, 2, -1, -3],\n [-3, -1, 2, 4, 1],\n [-3, -1, 3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, 2, -4, 4],\n [4, -6, 6, -3, 3],\n [-1, 6, -1, -2, -6],\n [3, 4, -6, 1, -2],\n [5, -2, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 0, 0, -6, 4],\n [-6, 3, 4, -3, 1],\n [-5, 2, 6, -4, 3],\n [-2, -3, 2, 0, -3],\n [-1, 4, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 4, 3, -1, -5],\n [-6, -3, 0, -4, 3],\n [-5, -5, -6, 4, 1],\n [-6, 3, 2, -4, -1],\n [0, 5, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 0, 5, 0, -2],\n [-3, -1, 2, 6, 2],\n [-2, -1, 1, 5, -3],\n [2, 2, 0, -2, 4],\n [-6, 6, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 1, 2, 5, 5],\n [5, 5, -5, 4, 4],\n [4, 3, 1, -5, -3],\n [3, -2, 1, -2, -4],\n [-6, -3, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 1, 4, 2, -3],\n [-5, 3, 1, 6, -6],\n [1, 5, 2, 2, 3],\n [3, 1, -3, 6, -3],\n [5, 0, 6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 6, 0, 1, 4],\n [2, 0, -4, 4, 2],\n [4, -3, -5, 6, 6],\n [1, 1, 4, -3, -2],\n [6, 0, -3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 4, 1, -4, -3],\n [0, -6, -1, 3, -6],\n [-6, -1, -6, -4, -4],\n [2, 4, 6, -4, 4],\n [1, 4, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -1, 1, 4, 5],\n [0, -6, 2, 2, 5],\n [-4, -1, 1, -6, -3],\n [6, -1, 3, 3, 5],\n [1, -6, 3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 5, -5, 6, 3],\n [3, -3, 1, -6, -6],\n [-1, 4, -5, -6, 0],\n [0, 1, -4, 2, 1],\n [3, -1, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -1, -5, 5, -1],\n [-1, 1, -3, 5, -1],\n [6, 5, -6, 0, 1],\n [-2, -3, -3, 4, 5],\n [6, 3, 6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 4, -1, 5, 3],\n [4, -3, 2, -1, -2],\n [3, 4, 4, -3, 5],\n [5, -1, -4, -4, 1],\n [1, 1, -5, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -6, 6, -4, 4],\n [2, -1, -1, -4, -2],\n [-4, 0, 0, 0, 5],\n [-4, 4, 2, 6, -2],\n [-6, -1, 6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -1, -1, -2, 0],\n [-1, 3, 0, 6, -4],\n [-1, 5, -4, -6, -4],\n [-4, 6, -1, -5, 1],\n [-4, 2, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 3, 1, 6, -3],\n [-1, 2, -6, -6, 3],\n [-6, 0, 4, 2, 2],\n [-3, -1, -4, 3, -1],\n [2, 5, 5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 5, -1, -5, -4],\n [4, 3, 5, 2, 6],\n [-3, 3, 1, -5, 1],\n [3, 2, 3, 3, -2],\n [2, -1, -2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -6, -1, 1, 6],\n [4, 6, -4, -1, 1],\n [0, -4, 3, 5, -6],\n [0, -1, 5, -4, 1],\n [-4, 6, 4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -3, 1, -4, -4],\n [-6, 5, 5, 0, 0],\n [6, -6, 0, 2, 4],\n [4, 4, -1, 1, -3],\n [1, -1, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 3, 5, -5, -5],\n [1, 6, -4, 3, -1],\n [2, -5, 6, 2, -3],\n [-6, 2, -3, 1, 5],\n [3, 5, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 3, 4, -5, -2],\n [3, 0, -4, 6, 3],\n [-5, -6, 6, -6, 6],\n [-1, 3, -4, 3, 4],\n [-2, -5, -6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 3, -2, 3, 4],\n [-1, 5, 3, 1, 3],\n [-5, -1, 1, -6, -1],\n [0, 5, -6, 0, 1],\n [3, -2, 4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -4, -4, -1, -4],\n [2, 4, 3, 4, 1],\n [-6, 2, -3, -6, 6],\n [6, -4, -2, -5, 2],\n [-6, 4, 4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 5, -3, -2, -3],\n [-6, 0, 3, 4, 6],\n [3, -5, -6, 0, 4],\n [-1, 6, 0, 2, 5],\n [-4, 3, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 0, 6, 6, 2],\n [-5, -1, -4, -5, 4],\n [6, -4, 5, -1, -1],\n [4, -5, -1, 5, 0],\n [-3, 6, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 4, -4, -4, -2],\n [-2, 1, 3, 2, 4],\n [-2, 5, 4, 6, 1],\n [-1, 2, -4, -3, -2],\n [2, -3, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 0, 2, 5, 3],\n [1, 4, -5, 1, 2],\n [1, -6, 4, -5, -6],\n [-1, -2, 2, -5, -1],\n [3, 2, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, 0, 0, 0],\n [-4, 4, 2, -3, -3],\n [-5, -4, 1, -6, -2],\n [-2, -2, 4, -6, 3],\n [-4, -1, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 2, 0, 5, 3],\n [-3, 1, 2, 0, -1],\n [3, 3, -6, 6, 1],\n [0, -2, 5, 5, -4],\n [-1, 6, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -5, -2, 6, 3],\n [6, 3, 4, 4, 0],\n [-2, 0, 6, 1, 2],\n [2, -5, -5, -1, 0],\n [6, -6, -1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -6, -4, 5, 4],\n [5, -5, -1, -6, -4],\n [-4, -4, -4, 3, -2],\n [5, 6, -6, -1, 2],\n [-1, 0, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, 5, -1, -4],\n [-3, -4, 1, -6, 1],\n [-1, 4, 0, 3, 0],\n [3, 0, 1, -4, 1],\n [6, -4, -3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -1, -2, 5, -4],\n [-1, -6, -6, 5, -6],\n [-3, 3, -1, 3, 5],\n [4, -5, 3, -1, -1],\n [-6, 5, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, 2, 5, -4],\n [-4, 2, -3, -1, 2],\n [4, 3, -5, 4, -6],\n [3, 4, 0, 2, 0],\n [6, 3, 0, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -6, 3, 3, 4],\n [-3, -4, -3, 2, -2],\n [5, -4, -1, 0, 3],\n [5, -4, -3, -6, 6],\n [1, -6, 3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -3, -5, 0, -2],\n [6, -6, -1, 3, 2],\n [-5, 2, -6, 6, -1],\n [0, -2, -6, -1, -2],\n [-3, 6, -3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 1, 5, -1, 6],\n [3, 4, 2, 4, -4],\n [0, 1, -5, 5, -2],\n [-6, 1, -2, -1, 5],\n [0, -3, 0, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -3, -5, -5, -4],\n [-1, 3, -5, 4, 6],\n [-5, 3, -6, -3, -4],\n [3, -4, 4, -5, 3],\n [2, 3, 5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -4, -5, 4, -5],\n [6, -5, -1, -4, 3],\n [-6, -5, -5, 1, 2],\n [4, 1, 4, -2, -3],\n [1, 3, 4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, 4, 2, -2],\n [-2, 3, -5, 5, 1],\n [-6, -6, 1, 0, -6],\n [1, -6, 5, 5, -5],\n [-3, -2, 4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -5, -1, 5, 1],\n [0, -5, -1, 5, 5],\n [0, 3, -1, -1, 4],\n [2, 6, -3, 5, -6],\n [6, 3, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 3, 6, 5, -6],\n [-4, 5, -6, 3, -3],\n [-4, -4, -3, 3, -3],\n [2, 4, 3, -1, -4],\n [-3, -3, 5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, 3, -5, -6],\n [1, -1, -6, -5, 3],\n [-2, 1, -4, 5, -4],\n [-6, -6, 1, -6, -3],\n [-3, -5, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, -6, -6, 5],\n [1, -2, -2, 5, 0],\n [-6, 2, 5, -6, -4],\n [-3, 2, 2, 3, -4],\n [-1, 5, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 0, 3, 0, -4],\n [4, 3, 0, 2, -6],\n [-5, 3, -5, -3, 5],\n [3, 3, -5, -1, -5],\n [6, -4, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -1, 6, 3, 1],\n [1, -5, -6, -4, -4],\n [4, -6, 2, -6, -5],\n [2, -6, -4, 4, 4],\n [-3, -5, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 1, 5, -6, 3],\n [-4, 3, -6, 3, 5],\n [-5, 4, 2, -5, 6],\n [0, 5, 6, -6, -2],\n [-4, -3, 2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 2, -4, -5, -6],\n [1, -2, 1, 0, -5],\n [0, 4, 2, 4, 2],\n [4, 3, -1, -2, -5],\n [-5, -4, 3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 0, 4, -3, -5],\n [-5, -2, 6, 3, 4],\n [-6, -3, -4, -4, -5],\n [1, 0, -1, -6, 3],\n [3, 4, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 4, -1, -4, 1],\n [5, 3, 3, 1, 1],\n [1, -3, -2, 0, 4],\n [2, 2, -5, 0, -5],\n [4, -3, 6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -2, 1, -3, 6],\n [-6, 3, -2, 5, -1],\n [4, -2, 1, -5, 4],\n [-4, 5, -5, 0, -6],\n [5, -6, -4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 4, 1, -6, 0],\n [6, 6, 5, 5, -6],\n [-6, -6, 4, 2, 0],\n [3, 4, 0, -5, -6],\n [-1, 4, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 6, -1, 6, 5],\n [-4, 4, 0, 5, 2],\n [6, -2, -5, -6, -6],\n [2, 2, -3, -1, -4],\n [5, -3, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -2, -2, 1, 0],\n [4, 2, 4, -5, 4],\n [1, -5, 3, -1, 0],\n [-1, -6, -6, -4, 1],\n [-2, -2, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 1, 5, 1, -6],\n [5, 0, -4, -6, 1],\n [-2, -1, 2, 1, 2],\n [6, 5, 2, 5, -6],\n [5, -3, -3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -6, -4, -3, 4],\n [4, 4, 2, -5, 6],\n [6, 5, 1, -1, 4],\n [2, -4, 6, 4, 4],\n [-2, -1, 3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, -5, -1, 2],\n [0, -3, 4, -5, 6],\n [2, -1, 1, 4, 4],\n [2, 2, -4, 0, 0],\n [-6, -1, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -5, -3, -4, 4],\n [3, -2, 6, 5, -3],\n [3, 5, 1, 3, 6],\n [2, -2, -2, 3, 2],\n [3, 1, -1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 6, -4, 2, 5],\n [5, 6, -4, 0, -2],\n [-1, -2, 6, 2, -1],\n [5, 4, -2, -1, 1],\n [-5, -2, -6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -6, -6, -6, 4],\n [-2, 1, 5, 3, 3],\n [6, 5, -1, 4, -2],\n [2, -1, -6, -1, -3],\n [2, 4, -1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 3, -6, -3, 0],\n [-1, 2, -1, -1, 1],\n [-1, 3, 0, 4, 4],\n [5, -4, 0, -4, -1],\n [6, -2, -3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -3, 5, 2, 5],\n [0, -5, 0, 2, 3],\n [-1, -6, 5, -4, 1],\n [-3, 2, 5, 2, -3],\n [-4, 4, -5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, -6, 0, -3],\n [3, -6, -4, -2, 0],\n [-5, -4, 5, -1, 6],\n [-6, -6, -1, 2, 0],\n [6, 0, -4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, 4, -4, -4],\n [5, -3, -5, -2, -4],\n [3, -2, 0, -1, -3],\n [0, -2, 0, 3, 4],\n [2, 4, 2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 2, -1, 4, 4],\n [-4, 5, 6, -3, -4],\n [4, 6, 0, 4, -5],\n [6, -1, 6, -3, -3],\n [-1, -6, 5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 3, 3, -5, 5],\n [-2, 4, -5, -6, 1],\n [-6, 2, -3, 2, 5],\n [1, 3, 6, 1, 0],\n [-1, -4, 5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -3, 2, -5, 5],\n [4, -5, -6, 0, -5],\n [1, 4, 0, 4, 2],\n [-5, 3, -2, 0, -6],\n [1, 6, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -1, 6, -4, 5],\n [1, 4, 6, -4, 6],\n [4, 6, -3, -1, 3],\n [5, -5, -3, -1, -4],\n [2, 2, 4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, -6, 6, 6],\n [0, -5, 0, 5, 4],\n [2, -3, 2, 5, 2],\n [-2, 3, -5, 5, 5],\n [3, 4, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -1, -5, -2, -3],\n [-5, -2, 2, 2, -6],\n [3, 3, -5, -6, -4],\n [-6, -2, -3, 6, 2],\n [1, 4, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 0, 6, -3, -3],\n [-4, 1, 2, -1, -4],\n [0, -2, 5, 2, 1],\n [-1, 6, -5, -2, -4],\n [-2, 4, -6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -4, -3, -6, -6],\n [6, -3, 0, -5, -3],\n [5, 1, -2, 4, -5],\n [-6, -6, 3, 2, 2],\n [5, -3, -3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 0, -6, -5, 5],\n [-1, -5, 5, 0, -3],\n [3, 5, -5, 0, -5],\n [-3, -5, 1, 5, 0],\n [0, -6, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 1, -6, 3, -6],\n [3, 2, -5, 0, 1],\n [0, 6, 3, 0, -4],\n [-3, 3, 6, -5, 3],\n [-3, 5, -3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 4, -6, -3, 6],\n [-3, -6, -4, 1, 1],\n [-2, -6, -4, -3, 0],\n [1, -6, 3, -6, -1],\n [-2, 1, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -4, -1, 0, -1],\n [6, 1, 0, 6, 0],\n [-6, -5, -2, -5, 1],\n [0, 1, 6, 3, -1],\n [0, 1, -6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -1, -3, -1, 2],\n [-5, 6, 5, 1, 3],\n [0, -4, 5, 6, -5],\n [4, -2, -3, 2, 3],\n [3, 6, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -6, -3, 2, -6],\n [0, 6, 3, -3, -2],\n [-2, 6, -5, -5, -1],\n [-4, -5, 1, -5, -4],\n [2, -5, -3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -5, -3, 6, -5],\n [-2, -3, 5, 5, 5],\n [2, -2, -1, -2, -3],\n [2, 2, -3, 5, 2],\n [1, 6, -3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, -3, -3, -2],\n [1, 2, 4, 1, -2],\n [-5, 2, -3, -6, 2],\n [1, -1, 3, 6, 3],\n [-2, -5, 3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -1, 0, 0, -3],\n [-2, 2, -3, 5, 6],\n [3, 1, 4, 2, 5],\n [-1, 5, 0, 6, 3],\n [-5, 4, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, 5, -4, 1],\n [2, -1, -3, -4, 6],\n [3, -3, -1, -6, -3],\n [3, -2, 4, 4, 3],\n [3, 6, 4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, 4, -5, -6],\n [-6, -6, 1, 5, -3],\n [6, 6, -6, 3, -6],\n [2, 4, -4, 5, 6],\n [-1, 0, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, 4, -6, 2],\n [1, -3, 4, 5, -6],\n [6, -2, 5, 1, -5],\n [-5, 3, -4, 4, -5],\n [2, 4, -5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 3, -5, 2, 2],\n [-2, 0, -4, -4, -4],\n [-5, -4, -6, -3, 0],\n [0, 1, -2, -1, -1],\n [-3, -3, 6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -3, -1, 3, -1],\n [-6, -4, 2, -1, 0],\n [-4, 5, 3, -3, 2],\n [3, 0, -3, 5, -5],\n [3, 2, 6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 4, -1, 0, -3],\n [2, -6, 0, 3, -3],\n [2, 2, -4, 2, 2],\n [6, -3, -5, 4, -4],\n [-4, 0, -2, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 3, 4, -6, 2],\n [4, -3, 4, -5, 2],\n [-6, 5, -2, 3, 6],\n [4, 4, -5, 5, -5],\n [-2, 0, -4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 0, -6, -6, -4],\n [5, 6, -2, 6, 2],\n [-2, 4, -3, -2, 1],\n [0, 6, 2, 5, -2],\n [2, -3, -5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 3, 4, 2, 1],\n [-2, -2, 1, 1, 1],\n [-6, -5, 0, -5, 2],\n [1, 1, -2, -1, 1],\n [5, 0, -3, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 0, 4, -4, 2],\n [-2, -2, 2, 3, 1],\n [-4, -3, -2, -1, 0],\n [-2, 3, -6, 4, 2],\n [0, 5, 5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -4, -4, -1, 6],\n [3, 1, -5, 3, 1],\n [5, 4, 5, 1, 3],\n [5, -1, -2, -1, -3],\n [4, 5, 5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 5, 5, 3, -6],\n [2, 2, 3, -1, 6],\n [-1, -1, -2, -4, -2],\n [-5, 4, -2, 0, 4],\n [0, 5, -6, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -6, -4, 4, 3],\n [0, -2, 4, 0, -4],\n [-6, -1, 5, 5, -5],\n [3, -2, 0, 1, -1],\n [-6, 4, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -4, 6, 2, 2],\n [-5, -5, 2, -1, 4],\n [4, -2, 2, 3, -2],\n [1, -1, 2, 0, 0],\n [4, -2, -1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -1, -1, -3, -6],\n [-1, 0, -6, -3, 6],\n [-1, 2, 0, 3, 3],\n [3, -4, 2, -1, 5],\n [-5, -2, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -3, -1, -1, 2],\n [5, 4, -4, 1, 5],\n [1, -6, -1, 1, -5],\n [-4, -1, -1, 0, -2],\n [2, -4, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -1, 6, -6, -3],\n [-5, -1, -3, -3, 6],\n [5, 0, 6, 5, 5],\n [6, -5, 4, 0, 5],\n [-1, -4, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, -2, -4, 4],\n [2, 1, -1, 2, -4],\n [-4, -6, 0, 3, -4],\n [6, -3, -6, 3, -5],\n [-2, 6, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, 4, 3, 2],\n [3, -2, -6, 1, 4],\n [5, -4, -5, -3, -5],\n [1, -2, 6, -3, 0],\n [4, -2, -1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 4, 3, -4, -4],\n [-2, 2, -3, -4, -6],\n [0, -4, 1, -5, 5],\n [-2, 4, 4, -1, -4],\n [2, 5, 6, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, -5, -3, 2],\n [1, 4, 4, 4, 0],\n [6, -4, -3, 4, 2],\n [-5, -6, -6, 1, -2],\n [5, -2, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 4, -6, 3, 2],\n [3, 2, 2, 4, 3],\n [6, -3, -6, 5, -6],\n [-2, -4, -2, -6, -6],\n [2, 0, 3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 6, 0, 2, -1],\n [1, 6, 3, 0, -6],\n [-5, 6, 6, 0, -3],\n [3, -3, 6, 1, -4],\n [-6, 0, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 5, 4, -6, 1],\n [0, 3, -6, 0, -6],\n [5, 3, 6, -2, 1],\n [-4, 6, 1, -1, -6],\n [4, 5, -1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 1, 5, 4, 6],\n [-3, -1, -6, 5, 6],\n [3, 5, 4, 5, -3],\n [3, 0, 4, -4, -5],\n [3, 0, 3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 6, -5, -6, 3],\n [1, 4, 3, -2, -3],\n [5, 6, -3, -6, 3],\n [-2, -5, -1, 3, -6],\n [4, -2, -6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 6, -6, -3, -2],\n [5, -3, 5, -2, -5],\n [4, 4, -1, 1, 4],\n [-1, 3, 0, 5, -1],\n [3, 4, 5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, -3, -4, -1],\n [-2, -4, 1, -6, -5],\n [0, -3, -6, -2, -4],\n [6, 0, -5, 2, 0],\n [3, 3, -6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -4, 6, 0, -4],\n [4, -3, -4, 6, -5],\n [-1, 6, -3, -5, 1],\n [3, 6, 6, -6, -1],\n [-2, 0, -5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, 3, -1, -3],\n [-2, -4, 2, -6, -2],\n [5, -3, -2, -6, 5],\n [-1, -6, 4, 2, 5],\n [-6, 5, 5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -2, 3, 6, -5],\n [2, 1, -5, -4, -3],\n [-3, 1, -1, 6, -4],\n [-3, -1, -1, 3, 0],\n [-2, 4, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 0, -4, -5, 1],\n [-6, -5, -1, 5, 0],\n [-4, 4, -3, 2, 2],\n [-4, 1, -1, 6, 6],\n [-6, 3, 6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, -6, 0, 2],\n [6, -5, -1, -4, 4],\n [6, -2, -6, 5, 2],\n [-6, 0, 1, -4, 1],\n [-2, -1, 5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -1, -2, 5, 6],\n [0, -3, 3, 2, -6],\n [4, 4, 5, 3, 4],\n [-2, 2, -5, -2, 1],\n [2, -2, 5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -5, -3, 5, 2],\n [-2, -5, -2, 5, 1],\n [5, 5, 2, -4, 5],\n [5, 1, -6, 5, 5],\n [4, 0, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 6, 2, -1, 0],\n [-2, -5, -5, 3, 1],\n [4, 3, 2, -1, -5],\n [4, -1, 0, 1, -1],\n [-5, 3, 3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -5, 0, -3, 0],\n [-4, 4, -5, 4, 2],\n [-6, 3, -2, 4, -4],\n [-3, 4, 2, 4, -6],\n [-6, -2, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, -6, 0, 3],\n [-2, -1, 0, 5, -1],\n [2, 0, 0, -4, -6],\n [6, 3, 3, 2, -4],\n [-5, -5, -5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, -4, -1, 1],\n [-2, -3, 6, 3, 3],\n [4, -1, -1, 4, -4],\n [0, 1, -4, -2, 0],\n [3, 4, 0, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -3, 6, -3, -5],\n [1, 6, -3, 6, 6],\n [-1, 6, -2, 4, -6],\n [-5, 0, 4, 3, 1],\n [-3, -5, 6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 5, -4, -2, 5],\n [-5, -5, -1, -2, 2],\n [6, 4, 1, -5, 2],\n [-2, 2, -1, -4, 3],\n [-6, -3, -5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -6, 0, 2, 2],\n [0, 6, 3, -3, 1],\n [6, 2, 0, 1, -4],\n [2, 6, -3, -1, -4],\n [-1, -2, 5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 2, 5, 2, -4],\n [3, 2, 2, -2, 0],\n [-1, -1, -2, 4, -5],\n [0, 5, 2, -6, -6],\n [2, 6, 1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -5, -4, -1, 1],\n [0, 4, 6, -3, 2],\n [1, -5, 2, 1, -2],\n [-6, -6, 5, -1, -4],\n [-1, 5, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 0, -5, 2, -6],\n [6, 1, 2, -4, 3],\n [5, 4, 0, -6, 2],\n [-3, 5, -2, 6, -5],\n [-6, 4, 3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 0, -2, 6, -3],\n [-1, -2, 4, -6, 3],\n [1, -3, 6, -2, 5],\n [6, -2, 4, -6, -4],\n [4, 6, -3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -4, 4, 5, -4],\n [-3, -4, 5, -3, -4],\n [-6, 2, 6, 5, -1],\n [-1, 4, -5, -1, 3],\n [2, 6, 1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -2, 2, -1, -3],\n [-6, -3, 3, -4, -1],\n [-1, 0, 1, 3, 4],\n [6, -4, 3, -2, -2],\n [-3, -6, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -1, 3, 2, 3],\n [5, -6, -2, -4, -5],\n [-1, 4, 2, -1, 2],\n [-2, 1, 5, 2, -2],\n [5, 4, -5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -3, 1, 6, 6],\n [-1, -2, -6, -4, -5],\n [0, -5, 6, -1, 3],\n [0, -1, 5, -4, 1],\n [-4, -5, -4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 1, 3, -1, -1],\n [3, -3, 4, 2, -5],\n [-1, -3, -1, -3, 1],\n [-6, -6, 2, 6, -2],\n [5, -5, -6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 4, 6, 6, -3],\n [1, 3, -4, 1, 4],\n [-6, 5, 3, 4, 5],\n [2, 6, 3, -2, -5],\n [-2, 2, -5, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 0, -5, -3, 3],\n [0, -3, 3, 1, -2],\n [0, 0, 6, -4, 2],\n [6, -1, -6, -2, -2],\n [1, -2, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -1, 2, -4, -6],\n [1, -6, -3, -2, -3],\n [-5, -4, 0, 2, -3],\n [-5, -1, -6, -6, 1],\n [5, 0, 4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -5, -6, -6, -5],\n [2, -4, 4, 2, -2],\n [4, -4, -4, 1, -3],\n [0, 4, -1, 1, 6],\n [4, 5, 1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 0, 6, 6, 1],\n [-3, 0, 1, -5, 2],\n [5, -6, 0, 1, -1],\n [-1, -4, -3, -2, -3],\n [-2, 1, -5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 3, -6, -1, -3],\n [1, -3, 4, 4, -1],\n [-6, 0, 4, 2, -4],\n [1, -5, 4, -2, -6],\n [-6, 0, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 6, -1, 4, 5],\n [-5, 0, 0, 1, 6],\n [3, 4, -4, -5, 1],\n [5, -1, 5, 6, -5],\n [-4, 1, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -3, 5, -4, 6],\n [4, -4, 0, -4, 2],\n [1, -3, -6, 2, 2],\n [-3, 1, -6, 3, 2],\n [6, 4, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 2, 2, -2, -1],\n [-5, -5, 6, 5, -1],\n [-6, 1, 6, -5, 4],\n [-4, -1, -4, -3, -6],\n [-3, -1, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, 6, -2, -1],\n [2, 2, 0, 6, 5],\n [4, 2, 2, -2, -6],\n [2, 1, 4, -4, -4],\n [3, -5, -6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -6, -2, 6, 0],\n [6, -1, -1, 0, -6],\n [-1, -6, -4, 5, 4],\n [-6, 3, 0, -4, 6],\n [-4, 2, -4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -1, 1, 1, 4],\n [1, 6, -3, 4, 4],\n [5, 3, -1, 0, -6],\n [-4, -6, 3, 0, 2],\n [-5, -6, 6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -1, 1, 2, -3],\n [-3, 6, -1, -1, 6],\n [-1, 6, 0, 1, 4],\n [-6, 6, 6, 1, 2],\n [2, 1, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -2, 0, 3, 5],\n [3, -3, 3, -6, 0],\n [2, 5, 0, -3, -2],\n [-4, -1, 0, -5, -6],\n [-2, 4, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, 4, 2, -3],\n [6, -5, -5, 2, -6],\n [-5, -2, 3, -1, 4],\n [2, -3, -6, 5, 1],\n [6, -3, 5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -2, -6, 6, 4],\n [0, -2, -3, -4, 6],\n [3, 2, -4, -1, 0],\n [1, -4, -6, 2, 4],\n [1, 4, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 2, -5, -1, -2],\n [3, -6, 0, 3, -5],\n [2, -6, -3, -1, 1],\n [6, 2, 5, -4, 4],\n [-1, -3, -2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 5, 1, -6, 2],\n [-1, -6, 6, -3, 2],\n [-4, -3, 4, -4, 6],\n [3, -5, -3, -3, -2],\n [6, 2, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 2, -3, 1, 6],\n [3, 6, -6, -5, -1],\n [4, -6, 4, 6, -6],\n [-5, 1, -4, 2, -6],\n [-1, 2, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 5, -1, -3, 6],\n [6, -6, -3, 2, -4],\n [5, 2, -6, -3, -3],\n [-4, -3, 5, 0, -5],\n [1, 1, -6, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -2, -2, -1, -1],\n [-2, 2, 2, -5, 6],\n [-6, 2, -6, 6, -3],\n [-3, -5, 4, -4, 6],\n [-1, 2, -6, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -3, 2, 3, -2],\n [-4, -5, -6, -4, -3],\n [4, 4, -4, 1, -6],\n [1, 3, 4, -4, 4],\n [1, -4, 5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -3, 6, 3, 0],\n [3, 2, -6, -5, -5],\n [-6, 2, 1, 5, -2],\n [5, -3, -1, -2, 0],\n [-3, 2, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -4, 2, -2, 2],\n [6, 5, 2, -3, 6],\n [-2, -4, -3, 6, 4],\n [4, -3, -5, 1, 5],\n [6, -2, 0, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 1, 3, -1, -5],\n [5, 0, -2, 1, -4],\n [5, -5, -6, -4, -5],\n [0, 1, 5, 0, 2],\n [-6, -5, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 1, 5, 4, 0],\n [-1, 0, -2, -6, -5],\n [3, -2, 2, 2, -4],\n [1, -2, 2, 0, 4],\n [-4, 1, -5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -5, -5, -5, -6],\n [-3, -5, -4, -6, 4],\n [-2, 2, -3, -6, -6],\n [-4, -5, -1, 1, 5],\n [6, 2, 2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 6, -1, 2, -5],\n [-2, -4, -1, 6, 4],\n [2, -4, 1, 2, -3],\n [-3, -3, -6, -6, -1],\n [3, -6, -1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -3, -5, 1, -1],\n [-1, 1, 2, -6, 3],\n [6, 3, 5, -1, -3],\n [2, 4, -5, -5, 5],\n [-6, 0, 3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 4, -3, -1, 0],\n [5, 5, -1, 0, 6],\n [3, 1, 0, 0, 1],\n [-2, -4, -2, 5, -2],\n [-2, -2, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 4, 3, -1, -1],\n [3, -2, -3, 4, 6],\n [-3, 0, -6, 6, 1],\n [-3, 0, -4, -4, -3],\n [-1, -1, -3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 0, -6, 2, 0],\n [-3, -2, 3, -2, -3],\n [-3, 5, 2, -6, -6],\n [-6, -3, 3, -3, 2],\n [0, 4, -3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -5, 5, 3, -3],\n [-4, -1, 6, -2, 5],\n [-2, -2, 0, 1, 1],\n [1, -1, 5, 1, -3],\n [-5, 3, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -1, 3, -1, -3],\n [3, -1, 3, -3, -3],\n [-5, -2, 5, -6, 5],\n [-6, 5, -6, -4, -5],\n [-5, -3, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 2, -3, 4, -4],\n [2, 5, -5, 2, 0],\n [4, 2, -3, -3, 5],\n [5, -4, 2, 4, -5],\n [5, -3, 3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 6, -2, -1, 2],\n [-1, 2, -2, 0, -5],\n [-3, 5, -5, -2, -3],\n [-2, 2, 5, -2, -6],\n [0, -2, -5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -4, 5, -6, 6],\n [0, -6, 0, 2, 5],\n [-6, 6, 5, 3, 1],\n [0, 1, -5, 5, 1],\n [4, 4, 3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 0, -6, -4, 4],\n [3, 1, 2, 4, 4],\n [4, 6, 2, 5, 5],\n [3, -4, 5, 4, 0],\n [0, 3, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -5, 5, -1, 2],\n [-6, 0, 6, -4, 4],\n [6, -4, -1, 1, -4],\n [0, -6, -1, 1, -3],\n [4, 5, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -5, -1, 5, -5],\n [6, 6, 5, -5, -2],\n [-2, 4, 4, 0, 6],\n [-6, -4, 4, -6, 4],\n [0, -5, -5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 6, -3, 1, -1],\n [-6, 0, -3, -1, 6],\n [0, -5, -4, -4, -2],\n [5, 0, -2, -5, 5],\n [-6, 2, 2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 4, 5, -4, -1],\n [6, -2, 4, -2, 1],\n [1, 2, 4, -4, -1],\n [-6, -3, 6, -3, 6],\n [-5, -2, 5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 4, 2, 4, 5],\n [-6, -5, -6, 4, -1],\n [2, 0, 0, 6, -1],\n [5, 4, 3, 6, -6],\n [2, 5, 3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -3, 5, 5, 0],\n [6, -2, -2, -2, 1],\n [1, -1, -5, -6, -4],\n [6, -3, 3, -6, 2],\n [4, -3, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -6, -6, 4, -4],\n [6, 5, -5, 5, 5],\n [6, 4, 1, -6, 3],\n [-2, 0, 2, 6, 6],\n [-1, 0, 5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -6, -1, -3, 0],\n [-6, 3, -6, 6, -5],\n [1, 3, 2, 1, 3],\n [5, 3, -3, -5, -5],\n [6, 2, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -5, 3, -5, 3],\n [2, 3, 5, -5, 1],\n [3, 1, -4, 1, -3],\n [1, 3, 3, -5, -1],\n [6, -6, -1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 3, -3, 3, 4],\n [6, 5, -5, -3, -1],\n [-4, -4, -6, 0, -3],\n [-1, 5, -6, -6, -5],\n [-3, -5, 0, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, -2, 6, -2],\n [5, -3, 2, -5, -6],\n [6, 1, 4, 5, 5],\n [1, 4, 3, 3, 5],\n [-1, -3, 3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -4, -3, -6, -1],\n [3, 4, -5, -4, -3],\n [5, 0, 0, 6, 6],\n [-4, -5, -2, -5, -2],\n [-1, 6, -3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -3, -6, 4, 1],\n [5, -1, 1, 1, 5],\n [0, -6, -1, 0, 6],\n [4, -6, -6, 1, -4],\n [-2, 0, 4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 4, -5, 2, 5],\n [0, 6, -4, -6, 2],\n [2, -1, 0, 0, -4],\n [3, 4, -3, -1, 2],\n [-1, 4, 3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -5, -4, 2, -4],\n [0, 1, 3, -5, -3],\n [1, 4, -6, -5, -3],\n [6, 5, -3, 5, 1],\n [3, -2, -2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 5, -2, 2, -3],\n [6, -6, 1, -6, -2],\n [6, -1, -1, 3, -5],\n [-3, 5, -4, 4, 5],\n [3, 0, 3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -1, -1, -5, 5],\n [1, 1, 1, 1, -1],\n [-4, 5, -6, 2, -3],\n [5, -3, 4, -1, 6],\n [-3, -1, -3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 5, -1, -2, 4],\n [-6, -2, 5, -6, -6],\n [3, 4, -2, -3, 6],\n [0, 4, 4, -6, -1],\n [-6, 1, 6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 0, 1, 4, 0],\n [5, 4, 6, -4, 3],\n [-3, 3, 2, -2, 6],\n [-3, 4, 2, -4, 3],\n [-3, 3, -6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 6, 6, 0, 6],\n [-5, 1, 1, 1, 1],\n [-1, 3, -4, -3, -1],\n [-2, 3, -3, 4, -2],\n [6, -1, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 0, 0, -4, -4],\n [-4, 3, 1, 1, 4],\n [-1, 1, -2, -5, -4],\n [4, -2, -6, -3, 1],\n [-3, 2, 6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -6, 3, -5, -6],\n [-3, -2, 2, -5, -4],\n [5, 2, 2, 5, 6],\n [0, 3, -4, 5, 3],\n [3, -2, 6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -4, 6, -4, 5],\n [0, 4, -1, -5, -6],\n [-6, 3, 6, 1, -2],\n [5, -5, 1, 3, -6],\n [-6, 0, -5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -3, 4, -1, -1],\n [-5, -6, 2, -4, 4],\n [2, -3, -5, 3, 4],\n [-5, 0, -4, 2, -5],\n [-5, -5, 5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -3, 3, -3, 4],\n [5, 6, -5, -5, -4],\n [6, -1, -4, 6, 3],\n [1, -6, 6, -1, -3],\n [-5, 1, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 6, 2, 1, 6],\n [3, -2, -3, 0, 5],\n [-6, 5, 0, 2, -2],\n [-3, -1, -4, 5, -1],\n [6, 6, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 5, 3, -5, -4],\n [-6, 2, -1, -3, 1],\n [-5, -1, -6, -1, -4],\n [6, 5, 1, -1, -4],\n [1, 0, -1, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -2, -1, -6, 1],\n [-5, 6, -1, 4, -6],\n [2, -6, 0, 0, 1],\n [0, 3, -3, -5, 3],\n [-5, 6, -3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, -2, -2, 2],\n [1, -3, -6, 1, 1],\n [-6, -2, 4, 6, -5],\n [1, 2, 0, 5, -5],\n [-6, 3, 5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -4, -4, 2, -4],\n [-3, 1, -2, 3, 3],\n [1, -2, 1, -5, 0],\n [-6, -1, -6, -5, 4],\n [0, 2, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 2, 2, -2, 5],\n [5, -5, -2, -1, 1],\n [4, -5, 2, 2, -1],\n [-3, 4, -2, 2, -2],\n [2, 0, -3, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 5, -1, 0, -1],\n [5, 1, -4, -6, 4],\n [-1, 6, -2, 3, 3],\n [-5, 5, -6, 6, -2],\n [-4, -5, 1, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 5, 2, 3, 0],\n [-6, 1, 5, 4, -2],\n [2, -3, 6, 3, 2],\n [1, -3, -3, -5, 1],\n [-4, -5, -3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -1, 5, -3, -4],\n [4, 0, 2, 5, 2],\n [5, 3, -4, -5, -5],\n [-6, -1, 4, 2, -4],\n [6, 4, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -6, -3, 3, -6],\n [-2, 5, -6, -4, 5],\n [-4, 6, 4, 1, -6],\n [-2, 0, -5, 3, 4],\n [-1, 3, -5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 1, 1, 3, 3],\n [5, -3, -2, 5, -5],\n [4, 5, 1, -6, 5],\n [6, 0, 6, 6, 3],\n [-6, 5, 3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -1, -5, -5, 3],\n [-5, 6, 1, 6, 6],\n [-3, -5, -3, 5, 2],\n [2, -5, -6, -3, -4],\n [3, -5, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 0, 0, 1, -6],\n [-3, 3, -3, 0, 1],\n [-6, 2, 1, -2, -5],\n [-1, 6, -2, 1, -1],\n [-1, 6, -5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 1, -6, -1, -4],\n [-2, 4, 0, 1, -1],\n [3, -1, -1, -3, -2],\n [6, -5, -1, -6, 4],\n [2, 3, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -5, 4, 4, -4],\n [5, -4, -5, 5, 6],\n [-5, 6, -6, -4, -2],\n [-3, -2, -6, -5, 1],\n [0, -1, 6, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 0, 5, 0, 0],\n [6, -5, -2, -1, 5],\n [-3, -5, 2, 3, -4],\n [-4, -3, -3, 2, 4],\n [0, 0, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, -6, 0, -5],\n [2, -1, 6, -6, 1],\n [1, -3, -6, 4, 2],\n [-3, -5, -5, 1, 2],\n [-5, 3, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 1, -1, 6, -1],\n [-3, 0, 2, -2, 2],\n [-3, -3, 0, -6, 3],\n [-2, 4, -6, 2, 2],\n [-2, 0, 2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 1, -6, -1, -6],\n [6, -6, 5, 4, 1],\n [1, 1, 5, 2, -5],\n [2, -3, 5, -3, 5],\n [4, 0, 1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 1, 0, -6, -1],\n [3, -6, 4, 2, 1],\n [-5, 2, 6, -5, 0],\n [-1, -2, 5, 1, 5],\n [2, 5, -5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -3, 3, 0, 2],\n [-6, 3, -2, 1, 0],\n [0, -5, 3, 4, 2],\n [3, 4, 2, -5, 2],\n [-6, -5, 3, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 1, 1, -5, -4],\n [-3, 0, -1, 4, 0],\n [5, 1, -2, -1, -3],\n [-5, 4, 1, 0, 0],\n [6, 3, -5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -3, -3, -5, 2],\n [-2, -6, 5, 4, 0],\n [-6, -6, -2, 1, -4],\n [-6, -2, -4, -2, 3],\n [0, -2, 5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -4, -3, 2, 5],\n [3, 3, -3, -4, -2],\n [-2, -3, -3, -5, 1],\n [-3, -1, 0, 2, -6],\n [-3, 3, 2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -6, -2, 5, 0],\n [4, 3, -3, 6, 2],\n [2, 3, -4, 2, -2],\n [-1, 5, 3, 2, 0],\n [-5, -3, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -1, 0, 0, -3],\n [3, -1, -4, 5, 5],\n [2, 0, 4, -1, -5],\n [3, 1, -4, -6, 0],\n [-3, -4, 6, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -4, 4, 5, -6],\n [1, 2, -4, 2, 6],\n [4, 2, 6, 5, -6],\n [4, -4, 2, 6, 5],\n [-1, -1, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, 1, -4, -1],\n [4, 4, -6, 3, -2],\n [-6, 3, 3, -5, -2],\n [-6, 4, -6, 0, 2],\n [4, 3, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 6, 4, 3, -6],\n [-3, -3, -2, 4, 1],\n [-5, 2, -1, -4, 5],\n [-3, 4, 1, 5, -3],\n [-2, -4, -3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 6, -3, 1, 5],\n [4, 0, 6, -2, -2],\n [2, -5, 3, 1, -4],\n [5, 1, -6, -4, 5],\n [-1, 1, 3, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -2, 1, 1, 1],\n [-5, -2, -4, -1, 5],\n [5, -4, -4, -1, 3],\n [0, 5, 1, 3, 3],\n [3, -3, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -5, -2, 5, -1],\n [-3, 4, -5, -5, -3],\n [3, -6, 4, 1, 3],\n [3, -5, -4, 4, -4],\n [-2, -3, 4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -5, -5, 0, 0],\n [-5, -4, 2, 6, -3],\n [4, 2, 5, -2, 5],\n [-2, -4, 5, 0, 5],\n [2, -1, -5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 5, 5, -3, -1],\n [0, -5, 3, 5, -1],\n [2, -3, 4, 5, 3],\n [-4, 6, -5, 3, -1],\n [-2, -3, -1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -5, -1, 0, -2],\n [0, 6, 5, -4, -1],\n [-1, 4, 1, 4, 5],\n [-5, 3, 2, 6, 6],\n [-1, -4, 3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -4, -6, 4, 5],\n [-5, 3, 0, 2, -4],\n [6, 3, -2, 3, 5],\n [-1, 6, -4, 3, -5],\n [2, 5, -3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 4, -4, -4, 1],\n [0, 0, -2, -2, -1],\n [4, -5, -5, -5, -6],\n [-5, -2, -1, 0, -4],\n [1, 1, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -1, -3, -4, 6],\n [5, 0, 4, -6, -4],\n [0, -6, -6, -4, -2],\n [-5, 5, -6, 3, -5],\n [-4, -4, 2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, -6, -1, 5],\n [-3, 0, 0, -1, -3],\n [5, 5, 3, -2, -6],\n [-1, 5, 0, 1, -3],\n [6, -5, -2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 2, -2, -3, -4],\n [0, -3, 3, 3, -1],\n [6, -6, -4, -3, 1],\n [-6, -3, -3, 5, 5],\n [-3, 1, -3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, 5, 4, 4],\n [-5, -5, -4, 2, 0],\n [3, -1, 3, 6, -1],\n [3, -5, -3, -6, -3],\n [-2, -2, 4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 6, 3, 1, 6],\n [-1, 0, -5, 1, 3],\n [-6, 5, 6, -4, 5],\n [4, 5, 1, -1, 0],\n [0, -4, -6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 3, 6, 2, 1],\n [4, 5, -4, -5, 0],\n [6, -5, 0, 2, -6],\n [6, -4, 6, 3, -3],\n [-4, 6, 4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 1, 6, 3, -6],\n [-6, -1, -3, -5, 1],\n [-4, -5, 5, -2, -2],\n [5, 1, 1, 5, 3],\n [0, -6, 6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 6, 6, 4, 1],\n [-6, 2, -3, 0, -4],\n [1, -3, -3, -5, -6],\n [-2, 1, -4, -1, -4],\n [-5, 1, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 1, -4, -1, -2],\n [-6, 6, -6, 1, 4],\n [-5, 5, 5, 5, 0],\n [1, -3, 5, 4, 5],\n [3, 6, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -1, 0, -5, -4],\n [-1, 3, -2, 3, 1],\n [4, -4, -2, 5, -4],\n [2, 2, 3, 2, 0],\n [1, -5, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 5, -5, 4, -1],\n [2, 5, 0, 4, -5],\n [0, 6, 2, 0, -3],\n [0, -5, -3, 0, 1],\n [-2, 0, -3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 6, -2, 4, 0],\n [4, 3, 4, -1, 6],\n [6, 5, -5, 6, -1],\n [1, 0, 0, 1, -2],\n [1, -1, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -5, -2, -4, -3],\n [6, -1, 3, 1, -2],\n [-1, 4, -6, 0, 2],\n [-4, 0, -6, -1, -6],\n [-6, 2, 6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 4, 0, -2, -4],\n [-5, -3, -6, 1, 1],\n [2, -1, -3, 1, -5],\n [-3, -5, -1, 4, 2],\n [4, 4, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 0, -4, -4, 5],\n [4, -6, -1, 3, -2],\n [6, -2, -6, -6, -3],\n [5, -2, -2, -4, -5],\n [6, 6, 2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 3, 2, 5, 5],\n [2, 6, 4, 0, 6],\n [3, -3, -3, 0, -1],\n [5, -4, -2, -2, -5],\n [0, 0, 6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 2, 1, 6, -3],\n [-2, 1, 1, -2, 3],\n [2, 2, -1, -3, -2],\n [-3, -2, 1, -5, -4],\n [-5, 3, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 5, 0, 2, -6],\n [5, -4, -5, 1, 0],\n [-4, 0, 0, 5, 0],\n [-3, 3, 2, -3, 0],\n [4, -5, -6, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -1, -5, -5, 2],\n [-1, 6, -1, 6, -2],\n [4, -4, 3, 1, -2],\n [6, -6, 5, -6, 5],\n [-2, -2, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -2, 1, 6, 1],\n [6, 3, 5, -3, 0],\n [-1, 6, 2, 2, 0],\n [3, -4, 2, -2, -1],\n [5, 5, -5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 0, 4, 2, 2],\n [-4, -4, 6, 1, 0],\n [-5, -3, 3, 4, 6],\n [-5, 6, 6, -6, 4],\n [5, 4, 5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -3, -6, 5, 3],\n [6, 2, -4, 0, -2],\n [2, 4, 4, 5, -5],\n [5, 4, 5, -2, 0],\n [-5, -4, 3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, 4, -5, 0],\n [3, 5, 3, -5, 5],\n [-4, -3, 1, -3, -2],\n [4, -5, 2, -1, -5],\n [-5, -4, 3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, -6, -3, 2],\n [1, -2, -1, -5, -5],\n [1, -2, -6, -5, -6],\n [5, -2, -6, 2, 0],\n [4, 3, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 6, -4, -6, 0],\n [-1, 0, 1, 4, 0],\n [-2, -5, -5, 4, 5],\n [5, 5, -3, 3, 4],\n [-2, 3, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 0, -5, -6, 6],\n [-6, 3, -6, -6, 6],\n [2, -5, 4, -3, -3],\n [-1, 4, 5, 6, 0],\n [4, -1, -3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -6, 2, 6, 3],\n [-5, 3, 3, 6, -4],\n [5, -2, 4, 0, -5],\n [6, 4, -3, 2, 2],\n [4, 2, -6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 0, -2, 4, 2],\n [5, -5, 3, 2, -6],\n [4, 1, 2, -6, 6],\n [-2, 3, -6, 2, -6],\n [5, 0, -6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -3, -3, 1, -1],\n [4, 3, -6, -6, -5],\n [3, -6, -3, -4, -4],\n [6, -4, 1, 3, 4],\n [-2, 0, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 5, -3, -6, 2],\n [-2, 5, 4, -5, -6],\n [3, 0, 5, 6, -1],\n [5, 4, -3, 4, 3],\n [-6, 1, 1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -2, 0, 5, -1],\n [0, -3, -3, 2, 5],\n [6, -4, 0, 5, 4],\n [2, -2, 6, -5, -2],\n [5, 6, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -3, 5, 3, 6],\n [0, 5, 6, -1, -2],\n [3, -1, -6, -5, 6],\n [-5, -6, 2, 5, -3],\n [2, 3, 0, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -3, 5, 0, -5],\n [-3, 3, -2, -3, -3],\n [-6, -4, -3, 6, -4],\n [2, -4, 1, -4, 2],\n [-1, -5, 2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -6, 1, -5, -3],\n [1, 1, -3, -5, -4],\n [-1, 3, -2, 1, -2],\n [3, 2, 1, -2, 3],\n [-5, -1, -5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -3, -6, 6, -2],\n [-2, 2, -4, -4, -4],\n [-2, -3, 6, 2, 0],\n [5, 3, 4, -3, -2],\n [-5, -5, 6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -6, -3, -3, -6],\n [-1, -1, 5, -4, 2],\n [-4, -3, -6, -1, -2],\n [-2, 3, -4, -5, 5],\n [-4, 5, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, -2, -3, -5],\n [4, -1, 5, -4, -1],\n [2, 1, -2, -1, 5],\n [-1, -1, -5, -5, 2],\n [6, -5, 5, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -1, -6, 0, -6],\n [-1, 6, 0, 6, -5],\n [-2, -3, 3, 0, 4],\n [4, 2, -2, 6, 6],\n [3, -4, 3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, -2, 4, 1],\n [4, 5, -1, 3, 6],\n [6, -6, 0, 4, -2],\n [-5, -6, 5, -3, 2],\n [-6, 6, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -1, -3, -2, -5],\n [-5, -2, 4, 3, -6],\n [4, 1, 4, 1, -1],\n [-3, 1, -6, -6, -5],\n [2, -5, -5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 5, 6, 6, -1],\n [5, 0, -3, -6, 2],\n [-2, -4, 4, 6, 2],\n [-1, 4, -3, 5, -1],\n [1, 3, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 5, -2, 5, 4],\n [2, 6, -6, 3, -1],\n [-3, 6, -2, -3, 6],\n [-6, 1, 0, 3, 5],\n [4, -3, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -4, 2, -5, 4],\n [-1, -4, 0, -4, -3],\n [-3, 5, -6, -6, -5],\n [5, -3, 2, 6, 0],\n [-2, -2, 2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, -6, -5, -4],\n [5, 3, 3, 1, 2],\n [-2, -2, 6, -1, -3],\n [-1, 0, 6, 1, 6],\n [-6, 3, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -1, -6, 5, -1],\n [-3, -1, 3, -5, 4],\n [-1, -2, -5, 3, 1],\n [2, 6, 0, -1, -2],\n [6, -6, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 6, -2, 3, 0],\n [-6, 2, 2, 5, -3],\n [-4, 2, 2, 4, -3],\n [-2, 0, -1, 0, 2],\n [-6, 4, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 5, 2, -4, 2],\n [6, -2, -5, 3, -3],\n [-2, -2, 2, 6, 4],\n [3, 3, -2, 2, -3],\n [-3, -6, 1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 6, 0, -1, 5],\n [5, -3, 1, 6, 2],\n [6, 5, 6, -4, -3],\n [-6, 3, -4, 0, 0],\n [-6, 0, 5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -5, 3, 4, 2],\n [2, -2, 4, 4, 2],\n [-1, 0, 1, -4, 3],\n [-5, 1, 0, 5, 2],\n [-5, -1, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 1, 5, 3, 2],\n [-2, -3, -3, 4, -1],\n [-6, 2, -2, 5, -3],\n [5, 0, 0, -5, 4],\n [1, 5, -2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 2, -5, 3, -2],\n [3, -1, -2, -4, -6],\n [4, -1, -2, -6, -6],\n [-4, -2, 4, -4, 5],\n [6, -1, -6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 6, 1, -5, 5],\n [-2, 3, -3, -4, 4],\n [4, -4, 6, 2, -1],\n [1, -1, -1, -2, -6],\n [-2, 6, 5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -1, -6, -6, -2],\n [-6, -4, -6, 2, 5],\n [6, 3, -3, 2, -6],\n [1, -2, -2, 0, 3],\n [2, 1, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -1, 1, 1, -5],\n [6, 5, -1, -4, 0],\n [-1, -2, 5, -1, 1],\n [-6, -1, 6, 5, -2],\n [6, -5, -1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -2, 3, 6, -3],\n [-6, 0, -3, -1, -6],\n [-3, 3, 1, -2, 6],\n [5, -2, -5, -5, -3],\n [-1, 2, 1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 4, 6, 1, 6],\n [5, 3, -3, -1, 3],\n [-2, -1, -3, -1, 3],\n [6, 1, 0, 1, 0],\n [-2, 2, -5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -5, -2, -4, 3],\n [3, -1, 1, 6, 4],\n [-3, 1, 4, -3, -4],\n [5, 1, 6, -6, 0],\n [5, -5, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 5, -5, -2, 3],\n [-1, 6, -3, 3, -2],\n [-4, -4, 5, -5, 5],\n [6, 2, 3, -2, -3],\n [-1, 5, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 2, -2, -4, -2],\n [0, 3, -5, 4, 5],\n [0, 6, -1, -6, -4],\n [3, -3, -4, -3, 3],\n [-2, -5, 1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 3, -6, 4, -3],\n [1, -1, 5, 1, -2],\n [3, -2, 0, 0, -2],\n [0, -5, 5, 1, 4],\n [-2, -5, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 0, 3, 5, 0],\n [-4, -2, 4, -2, -2],\n [3, -4, 0, 0, -1],\n [-1, 1, 6, 5, 3],\n [6, 2, -5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 2, 2, -4, 0],\n [5, 5, -4, 3, -5],\n [-3, -6, 6, -6, 2],\n [-1, 1, 4, 0, 1],\n [3, -2, 4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 3, -3, -3, -1],\n [-4, 2, -1, -2, 4],\n [2, -4, 3, -1, 1],\n [2, 1, -4, 1, -1],\n [0, 0, 2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 3, 5, 6, 5],\n [4, 1, -1, 6, 5],\n [6, 2, 1, 4, -4],\n [-6, -4, -6, 1, -5],\n [6, 4, -5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 5, 5, 3, 2],\n [3, -1, -3, 0, -5],\n [-2, 6, -5, 2, 6],\n [-5, -3, -1, -2, 6],\n [2, -6, 5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 0, 6, -3, -2],\n [-2, -2, -4, 1, -5],\n [-3, -2, 3, 1, 3],\n [4, 1, 5, -3, 2],\n [3, 5, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, -4, 4, 5],\n [0, -3, 4, 2, -3],\n [-4, 3, 4, 3, -2],\n [6, -6, 2, 4, -1],\n [5, -4, 6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 6, -4, -5, -4],\n [0, -5, -6, -5, 3],\n [2, 2, 1, -5, 0],\n [4, 3, -3, 0, 4],\n [-3, 5, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 4, 3, -3, -4],\n [-4, 4, -4, 6, -3],\n [1, -6, 3, 0, 5],\n [0, -2, 2, 6, 5],\n [-1, 0, -5, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 2, 1, 1, 4],\n [-5, -5, 4, 5, -6],\n [-3, 0, 2, 6, 2],\n [0, 3, -2, -5, -1],\n [2, 1, 4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 1, 2, 2, 1],\n [4, -5, 3, 0, -4],\n [5, 6, 4, 4, 1],\n [1, 1, 6, 6, 5],\n [6, 3, 1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 4, -6, 1, -6],\n [4, -2, -5, -1, 3],\n [6, 1, -6, 0, -4],\n [1, 5, -3, 3, 4],\n [-1, -1, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -6, -3, -6, 2],\n [6, -3, -6, 4, 4],\n [6, 2, 2, 3, -3],\n [1, 3, 4, 6, 2],\n [-5, -6, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 1, 3, -4, -5],\n [1, 6, -2, 2, 6],\n [3, -5, 5, 1, 0],\n [6, -6, -2, -3, 5],\n [1, -5, 4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 2, -5, -6, 2],\n [-6, -5, 1, 1, -3],\n [6, -6, 3, 4, -2],\n [3, 1, -4, 1, 2],\n [-2, 6, 0, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 5, 2, 0, 6],\n [-4, -3, 2, 4, -5],\n [1, -2, 5, -5, -4],\n [-2, -1, -4, -1, 4],\n [5, 6, -4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 0, -5, -5, -5],\n [-4, 5, 1, 6, 2],\n [0, -3, 3, 5, -4],\n [-4, -1, -5, 6, 0],\n [4, -3, 5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 2, -6, 3, 0],\n [-2, 3, -3, -3, -1],\n [-1, 4, -1, -1, -3],\n [6, 2, 4, 0, -3],\n [3, -3, 3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, -1, -6, -6],\n [-6, 5, 2, -3, 4],\n [-3, -1, 4, 3, 5],\n [3, 6, -4, 1, -6],\n [3, 1, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 1, 6, -3, 1],\n [1, -5, 5, 0, 0],\n [2, -3, 6, 2, 4],\n [-3, 3, -2, 6, -1],\n [-4, 0, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, -4, -3, -1],\n [-6, 1, 1, 4, 5],\n [-1, -6, -3, 4, 1],\n [6, 5, 1, -1, 4],\n [1, 3, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -1, 3, 6, -4],\n [0, 4, -4, -1, -6],\n [-3, -6, 5, 2, -4],\n [4, -2, 5, 5, 2],\n [4, 3, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 2, -2, 4, 0],\n [2, 3, -4, 3, 6],\n [4, -6, -6, -4, 3],\n [-4, -6, -3, -2, 0],\n [4, 6, 3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -3, -2, 6, -2],\n [5, -6, 4, 6, -3],\n [-2, -3, -6, 3, 2],\n [-6, -4, -3, 5, -2],\n [1, 4, -1, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 6, -1, -1, 3],\n [1, 1, -1, 2, -2],\n [-5, -2, -5, -5, -5],\n [5, 1, 5, 2, -4],\n [3, -2, 1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 0, 5, -5, -6],\n [0, -1, -4, -1, -5],\n [-2, 4, 1, -2, 5],\n [0, -3, 4, 5, 5],\n [-3, 1, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -5, 2, -3, -4],\n [3, -6, 1, 2, 5],\n [-5, -2, -1, -5, 0],\n [-4, -6, 4, 6, 1],\n [3, -2, 2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 3, 5, -4, 4],\n [1, -4, -3, 5, 3],\n [-6, -3, -4, 6, 3],\n [6, -6, 5, -2, 2],\n [4, -5, 5, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 3, 0, 1, -6],\n [-3, -3, 0, 2, -5],\n [-1, -2, -3, 3, 2],\n [-1, 3, -5, -3, 2],\n [5, 4, 4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -5, -3, -5, -6],\n [-2, 2, 1, -6, -4],\n [-2, 5, -6, -4, -6],\n [-6, -4, 0, 6, 6],\n [-3, -3, -1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -5, 6, -6, 0],\n [0, -6, 1, -4, -1],\n [-5, 3, -5, 5, 4],\n [-4, 4, -3, -6, -3],\n [-5, -4, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -6, 2, -2, 1],\n [-4, -5, 3, -6, 4],\n [6, 3, 2, -1, -3],\n [-1, 0, -1, 4, 4],\n [6, -3, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 4, 2, -1, 3],\n [6, 4, 1, 6, 4],\n [-3, -5, -3, 3, 3],\n [5, -1, -6, -1, 4],\n [-3, 2, 5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 1, 1, 3, -2],\n [-5, 0, -4, 0, -3],\n [3, -4, 0, 6, 1],\n [4, -4, -6, -3, -1],\n [1, 4, 3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 3, 2, -5, -4],\n [3, 5, -6, -6, 4],\n [-1, -5, -1, 5, 1],\n [5, -2, 3, -4, 6],\n [-4, 1, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, -6, -5, -6],\n [-3, -4, -6, -1, -4],\n [0, 1, 3, -3, 1],\n [6, -2, -4, -1, -1],\n [6, 6, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -6, -6, -6, 2],\n [2, 0, -5, 0, -2],\n [-2, -1, -3, 0, -2],\n [-4, 5, 2, 6, 4],\n [-3, -4, 3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -3, 2, 6, 0],\n [6, 3, -3, -5, 3],\n [-1, 0, -2, 1, 4],\n [-3, -1, 4, -6, -5],\n [-6, -5, 3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -4, 2, -4, 0],\n [-1, 6, -4, -5, -2],\n [5, 4, 6, -2, -1],\n [5, 3, 0, -1, 3],\n [1, 5, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 4, 1, -3, -5],\n [5, -3, -6, -3, 6],\n [1, 5, 1, 3, -3],\n [3, -1, 6, 5, 2],\n [0, -6, -6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 5, 3, 3, 4],\n [5, 2, 3, 1, -4],\n [6, 0, 3, -4, -2],\n [-2, 4, 6, -5, 6],\n [-3, 6, 5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -5, 3, 4, -3],\n [-1, 3, -5, 0, -5],\n [-5, 4, -1, 4, 1],\n [3, 2, 0, 6, 1],\n [-2, -6, -3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -3, 4, -1, -6],\n [1, -6, -5, -1, -3],\n [0, -5, 2, -5, 5],\n [4, -5, 1, 4, 0],\n [3, 3, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -4, 0, -6, 3],\n [6, -3, 3, 6, 6],\n [-4, 0, -6, 4, 1],\n [3, 6, -1, -2, -2],\n [4, 0, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -4, 3, 2, -4],\n [-2, 2, 3, 3, 2],\n [-5, 6, 5, -5, 3],\n [-4, 4, 4, -2, -5],\n [-3, -6, 5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -4, -3, -5, 6],\n [-3, -5, -3, -2, -6],\n [3, 1, 0, 5, 1],\n [5, -1, 0, 2, 4],\n [2, -1, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -1, 4, 3, -2],\n [4, -2, -5, 6, 3],\n [-6, -4, 5, -6, -4],\n [3, -1, 2, 3, 3],\n [0, 0, -4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 6, -5, 0, -3],\n [4, 1, 3, 6, 5],\n [2, 5, 6, 2, 4],\n [-6, -5, -4, -5, -3],\n [-5, -6, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 6, -5, -2, 2],\n [3, -3, 4, -6, -5],\n [5, 0, -4, -3, 4],\n [-3, -6, 6, -6, 4],\n [-4, -6, 0, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 4, -3, 1, -2],\n [2, -3, -1, 3, -6],\n [-5, 3, 5, -5, -2],\n [1, 2, 5, -1, 5],\n [-2, -6, 5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -2, 6, -5, 5],\n [4, -6, -2, -3, -3],\n [6, 0, -4, -5, 2],\n [-1, -4, -2, -4, -5],\n [-5, -3, -6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -1, -5, -3, -5],\n [-3, 0, -1, 6, -1],\n [-6, 5, 3, 0, 0],\n [-4, 2, 2, -5, -1],\n [-2, -1, 5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 1, 1, -1, 0],\n [0, -1, -6, -3, 4],\n [5, 3, -1, -2, -4],\n [3, -2, 5, -2, 6],\n [2, 1, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -1, 3, -2, 5],\n [1, -2, -1, -2, -6],\n [-2, -3, 3, 5, 4],\n [5, -6, -3, 6, 5],\n [-6, -3, -4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -6, 1, 0, -4],\n [0, -3, -2, 4, 1],\n [0, -1, 3, -1, 0],\n [1, -2, 2, -5, 6],\n [2, -4, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 3, 6, -4, 4],\n [3, -6, 1, -4, 4],\n [1, 6, 6, -1, -6],\n [5, 1, -2, -3, -4],\n [4, 6, -1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 3, -4, 3, 5],\n [1, 6, 3, -3, 1],\n [1, -2, -4, 3, 1],\n [3, 1, -2, 1, 3],\n [6, -1, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 2, -5, 5, 6],\n [-5, 0, -3, 4, -4],\n [2, -4, -3, -5, -1],\n [-4, 6, 4, 4, 2],\n [1, 3, 1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -1, 3, 5, -5],\n [0, 5, 0, -5, -1],\n [3, 6, -6, -5, 6],\n [-2, 6, -5, 0, 1],\n [4, -6, -6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 2, 6, 2, 6],\n [5, 0, 4, -3, 1],\n [5, 6, -2, -1, -4],\n [3, 6, 1, -6, -3],\n [-3, 5, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -4, -5, -5, -3],\n [3, 5, -6, -4, -3],\n [0, 0, 4, 2, 0],\n [1, -1, -2, 0, 0],\n [0, -2, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 0, -2, -1],\n [-2, 2, -4, -6, 5],\n [6, 6, -3, 6, 5],\n [5, 0, -4, 6, -4],\n [5, 3, -5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -1, 6, 2, 0],\n [5, -2, -1, 3, 6],\n [6, 1, -2, 1, 5],\n [-6, -5, 4, -5, -6],\n [0, 3, 6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -5, 2, -4, 5],\n [-3, -1, -2, 5, -5],\n [0, -1, -5, 6, -4],\n [2, -4, 6, -1, -1],\n [-3, -1, -6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 1, 1, -3, -2],\n [1, 2, -1, -6, -2],\n [-4, -5, 5, -4, 3],\n [-1, 1, 3, -4, -3],\n [3, -5, -4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 0, -3, 0, 5],\n [-1, 5, 5, -4, 5],\n [0, 0, -6, -5, 3],\n [-6, -6, 2, -4, -2],\n [1, 2, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -2, -2, 0, 4],\n [6, -1, -2, 6, -5],\n [-5, 0, 1, 1, -3],\n [1, 1, 5, -3, -2],\n [-2, 6, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -5, 2, 2, 6],\n [5, 5, 5, -5, -3],\n [2, 2, -5, 0, -6],\n [4, -5, -5, -3, 6],\n [-3, -4, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 0, 0, 2, 2],\n [3, 6, 2, 0, -4],\n [-2, -6, 2, 1, -1],\n [0, 5, 3, 1, -4],\n [-6, 0, 6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 6, -4, -4, 1],\n [-1, 5, -4, 4, 5],\n [2, -6, 5, 0, -3],\n [0, 6, -3, -4, -5],\n [-5, -5, -5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 1, 3, 3, 1],\n [5, -1, 0, -5, -1],\n [4, 0, -5, 4, 4],\n [6, 0, -5, 3, -5],\n [6, -3, 4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, 1, -4, 3],\n [3, 5, -2, 4, -5],\n [1, -2, -3, 1, -2],\n [1, -5, 4, -2, 0],\n [2, 0, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -2, 2, 2, 4],\n [3, 2, 0, -5, -6],\n [-6, 2, 2, -3, 5],\n [3, 3, -5, 3, 2],\n [1, -1, 2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -3, 3, -6, 5],\n [5, -3, 1, 2, 4],\n [3, 5, -5, -3, -2],\n [3, 0, -4, 0, -2],\n [1, 5, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -5, -2, 1, -6],\n [3, -4, 4, -2, -6],\n [5, -1, 6, -4, 1],\n [1, -4, -6, -4, 2],\n [-5, -1, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 4, 4, -4, 6],\n [1, -5, -4, -6, 3],\n [-4, -3, -5, -5, 4],\n [-3, 4, 6, 4, 4],\n [-1, 1, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -2, 5, 4, 3],\n [-1, 1, 6, 1, 4],\n [-2, -4, -2, 3, -2],\n [-5, 3, -3, 5, -4],\n [-1, 2, -5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 3, 4, 4, -5],\n [-1, -4, 1, -5, -5],\n [2, 2, -3, 6, -5],\n [3, -1, 5, -6, 1],\n [6, -4, -1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 0, -1, 1, -2],\n [0, 6, -5, 0, 5],\n [-1, -2, 6, -5, 5],\n [-4, -3, 6, 3, 6],\n [-6, -1, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 1, 2, -2, 0],\n [-3, -1, 3, 0, -1],\n [0, -4, 4, -3, 1],\n [6, -4, -6, 2, 4],\n [-1, -4, -5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 1, 5, -4, -1],\n [1, -2, 5, 6, -2],\n [2, -6, 1, -6, -1],\n [-6, 4, -1, -1, 2],\n [-1, -6, -2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -2, -3, -3, -2],\n [2, -4, 0, -6, -2],\n [-2, -5, -3, 1, -3],\n [-3, -2, 4, -2, 0],\n [-2, 3, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 4, -4, -6, 2],\n [-3, -2, 6, 3, -3],\n [-2, 3, 4, -6, -6],\n [5, -2, 3, 5, 3],\n [6, 6, 1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 0, 3, -5, 1],\n [-2, 2, 6, 1, -5],\n [3, 5, 2, -4, -6],\n [-2, 0, -2, 4, 6],\n [2, -1, 0, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 2, -5, 5, 5],\n [-5, 4, -6, 1, 6],\n [2, -6, -2, -1, 2],\n [-1, 3, 3, -2, 3],\n [6, -5, 1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -1, 3, 1, 0],\n [0, 1, 5, -1, -2],\n [0, 2, 0, 5, -3],\n [0, 0, -3, 2, 2],\n [4, -4, 5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -4, -3, -6, -1],\n [-5, -2, -2, 4, -2],\n [-6, -4, -2, -2, -2],\n [-3, 0, -2, 1, -2],\n [-2, 5, -1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 4, 1, 6, 4],\n [-2, -1, 6, 6, -5],\n [-6, 6, 5, -5, 1],\n [-3, 5, 5, -6, -2],\n [6, -3, -6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 0, -3, 6, 6],\n [6, 4, 5, -6, 4],\n [3, 2, 2, 2, 0],\n [-6, 3, 0, -2, -3],\n [-2, 6, 5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 6, -4, -2, 6],\n [-4, -2, 4, 4, 3],\n [5, 0, 3, -5, 2],\n [-2, -3, -3, -2, 6],\n [-4, -3, -5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 4, 5, -1, -2],\n [1, 5, -3, -4, 6],\n [-2, 6, -5, -1, 4],\n [2, -1, 3, -1, -3],\n [-2, 3, -6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 1, -1, -1, -2],\n [-2, -3, -5, -6, -2],\n [2, -3, -5, -3, 1],\n [2, 6, 4, 6, -3],\n [2, 3, -3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -1, -2, 5, 3],\n [-6, -4, -4, 0, -4],\n [5, 4, 1, 0, -6],\n [2, -2, -2, 4, 3],\n [0, 2, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 2, -3, 3, -3],\n [-5, 6, 0, 1, 1],\n [1, -6, 4, -4, 6],\n [-3, 1, -5, 5, -5],\n [4, 4, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 2, 5, 6, -6],\n [6, 2, 0, 3, -5],\n [1, -6, -1, 5, 4],\n [0, 4, -1, 0, -6],\n [-5, -4, -6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 4, 6, -4, 5],\n [4, -6, 5, 6, -5],\n [1, -6, 4, 1, 0],\n [-5, -4, -2, 1, 4],\n [-3, -3, 1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -1, 4, -6, 6],\n [-4, -6, 0, 2, -3],\n [-6, 6, 6, 2, 4],\n [1, 2, 0, -6, 0],\n [1, 1, 2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -5, -2, -4, 1],\n [-4, -4, 6, -2, -6],\n [6, 3, 4, 1, -2],\n [6, 1, 0, 4, -3],\n [0, 3, -6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -2, -4, -3, -5],\n [3, -5, 4, -6, 4],\n [1, 3, -5, -3, 0],\n [6, 2, -3, 6, -5],\n [-3, 6, -3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 2, 1, 3, 5],\n [0, -6, -4, -6, 0],\n [-1, 4, -1, -3, -4],\n [-2, -6, 3, -1, 6],\n [-3, 2, -3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 0, -5, 4, 6],\n [-6, -1, -3, 6, -2],\n [-2, -3, 4, 0, 1],\n [-5, 3, 2, 5, 4],\n [0, 5, 5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, -6, -1, 2],\n [1, -5, 3, -2, 5],\n [-2, -4, -6, 1, 1],\n [5, 0, 6, 1, 6],\n [-6, 6, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -3, -6, -2, -2],\n [5, 3, -1, 3, 2],\n [-5, 1, -5, -6, 3],\n [1, 3, -5, -4, 5],\n [-6, 3, -5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 5, 4, 3, -6],\n [3, 6, 4, 0, -2],\n [6, -5, -4, 4, 2],\n [6, 0, -6, -2, 5],\n [1, -6, 5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 4, -5, 1, 6],\n [5, 6, -6, -2, 1],\n [0, -6, -3, 4, 6],\n [-5, 0, 4, -1, 1],\n [3, 3, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -3, 1, 1, -6],\n [4, 4, 4, -4, -3],\n [-6, -1, -5, -5, -6],\n [6, 1, -1, 5, 3],\n [-4, -3, -6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -2, -4, 1, 2],\n [5, 4, 3, 6, -6],\n [-1, 6, -2, 5, 6],\n [-2, 5, 3, -5, -4],\n [-6, -1, 6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, 2, 0, -4],\n [-6, -2, 6, -5, 6],\n [4, -2, 6, -4, 3],\n [-1, -6, 2, -4, -5],\n [3, 5, -1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -4, -6, 3, 3],\n [-3, 3, 0, 3, -1],\n [2, -6, -4, -4, 1],\n [-6, -6, -5, 0, -1],\n [5, -2, 2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -2, -3, -3, 2],\n [0, 1, 0, -6, -1],\n [2, -4, -3, 5, -2],\n [-4, 6, -3, 6, 6],\n [0, 1, 5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, -6, -3, 1],\n [3, 2, -1, 4, -2],\n [1, -1, -1, -6, 0],\n [6, 2, -3, -4, -2],\n [3, 0, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 6, -4, 4, 3],\n [3, -1, -6, 1, -6],\n [6, -2, 1, 3, 4],\n [1, -1, 2, -5, 3],\n [-6, -3, -1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 0, 0, -1, 1],\n [4, -4, 1, 3, 6],\n [5, -4, -2, -2, 3],\n [-4, -4, 2, -4, -4],\n [0, 0, 6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, 1, -4, 1],\n [-6, -6, -1, 3, 0],\n [2, -4, 0, 3, 5],\n [4, 1, 5, 6, 1],\n [1, -6, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 0, 4, -5, -5],\n [4, 2, -3, 5, 5],\n [4, -6, 6, -4, -3],\n [2, -1, -5, 3, 0],\n [-1, -6, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 5, -2, 6],\n [-6, 1, 4, -1, 6],\n [-6, 6, -4, -6, 3],\n [-3, 1, -2, 0, 4],\n [-5, 6, 5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 2, -6, 6, 2],\n [1, 6, 3, -3, 1],\n [6, 0, -4, 5, -2],\n [0, 1, -2, -1, 2],\n [-1, 3, 6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -3, 1, 2, 2],\n [-2, -1, -6, -5, 5],\n [4, 4, -2, 0, 1],\n [3, -5, -4, 2, 1],\n [-4, -5, 1, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 6, 5, -2, -1],\n [-6, 6, -6, -3, 3],\n [6, 2, 5, 6, -3],\n [-3, 6, -6, -5, 3],\n [-3, 2, -2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 0, 5, 1, -1],\n [2, -5, 6, 3, -4],\n [-2, -4, 0, 2, 5],\n [3, -1, 2, 6, 1],\n [4, 5, 3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 0, -1, 1, -3],\n [1, -4, 4, -2, -5],\n [0, -6, 4, 0, -2],\n [-6, -3, 0, 0, -3],\n [2, 6, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 0, 5, 3, -6],\n [4, 3, 0, -1, -4],\n [-5, -2, -5, -3, 4],\n [0, 2, 2, 2, -4],\n [-4, -4, -3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 6, 5, 0, 3],\n [-2, 3, 0, 2, -5],\n [-2, 0, -4, 5, -4],\n [-6, -3, -1, -4, -6],\n [3, -5, -6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 1, 6, -3, 2],\n [-5, 5, -4, 1, 4],\n [2, -4, 4, 0, 2],\n [-2, -2, -6, -1, 2],\n [-6, -3, -5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 0, -5, -1, -1],\n [1, -1, -4, 3, 1],\n [-4, 2, -6, 0, 3],\n [-5, 3, 6, 6, -6],\n [3, -1, -2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 2, -4, 2, -3],\n [5, -3, -4, -3, -6],\n [-2, -6, -2, -5, -2],\n [3, 2, -1, 5, -6],\n [-4, 3, -2, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -5, 2, 1, 4],\n [4, -1, 6, 6, 2],\n [-2, 5, 1, -3, -6],\n [-4, 5, -1, -6, -2],\n [5, -1, 6, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 2, 1, -3, -3],\n [3, 3, 6, -1, -4],\n [3, 3, 0, 5, -5],\n [-3, -2, 4, -1, 3],\n [3, -6, -1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 3, -3, 2, -4],\n [-1, -2, -3, -5, -3],\n [1, 5, -1, -5, -6],\n [-3, -6, -6, 1, -6],\n [2, 4, 1, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 4, -4, -4, -3],\n [1, -6, 4, -2, 0],\n [-4, 5, 4, 3, 3],\n [-5, 2, 6, -5, -3],\n [4, -2, 4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 0, -5, -6, 4],\n [-4, 1, -5, 3, 3],\n [6, -3, 3, 2, -2],\n [-5, 5, 3, -3, -6],\n [6, -3, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -5, 6, 6, 5],\n [2, -1, 4, -1, -1],\n [-5, -2, 6, 3, 0],\n [-6, 1, -4, 0, 5],\n [-1, 5, -5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 6, 2, 1, -6],\n [5, 0, -3, -1, -4],\n [-3, -2, 1, 0, -4],\n [4, 3, -2, 0, -5],\n [4, -4, 3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 5, 5, -5],\n [-2, -6, 2, -4, -6],\n [-2, 3, -1, 2, -5],\n [-5, 6, -1, -6, 4],\n [-6, 2, -4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, 2, -3, 0],\n [3, 1, -1, 0, 3],\n [1, 3, 3, 5, -6],\n [-3, -5, -3, 5, -6],\n [2, 4, 3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -2, 0, -3, -6],\n [-5, 3, 5, 0, 4],\n [0, -1, -2, 5, 2],\n [5, 0, 3, -5, 3],\n [3, -3, -2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, 6, -5, 1],\n [4, -3, 2, 5, -3],\n [2, 1, 5, 0, -5],\n [-2, -4, -6, -2, -3],\n [-3, 5, -1, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -5, 5, -2, 2],\n [3, 0, -6, -4, 0],\n [5, -6, -3, -6, 6],\n [-2, 0, 0, -4, -4],\n [0, 3, -5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 0, -5, -1, 3],\n [5, 0, 4, 2, -4],\n [-6, 3, -3, 3, -3],\n [-2, 1, 6, 2, 1],\n [6, 4, -1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 1, 2, -3, 5],\n [-3, 2, -6, 3, 0],\n [2, 6, 4, -3, -5],\n [6, 2, -6, 0, -4],\n [1, 0, -6, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, 6, -1, -4],\n [6, 5, -6, 0, 1],\n [6, -2, 5, -2, 6],\n [-5, -4, -3, 5, 5],\n [2, -2, -5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 4, -2, -2, -6],\n [2, 2, 2, -6, 4],\n [-3, 2, 6, -3, 0],\n [0, -6, 0, 0, -2],\n [-3, -6, 3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 5, -6, 1, -6],\n [4, -2, 4, 3, -2],\n [6, 3, 3, -2, 1],\n [-5, 4, -5, 5, -1],\n [6, -5, -2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -1, -5, -1, 0],\n [-6, -1, -1, -6, 1],\n [-3, 2, 5, -2, -6],\n [6, -1, 4, 2, 6],\n [2, 1, 5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, -4, 1, -3],\n [-4, -1, -1, 1, -3],\n [2, -4, 3, -4, 0],\n [-5, 6, 1, -6, -5],\n [6, -1, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 4, -2, -4, 3],\n [6, 5, 6, -3, -5],\n [-3, 4, 4, 2, -5],\n [0, 0, 3, -4, -6],\n [-5, 1, -1, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 6, 2, 2, 1],\n [-1, -1, 4, -3, 4],\n [2, 1, -3, 4, -6],\n [-5, 2, 0, 4, 4],\n [-2, -2, 1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 4, -6, 5, -3],\n [1, 6, -5, 6, 2],\n [3, -2, -2, 6, -4],\n [-5, 2, -4, -6, 0],\n [-3, -2, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, 6, 3, 6],\n [-1, 4, 0, 4, 2],\n [2, -1, -4, 0, 0],\n [-4, -2, 0, 1, -4],\n [0, 3, -3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -4, 2, 0, 4],\n [2, 6, 1, 0, -5],\n [2, 3, 1, 4, 6],\n [1, 6, 0, 1, -4],\n [-4, -3, 3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -3, 2, 0, 1],\n [-2, 1, -6, -6, 6],\n [6, 6, 5, 3, 3],\n [-6, -2, 4, 6, 2],\n [3, -5, 5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -5, 3, 0, -5],\n [-1, 6, -1, -1, -4],\n [-5, -3, 2, 5, 1],\n [3, 4, 3, 1, 5],\n [-5, -3, -3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, 6, 2, 5],\n [3, -6, 0, -1, 6],\n [-1, -5, 2, -2, -3],\n [1, 6, -6, 3, -2],\n [-6, 1, 0, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, -6, -3, 2],\n [-2, 0, 3, -4, 6],\n [-2, -4, -2, -6, -6],\n [2, 4, -3, 0, 4],\n [1, 3, 5, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -4, 3, -4, -3],\n [1, -2, 0, -3, 6],\n [-6, -2, 6, 2, 0],\n [4, 4, 4, 0, 1],\n [-6, 4, 6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -5, 6, -5, -3],\n [1, 4, 4, 3, 4],\n [-3, -5, -3, -5, 0],\n [-3, 1, -4, 0, -5],\n [-6, 6, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 3, 5, -2, 1],\n [-3, 5, -1, 0, -1],\n [3, 0, 6, 0, -3],\n [5, 1, -5, -5, 1],\n [3, 6, 0, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -5, 5, 6, 3],\n [2, 3, -1, 0, 0],\n [0, -4, 3, 0, -4],\n [0, 5, 2, 5, -6],\n [-1, -5, 4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 2, 2, 1, 5],\n [5, 6, -3, 5, 2],\n [-5, 6, -5, 6, -3],\n [3, -5, 5, 4, 3],\n [0, -4, 1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -4, 6, 1, 4],\n [-3, 6, 5, 6, 5],\n [6, -1, 0, 3, -1],\n [1, -1, 0, 3, 2],\n [5, 0, -5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -4, 0, 1, 2],\n [4, -3, 3, 2, -6],\n [2, -5, -3, -3, 4],\n [-1, -3, -5, 5, 0],\n [6, 6, -3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 1, -3, -4, 5],\n [-6, -2, 6, -3, -5],\n [6, -2, 0, 3, -6],\n [-2, 2, 2, -3, -5],\n [-6, -4, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -1, 0, -2, -3],\n [0, 5, -1, -4, 5],\n [2, 2, -6, -1, -6],\n [-1, 3, 6, -4, 5],\n [5, -2, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 5, 3, 2, -3],\n [4, -4, 0, 5, 6],\n [-5, -1, -1, 6, -4],\n [-4, 1, -2, 1, -6],\n [-2, -5, -5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 0, -5, 0, 5],\n [-4, 4, -3, -3, -3],\n [4, 4, 0, 5, -3],\n [1, -3, 5, 1, 5],\n [-4, -4, -5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 4, -6, -2, -1],\n [-6, 1, -4, -5, 6],\n [-6, -2, -6, -5, -1],\n [6, 1, 1, 5, -3],\n [-3, 3, -5, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 1, 6, 2, 5],\n [4, 5, 4, 4, -4],\n [-3, 2, 1, 4, 6],\n [-3, 3, 0, 3, -6],\n [0, -6, -4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -3, -2, -4, 6],\n [3, 2, 4, -1, 6],\n [-3, 4, 0, -5, 3],\n [-6, -6, -4, 1, -3],\n [-2, -6, -3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, -2, 1, 5],\n [1, 5, -5, 1, 4],\n [-6, 2, 2, 6, 2],\n [-2, -1, -2, -6, 0],\n [-3, 2, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -2, 0, 4, 4],\n [4, -1, 4, -2, -6],\n [6, 4, 0, 3, 0],\n [-1, -1, 4, -1, -5],\n [4, 5, 1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 3, 0, -5, -6],\n [-4, 5, 3, 2, -6],\n [-2, -1, 6, -6, 2],\n [6, -6, 1, -5, 1],\n [1, 4, 2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 2, 1, -2, 1],\n [-6, -2, 1, -2, 1],\n [-3, 3, 1, 6, 3],\n [-5, -4, 3, -2, -4],\n [-1, 2, -3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 1, -1, -4, -1],\n [-4, -5, 3, 5, -5],\n [1, -4, -5, 1, -3],\n [-4, -4, 2, 0, -1],\n [-5, 0, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -5, -4, 3, 6],\n [-2, 3, 4, 3, 6],\n [5, -6, 6, 0, 6],\n [-4, -3, -2, 6, 0],\n [-3, -4, 0, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 5, -5, -2, -3],\n [-5, 6, 4, -3, -6],\n [5, 0, 0, 0, -1],\n [5, 4, 5, -6, -1],\n [1, 5, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, 1, 0, 1],\n [1, -3, -2, -3, 3],\n [3, 5, 0, -3, 1],\n [-3, 4, -5, 3, 3],\n [-4, -3, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 3, 6, 5, -6],\n [-5, -6, -3, -2, -1],\n [5, 0, -4, -2, -1],\n [2, -5, 6, -3, -5],\n [3, 1, -6, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -3, -5, 5, 1],\n [2, 1, 6, 2, 3],\n [-6, -1, 3, -5, -4],\n [6, 2, -6, 0, 6],\n [6, 1, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 4, -1, 0, 5],\n [-3, 2, 4, -1, -2],\n [-6, -1, -5, -3, 4],\n [-4, 1, -5, 2, 2],\n [-3, 5, 6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -2, 2, -1, 5],\n [0, -1, 1, 3, 2],\n [-4, -3, 6, -3, 1],\n [-4, 1, 2, -4, -6],\n [3, 2, -2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -4, 4, -3, -6],\n [1, -4, 1, -6, 4],\n [1, 6, -1, -3, -4],\n [2, -4, -2, 6, -5],\n [-4, -2, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -5, -4, 2, 2],\n [5, 2, -5, 1, 5],\n [0, -3, -3, 4, -2],\n [3, 0, -4, -5, -1],\n [1, -4, -1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 2, 5, -2, -1],\n [1, -1, -1, -1, 0],\n [5, 4, 5, 4, -4],\n [-4, 5, 4, 4, -5],\n [-4, 0, -4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -6, 1, -4, 4],\n [-4, 6, -4, -2, -6],\n [3, 6, 0, 4, -5],\n [2, -5, -4, 5, 2],\n [-6, 1, 0, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -5, 1, 0, 1],\n [4, -5, 5, 4, 2],\n [6, 0, 4, 1, -1],\n [-5, 6, -4, 1, -1],\n [-5, 1, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -5, 2, 1, 6],\n [3, -6, 1, 3, 1],\n [-3, -5, 2, -3, 4],\n [-5, 0, 4, -5, 5],\n [1, -4, -5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, 3, 1, 2],\n [1, 1, -1, -5, -5],\n [3, -4, -3, 4, -1],\n [1, 0, 6, 6, -2],\n [-1, -3, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, 2, -2, 4],\n [-4, 4, 0, -6, -1],\n [-2, -3, 1, -6, -4],\n [0, 1, 5, 5, -2],\n [5, 5, -5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -1, -4, -2, -3],\n [-5, 5, -1, 2, 4],\n [0, 4, 4, -4, -6],\n [1, 0, 0, 6, 1],\n [-2, -4, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, -1, 6, -3],\n [-5, 0, 6, 5, 0],\n [-1, 1, 5, 2, -6],\n [-4, -3, -1, 6, -5],\n [6, 5, -5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 4, -3, -4, 4],\n [-2, 5, -3, 5, 6],\n [6, -3, 6, 6, 2],\n [3, 5, 4, 1, -3],\n [-6, -3, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, 3, 1, -4],\n [-6, -2, 2, -1, -6],\n [-6, -4, 0, 6, -4],\n [-5, -4, -3, -3, 1],\n [1, 4, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -5, 6, -5, 4],\n [-4, -6, 3, 6, 3],\n [-4, 2, 1, -5, -6],\n [0, 4, 1, 4, 3],\n [0, 1, -6, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -1, 4, -3, -1],\n [-5, 0, -3, -4, 2],\n [-6, -2, -4, 4, 4],\n [-4, 1, 5, 3, 4],\n [1, -5, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -2, 6, 5, 3],\n [-6, -5, 2, -4, 1],\n [-3, -2, 2, 3, -5],\n [1, -2, 6, -2, -2],\n [-5, 1, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 3, -1, 2, -4],\n [5, -1, -5, 2, 6],\n [6, 6, -4, -4, 1],\n [0, -2, -5, -1, -2],\n [0, 5, 4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 1, -4, -3, -3],\n [-1, 2, -2, 4, 5],\n [5, 1, -1, 2, -2],\n [4, 2, -6, 1, -1],\n [-4, 6, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 0, 1, 5, 6],\n [2, 5, 4, -5, 5],\n [-6, 4, 3, -4, -3],\n [3, -2, -2, -5, 6],\n [1, -6, 1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, 5, 5, -5],\n [-5, 6, -4, -1, 3],\n [-6, 2, -4, -4, 2],\n [1, -1, -1, -2, -5],\n [2, 3, 3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 6, 3, 0, 5],\n [-2, 2, 2, -3, 0],\n [-1, 3, 3, 5, -1],\n [1, 5, 6, -4, -2],\n [-5, 6, 1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -1, 6, 6, 1],\n [-6, 3, 0, -6, -4],\n [5, 5, 4, -4, 4],\n [-1, -4, 5, -1, 3],\n [4, -3, 3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 2, 5, 4, -1],\n [-3, 5, 3, 3, -4],\n [-2, 3, -2, 3, -3],\n [3, 5, 0, -6, 6],\n [-5, 6, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -2, 6, 1, -5],\n [-3, -1, 4, 5, 4],\n [-3, 2, -5, -5, -1],\n [-4, 1, -3, 4, 2],\n [-5, -6, -4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -4, -1, -1, -2],\n [1, 2, 6, 6, 5],\n [3, -2, 6, -2, 2],\n [3, -3, 4, 4, -6],\n [-6, 0, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 5, 6, 2, 5],\n [5, -4, 0, -2, -5],\n [3, 6, -4, 4, -6],\n [2, 2, 1, 2, 2],\n [4, -3, 1, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 0, 4, 6],\n [-2, -6, -6, -2, -3],\n [-1, -1, 1, -3, -6],\n [-6, 3, 3, -2, -1],\n [1, -3, -1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -4, 4, -1, 1],\n [0, 0, -5, 3, 5],\n [-2, 3, 5, -2, -5],\n [2, 4, -2, -6, 5],\n [6, 5, -2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -1, 4, -1, 6],\n [0, 1, -4, 5, 0],\n [-4, -6, 0, -3, -6],\n [3, 0, 3, 1, 4],\n [-6, 2, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -4, -2, -2, 5],\n [-4, 0, 4, -3, 3],\n [4, 5, -3, 0, -5],\n [5, -4, -3, -6, 6],\n [4, 5, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -1, -1, 1, 4],\n [-3, -2, -1, 6, -2],\n [-2, -4, 2, 0, 2],\n [-3, -3, 2, -5, -5],\n [-1, 6, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -6, -3, 6, 3],\n [4, -1, 3, 0, -4],\n [-1, -1, 2, 0, 5],\n [4, 3, 0, -3, 0],\n [-3, 5, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, 3, 6, 0],\n [3, -5, 0, -2, 0],\n [-5, 4, 1, 3, 0],\n [1, 0, 3, 3, -3],\n [2, 1, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -3, -5, 4, 1],\n [-5, 3, -1, 3, -1],\n [2, -3, 3, -4, -2],\n [6, -1, -1, -2, 2],\n [-3, -6, -1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 2, 4, 2, 3],\n [5, 3, 5, -1, 4],\n [6, 4, -2, -4, -2],\n [-1, -1, -2, 3, 2],\n [-2, 1, -1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 6, 3, 4, 5],\n [3, -4, 6, -2, 0],\n [1, 6, 5, 5, -3],\n [6, 6, -5, 2, 3],\n [4, -4, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 4, 3, -2, 4],\n [0, -2, 2, -6, -1],\n [0, 3, 5, 5, -4],\n [-1, -1, 6, -5, -5],\n [-5, 6, 6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 3, 5, 3, -6],\n [-3, 1, 2, 3, 6],\n [5, 0, 2, -5, 1],\n [-3, 3, 6, -6, -3],\n [5, 5, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, 5, 6, -3],\n [4, -5, 1, -4, 1],\n [-5, 6, 1, -5, 6],\n [-3, -4, 0, -1, 4],\n [-3, -4, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 6, 5, 6, 2],\n [-3, 6, 1, 4, 1],\n [-6, 3, 2, 0, 2],\n [-1, 2, -1, 6, -2],\n [-1, -2, -6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 4, -4, -5, 3],\n [0, 1, 4, 3, -1],\n [2, -5, -4, -2, -3],\n [-5, 3, 3, 1, -1],\n [6, 0, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, -4, -1, 6],\n [-1, 4, -3, 6, 6],\n [-4, 4, 5, -2, 4],\n [-4, -2, 3, -6, -1],\n [4, -3, 5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, -3, -6, 6],\n [3, 0, 1, 3, 6],\n [1, 6, -2, 3, -2],\n [-4, 0, -5, -1, 5],\n [-5, 2, -6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 1, 0, 1, -3],\n [4, -3, 0, -3, 0],\n [4, -5, -4, -1, -2],\n [-2, -1, 6, 5, 4],\n [1, 4, 3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 6, -2, 4, -2],\n [-5, -3, -1, 6, -2],\n [1, 1, -5, -1, -4],\n [5, 0, -1, -4, 1],\n [6, -3, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 5, 3, -1, 3],\n [-6, -4, 0, 3, 2],\n [-3, 1, 4, 5, 0],\n [5, 1, 1, 3, 1],\n [0, 0, -4, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 5, 4, -3, 0],\n [-5, 5, -3, 3, -5],\n [2, 3, 5, -1, -3],\n [3, -2, 1, -2, -2],\n [1, 0, 6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -3, 6, -5, 1],\n [6, 6, 6, 0, 1],\n [-1, -2, -2, 3, -5],\n [-2, 3, -5, -5, 2],\n [-1, -4, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 0, -6, 2, -3],\n [6, -1, -5, 4, -3],\n [3, 4, -1, 4, 5],\n [-6, -3, -6, 5, -2],\n [-1, -6, 4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 5, 2, 3, -5],\n [0, 0, -5, 6, -4],\n [-2, -3, 4, -5, 0],\n [-4, 2, 0, -3, 3],\n [-6, 3, 3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 3, -3, -2, 1],\n [2, -5, 5, 0, -3],\n [-3, 2, -2, 5, -4],\n [-4, 5, 4, -4, 0],\n [-2, -6, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 5, 5, 3, -4],\n [-4, 0, -4, 4, 5],\n [4, -3, 6, -4, -2],\n [-6, 1, -4, -3, 6],\n [2, 5, 3, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -4, -1, 6, -2],\n [4, 0, -6, 2, -6],\n [-4, -5, -1, -3, 1],\n [4, -5, -4, 2, -5],\n [6, 6, 5, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -4, -3, 0, 5],\n [5, 2, 2, 3, -3],\n [5, 2, -3, 6, 2],\n [-5, 1, 2, 0, -2],\n [5, 5, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -2, 2, 3, 6],\n [4, -3, -4, 5, 1],\n [-1, -6, -2, 5, 4],\n [5, 2, 1, 0, -3],\n [5, 2, 5, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -3, -6, 4, -5],\n [-5, -3, -5, -2, 3],\n [-3, 2, -1, -1, 2],\n [-4, 4, 0, 0, 1],\n [0, 5, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -6, 6, 3, 2],\n [-4, -5, -6, 0, -6],\n [1, 3, 6, -2, 0],\n [5, -6, -5, 2, -5],\n [-6, 0, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 6, -2, 6, 6],\n [0, 0, 3, -6, -5],\n [-2, 3, 0, 4, -3],\n [-4, 5, -6, -3, -4],\n [-6, 4, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 2, 1, -3, 2],\n [6, -5, -1, 0, 2],\n [-6, 1, 2, 6, -6],\n [-6, 2, 4, 4, 4],\n [3, 1, -4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -1, 3, -2, 0],\n [-2, 4, -1, 0, 5],\n [5, -1, -3, 6, 2],\n [4, -4, 5, 5, 0],\n [3, 5, -5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -6, -4, 0, -1],\n [3, -2, -1, 2, -3],\n [-3, 3, 3, 6, -1],\n [-3, 4, -2, 0, -4],\n [-5, -6, -4, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -5, 1, 2, 2],\n [-3, -3, 6, -3, 6],\n [3, -3, 1, 2, 4],\n [2, -1, -2, 0, -4],\n [0, -2, 6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -1, -4, 0, 4],\n [6, 5, -1, -2, -3],\n [-2, -3, -2, 4, 2],\n [-6, -3, -5, -1, -1],\n [1, 2, 5, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 1, -2, 5, -2],\n [3, -5, 1, -2, -6],\n [2, 6, 5, -4, 2],\n [-4, 3, 4, -3, -1],\n [-4, -3, 3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 6, 5, -5, 0],\n [-3, 4, 4, -2, 0],\n [3, 5, 3, -4, 4],\n [6, 3, -4, -3, 0],\n [-6, 0, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 2, 2, 2, 0],\n [1, -4, 6, 3, 0],\n [-4, -5, -6, 1, -1],\n [4, -1, 3, 3, 3],\n [-3, 5, 5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, -3, -2, 2],\n [-5, 3, 5, -3, -6],\n [1, 5, -6, 3, 5],\n [6, -2, 5, -4, 2],\n [-6, -5, 2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 0, -1, 4, 5],\n [0, 6, 5, 6, 2],\n [6, 5, 5, 6, -4],\n [-4, -5, 3, -5, -6],\n [1, -6, -3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -5, 1, 2, 4],\n [-1, 1, 3, 4, -3],\n [6, -3, -5, 1, -6],\n [0, -5, 3, -3, 5],\n [0, 5, -5, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -3, 0, -1, 0],\n [4, -6, -5, -1, 0],\n [-4, -2, -2, -4, 5],\n [-3, -2, -3, 1, 4],\n [4, 2, -1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -6, -5, -4, 3],\n [4, 1, 4, -3, 5],\n [-2, -4, -5, 6, -2],\n [-6, -2, -5, -5, 3],\n [3, 6, 2, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 5, 0, -3, 1],\n [4, -2, -2, 4, 4],\n [3, -2, -4, 4, 4],\n [-4, -6, -4, 4, -3],\n [6, -3, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -6, -5, -6, -2],\n [-4, 0, 0, -2, -4],\n [-5, -1, 6, -1, 2],\n [-6, -1, -6, 2, 3],\n [3, 1, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 0, 5, -2, -2],\n [3, -6, 5, 4, 0],\n [5, 3, 2, 5, 4],\n [-1, 1, 1, -1, 2],\n [-3, -2, -2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -6, 6, 6, 3],\n [-6, -4, 0, -4, 6],\n [4, 3, -5, 6, 0],\n [2, -4, 1, 5, 4],\n [-1, -1, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 6, 6, -6, -6],\n [3, 6, 1, -5, -5],\n [0, 1, -2, 5, 3],\n [-1, 5, 3, -5, 2],\n [-2, 1, -3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 6, 3, -4, 1],\n [-3, 1, 0, -5, -5],\n [1, 3, 5, 0, 3],\n [-2, -5, -1, -5, 1],\n [-2, 5, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, 0, -6, 2],\n [-3, -6, -5, -2, -5],\n [5, 4, -6, -5, 3],\n [-2, 2, -4, -5, -4],\n [5, 5, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -6, -5, -3, 5],\n [6, 3, 6, 6, 4],\n [1, -2, 4, -3, 1],\n [-5, 5, 3, -1, 4],\n [1, 6, 1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, -4, 6, 2],\n [-2, -4, 3, 1, 1],\n [2, 6, 6, 2, -2],\n [-4, -5, 5, 3, 1],\n [0, -6, -6, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -4, -6, 5, 0],\n [4, 0, 3, 0, -3],\n [5, 3, 5, -2, 0],\n [2, 1, 4, 6, 1],\n [0, -3, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 6, -2, 1, -5],\n [6, 4, -3, 6, 3],\n [-5, 3, 3, 0, -5],\n [0, -6, -5, -5, 0],\n [-5, 3, 2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, 4, -2, -6],\n [-4, 6, 3, 6, -3],\n [-6, 6, -5, 1, 1],\n [-1, -4, -4, 2, 5],\n [-6, 1, 3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, -1, -5, 1],\n [2, -2, 4, -2, -5],\n [-3, -2, 0, 5, 0],\n [3, -3, -5, 2, 1],\n [2, -4, -3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -1, -4, -1, -4],\n [6, 2, -5, -2, -1],\n [-2, -2, 1, 3, 5],\n [2, 3, 1, 6, 0],\n [-6, 1, -1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -1, -6, -2, -6],\n [-5, -1, 1, -4, 6],\n [-3, 3, 4, -3, -2],\n [4, 3, -4, -6, -2],\n [3, -1, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -1, 3, 0, 3],\n [5, -3, 4, 0, 3],\n [4, 5, -4, 6, -5],\n [-3, 2, -6, -4, 4],\n [5, -3, 3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 6, -4, 1, -2],\n [5, -2, -6, 3, 2],\n [-4, 5, -5, -4, 1],\n [5, 1, 4, 0, 4],\n [0, 1, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 1, -2, -4, 5],\n [-2, -4, -4, -2, 3],\n [2, -1, -2, -5, -4],\n [5, -3, 5, 0, -3],\n [-4, -6, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 4, 6, -6, 1],\n [2, -4, 1, -6, 5],\n [6, -2, -5, -5, 3],\n [-1, -1, 0, 2, 0],\n [-6, -5, 0, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, 0, -3, -5],\n [-6, -3, -1, 6, 5],\n [-5, -4, -2, -4, 2],\n [0, -6, -2, -4, -3],\n [-3, 3, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -4, 0, 6, -4],\n [0, -4, 5, 5, -2],\n [-5, -5, -4, 4, -6],\n [-3, 2, 1, -4, -3],\n [-6, 3, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 5, 5, 4, 0],\n [4, -2, -2, 0, -5],\n [-5, 1, 3, -6, 6],\n [3, -2, -4, -2, 1],\n [0, 5, -1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -6, 4, 4, -1],\n [2, 1, 0, -6, -2],\n [-2, 4, 0, 3, -5],\n [-4, -5, 2, 2, 5],\n [-4, 5, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -6, -5, -3, -5],\n [1, -2, -5, 3, -3],\n [-2, 5, 3, 2, 1],\n [-4, 3, 5, 4, 2],\n [6, -3, 6, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -5, 1, -2, -6],\n [-4, 3, 5, 0, 5],\n [5, -2, 0, 1, -4],\n [2, -1, 2, 4, 3],\n [6, 0, 6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 5, 3, 0, -1],\n [1, 6, -6, -2, -1],\n [-5, 0, 1, 6, -6],\n [6, -3, 2, -3, 4],\n [0, 0, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -5, -3, 2, 4],\n [0, -6, -4, -3, -1],\n [-5, 5, 1, 3, -5],\n [2, 3, -6, -5, -5],\n [0, 3, 3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 5, -2, -1, 2],\n [-2, 0, 6, 3, 1],\n [-2, -5, -3, -1, 4],\n [2, 2, -6, -2, -3],\n [1, -4, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 1, -4, 4, 5],\n [-6, 2, 2, -1, -5],\n [4, -6, -3, -1, -4],\n [1, 6, 2, -3, 6],\n [4, 2, 4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -5, 0, 4, 6],\n [4, -5, 6, 1, 5],\n [5, 6, 3, 4, -3],\n [-3, -3, -1, -4, -2],\n [-4, 5, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 1, 2, -5, -5],\n [5, 5, 1, 3, -5],\n [-3, -4, 5, 0, 5],\n [6, 1, 2, 3, -3],\n [3, 3, 3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 2, -6, -1, 2],\n [-4, -4, 4, 3, 0],\n [-5, 3, -3, -1, 1],\n [3, -5, -2, 0, -1],\n [0, -1, 4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -3, -4, -5, -3],\n [5, 2, 6, 1, 2],\n [5, 5, -5, 6, -3],\n [1, 1, 0, 5, -4],\n [-6, 0, -3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, 6, -6, 2],\n [-6, -1, -6, 1, -4],\n [-5, 3, 4, 3, 6],\n [5, -1, 4, -3, -1],\n [-3, -4, 1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -1, 0, 6, -3],\n [-4, -6, -1, -6, 6],\n [-6, 5, 6, 2, -2],\n [-4, 1, -5, -4, 2],\n [5, -6, -2, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -3, -5, 2, 2],\n [3, 1, -6, 6, 3],\n [4, 5, -6, -4, -4],\n [0, -5, -1, 0, -3],\n [-5, 4, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 3, -3, 5, 2],\n [5, -4, 6, 4, 3],\n [-6, -2, -4, 1, -3],\n [1, 6, -6, 2, 6],\n [6, 4, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 6, 1, 1, 5],\n [6, 4, -4, 6, 2],\n [4, -1, -6, 1, 1],\n [-2, -5, -1, 5, -6],\n [-1, -5, -4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -2, 4, 5, -6],\n [2, 2, -1, -3, 3],\n [5, -4, 1, 1, 1],\n [5, 3, 3, 3, -2],\n [-1, 6, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -5, 1, -1, -3],\n [-4, 2, 5, 6, -5],\n [-6, 6, -3, -4, 2],\n [4, 2, -6, 2, -5],\n [-4, 1, 5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 0, 2, -6, -1],\n [-1, -3, -4, -1, 0],\n [-2, -6, -4, 0, -6],\n [-3, 1, 5, 4, 6],\n [3, -4, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -4, -4, -5, 6],\n [-3, -3, -4, -1, 6],\n [0, 6, -6, 2, -2],\n [-3, -2, -2, -3, -1],\n [-4, -3, -2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 3, -2, -3, 3],\n [2, 2, -2, -5, 1],\n [-1, 2, -6, 4, -3],\n [-1, 1, 0, 5, 5],\n [-1, 0, 5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 2, 5, 6, 5],\n [4, 3, -3, -6, 5],\n [6, -3, -6, -5, 3],\n [4, 1, 1, 1, -6],\n [-5, 6, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -6, 3, -4, 1],\n [4, 4, -5, 5, 6],\n [2, 6, 3, 4, 6],\n [3, 0, 3, 5, 2],\n [4, -5, 1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 1, -4, 5, -1],\n [6, 2, 6, -4, -3],\n [-5, 6, 2, 1, 5],\n [3, 1, -6, 0, 0],\n [-1, -3, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -4, -5, 6, -2],\n [-2, -3, -4, -2, 6],\n [-2, 6, 5, 0, -3],\n [-6, -3, 0, 0, 4],\n [6, -6, 5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 6, 1, 4, -3],\n [-4, -4, 0, -3, -2],\n [1, -1, -3, -2, 1],\n [-1, -3, 3, 5, 5],\n [-5, -4, 4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -2, 1, -1, 0],\n [3, -6, 0, -6, 0],\n [-4, 5, -2, -1, 3],\n [4, -2, 4, -6, 0],\n [2, -5, -5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 2, 4, -1, -6],\n [2, 3, 0, 4, 0],\n [5, -4, -3, 6, -4],\n [-2, 6, -5, -6, 2],\n [-1, 3, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 6, 5, 4, 6],\n [4, 1, 5, -2, -1],\n [-4, 2, -6, 1, -6],\n [0, 6, -4, -2, 5],\n [5, 2, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, -2, 6, 1],\n [-6, 4, -4, 1, -4],\n [-1, -1, 5, -2, 1],\n [2, 3, -6, 1, 3],\n [-3, -1, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 5, 1, -2, 6],\n [-1, -5, 5, 6, -4],\n [4, -2, 0, 2, -5],\n [-1, 1, 5, 3, 3],\n [-5, -3, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -1, 2, 2, 0],\n [2, 2, -4, -3, -1],\n [-1, -3, 4, -5, 5],\n [-6, -2, 5, -2, -3],\n [4, -5, 0, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 0, 3, 0, 5],\n [0, -4, -2, -2, -1],\n [-1, -1, -6, 0, -3],\n [4, -6, 2, 2, 2],\n [-2, 2, -5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -4, 0, 4, 1],\n [6, -6, -3, 2, -2],\n [6, -6, -6, -5, -2],\n [-6, 5, 0, 4, 1],\n [4, -4, 3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, 0, 4, -3],\n [4, -2, -3, 1, 2],\n [3, -4, 6, 4, 4],\n [3, -5, -3, -1, -5],\n [6, 5, -4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -1, 0, -2, 5],\n [-2, -4, -4, -4, -5],\n [1, -4, 3, -6, -6],\n [2, 6, -3, -6, 3],\n [6, -6, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -1, 5, 2, -6],\n [-1, 3, 3, -5, -3],\n [0, -3, -2, -1, -2],\n [-5, 3, 3, -6, 4],\n [-4, 0, 3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -1, -1, -1, 1],\n [4, 3, 6, 0, -1],\n [-5, -2, 2, 5, 4],\n [5, -5, 1, 6, 6],\n [2, 2, -3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 2, 3, -5, 6],\n [5, 4, -1, -1, -3],\n [6, -3, -1, 1, -6],\n [-5, -6, -5, 4, -5],\n [-6, 5, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -1, 5, 2, -5],\n [2, 1, -1, -5, -3],\n [-4, 5, 1, 5, -2],\n [-3, -5, -2, -5, 5],\n [6, 0, -3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -2, 5, 6, -2],\n [-2, -5, 4, -6, 3],\n [-6, -1, -1, 3, 0],\n [-4, 2, 2, 3, 6],\n [4, -3, 0, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -1, 5, 1, -5],\n [2, 6, -3, -3, 1],\n [6, -5, -5, -4, -1],\n [5, -4, -3, -5, -6],\n [6, 1, -5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 4, -1, 4, -2],\n [0, -3, 4, -3, 3],\n [6, 6, 6, -6, 0],\n [3, 0, 0, -4, 2],\n [-5, -4, -4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 0, -1, -5, -6],\n [2, 6, 0, 6, -3],\n [0, 0, 1, -2, 0],\n [2, 5, 6, -5, 4],\n [2, 6, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -5, -1, 6, -1],\n [-6, 5, -2, -3, -4],\n [3, -3, -3, 5, -2],\n [4, -2, -5, 0, -5],\n [1, -5, -3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 3, -3, 6, 1],\n [0, -5, -1, 6, 5],\n [-1, -2, 1, 5, 3],\n [5, -3, 2, -2, 1],\n [1, -4, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, -4, -1, 1],\n [-4, 1, -6, 6, 2],\n [4, 6, 0, 3, -6],\n [2, 5, 6, 0, 3],\n [0, 1, -6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -1, 2, 4, -5],\n [6, -2, 2, 5, 4],\n [-1, 3, 2, 4, -5],\n [5, 4, -5, -1, -6],\n [-2, 3, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -1, 4, 3, 4],\n [-5, 5, 2, 6, -6],\n [-4, 1, 3, 6, -5],\n [-2, 6, -4, -6, 5],\n [-1, 0, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, -4, 3, 2],\n [-3, 4, 5, -1, 4],\n [0, -6, 6, 5, -6],\n [6, -6, -4, -2, -4],\n [4, 2, 5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 3, -5, 4, -6],\n [5, 5, 6, 4, 1],\n [6, 3, 6, 1, 4],\n [-1, 5, -2, -6, 0],\n [-2, -3, -1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -1, 5, -3, -2],\n [5, 3, 5, 2, -1],\n [4, -1, 0, 4, 0],\n [-5, -5, 1, 0, -4],\n [2, -1, 3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -5, 0, -3, 5],\n [-6, 2, 0, 0, -1],\n [5, 4, -3, 1, -4],\n [4, -3, -3, 1, 5],\n [3, 2, 2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 1, -4, -6, 5],\n [5, 0, -5, 6, 2],\n [3, 4, 2, -5, 4],\n [2, 2, 4, 3, 2],\n [-3, -2, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -1, -6, 4, -2],\n [-1, 2, 6, 6, 6],\n [4, -2, -6, -4, 0],\n [-4, 3, -3, -6, 2],\n [2, -4, 5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 1, -4, 1, 1],\n [3, -4, -2, -1, -6],\n [4, -5, 0, 6, 2],\n [5, -6, 1, 4, 5],\n [6, 3, -6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -4, 6, 1, -2],\n [-3, 4, 2, -5, 1],\n [5, -5, 2, 2, -3],\n [1, -4, 5, -5, 3],\n [-2, 6, -6, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 4, -5, -2, -6],\n [-3, 0, 6, -3, 5],\n [5, -5, 2, 4, 0],\n [5, -3, -3, 6, 1],\n [-5, 1, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -3, 0, -3, -6],\n [-1, 3, 5, 5, 0],\n [-4, -5, -6, -1, -2],\n [-6, -6, 0, -5, -3],\n [-3, -6, -5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -1, 1, -4, 1],\n [-4, 4, -4, 2, 6],\n [-3, -2, -3, -6, -1],\n [4, -6, 6, -1, -6],\n [-2, 1, -4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 0, -6, 2, 4],\n [4, 2, 3, -1, -3],\n [2, -5, -2, -6, 3],\n [-5, 3, -2, -1, -2],\n [-2, 1, 3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 1, 5, -4, 4],\n [-3, 2, 6, 0, 3],\n [-2, 4, -2, 1, 3],\n [-2, 6, 6, -5, -1],\n [-4, 4, 1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -4, 1, -1, 4],\n [-5, -2, 0, 6, 4],\n [-6, -3, 3, -1, 2],\n [-2, 5, 1, -6, 4],\n [-1, 4, -6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 1, 1, -4, 5],\n [-4, 3, -5, -2, 6],\n [4, -4, -4, -5, 0],\n [-2, -3, -5, -5, 3],\n [0, 2, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 4, 5, -4, -6],\n [0, 1, -5, -1, -6],\n [-4, -4, 1, -2, 1],\n [-1, 3, 6, 5, 1],\n [-3, -3, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 5, -2, -6, 4],\n [5, -6, 6, 3, -2],\n [-6, -1, -5, 0, -3],\n [3, -5, -3, -6, -1],\n [-2, -4, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 4, 0, 4, 5],\n [0, 4, 6, -1, -2],\n [-1, 2, 6, -4, 3],\n [3, 1, 5, -1, 5],\n [0, -1, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 6, 0, -6, 3],\n [0, -3, 4, -4, 3],\n [3, -1, -4, 5, -6],\n [5, -6, 5, 3, -3],\n [2, 0, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 2, 0, -2, 2],\n [-1, -1, 0, -6, 4],\n [-6, -6, -4, 4, -6],\n [-4, 2, -3, 2, 5],\n [-4, 3, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -1, 0, 5, 2],\n [-2, 0, 3, 5, 2],\n [-6, -4, -2, -4, 5],\n [2, -5, 4, -3, 5],\n [-4, -5, 1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 6, -1, -1, -4],\n [-6, 6, 4, 5, 5],\n [0, 6, -2, 4, -2],\n [-3, -1, 0, 1, -3],\n [2, 5, -1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 0, -1, 0, 3],\n [1, -3, 0, 2, -2],\n [-6, 2, 3, 1, 2],\n [1, 0, 6, -1, -6],\n [2, -1, 5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 0, 2, 0, -3],\n [-4, 0, -2, -4, -1],\n [-2, -5, 3, 3, -2],\n [-6, 2, -2, -5, -6],\n [6, 5, -4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 3, -3, -4, -4],\n [2, 0, -4, 5, 4],\n [4, 4, -5, 2, -3],\n [4, 3, -5, -6, -1],\n [6, 2, -5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 1, -4, -5, -3],\n [-3, 1, -4, -5, -5],\n [-2, -2, -4, 6, -5],\n [4, 2, -6, 2, -5],\n [0, 6, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 5, -3, -2, 2],\n [5, 2, -1, 2, 0],\n [1, 3, -3, 1, 4],\n [4, -3, -6, 3, -1],\n [2, 1, 6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, -4, -6, -5],\n [-4, 3, 2, -1, -1],\n [2, 2, -4, 5, -1],\n [0, -3, -2, 5, -5],\n [1, -1, 2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 0, -1, 3, 0],\n [1, 0, 2, -4, -6],\n [4, 3, 3, 4, -1],\n [0, 2, -3, -2, 6],\n [0, -4, 0, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 5, 4, -3, 1],\n [-3, -1, -1, 6, 1],\n [-5, -6, 3, 0, 3],\n [-6, -1, 4, 2, -5],\n [-5, 0, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -4, -2, -1, -3],\n [3, 1, -2, 0, -2],\n [0, -6, -1, 6, -4],\n [5, -4, -6, 0, 6],\n [5, 4, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -1, -6, 3, -1],\n [-2, -1, -4, 2, -1],\n [2, 0, -1, 1, -4],\n [2, -4, -2, -1, 4],\n [5, -3, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 0, -5, 6, 6],\n [2, 6, 0, -6, -4],\n [2, -1, -6, 2, 6],\n [-4, 2, -1, -1, 6],\n [0, 0, -4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -6, -4, 4, -3],\n [-1, 1, 0, -2, 0],\n [4, 0, 1, -2, 4],\n [5, 4, 6, -1, 6],\n [3, 3, -3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -5, 0, 5, 3],\n [0, 1, -5, 3, 4],\n [-3, 4, 1, -3, -1],\n [3, -2, -4, -6, -3],\n [4, -5, -3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -2, 1, 0, 4],\n [-5, 4, 2, 6, 3],\n [6, -4, 3, -4, -5],\n [4, -1, 2, 0, 5],\n [-3, 5, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -6, 5, 0, -6],\n [0, -6, 6, 5, -3],\n [-2, -4, -5, -4, -3],\n [-5, 6, -1, -1, -4],\n [6, -4, 5, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -6, 0, 0, -6],\n [-2, -5, 5, -4, -1],\n [-2, -6, 4, 6, -1],\n [-5, 6, 6, 6, -5],\n [5, -2, -3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 6, -3, -3, 5],\n [-5, 3, 2, 3, 3],\n [3, 6, -2, 6, -4],\n [-4, 0, -4, 4, 4],\n [1, 1, -3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 0, 4, -5, 4],\n [5, 2, -5, -6, -2],\n [5, 4, 4, -6, 0],\n [-4, 1, -1, -1, -4],\n [-1, 3, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 1, -3, -3, -5],\n [2, -3, -1, -2, -6],\n [6, -5, 4, 4, -6],\n [-1, -2, -6, 3, 1],\n [-4, -4, 5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -2, -4, 3, 4],\n [6, -2, 0, -1, -4],\n [6, -6, 0, 3, 6],\n [-6, 3, -4, -4, 4],\n [3, 2, -6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -4, 2, 5, 5],\n [-2, 0, -1, 3, -3],\n [-6, -6, -6, -6, 0],\n [2, 0, 1, 1, 6],\n [5, 0, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 0, -6, -3, -3],\n [5, 6, 2, 2, -2],\n [0, 0, -5, -5, 3],\n [2, -1, 4, -4, -5],\n [3, -5, 1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 6, 5, 3, -4],\n [-1, -4, 0, 3, 5],\n [3, -6, -6, -5, -4],\n [3, 6, -2, 2, 1],\n [-4, -1, 0, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 6, -2, -6, -1],\n [-2, 6, -3, 6, -4],\n [-5, -6, -1, -6, -2],\n [-1, -6, 5, 2, -3],\n [-1, 5, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 6, 2, -6, -6],\n [2, 4, 5, -2, 1],\n [-4, 3, 0, -1, -1],\n [4, 0, 2, -4, 2],\n [0, 3, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -5, -2, -6, 1],\n [2, 6, 1, -2, 1],\n [4, 2, 5, 5, -3],\n [5, -2, 5, 0, 2],\n [-2, -5, -5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 0, -1, -5, -1],\n [-5, 0, -2, 0, -4],\n [1, -3, 2, 2, 6],\n [1, 4, -1, -2, 5],\n [-5, -3, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 1, 5, 1, -5],\n [4, 1, -6, 4, 1],\n [-1, -2, 6, -5, 0],\n [4, -5, -3, -1, 5],\n [1, -6, -5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, 2, -4, 0],\n [6, -6, -3, -4, -5],\n [4, 4, -4, 5, -1],\n [-2, 4, 5, 3, 5],\n [-1, -5, -6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 2, 5, 3, 5],\n [0, 2, -4, 3, 2],\n [1, -3, -1, -6, -1],\n [-6, -5, -4, 6, 0],\n [6, -2, -6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -2, 3, -1, -6],\n [3, -6, 6, -3, -5],\n [-4, -5, 5, -4, -2],\n [1, -6, 5, 4, -1],\n [4, 1, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 2, 0, -1, -1],\n [5, -3, 6, 5, -4],\n [3, -5, 5, 4, -1],\n [-1, 0, 1, -2, -4],\n [6, 4, 3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 0, -2, 3, -5],\n [-5, -3, -1, 1, 4],\n [1, -5, 6, -6, 3],\n [4, 4, -4, 4, 2],\n [5, -2, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -6, -6, -6, 5],\n [1, -2, -3, 1, 1],\n [3, -6, 5, 3, -4],\n [-4, -1, -6, -6, -5],\n [-6, 3, -3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 5, -5, 6, 5],\n [4, 3, -6, -1, 1],\n [2, -3, -4, 4, 5],\n [0, -4, 1, 6, 0],\n [-6, 6, 4, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -6, 1, -2, 2],\n [5, -3, -2, -6, -4],\n [-2, 5, -4, 6, -5],\n [-2, 2, -2, -3, -1],\n [3, 0, -5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 1, 6, -5, -3],\n [5, -2, -2, 4, -3],\n [-4, 4, 0, 2, -5],\n [4, -4, -2, 5, -1],\n [5, -5, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -1, 0, -5, -3],\n [1, -5, 5, -3, -3],\n [5, 1, 3, 2, -4],\n [-1, -3, -1, -2, -2],\n [5, 5, 4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -5, -6, -4, -4],\n [-1, 4, 6, 2, 6],\n [6, -4, -3, 4, -3],\n [-1, 1, -5, -1, -6],\n [6, 4, 4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, 2, -2, -1],\n [0, -5, 2, -2, 0],\n [-1, -2, -1, 5, 4],\n [5, -2, -2, -4, 3],\n [0, -6, 4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 2, -4, -2, 2],\n [3, -5, -4, 6, -3],\n [-2, -3, -5, 5, 3],\n [3, 6, -5, -3, -1],\n [-5, 4, 6, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 2, 0, 3, 5],\n [-3, 5, -1, 4, 5],\n [3, -6, -2, -2, 5],\n [-5, 0, 6, 2, 6],\n [4, 0, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -1, 1, -3, -1],\n [-5, 5, 1, -5, -5],\n [-5, -1, 1, -5, -5],\n [3, 3, 2, 6, 6],\n [-4, 1, 0, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -2, -4, -4, 4],\n [-1, 3, -2, 0, 2],\n [2, 1, -5, -4, -2],\n [-5, 0, 4, 5, 3],\n [-3, 0, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 1, 1, 0, 5],\n [1, -4, 0, -5, 0],\n [2, -6, -5, -3, 2],\n [-1, 3, -2, -2, -6],\n [3, -2, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -6, 6, -1, -3],\n [0, 1, 5, 2, -2],\n [5, -4, 3, 1, 5],\n [0, -5, 3, -1, 3],\n [-6, -5, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, -3, 5, -1],\n [-2, 2, -6, -2, 6],\n [-6, 5, 4, 0, -4],\n [-4, 0, -6, 4, 6],\n [5, 5, 3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, -6, -5, 5],\n [3, 6, -4, 4, 2],\n [-6, 4, 0, -6, 2],\n [4, 2, 2, 1, -3],\n [-5, 0, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 5, 4, -4, -1],\n [6, -5, -5, 1, 1],\n [-6, 6, 0, 3, -3],\n [3, 0, 1, 1, 6],\n [-2, 3, -3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 1, 3, 5, 2],\n [-5, -3, -6, 3, 0],\n [0, 3, -1, -5, 4],\n [-6, 2, 4, 1, 2],\n [-6, -6, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -3, 3, 5, 1],\n [2, 3, 5, 6, -3],\n [0, -1, 6, -3, -6],\n [2, -4, -1, 1, -4],\n [1, 6, -1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 2, 4, -3, -3],\n [4, 3, -5, 0, -6],\n [6, 5, -3, 5, 2],\n [-1, -5, 5, 5, -5],\n [6, 2, 0, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -5, -2, 0, -2],\n [0, 4, 0, 3, -3],\n [-1, -5, 6, -5, 5],\n [-3, -3, -5, -6, -1],\n [3, -3, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -4, 6, 4, 0],\n [-3, 2, 5, -1, 2],\n [-6, 0, 2, 0, -4],\n [5, -3, 3, -2, 0],\n [6, 5, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 5, 5, 2, 3],\n [0, -1, 1, 5, -1],\n [5, 2, -6, 4, -5],\n [2, 5, -3, -5, 4],\n [-3, 5, -5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -3, -2, 6, 6],\n [-5, -2, -1, 4, 3],\n [0, 1, -1, 5, 2],\n [3, 5, -4, 0, -5],\n [1, -2, 3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -1, -2, -2, -2],\n [1, -1, 5, -1, 3],\n [-3, -2, 5, -4, 0],\n [1, 1, 6, -5, 4],\n [-3, 6, 4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -2, -2, 3, 2],\n [4, -1, -6, -1, 1],\n [-4, 2, -3, 0, 4],\n [6, 4, 4, -6, -1],\n [5, -6, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -1, 3, -3, -1],\n [-6, -5, 0, 6, -1],\n [-4, 2, -1, 1, -5],\n [4, 3, 0, 4, 0],\n [-6, -5, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 2, 0, -2, 4],\n [3, 1, 2, 0, 5],\n [-1, 4, -5, 3, -5],\n [-4, 0, 1, 2, 6],\n [-6, 3, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -1, -3, 3, -1],\n [5, 1, -2, -3, 5],\n [-3, -4, 1, -4, -1],\n [4, 4, -1, 1, -1],\n [6, -5, -6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 5, -4, -3, -6],\n [-3, -2, 1, 4, 6],\n [2, -2, 6, 3, -2],\n [2, -6, 4, 4, 6],\n [-6, -1, -6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 5, -4, 2, -5],\n [-4, 3, -6, -5, -6],\n [-4, -6, -4, -3, -4],\n [3, -4, 3, 5, -6],\n [1, 6, 2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -4, 6, -4, -6],\n [0, 1, -6, -1, 5],\n [-4, -4, 4, 6, 2],\n [-2, -6, -3, -2, 1],\n [-3, -3, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 6, -1, 4, -5],\n [6, -1, -3, 6, -4],\n [-6, -2, -4, -3, 4],\n [-4, 6, -6, 2, 6],\n [3, 2, 2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 1, 0, 5, -3],\n [2, 0, 3, 3, 3],\n [1, 0, 0, -6, 3],\n [4, 6, -2, -5, -1],\n [-4, 0, 6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 6, -6, 6, 4],\n [-3, -4, 5, -2, -3],\n [6, 1, 5, 5, 4],\n [-3, 1, -3, 3, -1],\n [-4, 1, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, 2, -3, 6],\n [-6, 6, 0, 5, 2],\n [-4, -6, 4, 5, 1],\n [-3, 6, -4, 2, -5],\n [-3, 2, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 5, -6, -4, 5],\n [-6, -6, 4, 6, -4],\n [0, -2, -1, -3, -5],\n [-6, 6, -3, 5, -6],\n [6, -6, 1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -6, -4, -1, -4],\n [4, 4, 2, -2, 0],\n [-3, 1, -4, -6, 5],\n [4, 1, 5, 6, 3],\n [3, 1, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 2, 5, -3, -6],\n [-4, 4, 4, -1, -6],\n [6, -1, 4, -5, -3],\n [-6, -1, -1, 5, 4],\n [5, 2, -2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, 4, -2, -2],\n [3, 3, -4, -1, 1],\n [2, 4, -1, 0, -3],\n [-4, -2, 5, 5, 4],\n [-6, -5, 5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 2, -4, 4, 5],\n [4, -4, 2, 2, -6],\n [0, -6, -2, 2, 2],\n [-3, 0, 4, -2, 4],\n [1, 0, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 0, 0, 0, -4],\n [-3, 6, -5, 6, 6],\n [5, 2, -2, 3, -5],\n [1, -2, -6, 0, -5],\n [3, -4, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -3, 6, 6, 1],\n [1, 2, 3, 2, -2],\n [-5, -5, -2, -1, 5],\n [0, -1, -3, -4, -1],\n [-4, -4, -1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 2, -6, -2, -6],\n [-6, -1, -5, -3, -2],\n [-3, -6, -6, -4, 4],\n [-2, -1, 2, -2, -2],\n [0, -2, 0, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 3, 3, 5, 6],\n [3, -3, -3, -1, -6],\n [0, -2, 4, -3, 0],\n [-6, -5, 5, -4, 1],\n [-6, 5, 3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, -1, -3, -2],\n [1, 0, -3, -2, 6],\n [-5, -6, -5, 3, 4],\n [4, 6, -2, 4, -5],\n [4, -3, 2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 1, 2, 2, 3],\n [5, -5, 0, -5, -2],\n [3, 6, 3, -2, 1],\n [-5, 0, 6, 2, -6],\n [1, -2, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -3, 5, 5, 5],\n [-1, 1, 3, 4, -3],\n [-5, -2, -6, -1, 1],\n [5, 6, -4, 4, 5],\n [6, -1, -3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 1, -4, 4, 3],\n [5, 3, -1, -3, -4],\n [-1, 0, -2, 3, 1],\n [6, -6, 4, 0, -1],\n [6, 1, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -6, 3, 0, -5],\n [6, -4, -1, -2, -3],\n [5, 3, -1, 1, 0],\n [-5, 0, 1, -5, -2],\n [1, -3, -6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -2, -5, -4, 6],\n [4, 2, 5, 2, 0],\n [6, 0, -2, 2, 6],\n [1, -6, -5, -4, -3],\n [-5, -4, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 6, 6, -6, -5],\n [-5, -4, -6, -6, -2],\n [1, -3, -1, -1, -5],\n [6, 0, -2, -5, 5],\n [-1, 2, -4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 1, 3, 1, 0],\n [-6, -6, -5, 1, 0],\n [2, 3, 6, 5, 2],\n [1, 0, -5, 6, -2],\n [3, -5, 5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -4, 6, 4, -5],\n [2, 1, 2, -1, 4],\n [6, -2, -4, 3, 3],\n [-6, 5, 3, 0, -1],\n [-2, -5, -3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, 6, 1, -4],\n [-5, 6, 6, 5, 1],\n [2, -1, -5, 0, 0],\n [-1, -2, 6, 5, 2],\n [-1, 4, 1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -5, -4, -3, 1],\n [3, -5, -6, 1, 6],\n [0, -2, -3, 3, 6],\n [-1, -4, -3, -3, -1],\n [1, -5, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 2, 3, -4, -4],\n [5, -2, -4, -4, -6],\n [-2, 0, -4, 4, -6],\n [5, -5, 4, 4, 5],\n [6, 3, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -1, 6, 4, 4],\n [6, -6, 2, 2, -1],\n [-4, 4, 6, 5, 2],\n [5, 4, -1, -2, -1],\n [5, 4, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -2, 2, 1, -6],\n [0, -2, -1, 2, 6],\n [-6, -5, -4, 2, -3],\n [-1, -5, -6, -6, 2],\n [-6, -6, -3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 2, 6, 3, 1],\n [4, -1, 0, 1, 0],\n [-5, 1, 0, 3, 0],\n [-1, 0, 4, -4, 0],\n [-5, -2, -4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 4, 2, 0, -6],\n [-2, -2, -2, -4, 1],\n [6, -3, 3, -1, 3],\n [3, -4, -1, 1, 1],\n [-6, -3, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 1, 1, 4, 3],\n [4, -2, 3, -4, -2],\n [-4, 5, -1, 0, 4],\n [0, -1, 4, 3, 0],\n [0, 6, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -2, 4, 5, 3],\n [2, 5, 3, -5, 1],\n [3, -5, -4, -2, 1],\n [-2, 2, -5, 0, 0],\n [6, -4, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 4, -6, 4, -5],\n [5, -2, 4, -1, -2],\n [6, -6, 5, -3, -6],\n [-4, -5, 3, -6, 5],\n [-1, 4, 6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -6, -4, 3, -3],\n [-4, 6, -5, 4, -4],\n [-3, 3, 6, 4, 2],\n [-1, -6, 0, -2, -4],\n [-6, -5, -5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 1, -4, -5, 1],\n [-5, 6, 6, 2, -1],\n [0, -1, -4, 2, 6],\n [2, -5, 0, 0, -3],\n [6, 1, -3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 5, -5, -6, -6],\n [-2, 2, 4, 6, -1],\n [-5, -2, 1, -1, 3],\n [1, -3, 2, -6, 2],\n [6, 3, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 1, -4, 2, -5],\n [-6, 0, -3, 2, 5],\n [6, 2, 2, -4, 5],\n [-4, -2, -1, 2, -4],\n [4, 3, 6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 4, 4, 2, 6],\n [-3, 4, -5, 4, 4],\n [-3, 2, 4, -3, 6],\n [-1, -3, -3, -1, 4],\n [-1, -3, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 5, -2, -4, 3],\n [4, -5, 6, 4, -3],\n [-5, -2, 1, -5, 0],\n [-1, -4, 4, -5, -2],\n [2, 4, 5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, -2, 0, 4],\n [-6, 5, 5, -2, 0],\n [-4, 6, 6, 1, -3],\n [3, -1, -5, 0, -6],\n [-2, 4, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -6, 5, 6, -2],\n [-4, 3, 1, 3, 1],\n [1, 2, -3, -2, -5],\n [-1, 0, -2, 2, 4],\n [4, 5, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -4, -4, 3, 6],\n [1, 5, 4, 4, 5],\n [3, -6, 4, -1, 1],\n [-3, -2, 3, 2, -4],\n [5, 6, 4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 6, -5, -3, 6],\n [2, 0, 6, 5, -6],\n [0, 1, 4, 3, 5],\n [-3, -4, 0, 0, 1],\n [0, -4, 0, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 2, 2, 4, -6],\n [5, 1, 6, 6, 0],\n [-5, -6, 2, 5, -5],\n [3, 3, 5, -1, -5],\n [0, -6, -6, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 2, -4, 4, 4],\n [-6, 0, -3, -6, -2],\n [-3, 2, 6, -3, 4],\n [-4, 2, -5, -5, 0],\n [1, -4, 3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 6, -5, -4, -2],\n [-6, -2, 0, 3, -4],\n [6, 3, -6, 6, 5],\n [1, -6, -5, 2, -6],\n [0, -6, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 6, -3, -3, 3],\n [-1, 0, -6, 5, 3],\n [0, 3, -1, -2, 6],\n [5, -4, 3, 5, -4],\n [-6, -2, 3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, -6, 3, -2],\n [3, 3, -1, -4, 3],\n [6, -5, 0, 4, -4],\n [5, 1, 0, -5, 2],\n [5, -6, -4, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -4, 6, -1, -4],\n [-3, -2, -2, 5, 1],\n [-6, 6, 4, -6, -1],\n [5, 2, -6, -4, 2],\n [3, 1, -5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 0, -1, 2, 5],\n [5, 6, 1, 0, -5],\n [-5, 4, -3, -2, 4],\n [-6, 0, -3, -3, -6],\n [-6, 3, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 3, 1, -1, 4],\n [-6, 3, 6, 5, -6],\n [4, 2, 0, -2, 1],\n [1, -1, -4, 3, 1],\n [5, -4, 0, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 0, 0, -1, -3],\n [0, -3, 6, 4, 0],\n [3, 2, -5, -2, -3],\n [6, -3, -4, 0, 1],\n [-3, 5, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 6, -1, 6, 3],\n [-5, -1, 1, -6, -5],\n [2, -6, -1, 0, 4],\n [5, -2, -3, 0, -2],\n [6, -4, 2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 3, 6, -2, 1],\n [-3, 6, -4, 2, -5],\n [6, 0, 6, 1, -1],\n [-6, -2, 6, -2, 5],\n [-4, 6, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -1, -1, -5, 5],\n [5, -2, 1, -5, 6],\n [4, -3, -6, -5, 3],\n [-3, -5, 4, -1, -1],\n [-1, -6, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -1, 6, 1, -5],\n [-2, -1, -4, 6, -4],\n [5, -6, 4, 2, 4],\n [-4, -3, 4, 0, 1],\n [-3, 6, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 2, -3, 5, 5],\n [3, -6, -3, 3, 0],\n [6, 1, 5, 2, 0],\n [2, -6, 6, 0, 3],\n [0, -4, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -5, 3, -5, 3],\n [-4, -3, 0, 5, -6],\n [-4, 3, 5, -1, 4],\n [-5, 1, 5, 2, -3],\n [4, 1, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 4, 5, -4, -5],\n [-5, 0, -4, 5, -1],\n [3, 3, 2, 4, -4],\n [-6, 5, -2, 4, 3],\n [4, 0, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -5, -1, 2, 3],\n [0, 1, 3, -4, 3],\n [-1, 5, 6, -5, -5],\n [1, 1, 1, -5, -2],\n [-2, 3, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 3, 6, 1, 4],\n [6, 2, -3, 0, 1],\n [2, 6, 1, 3, -1],\n [3, 5, 4, -5, -6],\n [-2, -5, 6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -6, 5, 5, -2],\n [3, 2, -2, 6, 3],\n [-1, 6, -6, 6, -2],\n [-1, 4, 3, -2, 6],\n [0, 1, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 0, 0, -1, -2],\n [6, -5, -3, 1, -1],\n [4, -5, -2, 1, 3],\n [5, 3, 2, 3, -5],\n [-3, -3, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, -1, 5, 6],\n [3, 4, -4, 2, -4],\n [-3, -3, 1, -6, -5],\n [4, 1, 5, 0, -4],\n [2, 4, 3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -2, -6, 4, 0],\n [5, -1, -3, 4, 5],\n [0, 0, 2, 2, 5],\n [-4, -4, -3, 2, 4],\n [1, 2, 6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -2, 4, 1, 5],\n [4, -1, -6, -3, 1],\n [-2, 0, -1, 2, 6],\n [-5, -1, -3, 0, -6],\n [6, 6, 6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 6, 0, -1, -1],\n [-5, 1, -3, 4, -4],\n [6, -2, -5, 2, 6],\n [3, 3, -2, -4, 0],\n [-4, 2, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -1, -6, -5, -6],\n [-5, 5, -3, 3, -3],\n [0, 2, 3, 2, 1],\n [1, 1, 6, -4, 1],\n [3, 3, 1, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -6, 6, 6, 4],\n [2, 2, -1, -2, -2],\n [4, -4, -5, 0, 1],\n [2, 0, -1, 3, -1],\n [6, -2, 6, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 6, -2, -2, -3],\n [2, 6, -5, 5, 1],\n [-5, -1, -3, 1, 1],\n [-1, 2, 0, -6, 6],\n [-2, -2, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -3, -4, -6, 3],\n [-3, -3, -6, -5, -1],\n [1, 0, 4, 4, -6],\n [-2, 4, 4, -4, -5],\n [-3, -4, -6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 5, -5, -1, 5],\n [2, 5, 0, -4, -6],\n [1, -4, -1, 3, 1],\n [-6, 4, 5, 0, -1],\n [2, -4, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 6, 0, 5, -4],\n [6, 4, -6, 5, 0],\n [-5, -4, -6, -4, 6],\n [2, 6, 3, 6, 0],\n [0, 3, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 1, 1, 2, 2],\n [-2, -3, -3, -4, 1],\n [-5, -5, -6, -1, 6],\n [2, 5, 3, -4, 5],\n [2, -4, 5, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, -4, -3, 5],\n [-1, -2, -5, 6, -1],\n [0, 5, 0, -2, -3],\n [-2, 0, 2, 6, -2],\n [-4, -2, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 1, -3, -5, -2],\n [-3, 0, -6, -5, 6],\n [6, -5, -2, 5, -5],\n [0, -4, 5, -6, 4],\n [-1, 4, -1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 6, -2, 0, -1],\n [-1, 0, -5, -4, -2],\n [-1, 3, -2, -5, 3],\n [2, 3, -3, 3, -1],\n [-3, -2, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -5, -6, 2, -4],\n [5, -4, -3, 1, 4],\n [3, 5, 6, -3, 6],\n [-2, 2, 4, 2, -6],\n [-5, 3, 6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -5, 2, 4, -5],\n [4, 6, 2, 4, 4],\n [-5, -3, 2, 2, -5],\n [2, 4, 5, 6, -5],\n [-6, -3, 4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -4, -5, -6, 5],\n [0, 4, 6, 6, -6],\n [3, -5, 6, 5, -2],\n [5, -4, -4, -1, 1],\n [6, 3, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -2, 2, 5, 0],\n [6, -4, 2, 6, 5],\n [-3, 1, 3, -1, 0],\n [0, -3, 4, -3, -1],\n [6, -1, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -5, 6, -4, -6],\n [4, 3, -4, -3, -1],\n [-3, 3, -4, 6, -6],\n [6, 2, -5, -1, 4],\n [-4, 3, -6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -4, -4, 0, 3],\n [5, -5, 6, -6, 4],\n [3, -6, -4, -6, 5],\n [-4, 1, 3, -6, 0],\n [2, 5, 6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -4, 5, -4, -4],\n [5, 5, 3, 1, 1],\n [-5, -5, 3, -1, 2],\n [0, -1, 0, -6, 6],\n [5, -3, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 3, -5, -4, 3],\n [-3, 3, 5, -3, -1],\n [0, 4, 3, 3, -3],\n [1, 6, -6, 6, -5],\n [1, -6, 3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 1, -2, -3, -2],\n [-2, -6, 2, -1, 2],\n [4, 2, 5, 1, 1],\n [-5, 0, 2, 4, 2],\n [0, 1, 0, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -1, -1, -2, 3],\n [4, -1, -1, 5, -4],\n [-4, 4, 4, -6, -1],\n [-3, -5, 1, 6, 0],\n [-1, 4, 5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -1, 1, -2, -6],\n [-1, 0, 3, 2, 1],\n [-3, 1, 2, -5, -1],\n [2, -1, -4, -3, 1],\n [-4, 0, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 1, 0, -3, 0],\n [2, 5, -3, 3, -4],\n [-2, 1, 5, 2, -6],\n [4, -4, 1, -5, 3],\n [0, 0, 3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 0, 1, 5, 1],\n [-3, -2, 0, -4, 5],\n [0, -6, 3, 2, 1],\n [6, -3, -4, -6, 6],\n [-6, -5, 1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 5, 6, -2],\n [6, -6, -3, 0, 5],\n [-5, 3, -3, -2, 2],\n [-1, -1, 1, -5, 3],\n [6, 2, 1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, -3, -1, -4],\n [-6, 6, 3, 3, 3],\n [5, 6, -1, -5, 1],\n [2, 3, 5, -2, -2],\n [0, -4, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -3, -1, 0, -4],\n [-6, 2, -2, 6, 1],\n [6, -2, -1, 1, -1],\n [2, 3, 0, 1, -3],\n [-2, 4, -5, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -4, 6, 0, 4],\n [5, -4, 5, 1, -6],\n [4, 5, 5, 0, -2],\n [4, -4, -4, 0, 1],\n [3, -6, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -6, -6, 4, 4],\n [1, 1, 6, -5, 0],\n [4, 4, 4, -4, -6],\n [-4, 0, -1, -6, -3],\n [-2, -2, 3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 5, 5, 0, -1],\n [-1, -5, -4, 2, -1],\n [2, 1, -5, -4, 1],\n [1, 2, -4, 6, 6],\n [-3, 1, 3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, -4, 0, -6],\n [-4, -3, 2, 5, 6],\n [-1, 6, -3, -2, -4],\n [6, 3, 3, 1, -1],\n [-3, 0, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, -5, -5, 4],\n [-5, 3, -2, 4, 3],\n [-2, -6, 5, 6, -4],\n [-4, -6, 2, -4, -5],\n [-6, 2, 4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -2, 6, 4, -6],\n [0, -3, -1, 6, -3],\n [6, 0, -6, -3, -3],\n [-2, 4, 3, 2, 3],\n [3, 4, 3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 5, -5, 5, 5],\n [-1, -2, 6, 4, -3],\n [4, -4, -4, -6, -1],\n [5, 4, 5, 1, 3],\n [-4, -1, 1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 2, -5, -2, -1],\n [2, 2, 2, 4, 1],\n [-2, -5, -3, -4, 1],\n [-2, -4, -4, -1, 4],\n [-3, -2, 2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -5, -1, 1, -3],\n [0, -2, 3, -3, -6],\n [3, -1, -3, 4, -6],\n [-1, 3, 3, -3, 4],\n [-4, -5, 2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 5, 2, 1, -4],\n [-2, 4, 4, -6, 2],\n [-2, 5, 6, 1, -2],\n [6, 1, -5, 1, 4],\n [5, -2, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 6, 6, 2, 1],\n [5, 3, -6, -1, -2],\n [-6, -5, 3, 5, 0],\n [2, -6, 1, 2, -3],\n [-1, 0, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 3, -4, 1, 4],\n [3, 2, -4, -4, 4],\n [2, -5, -5, -6, -2],\n [4, 3, -5, 3, -3],\n [-6, 5, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -2, -4, -1, -1],\n [6, -4, -1, -2, -5],\n [-6, 0, 3, -3, 6],\n [5, 6, 0, 4, -2],\n [0, -6, -6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, 6, 1, 4],\n [6, 2, 0, 0, 5],\n [4, 3, -3, 0, 4],\n [4, 3, 2, 3, 0],\n [1, 2, 5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 3, 2, 0, 3],\n [-4, 6, -3, 0, -6],\n [0, 6, 2, -5, 5],\n [1, -3, -2, 4, -2],\n [-5, 5, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 6, -5, -6, 6],\n [-4, 1, 3, -6, -4],\n [-3, -6, -6, -5, -1],\n [3, -3, -4, 0, 0],\n [-5, 3, 0, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -2, -6, -5, -4],\n [2, 0, 6, 2, -5],\n [-5, 4, 4, 6, 0],\n [0, -1, 1, 0, 1],\n [-3, -2, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 1, 6, 2, -1],\n [-1, -4, -4, 2, -6],\n [6, -3, 6, 2, -1],\n [4, 3, 4, 6, -5],\n [2, 2, -6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, -6, 2, -2],\n [-2, 5, -4, -4, 1],\n [-1, 3, -4, -5, 2],\n [-4, -1, 3, -1, -4],\n [5, -5, 6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, -6, 4, -1],\n [-3, 0, 5, -3, 1],\n [6, -4, -2, -3, 2],\n [5, -6, 6, 1, -1],\n [5, -1, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 5, -5, -6, -6],\n [4, -3, 3, -4, 4],\n [1, 0, -4, 3, 3],\n [-3, -4, 3, -3, -1],\n [1, -2, -5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -6, 0, -5, 1],\n [6, -4, 1, -3, -3],\n [0, 6, -2, -2, -5],\n [4, -2, 3, -5, 0],\n [2, 2, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -3, -1, 2, -6],\n [4, -4, 5, -4, -6],\n [-4, -1, 5, 3, -3],\n [3, -4, -3, 6, -1],\n [2, 0, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -3, -5, -1, -4],\n [-4, 0, 4, 2, 3],\n [-5, 5, -2, -3, -6],\n [4, 6, -4, -4, 1],\n [-5, -3, -5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, 1, 2, 1],\n [-3, 1, 5, 4, 4],\n [-3, -4, -3, 4, -6],\n [2, -1, 0, 2, 3],\n [1, 6, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -4, -5, 1, 4],\n [-2, -6, 0, -4, 0],\n [3, 2, -4, -5, 3],\n [-4, -1, -6, -2, 2],\n [5, 1, -2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -2, -2, -6, 0],\n [2, 0, -5, -6, 3],\n [-4, 4, 2, -1, 5],\n [0, 6, -4, 4, 5],\n [-3, 0, 6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, 1, 5, -6],\n [5, 6, 4, 0, -3],\n [1, 1, 0, 5, -4],\n [-5, -2, -1, -4, -6],\n [3, -4, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -5, 0, -6, 3],\n [3, 3, 6, 4, -5],\n [0, -3, -4, -1, -3],\n [-4, -6, -6, -4, 1],\n [-6, -1, -2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 5, -5, 5, -2],\n [6, 0, 6, -5, 5],\n [0, -2, 0, -6, 4],\n [4, 6, 1, 6, -4],\n [-1, 3, 0, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -2, -3, -1, 2],\n [3, -2, -3, 1, 4],\n [-4, 2, -6, -6, 5],\n [-2, -6, 4, 6, 1],\n [0, -4, 1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 3, -2, -6, 3],\n [-3, -6, -1, -2, 6],\n [0, 3, 5, 2, 6],\n [-3, 2, 5, 3, 4],\n [-2, 5, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 5, -1, 6, 6],\n [-6, -6, -2, 3, -6],\n [-4, 5, 6, 5, -5],\n [-6, -3, 1, 2, -4],\n [4, -2, -5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -5, 3, 2, -2],\n [5, -6, 0, 2, -6],\n [-6, 6, 6, -2, 5],\n [-4, 1, 5, -1, 0],\n [2, -6, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -5, 3, 6, -3],\n [-5, 3, 5, 4, -6],\n [-2, -5, -2, -2, 1],\n [-2, -4, -3, 0, -4],\n [-6, 4, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -4, 4, 5, 1],\n [1, 4, -3, 4, 2],\n [2, -2, -1, 6, 2],\n [4, -6, 0, -5, 4],\n [0, 6, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, -1, -4, 6],\n [-2, -2, -6, -1, -1],\n [-5, 3, 5, 2, 2],\n [-6, -4, -5, -1, -2],\n [5, -4, 6, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, 5, 4, 1],\n [0, -2, 5, -2, -3],\n [-4, 2, -3, -1, 6],\n [-1, 0, 4, -4, -6],\n [4, -6, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -3, -6, 5, 2],\n [-3, -3, 3, -5, 5],\n [2, 2, -4, 6, 2],\n [1, -4, -1, 1, -6],\n [3, 5, 6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -5, -4, 4, 6],\n [5, 0, 1, 5, -6],\n [-6, 2, -6, 4, 5],\n [-4, 1, 4, -2, 6],\n [6, 4, -1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -5, -4, 4, 4],\n [-3, 1, -1, -1, 1],\n [2, 5, -3, -2, 6],\n [6, -4, 2, 5, -5],\n [-6, -6, -6, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -3, 1, 5, 1],\n [0, -6, -4, -6, 4],\n [4, -5, -2, -4, -5],\n [-2, -3, 0, 1, -1],\n [2, -2, 2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, 3, 2, 4],\n [-5, -2, -1, -4, 3],\n [-1, -3, -5, 1, -5],\n [4, -4, 3, -5, 5],\n [4, 5, 6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 1, -2, 2, 4],\n [-3, 1, -6, 2, -5],\n [-4, 2, -6, 1, -1],\n [6, -3, 2, 2, -2],\n [5, -5, 5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 6, -4, 6, 6],\n [-4, 1, -5, -4, -6],\n [-6, 0, 2, -2, 2],\n [-4, -1, -2, -5, 5],\n [5, -1, 6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 3, 4, -6, -5],\n [0, 1, -3, 2, 5],\n [-4, 6, 5, 5, 3],\n [-1, 3, -1, -1, 6],\n [1, -3, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 4, 3, -6, 2],\n [-4, -3, 5, -4, -4],\n [3, -2, -3, 0, 2],\n [1, -3, 4, -1, 4],\n [1, -3, 4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 2, -6, -5, 0],\n [2, -1, 1, -1, -2],\n [3, 2, 6, 6, 5],\n [3, 5, -3, 0, -3],\n [-2, 4, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 5, 0, -5, 0],\n [3, 6, -4, -1, 5],\n [-3, 1, 2, -5, 5],\n [-6, -1, 0, 5, -1],\n [6, 4, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 5, 4, 6, 4],\n [5, -3, 1, 0, 2],\n [3, 1, -3, -4, -2],\n [-1, 3, -6, -3, 5],\n [-2, 0, -1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 3, -3, 3, -5],\n [-6, -1, 2, -2, -3],\n [-6, -3, 6, -3, -1],\n [1, 6, 1, -6, 3],\n [4, 5, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 3, -5, 0, 5],\n [-3, 0, 4, 2, 0],\n [4, 4, -4, 0, -3],\n [4, -2, 3, -5, -2],\n [-3, -5, -6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, -3, -3, -4],\n [0, -6, -3, -1, -1],\n [-2, -6, 1, -6, 5],\n [3, 1, 5, 4, 1],\n [2, 4, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 6, 3, -2, 4],\n [5, 4, 4, 5, 0],\n [1, 2, -6, 6, 3],\n [6, 5, 0, 2, 6],\n [6, -3, 4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -2, 5, 6, 5],\n [-2, 4, 1, -6, -6],\n [2, 5, 3, 5, 1],\n [0, -3, 5, -5, 5],\n [4, -5, -6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 4, -5, -6, 1],\n [4, -2, -3, 0, -5],\n [-4, 0, -4, 1, 2],\n [6, -2, 1, 0, -1],\n [1, -6, -1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -3, 1, -3, 2],\n [-6, -2, -5, 3, 4],\n [2, 1, 2, -1, 1],\n [0, 4, 6, 5, -1],\n [2, 4, -5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 5, 0, -2, 5],\n [2, 5, 2, 1, 1],\n [-1, 0, 5, -1, 3],\n [-5, 4, -1, 2, 4],\n [-4, 2, 5, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 6, -2, -4, -2],\n [2, -1, -5, -6, 4],\n [3, 4, 6, 2, 2],\n [-6, 4, 3, 4, 1],\n [-2, -3, 3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 3, 1, -2, -5],\n [0, -6, 0, 3, 5],\n [-6, -2, -6, -2, -4],\n [0, 2, 3, 4, 0],\n [-3, -2, 1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -2, -2, -1, 1],\n [-4, 0, 2, 1, 6],\n [6, 3, 6, -1, 5],\n [0, 6, 0, 6, -4],\n [0, 3, -3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 6, 2, 5, 4],\n [-5, -1, -5, -6, -3],\n [0, -4, 0, -1, 5],\n [-5, 1, 6, 2, 6],\n [-1, 1, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -5, -4, 1, 0],\n [6, 6, -5, 2, 3],\n [4, -1, -4, 3, 1],\n [1, -6, 2, -5, -5],\n [5, 0, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -2, -3, 2, -3],\n [5, 2, 0, 3, 6],\n [0, -4, -1, -3, -4],\n [4, 1, -2, -6, -3],\n [0, -1, -1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -1, -3, 1, 2],\n [6, 5, 4, -1, 6],\n [-4, 1, -6, 3, 1],\n [-5, -1, -4, -3, 0],\n [5, 0, -4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -1, 0, 1, -3],\n [1, -2, -2, -2, -3],\n [0, -4, -6, 0, -4],\n [-5, 4, 3, -1, -2],\n [1, 3, 4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 6, 4, 2, 1],\n [-3, -2, -2, -3, 6],\n [1, 4, -2, -6, -2],\n [2, 1, 4, 4, -3],\n [-2, -6, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 3, -6, 3, 4],\n [-4, 5, 5, -6, 5],\n [-1, -1, 2, -1, 5],\n [3, 2, -4, 2, -5],\n [0, -2, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, -4, -3, -5],\n [-3, -3, -1, 0, 0],\n [4, -4, -4, 0, 0],\n [-4, -5, 6, 6, 2],\n [-6, 1, 3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 0, -3, 5, 4],\n [1, -3, 1, -1, -1],\n [5, 4, 0, 4, -3],\n [1, 2, -4, -2, -6],\n [-6, -2, -1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -2, -1, -2, -5],\n [-2, 6, 2, -2, 6],\n [6, 5, 1, -1, 3],\n [6, -1, 5, -5, 2],\n [-5, -6, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -4, -1, -1, 2],\n [-4, 3, -3, 1, 1],\n [-4, -1, 6, 6, 0],\n [1, 2, 5, 3, 3],\n [0, 1, -4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 3, 6, 5, 1],\n [-5, 1, 2, 3, -2],\n [0, 6, -2, 0, -6],\n [-5, 1, -5, -4, 2],\n [3, 0, 5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -4, 6, 2, -3],\n [0, 2, -2, 6, -2],\n [-1, -3, -5, -4, 0],\n [-1, -1, 4, 0, 4],\n [2, 4, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -1, 6, 6, 2],\n [-3, 4, -2, -4, -2],\n [4, -3, -4, -6, -3],\n [6, -2, -6, 0, 4],\n [5, -5, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 4, -5, -2, 6],\n [-5, 3, -5, -1, 4],\n [5, 0, 1, 1, -1],\n [2, -3, -1, 1, 3],\n [4, -5, 0, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -4, -3, 2, 5],\n [-6, -4, -4, -6, 3],\n [-1, -5, 4, -1, -3],\n [1, 3, -6, 6, 2],\n [-2, -2, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, -5, 5, -3],\n [1, 2, -6, 2, 5],\n [2, -6, -2, 4, -3],\n [3, 0, 4, -1, 6],\n [1, -4, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, 1, 4, 6],\n [5, 2, 4, -5, 2],\n [6, -4, 6, 2, 5],\n [-6, 1, 6, 1, 4],\n [-2, -4, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, -1, -4, -4],\n [-6, 2, 6, -5, 0],\n [1, 2, 4, -6, 2],\n [0, -5, 4, -6, -6],\n [4, 5, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, 1, -5, 5],\n [6, 4, 0, 0, 1],\n [-4, 6, -4, -2, 4],\n [2, -4, 1, 4, -6],\n [5, -2, 6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 0, -2, -3, 1],\n [0, 6, 6, 1, -2],\n [-3, 2, -1, -2, -4],\n [-5, 6, 1, 1, 6],\n [-6, -2, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 6, 5, 5, -4],\n [0, -4, 2, -6, -1],\n [1, -1, -5, 1, -5],\n [0, -3, 0, -3, -6],\n [4, 6, 0, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 4, 0, 4, 2],\n [-3, 3, 4, 2, 4],\n [-1, 3, -3, 3, -6],\n [-4, -4, -1, 2, 1],\n [3, 0, 4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 2, 1, -3, 4],\n [5, -5, 1, 2, 3],\n [-5, 2, -5, 4, -3],\n [6, 3, -3, 6, -4],\n [5, -3, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 3, 5, -5, -5],\n [0, -2, 1, 3, -5],\n [0, -1, -1, 3, 2],\n [5, 4, -5, 3, -3],\n [-3, 1, 0, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -1, -3, -6, -6],\n [-6, 1, -2, 4, -1],\n [4, 6, 3, -2, 3],\n [-2, -2, 2, 3, 6],\n [-6, -4, -2, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 0, 4, -3, 5],\n [-3, 0, -6, -2, 1],\n [6, 1, -2, -6, -3],\n [-6, -2, 1, 3, 6],\n [-6, 3, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, -4, -3, 2],\n [1, -6, 6, -2, 4],\n [3, -4, 1, 0, 6],\n [-3, 1, 1, 2, -4],\n [-2, 2, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, -1, 2, -1],\n [-2, 2, -5, 0, -5],\n [-3, -3, -1, -4, -1],\n [-2, 1, 2, 5, 0],\n [5, 0, 4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, 4, 4, -6],\n [3, 6, 6, 0, -6],\n [6, -6, -4, 1, 6],\n [5, 4, -1, -3, -2],\n [-3, 0, -2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 4, 1, 0, -4],\n [0, 0, 1, 5, 6],\n [0, -5, 6, 6, 0],\n [1, -4, 4, 2, -2],\n [-5, -4, -5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -5, 4, -1, -3],\n [-5, 2, -5, -2, -6],\n [-3, -6, 2, 3, 0],\n [-3, 2, 4, 0, 5],\n [-2, 1, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, -5, -4, 5],\n [6, 0, 4, 6, -5],\n [-3, -4, -1, 2, 3],\n [5, 0, 0, -1, -2],\n [-5, -5, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 6, 6, -2, -6],\n [-4, -4, -5, 2, 0],\n [-1, 6, 5, -2, 4],\n [6, -4, -5, -1, -5],\n [5, -6, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -4, 0, -5, 6],\n [-6, 0, 3, -3, -2],\n [6, -6, 0, -5, 5],\n [4, -2, 4, 2, 4],\n [4, 4, -4, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -5, -2, -1, 0],\n [-3, 4, 2, -6, -6],\n [-4, -1, -6, -5, -5],\n [1, 4, 1, 4, -2],\n [5, 3, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -6, 2, -5, 4],\n [-5, -3, -3, 6, 3],\n [-6, -6, 6, -6, -2],\n [-2, -2, 5, 4, -1],\n [2, 4, -3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -2, 6, 4, 5],\n [-3, 3, -3, 1, 1],\n [0, 1, 1, 1, -2],\n [3, -4, -4, -5, 6],\n [6, -2, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 5, -3, -4, -3],\n [-2, 3, 1, 4, 6],\n [-1, -3, 4, -4, -1],\n [2, 6, -5, 3, 5],\n [-3, 1, -3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -4, 2, 5, 0],\n [5, 1, 2, 0, -3],\n [6, 6, 3, 0, 0],\n [0, -2, 0, 2, -4],\n [-4, 3, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 3, -2, 5, -6],\n [-3, -5, -6, 6, 6],\n [-6, 2, 4, -4, 1],\n [6, -2, -3, -4, 5],\n [2, 6, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 5, 1, -1, 0],\n [-3, 0, -5, 2, -1],\n [-3, -6, 0, -3, -3],\n [-6, -5, 6, -3, -2],\n [-6, 5, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 4, 5, -1, -1],\n [-3, 6, -6, 0, 2],\n [-5, 3, 2, 1, 1],\n [-4, 2, 1, 1, -1],\n [2, 1, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -6, -2, 5, 4],\n [6, 3, -6, 5, -6],\n [-3, -4, -5, 2, 2],\n [-6, 0, 6, 1, -3],\n [-3, 6, -5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -3, 1, 4, -3],\n [-5, 1, 1, 2, 4],\n [-6, -5, 1, -3, -4],\n [-4, -4, -2, 2, 2],\n [-3, 2, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 3, -5, -5, 2],\n [-5, 3, 2, 2, 5],\n [4, 3, -6, -3, 0],\n [1, -6, 0, 6, -5],\n [-3, -2, 2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -6, -1, 3, -5],\n [-1, 3, -2, -2, 1],\n [1, 5, 5, -3, -6],\n [-3, 0, 5, -1, -4],\n [1, -3, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -2, 5, 5, -2],\n [-5, 2, -2, -4, 3],\n [6, 5, -1, -2, -6],\n [2, -1, -6, 3, -2],\n [-1, 2, 5, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -1, -5, 4, -6],\n [5, 1, 0, -2, 1],\n [-3, 2, 4, -3, -5],\n [-3, 3, -2, 5, 6],\n [1, 0, 5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 0, 5, 6, -4],\n [-4, -2, 2, -1, 4],\n [-5, 6, -5, -6, -4],\n [2, 6, -6, 0, 3],\n [6, -6, 1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 3, -1, 6, 5],\n [2, 1, -5, 4, -3],\n [2, 1, -4, -3, -5],\n [-4, 4, 6, -4, -1],\n [-6, 3, -1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 3, 5, -1, -3],\n [5, -6, 0, -5, -4],\n [4, -4, -5, 3, 0],\n [4, -2, 2, -4, 3],\n [5, -6, -4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 0, -3, 5, -1],\n [2, 6, -4, -5, 0],\n [-2, 1, -5, -3, 2],\n [6, 3, 2, -3, -3],\n [-2, 0, 3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 1, -6, -5, 2],\n [-4, -1, 0, -3, 4],\n [-6, -6, -5, 4, -5],\n [-1, -5, 2, 0, -5],\n [-6, -1, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -5, 0, 5, -6],\n [0, 6, 3, -6, 0],\n [-5, -6, 6, -6, 1],\n [6, 2, 5, -3, 5],\n [-1, 3, 6, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -2, -4, -6, -2],\n [-6, -4, 1, 3, 4],\n [0, 6, -1, -3, -3],\n [-6, -4, -4, 4, 6],\n [-4, 1, -5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -3, -2, -6, -1],\n [4, -5, -6, -4, -2],\n [-3, 2, -3, 0, 5],\n [2, 5, -5, 5, 6],\n [1, 1, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -5, 6, 6, -4],\n [-3, -2, 0, 3, 6],\n [-5, 1, -3, 0, -1],\n [1, 3, 2, -6, 1],\n [6, 6, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 5, 6, 2, -3],\n [2, -5, -3, 4, 3],\n [2, 5, -3, 4, -4],\n [-2, 0, 1, 2, -6],\n [-1, 3, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -6, 2, 0, 1],\n [6, 3, -2, 1, 0],\n [4, 5, -1, -5, -1],\n [-3, 6, 1, -1, 5],\n [4, 1, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 1, 1, -3, -5],\n [-4, 5, -2, 0, -6],\n [3, 3, -3, 0, 6],\n [2, 6, 4, -6, 1],\n [-3, -6, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 1, -1, -3, 1],\n [-4, 6, 3, -3, -3],\n [-6, -2, 3, -1, -1],\n [-6, 1, -5, -4, -3],\n [4, -5, 5, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -6, 4, -4, -5],\n [2, 5, 6, 1, -6],\n [6, -5, 5, -4, -6],\n [4, -5, -6, 0, 1],\n [-6, 3, 5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 5, 1, 6, 5],\n [3, -2, 1, 1, -6],\n [4, 6, -4, 1, 5],\n [-3, -6, -3, 5, -2],\n [1, 5, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -6, -3, 0, -1],\n [-5, 3, 4, -6, 0],\n [-4, 4, 1, 1, 4],\n [1, 6, 4, -2, 5],\n [5, -3, -3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 2, -4, -6, -2],\n [2, -6, 2, -5, -3],\n [-3, -4, -4, -5, -2],\n [3, -4, -1, 1, 2],\n [-2, 2, -1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, 6, 2, -4],\n [-2, 1, 6, -4, 3],\n [5, -4, 1, -3, 5],\n [6, 0, -3, 0, -3],\n [-4, 4, -1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, 2, 1, 4],\n [1, -4, -2, 2, -3],\n [1, 3, 5, 2, 6],\n [6, -4, -4, 4, -1],\n [-1, 5, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, 4, -3, 4],\n [-6, -6, 1, -4, 6],\n [5, -2, -4, 5, 0],\n [-6, -1, 6, 3, -4],\n [-3, -2, -6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -1, 4, 0, -6],\n [-5, 5, -3, -3, 3],\n [-3, 0, -3, 6, 5],\n [4, -1, 6, 3, -4],\n [3, -2, 3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 6, 1, 2, 5],\n [-3, -4, 3, -1, 4],\n [-2, -5, -2, -4, -6],\n [-5, 6, 2, 2, -4],\n [4, -2, 3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -5, -6, 2, -6],\n [5, -3, -4, -2, 6],\n [5, 2, -3, 6, -1],\n [-3, -5, -1, 5, 4],\n [3, 3, -2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -4, -1, 0, -4],\n [-1, 5, 6, 4, 3],\n [-6, -2, -2, 1, 6],\n [-5, 3, -6, -3, -1],\n [2, 6, 0, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -2, 4, 1, -3],\n [4, 1, 4, 4, 6],\n [-1, 1, -6, 2, -5],\n [0, -1, -2, -6, 4],\n [1, -5, 2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, -6, 6, -6],\n [-5, -2, -3, -5, 5],\n [4, 5, 6, -4, 6],\n [-1, 1, 4, 6, -3],\n [2, -6, -3, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -6, -3, 2, 0],\n [3, 5, -4, -2, 3],\n [0, 6, 0, -2, 2],\n [-3, 1, -6, 3, -3],\n [-3, -5, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -2, -6, -6, -5],\n [6, -4, 2, -3, 6],\n [-1, -4, 4, 4, -5],\n [-4, -5, -1, 4, 1],\n [4, 1, -2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 3, -3, -2, -3],\n [6, -3, 5, 2, 4],\n [-4, 6, -2, 1, 3],\n [6, -1, 6, -2, -5],\n [3, -5, -5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 6, 5, -2, 0],\n [5, -1, -1, 6, -6],\n [-2, -4, 5, -3, 2],\n [0, -6, 0, 5, 3],\n [3, -3, -1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -2, -2, -2, -3],\n [-6, -5, -4, 2, 6],\n [-3, -4, -2, -4, 1],\n [1, -1, -1, -4, -3],\n [-1, -2, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 3, 2, 2, -6],\n [3, 1, -4, 3, -2],\n [2, 1, 2, -5, -2],\n [4, 5, 1, -5, 1],\n [1, 2, 6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -2, 4, -2, 1],\n [1, -4, 6, -2, -2],\n [-2, -5, -3, -1, 0],\n [-5, 1, 3, -6, -2],\n [-2, -6, -4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 3, -5, -4, -6],\n [-4, 0, 2, 1, 4],\n [-6, -6, -4, 1, -4],\n [-5, 2, 3, -5, 6],\n [1, -6, 1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 5, 6, 5, 0],\n [4, 3, -6, 2, -6],\n [2, 5, -6, 5, 3],\n [2, -4, 4, -2, 4],\n [0, -1, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -1, 5, -5, 2],\n [-3, 3, -5, -2, -5],\n [3, 6, 5, 3, 6],\n [4, 6, 2, -2, 5],\n [-2, 1, 0, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -5, 2, 5, -3],\n [-3, -5, -2, -2, 5],\n [1, 1, 2, 0, 3],\n [-3, -5, -6, -3, 2],\n [-6, 2, -6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -6, -6, 4, -6],\n [5, 4, -6, 0, 1],\n [4, -5, 0, -6, 1],\n [3, 6, -1, -3, 5],\n [4, -6, 2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -2, 5, -1, -6],\n [4, 1, 3, -5, 3],\n [3, 4, -1, -3, -2],\n [4, 4, -4, -4, -3],\n [-2, -1, -6, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, 6, -4, 0],\n [4, 3, 6, 2, 5],\n [6, -1, -2, -5, -3],\n [-5, 5, -5, 4, -2],\n [-4, -3, -1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 0, -5, 1, -1],\n [-5, -3, 1, 6, -5],\n [5, 2, 4, 1, 1],\n [6, 2, -6, 5, -3],\n [-5, -4, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 5, 2, -2, 4],\n [-3, -5, -1, -5, 2],\n [-4, 2, 0, 3, -3],\n [6, -3, 1, 2, 3],\n [-1, -6, -4, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, -5, 0, -5],\n [5, 5, -4, -6, -1],\n [0, -4, -5, 3, 3],\n [-2, 3, -2, 6, 4],\n [6, 4, -2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 3, 6, 2, -2],\n [5, 1, 2, 0, 6],\n [-5, -1, 2, 3, -3],\n [3, 6, 3, 5, -3],\n [2, 4, -3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 2, 0, 3, -6],\n [-6, -4, -2, 2, -3],\n [-6, -2, 2, -1, 5],\n [-3, -2, 5, 6, 6],\n [1, -5, -4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -1, -4, -3, -4],\n [-3, -1, -6, -5, 0],\n [-4, 0, 6, 6, -1],\n [-3, -1, -4, -5, 5],\n [-4, -4, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 0, -6, -3, -1],\n [-2, -6, 3, -4, 6],\n [-3, -5, -1, 4, 2],\n [6, -5, -6, 4, 4],\n [-3, -5, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, -6, -5, 4],\n [3, -5, 4, -4, 1],\n [-5, 6, -6, -4, 3],\n [5, -2, 3, 6, -5],\n [2, 6, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 2, -5, 0, 2],\n [5, -2, 1, -3, 0],\n [3, -2, 2, -5, -5],\n [2, -1, 5, -1, 4],\n [1, -6, 5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -4, 4, 3, 2],\n [-3, -5, -1, 3, 6],\n [6, -2, 0, 5, 5],\n [-6, 6, 0, -5, 3],\n [-2, 0, 1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -5, -4, 5, -6],\n [-2, 6, -3, 6, 6],\n [3, -3, -2, 4, 4],\n [5, -2, -1, 2, -1],\n [3, -1, 1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 0, -1, -5, -5],\n [-6, 6, 3, 1, 3],\n [0, -3, -5, -3, 2],\n [-1, 5, -1, 0, 4],\n [-6, 3, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 3, 2, -2, -2],\n [5, -3, 4, -2, 4],\n [-3, -6, -1, 5, -1],\n [-6, -5, 3, -1, -6],\n [6, -5, -3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 0, 3, 3, -5],\n [6, -5, 1, -1, 5],\n [-2, -6, -6, -5, 0],\n [-2, -1, 2, -5, 5],\n [2, 6, -1, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 2, 1, -4, 1],\n [2, -6, 4, -1, -5],\n [4, 5, 6, -1, -5],\n [5, -3, 2, -6, -6],\n [-3, -2, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, -6, 3, 1],\n [-4, 0, 6, 1, 4],\n [-3, 4, -3, 1, -5],\n [4, 3, -3, -4, 1],\n [4, -5, 1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 1, -2, 3, -6],\n [3, -4, -4, -2, 6],\n [-1, -2, 5, -4, 5],\n [6, 1, -4, -2, 6],\n [-2, 6, -4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 2, -2, -3, 1],\n [-4, 5, -2, -4, -6],\n [3, -4, 5, -6, -1],\n [1, -3, -3, 3, 0],\n [2, 6, -1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 1, 0, 3, 3],\n [2, -2, 3, 0, -5],\n [1, 0, 0, 0, 6],\n [-5, -1, -6, -2, -1],\n [6, 0, 1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -4, -5, -5, 5],\n [5, 1, -3, 6, 6],\n [0, 3, 1, 1, 1],\n [-2, -6, -1, -6, -6],\n [-5, 0, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -3, 1, -5, -3],\n [-6, 3, 5, -1, 2],\n [-1, 6, 1, -3, 0],\n [-2, -6, -3, 4, 1],\n [2, -2, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 5, -1, 5, 0],\n [-3, 4, -1, 0, -6],\n [1, 3, -6, 4, 1],\n [-6, -4, 0, 3, 1],\n [3, -4, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -2, -5, 0, -4],\n [4, -6, -3, -5, 3],\n [6, 0, -3, -3, 1],\n [0, 4, -2, 0, -4],\n [0, -3, 3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, 4, 6, 6],\n [-4, -3, 5, 4, -5],\n [0, 5, 6, -4, 2],\n [0, -4, 2, 0, -2],\n [2, 5, -3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -1, 5, -3, 4],\n [5, -2, 4, 5, 3],\n [-5, -3, 1, 1, -1],\n [-4, -6, -1, -6, 0],\n [0, -5, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -2, 1, 1, 6],\n [4, -1, 2, 6, -6],\n [-5, 1, -1, 1, -5],\n [0, -4, 4, -3, 0],\n [5, -5, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -5, -4, 1, 3],\n [-2, 2, 2, 5, -5],\n [5, 3, 3, -4, 4],\n [-3, 4, -4, -3, -1],\n [-3, -5, 1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 1, -4, 0, 5],\n [1, 2, 5, -5, -6],\n [5, 3, 4, 0, 0],\n [-5, 0, -6, 0, 1],\n [2, 1, 0, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -1, 3, -2, -2],\n [4, -5, 1, -5, -3],\n [6, 0, 6, 1, -5],\n [2, 0, 3, 6, 4],\n [-6, 5, 6, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 2, 5, 1, -1],\n [6, 5, -5, -4, 0],\n [4, 4, -2, -3, 6],\n [1, 3, 2, 4, -3],\n [6, -5, 4, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 2, -6, -2, -6],\n [-6, 2, 1, -5, 0],\n [-1, -4, 5, 6, -4],\n [6, -4, 4, -2, 4],\n [4, 3, 6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -5, 4, 3, -1],\n [4, 2, -6, -3, 6],\n [3, 3, -3, 0, 2],\n [3, 6, 6, 6, -4],\n [5, -3, 0, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -3, 0, -3, -4],\n [0, 1, -3, -6, 0],\n [-3, -3, 6, 1, 0],\n [-5, -3, 6, -5, -3],\n [4, -6, 3, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 0, 5, 2, 5],\n [6, -5, -5, -5, -5],\n [6, 2, 5, 2, -3],\n [4, -5, -5, -6, -1],\n [-3, -4, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -4, 1, -2, -2],\n [1, 1, -2, 1, -1],\n [2, 5, -3, 6, 5],\n [-6, 2, -1, 0, -3],\n [-3, -4, -6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 4, -6, -3, 2],\n [-3, -5, 6, 6, 3],\n [-6, 2, 1, -6, -2],\n [-3, 3, -3, -1, -2],\n [-2, -4, 1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 0, 1, 2, -4],\n [-5, 6, -3, 0, -4],\n [-2, 4, 3, 4, -5],\n [-6, 4, 3, 0, -5],\n [-3, -4, -1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -6, -1, -6, 4],\n [-2, 6, 4, -5, 3],\n [-5, -1, 5, -4, 3],\n [-6, 5, 6, -5, 1],\n [3, 2, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 5, 0, 0, 0],\n [0, -4, -4, -4, 0],\n [0, 6, -4, -3, -3],\n [2, 4, 5, 6, -1],\n [-2, 6, 1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -2, 2, -6, -5],\n [0, -4, 0, -6, 2],\n [3, 6, 3, 5, 2],\n [-4, 3, -5, -3, -1],\n [3, -1, 0, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 4, -5, 6, 5],\n [-3, 3, 1, -2, 0],\n [-1, -3, 4, 3, -2],\n [1, 6, 3, 2, -1],\n [-6, -1, 5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -5, -2, -6, -6],\n [1, -1, -2, 6, -2],\n [-2, 5, -2, 5, 5],\n [-4, 4, 6, -1, 0],\n [-5, -4, 3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 5, 4, 3, -5],\n [-3, 3, -3, -5, 5],\n [0, 1, 2, 0, 4],\n [-6, -4, 5, 1, -3],\n [3, 2, 3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 5, 2, 6, 6],\n [1, -4, 0, 6, 1],\n [-1, 6, 4, -6, 6],\n [-4, -4, 5, 4, -3],\n [-3, -2, 0, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 0, 2, -3, 0],\n [-6, -2, 1, -1, 4],\n [1, 1, 5, -5, 6],\n [0, 1, 5, 0, -2],\n [0, 1, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -1, -3, -1, 0],\n [-3, -5, 5, 4, 1],\n [2, -5, -5, -2, -4],\n [-5, 5, 1, 2, -2],\n [4, -3, 2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -4, -2, 4, -2],\n [-6, 5, 1, 3, 6],\n [-5, -1, 3, 3, 2],\n [-1, -3, 1, 6, -5],\n [-4, 4, 2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -2, -4, -2, 2],\n [-3, 5, 2, 1, 6],\n [3, -6, -6, 5, 0],\n [4, 5, 2, 3, 3],\n [-1, 3, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -2, -3, -6, -4],\n [-5, 4, -2, 1, 3],\n [5, 5, -2, 1, 2],\n [-6, 0, 6, -3, 3],\n [-2, -5, 6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 0, 0, 3, -6],\n [5, 3, 1, 3, 5],\n [-6, 3, -4, -5, -1],\n [2, 0, -5, 0, -2],\n [4, -6, 2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -4, 5, 5, 4],\n [6, -2, 3, 3, 6],\n [3, 0, 5, -6, -2],\n [-5, 2, -3, -4, -1],\n [2, 5, -3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -5, 3, 3, -1],\n [0, 3, -5, -2, -3],\n [5, -1, -3, -4, 0],\n [-1, 1, -5, 4, -4],\n [-2, -1, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 3, -2, 3, 0],\n [-2, 0, 6, -6, 4],\n [-2, 0, -6, -3, 2],\n [3, -6, 5, 6, -5],\n [2, 6, 5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, 0, 1, 3],\n [3, 6, -4, -3, -6],\n [-4, 5, 6, 5, 3],\n [6, 1, -2, -2, -2],\n [-1, 3, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -2, -4, -1, -1],\n [4, -4, -5, 6, 4],\n [-6, 4, 3, -5, -5],\n [-1, -1, -2, 2, 4],\n [2, 0, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -5, -4, 1, -4],\n [1, 2, 5, 4, -6],\n [-3, 6, 4, 4, 0],\n [1, 5, 2, -4, -6],\n [2, 6, -3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -1, 0, 2, 1],\n [3, -2, 0, 1, 4],\n [-2, 0, 1, -6, 1],\n [2, 6, -4, 1, -6],\n [5, 3, 5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -5, -1, 0, 2],\n [-6, 6, 1, -2, 3],\n [-1, -6, 1, 4, 6],\n [3, 4, 4, 0, 2],\n [3, 1, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 2, -5, 1, -4],\n [-1, 0, 5, -6, 3],\n [3, 0, 6, 5, -1],\n [0, 6, -3, -3, -2],\n [3, -1, 0, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 1, -4, 1, 2],\n [-3, -6, -3, -6, -2],\n [4, 4, -1, 5, 3],\n [2, -6, -6, -2, -4],\n [-6, -6, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 0, 3, -2, -5],\n [-4, 5, -6, 6, -2],\n [5, -2, -2, 3, 6],\n [5, 2, 2, -2, 4],\n [3, -3, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -6, 2, 2, -6],\n [-3, 6, -3, 5, 4],\n [-6, -1, 3, 3, -4],\n [4, 2, 2, -4, -3],\n [0, -4, 5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -4, -4, -6, 4],\n [-5, 0, -6, 6, 1],\n [4, 1, -2, -3, -2],\n [-4, -4, -5, -3, 4],\n [-2, 0, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 0, -5, -2, -5],\n [6, -6, -2, 4, 6],\n [2, 2, 4, 6, 4],\n [2, -4, 0, 2, 3],\n [3, -6, 5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -1, -3, 4, 4],\n [5, -1, 4, -3, -3],\n [6, 2, 1, 3, 4],\n [-4, 0, -2, 3, 0],\n [3, 0, 3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -1, -2, -5, -3],\n [-1, 1, 5, 5, 0],\n [-3, -4, -1, 5, 0],\n [2, 3, 4, 2, 2],\n [4, -2, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -6, -3, 1, 4],\n [0, 0, -3, -1, 0],\n [3, -4, 1, 5, 5],\n [6, -5, -6, 1, 6],\n [-2, 4, 5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -3, -5, 6, 4],\n [-1, -6, 3, -2, -1],\n [0, -5, 5, 4, 6],\n [1, 2, -3, 5, 6],\n [6, -4, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -6, 6, -1, 2],\n [1, -3, -5, 2, -5],\n [0, -3, -6, 5, 6],\n [-4, 3, 6, -1, -3],\n [5, 0, 2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 2, 5, -4, 0],\n [-2, -1, 4, 4, 1],\n [-2, 6, -5, 6, 3],\n [5, 0, 4, -1, -2],\n [-6, 1, 4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 2, 1, 5, -5],\n [1, 5, -2, 1, 4],\n [-4, -4, -6, 3, 2],\n [-1, -4, 0, 4, 4],\n [-1, -4, -6, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 5, 3, 2, -4],\n [-3, 6, 2, -5, 2],\n [-6, -6, 3, -4, -1],\n [-6, -5, 3, -4, -3],\n [0, 0, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, 2, -5, 6],\n [4, 5, 5, 6, -1],\n [2, -4, 4, -5, -5],\n [6, 5, 2, 3, -1],\n [0, 3, -2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, -4, 4, 6],\n [5, 1, -5, 3, 5],\n [4, -5, -6, -1, -3],\n [4, 2, 0, -5, 1],\n [-6, -4, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 2, -1, -4, 0],\n [-1, -1, -5, 6, 3],\n [5, 4, -4, 0, -4],\n [-5, 3, 2, 6, 3],\n [0, 1, 1, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -2, 3, 0, -4],\n [-2, 0, 1, 5, 3],\n [0, 0, -1, 1, 0],\n [-1, 5, -2, 1, 5],\n [1, -5, 1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 0, -6, 2, 6],\n [-5, -4, -2, 4, 0],\n [0, -4, -3, -4, 3],\n [-2, 2, -6, -6, 4],\n [-1, 6, -5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 0, -1, 4, -3],\n [1, -1, -2, -2, -4],\n [-6, 1, -3, 1, 0],\n [-6, -1, 0, -6, -2],\n [0, -5, -5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 2, -3, -3, 5],\n [3, -3, 2, 1, 2],\n [4, -5, -2, 3, 2],\n [-3, -6, -2, 4, 6],\n [4, 0, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 5, -2, 4, -1],\n [-3, -2, 6, 6, 6],\n [-6, -5, 4, 3, -2],\n [4, 3, 5, 6, 2],\n [-6, -3, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -3, -2, 0, -5],\n [-5, -6, -2, 3, -5],\n [2, 1, -6, 1, 4],\n [3, 2, 1, 6, 0],\n [1, 4, -4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -5, -3, 2, -5],\n [3, 3, 6, 4, -1],\n [1, 2, -3, -4, 0],\n [4, -2, 5, 3, 6],\n [-4, 1, 4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, 4, 3, 6],\n [-1, 3, -4, -3, 2],\n [2, -3, 4, -3, 4],\n [4, 2, -3, -5, 2],\n [3, 2, -5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 3, 3, -5, 6],\n [-5, -5, 0, -3, -1],\n [2, -4, 2, -4, -4],\n [4, 5, 1, 5, -6],\n [-2, 3, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 1, -5, -2, -6],\n [-3, -5, 6, 0, -2],\n [-2, -4, 0, 1, -6],\n [-4, 6, 4, -5, 1],\n [5, 3, -3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -6, -5, -3, 5],\n [-2, -2, -5, 4, 5],\n [4, 4, 5, -4, 4],\n [4, -5, -1, -2, -6],\n [-3, -3, -4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, -1, -1, 5],\n [4, -3, 2, -1, -5],\n [-4, -1, 4, 0, -3],\n [6, -4, 6, 0, -6],\n [-5, 0, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 5, -3, 6, -5],\n [3, 3, 6, -3, 0],\n [-3, 5, 6, -3, -5],\n [-6, 2, 5, 3, 6],\n [4, -1, -5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 0, 6, -1, -4],\n [4, 3, -6, -6, -5],\n [2, 3, 1, -3, 4],\n [3, 2, -1, 3, -5],\n [6, 0, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 1, 4, 5, 0],\n [-5, 1, -6, -4, -1],\n [6, -3, 1, -2, -4],\n [6, 1, 3, 4, -1],\n [-3, -1, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 5, -3, 6, 3],\n [-4, 6, 2, 5, -6],\n [-5, 3, 2, 0, 5],\n [5, -5, -5, -3, 2],\n [-6, 5, 1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -6, -1, -3, 0],\n [-5, -2, -1, 4, 4],\n [6, -6, -4, 6, 4],\n [6, -4, -6, -1, 2],\n [-4, -2, -3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -5, 1, -2, -4],\n [5, 0, -1, -4, -4],\n [-3, -2, -3, 6, 2],\n [2, 1, -5, 2, 5],\n [-4, -5, -4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -4, -2, -5, 3],\n [1, -4, 5, -5, 2],\n [-3, -1, -6, -3, 4],\n [2, 3, -4, 5, 2],\n [4, 6, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, 5, 2, -6],\n [-4, 5, 1, 1, 1],\n [0, -1, 6, 3, 1],\n [1, 5, -6, 5, -2],\n [1, 4, 5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -4, 6, -2, -1],\n [-5, 0, -3, 6, -2],\n [-5, -3, 4, -6, -4],\n [3, 4, -6, -1, -2],\n [6, -6, 1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 6, 2, -1, 4],\n [-5, -5, 3, 3, -2],\n [-3, 2, 2, -6, -2],\n [0, -3, 3, -2, -2],\n [1, 2, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, 3, -4, -4],\n [6, -6, 5, -1, -1],\n [-5, -4, -2, 0, -1],\n [0, 6, -2, 4, 6],\n [2, 0, 1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 4, 1, 4, -2],\n [-5, 1, 5, -5, 6],\n [3, -1, -4, 6, -6],\n [6, 1, -3, -6, 3],\n [-3, 5, 5, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 4, -3, 0, 3],\n [-2, -1, 2, -4, -4],\n [-6, 6, -5, -1, 6],\n [1, 0, 0, 1, -6],\n [5, -5, -4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 1, -3, -4, 2],\n [-6, 6, 2, 0, 5],\n [2, -6, 6, 5, -2],\n [-4, -4, 3, -1, 6],\n [0, 5, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -5, -2, 1, 2],\n [-5, -5, 4, -2, -3],\n [1, 4, 2, -6, 2],\n [-3, -6, 1, -6, -2],\n [-1, 4, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 6, 1, -4, 1],\n [1, 4, -6, 5, 6],\n [-6, 1, 1, -6, 5],\n [-2, 6, 0, -1, 6],\n [5, -5, -1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 1, 5, 0, 6],\n [-4, 4, -6, 0, 3],\n [-2, -5, -4, 4, 0],\n [-1, -1, 4, -3, -5],\n [-2, -2, 2, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -1, -2, -4, -3],\n [-6, 5, 5, 6, 2],\n [-2, 2, -5, -4, 5],\n [-4, -5, 6, 2, 0],\n [-1, 6, -5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, 0, -4, -5],\n [-5, 4, 6, 2, 1],\n [-5, 1, 2, -2, 6],\n [0, 1, -6, 0, 1],\n [4, -3, -6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -5, 0, 0, 2],\n [3, -4, -2, -6, 0],\n [0, 0, 5, 1, 1],\n [-3, 0, -4, 0, -3],\n [-4, 6, -5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 5, 2, 3, -1],\n [-3, -2, 3, -4, 3],\n [-3, 1, 5, 1, -2],\n [-5, 4, 4, 4, 5],\n [-2, -6, 0, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 3, -3, -6, 6],\n [5, -2, -2, -1, -3],\n [-6, -1, 6, 1, -4],\n [0, 1, -1, 4, -4],\n [-5, 0, 4, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -2, 1, 6, -4],\n [4, -4, 0, 4, -1],\n [4, 2, 0, -1, -1],\n [3, -4, 5, 2, 6],\n [-2, -3, 5, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -1, 3, -6, 1],\n [-3, -4, 6, 3, -3],\n [3, 1, -2, 0, 4],\n [-3, -4, 1, -2, -2],\n [4, 0, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 4, 1, -1, 0],\n [1, -1, 5, 1, 3],\n [-1, 2, 6, -3, 5],\n [-6, -2, -5, -4, -1],\n [6, -5, 5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 2, -2, 3, -4],\n [-3, 1, 4, 5, -2],\n [-1, -1, -1, 0, 2],\n [2, 5, 1, -3, -5],\n [1, -2, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 1, 2, -5],\n [6, -2, -2, 5, -1],\n [3, -3, 2, -3, 6],\n [-4, 4, 0, 0, 3],\n [-5, -5, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 5, -2, 4, 2],\n [5, 5, 2, -3, -4],\n [0, -5, -2, 3, -5],\n [3, -3, -6, -5, -5],\n [-5, -1, 4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -1, 5, -2, 3],\n [6, -5, 2, -3, -4],\n [3, -1, 6, -2, 5],\n [5, -6, -4, 1, -1],\n [-5, 5, 4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -2, 1, 6, 5],\n [-5, -4, -2, -2, 0],\n [-6, -2, 3, 6, -2],\n [1, 0, 1, 5, 1],\n [5, 6, -3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 1, -5, 2, 0],\n [-6, 5, 6, -1, -3],\n [-1, -2, 0, -1, -3],\n [-3, -2, 4, -2, 6],\n [4, -2, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, 1, 3, -4],\n [5, -2, -2, 6, -6],\n [-2, -3, 3, 1, 2],\n [4, -2, -4, -4, -5],\n [4, 1, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 6, -4, -4, -5],\n [-1, -5, 3, 6, 2],\n [-4, 1, -4, -4, -1],\n [5, -6, 3, 6, 1],\n [-2, 3, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 5, -2, 3, 5],\n [-1, 1, -2, 6, -5],\n [2, -5, -3, 4, 5],\n [3, 1, -1, 2, -2],\n [0, 6, 3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -2, -2, 4, 1],\n [-5, -3, -6, -3, -3],\n [3, -4, -4, 0, 2],\n [-3, 3, 1, 3, 6],\n [2, 3, -1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -4, 0, 0, 6],\n [5, -4, 6, -3, -2],\n [0, -6, 5, 0, -3],\n [6, -3, -4, 4, 2],\n [1, 6, -6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 4, 0, -6, -2],\n [-4, 0, -3, -4, 4],\n [5, 6, 2, 4, -2],\n [2, 1, 0, -3, 6],\n [1, 3, 1, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -6, 2, 0, -5],\n [-3, 6, 5, 4, 1],\n [0, 0, 2, 1, -5],\n [4, -2, 2, 3, 4],\n [-2, -4, 6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -6, -1, -2, -3],\n [-5, 4, 6, 4, 6],\n [-2, 1, -5, 1, 2],\n [-5, -2, -6, 1, 2],\n [-2, -3, 4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -6, 2, 2, -2],\n [-4, 3, 1, 2, -3],\n [1, 3, -4, -6, 2],\n [4, -2, -3, 1, -6],\n [-2, -5, 6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, 4, 4, 6],\n [1, -1, 2, 2, 5],\n [0, -1, 4, -5, -6],\n [5, -4, -6, 6, 5],\n [-6, 1, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 6, -2, 3, 1],\n [2, -2, 5, 3, 5],\n [5, -1, 1, -6, 6],\n [3, 5, -2, 0, -5],\n [-1, -5, -3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 6, -5, 3, 1],\n [-1, -5, 6, -4, -6],\n [1, -1, -4, -6, 5],\n [-5, 5, 2, 3, 5],\n [-6, 3, 6, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -2, -3, -5, 6],\n [-2, -3, 1, 3, -4],\n [-1, 3, -5, 3, 5],\n [6, 2, 0, 0, -1],\n [-1, -5, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -1, -4, -6, -4],\n [2, 5, -2, -1, 3],\n [5, -2, 6, 1, 4],\n [-5, 0, 5, -4, -2],\n [3, 1, -5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -6, -4, -2, 3],\n [6, -1, 5, -5, -1],\n [2, -3, 6, 5, 2],\n [-3, 4, 2, 5, -5],\n [-5, -1, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -4, 4, 0, 3],\n [1, -6, 2, 2, 2],\n [-5, -1, -6, 6, 4],\n [5, 6, 5, 6, -1],\n [6, -5, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -2, 0, 5, -6],\n [-1, 4, 3, 6, 2],\n [5, 1, 5, 5, -6],\n [6, -3, -3, -6, -2],\n [5, 4, -2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -3, 3, -3, 6],\n [-1, 4, 2, -6, -1],\n [1, 6, -3, -4, -1],\n [-5, -2, 6, -1, 3],\n [-1, -2, -1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 2, 0, -2, -2],\n [5, 5, 3, 0, -2],\n [5, 4, -4, 0, -4],\n [2, 0, -2, -5, -5],\n [-3, -4, -6, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 6, -5, 2, -5],\n [-5, -5, 5, -6, -3],\n [2, 1, 2, -5, 5],\n [4, 0, 3, -4, -3],\n [-5, 4, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 3, -5, 6, 5],\n [0, -1, -3, 5, -3],\n [3, -6, 0, -6, 3],\n [2, 5, -4, -2, 0],\n [-1, 6, -5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 5, -6, -1, 4],\n [3, -4, -2, -2, -5],\n [-3, -5, 5, -6, 5],\n [-4, 2, 3, -6, -4],\n [4, 6, -6, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -3, -5, -3, 0],\n [0, 2, 0, -4, 1],\n [-4, 5, -6, -2, -2],\n [1, -4, -5, 6, 5],\n [-2, -5, 5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -5, -5, -4, 5],\n [-1, -4, 3, 0, 2],\n [-3, 4, 1, 5, -4],\n [4, 6, 4, 5, -5],\n [5, -2, 5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 4, 3, -2, 0],\n [-2, 6, -6, 6, -1],\n [3, 4, 2, -4, 0],\n [-3, 0, 1, -2, 3],\n [5, 6, -3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 5, -6, -6, -5],\n [5, 4, -5, -4, -4],\n [2, 2, 0, 0, 1],\n [4, 3, -4, -5, -2],\n [5, -1, -3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -2, 2, 4, -4],\n [3, -5, -3, 0, 2],\n [6, 5, 4, 5, -4],\n [4, -2, 1, 2, -1],\n [-4, 1, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 1, -5, 1, 3],\n [-2, 2, -4, 5, 3],\n [-1, -2, -4, -1, -4],\n [1, -2, -6, -5, -1],\n [-6, -5, 1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 2, 5, 2, 0],\n [-3, 0, -2, -3, -2],\n [-1, -5, 2, 1, 6],\n [4, 6, 0, -1, 4],\n [0, 2, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -5, 5, 4, -3],\n [-5, 1, 4, -1, 0],\n [2, 4, 1, 2, 3],\n [-5, 6, 6, 5, -4],\n [-1, -1, 6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 6, 0, 2, -2],\n [-3, -2, 2, 1, 5],\n [-2, -1, 2, 0, 6],\n [0, 1, 4, -2, -5],\n [-1, 0, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 2, 2, 3, -2],\n [3, -1, 6, 0, -2],\n [0, -1, 0, 1, -3],\n [-3, 6, 5, 6, -3],\n [-1, -4, -5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 5, 2, 1, 1],\n [0, -2, -2, 6, -5],\n [6, -6, -5, -5, -5],\n [-5, 5, 3, -3, 4],\n [5, 6, 2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 3, 2, 4, 2],\n [-2, -4, 4, -1, -5],\n [2, 6, -5, 0, -4],\n [2, 3, 3, 2, 5],\n [-5, -6, -3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 5, 5, 3, 6],\n [-4, 4, -4, 0, -1],\n [-1, -1, 0, -4, -2],\n [3, 3, -1, -3, 2],\n [-5, -4, -2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, 5, -5, 2],\n [-1, -1, 2, 1, -4],\n [4, 2, 2, -4, 0],\n [0, 1, 1, 2, -4],\n [2, -5, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, -3, 1, 1],\n [2, -3, 3, 0, 0],\n [4, -3, -5, -1, -5],\n [3, -6, 2, 3, 0],\n [2, 4, -3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 0, 6, -2, -4],\n [-3, -3, -4, 0, 2],\n [5, 5, 3, 4, -6],\n [4, 5, 3, -2, 1],\n [2, -6, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 0, 3, -6, 0],\n [-5, 4, 4, 4, 4],\n [6, 5, 1, 0, 0],\n [0, -5, 1, 3, 5],\n [0, 1, 5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, -1, -1, 4],\n [-3, 6, 0, 6, -2],\n [-1, 0, 3, 3, -5],\n [-5, 4, -1, -5, -2],\n [1, -5, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, 2, 1, -6],\n [-6, 3, 6, -4, -2],\n [1, 5, -4, -2, 5],\n [0, -5, 0, 6, -4],\n [1, 4, 4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 6, 0, -1, 4],\n [-4, -1, -1, -1, -4],\n [6, -3, 4, 0, -4],\n [-4, 2, 5, -1, -2],\n [2, 3, 6, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -2, 0, -3, 1],\n [1, 5, 3, -1, -6],\n [-3, 4, 3, 4, -4],\n [5, 3, -1, 0, -6],\n [6, -5, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, -4, 2, -5],\n [4, -3, 0, 2, 4],\n [2, -3, 1, 4, 3],\n [-6, -4, 3, 3, 3],\n [-3, 4, 2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -6, -2, -1, 1],\n [-1, 2, 4, 3, 6],\n [-2, -1, 0, 0, 1],\n [-4, -3, 4, -5, -6],\n [4, -2, -1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -4, -3, -2, 6],\n [-4, -2, 6, 0, -5],\n [0, 0, -2, -6, 0],\n [0, -2, 1, 1, -1],\n [6, 6, 4, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -5, 0, -3, -4],\n [5, 5, -4, -3, -4],\n [-4, -2, -5, -4, -4],\n [-5, -2, -5, 3, -5],\n [-6, 6, 1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 2, -4, -5, 5],\n [4, 1, 1, -5, 5],\n [-1, 1, 1, 0, -1],\n [-1, 1, -1, -1, -2],\n [5, 0, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -4, -4, -6, 5],\n [2, 4, 6, 5, 4],\n [-5, 6, -6, -2, -2],\n [2, 6, -6, 6, 5],\n [-3, -4, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 0, -6, 0, 0],\n [-2, 6, -1, 1, 1],\n [6, -1, -3, 2, 1],\n [1, 1, 3, -3, 5],\n [6, 4, 4, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 3, -1, -4, -2],\n [-6, -5, -3, 2, -4],\n [5, -4, -3, -1, -2],\n [-5, -2, 4, -3, -2],\n [-1, -2, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -3, 6, 4, 4],\n [-5, -1, 2, 3, -3],\n [1, -6, -6, -5, -6],\n [0, -3, 5, 1, -6],\n [4, -4, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, 5, 4, 2],\n [3, 1, 2, 5, 0],\n [4, -5, 2, -1, 3],\n [5, 2, 1, -4, 3],\n [-5, -3, 6, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 3, -5, 2, 3],\n [-2, -6, -2, 6, -2],\n [5, 3, 3, -2, 1],\n [2, -6, 3, 3, -1],\n [-4, -1, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -2, 4, -6, 5],\n [-3, 6, 0, 2, 4],\n [-3, -6, -2, 6, -3],\n [-3, -2, -6, 3, -1],\n [-2, 6, -1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 4, 2, 5, -2],\n [5, 1, -4, 2, 2],\n [-4, -5, -5, -4, -3],\n [-3, 2, 3, 6, 0],\n [1, 6, 3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -6, -4, 1, -4],\n [5, 1, -4, -4, -2],\n [2, 1, 2, -3, -1],\n [-1, -3, -5, 4, 6],\n [1, -1, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, 6, 5, 2],\n [3, 3, 2, -2, 5],\n [3, 3, -6, -6, -3],\n [-1, -5, -6, -6, -4],\n [-1, 6, -6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 4, -2, 6, 5],\n [3, 2, -3, -3, -3],\n [-4, 0, 0, 1, -3],\n [6, 6, 1, 6, -3],\n [5, 3, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 6, 0, -6, -5],\n [2, -1, -5, -5, -4],\n [-3, 2, -3, -2, 4],\n [-6, -4, -5, -6, -1],\n [-3, 5, -1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 1, 1, -5, -1],\n [3, -6, 2, -4, 0],\n [-5, 4, 0, -6, 5],\n [4, -3, -6, 3, -4],\n [-6, -4, 0, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -3, 6, 5, 3],\n [4, 0, -3, 0, -6],\n [5, 2, 0, -2, -1],\n [1, 0, 2, -4, 5],\n [4, 6, 6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 3, -2, -1, -6],\n [3, 6, -2, 1, 3],\n [4, -3, -4, -5, 1],\n [-1, -6, -3, -5, 6],\n [2, -3, -6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 2, 4, -4, 6],\n [2, -5, 3, 6, 3],\n [4, -2, -5, 2, -4],\n [5, -4, 1, 6, 1],\n [-1, 3, 1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 5, -1, 1, -2],\n [-4, -1, 4, 4, -4],\n [2, -2, -5, -2, -5],\n [-2, -5, -3, 2, 6],\n [1, 4, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 0, -2, -2, -5],\n [-5, -3, -4, -1, 5],\n [-2, -4, -4, 1, 4],\n [-5, 4, 6, -1, -4],\n [1, 3, -1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, 5, -4, 2],\n [-2, -4, -3, 3, 5],\n [1, 6, 3, 6, -3],\n [-3, -1, -5, -3, -5],\n [2, 5, -5, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -2, 3, -6, -4],\n [4, -6, 6, 4, -2],\n [2, -1, -1, -5, -1],\n [-5, 0, -4, -1, 4],\n [-5, -6, -5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -3, 0, -4, -4],\n [-3, -1, 4, 5, 5],\n [-5, -4, -2, 1, 3],\n [-2, -5, -4, -3, 2],\n [0, -4, -6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -2, 1, 4, -4],\n [1, 6, 1, 1, 0],\n [3, 3, -3, -2, 6],\n [3, -3, 3, 5, 2],\n [-4, 5, 2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -2, 2, -6, -6],\n [-4, 2, -4, -5, -6],\n [6, -6, -2, -1, 4],\n [2, -2, -2, 4, 5],\n [-5, 5, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -3, -4, 1, 3],\n [6, -3, 5, 3, 1],\n [-4, 2, -1, 1, 0],\n [-4, 6, 1, 3, -1],\n [2, -2, -4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 5, 3, 1, 0],\n [4, -2, 2, 5, -2],\n [3, 0, 2, -2, -1],\n [0, 4, 4, -2, 1],\n [2, 1, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -3, -2, 2, 4],\n [-1, -3, -2, 0, 5],\n [-3, -6, 1, -6, 3],\n [6, 6, -6, 1, 2],\n [6, 0, 5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 2, -3, -5, -1],\n [2, 6, 5, 4, 4],\n [5, -4, 0, 3, 2],\n [2, 3, -3, -3, 6],\n [1, -5, 5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 0, -6, -4, -5],\n [4, -3, 3, 3, 2],\n [0, -3, 4, -6, 0],\n [4, 2, 6, 2, 5],\n [-4, -4, -6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 3, -6, 6, -5],\n [-4, 4, -6, 6, 6],\n [-4, -4, -4, -3, -6],\n [0, 5, -1, 5, 6],\n [1, 0, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 5, -5, -5, 5],\n [-5, -2, 1, -2, -2],\n [4, 0, -1, 4, -1],\n [4, 3, -4, -1, -6],\n [0, -2, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -1, 4, 5, 1],\n [5, -4, 6, -6, 6],\n [-2, -6, 0, -4, -2],\n [-5, -6, 5, 0, -2],\n [3, 3, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -3, -1, -3, 3],\n [-6, -3, -4, -2, -3],\n [0, -6, 5, -5, 6],\n [6, 0, 0, -5, 5],\n [-4, 1, 4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -1, 5, -2, 0],\n [-5, 6, -4, -5, 4],\n [4, 0, 0, 4, -1],\n [-4, -3, 6, -3, -2],\n [1, -1, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -1, -4, -1, 4],\n [6, 5, -4, -5, 6],\n [-6, 1, -6, -6, 4],\n [6, 2, 6, -2, 1],\n [0, 5, 0, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 4, 3, 3, -5],\n [2, -2, -6, 2, 1],\n [-2, 3, -1, -4, -1],\n [-6, -6, 5, -4, -4],\n [-3, 4, 5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 4, 6, -4, -4],\n [-2, -2, 2, 5, -4],\n [1, -6, 0, 4, 3],\n [-4, -2, 2, -3, -5],\n [-5, -6, -5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 3, 1, -4, 4],\n [4, 3, 2, -3, 3],\n [-4, -5, 0, 2, 2],\n [0, 2, 3, 0, -3],\n [4, -4, -3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -3, -1, -6, 6],\n [4, -6, 1, 2, -1],\n [3, 2, 2, 4, 2],\n [-4, -5, 6, -2, 4],\n [6, -1, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, 3, -6, -5],\n [4, 5, -5, -3, -1],\n [-4, 1, -2, -6, 4],\n [-3, -4, 1, 4, 1],\n [1, 1, 4, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 4, -3, 1, 0],\n [0, -1, 3, 3, 4],\n [3, -1, -6, -5, -5],\n [5, 6, 0, 5, -6],\n [-5, -3, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 1, -4, 0, -5],\n [6, 2, 3, 5, 1],\n [-5, 2, 4, -6, 2],\n [1, 3, 6, -4, 4],\n [-6, 5, 4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -6, 3, 3, 2],\n [0, -3, 2, -3, 0],\n [2, -3, -3, 4, -5],\n [-4, -1, -2, 1, 5],\n [3, 4, -6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 3, -5, 6, 6],\n [0, -6, -3, 3, 0],\n [6, -4, -2, 4, -6],\n [4, -4, 3, 6, 2],\n [-6, 6, 5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, 3, -6, 3],\n [-3, 4, 5, 0, -5],\n [-5, 1, -1, 5, -3],\n [-3, -2, 6, -1, -5],\n [-4, -4, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 6, 2, -2, 6],\n [-6, 0, -2, 2, 4],\n [-3, 0, -5, -5, -2],\n [-1, -5, -2, -5, 6],\n [-5, -4, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 1, 2, -2, 0],\n [-5, -2, 5, -4, 6],\n [5, 1, 4, 2, -5],\n [6, 0, -2, 3, -5],\n [5, 4, -5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 4, -4, -4, -3],\n [2, -6, 5, 0, -4],\n [0, 6, 4, -2, 5],\n [0, -2, 4, -3, 2],\n [-6, -2, 6, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -4, 2, 5, -2],\n [6, -2, -3, 5, -6],\n [2, -1, -4, 2, -3],\n [-4, 1, -1, -2, 5],\n [0, -1, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, 6, 3, -5],\n [-4, 2, -6, -5, 0],\n [-2, 6, 6, 4, 3],\n [-1, 4, 6, -6, -1],\n [3, 4, 3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -3, -5, -2, 2],\n [-5, -2, 4, -3, -1],\n [3, -6, 4, -6, 0],\n [0, 6, -6, 1, 0],\n [6, -4, -1, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -1, -6, 3, -1],\n [-5, 6, 2, -2, 1],\n [5, -2, 5, 3, -2],\n [-3, -2, 6, 5, 4],\n [-3, -5, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -1, 0, 0, -6],\n [-6, -1, -5, -2, 2],\n [-1, 5, -5, 4, 5],\n [6, 0, 1, 0, -6],\n [4, -3, -5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 1, 0, 0, -1],\n [4, 2, 6, 6, -4],\n [1, 4, 2, 3, -5],\n [-4, 6, -4, -4, -5],\n [3, 6, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 1, -6, -6, 4],\n [6, -1, 0, 2, -2],\n [0, -1, -6, -4, 2],\n [6, -2, 6, -6, 2],\n [-1, 1, -5, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -1, 5, -1, -4],\n [-2, 4, 0, -3, -4],\n [-5, 2, 0, -6, 3],\n [3, 2, 3, 0, 5],\n [0, 0, 4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -1, 4, 2, -1],\n [-4, 6, 5, 4, 1],\n [4, -4, -4, -1, 4],\n [2, 3, 2, -4, 0],\n [-5, -4, 4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -2, -3, 1, -3],\n [-1, 2, -3, 6, -6],\n [-4, 4, 5, 5, 5],\n [6, 4, -1, -2, 4],\n [-4, 4, 6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -3, 6, -1, 3],\n [2, -5, -3, -3, 6],\n [-5, 4, 5, 0, -6],\n [2, -2, 0, 1, 2],\n [-3, 2, -6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, 0, 6, 4],\n [2, 2, 4, 2, 1],\n [-3, -2, -6, 6, 3],\n [4, 1, -1, 1, -6],\n [3, 0, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 0, -2, -5, 2],\n [2, -1, -3, -4, 6],\n [-5, 0, -4, -6, 1],\n [-3, 1, -2, 3, 4],\n [0, 2, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 4, -5, 2, 6],\n [4, -2, 4, -6, -5],\n [1, 1, -2, 3, -4],\n [2, 0, 6, 3, 5],\n [-2, -3, 3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -2, 5, 5, -5],\n [2, 1, -1, -3, 2],\n [6, 4, -1, -4, 0],\n [6, -3, -5, -2, -5],\n [-1, -4, 6, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, 6, 2, -6],\n [0, 4, -5, 1, -3],\n [4, 4, 4, -2, -1],\n [0, 2, 4, 5, 6],\n [6, 4, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, 0, -2, -1],\n [3, -5, -6, 4, 4],\n [-3, 6, 0, 0, -3],\n [5, 4, -4, -5, 0],\n [-6, -5, 1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 1, -5, -6, -2],\n [-2, 6, 6, 6, -6],\n [3, -3, -3, -5, -4],\n [-2, 2, -1, 3, -3],\n [-2, 3, -5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 0, 3, 6, -6],\n [5, -2, -5, -2, -5],\n [-4, 3, -1, 6, 6],\n [-1, 2, 4, 5, -4],\n [3, -5, 6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 1, 6, -5, -5],\n [2, -4, -1, 3, 5],\n [1, -4, -2, 4, -6],\n [1, -3, 3, 5, -4],\n [0, -5, -3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -5, -2, 0, 0],\n [-4, 0, 2, 5, -6],\n [-5, -6, 4, -4, 1],\n [-6, -6, 0, 4, 6],\n [-2, -5, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 6, -4, 6, -5],\n [-1, -1, -4, 4, -6],\n [-3, 2, -2, -4, -4],\n [-3, 2, 5, -4, 5],\n [6, 5, 5, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, -6, 6, 2],\n [1, -4, -4, -3, -3],\n [-1, 1, -6, -3, -4],\n [3, 5, 6, 2, 4],\n [0, 5, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 1, -5, 0, 0],\n [6, 2, 6, -3, 1],\n [5, -5, -2, -6, 5],\n [-6, -2, 3, 0, 6],\n [6, 3, -1, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 1, -2, -6, 4],\n [-1, 2, -5, 3, -4],\n [5, 5, 0, -6, -5],\n [-5, 5, 2, 4, -1],\n [3, -5, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 2, 3, -1, -1],\n [0, -1, -4, 5, -2],\n [-1, -5, 3, 1, 5],\n [4, 5, -6, 4, -3],\n [2, -3, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -2, 1, -6, 3],\n [-6, 6, -6, -4, -3],\n [6, 3, -2, -5, -6],\n [-3, 6, -2, 3, 3],\n [6, 3, 4, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -1, 1, -6, 4],\n [6, -2, 6, -4, -6],\n [1, 4, 5, 5, 5],\n [-2, -1, -3, -1, 2],\n [-2, 2, -5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 5, -3, 1, 5],\n [4, -3, -5, 4, 2],\n [-5, -5, 5, 5, -6],\n [-6, 0, 4, -4, 1],\n [5, 6, 2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 4, 2, 6, -2],\n [6, 2, 4, -1, -6],\n [-1, -4, 6, 0, 4],\n [2, 3, -3, 2, 5],\n [1, 1, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 6, -1, -4, -6],\n [-3, 3, -6, 6, 5],\n [-2, 0, -4, 4, 4],\n [-6, 2, -6, 0, 1],\n [-4, 6, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 0, -2, -1, -2],\n [2, -1, 2, -4, -4],\n [-1, 6, 6, -5, -1],\n [2, -6, -2, -1, -4],\n [3, -1, -4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 5, -6, -4, 2],\n [-3, -4, -2, 4, 0],\n [5, 3, -3, 2, 5],\n [2, -2, 5, -2, -1],\n [-5, 0, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, 5, 6, -2],\n [5, 2, 5, 6, -3],\n [-4, -2, 1, -6, -4],\n [3, -1, 4, 6, -3],\n [5, -4, 4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, -4, 1, -5],\n [-4, 3, 1, -6, 5],\n [6, 0, -5, 6, 5],\n [6, 6, -2, 6, -6],\n [-5, -6, -6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -5, 6, 1, 1],\n [-6, 1, -1, -5, -3],\n [3, -2, 5, 2, 1],\n [5, -1, -1, -2, 5],\n [-5, 5, -5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 0, -1, 3, -5],\n [-5, -2, -5, 2, 4],\n [6, 2, 5, -1, -3],\n [4, 2, 6, -1, 3],\n [5, -2, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 1, 4, -6, 6],\n [-5, 0, 5, -4, 1],\n [6, 2, 3, -4, 3],\n [2, -6, -5, -5, 0],\n [-3, -1, 1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -2, -5, -1, -6],\n [3, 6, -2, 6, 6],\n [4, 3, 4, 2, -3],\n [4, 0, -3, -4, -3],\n [6, 6, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -1, 3, -2, 6],\n [0, 6, -4, 4, 1],\n [6, 2, 2, 1, -3],\n [4, 0, 3, -6, -4],\n [4, 4, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 0, -3, 5, -1],\n [-3, -4, -2, 1, 3],\n [-4, 1, 5, 1, 0],\n [5, 0, 4, 3, -4],\n [-6, 4, -1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 0, -2, -3, 0],\n [6, 1, -5, 5, -2],\n [2, -4, -3, 0, 6],\n [5, -1, 1, 1, 4],\n [-1, -1, -3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 5, -6, -2, -3],\n [-4, -2, -5, -3, 0],\n [-1, 4, -4, -1, 6],\n [-5, -3, -6, 6, 3],\n [6, 5, 5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -4, 1, 6, 1],\n [-3, 5, 4, 3, -4],\n [-4, 4, 1, -2, -3],\n [-1, 0, 2, -5, 5],\n [3, 6, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 1, -6, 6, 4],\n [-5, 5, 6, -1, -3],\n [0, 5, -6, -6, -6],\n [3, 6, -3, 6, -5],\n [1, -4, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 4, 0, 0, 4],\n [6, 3, -5, 4, -6],\n [-6, -6, 4, -4, 6],\n [-2, -4, -4, 2, 2],\n [0, -1, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, -6, -3, -3],\n [1, -3, -4, -6, -5],\n [0, 2, 0, -2, 2],\n [-5, -5, -3, -2, 6],\n [3, -2, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 0, 0, 3, -1],\n [-2, 0, 6, -2, 1],\n [3, 3, 2, -3, 4],\n [0, 4, 0, -6, 5],\n [-5, 0, -1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, -3, -3, 0],\n [-3, 0, 5, -3, 0],\n [5, -1, 4, -6, -5],\n [1, 6, -1, 0, -1],\n [4, 6, 1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -4, -3, -1, 5],\n [-2, 6, 6, 4, 4],\n [-3, 3, 4, 4, -3],\n [5, 3, 6, -6, 4],\n [4, 5, -4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 2, -3, -6, 2],\n [-3, 2, 4, 2, -4],\n [-5, 2, -1, -3, -3],\n [0, -2, -5, 2, -6],\n [2, -1, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 6, 5, 2, 6],\n [-6, 6, -5, -6, -5],\n [3, -2, 6, 6, -6],\n [0, -2, -2, 3, 5],\n [3, -3, 1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -2, 4, -3, 4],\n [5, -3, -6, 6, -6],\n [-5, 6, 1, 5, 3],\n [-4, -1, 2, 3, 0],\n [-5, 6, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 4, -4, -2, 5],\n [1, -3, 6, 1, 6],\n [-4, 0, -6, -3, -3],\n [5, 3, 1, 0, 4],\n [-4, -2, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -3, -6, -5, -2],\n [6, -6, 3, 5, -1],\n [4, 3, -1, -3, -3],\n [-5, -4, 4, 2, 3],\n [2, -2, -1, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 2, -6, -5, -1],\n [-2, 3, -5, -5, 1],\n [-6, 5, 1, -6, 3],\n [-3, 0, 0, -5, -1],\n [-2, -2, 6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 4, -2, -5, -6],\n [-2, -4, 0, 4, -4],\n [2, 1, 3, 0, 3],\n [5, 6, 3, 2, 6],\n [4, -2, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -3, -6, 1, 0],\n [-6, 6, -2, 3, -1],\n [-6, 1, 0, 1, -2],\n [-1, 2, 0, -1, 1],\n [-4, -4, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 1, 5, -2, -2],\n [-1, -6, 0, 3, 3],\n [-6, -1, -5, 5, 6],\n [-4, -5, -2, 2, -3],\n [1, -6, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -1, -5, 6, -3],\n [2, 5, 5, 4, 0],\n [-6, 1, -1, -5, 1],\n [-5, 4, -6, -2, -6],\n [-5, 5, -3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 5, -6, 5, -5],\n [5, 1, -3, -2, 3],\n [-2, 6, -3, 0, 5],\n [5, 6, 5, 6, 5],\n [-3, 1, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -2, -3, 0, 0],\n [2, 3, -3, -4, -6],\n [0, 2, 4, 4, 5],\n [-2, -2, 1, 0, 3],\n [-5, 3, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -5, 5, -5, -3],\n [-3, -4, -1, 2, -5],\n [-6, -1, 6, 4, 1],\n [-3, 6, -2, 6, -3],\n [5, 2, 6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 2, 3, 0, -2],\n [-4, 3, -4, 6, -2],\n [4, 0, 4, 5, -5],\n [6, -6, -3, 6, -5],\n [1, 2, -3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 3, -3, 2, 0],\n [-1, 4, 1, -3, 4],\n [-1, 4, -3, -2, 1],\n [4, -5, -2, -5, -1],\n [-6, -5, -1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -3, -1, 2, -4],\n [4, -3, 6, 5, 4],\n [1, 4, 1, -5, 2],\n [6, 1, -3, 4, -3],\n [-2, 3, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 5, -3, 6, -5],\n [-5, 2, -3, -1, -4],\n [-6, 2, 1, 2, 4],\n [-5, 3, 3, -3, 1],\n [5, 0, -5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, -3, -4, -2],\n [3, -4, -3, -3, 4],\n [-5, -2, -6, 1, 0],\n [5, 4, -5, -3, -3],\n [-2, -4, 5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -5, -4, 6, -4],\n [5, 3, 4, -1, -3],\n [-6, 5, -6, -5, -5],\n [-2, 5, 3, 5, -1],\n [-3, -4, 6, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, 6, 6, 6],\n [-5, -5, 0, 4, 3],\n [0, -5, -3, 0, 1],\n [-3, -5, 6, -4, 6],\n [4, -2, 6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 4, -4, -1, 0],\n [4, -1, -2, -6, 4],\n [-6, -4, 3, 3, -3],\n [3, -6, 5, -2, 2],\n [0, 6, -5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -4, 1, -6, 2],\n [3, 0, 6, 0, -5],\n [1, 2, 0, -3, 0],\n [6, 5, 5, 2, -6],\n [-4, 3, 2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 2, 2, 2, 2],\n [-4, -5, 6, -2, 0],\n [-2, -6, 2, -2, -4],\n [-1, 3, -2, 2, 1],\n [3, 3, 5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, 1, 2, 5],\n [1, 4, -1, 2, 4],\n [2, 6, 3, -3, 2],\n [3, 6, -2, 0, 6],\n [-6, -3, 5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -1, -6, -3, -3],\n [-6, 6, 1, -2, -4],\n [1, -2, 3, -4, 0],\n [0, -1, -6, 6, 5],\n [3, 5, 2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -1, -1, 5, -5],\n [-4, -2, -1, -3, -4],\n [6, 3, -1, 3, 0],\n [-1, -2, 0, -1, -6],\n [4, 1, 3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -1, 6, 2, 4],\n [-6, 1, -4, 2, 6],\n [-1, -6, -1, 2, 2],\n [5, 2, -4, 1, -6],\n [4, -2, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 2, 4, -1, 1],\n [0, 0, 2, -5, -6],\n [-5, -5, 6, -1, 1],\n [3, -6, 1, -3, -2],\n [0, 5, 5, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, -1, -5, 6],\n [3, 1, 6, -2, -3],\n [3, -5, 2, 3, -6],\n [-2, 2, -3, -6, -1],\n [-5, 0, 4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -1, -4, -3, 5],\n [-6, 1, 5, -1, -1],\n [5, 4, 2, 3, -4],\n [-1, 5, 3, -4, -2],\n [3, -6, 6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 3, 3, 6, -2],\n [1, 3, -3, -2, -5],\n [-2, 4, 0, 6, -1],\n [3, 2, 6, 2, -6],\n [4, -4, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, 5, 0, -1],\n [0, -2, 3, -1, 6],\n [1, -5, 0, 5, -6],\n [3, 0, -1, 2, 5],\n [-6, 5, -4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -2, -2, -6, 0],\n [2, -5, 1, -6, -3],\n [-6, 3, -3, -3, 5],\n [6, 0, 0, 2, 3],\n [-6, -5, 3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -3, 2, -2, -5],\n [0, 2, 5, -3, 1],\n [0, 4, 1, -6, 0],\n [3, -5, -3, 5, 6],\n [-6, -6, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 3, -6, -5, 0],\n [6, 4, -1, -2, 0],\n [6, 5, -2, 6, -4],\n [-6, 1, 1, 2, 6],\n [-6, 1, 1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 6, 4, -4, 6],\n [2, -1, 3, -2, -4],\n [3, -4, -1, -2, -2],\n [4, 3, -1, 1, 5],\n [2, 3, 2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 1, 4, -3, 1],\n [5, -1, 1, -3, -3],\n [0, 6, -4, 3, 1],\n [6, 1, -2, -3, 6],\n [-1, -1, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -1, -4, 5, 4],\n [-3, 5, 0, -6, -4],\n [4, -6, 1, -3, -1],\n [3, 5, -6, -3, 6],\n [5, 0, 4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 5, 2, -4, 0],\n [0, -4, 5, 4, -6],\n [2, -1, 3, -4, 6],\n [-1, -4, 5, -6, -2],\n [-2, 0, -5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -3, 6, -4, 3],\n [0, 1, -1, -5, -4],\n [5, 2, 5, 4, -1],\n [-5, -2, -3, 6, -5],\n [5, -6, 5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 4, 4, 1, -1],\n [-1, -4, 0, -2, 5],\n [6, 5, -1, 2, -3],\n [2, 3, -6, -3, 5],\n [2, -2, 0, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -6, 1, 6, -2],\n [4, -5, 0, 6, 5],\n [-4, -6, 5, -5, -1],\n [-4, -5, 3, -5, 2],\n [5, -3, -3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 5, -1, -1, -1],\n [-6, 2, -6, -6, -1],\n [5, 6, -4, -6, 1],\n [-5, -4, 2, -1, 3],\n [-2, -3, -5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -5, -5, -1, -3],\n [-6, 0, 2, 1, 4],\n [-5, 2, -6, 2, -2],\n [-6, 0, 2, 5, 0],\n [1, 2, -1, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, -1, -6, -1],\n [3, 4, -4, 4, 6],\n [0, 0, 6, -2, 2],\n [2, -1, -4, 6, 0],\n [5, 5, 6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -2, -5, -2, -5],\n [6, -3, 4, -3, 3],\n [1, 5, -4, 3, 1],\n [3, 1, 6, 1, -3],\n [0, 1, 1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -3, 3, 2, -5],\n [-3, -6, 4, -6, 6],\n [0, -3, 1, -6, -4],\n [0, 6, 5, 3, -6],\n [-1, 0, -6, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -6, -4, 4, 2],\n [6, -2, -1, 5, 4],\n [1, -6, -1, -4, 6],\n [-4, 3, 6, 6, -5],\n [5, -4, -5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 2, -1, -5, -6],\n [0, 6, 5, 1, 5],\n [0, -6, -2, -1, 5],\n [2, -5, -4, -4, -3],\n [-3, 2, -3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 3, 5, 1, -2],\n [3, 6, -6, 3, -5],\n [-4, 5, -4, -2, 0],\n [3, -6, -4, 6, 4],\n [-3, 3, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -3, -3, 5, -3],\n [-2, -1, 3, -4, -6],\n [6, -6, 3, -1, 5],\n [-6, 3, 5, -6, -6],\n [1, -2, 6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -4, 2, -3, -3],\n [4, -1, -6, -1, -1],\n [6, -6, -1, 3, 2],\n [0, 3, -6, 4, 0],\n [5, -4, 5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, 2, -2, 5],\n [3, 5, 2, -6, 6],\n [2, -4, -3, -1, -1],\n [-5, 5, -3, -4, -4],\n [5, 1, -4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 4, -2, 3, 5],\n [-2, 1, 6, -4, 4],\n [-5, -3, -2, 1, 0],\n [-5, 4, 2, -4, -6],\n [3, -2, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 0, 3, -2, -6],\n [-2, 2, 0, -1, 6],\n [5, -3, -1, -2, -2],\n [-6, -5, -5, -1, -5],\n [6, -3, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 6, -2, 5, 0],\n [6, 5, 1, -2, 4],\n [0, 4, 0, 4, 5],\n [-5, 6, -4, 4, 6],\n [-3, 1, 5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -4, -3, 3, -6],\n [-2, -2, 6, -6, -6],\n [-4, 2, 0, 2, 1],\n [2, 2, -2, 5, 5],\n [-4, -5, 5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 6, 6, 3, -3],\n [1, 3, -1, -4, 3],\n [-4, -1, -3, 6, 6],\n [3, 6, -4, 1, 5],\n [-6, -1, 1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 5, 2, 2, 5],\n [-5, -2, -1, 5, 3],\n [3, 3, -1, -3, 0],\n [4, -2, -4, 2, 6],\n [3, -5, 3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -5, 4, -4, 4],\n [-5, 0, -4, -2, -2],\n [-4, -5, -3, 2, -6],\n [-4, 5, 1, 6, -3],\n [1, -6, -4, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 2, -1, -6, -6],\n [-1, -2, -2, 3, -5],\n [0, 5, 3, 1, 2],\n [1, 3, -4, -2, 4],\n [6, -3, 0, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 4, -3, 1, 1],\n [2, 4, 6, 0, -2],\n [-3, -2, 3, 4, 6],\n [-3, 1, -3, -2, -4],\n [-6, -4, -4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 1, 4, 0, -3],\n [5, 6, 2, -5, 4],\n [5, -3, 5, -3, 6],\n [-6, 6, 4, 4, 4],\n [-4, 1, -1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -4, 0, 3, -3],\n [3, 6, -2, 5, 3],\n [4, 3, 1, 4, -5],\n [-5, 4, 0, 6, 4],\n [3, 4, -4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 2, -4, 2, -2],\n [1, 3, -4, -2, -4],\n [-1, -2, -4, 3, 4],\n [-4, 5, 3, -4, 3],\n [-1, 5, 0, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -1, 1, -1, 0],\n [6, 0, -5, 5, 4],\n [3, 0, 6, -4, -2],\n [6, -4, 3, -5, -6],\n [-1, -6, -4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 3, 6, 6, 0],\n [0, 0, -4, -6, 0],\n [-1, -3, 2, -6, 1],\n [0, 4, -2, 3, 3],\n [4, 6, 0, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 4, -6, -1, 6],\n [-2, -5, 2, 4, 6],\n [2, -3, 5, -2, -3],\n [4, -2, -1, 6, -2],\n [-3, -3, -6, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -2, 1, 6, 3],\n [-6, -5, -6, -6, -4],\n [4, 5, -5, -1, 6],\n [5, 6, 6, 1, -2],\n [2, 6, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -4, -4, -1, 6],\n [3, 3, -4, -3, 3],\n [4, -1, -6, 0, -6],\n [6, 4, -1, -1, 3],\n [0, 6, -5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -4, 0, -2, -6],\n [-6, 1, -3, -1, -3],\n [4, 1, -4, 5, -2],\n [6, 0, 1, 4, 6],\n [-2, 3, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, -4, -5, 1],\n [-2, 3, 5, -1, 1],\n [0, -1, 6, -4, -2],\n [-6, 0, 0, -1, 5],\n [-1, -2, 1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -2, -3, -4, -5],\n [1, 4, -5, 2, 2],\n [5, 2, -4, 3, 6],\n [-3, -1, -2, 0, 4],\n [3, 1, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 5, -5, -1, 5],\n [0, -2, -5, 1, -1],\n [1, -1, 4, 3, 2],\n [1, 2, -4, 6, -5],\n [5, -6, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 3, 4, -1, 2],\n [2, 5, -1, 4, 0],\n [2, 1, -5, -2, -2],\n [-1, 4, 5, -6, -5],\n [2, 1, -3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 1, -4, -1, -4],\n [-4, -4, 6, 6, 6],\n [0, -6, 0, -3, -4],\n [-1, 4, -4, -2, 6],\n [-2, 2, 2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -2, 2, 5, 0],\n [5, -2, -2, 5, -5],\n [-3, 0, 3, -2, -6],\n [1, -4, 1, -5, 0],\n [-5, -4, -1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -4, -4, 2, 1],\n [4, -5, 2, -4, 2],\n [6, -2, 3, 0, 0],\n [-2, -4, -4, 0, -2],\n [0, -6, -1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 5, 2, 4, 5],\n [3, 6, -6, 6, -4],\n [-4, 3, 6, 0, 0],\n [-3, 5, 4, -1, 5],\n [-6, -3, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -4, 4, 6, 2],\n [-3, -4, 2, 3, 6],\n [0, -2, 1, 3, 1],\n [0, -4, -4, -4, -5],\n [0, -2, 4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 2, -1, 6, 4],\n [-5, 0, -6, -5, -2],\n [5, 4, 5, 0, -5],\n [5, 2, 1, 4, -5],\n [0, -2, -6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -6, 2, 2, -6],\n [1, 5, 5, 0, -5],\n [3, 2, -2, -2, 1],\n [-1, -5, 0, -6, 4],\n [-5, 4, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -2, 6, -3, -2],\n [-2, -2, 0, 3, 1],\n [1, 5, 4, -5, 6],\n [3, 2, 3, 0, -6],\n [-5, 0, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, -2, -6, 1],\n [-2, 0, -5, -3, 0],\n [3, -5, 6, 4, 6],\n [0, -3, 4, -6, 6],\n [3, -3, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 6, -5, 4, -2],\n [-2, -1, -5, 2, -3],\n [-3, -5, -6, 4, -3],\n [-4, -1, -5, 6, 4],\n [2, -4, 6, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 1, 3, 3, 4],\n [4, -1, -5, 6, -3],\n [-3, -4, -6, -3, 1],\n [-4, 3, -3, 5, -4],\n [3, -5, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -1, 0, -3, 0],\n [-1, -3, -1, 4, -1],\n [0, -6, 6, 1, -3],\n [0, 0, -1, -6, 6],\n [6, 1, -2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 2, 4, -1, -3],\n [-2, 4, 4, -1, -6],\n [2, 3, 1, -5, 0],\n [-3, -4, -1, -1, 0],\n [1, 1, 5, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, -2, -2, 0],\n [1, 4, -2, 5, 0],\n [2, 6, 5, -3, -6],\n [-2, 2, -1, 6, 6],\n [5, 0, -5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 0, -2, 3, 1],\n [4, 4, 1, -3, -3],\n [-6, -4, -1, 2, 1],\n [0, 1, -4, 6, -4],\n [6, 6, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -1, 5, -5, 6],\n [-4, -5, -6, 4, 1],\n [-6, 1, -3, -6, -4],\n [-6, -6, -6, 3, 0],\n [-3, -4, -5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -1, 6, 1, 1],\n [0, 0, -6, 3, 5],\n [-4, 0, -4, -4, -3],\n [-1, -2, -4, 2, -6],\n [2, 5, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -3, -1, -3, 0],\n [6, 5, -2, 5, -4],\n [1, -5, -5, 3, 6],\n [-1, 5, -2, -1, 2],\n [4, -1, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -5, -3, 3, 1],\n [-4, -1, -2, 4, -1],\n [-5, -1, -6, -3, 6],\n [-6, 1, 5, -1, 2],\n [-2, 1, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, -6, -2, -6],\n [-1, 4, 1, 5, 4],\n [-5, 5, -1, 2, 5],\n [2, 4, 4, 6, -5],\n [-3, 0, 1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 4, -1, 1, -3],\n [-1, 0, -5, 3, -1],\n [-2, -5, 3, -1, -5],\n [3, 4, -6, 6, -5],\n [1, -6, 2, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 0, -6, -3, -6],\n [-3, -6, -5, -5, -4],\n [2, 5, -1, 4, -3],\n [6, -4, 4, -2, 5],\n [5, 1, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 2, 4, -3, 5],\n [-3, -4, 1, 3, 3],\n [-6, 1, 3, -6, -4],\n [2, 3, 0, 2, 4],\n [0, -1, 4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 3, 3, 4, 1],\n [-5, -5, -2, 5, -6],\n [5, -4, 4, 1, 1],\n [2, 3, 1, -4, -4],\n [-5, -6, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 2, -5, -3, 2],\n [5, 4, 2, 2, 4],\n [1, -1, 4, -6, 2],\n [-6, 5, 4, 2, 3],\n [4, 1, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, -5, 6, -6],\n [-5, -5, 3, -5, 1],\n [-5, 0, -6, 4, 3],\n [-3, -5, -1, 6, -1],\n [6, 4, 3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -6, -5, -1, -3],\n [0, -1, -3, -3, 0],\n [-6, -1, 5, -2, 4],\n [-3, -2, -2, -2, -5],\n [5, 0, -5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 4, 2, 3, 5],\n [6, -4, 6, 0, -6],\n [4, -6, -3, -5, -3],\n [-6, -1, -5, -2, -2],\n [-2, -1, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, -3, 6, 6],\n [-5, 4, -6, -6, -6],\n [1, -1, 5, -2, 4],\n [0, 0, -4, 3, -3],\n [-4, 3, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 2, 2, 1, 3],\n [0, -3, -3, -2, -3],\n [4, 4, 6, 6, -6],\n [-3, 4, 4, 4, -5],\n [-5, 6, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 6, -6, -2, -5],\n [2, -3, 1, -1, 3],\n [-5, 5, 0, 3, -1],\n [4, 3, -6, -5, 2],\n [-3, 6, -1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 0, 2, 1, 6],\n [5, -4, 0, 2, 2],\n [1, 0, -4, -4, 1],\n [0, -5, 4, -3, 4],\n [1, 6, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 5, -4, 0, -2],\n [0, 2, 4, 2, 3],\n [-3, 4, -2, -2, -6],\n [-5, -1, 3, 2, -1],\n [3, 0, 1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -2, 1, 1, -4],\n [2, 0, -6, -1, -6],\n [-3, 1, -6, -2, 1],\n [1, 0, 3, 1, 6],\n [6, 4, 2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -2, 4, 6, -1],\n [-3, -3, -4, -2, -6],\n [-5, 0, 0, 6, 4],\n [-6, -5, 5, -3, -5],\n [-2, 3, 3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -1, -3, 5, -1],\n [2, -5, -1, 5, 6],\n [-4, -4, 1, 0, 2],\n [5, 5, 1, 6, -5],\n [-1, -4, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -4, -6, -4, -3],\n [6, -4, 3, -4, 4],\n [-4, -6, -4, 1, 2],\n [4, -3, -5, 1, -5],\n [-1, -3, 3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, 0, 2, 6],\n [-5, 6, -6, 5, 0],\n [2, 5, 1, -6, -1],\n [-6, -2, 0, -1, -2],\n [1, 0, -6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 3, 3, 0, -5],\n [-2, 6, 6, 6, 5],\n [1, 6, 4, 4, 3],\n [-1, 1, 4, -6, 5],\n [-6, 4, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 2, -3, 2, 1],\n [0, -6, -1, -1, 0],\n [-2, 1, -5, -5, 1],\n [1, 0, -6, -3, 1],\n [-1, 0, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -4, 0, 4, 2],\n [2, -2, -6, 5, 6],\n [-3, -3, -5, 2, -6],\n [-3, -5, 5, -2, 0],\n [3, -3, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -2, 0, -1, 1],\n [2, -5, -6, -1, 6],\n [-3, 5, 1, 1, -4],\n [5, 6, 3, -4, 0],\n [5, 6, 5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -2, 4, 5, 1],\n [4, -5, -5, 0, 4],\n [2, -2, 4, 1, 1],\n [-4, -3, -2, 0, -2],\n [-6, -3, -3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -2, -1, 2, 2],\n [6, -6, -2, -3, 5],\n [6, 5, 5, -4, 3],\n [1, 0, 6, 1, 6],\n [-1, -1, 6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -3, 3, -5, 2],\n [-1, 0, -2, 4, -1],\n [1, 5, -3, 3, -6],\n [-4, -2, -3, -6, 2],\n [-3, -6, 0, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 1, 2, 0, 5],\n [2, -4, 3, -6, -6],\n [5, -4, 2, -4, -5],\n [4, 5, -2, 3, -6],\n [-3, 0, -5, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 4, 1, -4, 3],\n [2, -6, -2, 5, 6],\n [6, 4, 2, -1, -2],\n [0, 2, 0, -6, 1],\n [5, -6, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -5, -4, 2, 2],\n [-2, -4, 2, -2, 1],\n [-5, 2, 2, 6, -4],\n [5, 1, -1, 0, -5],\n [0, -4, -1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 0, -2, -3, 6],\n [2, 4, -3, 0, -4],\n [4, -3, 2, 2, -2],\n [3, -1, 0, -6, -5],\n [-3, 5, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -2, 3, 5, 6],\n [-6, 6, 2, -3, -5],\n [5, 1, 1, -3, 3],\n [-2, -6, -6, -5, 6],\n [-5, -4, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -3, 5, 3, -5],\n [-1, -4, -1, 2, -1],\n [-5, -5, -2, 0, -6],\n [3, -2, -6, 4, 4],\n [-6, -6, 4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -3, -5, -4, -6],\n [4, 1, 3, 4, 2],\n [-2, -1, 0, -1, -4],\n [-2, 6, 3, 1, 4],\n [3, 6, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -5, -5, -2, 1],\n [4, -1, 6, -2, 5],\n [-5, 4, -2, 3, 0],\n [-5, -1, 6, -3, -6],\n [1, -5, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, 0, 0, 0],\n [0, 3, 4, -5, 6],\n [1, -5, 2, 6, 5],\n [4, 2, -5, 4, 2],\n [-6, -2, 1, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 2, 5, 5, -1],\n [-1, -5, 6, -5, -3],\n [3, -6, -4, 3, -6],\n [0, -1, 5, -3, -1],\n [1, 5, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -5, 6, 5, 5],\n [3, 2, 1, -3, -5],\n [0, 0, -5, -4, 5],\n [1, 3, -6, 5, 3],\n [-1, 5, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -4, 2, -6, -2],\n [-2, 1, -6, 5, -2],\n [1, 3, 2, 2, 3],\n [1, -6, 1, 4, 0],\n [-4, 2, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -2, -2, -1, 1],\n [1, 2, -1, 3, -1],\n [2, 6, -1, -3, -6],\n [-3, -2, 1, 5, -6],\n [6, 1, 0, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 4, -2, -6, 2],\n [6, 2, -4, -4, 4],\n [1, -5, 1, -2, 6],\n [5, -5, -1, -3, 4],\n [-6, 3, -5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 5, 5, 5, -5],\n [4, -1, -3, 2, 1],\n [-6, -5, -5, 2, 5],\n [-2, 3, -3, -2, 2],\n [0, 4, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 4, 1, 1, -4],\n [-1, 0, 6, -2, 3],\n [0, 6, 5, 3, 0],\n [2, -3, -3, -6, -4],\n [1, -5, 6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -5, 3, 2, -5],\n [4, 6, -2, 6, 5],\n [-4, 4, 0, -1, -2],\n [5, 6, 3, -1, 3],\n [-6, 0, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -6, -5, -2, 4],\n [-5, 5, -4, 1, 4],\n [2, 2, 3, -3, 5],\n [-1, 3, 6, -2, -6],\n [4, -1, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 2, -2, -2, -6],\n [-4, 4, 1, -4, -5],\n [-5, -5, -6, 5, -4],\n [-4, -2, 3, 6, 5],\n [-2, 2, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 2, -2, -4, 1],\n [0, 5, 5, -4, -4],\n [5, -5, 5, 4, -4],\n [-2, 4, 6, -5, 1],\n [-5, 0, -1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -4, 2, -3, 1],\n [-1, 1, -1, -3, -3],\n [-4, 0, 0, 6, -1],\n [1, -1, 0, -1, 4],\n [5, -2, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -6, -2, -3, 0],\n [-4, 4, -4, -1, -4],\n [0, 4, 6, -1, 0],\n [-4, 2, -4, -4, -6],\n [5, -2, -1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, -1, -6, -5],\n [-6, -3, -1, 0, 4],\n [5, 3, 2, -6, 1],\n [4, 1, 6, -3, 5],\n [3, -5, 1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 2, 5, 4, 2],\n [-5, 4, 5, 2, -4],\n [1, 3, 3, -2, -5],\n [-5, 6, -5, -3, -5],\n [2, 4, 1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -1, -5, -4, -4],\n [4, 1, 3, -2, 3],\n [0, 6, 6, 4, -6],\n [-3, -6, -6, 5, -5],\n [-4, 4, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -3, -1, 6, -2],\n [-5, -5, 0, -4, -3],\n [-2, 3, 2, -6, 4],\n [2, -2, 5, 4, 1],\n [-3, 1, -3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 6, 1, -5, 1],\n [-4, -6, -1, 4, -2],\n [-6, -2, -2, -6, 0],\n [4, 2, -1, 3, 3],\n [-1, -5, -3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -3, 0, -4, -1],\n [-4, 4, 3, -4, -5],\n [1, 2, -4, -1, -2],\n [1, 2, 0, 3, -2],\n [5, -4, -1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 6, 3, -4, 1],\n [-1, 1, 3, 6, -5],\n [3, 2, -6, 5, -6],\n [-3, 5, 5, -4, 1],\n [3, -4, 3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -5, -6, -2, -3],\n [-4, -6, 2, -3, 5],\n [6, -6, -3, 6, 2],\n [-3, -2, -2, 4, -5],\n [-1, -1, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 2, -2, 0, -6],\n [-5, -3, 6, 4, 4],\n [2, 4, 5, 2, 4],\n [-2, 3, 2, 6, -4],\n [-3, -3, 1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 4, 3, 2, 2],\n [5, -4, -6, 5, -2],\n [-5, -3, 1, -5, -4],\n [5, -1, 4, -3, -5],\n [-5, -6, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 3, -4, -5, 5],\n [-2, -5, -2, 4, -5],\n [-6, -6, 4, -2, 1],\n [-2, 1, 6, -1, 6],\n [6, -2, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 6, 4, -3, 2],\n [-1, 0, -1, -3, 4],\n [6, 1, 0, 3, -4],\n [-1, 6, -4, 0, -1],\n [0, 4, -2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -1, 0, -6, 0],\n [1, -6, -4, -2, 5],\n [3, 0, 2, 1, 2],\n [3, -4, -5, -6, 0],\n [-3, -3, 6, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 6, -1, -6, -4],\n [-3, 3, -6, -4, -1],\n [5, 5, 5, 6, 5],\n [-6, 6, -1, 0, 6],\n [3, -4, 4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 6, 5, -5, -6],\n [-4, -4, -4, -3, -2],\n [1, -5, -6, -4, 3],\n [2, -6, 1, 3, 3],\n [5, 3, -1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, -6, 5, 3],\n [-1, -4, -2, 1, 2],\n [-2, 2, -6, -6, -1],\n [3, 1, -5, -1, -3],\n [6, -5, -2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 4, 4, 5, -2],\n [3, 1, 5, 6, 6],\n [2, 6, -1, -1, 1],\n [6, -2, 3, 4, 5],\n [-2, -2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -2, 3, 0, 2],\n [-3, -5, 1, -5, -6],\n [6, 4, 5, -2, 1],\n [-6, 1, 2, -4, 6],\n [1, -3, 6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -3, 5, -6, -6],\n [2, 1, -4, 0, -4],\n [-5, -5, -3, -5, 5],\n [0, 5, 2, -5, 4],\n [-5, -2, -5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, -5, -2, 2],\n [1, 2, 0, 0, -3],\n [0, 0, 2, -1, 2],\n [6, 4, -5, 0, 1],\n [5, -1, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 3, -2, 0, 0],\n [3, 4, 3, -1, 6],\n [-2, -2, 2, 1, 6],\n [4, 1, -2, -1, -4],\n [-4, -1, -5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 6, 3, 5, 2],\n [-1, -5, 1, 5, 4],\n [0, -5, 4, -4, 5],\n [-1, 6, 5, -4, 5],\n [-6, -3, 0, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -1, -3, 0, 1],\n [0, 4, 1, -3, -6],\n [0, -1, 4, -5, 1],\n [2, 0, 1, -1, -2],\n [-1, -5, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -2, -1, -2, 5],\n [1, -1, 6, 6, 2],\n [2, 6, -1, -2, 6],\n [1, -3, -6, 3, -1],\n [-2, -4, -2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -6, -2, 1, 4],\n [0, 5, -2, 4, -1],\n [-1, 0, -1, 5, 1],\n [-5, -6, 1, 0, 6],\n [-3, 0, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -2, -2, 1, -3],\n [4, 5, 3, 5, -3],\n [5, -5, -2, 4, -3],\n [6, -1, 2, 0, -4],\n [3, 1, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, 4, 4, 5],\n [-2, -4, -3, 3, 1],\n [3, 2, -3, 2, -1],\n [5, 5, 0, 2, 4],\n [0, -6, 5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -5, -6, -6, 1],\n [-6, -2, -6, -5, -5],\n [4, -3, -5, -1, 4],\n [6, -3, 5, -3, -5],\n [-2, -4, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 1, -3, -4, -2],\n [-1, -3, -6, -1, -4],\n [-5, 0, 2, -3, -3],\n [1, -5, 3, -1, 4],\n [5, 1, 3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -5, -5, 3, 4],\n [3, -6, -2, 0, 1],\n [3, -4, 5, 2, -1],\n [-2, -4, 6, 5, -1],\n [1, 1, 5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 3, 0, 3, 0],\n [1, -2, -1, 4, -4],\n [-2, -3, 6, 2, -1],\n [-4, -5, 1, 1, -3],\n [0, 1, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 0, -3, 4, -3],\n [-3, -6, 2, -5, 2],\n [4, 1, -5, 3, -4],\n [4, 0, -3, 4, -6],\n [-5, -2, -3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -2, 5, -4, -4],\n [2, -4, -5, 6, 2],\n [4, -1, -6, 6, 4],\n [-3, 3, 3, 2, -4],\n [-5, 6, -6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -6, 2, 2, -5],\n [-1, -2, 3, 1, 4],\n [6, 1, -3, -2, 1],\n [4, -3, 2, -4, -1],\n [-6, 6, -3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 6, -2, 5, 4],\n [-2, -2, 2, 4, 5],\n [4, 1, 4, -1, -4],\n [3, -2, -2, -3, 6],\n [1, 5, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -5, -3, -5, -3],\n [-5, 0, 0, -1, -4],\n [4, 4, 5, -3, -1],\n [-1, 5, 0, 6, 2],\n [4, 2, -2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 4, 3, 1, 0],\n [-6, 1, 6, 4, 5],\n [-6, -1, 4, -3, -1],\n [-6, 5, 4, -5, 4],\n [-5, -5, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 4, 1, 0, -3],\n [2, 3, 5, -2, 1],\n [6, -5, 1, 4, -3],\n [4, -2, 4, -5, 2],\n [-4, 0, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -3, 0, -4, -1],\n [-5, 6, 0, 4, -4],\n [0, -6, -3, -3, 5],\n [3, -1, 3, -4, 4],\n [2, -2, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 6, -5, -4, 4],\n [6, 4, 0, 4, 6],\n [3, -5, -2, -4, 5],\n [-5, -2, -5, 3, 2],\n [-3, -6, 1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -1, -6, 5, 2],\n [-1, -3, -4, 4, -6],\n [2, 3, -1, -3, -6],\n [5, -1, -2, -3, -1],\n [2, -3, 1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -1, 1, 3, -5],\n [-3, -6, 3, 1, 2],\n [-4, 1, -1, -1, 6],\n [-5, -1, -2, 2, -4],\n [6, -5, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, 0, -5, -4],\n [-2, 4, 4, 2, -6],\n [3, 2, -2, 1, 3],\n [-4, 5, 0, -1, 1],\n [5, 6, 1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -4, 2, 6, -1],\n [-5, 4, 3, 3, 5],\n [-2, -3, -1, -4, 6],\n [6, -6, 0, -5, 3],\n [-6, 5, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -1, -6, -2, 6],\n [0, -1, 0, 0, 2],\n [-6, -4, -2, -6, 4],\n [-5, -2, 3, 6, -2],\n [-3, 4, 6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 6, 5, 6, -2],\n [0, -1, -4, -5, -4],\n [1, 1, 5, 0, -5],\n [-4, 1, 1, 1, -2],\n [-1, 3, -6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 6, 2, -3, 0],\n [-2, 6, -5, -6, -4],\n [-1, 2, -5, 4, -5],\n [5, 0, -3, 5, -4],\n [0, 0, 2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 0, -3, 2, -1],\n [5, 5, -6, -2, -3],\n [1, -3, 6, -3, -2],\n [-1, -5, -1, 2, 5],\n [-5, -4, -1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 6, -1, -4, 6],\n [5, 2, 4, 0, -3],\n [-6, 0, -3, 3, -4],\n [2, -3, -5, 1, 5],\n [-1, -3, -4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 2, -1, 0, 0],\n [-6, 4, -3, 5, 0],\n [0, -5, -2, 3, 3],\n [3, 6, 5, -1, -6],\n [5, -1, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 3, -6, 0, 4],\n [5, -3, 1, 5, -6],\n [-6, 4, -1, 5, -1],\n [-1, 2, 0, 6, 6],\n [-1, -4, 0, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -3, 0, -5, 5],\n [5, -3, 4, 5, -4],\n [1, 4, -2, 0, -3],\n [1, 0, 0, 5, 5],\n [-4, 1, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -5, 0, -2, -1],\n [6, 6, -4, 4, 2],\n [2, 6, 6, 6, -6],\n [4, 1, -6, 5, 5],\n [0, 4, -5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, 3, -1, 0],\n [2, 1, 0, -4, -6],\n [-1, -3, 2, -5, 4],\n [-2, 4, -3, 2, -2],\n [5, 0, 4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 1, -3, -3, -5],\n [5, 3, 5, -2, 2],\n [0, 2, 0, 3, -3],\n [-4, 2, -1, -5, -5],\n [-6, -4, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -2, -3, 2, 4],\n [5, 3, 4, 4, -5],\n [3, 1, 2, -4, 1],\n [-1, -6, 6, 6, -5],\n [-5, -2, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, -4, 3, 4],\n [3, -4, 1, -3, -5],\n [5, 3, 1, 6, -3],\n [4, -4, -6, -4, -6],\n [1, -2, 0, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 1, -3, -3, 4],\n [-2, 4, 0, -2, -5],\n [-1, 3, -1, 4, -3],\n [-2, -1, 4, -6, -3],\n [4, 4, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 2, 3, 6, -1],\n [1, 2, -1, -3, 2],\n [5, -2, 6, 1, 6],\n [-2, -5, 0, 4, -1],\n [6, 3, -3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 6, 6, 5, -5],\n [0, -5, 6, 2, 1],\n [-6, 4, 4, 0, 6],\n [-3, 5, -5, 6, 2],\n [1, 3, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 2, -2, 3, 2],\n [-5, -2, 6, -1, 6],\n [2, -1, 1, 3, 1],\n [-1, -3, -1, 0, 6],\n [3, 1, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -1, -3, 0, 5],\n [4, -2, 5, 0, 2],\n [1, 2, 3, 2, -3],\n [3, 4, 1, -3, -1],\n [-3, 3, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -4, 1, 1, 5],\n [6, 4, 4, -1, 0],\n [6, -2, 5, 4, -3],\n [-1, 0, 3, -6, -2],\n [2, -5, -3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -3, 3, -3, 6],\n [3, 2, 2, 0, 1],\n [2, -3, 0, 6, 4],\n [-2, 3, -2, -2, 5],\n [-3, 3, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -5, 6, 4, 2],\n [0, 6, 5, 6, 3],\n [-3, -3, 4, -3, -3],\n [-4, 2, 5, -4, -5],\n [5, 1, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 1, -4, -3, -4],\n [-3, 1, 2, 3, -3],\n [-1, 5, 4, 3, 3],\n [-5, 3, -6, -6, -5],\n [2, 1, 6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 3, 3, 0, 5],\n [4, 5, -2, -3, 3],\n [1, 3, -2, -5, 1],\n [1, -4, -4, 3, 2],\n [-2, -6, 2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -6, 0, 5, -1],\n [3, -4, 2, -5, -3],\n [-2, -6, 2, 6, 5],\n [-3, -5, 0, -5, 4],\n [6, -6, -6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -3, -3, 5, -1],\n [6, -3, -5, -6, -6],\n [-4, -2, -1, 5, 1],\n [4, -2, 2, -6, 5],\n [-2, -6, 6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 0, 5, 5, -2],\n [2, -1, -5, 0, 3],\n [-3, -6, -4, -2, 6],\n [-4, -3, 3, -2, 1],\n [-4, -5, 0, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -4, 4, -5, -6],\n [-2, 3, 5, -1, -3],\n [6, 4, -2, -2, 2],\n [-3, -1, -6, 5, -3],\n [-6, 5, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -4, -5, 4, -4],\n [-3, 0, 2, 3, 4],\n [-4, 4, 1, -5, 1],\n [2, -4, 0, 2, 6],\n [-4, 6, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -4, 1, -2, -2],\n [0, 1, -6, -4, -6],\n [-1, -1, -2, -2, 5],\n [-2, -5, 2, 6, 1],\n [-5, -3, 5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -1, -4, 6, 2],\n [1, 0, -2, -2, 1],\n [-3, 3, 2, 1, -2],\n [2, -1, -5, -1, -3],\n [6, 1, 3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -2, 1, -2, 2],\n [-1, 0, -5, -6, -1],\n [-2, -1, 5, -3, 4],\n [-3, 5, -2, -3, -4],\n [-2, -4, -6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 2, 0, -3, 6],\n [0, 2, -4, 3, 0],\n [-2, -4, 6, -6, -5],\n [-5, -1, -3, -4, 1],\n [3, 5, -5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -3, -6, 4, -6],\n [3, 4, 6, 1, -2],\n [-2, 3, -6, -3, 6],\n [1, -2, -6, 5, -4],\n [2, 3, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -6, 4, -4, 5],\n [-4, -1, -2, 4, 5],\n [5, -5, 3, 0, -5],\n [0, -1, 3, -4, -3],\n [0, -1, 5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 0, 0, -1, 2],\n [-2, 2, -5, -1, 3],\n [-1, -6, -2, -5, 6],\n [6, 5, -4, 2, -2],\n [-1, 0, 3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, 5, 3, 4],\n [4, -1, 0, 5, -4],\n [0, -6, -1, -2, 0],\n [5, -4, -1, -5, 1],\n [1, -3, -1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 5, -3, -1, 5],\n [3, -2, -1, 3, -2],\n [1, -5, -5, 4, 6],\n [5, 1, 0, 3, -3],\n [4, -1, -1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 3, -4, 0, -4],\n [-6, -2, -5, -3, -4],\n [0, 4, -6, -2, 5],\n [2, 6, -1, -6, 0],\n [-4, 1, 5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -2, -6, 3, 2],\n [0, -5, 1, -4, 6],\n [2, 3, -3, 6, 6],\n [2, 3, 4, 3, -1],\n [6, 1, 3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -1, 2, 0, 0],\n [6, -6, -1, -3, 6],\n [-4, 5, 5, 1, -6],\n [-2, 2, 6, 4, 1],\n [-3, -2, -1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 3, -2, -1, -6],\n [5, 0, -6, 4, 4],\n [-1, 6, 4, -2, -5],\n [-2, 6, -6, -4, -4],\n [2, -6, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 2, -6, -4, 2],\n [-1, 2, 6, -4, 1],\n [4, -1, 2, 4, 2],\n [1, 4, -3, 0, -2],\n [6, 4, -3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -1, 2, 6, 0],\n [-5, -6, -6, -5, -1],\n [2, -3, 2, 0, -6],\n [-5, 2, 4, 5, 6],\n [1, -5, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 3, 5, 4, -3],\n [4, 5, 4, -3, -2],\n [-6, 0, -4, -2, -2],\n [-5, -1, -1, 4, 5],\n [4, 5, -5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -1, -4, 1, -3],\n [-1, 0, -5, 1, 1],\n [5, -6, -1, 4, 1],\n [5, 5, -1, 3, 3],\n [-6, 2, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 2, -6, 1, -5],\n [4, -6, 0, 1, -4],\n [6, -6, 4, 6, 0],\n [-5, -5, -1, -6, -4],\n [-5, 6, 1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 0, 1, -1, 3],\n [-4, -1, 0, -1, 2],\n [-2, 1, 6, -2, 1],\n [3, 6, 3, 4, 5],\n [-2, -6, 5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -1, 4, 5, 3],\n [4, 2, -2, -1, -5],\n [-1, -4, -2, 5, -4],\n [-5, -1, 0, 6, 5],\n [-4, 2, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -6, -6, -6, 2],\n [5, 4, 6, 3, -2],\n [-1, 4, -5, 5, 4],\n [3, 2, -6, -3, 3],\n [1, 2, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 0, 2, 3, 5],\n [-1, 2, 0, -4, 5],\n [5, -5, -2, -3, 0],\n [-2, 5, 0, 5, -5],\n [0, 1, -6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -4, -1, -5, 1],\n [-2, 1, 5, -6, -6],\n [5, 6, 3, -2, -1],\n [-5, -6, -4, 3, -5],\n [1, 5, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -4, 5, -1, 0],\n [-4, 3, -3, -4, 4],\n [4, 3, 2, 0, 5],\n [-1, 3, 2, 2, -6],\n [-1, 0, 0, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -4, -2, 2, -5],\n [3, -6, -5, 0, 2],\n [0, 4, -4, -6, -5],\n [2, -3, 6, 2, 3],\n [-6, 1, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 4, -3, -2, -4],\n [-3, -2, -2, -6, -1],\n [1, -4, -3, 0, 6],\n [-6, -3, 6, -5, -5],\n [-4, 5, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -4, 4, 4, 0],\n [-3, -5, -6, 6, 1],\n [-6, 0, 5, 0, -4],\n [1, 6, 0, -4, 1],\n [5, -2, 6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 5, -5, -1, 2],\n [0, 2, 4, 5, -3],\n [-3, -6, 2, 5, -3],\n [-1, 1, -3, -1, 4],\n [1, 2, 6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -5, 3, 3, 2],\n [3, 2, -4, -6, -5],\n [-3, -1, -4, -3, 3],\n [2, 4, -1, -3, 3],\n [-5, -2, -4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 4, -5, 4, 4],\n [0, 1, 3, -1, 0],\n [-5, -2, 4, 4, -1],\n [-3, -6, 3, 6, 4],\n [4, 0, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -6, -3, 5, -4],\n [-1, -4, 1, -6, -5],\n [-2, -3, 6, -5, 0],\n [1, -5, 5, 4, -2],\n [5, -4, -6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -5, 1, 3, 0],\n [3, 0, 2, 3, 3],\n [6, 5, 1, -5, 0],\n [1, -3, -1, 5, 4],\n [-6, 3, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, -4, -4, -4],\n [-4, -1, 5, -2, -3],\n [3, -6, 6, -6, 1],\n [4, -3, -6, 0, 3],\n [-1, -5, 3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -6, 6, -3, -4],\n [-5, -1, -3, -3, 0],\n [-6, -2, 0, 4, -4],\n [-1, 2, -5, 2, 2],\n [4, -4, -6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, -5, 2, 4],\n [-3, 4, 6, -4, 3],\n [6, -3, -6, 1, -2],\n [-1, -3, 5, 1, -1],\n [4, -3, 2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -3, -6, -6, -3],\n [4, 0, 0, 6, 1],\n [4, -4, 3, 4, -4],\n [-4, -4, 1, 0, 3],\n [5, 6, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -3, -6, -6, 3],\n [1, 6, 3, -4, 1],\n [-2, -2, -2, 1, -2],\n [1, 2, 4, -2, -6],\n [-6, -6, 1, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -2, 1, 3, -4],\n [-5, 0, 3, 4, -6],\n [2, 3, 2, -4, -5],\n [2, 5, 0, -3, -2],\n [5, -3, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -4, 5, -3, -6],\n [1, -2, -5, 3, 3],\n [0, 2, -4, 0, 5],\n [2, 0, -3, -6, -3],\n [4, 0, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 0, 6, 1, 5],\n [-6, 1, 5, -6, 2],\n [-4, -6, 0, 5, -6],\n [-2, -6, 0, 5, 6],\n [-4, 4, 3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 3, -5, -6, -3],\n [-3, 0, -5, 1, -5],\n [-3, 4, -4, -2, 3],\n [0, 2, -4, 1, 1],\n [-4, 5, -1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 5, -4, -3, 6],\n [0, 6, 4, -2, 0],\n [0, 1, 0, -5, 3],\n [-1, -1, 2, 4, 2],\n [1, -2, 3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 4, 6, 4, -1],\n [5, 5, 1, -5, -4],\n [-6, 0, 5, 3, 1],\n [6, -6, 3, 4, 2],\n [2, 6, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -2, 3, 3, 0],\n [-1, -3, 6, -4, 4],\n [1, 4, -6, -5, 3],\n [6, 5, -1, -1, 0],\n [1, -2, 5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 1, 5, -5, 4],\n [-4, 6, -4, -2, 0],\n [-2, -3, -4, 5, 2],\n [-3, -5, -4, -4, 1],\n [1, -5, -3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, 1, -4, -5],\n [5, -6, 3, 5, -3],\n [3, -4, 5, 2, -5],\n [-3, -5, -2, -5, -6],\n [-4, 3, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 2, -5, 2, -2],\n [2, -4, 5, 5, 6],\n [6, 1, 3, 0, 3],\n [-6, 2, 3, -6, 1],\n [3, 3, 3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 6, 1, 1, -6],\n [-1, -4, -6, 3, 0],\n [-2, 4, -1, -6, -4],\n [-5, 4, 0, -3, 0],\n [5, -5, 5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -3, 3, 0, -4],\n [-6, 1, 2, -4, 4],\n [5, 4, 6, 3, -2],\n [6, -3, -5, 6, -4],\n [-5, -3, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 3, -3, 2, -6],\n [5, 6, -6, -3, 4],\n [4, 5, 6, -6, -2],\n [6, 3, -2, 2, 1],\n [0, 3, 0, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 0, -3, 3, 1],\n [-3, -6, 6, 1, -4],\n [0, 5, 1, -3, 1],\n [-6, -4, 4, 6, 1],\n [5, 3, -2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, 4, 0, -3],\n [-6, -5, -5, -5, 2],\n [4, -3, 2, -5, 0],\n [4, -3, 1, 0, 0],\n [2, 0, 6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -4, 5, 4, -3],\n [1, 0, -6, -5, -2],\n [-5, 2, 5, 4, 1],\n [-5, -5, 0, -4, 0],\n [4, 1, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, -1, 1, 0],\n [0, -2, -1, 0, 2],\n [0, -4, -6, 0, 5],\n [-5, -1, 0, -3, 4],\n [2, 2, 1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 0, -5, 4, 2],\n [-3, -1, 0, 3, 5],\n [-2, 4, -5, 0, -6],\n [-3, -2, -1, 3, -1],\n [-4, 0, -2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -2, 4, -3, 1],\n [4, 6, 4, -2, -4],\n [1, -5, -1, -4, -5],\n [-5, 0, 4, 6, -2],\n [3, 1, 2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, -4, 2, 4],\n [-2, 5, -1, 0, -3],\n [2, -3, -5, 3, 4],\n [0, -3, 5, 6, 3],\n [0, -3, 3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, -2, 4, -6],\n [5, 5, 2, -5, 2],\n [5, 5, 0, 5, -5],\n [-5, 5, -5, 1, 4],\n [5, -6, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -4, -4, 6, -3],\n [0, -5, 3, 3, -1],\n [-4, -5, 4, -1, 1],\n [4, 5, 6, -6, -3],\n [0, -5, -2, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 2, 6, -4, 6],\n [-4, 1, -4, -5, -2],\n [3, -5, 1, -4, -6],\n [-2, -2, 4, -3, 3],\n [-5, 1, -3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 6, 0, 5, -5],\n [5, 4, 6, 0, 2],\n [-3, -1, 5, 0, -6],\n [1, -1, 0, 3, 1],\n [1, -2, -5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 4, 5, 3, -3],\n [-2, -3, 5, 4, 1],\n [4, 0, -1, -5, -4],\n [-2, 4, -4, 6, -5],\n [-1, 5, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 3, -3, -1, -1],\n [-6, 4, 0, -2, 6],\n [-4, 0, -5, 4, 0],\n [6, 2, 2, -2, -3],\n [4, 6, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 2, -6, -5, -6],\n [-4, -3, 0, -5, 0],\n [-3, 2, 6, 1, -6],\n [-2, -3, -6, 5, 6],\n [2, 3, 6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 5, 5, 1, 3],\n [2, 5, -3, 3, 6],\n [-6, 1, 5, -1, -1],\n [0, -1, 6, -5, -1],\n [0, 3, 2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 5, -1, 6, -5],\n [6, -2, -6, -2, 2],\n [-6, -5, 5, -5, -6],\n [-5, 3, -2, 1, 4],\n [0, -1, -5, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 5, -2, -4, 5],\n [-4, -3, -4, -6, -2],\n [6, -1, 1, 3, 6],\n [-5, -3, -3, -5, 3],\n [-6, -3, 1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -3, 1, -3, -2],\n [-5, 2, 5, -2, 6],\n [3, 1, -5, -5, 5],\n [-4, 6, -5, 6, 5],\n [2, -6, 6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 1, 5, 4, -2],\n [1, 0, -6, 5, 4],\n [-4, -1, 3, 2, 4],\n [2, 3, -5, 6, -2],\n [6, -6, 0, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 3, -2, 6, 6],\n [-1, -3, 4, 6, -2],\n [-3, -4, -6, 4, 2],\n [5, -6, -5, -6, -2],\n [4, -1, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -5, 4, -2, -3],\n [-5, 4, 6, 1, 4],\n [5, 6, -1, -3, 1],\n [-4, 2, -3, -3, 6],\n [1, -3, 3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 0, -4, 2, 5],\n [4, 0, -5, 0, -3],\n [5, 2, -3, -6, -5],\n [6, 0, -5, 2, 5],\n [-4, 0, -4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, 1, -3, -4],\n [5, 5, -5, 3, -3],\n [5, -4, 2, 5, -4],\n [-1, 4, -2, 1, 1],\n [-4, 4, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 4, 4, 1, 3],\n [0, 5, -3, 6, 6],\n [-2, 4, -6, -4, -5],\n [3, -3, 1, -4, -6],\n [5, 5, -6, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -1, 2, -1, -1],\n [-2, 5, 6, 6, 1],\n [5, -2, -6, -6, 5],\n [6, 3, 5, 0, -5],\n [-2, -6, 5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 1, 6, 1, -2],\n [6, -4, 4, -2, -4],\n [-2, 3, -1, 4, -1],\n [-3, -4, 6, 0, 6],\n [-5, 5, 1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -4, 4, 6, 3],\n [-4, 0, -3, 4, -6],\n [-4, -4, 1, -2, -3],\n [-5, 2, 4, -1, 2],\n [-2, -1, 6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 2, 3, 5, -2],\n [-2, 4, 6, -1, -2],\n [-6, -3, 3, -2, 1],\n [1, 1, 3, -4, -3],\n [-2, -5, 5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 3, 0, -1, -5],\n [4, 5, 0, -3, -6],\n [4, 2, 6, -5, 1],\n [-5, 4, -5, 6, -4],\n [-6, -6, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -1, -6, -1, -1],\n [-4, 0, -3, -1, -3],\n [5, -4, -1, 2, 5],\n [0, -5, -5, -4, 0],\n [-3, -3, -6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, 4, -6, 6],\n [1, 0, -2, 0, 3],\n [2, -5, 3, -2, 1],\n [2, -1, 1, -1, -4],\n [3, 6, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -4, 2, 3, 6],\n [1, 1, -1, 1, -3],\n [-2, -1, 6, 3, -5],\n [-5, 4, -2, 2, 6],\n [5, 2, -4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -3, 1, 4, 4],\n [0, -4, 4, -4, 6],\n [-5, 4, -1, -1, -4],\n [-6, -3, 1, -6, -4],\n [-4, -6, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 3, -5, -4, 5],\n [5, 5, 3, -2, -5],\n [-4, 6, 0, -4, -6],\n [1, 2, 1, 6, 0],\n [4, 1, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 5, -1, 0, 4],\n [2, 1, 4, 0, 5],\n [-1, 4, -4, 0, 3],\n [0, -1, 4, 1, 1],\n [-1, 5, 4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -2, 3, -3, 3],\n [-5, -6, -4, 6, 5],\n [3, 1, 5, 3, 2],\n [2, -1, -3, 6, -6],\n [-4, -3, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -3, -1, -3, -6],\n [-3, 1, 0, -6, 6],\n [-4, -4, 0, 0, 6],\n [-3, 2, 0, -5, -5],\n [-5, 5, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -6, -2, -6, 3],\n [-6, 3, 3, -3, -5],\n [1, 4, -6, -1, -2],\n [3, 5, -4, 2, 0],\n [6, 5, 6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 3, -2, -2, 0],\n [2, 0, 0, -2, 6],\n [1, 1, 6, -4, 4],\n [-4, 2, 2, -6, -2],\n [1, -6, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, -3, 0, -1],\n [4, -3, -5, 6, -5],\n [-5, 0, 3, 1, -4],\n [6, -6, -5, 1, 6],\n [1, 2, 4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, 0, 4, 0],\n [0, -1, -4, 4, 1],\n [0, 0, -4, 5, 6],\n [-4, -6, 3, 5, -3],\n [-4, -2, -3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -3, 4, 2, 6],\n [4, 6, 6, 0, 3],\n [4, 6, 4, -3, 6],\n [-1, -2, 3, 6, 0],\n [-3, -6, 1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 6, -2, -4, 2],\n [-3, -3, 5, -2, 1],\n [-1, 4, -3, 4, 0],\n [2, 1, -2, -4, 2],\n [-5, -3, 1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -2, -1, -1, 1],\n [-4, -2, -6, -5, -5],\n [5, -3, -3, 3, -1],\n [2, 2, 4, -6, -4],\n [5, -4, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 1, -1, -3, -5],\n [-2, -2, 2, 2, -4],\n [-1, -4, 4, -4, 1],\n [-2, -2, -6, 6, 1],\n [6, -3, -5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -1, 1, -2, -3],\n [-4, 3, 3, 4, 5],\n [-4, -6, 0, 0, 1],\n [-2, 1, -4, 6, -3],\n [6, -5, 6, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 1, 4, 4, 2],\n [1, -4, 5, -5, -5],\n [-5, -4, -5, 2, -6],\n [-5, 5, -2, -1, 1],\n [3, -1, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 5, 1, -5, 5],\n [0, -3, -1, 4, -2],\n [-3, -3, -5, -5, -4],\n [5, 3, 0, -4, 3],\n [-2, 0, 4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -5, 3, 4, -6],\n [-4, 2, 5, -1, -4],\n [-2, -3, 1, 3, 1],\n [0, -6, 1, -3, -4],\n [5, 0, 3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, -2, 6, -1],\n [0, 0, 0, 2, -3],\n [-2, -2, -2, 6, -1],\n [5, 2, 2, 4, -3],\n [1, 0, -6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, 1, 3, -1],\n [-1, -4, -5, -5, -2],\n [4, -4, -6, 3, 6],\n [1, 2, 6, 6, 4],\n [-2, 1, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, -1, 5, 0],\n [4, 1, -5, 0, 3],\n [-1, 2, 2, -4, -6],\n [4, 1, -2, -6, -2],\n [5, -2, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -4, 0, 1, -3],\n [-2, -4, -4, 6, 6],\n [-6, 2, 1, 0, 4],\n [-4, 3, 1, -6, 1],\n [-2, 4, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, 4, 2, 1],\n [6, 2, 1, -1, -5],\n [-5, -1, -3, 3, 2],\n [1, 2, -6, -3, 2],\n [-5, 0, 0, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, -5, 6, -5],\n [1, 0, -6, 2, -4],\n [3, -2, 4, 5, -4],\n [2, 5, 1, 1, -1],\n [-2, -4, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -3, 5, -3, 0],\n [-1, 1, 1, -1, -4],\n [-5, 5, -3, 2, 5],\n [5, 6, -5, -2, -1],\n [1, 4, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 6, -1, -2, -5],\n [-4, -2, -1, -3, -4],\n [6, -2, 2, 1, -6],\n [-6, 1, 2, 4, -5],\n [-2, 5, 1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -3, -2, -3, 3],\n [1, 5, -5, 5, -1],\n [4, -6, 5, 5, -2],\n [-2, 0, 0, 3, -1],\n [2, 6, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 1, 1, -2, 4],\n [3, -5, 4, 6, -2],\n [5, 2, -3, 4, -5],\n [-2, -3, 5, -2, 6],\n [-3, -1, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -6, 3, -6, 4],\n [-2, 5, 2, -4, -2],\n [5, 6, -3, 6, -4],\n [-6, -1, -1, 5, -3],\n [5, -6, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 6, -6, 1, -2],\n [0, 6, -5, -3, -4],\n [0, -1, -2, -5, -6],\n [0, 5, 3, -3, 3],\n [-4, 0, 1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -4, -1, -1, -4],\n [-2, -2, 6, -4, -3],\n [2, -2, -5, 0, -1],\n [4, 5, 4, 3, 6],\n [4, 5, -5, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -2, 2, 5, -6],\n [0, -5, -5, 2, 3],\n [-5, -5, -6, 5, 6],\n [-1, 5, -3, -6, 0],\n [3, 3, -6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 3, -2, 3, 0],\n [-3, -5, 6, 0, -2],\n [0, 5, -3, 0, -2],\n [6, 4, 3, -6, -3],\n [-5, 3, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -5, -5, -2, 6],\n [3, -5, -4, -2, 2],\n [-2, 4, -2, 6, -1],\n [6, 0, -2, 4, 6],\n [2, -6, -3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 3, 0, -4, 5],\n [-4, 5, 0, 4, -4],\n [3, 3, 1, 2, 3],\n [1, -1, 0, 0, -6],\n [-6, -6, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -4, -4, 4, 2],\n [5, -4, 2, -1, -4],\n [6, -1, 3, 3, -6],\n [3, 6, 4, 6, 1],\n [-5, 2, 1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, 1, 4, 0],\n [3, 1, -5, -3, -1],\n [5, 2, 0, 4, -3],\n [4, 4, -5, -3, -1],\n [1, -3, -1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -4, 1, -3, -2],\n [-4, 2, -2, 3, -4],\n [-1, 3, 2, 2, 2],\n [5, 2, 3, 5, 4],\n [2, 3, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, -4, 6, 1],\n [6, -1, 1, -1, -2],\n [0, -2, -1, 5, -6],\n [-6, -6, 4, 0, 6],\n [6, -5, 6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 3, -1, 5, -5],\n [4, 3, 0, 1, 3],\n [3, -5, 4, -1, -6],\n [-6, 5, 2, -5, 5],\n [6, 0, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -5, -2, 2, 6],\n [2, -5, 5, 3, -5],\n [4, 0, -3, 5, -3],\n [4, -4, 1, -2, -1],\n [1, -3, 1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 6, 3, 6, -4],\n [3, 1, -4, -5, 1],\n [1, -5, 3, 6, -6],\n [4, -6, 0, -1, 1],\n [-6, -2, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -4, -3, -1, -5],\n [-5, -4, 3, -1, -4],\n [3, -1, 3, -5, 5],\n [3, -6, -4, 1, -2],\n [1, 5, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 6, -1, 5, 3],\n [-1, 5, 3, -6, 3],\n [-2, -6, 1, -1, 6],\n [-1, 0, -5, -5, -1],\n [1, 2, 6, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 1, -2, 1, 2],\n [4, 1, -1, 0, -5],\n [1, -2, -3, -1, -3],\n [3, -1, -2, -3, 4],\n [-1, -5, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 0, 1, 5, -5],\n [-2, 2, -3, -5, -4],\n [3, 2, -1, -3, 2],\n [5, -3, 1, 5, -4],\n [-2, -2, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -5, 3, -3, 3],\n [-2, -1, 2, -6, 2],\n [-3, -5, 3, -6, 6],\n [5, 3, 4, 1, 1],\n [-6, -2, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, 2, -5, 0],\n [-5, -2, 3, -4, 5],\n [1, -2, -6, 6, -1],\n [2, 3, -1, -4, -5],\n [2, -6, 6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 3, 5, 2, 3],\n [-5, -1, 5, -5, 5],\n [-4, 2, 5, -3, -5],\n [-5, -3, 4, 2, 6],\n [0, -6, -3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 5, -2, -2, -1],\n [-3, -1, 0, -2, -3],\n [2, 4, 3, 5, -4],\n [5, -6, 6, -4, -5],\n [-4, 6, -1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 2, 4, 4, 0],\n [-1, 4, -2, 3, -4],\n [-4, 6, -5, 1, -6],\n [2, -4, 2, -5, -1],\n [-5, -1, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -1, -4, 3, -6],\n [4, 4, 0, -2, 4],\n [-6, -1, 0, -1, -3],\n [-5, 3, -6, 4, 6],\n [-5, -3, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 4, -4, -4, 6],\n [-2, -3, -5, -2, 0],\n [-2, 4, 5, 3, -6],\n [-1, 0, -4, 2, 2],\n [-5, -2, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -4, 4, -2, 0],\n [6, 6, 5, -1, -3],\n [0, -2, 6, -2, 3],\n [-6, -6, -6, 6, -6],\n [-6, 2, 0, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -1, -2, 0, -3],\n [4, 2, 5, 6, -4],\n [3, 0, 5, -3, 3],\n [0, -2, -2, 4, -2],\n [-5, -1, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, -4, -1, -3],\n [5, 6, 0, 1, -4],\n [5, -6, -5, -2, -3],\n [4, 1, -3, 2, 3],\n [-5, -3, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -3, -1, -2, -3],\n [-2, -1, 1, 2, 6],\n [6, 3, 3, -6, 3],\n [5, 4, 0, 2, -2],\n [-5, -5, 5, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -2, 4, 1, 0],\n [-1, 4, 5, -5, -5],\n [-5, -6, -4, -4, -5],\n [-4, 1, -1, -3, 0],\n [-3, 2, 4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -1, -5, 5, 5],\n [0, -1, 3, -3, -5],\n [2, 6, 6, 6, 3],\n [4, 2, 1, 6, 5],\n [-3, -4, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -3, 2, 1, 1],\n [-3, -5, 0, 5, 5],\n [4, 2, 2, 6, 2],\n [3, -2, 2, 4, -6],\n [2, 0, 5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -5, -4, -5, 3],\n [-5, 3, 2, 4, 1],\n [2, 6, -2, 0, -4],\n [-4, 6, -3, 1, 1],\n [5, 6, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -6, 5, -6, 3],\n [1, 4, -3, 0, 1],\n [6, -4, 5, -1, 0],\n [-4, 4, 6, -2, -1],\n [1, -5, 6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -1, 5, 6, -4],\n [-1, -6, 4, 4, -2],\n [1, -4, -2, -5, 1],\n [-5, -1, -1, 4, -6],\n [6, -4, -1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 6, 4, 1, -2],\n [-4, 4, 0, -1, 3],\n [6, -4, -1, -4, 3],\n [-5, 2, 5, 0, 2],\n [3, -3, -1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 4, -1, 0, 1],\n [-6, -3, 5, 6, -5],\n [1, 4, -3, 3, 2],\n [5, -3, 4, 4, -2],\n [-4, -3, 5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 6, -6, -5, -3],\n [1, -3, 6, 3, -5],\n [1, -5, -1, 1, 6],\n [4, -6, -5, -2, -6],\n [-5, 6, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 2, -5, 6, -1],\n [-6, -6, -5, -3, -4],\n [-5, 0, 0, 0, 6],\n [-5, -2, 3, 5, -4],\n [-5, 3, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -4, 1, -5, -3],\n [-4, 5, 3, 0, -1],\n [5, 6, -2, -5, -5],\n [-6, -6, -6, 6, -1],\n [2, 3, -3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -6, -4, 4, -1],\n [-6, 0, -5, 3, -1],\n [2, 1, -6, 4, 2],\n [-6, -6, -2, -6, 3],\n [-6, 5, 5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 4, 0, -5, 2],\n [-3, 0, -2, -1, -5],\n [-6, -2, 6, 2, -4],\n [6, 6, 0, 2, -5],\n [0, -5, -5, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 5, 4, -1, -6],\n [-4, -6, -5, 4, 2],\n [4, 6, 5, -6, -4],\n [3, -6, 5, -3, 5],\n [-4, 3, -6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 0, -3, -2, 4],\n [4, 1, 5, 5, 5],\n [6, -2, 0, 3, -5],\n [-4, -3, 4, 4, 0],\n [-5, 0, -3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, 2, 4, -1],\n [1, -2, 4, -6, -3],\n [-4, -1, -3, 4, 0],\n [-3, 4, 2, 0, 5],\n [-1, 4, 6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 1, -1, 3, -6],\n [-5, 3, -4, 2, 1],\n [2, 2, -4, -4, -3],\n [6, -5, 3, 6, 2],\n [1, -2, 3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 5, -3, 6, -1],\n [1, 1, -3, -3, -3],\n [-1, 2, 0, -1, 1],\n [-6, -6, 3, 6, 4],\n [-4, -6, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -2, -3, 2, 3],\n [1, 4, 1, -4, 4],\n [-6, 3, -1, -5, 1],\n [-4, -6, -6, -3, 5],\n [2, 2, 0, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 0, -6, 5, 4],\n [-4, 2, -3, -6, 3],\n [-6, 5, -6, 5, 6],\n [0, 6, -6, 5, -4],\n [3, 2, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 5, -6, -2, -4],\n [-4, -5, -2, -5, -3],\n [0, -1, 0, 2, 1],\n [-3, -2, 5, 3, -6],\n [1, 5, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 5, -6, -6, 6],\n [-6, -1, 1, 6, 1],\n [2, -6, 4, 1, 5],\n [-2, -5, 0, 1, -1],\n [-5, 3, 6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -1, 0, 2, 2],\n [4, -1, -4, 3, -4],\n [-4, 0, -4, 5, -5],\n [5, 3, 4, 5, -1],\n [-1, -2, -6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 0, -5, 2, -5],\n [-3, -1, -1, -1, -5],\n [-4, -6, 3, -6, -1],\n [0, -1, -5, 4, 0],\n [-3, 2, 4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -2, -1, 6, -2],\n [0, -3, -6, 2, -1],\n [-1, 5, 2, -4, -1],\n [0, 1, 1, -5, -4],\n [5, -5, -6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, -4, -6, 1],\n [-2, 2, -6, -2, 3],\n [-2, -1, -5, -1, -4],\n [0, 4, -2, -1, 6],\n [2, -1, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 6, 1, -3, -6],\n [-3, 2, 2, -6, 5],\n [3, 3, 5, 4, -4],\n [-2, -2, -5, -2, 5],\n [1, -4, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 2, -5, -5, 0],\n [3, -5, -2, 5, -6],\n [1, -2, -4, -3, 5],\n [3, 3, 1, -1, 4],\n [2, -1, 6, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 4, 2, 3, 2],\n [-5, 0, 5, 6, 3],\n [0, -5, -3, 3, -6],\n [-2, 1, -1, -2, 1],\n [-3, -6, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -4, 5, 1, -3],\n [-5, 1, 1, 5, 3],\n [-2, 6, -4, 3, 6],\n [6, 2, 3, -1, 4],\n [3, -4, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -6, -2, 3, 4],\n [2, 1, -3, 3, -3],\n [4, -5, -6, -4, -2],\n [1, -5, -2, 0, 1],\n [1, 1, 6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -1, -3, 2, -4],\n [-1, -6, 6, -5, 1],\n [-3, -2, -4, -5, 4],\n [5, 3, 2, 4, 0],\n [-3, 5, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, -2, -2, -4],\n [-4, -1, 6, -4, 1],\n [-1, 5, -5, 4, 2],\n [3, 6, 0, 3, 3],\n [5, 1, 4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -5, 0, 2, 2],\n [-2, -1, -1, 3, 6],\n [-4, 4, 0, 3, -2],\n [3, 3, -6, 3, 4],\n [-4, -2, 0, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 3, 1, -2, -1],\n [-5, -3, -5, 3, -5],\n [-1, -3, 5, -1, -3],\n [6, 0, -4, 4, 0],\n [0, 4, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 3, -1, 4, -4],\n [3, 3, -3, -3, -5],\n [-6, -2, -4, 3, 0],\n [-5, 6, -2, -3, 5],\n [4, 6, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, 3, -2, -4],\n [-4, 0, 1, -1, 4],\n [-1, -1, -4, -4, 0],\n [-6, 4, 0, -5, 3],\n [-5, 4, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 3, 5, -3, 6],\n [6, 6, -1, 4, -4],\n [-5, -1, -2, 5, 5],\n [-6, -6, -6, 5, -2],\n [1, -5, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -1, -2, -3, -6],\n [4, -3, 4, 2, 3],\n [4, -3, -1, -6, -2],\n [0, -4, 1, -3, -5],\n [5, 5, 4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 5, -6, -4, 4],\n [2, -5, 3, 4, -3],\n [0, 3, 1, 2, 0],\n [1, -4, 3, -1, 0],\n [2, 1, -2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 1, 6, -6],\n [1, 1, -4, -2, 0],\n [-3, 4, 4, -4, -6],\n [1, 6, 6, 1, -4],\n [-6, -6, 0, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 2, -2, -1, 5],\n [-4, 5, -2, 1, -5],\n [-3, -5, 5, 1, -4],\n [-3, -5, 6, 1, -5],\n [-1, -6, -4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 5, -1, -3, -2],\n [6, -4, -1, -2, -6],\n [3, -5, 6, 5, 6],\n [3, -3, -5, 2, 3],\n [0, -5, -2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -4, -6, -3, -2],\n [-3, 2, -1, 6, 2],\n [-5, 3, 6, 3, -1],\n [-5, 2, 2, -3, 0],\n [-1, -5, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -3, 4, -5, -6],\n [3, 2, -3, 3, -4],\n [-6, 5, 5, 5, -1],\n [5, -2, 4, 4, 3],\n [-5, 3, 6, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -4, 1, -1, 1],\n [0, -3, -4, -6, -6],\n [-4, -1, -6, -1, 3],\n [-2, 1, -1, 6, -4],\n [5, -6, 4, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 5, 5, -1, 6],\n [3, 3, 2, 6, -3],\n [3, -4, 3, -4, 0],\n [6, -3, 1, 4, 3],\n [6, -5, 1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -5, -2, 2, 6],\n [3, 6, 3, -1, -3],\n [0, 4, 6, -1, -5],\n [-1, -1, -6, 0, 2],\n [1, -4, 1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 4, 3, -4, 2],\n [0, 1, 3, 3, -2],\n [3, 6, -5, -6, -1],\n [1, 3, 3, 3, 4],\n [2, -3, 6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 6, 6, 4, -4],\n [-6, 0, 6, -1, 3],\n [0, 6, -4, -2, -5],\n [2, -4, 5, 3, 5],\n [5, 1, 2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 2, -6, -2, -6],\n [0, -1, -3, -3, -6],\n [-1, -3, 3, -4, 2],\n [-6, -4, -6, -6, 5],\n [2, 4, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -5, 5, 3, 6],\n [-4, 4, -5, -6, -2],\n [0, 3, -6, 5, -4],\n [-1, -2, 1, -5, -5],\n [-1, -6, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 2, -4, 4, 6],\n [-6, -4, -1, 4, -5],\n [3, -5, -5, -1, -5],\n [-3, -3, -4, -3, 4],\n [-4, -4, -1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 1, 5, -1, -2],\n [-6, -3, -3, 1, -1],\n [-2, -1, 2, 1, -1],\n [4, -3, -2, 0, 3],\n [5, 4, 3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 4, -3, 5, 0],\n [0, -1, 2, 4, -2],\n [0, -5, -2, 3, 4],\n [4, -3, 5, 0, 0],\n [-1, 6, -3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -5, 1, 4, 6],\n [4, 0, 0, 5, 2],\n [-6, 4, 1, -5, -3],\n [6, -5, 0, 5, 5],\n [3, -3, -3, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 1, -1, -1, -4],\n [6, 4, 2, -2, 0],\n [-1, -5, -4, -1, -4],\n [6, 0, 1, -4, 1],\n [-6, -1, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 5, 6, 6, 5],\n [5, 2, 4, -5, 0],\n [1, 2, -4, -4, -4],\n [-6, -3, -6, 2, -1],\n [4, 3, -1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, -2, -1, -5],\n [6, -2, 5, 1, 5],\n [-6, 0, 2, -4, -3],\n [2, -6, -6, 4, 4],\n [-2, -3, -5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 4, 4, 5, 4],\n [5, -5, -5, 0, -1],\n [2, 5, 4, 3, -5],\n [-6, 4, -1, 0, -6],\n [4, 1, -4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 2, 6, -6, 4],\n [4, -6, 5, -1, 1],\n [-2, -2, 0, 0, -4],\n [-6, -4, -6, 4, -6],\n [-5, -3, 4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -3, 4, 1, -3],\n [-2, 5, 5, -3, -5],\n [5, 3, 2, -4, 6],\n [5, -5, -6, 4, -2],\n [0, 2, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -2, 5, 4, -1],\n [3, 1, 3, 2, 4],\n [4, -6, 0, 0, 5],\n [-5, 2, -5, 2, -3],\n [3, 2, -5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -5, 1, 1, -5],\n [-4, -6, 6, 1, -1],\n [2, 1, 5, 5, 0],\n [5, 1, -4, -6, -5],\n [1, 4, -5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -4, -3, -5, -4],\n [1, -5, 6, 0, -3],\n [-6, 0, -4, 2, -1],\n [-2, -5, -1, 6, -3],\n [1, -4, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, 3, 2, 2],\n [6, -6, -6, 3, 0],\n [3, 2, 3, -6, -5],\n [0, -2, -1, 3, -5],\n [3, -5, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 1, -1, 3, 1],\n [1, -1, -4, -4, 5],\n [-6, -5, 0, 0, -3],\n [2, 1, 2, -3, -3],\n [3, -6, 4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 5, -3, 4, 4],\n [2, -1, 6, 1, -6],\n [6, -1, -4, 4, -5],\n [-5, 5, 4, 6, 1],\n [-3, 1, 3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -1, 1, 5, -1],\n [-1, -4, -1, -4, -6],\n [-5, -5, -5, 0, -1],\n [-4, 6, 6, -4, -3],\n [5, 3, 3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -5, -1, -2, -2],\n [-4, 5, 6, 1, 0],\n [6, 1, 4, -6, 4],\n [-1, -6, -5, -2, -2],\n [3, -3, -1, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -3, 2, -2, 6],\n [-4, -2, -3, -1, -6],\n [-4, -6, -4, 4, 0],\n [-4, 2, -3, 5, 4],\n [3, 3, -5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 6, -6, 5, 3],\n [0, -1, 3, -3, -2],\n [-5, -1, 4, -3, 3],\n [4, -3, 2, 5, 3],\n [2, 4, -6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 3, 0, 0, -4],\n [-6, 5, 5, -6, -3],\n [-2, 2, 0, -1, -3],\n [6, -5, 3, 2, -5],\n [-1, 6, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, -3, -4, 0],\n [3, 2, -2, 5, 5],\n [0, 4, -6, 1, 4],\n [6, 3, 2, -4, 5],\n [-1, 5, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -6, -1, 5, -6],\n [-5, -6, 0, -5, -5],\n [4, -4, 2, 6, 3],\n [-1, 4, 4, -5, 3],\n [-1, 6, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 3, 0, 6, -4],\n [5, 4, 2, -1, 1],\n [4, 3, 6, 5, 5],\n [2, 3, 0, 5, 5],\n [5, -4, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -6, -1, -2, -4],\n [0, -5, -3, -1, -2],\n [4, 2, 5, 3, -4],\n [-1, -5, -2, 1, -6],\n [-5, -2, -5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, 2, 3, -6],\n [-3, -3, 2, 5, 1],\n [2, -4, 2, 2, -1],\n [6, -6, 1, -1, 2],\n [4, -1, 1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 0, -3, 6, 3],\n [-4, 2, -2, 2, 6],\n [-2, 2, -5, 3, -1],\n [3, 4, -1, 5, 6],\n [-6, 3, -5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -2, 0, -5, 2],\n [-4, -5, -4, -6, 4],\n [3, 6, -4, 2, -5],\n [-5, 2, -6, -5, -3],\n [-1, -4, -4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 2, 2, -4, -3],\n [1, -6, 0, 5, 1],\n [6, -5, 6, -2, -6],\n [-2, -4, -4, -2, 0],\n [3, 2, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 1, 1, 2, -5],\n [5, 0, 1, 0, -2],\n [0, 2, 2, -4, -3],\n [4, -1, 1, -3, 1],\n [-6, 5, -3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, 4, -4, -3],\n [1, -3, 6, 2, 4],\n [-5, 4, 2, -4, 2],\n [3, 0, 2, 1, -2],\n [-3, -5, -4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, 2, -2, 1],\n [-4, 0, 5, 1, -4],\n [1, -5, 5, -5, -4],\n [6, 2, -3, 1, -6],\n [-1, 6, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 5, -2, -4, 2],\n [-3, -1, 6, 5, 2],\n [5, -1, 1, -3, -2],\n [4, 0, 5, -3, -4],\n [-6, 5, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 5, 5, -3, -3],\n [2, 0, -6, -4, 6],\n [5, 1, -5, -3, 2],\n [-3, -6, 4, -2, -4],\n [-2, 4, 4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 6, 2, -4, -4],\n [-6, 0, -1, 5, 6],\n [2, -4, 4, 6, 4],\n [-3, 0, 0, 0, -4],\n [-1, 3, -4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 1, -5, -4, 0],\n [1, 1, 6, -4, -1],\n [-5, 3, -1, 4, 1],\n [1, 3, -3, 4, -2],\n [3, -2, -5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -5, 3, -1, -2],\n [3, 6, -4, -2, -2],\n [3, 3, 6, -4, 2],\n [-6, -4, -5, -1, -2],\n [-6, -1, 1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 4, -1, -2, -6],\n [1, -3, 3, 2, 2],\n [-4, -4, 4, -3, 5],\n [3, -1, -1, 3, -1],\n [1, 3, -5, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, 6, 2, -5],\n [-4, 4, 3, -3, -3],\n [5, -2, 1, 4, 4],\n [2, -6, 2, -1, 0],\n [-2, -4, 3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -1, 4, 0, 6],\n [-2, -5, -3, 1, -4],\n [-4, -5, -5, 5, -2],\n [1, 6, 4, 5, -5],\n [4, 5, 5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -4, 2, -6, -4],\n [0, 5, 1, -1, 0],\n [4, 6, 3, 3, -3],\n [-3, 4, -6, -5, 3],\n [-4, -1, 5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -5, 0, -3, 4],\n [3, 2, 3, -5, -6],\n [2, 3, -4, 3, -3],\n [1, 6, 4, 0, 1],\n [-5, -2, -2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -4, 6, -3, 1],\n [-5, 4, 6, -4, 4],\n [6, -5, 1, -5, -1],\n [2, -4, 0, -2, 5],\n [-5, 5, 5, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, 1, -3, 0],\n [-5, 1, -3, -5, -1],\n [6, 4, 4, 6, -6],\n [5, 1, 4, -2, -6],\n [3, 1, -5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 5, -6, -4, -2],\n [3, -5, 3, -3, 4],\n [-3, -1, -1, 4, 0],\n [3, -3, -1, -4, -2],\n [1, 6, -4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -6, -2, 0, -1],\n [5, -3, -4, -5, -6],\n [-3, 2, -4, 0, 6],\n [3, -4, 1, 1, -4],\n [1, 2, 5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -3, -4, 3, -3],\n [2, -1, 2, -6, -5],\n [3, -2, 1, 4, 3],\n [5, -5, -3, -3, -4],\n [-2, -3, 5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -6, -3, -1, -6],\n [6, 3, 4, -1, 6],\n [-3, 5, 4, 3, 0],\n [1, -5, -3, -3, 3],\n [-6, 6, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, 0, 0, 5],\n [0, 6, 2, 2, 2],\n [-5, -5, -4, 6, 6],\n [3, 2, -3, -2, -1],\n [4, 5, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -5, -2, 1, -6],\n [3, 4, 4, 5, -5],\n [0, -4, -6, -2, -4],\n [-6, 5, -3, -6, -6],\n [-1, -1, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 1, -6, 5, 4],\n [1, -2, -2, 5, 1],\n [-2, -5, 0, 0, 4],\n [-6, 2, -1, 1, 1],\n [-6, -6, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 0, -5, 0, -5],\n [3, -6, -4, 6, 4],\n [-5, -6, 3, 3, 0],\n [6, -4, 4, -4, -2],\n [-4, 6, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -6, 1, 6, 2],\n [3, -1, -2, 0, 0],\n [0, 4, 0, -3, -4],\n [4, 3, 2, 4, 4],\n [-5, 2, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -4, 2, -1, -1],\n [-6, 2, -3, 3, -3],\n [-6, -1, 2, -5, 2],\n [6, 0, 1, -6, 0],\n [-5, -5, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -4, -1, 3, 6],\n [-2, 6, -5, 1, 2],\n [6, -4, -3, -1, 1],\n [0, 6, 1, -6, 3],\n [4, 5, 5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 6, 4, -4, 2],\n [-2, -6, 0, 6, 2],\n [5, 3, -6, -6, -1],\n [3, 1, 3, -6, 0],\n [4, 2, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -4, -4, -1, 5],\n [-5, -2, -3, 3, 5],\n [1, -2, 3, 0, 2],\n [-4, -2, 6, 0, 4],\n [-5, 3, 6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -2, 1, -6, 6],\n [-3, 2, -3, 0, 2],\n [-5, -5, 6, 5, -5],\n [5, 5, -6, 2, 4],\n [6, -6, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -1, 5, 1, 3],\n [1, -6, 6, -1, -2],\n [5, 4, -1, -6, -4],\n [4, 6, 4, -2, -1],\n [-2, -2, 6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 1, -2, 4, -5],\n [2, -6, -2, 3, -2],\n [-3, -6, 5, 3, -3],\n [0, 2, 2, 4, -1],\n [4, 0, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -6, 3, 3, 0],\n [1, -3, 2, -6, 0],\n [0, 2, -1, 5, 6],\n [-2, 3, 0, 3, 0],\n [-6, 3, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 1, 6, 2, 4],\n [3, 2, 0, -5, -6],\n [-2, 6, 5, 2, -3],\n [0, 2, 1, -4, 2],\n [-3, 2, -1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 0, 0, 4, -6],\n [0, 2, 2, 6, -5],\n [2, 6, 4, 0, -2],\n [-3, 5, 1, -6, 3],\n [3, 2, -6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 5, -2, 0, -1],\n [4, 6, 1, 1, 4],\n [-2, 4, 4, -5, 1],\n [-5, -4, 4, 6, 4],\n [4, 2, -5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -2, 1, -4, -3],\n [2, -2, 1, 4, 6],\n [5, 0, -6, -6, 2],\n [-2, -3, -6, -1, 3],\n [0, -1, -2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 6, -2, 4, 3],\n [2, -3, -4, 5, -6],\n [1, -5, 6, 3, 2],\n [6, 4, -3, 4, -3],\n [-5, 4, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -4, -1, 1, -3],\n [4, -5, 1, -4, -3],\n [4, 2, -1, -2, -2],\n [-1, 6, -4, -3, 2],\n [-4, -5, 4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, -4, -4, 6],\n [4, -2, 5, -6, -5],\n [0, -2, -4, -6, -1],\n [-4, 5, -6, 0, -5],\n [2, -3, -1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 0, 4, -3, 6],\n [-5, -4, -3, -4, -6],\n [0, 5, 3, 3, 2],\n [4, 6, -6, -6, 4],\n [2, 6, -3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -3, 6, 1, -5],\n [4, 3, 3, 5, 1],\n [5, -1, 3, 2, -6],\n [-3, 4, -5, 4, -2],\n [-5, 0, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -2, 0, 4, 6],\n [-5, 4, 5, 3, -5],\n [-2, -5, -6, 3, 2],\n [0, -2, 4, -5, -4],\n [0, 1, 3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -3, -4, 4, -3],\n [-4, -4, 5, 0, -4],\n [-4, -1, 2, -6, 4],\n [-1, -1, -3, -1, -6],\n [-2, 4, 6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 5, 6, -2, -6],\n [6, -5, 4, 1, 2],\n [1, 6, -5, 2, -2],\n [-2, -1, -1, 3, 3],\n [-3, 3, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 4, -4, 3, 2],\n [5, -4, -2, 1, -4],\n [-2, -4, -6, 4, 2],\n [-2, 5, 3, 2, -2],\n [-3, 3, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -4, 4, 3, -6],\n [5, -4, -2, -3, 2],\n [-4, -3, 5, -2, -6],\n [5, 4, 0, -6, 4],\n [1, 1, 5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 6, -3, 1, 6],\n [1, -3, 1, 1, 5],\n [-4, -1, -2, 0, 3],\n [-3, -4, -5, -5, 4],\n [-5, -1, 1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -6, 3, 1, 1],\n [2, 2, 0, -2, -2],\n [1, -5, 2, 5, 1],\n [-3, -2, -3, 3, -6],\n [2, 5, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 1, -5, -6, -6],\n [-3, -3, 2, 0, -6],\n [-2, -3, 6, 5, 0],\n [-6, 4, 2, -2, 2],\n [-2, -5, 3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, 6, -1, 6],\n [5, -3, 2, -6, -6],\n [3, -1, 5, 5, 3],\n [6, -2, -2, -3, 5],\n [2, 6, -6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -3, 0, 2, 0],\n [-6, -2, 4, 2, 1],\n [4, -3, -6, 6, 6],\n [-3, 2, -6, -5, 5],\n [-1, 2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -6, 0, -6, -1],\n [-1, 3, -2, 1, 4],\n [4, -3, -5, 0, -3],\n [-5, -4, -5, 1, 6],\n [-4, 2, -2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -5, 3, 3, -3],\n [3, 4, -2, 3, -5],\n [4, 2, -1, -3, -6],\n [2, -5, 3, 4, -5],\n [0, -6, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -2, 1, -5, -4],\n [-3, -3, 1, -6, -6],\n [1, 6, 2, -2, 0],\n [-4, 1, 5, -1, 6],\n [-6, -4, -5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 0, -5, 1, -6],\n [5, 4, -2, 2, 0],\n [0, 2, -1, -2, 3],\n [-5, 1, 5, 1, 2],\n [-1, -2, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -4, 1, 1, 1],\n [-5, 3, 0, 6, -4],\n [-2, -6, 3, 3, 4],\n [4, 5, 0, -5, 6],\n [-1, 6, -4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -4, 2, -1, 3],\n [2, 6, 6, 2, -4],\n [0, 0, 6, 5, 4],\n [5, 1, 6, -2, -4],\n [-5, -4, -3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, -4, 3, -4],\n [2, -3, 3, -1, 4],\n [0, -2, 3, -2, -5],\n [1, -5, 4, -2, -6],\n [6, 2, 1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 0, 3, -3, -1],\n [4, 5, 0, -1, 4],\n [-5, 4, -4, 6, 2],\n [2, 3, -4, -2, 3],\n [-2, -2, -6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -1, 4, -1, -4],\n [-5, -5, -5, 3, -3],\n [5, 3, 3, -3, 2],\n [5, -3, 0, -5, 6],\n [-3, 3, 1, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -1, 6, 6, 2],\n [-4, -1, 1, -2, 3],\n [3, -2, 4, 0, 3],\n [3, -2, -5, -3, 0],\n [2, 5, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -1, 0, -3, 1],\n [1, 2, -1, 0, -6],\n [-6, -2, 6, -3, 5],\n [5, 2, 6, 4, -1],\n [0, 0, -6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -2, 3, 6, 5],\n [2, 4, 6, -4, 5],\n [1, -2, 6, 3, 3],\n [6, 1, 4, 4, -6],\n [-1, -5, 6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -1, -5, -4, -6],\n [-3, -2, -2, -1, -5],\n [-3, 3, 5, -1, -1],\n [0, 6, -4, -1, -5],\n [-2, 3, 0, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -1, 4, -1, -4],\n [-3, -4, -3, 0, 3],\n [-4, 5, 1, 5, 3],\n [5, -4, -6, 5, 5],\n [-3, 0, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -3, 1, -1, -3],\n [-4, -2, 2, -3, 6],\n [-2, 1, -5, 2, -5],\n [2, 6, -1, 3, -2],\n [6, 4, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 2, 6, 3, -1],\n [2, 6, -5, -5, 4],\n [5, -2, 4, 5, -6],\n [-6, 1, 4, -3, 1],\n [-1, 6, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -6, -5, 4, -4],\n [4, -1, 4, 1, 3],\n [-3, 5, 0, -3, 2],\n [4, -1, -2, -3, -2],\n [-2, -1, 5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 5, -2, -1, 3],\n [-1, 2, -4, -4, -1],\n [6, -1, 4, -4, -2],\n [6, -3, 6, 1, -6],\n [6, 4, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, 0, 4, 6],\n [-3, -3, 1, -6, -6],\n [3, 4, 4, -6, -3],\n [-6, -2, -3, 0, -3],\n [6, 1, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 2, 4, -4, -2],\n [-5, -3, 4, 3, 2],\n [4, 5, -3, 2, 2],\n [-5, -2, 0, 3, 2],\n [-5, 4, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -6, -2, 3, -4],\n [-2, 6, 2, -1, 5],\n [-6, -3, -6, -1, 0],\n [1, 0, -2, -6, -3],\n [-4, 3, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, 0, 2, -1],\n [5, 6, -2, 6, -5],\n [2, -4, 0, -4, 4],\n [2, 2, 6, -2, -3],\n [0, 6, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, -2, -6, 3],\n [6, 5, 4, 3, 5],\n [1, -5, 5, -1, -6],\n [-5, -5, -3, -6, 4],\n [0, 0, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -2, 0, -4, -3],\n [-1, -2, 1, 2, 0],\n [5, 0, 2, 0, -4],\n [2, -2, 3, -5, -1],\n [-4, 1, 4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -3, -1, 6, -2],\n [-2, -3, -5, 2, 5],\n [5, 3, 5, 3, 0],\n [6, -1, -2, -4, 6],\n [-5, -3, 3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 4, -3, -1, -1],\n [3, 6, 2, 1, -3],\n [-2, 5, -1, -1, -6],\n [1, 1, -4, -5, 5],\n [-2, -2, 4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -3, 5, -4, 2],\n [5, 4, -3, -4, -4],\n [-3, 4, -1, 5, 5],\n [0, 6, -5, -3, -1],\n [-4, 2, 4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -4, 2, 1, -4],\n [3, 6, 6, -5, -5],\n [4, 3, -4, 1, 1],\n [-5, -1, 6, -3, -4],\n [3, -4, 6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 3, 1, -2, 1],\n [5, 6, 0, 4, 1],\n [-1, -6, 1, 6, -1],\n [2, -6, 1, -3, 1],\n [-6, 6, -5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 6, -3, -6, -5],\n [0, 0, -1, -5, -4],\n [-5, 0, -4, -4, 0],\n [3, 2, 1, -5, -3],\n [1, 3, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -1, -3, 1, -5],\n [6, 0, 2, 4, 5],\n [-5, -5, -4, 3, -6],\n [-4, -5, 1, -2, 3],\n [-3, -5, -6, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 1, 0, 1, 0],\n [1, 5, 4, 1, 5],\n [6, 5, -1, 4, 3],\n [-2, -1, 2, 0, -3],\n [2, -1, -4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -4, -5, -2, -1],\n [-6, 1, -4, 3, 0],\n [-4, 2, -2, 5, -3],\n [0, -4, -1, 5, 5],\n [3, 0, -1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -2, -2, 5, 0],\n [-4, -3, -2, -3, -1],\n [-2, -1, 6, -2, -1],\n [6, 3, 1, -4, 4],\n [6, 3, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, -4, -6, -5],\n [-1, -5, 4, 3, 2],\n [-5, 2, -3, -3, -1],\n [-4, -2, 4, 2, 1],\n [0, -4, -6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 6, -3, 6, -6],\n [3, 0, -2, -2, -4],\n [3, -4, 4, 3, 4],\n [5, -5, -3, 1, 5],\n [1, 0, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -2, 4, -5, -3],\n [5, -3, 4, -5, -5],\n [6, -4, -2, -3, 0],\n [-3, -2, -5, 0, -5],\n [-1, -3, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -6, -6, 3, 1],\n [4, 4, 1, -3, -5],\n [-5, 3, 1, 0, -2],\n [-2, -2, -3, 4, 1],\n [-6, -6, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -1, -1, 3, 5],\n [0, -3, -6, 4, 5],\n [-2, 2, 1, 0, -5],\n [-2, 6, 5, -4, -5],\n [-4, 0, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 4, -4, 6, 1],\n [2, -1, 3, -5, 0],\n [-3, 1, -5, 5, 3],\n [-3, 0, -3, -2, -1],\n [-1, 3, 1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, 0, -5, 3],\n [6, 4, 5, -4, -5],\n [1, -1, 3, -6, 0],\n [-2, -4, -4, -3, 2],\n [2, -1, 5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, 1, 4, 1],\n [2, 6, -6, -4, 6],\n [4, -4, 6, 5, -2],\n [6, 5, 5, 5, -4],\n [0, -2, 0, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 0, -1, -6, -4],\n [5, 6, -6, 2, -6],\n [-2, -1, -4, 2, 5],\n [-1, 5, 3, 5, 0],\n [6, 1, -3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, -2, 0, -3],\n [2, 5, 6, 6, -2],\n [3, -5, -6, -3, -1],\n [1, -3, -1, 4, 1],\n [-2, 1, -6, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 5, -1, 2, 6],\n [4, -6, 5, 0, 5],\n [-5, -5, 3, 3, 3],\n [0, -2, 6, 4, -2],\n [2, -2, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 0, 4, -4, 1],\n [0, 0, -6, -4, -1],\n [-2, -2, 3, 4, -2],\n [-4, 5, 6, -2, 1],\n [-5, 0, 6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -3, -2, 5, -3],\n [5, 1, 4, 0, -1],\n [-2, -4, 4, 4, 2],\n [-6, -3, -2, 5, 6],\n [-6, -2, 6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 5, 2, 3, 0],\n [2, -3, 6, -2, 4],\n [-4, -6, 5, 3, 2],\n [-5, -1, -2, -1, 6],\n [-6, -6, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 2, 1, 1, 2],\n [3, -2, -3, 3, -2],\n [-4, -1, -1, 3, -5],\n [-4, 6, -4, -2, 0],\n [4, 4, -5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, 5, 6, -4],\n [1, 0, 0, 6, -4],\n [-3, 2, -6, -3, 6],\n [1, 3, -1, 4, 5],\n [3, -1, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -2, -4, 6, -1],\n [-1, -3, 4, -2, 1],\n [-4, 0, -6, -2, 1],\n [1, -5, 6, -6, -5],\n [-1, 2, -1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, 2, -5, -6],\n [1, 2, 6, 4, 6],\n [-5, -3, -1, 4, 2],\n [-2, -6, -5, -5, 4],\n [2, 5, -5, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -6, -1, 4, 2],\n [0, 0, 6, 1, 1],\n [4, 3, 0, -1, 6],\n [0, -4, 4, -2, -5],\n [-4, 6, 6, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -1, -6, -4, -4],\n [3, -2, -3, 2, 4],\n [-4, 4, -2, -2, 6],\n [2, -5, 1, 6, -5],\n [1, 0, -4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 1, 6, -4, -6],\n [-3, -2, -5, -5, 4],\n [-4, 6, 0, 0, -6],\n [-3, 0, 2, 6, 1],\n [-2, 4, 4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -2, 4, 4, -3],\n [4, -6, -6, 4, 4],\n [1, 5, -6, 6, -5],\n [0, -1, -5, 0, -5],\n [-3, -4, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 1, 1, -6, 1],\n [3, -3, -1, 5, -3],\n [-6, 4, -6, 3, 2],\n [-3, 1, -6, -1, -1],\n [-3, 2, 4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 0, -2, 3, 0],\n [-6, 6, 6, 2, -6],\n [-1, 1, 3, 3, -2],\n [2, -1, 6, -6, -5],\n [5, -3, -3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 4, -1, 0, 5],\n [5, 5, 0, -2, 3],\n [-3, -2, 2, 5, -4],\n [2, 3, -4, 1, 3],\n [2, 6, -5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -5, 4, 6, -6],\n [4, 4, 4, -2, -3],\n [1, 4, 1, 6, 4],\n [3, 2, -1, 1, -6],\n [-1, 2, 6, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -4, 1, 4, -5],\n [5, 4, 6, -6, -3],\n [-1, -1, 5, -4, -6],\n [-2, -1, -6, -6, 2],\n [-5, 5, 6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -5, -5, 3, -4],\n [0, -1, -3, -4, -6],\n [-3, 5, -5, 2, 3],\n [0, -2, 6, -4, -3],\n [6, 4, -3, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 2, 1, -1, -2],\n [6, 3, -5, -6, -1],\n [5, 0, 0, -6, 5],\n [0, -5, -5, 6, -1],\n [-1, 5, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 1, -6, -1, -2],\n [1, 0, -1, 1, 2],\n [-1, 4, 1, -3, 4],\n [2, -2, 5, -4, -6],\n [6, 4, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 5, -4, 5, 4],\n [6, -5, 0, -6, 0],\n [0, 0, 2, -2, -6],\n [1, 6, 3, 3, -4],\n [0, -5, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -2, 4, -5, -6],\n [0, 5, 0, 0, -2],\n [-1, 2, -4, -3, 3],\n [6, 2, -1, 3, -3],\n [-2, -5, 6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 3, -1, -1, 0],\n [0, 1, -3, -5, -6],\n [-6, 2, 6, -6, 6],\n [-4, -6, 2, -5, 2],\n [2, -5, -2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -6, -5, -3, -1],\n [-3, 5, -2, 4, 1],\n [-5, -1, -5, 0, -3],\n [-4, -5, -5, 4, -5],\n [6, 1, -6, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -3, -6, -5, 6],\n [0, -5, -6, 3, -3],\n [-5, 3, -4, 6, 1],\n [0, -5, -6, 2, -5],\n [-1, 3, 6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -4, -6, -4, 0],\n [-6, 6, 1, 6, 5],\n [6, -4, 5, 4, 3],\n [2, -3, 4, 5, 6],\n [2, 4, 1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 3, -6, 3, 1],\n [4, 4, -6, -1, -4],\n [4, 2, 3, 1, 5],\n [-1, 3, 6, -6, 0],\n [-2, -3, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 3, 6, 0, -5],\n [0, -4, -4, 2, -2],\n [1, 5, 6, 1, 4],\n [3, 0, 0, -5, 3],\n [1, -2, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -2, 0, 6, 4],\n [-5, 4, 3, 6, -4],\n [-4, -3, 2, 0, -1],\n [2, -6, 3, -5, -4],\n [-3, -1, -3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 4, -3, 3, -2],\n [6, 6, -6, -3, -5],\n [-6, -6, -2, 4, 4],\n [-2, 0, 0, 5, -6],\n [-3, 5, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -1, 5, 0, 3],\n [-3, 6, -2, -5, -3],\n [-3, 0, 3, -4, -3],\n [4, 5, 0, -5, -3],\n [-5, -5, 1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 3, 0, -3, -3],\n [-6, 3, 1, 0, 4],\n [1, -4, -1, 1, -4],\n [2, 6, 5, 3, -3],\n [5, -6, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -2, -2, 3, -6],\n [-1, 3, -5, 2, 3],\n [-3, -5, -6, 6, 5],\n [-1, 4, 4, -6, 5],\n [-5, -3, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, 2, 2, -4],\n [5, 1, 6, 4, 4],\n [4, -6, 1, 0, 6],\n [-4, 3, 5, 5, -4],\n [-4, 1, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -5, 3, 2, 6],\n [1, 6, -6, 2, 3],\n [-2, -1, 4, -2, 5],\n [2, -4, 0, -3, 3],\n [6, -2, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -1, -3, -4, 3],\n [1, 1, -4, -1, 5],\n [-4, 2, 5, 1, -6],\n [-4, 4, 0, 6, -1],\n [-4, 2, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 5, 4, 3, 6],\n [1, 5, 1, 3, 6],\n [-5, 3, 2, -2, -3],\n [6, 1, 6, 0, 2],\n [0, 4, -1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -4, -6, -5, 4],\n [1, 1, -3, 1, -1],\n [3, -4, 5, 0, -4],\n [1, 6, -2, 6, -4],\n [-2, -6, 6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 0, -6, 2, 3],\n [4, -3, 4, -2, 2],\n [-2, 6, -4, 5, 3],\n [2, -5, 1, -4, 0],\n [1, -6, -1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -6, 4, 6, 6],\n [2, 3, 0, 2, -6],\n [-2, -3, -5, 3, 2],\n [0, 2, 0, -6, -2],\n [-5, 4, -2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -6, -4, 2, -1],\n [-4, -4, -5, 0, 3],\n [4, 5, -6, 2, -4],\n [2, -2, 0, -1, 3],\n [2, -3, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 3, 2, 5, 5],\n [4, 1, 2, -4, 5],\n [0, 5, -5, -2, -3],\n [3, -1, -4, -3, 2],\n [-6, -3, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -1, -5, 6, -6],\n [3, -2, -6, -2, 6],\n [4, -5, -4, -5, -6],\n [-3, 0, 1, 6, 3],\n [1, 2, -3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 5, -3, -4, 2],\n [0, -5, -5, 0, -2],\n [5, -3, -6, 5, 4],\n [-6, 6, 0, -5, -3],\n [-2, -4, -4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 6, -5, -1, -3],\n [4, -3, 0, -4, 6],\n [1, 3, 4, 1, 1],\n [6, 6, -3, 1, -3],\n [0, 4, 5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 3, 0, 2, 3],\n [-5, 1, -4, 3, -6],\n [-5, 3, -3, -1, 3],\n [6, 5, -1, -1, -3],\n [2, -4, 5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -2, 2, -5, 6],\n [5, -1, 1, 2, 1],\n [-6, 2, -4, -1, 1],\n [6, -6, 5, -6, 1],\n [0, -4, -2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 0, 0, 0, 0],\n [4, 3, 5, -4, 0],\n [1, 4, -6, 4, -6],\n [-1, -5, 5, 5, -6],\n [3, -1, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 1, 0, 4, 2],\n [-6, 4, 2, -2, -1],\n [6, 1, 3, 3, -4],\n [-3, 0, 5, 1, -3],\n [-5, 2, 6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 0, 2, -1, -6],\n [-4, 6, 5, -5, -4],\n [0, 1, -2, -4, -5],\n [-2, 4, -2, -3, -6],\n [4, -5, -1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 1, 1, -2, -1],\n [-5, -4, -4, 4, 1],\n [0, -5, 1, 6, 3],\n [3, 6, -2, -3, 3],\n [3, -3, 2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -5, -5, -3, -3],\n [1, 0, 4, 6, -4],\n [-5, 1, 6, 3, -3],\n [-6, 5, -5, -2, -4],\n [-2, 2, 4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -6, -2, 6, 6],\n [-1, 0, 5, -6, 1],\n [-6, -4, -5, 4, -5],\n [-3, -6, 3, 6, 6],\n [-3, 0, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, 1, 2, -2],\n [-3, -4, -2, -1, 3],\n [-5, -2, 6, 4, 5],\n [4, 0, 5, -6, 3],\n [-3, 3, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 4, -1, 1, 4],\n [4, 4, -4, -5, 0],\n [-6, 1, 1, 0, -3],\n [5, 4, 4, 3, -5],\n [3, -4, 6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 3, -2, -3, -6],\n [4, -3, 5, 0, 5],\n [3, 2, -2, -3, 6],\n [5, 0, 2, 4, -3],\n [5, -3, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 4, 6, 2, 2],\n [-1, 1, 2, 5, 3],\n [-6, 3, 3, -6, 4],\n [-3, -2, 1, -6, 4],\n [2, 0, -3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 4, 1, 1, 6],\n [-6, 2, 6, -5, 0],\n [-5, 2, -2, 3, 4],\n [4, 3, -5, 4, 0],\n [-4, -3, -4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -2, -4, 2, 0],\n [2, 3, -6, 4, 4],\n [-4, -1, -4, -4, 3],\n [0, 5, 5, -6, -1],\n [-3, 3, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -2, 2, 0, -6],\n [0, -3, 1, -1, -3],\n [-3, 1, -4, -6, -3],\n [-6, 0, -5, 2, -2],\n [6, 1, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 5, 6, 2, -6],\n [5, 5, 3, 0, 6],\n [3, -5, 3, -2, 5],\n [3, -1, -4, -3, 0],\n [3, -1, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 6, 6, -5, 4],\n [3, -4, -3, -4, 6],\n [-5, 3, 1, -6, -1],\n [5, -2, 5, 0, -2],\n [0, -6, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -5, -2, 2, -5],\n [5, 1, -1, -1, -3],\n [-2, 2, -1, 6, -1],\n [3, -6, 3, 4, -6],\n [0, 2, 1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 2, 3, -2, -2],\n [3, -2, 2, 1, 6],\n [2, 3, -2, 6, 3],\n [2, 4, -5, -1, 5],\n [-3, 0, -3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 5, -2, -3, -4],\n [1, 0, -5, -2, 3],\n [5, 5, 4, -1, -4],\n [3, -5, -3, 0, 6],\n [-5, -3, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, 6, 4, 0],\n [0, -3, -2, 2, 4],\n [-6, 0, -1, -3, -2],\n [3, 4, -6, -2, 5],\n [-5, -4, -5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, 0, -5, -4],\n [6, -3, -2, -5, 3],\n [4, 0, 6, -5, 2],\n [2, -1, 1, 4, 2],\n [-1, 2, 5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 4, 4, 0, 2],\n [-4, 4, 6, 1, 6],\n [-6, 1, -3, 5, -6],\n [-1, 0, -1, 0, 6],\n [-1, 6, 2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 2, 0, -2, 2],\n [2, 2, -4, 1, 5],\n [-1, -1, 5, 1, -6],\n [-1, -1, -6, 1, 1],\n [-1, 3, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -1, 5, -4, 6],\n [-1, 0, -5, 2, -4],\n [-6, -1, 3, 4, 1],\n [-3, 1, 3, 0, 3],\n [-4, -1, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 6, 1, 0, -5],\n [6, 5, 4, 0, -3],\n [-4, 1, -5, 2, -3],\n [-4, 6, -6, 5, -4],\n [4, 0, -4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 2, 1, 3, 3],\n [2, 2, 0, -3, 6],\n [-4, -1, -6, -1, 4],\n [-6, 1, 2, -1, -4],\n [-3, 3, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -3, -6, 5, -6],\n [-6, 2, 1, 0, -6],\n [4, -4, 1, 6, 5],\n [3, -6, 2, -1, 0],\n [5, 5, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -2, -5, 3, 5],\n [-3, -4, 6, 1, -3],\n [-6, 0, -4, 2, 0],\n [2, 2, -2, 4, -1],\n [1, 1, -5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 4, 5, 0, 5],\n [-3, 6, 5, -4, -5],\n [-4, 3, 4, -2, 3],\n [-5, 0, 6, 5, 0],\n [-5, -5, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 0, -6, 5, 1],\n [3, -4, 3, -4, -2],\n [3, -6, -6, 5, 2],\n [-4, 2, 5, 3, 3],\n [-6, 6, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 4, 2, 2, -4],\n [-6, 0, -1, 5, -6],\n [-5, -4, -3, 2, -4],\n [4, 3, 5, 1, -3],\n [-2, 3, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 6, -5, 4, 1],\n [-6, -2, 0, 5, 5],\n [-4, -1, -3, 4, 4],\n [-1, 4, -3, 2, -1],\n [-4, -3, -6, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 2, -6, 5, -4],\n [-4, 0, 3, 1, -3],\n [-5, -6, -3, 5, 1],\n [-1, -5, 0, -3, 0],\n [3, -4, 3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 0, 1, 4, -1],\n [-2, -4, 6, 6, 0],\n [4, -5, -3, -2, -1],\n [0, 5, -1, 5, 3],\n [-1, -1, -4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -5, 1, -1, -6],\n [-6, -5, 3, -2, 2],\n [-5, 6, 3, -3, -2],\n [3, 5, 1, -2, 1],\n [0, 2, 5, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -1, 3, 1, -5],\n [-3, 1, 6, -2, -5],\n [1, -3, -6, -6, 0],\n [5, -6, -2, 2, -3],\n [-3, 2, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -5, -6, 0, -1],\n [-4, -3, 1, 4, -6],\n [1, -3, 6, -6, -2],\n [2, 5, -2, 4, 3],\n [6, 3, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -2, -6, 2, -3],\n [3, -4, -2, -5, 3],\n [-4, -6, 6, 1, 2],\n [2, -3, 1, -6, 0],\n [-4, 5, 6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 2, 1, -1, -4],\n [4, -4, -4, -1, -5],\n [-1, 4, 3, 4, -5],\n [-6, 1, 4, 0, 2],\n [4, 3, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -5, -4, -2, -2],\n [-4, -3, 0, 5, -4],\n [-2, 6, 5, -3, 2],\n [-6, 0, 4, 4, -2],\n [0, 5, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -6, 1, -5, -5],\n [0, 1, 0, -4, -6],\n [1, -2, 6, 5, 2],\n [-6, 3, -4, -3, 2],\n [4, 6, 2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 1, -1, -5, 0],\n [3, 1, -4, 0, -2],\n [-2, -3, -2, 6, -4],\n [1, -6, -3, 3, -6],\n [4, 5, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -4, 0, -1, -3],\n [5, 5, 4, 6, 1],\n [2, 2, -2, 0, 2],\n [-2, 4, 1, -1, -6],\n [0, -2, 5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 0, 3, -4, 0],\n [-6, 5, -3, -1, 6],\n [1, -6, 2, 3, 5],\n [0, -4, 6, -2, -3],\n [-4, 2, -2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -5, 5, -4, -1],\n [0, -5, -2, -5, 1],\n [-4, -3, 3, 0, -1],\n [2, 4, -1, -6, -4],\n [-3, 5, 3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 0, 2, -2, -5],\n [-5, -6, -1, -3, 5],\n [4, 4, -4, 4, -4],\n [-6, 0, -6, -6, 2],\n [-6, 0, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -2, -1, 2, 0],\n [1, 1, 6, -3, -5],\n [-2, 3, 1, 3, 1],\n [-1, 5, 0, 4, 2],\n [-1, 2, 4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 6, 0, -5, -1],\n [5, -2, 3, 1, 6],\n [-4, -6, -4, 3, 2],\n [-5, 3, 6, -6, -2],\n [-6, -5, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 1, 5, 3, 5],\n [1, -3, -2, 5, 0],\n [-2, 2, 3, 6, -3],\n [4, -2, -6, -2, 5],\n [-5, -6, 6, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, -3, 5, -4],\n [-2, 1, 6, -5, 5],\n [-5, 2, 5, -1, 3],\n [2, 4, 3, 2, 4],\n [0, 4, 4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 6, -2, -3, 2],\n [-5, 6, 1, 2, -5],\n [-6, 1, 4, -5, 4],\n [-3, -4, -4, 6, 6],\n [-6, 3, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 1, -2, 4, -5],\n [-5, -4, 2, -4, -4],\n [6, 3, 3, -3, 2],\n [5, -5, -3, -3, -2],\n [2, -2, -3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -4, -4, -1, -3],\n [-2, -1, 1, 2, -5],\n [-5, -1, -6, -1, -3],\n [3, -4, 0, -4, 1],\n [3, 4, -6, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 2, 4, 0, 3],\n [4, 4, -5, 6, 2],\n [4, 1, 1, 1, 4],\n [4, -5, -3, -3, -2],\n [-3, 2, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -6, 0, 4, 5],\n [-4, -5, 1, 4, 3],\n [-3, -4, -6, 4, 1],\n [-6, -4, -3, 1, 5],\n [-1, 3, 4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, -4, 2, -1],\n [-1, -4, 1, -4, 6],\n [-4, 4, 5, 6, 3],\n [2, 2, 5, -6, 5],\n [-5, -6, 1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 0, -1, -6, -6],\n [4, 6, -2, -3, -3],\n [-5, 2, -2, -1, 5],\n [0, -3, 2, -5, -6],\n [-3, 5, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 2, -3, 1, 5],\n [-5, 4, -1, 5, 5],\n [-5, 0, 2, -4, 1],\n [0, 6, -5, -3, 2],\n [5, -1, -4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 0, -1, -2, -5],\n [-1, 4, 3, -6, -6],\n [-1, 5, -2, -2, -3],\n [1, 0, 2, -5, 6],\n [4, 3, 3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 2, -4, 5, 5],\n [-1, -5, -6, 6, 0],\n [5, 5, 0, 0, -2],\n [-1, 2, 2, 3, 2],\n [0, 6, 3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 0, -4, 4, 1],\n [-6, 2, -5, 6, -5],\n [-5, -1, -4, 0, 1],\n [3, -5, 6, 6, 4],\n [-3, 5, 5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -5, -6, 1, 2],\n [-5, 5, 1, -2, -6],\n [-1, 2, 2, -4, -1],\n [-5, 4, 2, 0, 2],\n [-6, -5, 3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -6, -1, 1, -3],\n [1, -6, -3, 1, 2],\n [4, 4, 6, 1, -5],\n [3, 5, 2, 5, -2],\n [-4, -4, 5, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 3, -6, 2, 2],\n [-3, 5, 6, 0, 1],\n [1, 5, 2, 6, -6],\n [-5, 1, 2, 0, 1],\n [2, 1, 3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 2, 3, 3, -3],\n [-4, 5, -4, -6, -2],\n [-3, 3, -4, -6, 6],\n [-3, -3, 4, 5, -5],\n [3, -6, -5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -1, -2, 0, -2],\n [-1, 3, -1, -5, -1],\n [6, -2, -5, -2, -5],\n [5, 2, 6, -3, 4],\n [2, 3, 5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -4, -1, -2, -4],\n [1, 3, 2, -4, -4],\n [-6, -5, -2, 3, 2],\n [2, 5, 6, -4, 2],\n [4, -5, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -6, 5, 0, -1],\n [6, 2, -6, -2, 4],\n [3, -2, 0, -5, -1],\n [1, 0, 5, -4, -1],\n [-4, 1, 5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -5, 5, -3, 3],\n [0, -1, 1, 0, 3],\n [3, -4, 2, -4, -6],\n [-6, -6, -1, -5, -1],\n [1, -4, -3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -2, 4, 6, -6],\n [0, 1, 4, 3, 3],\n [6, 2, -6, 0, -1],\n [-3, 1, 4, 3, -1],\n [-5, 4, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -2, -4, 4, -5],\n [-5, 4, 4, -5, 6],\n [0, 5, 5, -4, 4],\n [0, -5, -2, 5, -1],\n [5, -1, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 3, 3, 3, 5],\n [4, 0, 1, 0, -5],\n [-5, -5, 4, 4, 4],\n [5, -4, 3, -4, 4],\n [5, 1, -5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 6, -5, 0, -4],\n [-5, -4, -4, 3, -6],\n [0, 5, 1, 5, -6],\n [3, -1, -3, -3, 6],\n [5, 1, -6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -5, -2, 5, -4],\n [6, 6, -2, -6, 3],\n [-1, -4, 0, 4, 1],\n [5, -3, 6, -3, -4],\n [6, -1, 5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -3, 6, 4, 1],\n [4, 3, -1, 6, 2],\n [-1, 6, 2, 0, -5],\n [1, 3, 5, 1, 2],\n [0, 0, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 3, -5, -3, -6],\n [0, 0, -3, 2, -1],\n [-2, 0, 2, 6, -2],\n [-1, -2, 1, -3, 3],\n [6, 5, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -3, 2, 1, 5],\n [1, 5, -2, 6, -1],\n [-4, 0, 1, -3, 2],\n [2, -1, 3, 6, 5],\n [-4, -4, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 2, 4, -4, -2],\n [1, 6, -4, -3, 4],\n [-5, -5, -3, -1, 6],\n [-6, -3, -6, -5, -3],\n [5, -5, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -1, 1, 6, -6],\n [5, -1, -5, -6, 3],\n [-1, 4, -1, -4, 0],\n [-3, -2, 3, -3, 1],\n [-1, 4, 1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -6, 6, 2, 2],\n [-2, -3, -5, 1, 2],\n [-3, 1, 3, 4, -2],\n [-3, 5, -3, -2, 4],\n [0, -2, 5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 0, -2, -5, 2],\n [-5, -3, 3, 1, -5],\n [6, 6, 4, -5, -1],\n [1, -5, 1, -1, -3],\n [-3, -2, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, -3, -5, -1],\n [1, -4, 2, -5, -4],\n [-3, 3, 4, 5, 1],\n [4, -2, 6, 6, -3],\n [-4, -3, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, -3, -4, -1],\n [-4, -5, 0, 3, -5],\n [-5, 1, 0, -4, -3],\n [5, 2, -2, -5, -2],\n [5, -2, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -3, 1, 6, -2],\n [2, 4, 0, 2, -5],\n [-6, -1, 5, 1, -5],\n [3, 0, 4, -3, -5],\n [-6, -2, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, -2, -6, -4],\n [6, -5, -6, -4, 4],\n [-2, -6, 5, -5, -3],\n [-3, -2, -6, -5, -1],\n [1, -1, 3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -5, 4, -3, 1],\n [-3, 3, 5, 0, -2],\n [-5, 1, -4, 5, 5],\n [2, -4, 3, 4, 4],\n [-2, -3, -6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -2, -4, 1, -1],\n [4, 4, -1, -5, -5],\n [-5, 2, -1, 4, 5],\n [5, -2, -2, 2, -3],\n [6, 6, -3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 4, 3, 6, -1],\n [-6, 4, -4, -6, -2],\n [5, 4, 6, 5, 0],\n [-3, -2, 6, 3, 0],\n [-1, 0, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 3, -6, 5, -1],\n [-1, -1, 0, 4, -5],\n [-6, -1, -3, -6, 6],\n [-6, 2, -6, 4, -3],\n [1, 0, -1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -4, 3, -1, -4],\n [-3, 0, -3, 3, 6],\n [1, 0, 3, 5, 5],\n [5, 4, -5, -6, 2],\n [-2, -6, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 1, 3, 3, 1],\n [4, -2, 1, -2, -1],\n [-5, 6, 2, -5, -2],\n [-3, -1, -3, 6, 6],\n [-6, -1, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -2, 5, -2, -6],\n [-3, 5, -3, 3, -4],\n [2, 3, -5, 6, 6],\n [-5, -6, -6, -5, -3],\n [2, -6, 1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 4, -4, -2, -2],\n [-1, 1, 0, 0, 1],\n [-6, -2, -1, 5, -2],\n [6, -5, -2, -4, 5],\n [4, 2, 5, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -6, 0, 4, 1],\n [3, -5, -6, 4, -4],\n [5, 4, -1, 5, 6],\n [2, 2, -6, 4, 1],\n [6, 5, -3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -5, 0, -2, 5],\n [4, 6, -5, -4, 5],\n [2, -5, 5, 1, 6],\n [6, -2, -3, -4, 2],\n [-3, 2, 2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -5, 6, -6, -3],\n [-2, 6, -4, 2, -6],\n [3, -5, -5, -5, 4],\n [4, -1, 5, 4, -3],\n [5, -2, 2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 1, 1, -5, -1],\n [3, 4, 2, -6, -3],\n [4, 6, 5, -3, 5],\n [1, -2, -6, 4, -2],\n [-3, -3, 4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, 0, -2, -3],\n [-3, 1, -2, 6, 2],\n [4, -1, 3, -2, 5],\n [0, 4, 1, -3, 3],\n [3, 6, 6, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -6, -3, 4, -2],\n [1, 0, -5, -4, -4],\n [0, -5, 1, 2, 6],\n [4, -2, 2, 0, 5],\n [-2, 5, -5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -2, -2, 0, -3],\n [6, 2, 3, -1, 2],\n [-4, 4, 5, -3, -1],\n [1, -2, 4, 0, 0],\n [3, 6, -5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, -4, -3, -5],\n [-3, 0, 2, 6, 4],\n [4, -3, -5, 3, -5],\n [5, 6, 6, -3, 4],\n [-2, -2, -3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -2, 3, 1, -2],\n [-1, 3, -2, 4, 3],\n [0, 6, 3, 6, -5],\n [6, 6, -3, -1, -1],\n [-5, 6, 5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -1, -3, -3, 3],\n [3, -5, -2, -3, 1],\n [-5, -2, -6, 2, 6],\n [5, 2, -2, -5, 0],\n [5, -6, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 6, -2, -2, -1],\n [0, 1, -6, -1, 2],\n [4, 5, 5, -4, 1],\n [3, 6, -1, -4, -2],\n [4, -2, 1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 6, 4, -1, 3],\n [-3, -1, 1, 6, 2],\n [1, 5, 2, -1, 0],\n [1, 4, -6, 1, -4],\n [6, -5, -6, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -1, -1, -2, -2],\n [-3, -6, -5, -4, 4],\n [2, 3, -1, 3, -3],\n [4, 6, -2, 0, 6],\n [2, -2, 6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -1, 0, 6, -1],\n [-6, 0, 3, -3, -5],\n [-1, 4, -1, -6, -2],\n [1, -6, 1, -1, -4],\n [-6, 0, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -4, 4, 0, 4],\n [-1, 1, -2, -2, 4],\n [5, 3, -1, 1, -1],\n [0, 4, 4, -6, -1],\n [1, 2, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -3, 6, -2, -5],\n [5, -4, -2, -2, 2],\n [6, -6, -2, -4, -3],\n [-2, 2, 6, -1, 3],\n [1, -4, -5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -4, -4, 2, 4],\n [4, -5, 4, -3, -4],\n [6, -2, -6, -1, 3],\n [-3, 4, -6, -4, 3],\n [4, -4, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 0, 5, -1, 5],\n [-2, 0, -5, -1, 4],\n [-6, 3, 4, -5, 0],\n [-1, -6, -3, 0, -2],\n [-4, 5, 2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 4, 1, 0, -4],\n [6, -1, -6, -1, -2],\n [6, -4, 2, -2, 6],\n [1, -5, 6, 2, -5],\n [3, 1, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -4, 1, -2, -1],\n [3, 6, -6, 6, 0],\n [1, 4, -2, 0, -1],\n [0, 0, -6, 4, -1],\n [-6, -4, 1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -2, -4, -5, -6],\n [6, -4, 0, 6, -5],\n [-5, -3, 2, -2, 4],\n [6, 2, -6, -5, 3],\n [1, -6, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 0, 1, 4, -2],\n [2, 2, -2, 4, 5],\n [-6, -1, -5, -3, -1],\n [-4, -3, -6, -3, 4],\n [2, 2, -2, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 3, 4, -3, 2],\n [0, -2, -1, -1, -1],\n [-3, -2, 2, 4, 5],\n [-6, 3, 0, 3, 3],\n [3, -6, 1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -3, -6, 4, 4],\n [-3, 4, 1, -6, -6],\n [-4, 2, 0, -2, -2],\n [1, 3, -2, 3, 0],\n [1, -4, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -3, 5, 4, 2],\n [4, 4, -1, 0, -2],\n [2, 6, 1, 0, -6],\n [2, -2, 3, -2, 5],\n [-1, 4, -3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -4, -2, 2, 0],\n [-2, 4, 3, -1, -6],\n [0, 1, -2, -3, 5],\n [-3, 4, -3, 6, -2],\n [3, -4, 6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 3, -3, -5, 1],\n [-1, -6, 5, 5, 1],\n [-5, -1, -4, 6, 4],\n [4, 5, 2, 6, -6],\n [6, -1, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 2, 3, -6, 2],\n [5, 3, 0, 5, -3],\n [1, -1, -6, 4, 4],\n [-4, -2, -2, -5, 6],\n [6, -3, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 4, 1, 2, 2],\n [1, 2, 1, 4, 5],\n [2, 4, -1, 6, -2],\n [-3, 4, -2, 5, -4],\n [-4, -4, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 6, -5, 6, -6],\n [2, -4, 5, 1, -3],\n [0, 4, 6, -1, -2],\n [-3, 0, 0, 1, 3],\n [-3, 2, 1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, 6, -4, 0],\n [3, 0, 3, -5, 6],\n [-3, -5, 1, 5, 0],\n [2, -4, -4, 2, -5],\n [-4, -5, 2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -2, -4, 3, -3],\n [5, -6, -1, 1, 6],\n [-4, -1, 0, -3, 5],\n [5, 3, 5, -6, -1],\n [-5, -4, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -3, -5, 3, 1],\n [-5, 4, -6, 2, -3],\n [4, 0, 4, -3, 2],\n [-5, 4, 4, 2, 6],\n [-6, -4, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 2, 0, -1, -2],\n [-5, -6, 2, -6, -4],\n [0, -5, 5, -2, 1],\n [-6, 1, 4, -6, -3],\n [4, -4, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 3, -3, -4, 6],\n [0, 5, -4, -4, -5],\n [1, -4, 4, -5, -6],\n [-1, -4, -5, 5, -4],\n [-5, 4, -5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -2, -2, -4, 4],\n [6, 2, 2, -4, -6],\n [-1, 0, 0, -1, 5],\n [4, -5, 2, -4, 2],\n [-5, 6, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 0, -3, 5, 1],\n [-6, -5, 1, 4, 2],\n [4, -2, -6, 0, -5],\n [-5, 4, 0, 2, -2],\n [3, -2, 4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 0, 2, 1, -1],\n [-3, -5, 3, -3, -5],\n [-5, 0, 4, 1, 3],\n [4, 3, -6, 5, -3],\n [4, -5, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -2, -6, 6, -4],\n [1, 6, 4, -1, 1],\n [-1, 3, 1, -3, -1],\n [5, -6, -3, -5, -3],\n [-4, -2, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -5, 0, 4, -5],\n [3, 5, -5, 5, -5],\n [-6, 2, 6, 6, 2],\n [-2, 0, 5, -4, 6],\n [6, -5, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 5, -4, -3, -4],\n [3, -5, -3, 2, 0],\n [-3, 1, -1, 0, 1],\n [1, 5, -3, -6, 0],\n [-2, -3, 2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, 3, 3, 6],\n [4, -4, -6, 2, 3],\n [5, 2, -6, 0, -3],\n [-5, 5, -5, 2, -6],\n [3, -6, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -5, 3, -1, 1],\n [-3, -4, 0, -2, -5],\n [-6, 2, 3, 5, -5],\n [5, -3, -6, -3, 1],\n [1, -6, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -6, -5, 4, 3],\n [-5, 6, 0, -3, -5],\n [2, -4, -3, 4, 4],\n [3, 6, 2, 2, -6],\n [5, 0, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 6, 1, 6, -5],\n [0, 0, 6, 6, -4],\n [3, 1, -4, 1, 2],\n [5, 5, -4, 5, -1],\n [-3, -3, -5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 4, -6, -4, 1],\n [-1, 3, 4, 6, -1],\n [4, -2, -4, 2, 3],\n [-5, -6, -2, 6, 4],\n [5, 6, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -5, -2, -5, 2],\n [3, -3, -5, -2, -4],\n [0, 3, 4, -5, -3],\n [2, 1, 2, 0, -6],\n [-6, 1, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -6, 2, 5, 3],\n [0, 1, -1, 6, -1],\n [6, -1, 0, 4, 4],\n [-4, -4, -3, 6, 2],\n [5, 3, 6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, 2, 1, -1],\n [3, -3, 6, 4, -6],\n [0, 3, -2, 2, -2],\n [0, 2, -4, -3, -1],\n [-6, 3, 3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 6, -6, 5, -5],\n [-5, 4, 3, 5, -1],\n [-6, 3, -1, 2, 0],\n [-4, 0, -1, 5, 4],\n [2, 6, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 6, 4, -6, -5],\n [-3, 0, -3, -6, 6],\n [5, -2, 4, 5, 2],\n [-1, -2, 4, 0, 1],\n [6, -2, 1, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -4, 3, -2, -1],\n [6, -1, 2, 5, 1],\n [-1, 6, 4, 0, -4],\n [4, -2, -5, 0, -2],\n [-1, 2, -5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -6, -1, 4, -1],\n [-2, 5, 4, -4, -6],\n [4, 4, 1, 1, 6],\n [-5, 4, 6, 2, -1],\n [-4, 5, 3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -3, 0, 1, 3],\n [-2, -2, -1, 0, -1],\n [5, -1, -6, 3, -3],\n [-2, -3, -2, 5, 3],\n [3, 1, 3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -5, -2, -4, 2],\n [-3, 2, 2, 1, 6],\n [5, -6, 3, 5, -2],\n [-3, 0, 0, 1, -5],\n [4, 2, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 5, -5, -1, -6],\n [0, -3, -1, 5, 6],\n [0, 5, -1, -6, -5],\n [-4, -2, -3, -2, 1],\n [1, 4, 1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 4, 6, -6, -3],\n [6, -5, 6, 2, 5],\n [-6, -2, 3, 1, -3],\n [2, -1, -6, -4, 4],\n [-1, -4, 4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, -2, -3, 0],\n [-5, 2, 4, -4, -1],\n [2, 2, -1, 1, 2],\n [-3, 5, 6, -3, 1],\n [-5, 3, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -2, -1, 5, -1],\n [0, 4, -1, 0, 1],\n [6, 5, 3, 0, 6],\n [-4, 5, 4, -5, 1],\n [2, -2, -1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -1, -1, -4, -4],\n [-4, 6, 2, 6, -4],\n [2, -2, 6, -2, 3],\n [2, 0, -4, 0, -2],\n [-1, 6, 6, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -1, -1, -4, 5],\n [4, -6, -1, 3, 4],\n [-2, -5, 4, -1, -3],\n [-5, -3, 2, -2, 5],\n [3, -4, -3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 2, 5, 5, -5],\n [1, 3, -1, 0, -3],\n [-4, -2, 1, -6, 4],\n [0, 3, -1, 0, 4],\n [-3, -4, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 0, -2, 4, 2],\n [4, 2, 6, -6, -4],\n [-4, 5, 0, 1, -3],\n [4, 2, -3, 2, 4],\n [-1, -5, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, -3, -6, 5],\n [-3, -4, 4, 1, 5],\n [-2, -6, -3, -6, 0],\n [1, 0, -6, 3, 0],\n [-1, 1, -6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 3, -2, 1, -4],\n [1, 3, -1, 1, -5],\n [5, -2, 1, 4, -4],\n [-2, -6, 1, 3, 1],\n [5, -5, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -3, -5, 1, 4],\n [4, -2, 3, -3, 0],\n [6, 6, 5, 4, 5],\n [-5, -5, -3, -3, 3],\n [-5, 5, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -3, -5, 4, 6],\n [1, -2, 2, 1, 1],\n [-4, -6, 2, -2, -4],\n [4, -5, 5, 2, -1],\n [1, 6, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 0, 5, -5, 2],\n [-5, -6, -1, 1, 4],\n [-4, 5, -5, -2, -5],\n [-6, -1, 0, -4, 6],\n [-4, -4, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -5, -4, 3, 1],\n [4, -2, -3, -6, 2],\n [2, -5, -5, -3, 6],\n [4, 6, -2, -1, 4],\n [0, -1, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 3, -3, -4, 3],\n [0, 0, 3, -1, 5],\n [4, -1, -5, 6, -2],\n [6, -2, -5, -6, 1],\n [-5, -6, -2, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 0, 2, 4, 4],\n [0, 4, -2, 3, -5],\n [4, -2, 1, -5, 2],\n [3, 3, 2, -1, -4],\n [3, -4, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, 3, 0, 1],\n [-1, 5, -3, -2, 1],\n [2, -4, -6, 1, -2],\n [4, 3, 0, -5, -3],\n [-2, -1, 5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 0, -1, 1, 2],\n [-3, 3, -4, 6, 4],\n [-4, -4, 6, -4, 4],\n [2, 3, 3, 2, 6],\n [6, 4, 1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 0, 4, 6, 3],\n [0, 2, -4, -2, -3],\n [-4, 5, -3, -4, 2],\n [-5, -5, -3, 1, 4],\n [-4, -3, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 1, -1, 2, 4],\n [2, -4, -6, 0, 1],\n [5, -1, 0, -5, 2],\n [1, -3, 3, 5, -4],\n [-2, -4, 3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 0, 2, 4, -6],\n [0, 3, -1, 4, -5],\n [1, 1, -5, -1, 4],\n [-1, 5, 2, 0, -3],\n [-4, -6, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 1, 3, -3, 4],\n [-1, 5, 3, -4, 4],\n [5, 1, -4, 0, 4],\n [5, 2, -2, -6, -4],\n [3, 3, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, 2, -3, -1],\n [-5, 1, -3, 1, -2],\n [-4, -1, 4, 2, 6],\n [6, 0, 4, 2, -5],\n [-5, 3, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -4, 1, -1, 5],\n [1, 1, -5, 2, -2],\n [-1, -4, 5, 1, -3],\n [-4, -4, 6, 0, 4],\n [5, 3, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -4, -6, -5, 6],\n [-6, -2, 2, 4, 6],\n [-1, 3, 5, 4, 4],\n [-4, 3, -2, 0, 6],\n [5, -1, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 2, 0, -2, 4],\n [0, 0, -3, 5, -1],\n [-4, -2, -5, 4, -6],\n [-6, -3, -6, 0, 4],\n [4, 6, 4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 3, 6, -1, 4],\n [-4, -2, 2, 1, -2],\n [2, 5, 6, 3, -5],\n [-4, 3, 5, -2, 3],\n [-3, 4, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, -4, 6, 0],\n [3, -2, -1, 2, -6],\n [2, 3, -4, -4, -6],\n [2, 4, 4, -6, 1],\n [1, 0, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 1, 3, 3, -2],\n [-6, -1, -4, -5, -6],\n [-5, -2, 4, -4, 0],\n [4, 3, 3, 4, 0],\n [3, -4, 5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 2, 4, 4, -1],\n [-6, 1, 2, 4, 1],\n [6, 5, 4, -2, 0],\n [2, 3, 3, 5, -5],\n [-1, 6, -2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 5, 2, 6, -1],\n [6, 3, -2, -2, 4],\n [5, 3, -2, 3, -3],\n [0, 5, 4, -5, 0],\n [4, 4, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -1, 1, -4, 6],\n [2, 0, 3, 1, 6],\n [-6, 0, 1, 1, 5],\n [-4, -4, -4, 6, 2],\n [5, 4, -6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 5, 2, 1, 4],\n [3, 0, 2, 2, -3],\n [5, -3, -5, 5, 1],\n [5, -1, -5, -2, -3],\n [3, 5, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -4, 5, -4, 2],\n [0, 4, 4, 3, 6],\n [-2, 3, 0, 0, -2],\n [6, -1, -3, 6, -4],\n [5, 6, 1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 2, 2, 5, -2],\n [1, -6, 4, 2, -4],\n [-5, -3, 3, 4, -6],\n [-4, -6, 0, -1, 3],\n [0, 4, 6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 1, -5, -2, 5],\n [0, -6, -5, 2, -2],\n [-5, 3, 0, 4, -2],\n [4, 0, -2, 5, 4],\n [6, 3, 6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 3, 1, -2, -6],\n [4, 4, -3, 5, 0],\n [-3, -6, -2, -2, 3],\n [1, -4, 2, -5, -6],\n [5, 5, -5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 5, 6, -6, -1],\n [-1, 6, 1, -3, -6],\n [1, -6, 0, 1, 6],\n [0, 5, -2, 3, 0],\n [-1, 3, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 3, 1, 2, 2],\n [4, -3, -4, -2, -3],\n [-6, 1, 1, -3, 1],\n [4, 2, 6, 5, 4],\n [-1, -6, -1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 2, -1, -1, 6],\n [0, 4, 5, 2, -2],\n [-2, 4, -1, 2, 0],\n [0, -3, 5, -6, 6],\n [2, 3, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 0, -2, 1, -3],\n [5, -1, 5, 5, 1],\n [5, 1, 4, -2, -4],\n [-4, -2, 4, 0, 3],\n [-5, 1, -4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 0, 2, -1, -6],\n [3, 3, 4, -1, 1],\n [5, -2, 4, 2, 2],\n [3, 4, 1, 1, 1],\n [-3, 6, 2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -3, 3, 6, -4],\n [-6, 4, 1, -5, -2],\n [-3, 2, 6, 1, 2],\n [-3, -1, 2, -1, 2],\n [1, 1, 5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -3, 4, -1, -4],\n [5, -5, -4, -4, 1],\n [0, -5, -1, -1, -5],\n [3, 4, -3, -6, -5],\n [4, 3, 4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -4, -6, 6, 0],\n [-1, -2, -6, -1, 5],\n [-2, 5, -2, -1, -4],\n [5, 6, 3, 1, -4],\n [-4, -4, 4, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -1, 2, 2, 0],\n [2, -1, 1, -3, 6],\n [-3, 6, 1, -1, -3],\n [-6, 6, 2, -6, -6],\n [-1, -5, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -6, 1, 1, 0],\n [5, -1, -5, 5, -1],\n [5, 1, -3, -2, 4],\n [6, 3, 3, -2, -4],\n [5, -6, -1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, -4, 0, 5],\n [0, 5, -3, -3, 5],\n [6, 0, -4, -2, -5],\n [4, -4, 3, 3, -3],\n [-1, 3, -1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -1, -6, 1, 4],\n [-5, 6, -1, -5, -2],\n [4, -4, -3, -3, 3],\n [-4, -5, 1, -3, -3],\n [-2, 6, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -2, -4, -3, 6],\n [2, -1, -1, 3, -6],\n [0, -3, 5, -6, -2],\n [4, 2, 3, -1, 6],\n [4, 5, 4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 3, -1, -2, 2],\n [2, -5, 5, 6, -4],\n [6, -4, -2, -5, 6],\n [-6, 1, -1, -1, -5],\n [-1, -5, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -1, 5, -3, 6],\n [3, -4, 4, -4, -3],\n [-2, 2, 4, -1, -2],\n [0, -2, 6, -5, 1],\n [-3, -4, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 0, -6, 3, -1],\n [2, 2, -3, -2, 2],\n [-5, 1, 5, 3, -3],\n [0, 6, 5, 6, -6],\n [-2, -3, -4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, 3, -4, 3],\n [-6, 5, -1, 5, 3],\n [-3, -3, -1, 1, 5],\n [3, -4, 5, -1, -3],\n [-5, 4, 5, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 4, 1, 1, -6],\n [2, -3, -1, -2, -3],\n [5, -4, 6, 5, 5],\n [1, 5, 5, 6, 1],\n [-3, 3, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -3, -4, -4, -4],\n [-2, -2, 1, 3, -6],\n [-4, -1, 6, -6, 4],\n [4, 3, 3, 0, 6],\n [-2, -4, -1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -6, -6, -6, 3],\n [0, 4, -2, -1, 2],\n [-5, 0, 4, 6, -1],\n [6, -4, 1, -3, -5],\n [3, 3, 0, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -2, -3, -1, 4],\n [-5, 3, -3, 2, 5],\n [3, -1, -3, 2, 3],\n [2, -2, 3, -6, 4],\n [6, -3, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 4, 5, 3, -4],\n [-6, -3, -5, 2, 6],\n [5, -2, 2, -5, 2],\n [1, -4, -2, 5, -2],\n [2, 3, 4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -1, -3, -6, 6],\n [0, -4, -4, -5, -1],\n [-5, 5, -1, -2, -4],\n [2, 1, 4, 5, 2],\n [2, -6, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, 2, 6, 1],\n [-5, 1, -5, -6, 2],\n [-4, -6, 4, -1, 2],\n [5, -1, -2, 1, -1],\n [-2, -1, 4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -6, 2, 2],\n [1, 4, 2, 4, 1],\n [3, -5, 5, 2, -5],\n [-4, -1, -2, -6, 6],\n [-4, -3, -1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -6, -1, -5, 0],\n [5, -3, -5, -5, 5],\n [6, 3, 4, -3, 1],\n [-1, 3, 0, -5, -1],\n [0, 0, 5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -2, 2, -1, 6],\n [0, 6, 1, 4, 5],\n [1, 1, -2, -3, -3],\n [-4, -1, 5, -5, 0],\n [2, -6, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 0, -3, -6, -2],\n [3, -3, 3, -6, 1],\n [-5, -3, 1, 3, 3],\n [-6, 3, -6, -4, 3],\n [-2, -4, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 0, -4, -4, -2],\n [1, 0, 2, -6, 3],\n [-6, 3, 3, -5, -6],\n [5, 5, 0, 3, -1],\n [5, -5, -2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 5, -6, 1, 3],\n [0, 3, -2, -5, 2],\n [5, 4, -6, 4, -3],\n [4, 2, -5, 2, 4],\n [1, -3, -2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -3, -3, -1, 3],\n [-5, -1, 4, 6, -3],\n [2, -2, -6, 1, -4],\n [-1, -4, -4, -5, -3],\n [-4, -1, 4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -5, 1, -1, -1],\n [-3, 3, -6, -5, 2],\n [-6, 0, 5, -1, -3],\n [-3, -1, 5, -6, -3],\n [2, 1, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 6, -1, 0, 5],\n [6, 0, 3, -5, 1],\n [-4, 3, 2, -1, -6],\n [1, -4, -6, -3, 3],\n [6, -1, -3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 3, -2, 0, 0],\n [-5, 0, 4, 3, 0],\n [3, -6, -6, 3, -5],\n [-4, 0, 3, 0, -4],\n [-2, 1, -2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 3, 2, 4, -4],\n [-3, 3, 3, -4, -6],\n [-3, -4, -5, 1, -5],\n [-4, 0, -3, -4, 5],\n [2, -6, 3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 4, 3, -2, 4],\n [5, 6, 1, 1, 0],\n [3, 4, -4, -6, -1],\n [6, 4, -2, 4, -3],\n [2, -2, -5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 4, 1, 5, 0],\n [4, 1, -3, -4, 3],\n [-2, 0, 0, 2, 4],\n [4, -5, 2, 4, 2],\n [4, -5, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -3, -1, 6, 4],\n [-6, 0, 6, -1, 5],\n [6, 5, 6, -6, -1],\n [3, 3, -4, -2, -5],\n [5, -2, -2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, 6, 3, 5],\n [5, 2, -5, 4, 5],\n [-4, 5, 6, -2, 2],\n [-5, 0, -1, 4, 4],\n [-3, 4, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 5, 2, -5, -1],\n [-4, -3, 4, 4, 1],\n [3, 3, 0, 5, 0],\n [-1, 0, -1, 1, -4],\n [4, 6, 3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -4, 4, 2, 3],\n [5, 6, -3, -1, -4],\n [5, -6, -1, 2, 0],\n [-1, -2, -2, -3, 2],\n [6, -5, 4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 5, -4, 2, 0],\n [6, 0, 4, 4, -5],\n [1, -1, -6, 6, -3],\n [-1, 2, -2, 1, 6],\n [-6, 4, 6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 0, -4, 5, 0],\n [-1, -2, -1, -5, 4],\n [3, 2, 3, 3, -1],\n [4, -5, -1, 3, -4],\n [-2, 4, 5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -6, 1, 2, -5],\n [0, 2, 1, 0, 3],\n [-4, 2, 5, -4, 1],\n [0, 2, -4, -1, 0],\n [0, -4, 1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -2, 2, -1, -2],\n [-4, -5, -2, -4, -4],\n [1, -3, 6, 5, -6],\n [3, -4, -2, -3, -1],\n [-3, 1, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 1, 2, 6, -2],\n [-4, 6, 1, 6, -4],\n [0, 3, 5, -1, 3],\n [-2, -1, 2, -6, -5],\n [1, -2, 1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 5, -4, 1, 1],\n [5, -6, 6, 5, 4],\n [5, -4, 5, 2, 6],\n [0, -5, 0, 5, 4],\n [3, 0, 5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 5, 3, 0, -3],\n [-1, 2, 0, 1, 4],\n [-1, 3, 6, 1, -1],\n [5, -6, 1, 5, 5],\n [-6, -2, 6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 4, -6, 1, 3],\n [0, 5, 5, -2, -5],\n [0, -2, 0, -5, -3],\n [5, -6, -1, -3, 3],\n [2, 4, 6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -4, 2, 1, -1],\n [-3, -5, 2, 0, 5],\n [-1, -3, -2, 3, 5],\n [2, -2, -1, -5, -2],\n [6, 3, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 6, -6, 0, 2],\n [-6, -5, 1, 0, 5],\n [-3, -3, -3, -5, 3],\n [-2, -6, 2, -1, 0],\n [1, 1, -5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -5, 1, 3, 4],\n [0, -5, 0, -1, 2],\n [4, 1, -5, 0, -5],\n [6, 5, 1, -2, 6],\n [-5, 0, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -6, -3, -6, -2],\n [-4, -3, -2, -4, -2],\n [3, 2, 5, 6, -5],\n [5, -2, 5, 2, 5],\n [4, -4, 6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 0, 2, 5, 5],\n [4, 1, -1, -4, -1],\n [1, 6, 4, -1, 6],\n [6, 5, 2, 6, -1],\n [-4, 6, -5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 2, -4, 6, 3],\n [2, 5, -6, 4, 0],\n [2, -3, -2, 6, -6],\n [2, 6, -1, -1, 5],\n [5, 6, 3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 2, 2, 6, 6],\n [4, 1, -4, 1, 3],\n [6, 1, 3, 1, 2],\n [3, -1, 4, 2, -1],\n [-4, -5, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 1, 2, 5, 2],\n [1, 0, 2, -6, 3],\n [4, 6, -2, 6, -1],\n [-3, -5, 4, 5, 6],\n [-2, 1, 6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 3, -2, 3, -2],\n [2, 4, 2, 1, 3],\n [-6, 6, 3, 2, 4],\n [-2, 4, 4, -5, 1],\n [-3, 1, 3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -2, -1, -1, 6],\n [-5, 4, -3, 1, 0],\n [-3, 1, -2, 6, -6],\n [5, -1, 5, -1, -1],\n [1, -3, 5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 1, 3, 4, -1],\n [3, -2, -5, 5, -2],\n [-1, -4, -2, 2, 2],\n [-6, 6, 1, -1, 1],\n [4, -6, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -5, -3, -2, -5],\n [-5, 2, -1, -5, 1],\n [-5, -5, 6, -1, -1],\n [-3, -5, 5, -1, -2],\n [-1, 6, 0, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 2, 4, 5, -1],\n [-3, 1, 1, -6, -4],\n [-3, 4, -3, 6, 4],\n [0, -5, 5, -6, -4],\n [-6, 3, 6, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, 5, -3, -2],\n [2, 0, -5, -4, 0],\n [4, -1, -1, -6, -4],\n [4, 0, 6, -4, 3],\n [-2, -2, 1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 4, -1, -3, 3],\n [6, 2, 0, 2, 4],\n [5, 0, 4, -3, -2],\n [5, 6, -4, -1, -6],\n [6, 6, 1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 1, 1, -6, -5],\n [1, 3, -4, 2, 1],\n [-5, -3, -5, 0, 0],\n [-6, -4, 2, -5, 6],\n [-6, 5, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 6, 6, 2, 3],\n [-4, -1, -5, -1, 0],\n [6, 4, 1, -5, 1],\n [-2, -6, -4, 4, 6],\n [-4, 0, 0, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, 6, -6, 0],\n [-5, -1, 5, 1, -4],\n [5, 5, -6, -5, -3],\n [4, 4, 6, 0, -6],\n [0, 3, -4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -2, 5, 5, -1],\n [-4, 3, 5, 2, 5],\n [-1, 6, -3, 1, -3],\n [-2, -4, 1, -3, -6],\n [-6, 1, 6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, -2, -2, -4],\n [-2, 1, 3, 6, -5],\n [5, 5, -3, -3, -1],\n [-4, -1, -5, -1, -1],\n [-1, 1, -3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -1, -4, -6, 6],\n [2, -2, 5, 2, -6],\n [5, -4, 3, 4, 3],\n [0, 2, 1, -6, -6],\n [-3, 0, -5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -4, -4, 1, -6],\n [-5, 3, 1, -5, 1],\n [-4, 4, 0, -1, -4],\n [5, -1, 6, 6, 3],\n [1, -3, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -4, -2, 0, 2],\n [5, -6, -5, 0, 3],\n [-3, -5, -1, -3, -2],\n [0, -2, -5, 2, -2],\n [1, -2, 6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 4, 0, 5],\n [2, -4, -1, -6, -5],\n [2, 4, 4, -1, 4],\n [-6, 0, 5, -3, 5],\n [0, 4, -4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 5, -2, -5, 2],\n [-3, -5, -3, 2, 0],\n [3, -2, -1, -4, -4],\n [2, -5, -3, -1, -1],\n [1, -6, 6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 0, 4, -6, -5],\n [-1, 6, -3, 3, 4],\n [-2, 6, 5, 3, -3],\n [-6, 2, 3, 3, -1],\n [1, 1, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, 2, -1, -6],\n [-2, 4, -3, 5, 6],\n [5, -6, -4, -4, 0],\n [-5, -2, 0, 5, -3],\n [-2, 6, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 4, -4, 6, -1],\n [3, -3, -5, -2, -6],\n [1, 5, -4, -4, 3],\n [-3, 2, -3, -1, -2],\n [-3, 3, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -2, 1, -3, 3],\n [-2, 3, -2, -6, -3],\n [-4, -6, -3, -2, -2],\n [6, -4, -5, -4, 6],\n [2, -2, 4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 4, 5, 6, 1],\n [-2, 4, 5, -4, 6],\n [-3, 0, -5, -3, 6],\n [-6, 4, -6, 4, 5],\n [1, -4, -5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 1, -2, 6, 0],\n [-4, 5, -4, -4, 4],\n [-6, 1, -5, -5, -4],\n [-1, 1, 2, -6, -5],\n [-3, -6, 1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 2, -5, -6, 5],\n [-5, 3, -5, -4, -5],\n [3, -6, -2, 2, 2],\n [2, -2, -1, 0, 6],\n [1, -1, 4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -2, 4, -6, 4],\n [-1, 6, 0, -2, 0],\n [1, 5, 3, 2, 6],\n [-6, -6, -2, -1, 2],\n [-5, -1, 1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 4, -6, -2, -2],\n [2, 3, -2, 1, 6],\n [5, -3, -6, -5, 5],\n [5, 6, 0, 4, -5],\n [3, -1, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, -5, -1, 0],\n [0, 6, -2, 6, 6],\n [1, -4, 5, -3, 2],\n [-2, -6, -6, -1, 6],\n [-1, 0, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -4, 0, 6, -2],\n [3, -3, 0, 6, -2],\n [2, 3, 4, -5, 2],\n [3, -6, -3, 4, -1],\n [6, -6, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 1, 4, -6, 6],\n [2, 5, -2, -6, 1],\n [-3, -3, 1, 3, -2],\n [4, 3, -1, -1, 1],\n [-2, -3, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 2, 4, 6, -3],\n [2, -5, -3, 3, 1],\n [-2, 6, 2, -6, 4],\n [-6, 2, -5, 1, 0],\n [0, 4, -5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, -6, 3, -1],\n [-6, 1, 4, -6, -5],\n [4, 6, 4, 6, 2],\n [2, -5, 6, -1, -4],\n [-3, 6, 4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 6, 2, -4, 2],\n [-4, -6, -2, 4, -6],\n [-2, 6, -6, -5, 1],\n [-4, 3, -4, 3, -6],\n [2, -3, 4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 2, -2, 4, -3],\n [-2, -4, -5, -4, -2],\n [-6, 1, -3, -2, -6],\n [-6, 4, -1, -6, 4],\n [-6, 0, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 1, -6, 1, 3],\n [4, 1, -4, -1, -1],\n [-3, 0, -2, -3, 2],\n [2, -3, 3, -3, -6],\n [0, -2, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 6, 1, 2, -5],\n [-4, 2, -3, -5, -3],\n [6, -2, 6, 0, 5],\n [4, 6, 5, -4, 6],\n [-2, -1, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, -4, 0, -6],\n [-4, 6, 2, 1, -1],\n [5, 5, -6, -3, 3],\n [2, -5, -3, 6, 3],\n [-6, -6, -1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 2, 0, 6, 4],\n [3, -2, 5, 5, 0],\n [-5, -6, 3, -1, 6],\n [2, 2, -6, -5, 0],\n [6, -2, -4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -6, -5, 5, 6],\n [-5, -4, 0, 1, -1],\n [0, 5, 4, -3, -3],\n [1, -3, 3, 3, -2],\n [6, -5, 5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -2, 2, 0, -3],\n [-4, -1, 0, -1, 0],\n [-5, -1, -6, 2, -6],\n [3, 6, -5, 5, 6],\n [3, 4, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -2, 4, -1, 2],\n [-2, 3, -2, 4, 4],\n [3, -6, 3, -5, 1],\n [-1, 3, -2, -4, 0],\n [3, 3, 1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 2, -1, -2, 1],\n [0, -1, 4, 6, -6],\n [-3, -4, -4, 6, 6],\n [0, -5, 6, -6, 0],\n [-3, -5, 5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 4, 3, 0, 6],\n [3, 3, 3, -6, 5],\n [-3, -2, 6, -4, 2],\n [3, -4, -1, -3, 4],\n [6, 2, 1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 2, 6, -1, -6],\n [-2, -4, -5, -1, 1],\n [4, 4, -5, 3, 6],\n [4, 1, -3, -3, -2],\n [-2, -1, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 5, -1, 2, 1],\n [0, -3, 1, 6, 0],\n [4, 5, -2, 3, 0],\n [2, -5, -4, 5, -4],\n [-4, -3, 0, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 0, 3, -5, 4],\n [-5, 2, -3, 3, 3],\n [6, -6, 6, 2, -6],\n [-3, 6, -2, -5, 1],\n [-1, -1, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 4, -3, -2, 4],\n [6, -3, -2, 1, -1],\n [-3, 3, -5, -6, 0],\n [-2, 3, -3, 6, 5],\n [5, -2, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -2, 4, 4, -4],\n [4, -5, -4, 4, -2],\n [-3, -6, 3, -1, 1],\n [1, 0, 2, -2, -4],\n [4, 6, 2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -2, -4, 1, -2],\n [3, -1, -1, -6, 0],\n [-1, -6, -5, 1, 2],\n [4, 0, -6, -1, 6],\n [4, 4, 6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -1, -4, -5, -5],\n [0, 6, 5, -6, -1],\n [0, 4, -4, -3, -2],\n [6, 3, 6, 4, 2],\n [1, 6, 4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 0, 5, 6, 4],\n [6, 2, 6, -1, -6],\n [6, -1, -6, 0, 5],\n [-3, -4, -6, 1, 3],\n [3, -4, 1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 3, -3, -5, -2],\n [1, 2, -3, -5, -4],\n [5, -4, -6, 3, 1],\n [-5, 2, -5, -2, 4],\n [6, 4, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 4, 3, 4, 4],\n [0, 4, 3, -3, 2],\n [2, 1, -4, 4, 6],\n [-5, -6, -2, 4, -4],\n [2, 5, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -4, -3, -3, -5],\n [0, 4, -2, 1, -3],\n [-4, -3, 0, -4, -4],\n [4, -5, -2, -4, 5],\n [-6, 4, 0, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 0, 3, -5, 2],\n [-2, 3, 1, 5, -6],\n [0, 1, -3, 1, -3],\n [-5, 0, -5, 5, -3],\n [0, 3, 1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 6, 2, -3, -2],\n [-3, -1, -5, 5, -2],\n [-5, 4, -3, -5, 5],\n [5, -5, 6, 5, -1],\n [-1, -4, -1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -4, 2, 2, -5],\n [-1, -1, -1, 1, 2],\n [-2, -4, -6, 1, 0],\n [-4, 3, 5, 3, 5],\n [-1, 2, -4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 4, 3, -5, 5],\n [1, -6, -2, 0, -5],\n [-4, 0, 0, 3, 0],\n [-6, -5, 4, -3, 4],\n [2, -1, -3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, 5, -6, 3],\n [-5, 4, 6, 5, 4],\n [-5, -2, 5, -2, -1],\n [1, 5, 5, -1, 5],\n [5, -3, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -5, 1, -3, 5],\n [6, 2, 1, -5, -1],\n [-3, 6, 0, 6, -5],\n [5, -5, 1, -1, 5],\n [4, -4, -2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -4, -5, -2, -3],\n [-2, -2, 5, 1, 2],\n [-4, -2, 1, 3, -6],\n [-2, 3, -5, -6, -5],\n [-3, 0, -1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 6, 3, 5, -4],\n [1, -2, 1, 1, -2],\n [-1, 0, 6, 5, 2],\n [5, -2, 5, 0, 5],\n [-5, -6, 5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 2, 5, -3, -3],\n [-6, -4, 6, -2, 3],\n [2, -1, -3, 3, 3],\n [-4, -6, 6, 4, -6],\n [3, -3, -4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 4, 5, 5, -2],\n [2, -2, -1, -5, -3],\n [2, -3, -5, 2, -4],\n [-6, 1, 5, 0, 4],\n [-2, -2, 1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -6, -6, -5, 3],\n [2, 1, 6, -6, 4],\n [2, -6, 0, 3, 6],\n [5, -1, 5, -4, 0],\n [-3, 5, -5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 6, 3, 6, -5],\n [-5, -4, -2, 4, -1],\n [5, 0, -3, 3, -3],\n [0, 3, -4, 6, -2],\n [0, -4, -2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 5, -6, -6, -2],\n [4, -3, -2, 0, -6],\n [1, -5, -5, 2, -5],\n [3, 2, -2, 5, 0],\n [1, -3, -6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 2, -5, -5, 0],\n [-3, -1, -6, 5, -1],\n [0, 2, 1, -4, 3],\n [2, 6, 5, -2, 2],\n [2, -6, -1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 2, -3, 2, 3],\n [-5, -5, 4, 2, -3],\n [4, 6, -1, -3, 3],\n [6, -2, 6, 1, 3],\n [-4, -6, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -1, -5, 2, 1],\n [5, -1, 2, 0, 4],\n [-1, -6, 2, 4, 4],\n [1, -1, -5, 4, 3],\n [-4, -2, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -4, 1, 2, 3],\n [-3, 4, 3, -5, 4],\n [0, -1, -4, 5, -5],\n [3, -1, -2, 2, 4],\n [-2, -1, -1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, -2, -1, 4],\n [-3, 6, -4, 1, 5],\n [-3, -4, 4, 1, -4],\n [-5, -4, -1, 0, -3],\n [-6, -4, -5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -1, 3, -3, 3],\n [0, -1, 2, -1, 1],\n [-6, -6, -5, -4, 3],\n [-4, 2, -6, 3, 4],\n [3, -2, -4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 0, -2, -3, 0],\n [3, -6, -5, -3, -4],\n [-1, -5, 6, 6, -6],\n [0, 2, -4, -1, 3],\n [-2, -1, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 3, 3, 4, -3],\n [1, -6, -2, -6, 1],\n [-4, 6, -2, -2, 4],\n [-1, -6, -1, -2, -4],\n [3, -1, -2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -3, 5, 0, 0],\n [-2, 5, -3, 3, 2],\n [-1, 4, 0, 5, -2],\n [-1, 6, 5, -3, -1],\n [-6, -1, 6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 4, 6, -3, -6],\n [0, -3, 6, 2, 5],\n [-1, 4, -6, 0, 5],\n [5, -5, -2, -3, -6],\n [-6, -1, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 5, -5, 4, -2],\n [3, -2, -2, 6, 6],\n [-1, -5, 5, 2, 3],\n [6, 4, 6, 0, -2],\n [1, -4, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 0, -1, -4, 6],\n [0, 1, -2, -3, -1],\n [5, 2, -6, 0, -3],\n [1, 0, -3, 3, 2],\n [-4, 2, -1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 3, -6, -1, 1],\n [-6, 2, -4, -4, -5],\n [-4, 6, 2, -6, -5],\n [-2, 6, -4, -5, 5],\n [-3, 2, -1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 6, 1, 1, 0],\n [-6, 4, 2, -5, -1],\n [0, 0, -2, -6, 1],\n [3, -4, 2, -3, 6],\n [-6, -3, -2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -6, -5, 5, 3],\n [-5, -1, 3, -3, -4],\n [5, -5, -2, -3, -3],\n [-5, 4, -1, -6, -4],\n [0, -6, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 5, -1, -1, 5],\n [-1, 4, 2, -6, -1],\n [5, 4, -5, -2, -4],\n [-5, 6, -4, -4, 3],\n [-4, -1, 2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 6, 6, 2, 6],\n [-2, 0, -2, -2, -6],\n [6, 1, 5, -5, 0],\n [-6, -5, 4, -5, 6],\n [1, -4, 4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -6, -5, -4, 6],\n [-6, -4, 2, 5, -1],\n [-4, -2, 6, -2, -3],\n [4, -6, -6, -5, 6],\n [-3, 6, 6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -5, -4, -1, 2],\n [-6, -5, 0, 5, -5],\n [2, 5, 6, 2, -4],\n [-6, -2, 0, -2, -4],\n [-1, 1, -6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 6, -4, -6, 5],\n [-5, -3, 6, -1, 1],\n [3, -3, -2, -4, 2],\n [-1, 3, -3, 0, -5],\n [4, -3, 6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 6, 2, 0, -2],\n [-4, 6, 2, 2, 6],\n [-6, 1, 5, 2, -3],\n [1, 4, -2, 0, -6],\n [-2, 0, -6, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 2, 1, -3, -4],\n [-1, 1, -6, 6, 3],\n [-6, -4, 2, -6, 2],\n [0, 5, 0, 6, 5],\n [0, -2, -6, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 6, 2, 4, -1],\n [2, -3, -1, -5, -4],\n [1, 6, -1, -4, 0],\n [6, 4, -3, 0, 0],\n [0, -6, 4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -1, -5, -3, -4],\n [4, 3, -5, -1, -5],\n [-1, -4, -1, -5, 0],\n [-6, -5, 1, -4, 4],\n [-1, 5, 5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -1, 1, -6, -2],\n [-6, 5, 6, 4, 6],\n [-4, -1, 2, 1, -4],\n [-1, -4, 6, -3, -4],\n [1, 5, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -6, 0, -5, 0],\n [-3, 6, 5, -2, -4],\n [0, 4, 5, 3, -1],\n [-5, -5, 5, -6, -5],\n [0, 2, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -1, -4, -5, -2],\n [4, -6, 1, -5, -1],\n [0, 4, 2, -3, -3],\n [-6, -3, 1, 1, 5],\n [-3, 3, -5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 2, 5, 2, 5],\n [5, -2, 5, 2, 4],\n [-4, -4, -4, 0, -4],\n [6, -4, -2, 2, 4],\n [-6, -4, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 3, -5, 3, -1],\n [0, -4, 2, 6, 4],\n [-1, -3, -1, -2, 0],\n [-4, 0, -3, 3, 5],\n [5, 1, 6, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -3, -6, 1, -5],\n [-3, 2, 6, 1, -3],\n [-6, 6, 3, 3, 0],\n [4, -4, -6, -6, -1],\n [-1, 4, 3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 5, 5, 2, 0],\n [1, -1, 6, 1, -6],\n [3, 2, 5, -1, -6],\n [6, 4, -2, 0, 4],\n [5, 0, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -6, -6, -3, 6],\n [-6, 6, -6, 0, 5],\n [2, 5, -1, 6, 3],\n [-1, 6, -5, 0, -5],\n [-1, 6, 3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 0, 6, -6, -4],\n [-2, -5, -5, 6, -3],\n [3, -4, -6, -2, -3],\n [-3, 0, -4, 4, 2],\n [-4, 5, -4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -1, 1, 5, -3],\n [-4, 4, -4, 5, 1],\n [-4, 1, 2, -5, -6],\n [0, 2, -2, 2, 2],\n [-3, -2, 5, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 3, -6, 3, 4],\n [4, -6, 3, 2, 4],\n [2, 0, -6, 1, 2],\n [-3, 6, 2, 3, -4],\n [-2, -6, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 1, 1, -2, 1],\n [5, 5, -6, -5, -6],\n [0, 3, 6, -6, -6],\n [2, 1, -4, 5, -5],\n [-6, -6, 2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 3, -2, -5, -6],\n [1, -2, -6, -5, 4],\n [-3, -3, -2, -3, -6],\n [-5, -6, 4, -3, 6],\n [2, 1, 6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -5, 1, -2, -2],\n [3, -4, 3, -2, 2],\n [-4, 3, 6, 0, 4],\n [-1, -5, 3, 6, -5],\n [-6, 1, 6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -5, -2, 4, -3],\n [-5, 5, -6, 6, 4],\n [6, 6, 2, -6, -2],\n [-1, 5, 4, 4, 0],\n [-4, -4, 6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -1, -3, -5, -4],\n [2, -4, -3, -3, 2],\n [-6, 2, 5, 3, -5],\n [1, 2, -1, 3, -6],\n [2, -3, 1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -5, 4, -3, -6],\n [4, -6, 3, 3, 5],\n [1, 3, 5, -1, -6],\n [2, 0, -1, -1, -5],\n [-1, 0, 3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -3, 3, -5, -5],\n [-5, 0, -2, -1, 2],\n [2, -5, 4, -3, -3],\n [-6, 1, -2, -6, -5],\n [4, 0, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 2, -6, -6, 0],\n [1, 1, 0, 4, 1],\n [0, 0, -2, -2, 0],\n [0, 0, -1, -1, -6],\n [2, 6, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 3, 5, -2, -6],\n [-4, -2, -1, -4, 2],\n [1, -1, 3, 4, -5],\n [2, 1, 6, 3, -1],\n [0, 1, 1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -2, -6, 0, -3],\n [2, 3, 1, 6, 0],\n [-6, 4, -6, -4, 1],\n [-1, 1, -2, -2, 6],\n [-4, 4, 1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, 2, 0, 6],\n [-5, -4, -3, -1, -2],\n [-2, 5, -5, 3, 2],\n [6, -5, 1, 1, 1],\n [-5, -5, -1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 0, 2, -3, -6],\n [0, -3, -1, -3, -1],\n [-6, 5, -4, 0, 0],\n [5, 5, -4, -1, 2],\n [6, -2, 3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 3, 6, -2, 1],\n [4, 6, 5, 6, -1],\n [0, -3, -1, -4, 1],\n [-1, -6, 0, -6, -5],\n [6, -6, 6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 2, 2, 6, 1],\n [-3, -5, -4, -6, -4],\n [1, -6, -1, -5, -3],\n [0, 3, 2, 3, -6],\n [1, -1, -4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 4, 1, -1, 4],\n [-1, 3, -5, -2, 2],\n [1, 5, 5, 2, 0],\n [5, -3, -1, -1, 3],\n [1, -5, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 2, 6, 0, -3],\n [1, 0, -5, 4, -4],\n [6, -6, -6, 5, -6],\n [6, 3, -2, 4, 2],\n [-2, -1, -4, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 2, -5, -1, 5],\n [1, 6, 5, -6, -5],\n [2, -5, -1, -5, 4],\n [4, -5, -5, -1, 4],\n [4, 2, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -4, 2, 5, -5],\n [3, 3, 6, -5, 6],\n [-2, -5, -4, -3, 6],\n [-6, 6, 6, 0, -3],\n [5, -3, -5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 4, -5, 0, -1],\n [4, -1, 0, -4, 0],\n [-4, 1, 6, -2, 2],\n [-6, 4, -1, 6, -3],\n [2, -2, 3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, -4, -1, -1],\n [5, 0, 3, 5, -1],\n [-5, 6, 2, -1, 5],\n [3, 4, -2, 3, -2],\n [0, 3, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -1, 5, 1, 3],\n [6, -1, 0, 2, -2],\n [-6, -6, 6, -5, -5],\n [-2, -1, -1, -2, -2],\n [3, 3, 0, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -4, -6, -5, -4],\n [3, 0, -5, -2, -1],\n [5, -6, 6, -4, -6],\n [1, 1, -3, -2, 6],\n [-1, 5, -3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -6, 6, -1, -5],\n [-3, 6, 3, 4, -3],\n [-2, -5, 3, -3, -4],\n [6, 0, 3, -4, 6],\n [0, 4, 6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -5, -1, -5, 0],\n [-6, 0, -4, -6, 1],\n [2, -2, 6, 6, -1],\n [1, -6, 6, 0, 3],\n [-4, 2, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 3, 0, 4, -2],\n [-1, 6, 5, 0, -4],\n [-6, 4, -4, -5, 1],\n [1, 4, 3, 3, 2],\n [3, 2, 4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 1, -4, -4, 5],\n [-2, -5, -1, -4, -4],\n [6, -4, 0, -1, 6],\n [-5, -6, -2, 1, -4],\n [-6, 3, -3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -1, -5, -4, 6],\n [5, 4, -5, 6, 1],\n [-2, -5, -6, 4, 4],\n [-2, 6, -1, -6, 5],\n [-3, 6, 5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -3, 1, 3, 3],\n [3, -3, 0, -6, 4],\n [2, 4, 5, 0, -2],\n [4, -2, 0, -3, -1],\n [-2, -1, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, 5, -1, -2],\n [6, -5, 1, 5, 6],\n [-5, -1, -1, -2, -6],\n [-2, 3, -5, 6, 4],\n [5, 4, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, 6, 1, 6],\n [-3, -2, 2, 4, 5],\n [4, 3, 1, 3, -6],\n [4, 4, 1, 6, 2],\n [-4, 4, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, 5, 0, -3],\n [6, -3, 6, 0, -1],\n [-4, -2, 1, 1, 0],\n [3, 6, 1, 4, -2],\n [4, 5, 4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 5, -6, 5, -1],\n [3, 1, 0, -2, 1],\n [-1, 0, -1, 3, -4],\n [-5, -3, -6, 0, 0],\n [2, -2, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -6, 4, 6, -6],\n [2, -4, 2, -5, 4],\n [3, -4, 6, 2, 4],\n [0, 6, 5, -1, 2],\n [6, 1, 5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -6, -6, -6, 0],\n [4, 3, -5, -6, -4],\n [4, 2, 5, 0, 5],\n [6, 1, -1, -5, -4],\n [-3, 0, -3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 1, 0, 3, 0],\n [-3, 3, 5, -6, 6],\n [-2, -1, 6, -5, -3],\n [-2, -3, -3, -4, 2],\n [3, 0, -4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -2, 0, 5, 3],\n [-2, 5, 6, -1, -2],\n [-6, 2, 1, -3, -3],\n [-3, -1, -6, 6, -5],\n [-1, 0, 6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 0, -3, 6, -3],\n [6, -1, -6, 6, 2],\n [4, -2, -2, -6, 0],\n [-4, -4, -3, -2, -3],\n [-5, -3, -5, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 1, -4, 1, -4],\n [0, 3, -5, 1, 0],\n [1, 5, -4, 6, 4],\n [-6, 2, 0, 4, 2],\n [-2, 0, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 4, -5, 2, -3],\n [1, -3, -3, -4, -5],\n [6, 3, 0, -3, 2],\n [-5, 5, 4, 5, -1],\n [-1, 6, 3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 0, -2, 2, 2],\n [5, -5, -5, -6, 1],\n [3, 1, 2, 6, -4],\n [-1, -1, 5, 2, 1],\n [-5, -1, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -5, -1, -6, -1],\n [4, -6, 4, 2, -4],\n [4, 4, 2, -5, 0],\n [4, 6, 3, 5, 3],\n [-6, -3, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -4, -5, -4, 3],\n [4, -1, 3, -5, -1],\n [-2, -4, 4, -5, 5],\n [-1, -4, -3, -6, 1],\n [2, 2, 5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -4, -6, -6, -4],\n [6, -2, 5, -5, 0],\n [-2, -2, -1, 0, -3],\n [2, 2, 2, -5, 0],\n [1, -2, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 4, 2, -5, -2],\n [-1, -3, -1, -5, -6],\n [6, 6, -5, 4, -2],\n [2, 5, 5, -6, 3],\n [-6, 3, -4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -4, 3, 1, -1],\n [-6, -4, -6, 1, -5],\n [-2, 2, -4, 1, -6],\n [-3, -6, 0, 5, 6],\n [-6, 5, -1, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 1, 1, -6, -4],\n [-2, 2, 3, -5, 2],\n [0, -6, -2, 6, -5],\n [-1, 6, 4, 6, 6],\n [3, -5, -5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 6, 4, -2, 2],\n [-1, -5, 2, -4, -3],\n [-4, 2, 3, 3, 5],\n [5, 5, 1, 3, 2],\n [5, 0, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 3, -4, 5, 3],\n [-2, -4, -4, 6, 0],\n [5, -1, 3, 1, -3],\n [1, 0, 6, -2, -5],\n [0, 2, 6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -2, 0, 4, 4],\n [2, 1, 1, -1, -6],\n [5, 0, -6, -1, 1],\n [-2, -2, 6, 3, -5],\n [-6, 3, 3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 2, 3, -2, -4],\n [-6, 4, -2, 0, -5],\n [0, 3, 6, -1, 5],\n [-3, 4, 4, 4, -6],\n [-1, 6, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -4, 4, 5, 6],\n [1, 2, 5, -1, 6],\n [4, 5, -4, -1, 5],\n [6, 3, 0, -1, 1],\n [2, 4, -2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 5, -2, 3, 4],\n [5, 4, 5, 0, 6],\n [1, 4, 4, -1, -2],\n [-5, -1, 2, 4, -3],\n [1, -1, -6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 4, -4, -5, 0],\n [-6, 6, 2, -1, -2],\n [6, 2, 4, 3, 0],\n [6, -3, -3, -2, -3],\n [1, 2, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 3, -1, -1, 2],\n [-3, -6, -3, 3, 3],\n [2, 2, -3, -6, -2],\n [0, 6, 1, 1, -5],\n [-4, 3, -2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -5, 3, 0, 4],\n [2, 2, 6, 1, 3],\n [2, 1, -6, 4, 5],\n [-1, -5, 6, 0, 0],\n [0, 0, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -6, 0, -3, 0],\n [-6, 4, -2, -2, 4],\n [-6, -4, 3, -3, -1],\n [-6, 5, -1, -3, -4],\n [-4, -6, -3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, -2, -2, -6],\n [0, 2, 4, 6, -2],\n [1, -3, 5, 0, 1],\n [4, 1, -2, 4, -1],\n [2, -1, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -2, -2, -6, -2],\n [-5, -5, -3, 5, 4],\n [6, -6, 5, 6, -5],\n [-2, 2, 6, 2, 5],\n [-4, 3, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -4, 4, 5, -1],\n [-4, 4, 4, -3, 3],\n [-6, 0, 1, -5, -5],\n [0, 1, -6, -4, 0],\n [1, -1, -2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 2, -3, 4, 4],\n [1, -6, 6, -6, 4],\n [4, 2, 1, 4, -4],\n [-4, -2, -4, 4, 2],\n [1, -4, -6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, 4, -3, -6],\n [6, 3, -5, 6, -4],\n [-3, 6, -5, 5, 4],\n [2, -2, -5, -4, -1],\n [-5, 4, 1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -3, -1, 4, 6],\n [3, 1, -4, -2, 6],\n [2, 4, 1, -2, -1],\n [-2, -4, -3, -2, -3],\n [6, -2, 0, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 6, 6, 4, -4],\n [1, -2, 1, 2, -1],\n [3, 4, 1, 1, 4],\n [0, -6, 4, 0, -6],\n [-1, -3, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 0, 4, 2, 6],\n [-2, 1, 4, 6, -1],\n [2, -2, 6, -3, 3],\n [0, 2, -5, -3, -4],\n [6, -5, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -2, -3, -4, 6],\n [-6, -3, 1, -2, -4],\n [-6, 3, 5, -6, -5],\n [-4, -5, -1, -1, -2],\n [-3, -1, 5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 5, 6, 2, 0],\n [2, -5, 2, 4, -6],\n [-3, 2, 6, 6, 0],\n [-5, 6, 2, -2, 1],\n [4, 2, -1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 1, 1, -6, -5],\n [1, -1, -2, 1, -5],\n [-1, 5, 1, 4, 2],\n [-6, -4, 4, 2, -3],\n [0, 5, 2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 4, 5, 2, 1],\n [5, -4, 1, 0, -1],\n [3, 6, 4, -2, -4],\n [2, -2, 1, 6, 4],\n [0, -5, -1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 6, 6, -1, -2],\n [4, -6, 1, 1, -5],\n [1, 1, 2, -1, 4],\n [0, 2, 4, 1, 6],\n [5, -1, -6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -4, -4, 6, -5],\n [4, -6, 3, 4, 1],\n [5, 1, 2, 4, 6],\n [5, 6, 1, 2, 2],\n [3, 3, -1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 0, 4, 1, 4],\n [-4, 2, 5, 0, 2],\n [4, 0, -2, 4, -3],\n [0, 6, -1, -3, 0],\n [2, -1, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -3, -3, 6, -3],\n [-6, -4, 2, -5, -4],\n [-2, -2, -4, 5, -2],\n [3, 2, -3, -2, 0],\n [1, -1, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, 3, 2, -2],\n [0, 3, 3, 2, -3],\n [1, 4, -6, -2, -1],\n [4, 3, -5, 3, -3],\n [6, 0, -6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, -5, 1, 3],\n [-1, 3, 1, -5, -2],\n [-4, 6, 5, 5, 4],\n [-1, -5, 2, -2, 1],\n [-5, -5, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 3, 0, -5, -2],\n [-3, -5, 6, 0, 6],\n [-1, 3, -3, -1, 5],\n [2, 2, 6, 1, 1],\n [4, 4, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 6, -1, 0, -6],\n [1, 0, 5, -5, 5],\n [-3, -3, -2, 6, 2],\n [-1, -5, 0, -1, 0],\n [-5, -6, 3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -1, -1, -6, -1],\n [5, 1, -4, 5, 1],\n [-6, -4, -5, 1, 4],\n [-1, 1, 6, -2, -4],\n [3, 4, 3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 4, 6, -2, -4],\n [-3, -6, 1, 4, -5],\n [0, -6, -1, -3, -2],\n [0, -5, 2, 3, -6],\n [0, 2, -1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 2, 2, -2, 2],\n [-4, -2, 2, 1, 2],\n [6, -1, 5, 5, 1],\n [4, -1, 1, 2, 4],\n [-5, -1, 6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 0, -5, -3, -4],\n [1, 0, 1, -3, -1],\n [5, -3, 6, 5, -6],\n [-3, -6, 1, -6, 5],\n [6, 5, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 0, 0, -5, 1],\n [-4, -2, -2, 6, -6],\n [-2, 5, 6, -5, 1],\n [4, 4, -3, -6, -4],\n [-2, 5, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -3, 1, -2, -6],\n [-1, 6, -2, -4, -5],\n [-4, 0, 3, 2, 0],\n [-2, 4, 2, -5, -1],\n [-3, 0, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -4, -4, 6, -6],\n [-2, 3, 2, -2, 0],\n [-2, 4, -6, 0, -3],\n [-6, -6, -5, 2, -1],\n [0, -3, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 6, -4, 5, -2],\n [3, 2, 6, 3, 0],\n [5, -1, 2, 5, 4],\n [5, -6, -6, 0, -5],\n [6, -5, 1, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -3, 4, 4, 1],\n [-4, 5, 1, 5, 4],\n [0, 1, -6, 5, 4],\n [-3, -3, -5, -4, -4],\n [2, -6, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 5, 4, 5, 6],\n [2, -2, -1, 5, 0],\n [-5, -6, 4, -1, 0],\n [-1, -1, 3, 4, -5],\n [3, -5, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -6, -4, -1, 6],\n [-3, 0, -3, -1, -4],\n [4, 5, -2, 4, -5],\n [0, -3, -1, -2, 4],\n [-4, 3, 0, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -5, 6, -2, -1],\n [3, 3, -5, -3, -5],\n [1, -4, 5, -2, 6],\n [0, -5, 0, 5, 1],\n [5, -1, 2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 5, -1, 0, 5],\n [0, 2, -5, -2, -5],\n [-5, 5, 3, -2, 6],\n [6, 4, -2, -6, 5],\n [-2, -3, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 3, -2, -5, -3],\n [0, 4, -2, 3, -1],\n [-5, -5, 2, 4, 6],\n [-5, 6, -5, 2, -2],\n [-4, 6, 3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 4, -1, -3, -1],\n [3, -1, -3, 5, 0],\n [4, 1, -2, 5, 2],\n [1, 5, -3, -2, -1],\n [1, 5, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, -1, 4, 5],\n [3, -6, -3, 4, -2],\n [1, -3, -4, 3, 2],\n [-4, -3, 1, -3, 3],\n [3, 2, 1, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 6, -5, -2, 5],\n [3, 1, -2, 6, 3],\n [-3, 3, 5, -5, 5],\n [-6, -4, 2, 3, 6],\n [0, 4, -5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -1, 3, 0, 1],\n [-6, -4, -2, -4, -6],\n [6, -5, -4, -6, -1],\n [2, 5, 0, 6, -5],\n [6, 6, 4, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -2, 0, -5, -3],\n [0, -3, -4, 4, 4],\n [2, 6, 6, 5, 6],\n [2, -1, -4, 4, 2],\n [0, 2, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -5, 5, -5, 5],\n [6, 2, -1, -1, 6],\n [-2, 1, -6, -3, 3],\n [4, 5, 1, -6, -6],\n [6, 3, 6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -3, 3, -2, 1],\n [1, 3, -1, -4, -6],\n [-1, -1, 3, 2, -1],\n [4, -6, -6, 5, -2],\n [1, 5, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -1, 3, 1, 2],\n [-1, 1, -3, -5, 1],\n [4, -4, -1, 4, 1],\n [0, -2, -3, -1, 5],\n [0, -3, 6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 5, 4, 3, 5],\n [-4, 1, -2, -1, 4],\n [-5, 1, -4, -1, -1],\n [5, 1, -1, -6, -3],\n [-6, -5, -3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -4, -3, -5, -3],\n [-3, 4, -1, 0, 5],\n [-5, 3, -3, -5, -4],\n [2, 5, -2, -5, -6],\n [-2, 5, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 5, 0, 0, -1],\n [3, 4, -4, 5, -3],\n [-5, 2, -6, 1, -5],\n [6, 4, 0, 3, 2],\n [6, -3, 3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -2, 5, 0, -1],\n [0, -5, 5, 3, 2],\n [1, -2, 3, -1, 6],\n [-5, 6, 3, -3, -5],\n [-1, 4, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -5, 4, 6, 5],\n [4, 3, 6, 1, -3],\n [-5, 1, 4, 0, -2],\n [2, -3, -1, -3, 3],\n [-5, -6, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -3, 6, 4, 6],\n [3, -6, 0, -2, 0],\n [-5, -1, -4, -4, 2],\n [-1, -2, -6, -4, -1],\n [2, 2, 3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 6, -2, 4, -1],\n [4, 6, 4, 1, 5],\n [3, 2, 2, 3, -6],\n [5, -4, 1, 5, -1],\n [0, -3, -5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -2, 6, -1, -1],\n [-1, 3, 1, -6, 3],\n [-1, -2, 2, -3, -5],\n [-6, -4, -2, 2, 0],\n [-5, 0, -6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -3, 2, 4, -2],\n [-6, 3, -2, 2, 1],\n [2, 5, 1, 2, 3],\n [2, -4, 6, -5, 5],\n [-6, -1, -4, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -5, -6, 1, -2],\n [2, -5, 5, 4, -1],\n [6, -6, 5, -5, 3],\n [-1, 0, 6, -3, -3],\n [6, -2, -3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, 5, 3, 4],\n [-6, -6, 0, 3, 1],\n [-1, 2, 0, 2, 0],\n [5, 3, 6, 0, -1],\n [4, 4, 0, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 1, -1, -6, 6],\n [-3, -3, -4, 6, 2],\n [6, -1, 3, 2, 4],\n [-5, 6, -6, 4, -6],\n [-6, 5, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -2, -3, 5, 3],\n [-1, 2, 4, 1, 5],\n [-5, 5, -6, 6, 0],\n [1, -3, 0, -1, -3],\n [6, -3, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 1, 1, -4, 1],\n [6, 2, -2, -3, 4],\n [-3, -5, 1, -5, -5],\n [5, -2, 1, -2, -2],\n [3, -6, -4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 5, 4, 1, -1],\n [4, -2, -5, -4, -5],\n [6, -4, -6, -1, -1],\n [-2, -6, 2, 3, 3],\n [-1, 0, -5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 4, -4, 0, -1],\n [0, 4, -6, 3, -2],\n [-3, 4, -4, -3, 6],\n [5, 4, -4, -2, 5],\n [5, 3, 3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -1, -5, -1, -4],\n [-5, -2, 3, -4, 5],\n [1, -5, -1, 5, -5],\n [-6, 4, 2, 2, -6],\n [-6, -2, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 1, 1, 0, 5],\n [1, 6, 4, -1, -5],\n [-6, 0, 3, -3, -5],\n [3, -5, 6, 3, -6],\n [-4, 4, 0, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 0, 2, 3, -2],\n [-4, 3, -5, -4, 0],\n [2, -2, 6, 4, 1],\n [2, -1, 4, 0, 1],\n [-1, -3, -2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, -1, -6, -3],\n [-3, 1, 6, -2, -4],\n [0, 1, 3, 5, -2],\n [6, 5, -2, -6, -6],\n [-4, -4, 5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -4, 0, -6, 4],\n [0, 0, -1, 4, 6],\n [-5, 3, 3, 5, -1],\n [-1, 3, -4, 0, 5],\n [-4, 3, -5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, 2, -6, 4],\n [2, -3, -2, 4, -3],\n [-4, -2, 2, 6, -1],\n [2, -6, -3, -1, -6],\n [3, 6, -3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 5, -5, -5, 4],\n [-4, -3, 1, 5, 2],\n [-4, 4, 4, 6, 1],\n [5, -5, -5, -5, 5],\n [-5, -4, -2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 6, -2, -6, 0],\n [6, -5, 0, -3, -6],\n [3, 2, 0, 5, -6],\n [5, 3, -5, 1, -3],\n [-3, 3, 5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -1, 2, -3, -2],\n [-3, -1, 0, 6, -5],\n [-6, -1, 1, 5, 5],\n [3, -4, 1, -3, -5],\n [-2, -1, -6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 2, 5, -4, 1],\n [-3, 4, 6, 4, -5],\n [-5, 4, 1, 1, 2],\n [6, 5, 6, -4, -5],\n [-6, 1, -6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -3, -3, -5, 0],\n [-5, 5, -2, -1, -2],\n [-5, 6, 3, 0, 3],\n [0, 0, -3, -2, 5],\n [3, 5, 0, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 3, 0, 3, -1],\n [-3, -2, 0, 3, 2],\n [2, -5, -2, 5, 2],\n [3, 1, 6, 5, -3],\n [2, -4, 5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -1, 5, -2, 6],\n [-4, -3, -1, 0, -3],\n [-3, 5, 1, 4, -6],\n [5, -6, 5, 1, 4],\n [-4, -1, -3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 0, -6, 5, 3],\n [0, 4, 2, 4, -3],\n [1, -1, 6, 6, 4],\n [6, -5, 0, -6, 4],\n [3, -2, -5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 4, -1, 5, 5],\n [-1, 2, 6, -4, 1],\n [-6, 4, -5, 2, -6],\n [-2, 5, -5, -5, 2],\n [3, 4, -6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -4, 4, 3, 4],\n [-3, 6, 3, 1, -4],\n [0, -2, 3, 3, 5],\n [-1, 0, -6, -1, -4],\n [6, -2, 6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -5, -3, -1, 2],\n [-3, -1, -2, -6, -3],\n [0, 2, -4, -2, -2],\n [-3, 3, -3, -3, 1],\n [-1, 2, -6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 3, -6, -2, -2],\n [-2, 0, 4, 5, -1],\n [5, 3, 4, -2, 5],\n [3, 4, -3, 1, -2],\n [1, -2, 3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 4, -6, -1, 4],\n [3, 2, 6, -2, 6],\n [-2, -1, -1, 4, 4],\n [-6, 1, 3, 4, 3],\n [3, 4, 2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 4, 4, 6, 5],\n [-4, 6, -1, 1, -6],\n [1, -3, 6, 4, -2],\n [-4, -1, 3, -2, -3],\n [-6, 5, 5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 5, -2, 5, 1],\n [2, 5, -6, 4, 5],\n [1, -5, -1, 5, 3],\n [0, -1, -1, 5, 6],\n [-2, -3, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 1, 5, 2, -3],\n [0, -2, 3, 6, 2],\n [3, 3, -6, 6, 1],\n [1, -2, -5, -4, 5],\n [3, -5, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 0, 0, -6, 4],\n [6, 6, 2, -6, 3],\n [-5, -3, -5, 3, -3],\n [-3, -6, 4, -3, 0],\n [3, 6, -2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -3, -1, -4, -5],\n [2, -5, -5, -5, 4],\n [-1, -6, -3, -3, -5],\n [-3, 5, 4, 0, -3],\n [-4, -1, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, 6, -5, -5],\n [-1, 6, 4, -5, 0],\n [2, 2, -1, 6, -4],\n [3, 0, -3, -5, 5],\n [-6, 1, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 5, 4, -3, 3],\n [-4, -6, -3, 0, -5],\n [-1, -3, 5, 6, -2],\n [1, 6, 3, 3, 0],\n [-5, -6, 6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -4, -1, 6, -3],\n [-2, -6, 0, 1, 5],\n [3, 6, -5, 4, 4],\n [-6, -2, 1, 4, -2],\n [-1, 4, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 0, 5, -4, 0],\n [-1, 3, -2, -3, 0],\n [5, 3, 1, 6, 5],\n [5, -4, -6, -5, -5],\n [5, 5, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -1, 4, -3, -3],\n [-2, 6, -2, 1, 2],\n [-1, -3, -2, -4, 4],\n [-5, -3, -2, 4, 3],\n [5, 4, -4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, -2, 3, 4],\n [-4, 0, 6, 1, 1],\n [-5, -6, -2, 6, -1],\n [4, 3, -1, 6, -6],\n [0, -5, -5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 0, 5, 2, -2],\n [1, -4, 0, -5, -6],\n [0, -4, 4, -6, 5],\n [1, -3, -6, 4, 4],\n [4, -5, -2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -5, -1, -6, 3],\n [-3, 3, 6, 6, 1],\n [-1, -1, -6, -6, -1],\n [1, 0, 4, -5, 5],\n [-6, -5, 5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 0, 5, -4, 5],\n [-1, -3, 0, 3, -4],\n [-6, 1, -6, 5, -1],\n [2, -3, -4, 3, -3],\n [-6, 4, -1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -6, 0, -6],\n [-3, -2, -1, 1, 1],\n [-3, -3, 3, -5, -3],\n [1, -2, 6, 4, -4],\n [-2, -4, 6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 1, 0, 2, -6],\n [-1, 4, -5, 4, 5],\n [3, -2, -4, -2, 1],\n [-2, 3, 6, -4, 5],\n [-2, 3, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 2, 3, -1, -4],\n [5, -1, 3, 3, 5],\n [4, 3, 0, 0, 6],\n [1, 0, 0, -2, 2],\n [4, 4, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 2, 0, -2, 6],\n [6, 0, 3, -4, 5],\n [3, -2, -3, 0, 2],\n [5, -4, -4, -1, -3],\n [4, -4, 5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -4, -2, 1, -4],\n [-3, 2, -1, -3, -5],\n [3, -2, 6, -5, -5],\n [-2, -5, 0, -2, -5],\n [-2, 5, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, 3, -4, -4],\n [4, 5, 1, -6, 3],\n [2, 0, -1, 5, -5],\n [6, -2, -5, 6, -6],\n [4, -2, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 0, 2, 2, -1],\n [-3, 3, 0, -3, -4],\n [-1, -6, -6, 6, 0],\n [-4, 5, 6, 5, 3],\n [4, -3, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -6, 4, 1, 4],\n [5, -1, -3, -4, -6],\n [6, 1, 6, 3, -1],\n [5, 3, 3, -5, -2],\n [-6, -3, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -2, -4, 5, -4],\n [1, 3, 4, 2, 6],\n [2, 6, -1, 3, 6],\n [5, 4, 2, -1, 4],\n [6, 0, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 2, -1, -6, -1],\n [-3, -3, -3, 0, 6],\n [-2, -4, 2, -3, 5],\n [4, 1, -2, 4, 0],\n [0, -4, 6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 3, -2, -6, 3],\n [-2, 4, 0, 1, 5],\n [-3, -3, 1, -2, 6],\n [-6, -1, 3, -6, 1],\n [-1, -2, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -6, -5, 6, 5],\n [-2, -5, -6, 0, 4],\n [1, 3, -5, 5, -2],\n [0, -1, 5, 1, 6],\n [-2, 5, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -5, -6, 2, 2],\n [-6, -2, 2, -3, -4],\n [0, -5, 2, 4, -4],\n [1, 4, 3, -6, 2],\n [-6, -3, -3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -4, 4, 5, -6],\n [5, -2, 3, -4, 1],\n [-6, -3, 5, -3, 6],\n [-6, -1, 3, 1, 3],\n [-3, -5, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -6, -1, 3, -3],\n [2, 2, 2, 3, 2],\n [-3, -5, 6, -2, 3],\n [0, 4, 6, -3, 1],\n [-6, 4, -6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 1, 2, 2, -1],\n [-6, -1, 0, 4, -5],\n [2, 5, 0, -6, -4],\n [-6, -3, 0, 2, -4],\n [2, -2, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 0, 4, -1, 5],\n [-2, -1, -1, 0, -1],\n [1, 6, 3, 4, 5],\n [1, -6, 0, 6, -1],\n [-3, -6, 5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 4, -1, -4, 4],\n [1, 3, 1, -2, -6],\n [-1, -5, 4, 1, 4],\n [-1, 0, -4, -2, 3],\n [3, -5, -2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 5, 3, -6, 4],\n [-3, 1, 1, 6, 1],\n [-6, -6, -2, 5, 1],\n [-2, -2, -2, 4, -6],\n [-1, 4, 3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 3, 2, 6, 5],\n [2, -3, 0, 6, -4],\n [-2, 1, -5, 3, 6],\n [0, -5, -2, -1, 4],\n [-5, -1, 5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 1, 2, -2, -5],\n [-4, 3, 1, -4, 4],\n [6, -1, 4, -5, 5],\n [3, 1, -1, 5, -4],\n [4, 1, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -6, 6, 1, 4],\n [4, 5, 2, 4, -3],\n [5, 1, 1, 5, 6],\n [4, -1, -5, 1, 6],\n [3, -5, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 0, 6, 3, 6],\n [-4, 2, -5, -6, -2],\n [2, 3, 3, 3, 6],\n [-3, 0, 0, -1, 1],\n [-4, 2, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 5, 6, 1, -4],\n [4, -6, -4, 0, -2],\n [6, 5, 0, -3, -6],\n [-5, 0, -4, 1, 2],\n [-4, 4, -3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -3, 1, -2, 3],\n [-1, 5, 0, -1, 2],\n [-3, -3, -6, -6, 0],\n [-2, 1, 0, -5, -2],\n [1, 6, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -3, 5, -3, -5],\n [3, 6, 2, 1, 1],\n [2, 4, 4, 6, 0],\n [1, 0, 4, 4, 6],\n [3, 3, -1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -1, -1, -5, -2],\n [-3, 5, 3, -4, 4],\n [3, 0, -5, 1, -4],\n [-4, -5, 4, -4, 0],\n [-5, 3, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -2, -3, 1, -6],\n [1, 2, -2, -6, -4],\n [-4, 5, -5, -2, 4],\n [-3, 0, 1, -4, 5],\n [-6, -2, -3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -1, 4, -5, 5],\n [1, -4, 4, -1, 6],\n [-6, 0, -6, 5, 0],\n [4, 0, 3, 0, -5],\n [-1, 6, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -6, -3, 0, -2],\n [-5, 0, 0, 3, 2],\n [-2, 6, -4, -2, -3],\n [2, 1, -4, -6, 5],\n [2, -2, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, 0, 0, -2],\n [5, 5, -5, -5, -3],\n [5, 2, -6, 1, -6],\n [6, -1, -6, 4, 0],\n [0, 0, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 1, 1, -5, -4],\n [-2, -6, 5, 3, 6],\n [-3, 2, -6, -5, 6],\n [2, -3, 6, -1, -2],\n [-6, -2, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 2, -6, -3, 4],\n [0, 3, -5, -5, 0],\n [5, 2, -4, -1, 1],\n [-2, -1, 2, 0, 1],\n [5, -6, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -4, 2, 1, 1],\n [-3, -4, 0, -3, 1],\n [0, -2, -4, -1, 3],\n [4, 4, 4, -1, 2],\n [-6, 0, 2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, 1, -5, 4],\n [-4, 3, 5, 5, -4],\n [-4, 5, 1, 2, -2],\n [-1, 1, -1, 1, -2],\n [-4, 1, -4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -5, 6, -6, -1],\n [-3, 4, 3, -2, -3],\n [3, -6, 6, 2, 6],\n [-6, 5, 6, -2, 2],\n [6, -1, 3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 5, -3, -4, 1],\n [-1, -3, 5, -2, -6],\n [3, 0, -6, -2, 1],\n [-6, -4, -2, -5, -5],\n [2, -2, 1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 0, 3, -4, -3],\n [6, 0, 4, -4, -4],\n [2, 2, 3, 0, 5],\n [3, -2, 2, 4, 3],\n [-2, -6, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 4, -3, -4, -5],\n [-1, 5, -2, -6, 5],\n [-2, 1, -3, 5, 6],\n [4, 4, -3, 4, 6],\n [-3, -2, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -2, 1, 5, 6],\n [5, -1, 1, -5, 2],\n [0, -2, -1, -1, 6],\n [-2, -4, -5, -2, 0],\n [-6, -4, 6, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, 5, 2, -3],\n [-3, 2, -6, 0, 0],\n [5, -4, -2, 6, -5],\n [-5, 3, 5, 0, -1],\n [6, -2, 2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -6, 0, 2, 5],\n [6, 4, -3, -2, 5],\n [-1, 5, 0, 2, -2],\n [5, -6, -6, 0, 4],\n [3, -6, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -5, -2, 6, 4],\n [-1, 1, 4, -6, -2],\n [-3, -1, -3, -5, 5],\n [3, -1, -4, -3, -1],\n [-1, 3, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, -1, 6, 2],\n [2, 0, -4, 2, 0],\n [1, -6, 0, 1, 3],\n [-2, -1, 1, -5, 3],\n [-1, -5, 6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -3, -5, -4, 6],\n [-1, -3, 6, -4, 5],\n [4, 1, 4, 5, -5],\n [0, -5, 6, -6, -1],\n [-1, 6, -5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -3, -4, 3, -4],\n [4, 5, 0, 5, -1],\n [0, -3, 5, -4, 5],\n [-4, -2, -4, 6, 5],\n [1, 6, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -3, -5, -1, 6],\n [-6, -5, -2, -1, -3],\n [3, -2, -1, -5, 2],\n [-5, -1, 2, -6, -4],\n [-4, -4, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 3, 2, -5, 6],\n [-5, 5, -2, -3, -3],\n [2, 4, -5, 6, 4],\n [-4, 6, -6, 4, -5],\n [-1, 2, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 2, 0, -6, -6],\n [-6, -1, -1, 4, 1],\n [-4, 4, 2, 4, 4],\n [4, -6, -5, 4, 6],\n [-5, -2, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -4, 0, 0, -5],\n [4, 1, -3, 0, -4],\n [-1, -4, 3, 5, -2],\n [-5, 2, -1, 3, 5],\n [4, 5, 5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -3, -2, -5, 2],\n [-4, 1, -2, 1, 2],\n [1, -2, -4, -3, 1],\n [5, 0, 0, 5, -6],\n [1, 3, -2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, -5, -3, 2],\n [1, 6, 4, 5, -2],\n [-5, 6, 4, 3, -6],\n [-5, 0, -4, -5, 3],\n [4, -2, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -5, -3, 6, 5],\n [-5, 5, 2, -1, 2],\n [-4, -1, -4, -2, -2],\n [1, 0, -2, -3, 5],\n [-5, 1, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -1, 1, -6, 1],\n [4, 6, -3, 3, 1],\n [0, 2, -1, -2, 1],\n [-6, -3, 1, -4, -4],\n [3, 1, -3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 5, 1, -3, -4],\n [3, -5, 3, -3, 2],\n [-3, -1, -1, -2, 4],\n [2, 4, 4, -2, 6],\n [6, -1, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 0, 3, -2, -4],\n [-1, -5, -6, 0, -6],\n [1, 2, 6, 5, 6],\n [3, -2, -5, -5, -3],\n [0, 4, 6, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 4, -4, 6, -1],\n [4, 1, 4, -1, -1],\n [5, -1, 6, -4, -4],\n [4, -3, -4, -1, -3],\n [4, 5, -6, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -3, -5, 5, 2],\n [-5, 4, -1, -3, 0],\n [4, 3, -6, -1, -5],\n [-4, 0, -5, -4, 4],\n [6, -2, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -6, 1, -2, 0],\n [-1, -6, 0, -2, 6],\n [-2, 4, -2, -6, 1],\n [-2, -4, -5, -4, -6],\n [-1, 0, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -5, 5, 6, -3],\n [3, 5, -5, -2, -1],\n [-6, 6, 6, 1, 5],\n [1, 0, 4, 1, -1],\n [0, -2, -3, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 6, 5, -3, -4],\n [-1, 6, 2, 4, -5],\n [-5, -6, 5, -5, -6],\n [-5, -5, -1, 3, -5],\n [-3, 1, 4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, 0, 0, -6],\n [3, 1, -3, 0, -5],\n [-1, -3, 6, 4, -4],\n [-5, 0, 4, 0, 5],\n [-6, -4, -1, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -3, 5, 4, 3],\n [2, 6, 0, 5, -4],\n [5, -3, 3, -3, -1],\n [4, 6, 3, -5, -2],\n [3, 5, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -6, 5, -1, 2],\n [0, -4, 1, -5, -2],\n [2, 2, 3, 1, -2],\n [0, -2, -1, -6, -6],\n [5, 4, -6, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, -6, 6, 2],\n [3, 2, -2, 2, 2],\n [-3, -2, 6, 2, 1],\n [4, 4, -2, -6, 6],\n [2, 1, 1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 0, -4, -2, 3],\n [4, -3, -2, 1, 2],\n [5, -6, 3, 0, 4],\n [5, -5, 0, -1, -4],\n [-1, 0, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -6, -2, 0, -6],\n [4, 4, 6, -3, 2],\n [-1, 4, 0, 4, -4],\n [-3, -3, 0, 2, 0],\n [-6, -4, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, -1, -5, 6],\n [-4, -1, 1, -1, 1],\n [-3, 4, -6, -3, 6],\n [6, 2, 2, 2, -4],\n [-1, 5, -1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 0, -2, 1, -5],\n [-1, -4, 6, -1, 4],\n [-2, -2, -2, -5, 5],\n [0, -1, 4, 1, 3],\n [0, 6, 3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 0, 5, -5, -4],\n [3, 6, 3, 6, -1],\n [1, 1, -1, -6, 6],\n [-6, 1, 1, 5, -5],\n [6, 4, 6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 3, -3, 4, -3],\n [1, 1, -4, -2, -5],\n [3, 6, 4, -6, -2],\n [6, 0, -5, 4, 4],\n [3, -3, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 4, -1, 4, 4],\n [0, 5, 0, -1, -5],\n [4, -6, 1, -5, 2],\n [-1, 2, 4, 1, 4],\n [-6, 4, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, -1, 4, -5],\n [-1, -6, -5, -6, 0],\n [1, 5, 1, 0, -3],\n [-5, 0, -4, 2, 1],\n [-6, 5, -5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 2, 2, -1, -5],\n [-3, 5, -6, 3, -2],\n [0, 1, -1, 0, 0],\n [-2, -4, -3, -2, 1],\n [-5, -5, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -2, -6, 2, 3],\n [5, 2, 2, 5, -4],\n [-1, 0, -5, -2, -3],\n [-3, -2, 4, -3, -4],\n [4, 4, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -4, -3, 0, -4],\n [3, 0, 4, -5, 2],\n [-4, 1, 3, -5, 0],\n [6, 2, -4, 0, -1],\n [1, -2, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 3, -5, -6, 0],\n [-2, -5, -5, 0, -1],\n [-4, -1, -3, 1, 2],\n [6, -3, -4, -3, 2],\n [-5, -5, 0, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 0, -2, -5, 3],\n [-6, -5, 6, 0, -3],\n [-1, 0, -3, -1, -3],\n [4, 5, 2, -1, -4],\n [-5, 1, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -4, -2, 5, -5],\n [6, 0, 4, -1, -6],\n [-6, 5, -6, -4, 6],\n [2, 6, 2, -6, 5],\n [-6, 2, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 6, -5, -6, 1],\n [1, -5, 4, -4, 6],\n [5, 2, 6, 0, -1],\n [6, 3, -1, 5, 3],\n [2, 2, -6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -4, 5, 2, 1],\n [-2, -4, 2, 1, -2],\n [-2, -5, -3, 5, -3],\n [-1, -1, 2, 3, 5],\n [1, -3, -5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -3, -2, 5, 1],\n [4, 3, 1, 2, -2],\n [-4, -2, -3, -5, 0],\n [5, -1, 0, -3, -1],\n [-6, 2, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 3, 1, -2, 0],\n [1, 0, 1, 3, -6],\n [-5, 1, -4, -6, 0],\n [3, 2, -3, -3, -3],\n [0, -3, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -4, 6, 4, 6],\n [-1, 5, 0, -1, -1],\n [3, -4, 5, 1, -5],\n [5, 5, 4, 1, 6],\n [0, -5, 3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 1, -1, 1, 4],\n [-5, -1, 4, 5, 6],\n [5, 3, 3, -6, 1],\n [-1, -5, -4, -1, 0],\n [-2, -6, 3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 0, 3, -6, 5],\n [4, -3, 2, 6, 1],\n [3, -6, -4, 4, -1],\n [1, -2, 5, -1, 3],\n [-6, -4, -4, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -4, -5, 4, 0],\n [-5, -3, -6, -1, -5],\n [-5, -1, -1, -1, -1],\n [6, 4, -3, -2, -4],\n [-1, -2, 6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 5, 3, 3, -4],\n [1, 0, 1, -5, 3],\n [6, 6, -4, 1, -4],\n [3, -2, 5, -6, 4],\n [2, 4, -1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 0, 2, -1, -1],\n [-6, -5, 3, 1, 0],\n [-1, 3, 5, -6, 0],\n [0, 4, 3, 6, -4],\n [2, -3, 5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, -2, -4, 0],\n [-3, -4, 0, -1, 0],\n [-1, 4, -4, 1, 4],\n [6, -5, 2, -5, 5],\n [-3, -4, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -4, -1, 1, -4],\n [1, 3, -5, -2, 2],\n [-1, -2, -5, -3, -1],\n [-5, 6, 3, -4, 3],\n [2, -2, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 3, -6, 2, -1],\n [5, -3, 3, -5, 1],\n [-1, -2, 2, 6, 3],\n [-6, -1, 4, -2, 5],\n [6, 3, 5, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -4, -1, 0, -3],\n [2, 0, 6, -2, -1],\n [0, -3, 4, 2, 6],\n [-2, -5, -1, 6, 2],\n [-1, 0, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 3, 4, -6, 6],\n [3, 5, 4, 0, -2],\n [-1, 1, 0, -3, 5],\n [-2, -1, 3, -2, 6],\n [3, -3, 6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 6, 5, 2, 0],\n [5, -5, -5, 4, -6],\n [1, -6, -4, 4, 2],\n [3, -4, -4, 4, 4],\n [2, -1, -6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 5, -3, -1, -5],\n [-2, 6, -3, -2, -5],\n [1, 0, -1, 1, -4],\n [2, 4, -5, -6, 6],\n [-2, 5, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 3, 4, -5, 0],\n [5, 5, 5, -1, -1],\n [-2, -2, -4, -1, -3],\n [2, 4, 2, -5, 2],\n [-5, -6, -4, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -4, -2, 4, 0],\n [5, 4, 2, 6, 3],\n [6, 2, -5, 4, 2],\n [5, 1, -3, -1, 2],\n [-5, 6, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -5, -5, -3, -3],\n [5, 6, 6, -3, 0],\n [-2, -3, -6, 4, -4],\n [3, 0, -4, 2, 2],\n [-1, 3, 5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 6, -6, -1, 5],\n [-3, -6, 4, 3, 6],\n [-1, 4, 4, 2, -5],\n [-3, -5, -1, 3, -1],\n [2, -1, -4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -6, 2, 4, -1],\n [-3, -1, -2, 4, 1],\n [2, -4, -4, 1, -4],\n [-5, 3, -1, -4, 1],\n [-3, 4, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 4, 3, 3, 4],\n [0, 6, -2, 2, 3],\n [-6, -4, 4, -6, 6],\n [4, -5, -2, -6, 2],\n [-5, -3, 5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 6, -2, 2, 1],\n [-1, -3, -4, 3, 5],\n [-3, -6, -1, -3, -4],\n [-4, -2, -6, -6, -1],\n [-5, -6, 3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -1, -5, 0, 2],\n [-6, 4, -6, -2, -4],\n [6, 1, 0, -1, 0],\n [5, -3, 5, -4, 1],\n [-1, -6, -1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, 5, -2, -4],\n [-4, 6, 5, 1, 3],\n [-5, 3, 0, 1, -1],\n [6, -4, 5, -4, -5],\n [6, 1, -6, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 0, 6, 1, -1],\n [-1, 3, -6, -3, 1],\n [-4, 5, -3, -2, -5],\n [-6, 5, -4, 5, 1],\n [-5, 5, -5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 5, 0, -6, 4],\n [2, 0, -3, 6, -1],\n [0, 2, -6, 2, 2],\n [-1, 4, -1, -2, -6],\n [-1, 5, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 4, -4, -1, -1],\n [3, 6, 0, 6, 4],\n [-4, 4, -3, -4, -3],\n [5, -2, 5, 5, 5],\n [-2, 6, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -5, -5, 3, -5],\n [3, 2, -6, 2, 0],\n [5, -5, -2, -5, -4],\n [4, 6, -6, -2, -4],\n [-6, 2, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -5, 5, -5, -1],\n [-1, 1, -3, -2, -1],\n [-2, -2, 2, 0, 4],\n [6, 1, 6, -2, -1],\n [-6, 0, -4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 4, 6, -1, -2],\n [-4, -5, 1, 0, -1],\n [-6, 4, -5, -2, 3],\n [4, 2, -4, -2, -6],\n [2, 4, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 0, 6, -1, 5],\n [5, 0, 5, 3, 3],\n [-5, 2, 6, 6, 5],\n [4, -1, -2, 0, 0],\n [-2, -1, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -2, 3, 2, -2],\n [2, -6, 1, 2, -5],\n [-4, 4, 6, -5, 0],\n [3, 5, 5, 4, 5],\n [2, 2, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 4, 1, -6, -2],\n [-5, -1, 0, 2, -5],\n [3, -2, -2, -4, -3],\n [1, 2, 2, 1, -6],\n [1, 1, -6, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 4, -2, -1, 1],\n [-2, 1, -3, -1, -6],\n [-5, -2, -4, -2, 4],\n [5, -6, -5, 1, -1],\n [-6, 4, -3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 5, -5, 5, 5],\n [6, 4, -1, -6, -3],\n [5, -4, 2, -5, 3],\n [0, -5, -3, -4, -1],\n [4, -1, 1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -6, -3, -4, -2],\n [-5, -2, -4, 1, -3],\n [-1, 0, 0, 4, 1],\n [-2, -3, 4, 1, -4],\n [-6, -6, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 0, 4, 3, -3],\n [-5, 1, 2, 1, 0],\n [-1, 1, 0, 0, 6],\n [5, 0, -4, 2, 0],\n [-6, 0, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, 2, -2, -4],\n [5, -1, -2, -2, -5],\n [-6, -6, 3, 5, 6],\n [5, -1, 6, 2, 0],\n [4, -4, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 4, 5, 0, 4],\n [5, -3, 4, 2, -4],\n [-2, 6, 2, 5, 4],\n [-2, -1, -2, 0, 1],\n [6, 2, 4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 2, 5, -3, 4],\n [-3, 4, -6, 5, -6],\n [0, 3, 2, 5, -4],\n [3, 4, 1, -6, -2],\n [1, -1, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -3, -2, 5, -3],\n [3, 2, -5, -4, 2],\n [3, -2, -1, 2, 4],\n [-3, 1, 2, -1, 0],\n [-5, 1, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 0, -6, -3, -4],\n [-1, -5, 1, -3, 1],\n [-6, -6, 6, -5, -5],\n [1, -4, -1, -3, -2],\n [-6, 5, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -5, -2, 1, 2],\n [-2, -3, 0, -5, -5],\n [5, 3, -2, 1, -3],\n [-5, 6, -5, -1, -2],\n [-6, 5, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -6, 1, 1, 4],\n [4, -5, 5, -5, 4],\n [0, -3, 2, 3, -5],\n [-2, -5, 1, 6, -3],\n [6, 1, 1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 0, 5, 4, -5],\n [-4, -2, 3, -4, -1],\n [2, 2, 3, -2, -2],\n [-3, -6, -1, -2, 6],\n [-5, 4, -4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 1, 4, 5, -6],\n [-1, 5, 3, -3, -6],\n [0, 1, -6, -4, 2],\n [1, -2, 1, 3, -2],\n [4, -6, -3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -2, -5, -3, 1],\n [3, -1, -3, 3, -1],\n [-1, 2, 5, -4, -5],\n [2, 5, 2, 5, 1],\n [-4, 2, -4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -4, -6, 6, -3],\n [0, 2, 5, 5, -5],\n [4, 1, -4, 1, -6],\n [-6, 3, 0, 5, -2],\n [3, -2, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 5, -2, -6, -2],\n [-3, -1, -2, -6, 4],\n [-3, 5, -6, -2, 5],\n [4, 6, 2, -2, 6],\n [6, -4, 2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 5, -3, 6, 0],\n [-5, -1, -5, -2, 6],\n [-6, 4, -6, 2, -4],\n [6, 1, -5, 4, 1],\n [-1, -2, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 4, 6, 4, -6],\n [2, 3, 6, -6, -4],\n [2, -6, -3, 4, -3],\n [6, -5, 0, 1, 4],\n [-3, -4, 2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 0, -5, 4, 3],\n [4, 0, 2, -4, -4],\n [1, -4, -1, -5, -4],\n [-3, 5, 4, 0, -2],\n [6, 1, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 0, 3, -6, 4],\n [-2, 2, 4, -3, 2],\n [-4, -3, -6, 4, -5],\n [5, 2, 4, 1, -4],\n [2, 3, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 1, -1, -6, -3],\n [-4, -5, 3, 4, 5],\n [4, -1, 2, -4, 5],\n [-2, 5, 3, -4, -6],\n [-4, -2, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 6, 1, 3, 1],\n [-3, -5, 0, 5, -5],\n [-1, -4, 3, 5, -3],\n [2, 5, 6, -1, -2],\n [6, 6, 6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 5, -1, -1, -3],\n [-5, -6, 1, -2, 1],\n [-1, 5, -1, 2, 0],\n [4, 3, -4, 6, 3],\n [-6, 4, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 3, -2, 1, 3],\n [1, -6, -5, 0, 2],\n [-6, 4, 5, 2, -1],\n [-3, 3, -1, 4, -4],\n [-5, 2, 6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 0, 6, 0, 2],\n [6, -5, 2, -5, -6],\n [-2, -4, 0, 2, -4],\n [4, 5, 4, -1, -1],\n [-5, -5, 5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, -4, 3, -5],\n [1, 6, 6, -3, 2],\n [-5, 1, 1, -3, 5],\n [3, 0, 3, 5, -2],\n [5, 4, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -6, -6, 0, 5],\n [5, 5, 4, -6, -2],\n [0, 6, 1, -4, 1],\n [5, 5, -2, -4, -2],\n [-6, -6, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -4, 3, -6, 1],\n [-6, 0, 0, -3, 3],\n [1, 0, -4, -3, 1],\n [6, -6, -1, 1, 2],\n [4, -2, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 5, 5, -3, 6],\n [1, 3, 3, -3, -4],\n [-6, 3, 4, 5, 0],\n [3, 5, -6, -2, 4],\n [-6, 6, 0, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, 6, 6, 4],\n [-6, 4, -3, -1, 4],\n [-4, -4, -1, -2, 4],\n [5, 0, -4, 0, 6],\n [-4, 2, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 3, -4, -2, 0],\n [5, -5, 6, 5, -1],\n [5, 1, -4, -1, 6],\n [-1, -2, -2, 4, 0],\n [-1, -1, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, 5, 5, -4],\n [4, 6, 4, -4, 3],\n [4, 1, 3, -4, -2],\n [6, -4, -1, -4, 5],\n [-5, -3, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 0, 5, -5, 1],\n [-1, 1, -4, -1, 3],\n [0, -6, -3, 6, 1],\n [2, 1, 5, 1, -1],\n [6, -5, -5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 2, 3, -5, 1],\n [-3, -4, 0, 4, -2],\n [4, 0, 1, -4, -3],\n [-4, -4, -4, 2, 1],\n [-3, 0, 4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, -2, -6, -5],\n [3, 0, -5, 6, 3],\n [3, -4, -2, 5, 3],\n [-2, -5, -1, -4, 6],\n [-6, -6, -2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, -1, -3, 0],\n [-4, 1, -3, 2, -1],\n [-2, 1, 4, 1, -6],\n [3, -6, 5, -3, -6],\n [6, -2, 1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -3, -1, -2, -5],\n [-1, -2, -6, -1, -2],\n [-1, -3, 1, 0, 0],\n [6, 5, 1, -4, 3],\n [6, 1, -1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -3, 5, 2, -5],\n [-1, 2, 5, 1, -4],\n [-3, 0, -2, 6, 4],\n [-4, 5, -1, 2, -4],\n [4, -2, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 1, -4, -1, 4],\n [-6, 6, -1, -4, -5],\n [-6, -3, 1, 1, -4],\n [-4, 3, -5, -2, -1],\n [0, -2, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 1, -6, -5, -4],\n [4, 5, 2, 4, -2],\n [-5, -1, 4, -4, 3],\n [4, 5, -3, -6, -1],\n [-5, 4, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -2, -5, 4, -1],\n [-1, -5, 0, -1, -5],\n [6, -3, -2, -5, -6],\n [-1, 5, -5, -5, -4],\n [-6, -5, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 0, 2, -3, -2],\n [-4, -3, -6, -3, 6],\n [-3, -1, 4, 5, 2],\n [3, 2, -5, 5, 4],\n [-1, 1, -5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 2, 2, -4, 2],\n [4, -5, 4, -5, -4],\n [-5, 1, 0, -4, 2],\n [0, 3, 6, 5, -3],\n [5, -5, -3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, 2, 6, -5],\n [5, -5, 0, 6, 4],\n [-1, -6, -1, 0, -4],\n [0, 2, 0, -1, 1],\n [6, -6, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -6, 2, -3, 0],\n [4, -5, -5, -3, -3],\n [4, 0, -4, 2, 2],\n [0, 6, -3, -2, -3],\n [5, 2, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -4, 0, 2, -5],\n [6, 5, 2, -1, -6],\n [-1, 1, -2, -3, -5],\n [0, -2, -5, -1, -5],\n [-6, -2, -5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 5, 4, -4, 2],\n [-6, 3, 0, -5, -5],\n [4, 0, 3, -6, -3],\n [-2, 5, 1, -3, -3],\n [-1, 5, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -6, 4, 5, -3],\n [-6, 5, -4, 1, -4],\n [6, 3, 3, 3, -1],\n [1, 2, 2, 5, 2],\n [-5, 5, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 1, 2, 1, -6],\n [1, 5, -2, -5, -4],\n [-4, -3, 6, -6, -5],\n [6, 1, 3, -1, 3],\n [-3, -3, -2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -2, -6, 1, 5],\n [-3, 0, 5, -1, -3],\n [4, 3, 3, -4, -5],\n [-4, 4, -1, -5, -4],\n [4, -4, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -6, -6, 0, 1],\n [5, -5, 6, -1, 0],\n [-3, -4, 3, 6, -1],\n [-2, -3, 0, 2, 2],\n [3, -5, 5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 3, -1, 6, -4],\n [0, -2, 0, 0, 4],\n [0, -2, -5, 4, 6],\n [-5, 1, 1, 0, -4],\n [-4, 5, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 0, 2, -6, -4],\n [4, 0, -1, 1, -2],\n [0, -1, 2, 4, 4],\n [5, -5, -2, 4, -6],\n [0, 6, 6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, -3, -2, -3],\n [-2, 4, 4, 3, -5],\n [-5, -6, 1, -3, 2],\n [-2, -5, 0, 4, -3],\n [4, 5, -6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, -1, 2, -6],\n [-3, 4, -6, 0, -3],\n [3, 1, -1, -3, 4],\n [-1, -6, -4, -6, 2],\n [-1, -5, 6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 5, -1, 0, 0],\n [0, 0, 3, 5, -1],\n [-3, 5, 2, 6, 2],\n [0, -1, -4, -6, -4],\n [3, -1, -2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -3, 3, 2, -1],\n [4, -6, -3, 5, -2],\n [-4, 4, -5, -6, 3],\n [-6, -2, 4, 6, 6],\n [-5, 3, 4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -5, 6, 4, -4],\n [-2, -2, -3, -4, 2],\n [2, 2, 5, 4, -5],\n [3, 1, 1, 0, 6],\n [2, 0, -3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, 0, -2, -1],\n [-4, 1, 0, 4, 1],\n [2, 6, 2, 2, -2],\n [4, 1, -3, 0, -5],\n [-3, -2, -2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -5, 0, -5, 6],\n [-3, -3, 1, 2, -1],\n [-1, 2, 2, -6, 3],\n [0, 6, 3, 1, 4],\n [-6, 3, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -5, 6, -5, -6],\n [1, -1, 0, -3, -5],\n [-6, -2, -6, -1, 4],\n [-1, 3, -1, 3, -6],\n [0, -4, -4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -5, -5, 6, -1],\n [-4, 2, 1, 6, 3],\n [1, -5, 1, -5, 0],\n [-1, -1, -4, -5, 4],\n [4, -5, -5, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, 5, 1, 3],\n [6, -6, -4, 5, 3],\n [-3, 4, -4, -2, 6],\n [-6, -1, -4, 3, -1],\n [0, -6, -4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -2, 2, -3, -3],\n [-1, 2, 6, -6, -5],\n [6, 5, -6, 5, -2],\n [-6, 1, 4, 6, 6],\n [-1, -2, -5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -2, 6, -4, -5],\n [-6, -1, 0, 1, -5],\n [-5, -4, -6, -5, -3],\n [-1, 6, 2, -6, 1],\n [2, 3, 5, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 6, -5, 2, -3],\n [-1, 2, 5, -6, -5],\n [5, 1, 2, 4, -1],\n [-5, -2, -5, 1, -5],\n [1, 1, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 2, 3, 0, 6],\n [-5, -1, -2, -1, -5],\n [2, 0, 1, 6, -4],\n [4, 6, 2, 0, -6],\n [5, -3, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 6, -2, -1, 0],\n [-2, 5, -3, -1, -5],\n [-5, 2, 1, -3, 2],\n [-5, -2, -3, 0, 3],\n [3, 2, -1, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 4, -5, 1, 1],\n [6, -5, 3, 6, -5],\n [-4, 5, 2, 2, -6],\n [3, 4, -6, 3, -6],\n [3, 4, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -1, -1, 6, 5],\n [-5, 4, -4, -3, 1],\n [5, -3, 1, -2, -1],\n [4, -1, 5, 2, -2],\n [-1, 0, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 2, 3, -1, 4],\n [-5, 0, 2, -5, 2],\n [6, -5, -1, -6, 6],\n [-4, -1, -5, 3, -6],\n [3, 4, 2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 1, -5, -1, 0],\n [1, -4, 0, 4, 2],\n [1, 5, 1, 3, -1],\n [6, 0, 2, -1, -5],\n [0, -6, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 1, 3, 5, -4],\n [1, -6, -2, 2, -1],\n [3, -2, -4, 0, 3],\n [-1, 6, -5, -5, -2],\n [-1, 6, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, 2, 2, 2],\n [-2, -3, 2, -1, -6],\n [-6, -4, 1, 6, -1],\n [2, -5, -2, 6, 6],\n [2, 0, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 5, -3, -5, -5],\n [-5, -3, -3, 1, -3],\n [-3, -4, -3, 5, 2],\n [2, 0, -4, 4, 2],\n [-6, -5, -2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 3, -2, 5, 0],\n [0, -1, -6, -3, -1],\n [2, -5, 4, 5, 2],\n [-1, 0, 4, -4, -1],\n [3, 0, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 1, 3, -6, -2],\n [0, 3, 5, -5, 2],\n [-6, 5, -2, 2, 4],\n [4, -1, -1, 5, 1],\n [3, 5, 1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -2, 6, 5, -1],\n [5, 4, 0, 3, 5],\n [1, 5, -1, 0, -6],\n [-2, 6, 3, -4, 1],\n [-6, -1, 3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -3, 4, -3, -4],\n [5, -5, -1, -6, -6],\n [-1, 3, -3, 3, 2],\n [6, 0, 6, -2, 1],\n [6, 4, 6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, 3, 6, 5],\n [-5, 1, 1, 4, 0],\n [-1, -1, 4, 5, 5],\n [6, -5, 5, 5, 4],\n [3, 2, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 4, 1, -3, -1],\n [-4, -6, 0, 1, -3],\n [-3, -3, -4, 3, 4],\n [5, -5, 6, 0, 0],\n [-5, 0, 0, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 3, -5, 4, 6],\n [0, 0, 2, 0, -4],\n [-4, -1, 2, -1, -4],\n [3, 6, 6, -6, -3],\n [4, 2, -4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, 1, 5, -1],\n [2, -4, 6, -2, -5],\n [-6, 0, -1, -3, 5],\n [-1, 2, -1, 5, 0],\n [1, -5, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -2, 5, 0, 6],\n [-4, 0, 5, 5, 3],\n [1, -6, -4, 0, -5],\n [3, 4, 2, -5, -4],\n [-3, 4, -3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 4, 4, -2, 1],\n [5, -1, 6, 2, 5],\n [-4, 3, 2, -2, 2],\n [2, 3, 6, -4, -5],\n [4, -6, -5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 1, -1, 0, -1],\n [4, 2, 0, 2, 3],\n [0, -5, 6, -5, 3],\n [6, 2, 0, 3, 2],\n [3, -5, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, 1, -6, -6],\n [-3, 6, 3, -5, 1],\n [-3, 3, 2, 6, 1],\n [-4, 0, -3, 6, -1],\n [-5, -6, 3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, 3, -1, -5],\n [0, -6, 2, 0, -4],\n [-5, -6, 3, 6, 6],\n [-1, 6, 4, -6, 3],\n [-2, -4, 3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 5, 6, 2, 6],\n [1, 3, 4, -5, -3],\n [-3, 6, 0, 3, -6],\n [-4, 5, 3, 4, -4],\n [0, 6, -6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -1, -5, 0, -1],\n [-4, 1, -4, -1, -1],\n [-3, -4, 5, 1, 5],\n [-4, 3, -4, 3, 3],\n [-3, 3, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 6, 4, 1, -1],\n [-4, 0, 0, -3, 3],\n [-1, -2, 0, -4, 3],\n [-2, -5, -5, -3, -4],\n [2, 4, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 1, 3, -3, -6],\n [1, -4, 6, -4, 6],\n [-5, -1, -1, 0, -5],\n [-4, 6, -6, -6, -1],\n [0, -1, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 4, 0, -2, 5],\n [6, -5, -6, 5, 6],\n [2, -5, 4, -2, -4],\n [-2, 6, 4, 1, 1],\n [-5, 0, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, 1, 4, -6],\n [6, 3, 1, -1, 1],\n [-6, -1, -6, 2, -1],\n [5, 0, -5, 3, -4],\n [1, -4, 3, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 0, 2, 5, 1],\n [-4, -2, -5, 1, 0],\n [4, -5, -5, 5, 2],\n [-1, 3, 4, 2, 1],\n [0, -4, -6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 3, 1, -3, 6],\n [0, 3, 4, -3, 2],\n [-1, -6, -2, 5, 2],\n [-4, -1, 6, 4, -3],\n [2, 6, -6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 0, 6, 4, -6],\n [-2, -3, 2, 5, 3],\n [2, -1, 1, 0, -3],\n [1, -4, -6, 5, -6],\n [0, 3, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 4, 2, 4, -4],\n [5, -3, -2, 5, 2],\n [-5, 3, 1, 4, 4],\n [-2, 2, -5, -4, -3],\n [5, -2, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 5, 1, -2, -5],\n [-2, 5, -1, -4, -6],\n [1, 0, 6, 6, 1],\n [-6, 2, 5, 1, 5],\n [2, 4, -3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 4, 6, 0, 4],\n [-5, 5, 5, 2, 0],\n [3, 1, -4, 0, -4],\n [4, -3, 2, 2, 4],\n [0, 1, 6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 6, -6, -5, -6],\n [-1, -2, -2, 6, 5],\n [-5, 1, 5, 0, -3],\n [-1, 3, 4, -2, -6],\n [-5, 6, 4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 4, 2, -5, 3],\n [0, -4, 5, 1, 5],\n [-3, 4, 2, 1, 0],\n [3, -3, 6, 0, -6],\n [0, -3, -3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 6, 1, -1, -3],\n [3, 5, -4, 6, 1],\n [-6, 2, 4, 1, -6],\n [4, 5, 4, -4, -6],\n [-5, -6, -3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, -4, 0, 6],\n [-3, 0, 5, 5, -4],\n [-2, 3, 4, -2, -1],\n [-6, -1, -6, 3, 3],\n [3, 0, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -2, -1, -5, -6],\n [1, 3, -5, -6, -2],\n [-1, -2, 4, -4, 3],\n [5, 2, -2, 5, 5],\n [-4, -2, -2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -2, -5, 3, -6],\n [5, -2, 4, 1, 3],\n [2, -5, -2, 2, -6],\n [1, -6, -3, -2, 6],\n [-2, 0, -6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 5, 5, 0, 2],\n [0, 2, 0, -6, 2],\n [-4, -5, -5, 3, -1],\n [3, -2, 3, 5, -1],\n [-4, 4, 4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -3, 6, 6, -1],\n [2, -4, -3, -3, 3],\n [0, 4, -5, -5, 3],\n [4, -2, 3, 2, 0],\n [0, 0, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -3, -3, -3, 0],\n [2, -3, 5, 5, -4],\n [-6, -5, -6, -1, -3],\n [-1, 3, 6, 0, -5],\n [6, 5, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, -1, 5, -3],\n [-1, -3, -2, 0, -2],\n [6, 5, -1, -1, 4],\n [4, 5, 4, 0, 5],\n [5, -6, 5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 4, -3, -3, -6],\n [-2, 3, -4, 4, 3],\n [4, 2, -3, 1, -3],\n [2, -6, 2, 0, -1],\n [-4, -5, -2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -3, -2, 3, 0],\n [3, 0, -1, 3, -5],\n [5, 4, -5, 6, -6],\n [1, -1, 4, 0, 1],\n [-2, -2, -2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -6, 2, 6, 1],\n [-4, 1, -1, -5, 6],\n [-4, -2, 1, -6, -5],\n [2, 2, 2, 2, 6],\n [1, -4, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 6, 3, 2, -6],\n [-5, -1, -4, -4, 5],\n [-2, 0, 5, 3, 1],\n [1, -3, -1, -6, -4],\n [4, -3, 0, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -2, -2, 5, 4],\n [-6, 4, 5, 6, 1],\n [1, 3, 0, 5, -1],\n [4, 4, 0, -6, 3],\n [4, 4, -6, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -3, -3, 2, 5],\n [5, -2, 3, 1, -3],\n [-5, 0, -6, 6, -2],\n [-6, 1, -3, 2, 0],\n [-4, 6, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -3, 6, -4, 0],\n [-1, 1, -2, 6, 5],\n [1, 6, -1, 2, 2],\n [-2, -5, 2, -1, 5],\n [5, 3, -5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -4, 5, -3, 1],\n [-6, 3, -6, -2, 6],\n [-6, -6, 3, 1, 2],\n [4, 0, 5, -1, -1],\n [-2, 6, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 1, 3, 2, 5],\n [-6, -2, -3, -6, 5],\n [-3, 0, -2, -6, 1],\n [-3, 6, 4, 6, -1],\n [2, 2, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 1, 3, -1, 4],\n [-6, 5, 4, -6, -4],\n [5, 2, 3, -2, -3],\n [1, -1, 2, -2, 6],\n [-1, -1, 4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -6, -3, 3, -6],\n [5, 4, 3, -4, -1],\n [-1, 6, 4, -3, 2],\n [-1, -2, 1, -1, -2],\n [1, -4, -6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 6, -1, -3, 6],\n [-2, -5, 4, 4, 0],\n [-2, -1, -4, -2, -2],\n [6, -3, 0, -2, 1],\n [-4, 6, 4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 0, 6, 5, -6],\n [5, -3, 2, 6, -1],\n [3, 3, -1, -3, 3],\n [3, -5, -4, -2, -6],\n [1, 3, 3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, 0, 3, 6],\n [5, 5, 1, -6, -2],\n [-4, 0, -6, -2, -4],\n [6, 1, -3, -4, 2],\n [6, 6, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 6, 3, -1, -4],\n [1, 2, 6, -5, 3],\n [4, -4, 3, 4, -2],\n [-3, 4, 4, -4, -2],\n [-1, 0, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 0, -2, 5, -5],\n [2, -6, 4, 1, 4],\n [-3, 1, -3, 1, -4],\n [-6, -1, -5, 1, -1],\n [2, -4, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 1, -3, 6, 1],\n [-3, -4, 0, 3, 4],\n [3, 4, -5, 3, 5],\n [-3, -3, -1, 1, 5],\n [5, -5, -6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -2, -3, 3, 1],\n [-1, -4, -1, 5, 4],\n [2, 1, -2, 5, -3],\n [-1, -2, 4, -3, 5],\n [-6, -5, -1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -4, 4, 5, -5],\n [-1, 1, -3, 5, 5],\n [-6, 2, 0, 5, 4],\n [3, -3, 5, -5, 5],\n [5, -1, 4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -3, -5, -2, 5],\n [4, 5, -5, 5, -5],\n [-1, 6, 1, -5, -6],\n [-6, 0, 4, 0, 3],\n [6, 5, 3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -4, -5, 2, -1],\n [4, 0, 6, -1, -5],\n [0, 4, 1, -4, -5],\n [3, -4, 1, 1, -3],\n [1, 5, -5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, 1, 3, -5],\n [-1, 0, -5, -1, -2],\n [0, 2, -4, 4, -5],\n [4, -4, 2, 0, 6],\n [-6, 6, -6, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -5, 5, 1, -5],\n [-1, 5, -1, 2, -4],\n [2, -2, 3, 3, -6],\n [3, -3, 5, 6, -5],\n [-4, 4, 5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 4, 3, 2, -4],\n [3, -3, 4, 1, 2],\n [-6, -6, 2, 5, 5],\n [-5, 1, -6, 2, -2],\n [-3, -4, 6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -2, 1, 1, 3],\n [6, 6, -5, 0, -3],\n [-5, 1, 0, -1, 0],\n [1, 5, 0, 0, -1],\n [4, -1, -2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -5, -3, -3, 0],\n [5, 6, -1, -4, 3],\n [6, -2, 5, 6, -5],\n [-1, 1, 3, -2, 6],\n [4, -6, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 4, 3, -4, 0],\n [-4, 1, 5, 6, 2],\n [6, -1, 5, 6, 2],\n [2, -5, 1, -3, 1],\n [0, -2, -1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 0, 5, -5, -4],\n [-4, -3, 2, -1, 3],\n [6, 0, 2, 2, -3],\n [4, -6, -5, 4, -3],\n [0, -3, 6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 5, -3, 5, -1],\n [2, 6, -6, -3, 0],\n [-1, 2, -6, 1, -4],\n [2, 6, -6, -4, -6],\n [-6, 4, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -1, -6, -2, -3],\n [-4, 2, 1, -2, 1],\n [3, 3, -1, -1, 2],\n [4, -5, 5, 4, -3],\n [-5, 1, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 5, 3, 3, 0],\n [-2, -4, 4, -6, 5],\n [0, 1, 6, 6, 6],\n [3, 0, 4, 3, 2],\n [-2, -2, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, 2, 2, -3],\n [0, -3, -2, -1, -6],\n [0, -4, -4, 1, 4],\n [-6, -1, -4, -2, 1],\n [-3, 5, 3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 0, 0, -5, -3],\n [6, -2, -1, 3, -4],\n [-1, 0, 0, 6, -3],\n [-2, 0, -5, 5, 2],\n [-4, 3, -5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, -4, -4, 0],\n [0, 2, -3, 2, 6],\n [1, -6, -3, -3, -4],\n [-5, -3, 3, 0, 6],\n [-2, -2, 3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, 6, -6, 5],\n [1, -3, 5, 4, -6],\n [6, 0, -5, 0, -5],\n [5, -4, 5, -3, 6],\n [-3, 5, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 0, -5, 3, 5],\n [-4, 0, 4, 1, -4],\n [-2, -1, 1, -5, 2],\n [-3, -2, 6, 1, -5],\n [-5, 0, -4, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, -3, -6, -1],\n [-5, 6, 5, 0, -2],\n [-5, -1, -2, 6, -4],\n [-5, 5, 5, -3, 3],\n [-3, 2, -4, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, 6, 2, -2],\n [0, -4, -5, 2, -3],\n [4, 1, 1, -2, -4],\n [4, 3, -2, -2, 6],\n [5, -5, 0, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -1, 4, 6, -6],\n [-5, -6, -3, -5, -4],\n [-5, 1, 4, -4, -5],\n [4, -1, -1, 1, 1],\n [1, -6, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 5, 6, -5, -4],\n [2, -5, -6, 0, 0],\n [-5, 0, -2, -2, 6],\n [-2, 5, 4, -4, 6],\n [3, 2, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -4, 0, -4, 5],\n [-2, 2, -2, 5, 5],\n [-3, 5, 6, -3, -4],\n [0, 5, 6, 3, 6],\n [-1, 2, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 1, -1, -2, 0],\n [4, 2, -3, 0, -2],\n [-1, 1, -2, -6, 2],\n [2, -3, 4, -1, -2],\n [-6, -2, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 5, -4, 6, 4],\n [-3, 6, 1, -6, -6],\n [-2, -5, 1, -4, 6],\n [4, -4, -3, -3, -3],\n [4, -5, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 5, -1, -1, 0],\n [-1, 0, -5, 0, 1],\n [2, -6, 3, 1, 4],\n [-3, 1, -6, -6, 6],\n [1, 6, 5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -5, -5, 4, -3],\n [0, 4, 0, -5, -1],\n [2, -1, -3, 1, 6],\n [-5, 0, -5, 3, 2],\n [6, -3, 2, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 6, 6, -3, 4],\n [6, 4, 6, -3, 6],\n [1, 6, 2, -6, 4],\n [6, -2, -2, -4, -6],\n [-6, -5, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -5, 1, 1, -6],\n [-3, -4, -3, -1, -1],\n [5, -6, 3, -5, 2],\n [2, -1, 5, -4, 5],\n [5, 1, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -4, -2, 6, 0],\n [6, 4, -6, 3, 2],\n [-4, 2, -3, -5, -5],\n [-2, 4, -6, 6, -5],\n [-6, -4, 2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 5, 6, 4, 4],\n [1, -5, -5, -1, 4],\n [2, -4, -2, -2, 1],\n [2, 6, -4, -3, 2],\n [2, 5, -5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 5, -3, -5, 3],\n [1, 0, 3, 4, -2],\n [-6, 4, 6, -1, 2],\n [-4, -2, 4, 1, 2],\n [6, 2, -5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 5, -5, 3, 0],\n [3, -3, 0, 6, 3],\n [6, 2, -5, -6, -6],\n [1, -3, 5, 1, -1],\n [-6, 2, -3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 3, 3, 2, 5],\n [6, 2, 3, 5, -3],\n [-6, -1, 5, 5, -2],\n [6, -4, 3, -2, -2],\n [-6, -6, -1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -6, 6, 6, 2],\n [-3, 4, 5, -3, -2],\n [-3, 1, 5, 3, -1],\n [0, 5, -6, -4, -4],\n [-3, 6, -3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 4, 3, -6, -5],\n [-5, 4, 6, 4, -2],\n [1, 1, -4, 4, -2],\n [6, -5, 2, -1, -6],\n [-3, 1, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -6, 2, -2, -4],\n [-6, 5, 0, -2, 6],\n [-2, -1, -6, 1, 0],\n [-6, 5, 2, -1, -1],\n [-6, -2, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, 1, -6, -2],\n [6, -1, 6, 2, -1],\n [4, 2, -3, -4, 4],\n [2, 6, 5, -6, 6],\n [0, -6, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -5, 4, 6, -2],\n [3, 6, -3, 4, -1],\n [-1, -5, 5, 0, -4],\n [-6, -5, -1, -1, 2],\n [2, 6, -2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -1, 1, -2, -5],\n [5, 3, 6, 4, -5],\n [0, -3, -4, 4, -4],\n [0, 1, 5, -1, -3],\n [-5, 4, 1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -4, -4, 5, -6],\n [-6, 3, -5, -4, 2],\n [6, -3, 3, 5, 5],\n [2, -6, -3, 0, 2],\n [-6, -4, 4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -5, 5, 1, -2],\n [-2, -3, -1, -6, -5],\n [-1, 5, -3, -6, 0],\n [-4, -5, 6, 3, 3],\n [-4, -4, 5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -5, 2, -3, -4],\n [-4, -4, -2, 2, 1],\n [-6, 0, -2, -5, 3],\n [-1, 2, 2, 6, 6],\n [-2, 6, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -5, 5, -1, 0],\n [1, 3, 1, -1, 6],\n [1, 6, 4, -5, -6],\n [5, -2, -5, -1, 1],\n [-3, 1, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -5, 4, 1, -6],\n [3, 1, 1, -4, -5],\n [-1, -5, 1, 3, -5],\n [0, 5, 0, -5, 0],\n [5, 3, -4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, -6, 0, 1],\n [1, 2, 1, -5, 6],\n [4, -5, 4, -5, -2],\n [2, -1, -4, 3, -2],\n [-4, -1, 3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 5, -6, -3, -6],\n [-1, 4, -4, -3, 2],\n [-1, -5, -3, 3, 2],\n [-5, -2, 0, 2, -5],\n [4, -5, -3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 3, 5, -3, -3],\n [3, -5, 5, -1, 1],\n [-5, 0, -6, -3, -5],\n [1, 5, 5, -4, -3],\n [0, -3, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 0, 4, -5, -1],\n [4, -4, 3, -5, -4],\n [6, 3, -4, -2, 1],\n [-1, 1, 2, 0, -4],\n [-3, -1, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -6, 4, -5, 6],\n [5, 1, 1, 6, -3],\n [0, -5, 1, 2, -3],\n [0, 6, 5, -1, 0],\n [6, 6, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 4, -4, -1, -4],\n [6, -6, -3, 3, 5],\n [-5, -6, 6, 5, 2],\n [-6, 0, -2, 5, 1],\n [4, -3, 1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, -1, -5, 0],\n [1, -3, -2, 0, -6],\n [0, 2, 5, 4, -4],\n [4, 0, 5, 2, 3],\n [-5, 6, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -4, 0, 0, 6],\n [4, -3, 2, 2, -3],\n [-3, 6, 4, 4, -3],\n [1, -5, 0, 5, 4],\n [5, 1, 5, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -1, -3, -3, 4],\n [-1, 6, -5, 4, -6],\n [0, 3, -1, -3, -2],\n [4, -6, -3, 1, 4],\n [-6, -5, -6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 0, 5, -2, -4],\n [0, 6, -4, -6, 1],\n [-5, -6, 3, -4, -2],\n [-5, 3, 5, -1, 0],\n [6, 0, 6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, -1, -4, 3],\n [3, -5, -3, 6, -6],\n [1, -5, 4, -4, 0],\n [-1, -6, -2, -3, -4],\n [1, -6, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -3, 5, -5, 0],\n [2, 5, -4, 5, 0],\n [-2, 0, 5, -2, 3],\n [4, 1, 3, 2, 3],\n [3, 6, 0, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -6, -4, 1, 1],\n [1, -3, 6, -3, 6],\n [-5, -6, 2, 4, 6],\n [5, -2, -5, 3, 4],\n [0, 3, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, -3, -5, -4],\n [-2, -2, 2, 2, 1],\n [-4, 5, 5, -3, -5],\n [1, 5, 1, 0, 0],\n [-3, -6, 3, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -3, 2, -6, -5],\n [3, -2, -6, -1, 6],\n [6, 2, 1, -5, 5],\n [0, 4, -2, -5, 4],\n [1, 3, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 3, -6, -5, 2],\n [3, 0, 2, 2, -1],\n [2, -6, 3, -2, -3],\n [0, 1, -4, 4, 3],\n [-3, -4, -5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 3, -3, 4, 0],\n [5, -5, 0, -5, -3],\n [-5, 5, 5, -4, -1],\n [-6, -6, -5, -1, -5],\n [-3, 2, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 3, -6, -2, 3],\n [-5, 2, -4, 4, 2],\n [6, 0, -2, -3, 2],\n [5, 2, 2, 0, -2],\n [4, -6, -3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 5, -2, -5, 3],\n [-2, 6, -6, -2, 2],\n [4, -1, 5, -6, 1],\n [3, 6, 3, -1, 2],\n [6, -5, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 0, 3, -3, -5],\n [-3, 4, -2, -3, 2],\n [5, 6, 5, 3, 3],\n [-6, 2, -4, -6, 4],\n [-1, -6, 4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -3, 2, -2, 1],\n [-2, 3, 0, -6, -1],\n [0, 5, -3, -6, 1],\n [1, 2, -6, 3, -6],\n [4, 4, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -5, 6, -6, 6],\n [-6, -4, 0, -1, 4],\n [0, -3, 6, 3, -2],\n [-6, 2, -5, 2, 0],\n [-4, 6, 5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -2, -5, 2, 4],\n [3, -6, 2, -2, 3],\n [3, 6, 5, -1, -3],\n [4, -2, 5, 3, -3],\n [5, 2, 2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, -6, 5, 4],\n [6, -3, 6, 2, 3],\n [-5, -3, 6, 2, -3],\n [-6, 0, -4, -3, -5],\n [-1, 5, -5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -5, -2, 5, 1],\n [-5, 5, 6, -4, 3],\n [2, -3, -6, -2, 3],\n [3, -4, -4, 3, 3],\n [0, -5, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 5, -5, -2, -1],\n [1, 6, -4, 4, 5],\n [4, -2, -5, 1, -6],\n [-2, 6, 5, 6, 4],\n [-6, -3, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, -6, 5, 0],\n [-2, 4, -6, -1, -3],\n [-1, 4, -1, -5, 3],\n [2, -4, -5, 1, 4],\n [6, -2, 5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -5, -4, 6, 5],\n [1, 2, -6, 3, -5],\n [1, 2, -3, 6, 0],\n [2, -3, -4, -1, -2],\n [2, -1, 1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, -4, 5, 4],\n [-5, 4, -4, -3, -4],\n [5, -4, 6, -3, -6],\n [-1, -5, -3, 5, 4],\n [3, -4, -3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -5, -1, 5, 5],\n [-1, -4, 2, 6, -2],\n [-3, -1, 2, 0, 0],\n [-1, 1, 6, -3, -1],\n [4, -3, -3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 1, 5, 1, 0],\n [-2, 5, 4, 5, -2],\n [-6, 2, 6, -1, -2],\n [-3, -6, -3, 6, 1],\n [-5, -6, 0, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 0, 0, -5, -3],\n [4, 5, 2, -1, -1],\n [1, 5, -1, -1, 5],\n [0, 2, -5, -3, 6],\n [3, 2, 0, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 5, 3, 5, -5],\n [2, 2, -1, -3, 5],\n [-2, -5, 4, 1, -2],\n [-1, -6, -4, 4, -5],\n [-5, -1, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 1, 3, -1, 5],\n [-6, 3, 1, 4, 5],\n [-3, 2, -6, -5, 5],\n [-1, -4, -4, -2, 4],\n [-2, -1, 0, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 2, -3, 2, 0],\n [-6, 0, -4, 1, -1],\n [3, -4, 4, 0, -3],\n [4, -6, 5, 3, -4],\n [-3, -6, 3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -5, 0, -5, 1],\n [2, -6, 3, -4, -4],\n [-5, -4, 5, 5, 6],\n [6, 0, 2, 2, 1],\n [-5, 3, 6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 2, -5, -3, -5],\n [-3, -2, 6, 6, -2],\n [2, -2, -2, 2, -1],\n [-1, 1, -6, 0, -2],\n [1, 6, 1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, 2, 3, -6],\n [-5, 3, -2, 4, -2],\n [3, -4, 2, -4, -5],\n [-3, -3, -3, 4, 4],\n [-2, 0, -5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -1, -6, 1, 0],\n [2, -1, -4, -1, -1],\n [-5, -4, 6, -3, 3],\n [-2, 4, 6, -5, 6],\n [2, -1, -5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 0, -1, 3, -4],\n [3, -5, -3, 0, 1],\n [2, -1, 1, 3, -6],\n [0, -2, -5, -2, -4],\n [-2, -5, -4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, -1, -3, -6],\n [-6, -6, 1, -3, 5],\n [0, 2, 2, -4, -6],\n [-5, -3, 2, -2, -6],\n [5, -3, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 0, 2, -1, 6],\n [3, 4, -4, -5, 6],\n [-2, -3, 6, 0, -6],\n [0, -4, 5, -2, 4],\n [-3, 4, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -4, -2, -5, 5],\n [3, 0, -1, 4, -4],\n [-6, 0, 6, 3, 1],\n [4, -4, 2, 0, 0],\n [5, -3, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 1, -3, 4, 0],\n [-1, 4, -1, 4, 0],\n [-3, 4, -5, -6, -2],\n [-1, 0, 3, 4, -3],\n [5, 6, 6, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 3, 3, 5, -4],\n [-4, -1, 5, -3, -6],\n [1, -5, 1, 4, -2],\n [-2, -1, 5, 3, 4],\n [-1, 4, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -6, 5, 1, -2],\n [6, 6, 4, 5, -1],\n [-1, -5, -3, -4, -3],\n [0, -3, 0, -5, -5],\n [-1, 6, -5, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -3, 6, 3, 4],\n [2, -4, -5, -1, 0],\n [-1, 3, -4, 2, -5],\n [-3, 4, -6, 1, -5],\n [-4, -1, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -4, 5, 5, 6],\n [-1, -4, -3, 6, -2],\n [4, 1, -4, -4, 3],\n [3, 1, 6, -6, -3],\n [-2, -2, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -5, -5, 4, 5],\n [-1, -2, 4, 5, 6],\n [0, -5, -2, -1, 4],\n [-2, -5, -2, 0, 2],\n [-5, 2, 1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -1, -5, -5, -4],\n [5, 4, -1, -6, 5],\n [6, 1, 6, 0, 4],\n [-1, 5, 5, 2, 4],\n [5, 3, 4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -2, -6, 3, -3],\n [3, -4, -3, -4, -4],\n [-3, 1, 0, -4, 2],\n [2, -4, 5, 1, 1],\n [-4, 1, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -6, 1, 3, 6],\n [-2, 0, -6, -2, -4],\n [4, 2, 0, 0, -1],\n [-4, 0, -6, 1, -1],\n [1, 3, -3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 2, 3, -4, -4],\n [-5, -4, 6, -2, 3],\n [6, 0, 6, -3, 2],\n [4, -4, 1, -1, 4],\n [-3, 1, -5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, 4, -3, -5],\n [5, 4, -3, -1, -6],\n [-5, 4, -2, 4, 5],\n [-5, -3, 2, -3, -1],\n [-6, 1, 1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 2, -4, 2, 6],\n [-3, -3, 2, 5, -6],\n [-3, -2, -2, -5, 5],\n [-4, 2, 3, 0, 2],\n [-1, 3, 3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, 6, 1, -6],\n [4, 0, -2, 3, -1],\n [2, 2, -3, 6, 4],\n [6, -5, -6, -6, -2],\n [4, 6, 3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 0, -2, 5, -1],\n [6, -5, 1, 6, -3],\n [2, -6, 3, 6, -5],\n [-4, 6, -1, 2, -3],\n [2, -4, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -6, -3, 2, 2],\n [4, 2, 0, -5, 5],\n [-5, 5, -3, -5, 1],\n [6, 2, -2, -3, -6],\n [-6, 5, -6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, -5, -6, 0],\n [-6, 4, 5, 0, -3],\n [-6, 0, 3, -5, -1],\n [6, -2, 2, 6, 1],\n [-6, -1, -1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, -5, 0, 5],\n [3, 3, 4, 2, 2],\n [2, -3, 0, 1, -5],\n [-1, -4, -3, 1, 0],\n [1, 6, 1, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 6, -1, -5, -3],\n [1, 6, 4, -2, 5],\n [1, 1, -5, -3, 6],\n [-2, 0, 1, 5, -3],\n [0, 1, 6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -2, 1, 1, 4],\n [-3, -1, -4, 2, 6],\n [4, 2, 0, 5, 1],\n [6, 4, 2, 0, 1],\n [4, 6, 6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 2, 0, -3, 2],\n [4, 6, 6, 6, -6],\n [5, -5, -3, 1, 2],\n [2, 1, 4, 5, 1],\n [4, -3, -1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -2, -2, -2, 2],\n [5, -4, -5, 4, -4],\n [-6, -4, 0, 0, -4],\n [-3, -4, -4, 1, 5],\n [1, -1, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -6, -2, -6, -6],\n [-6, 2, 6, -1, -4],\n [2, -4, -6, -3, -4],\n [1, 5, -3, 1, -3],\n [-4, 1, -6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 6, 6, 6, 2],\n [3, 4, 0, -4, -1],\n [-6, -5, -1, -2, -6],\n [2, 5, -1, 3, 1],\n [2, -4, 2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 6, 4, -4, -2],\n [6, -3, -3, -5, 2],\n [-4, 4, 0, 1, -3],\n [4, -6, -1, 2, 6],\n [2, -2, -3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 4, -2, -4, -5],\n [-3, 1, 6, 1, -1],\n [-4, 5, -2, 2, 5],\n [2, -2, 1, 2, -6],\n [6, 3, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, 6, -1, 6],\n [1, -3, -2, 2, -1],\n [4, 5, 0, 1, -3],\n [5, 1, 1, 1, 0],\n [-5, -6, 1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 3, 4, 6, -2],\n [6, -5, -5, -4, 6],\n [-6, 1, -2, -3, 4],\n [-2, -1, -2, -6, 0],\n [-3, 0, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -5, 2, -2, 0],\n [2, 3, -3, -4, 0],\n [5, 3, 5, -1, -6],\n [4, 3, -4, -6, 4],\n [6, 2, 2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -1, -1, 2, -5],\n [4, -4, -3, 2, -5],\n [-2, -5, 3, 2, -4],\n [-2, 6, -4, -5, 3],\n [1, 1, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 2, 0, 1, 2],\n [4, -2, -3, -4, -2],\n [-4, -3, -6, -5, -5],\n [-1, 6, 2, 2, -5],\n [5, -4, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, 4, 5, -2],\n [-6, -2, -6, -1, 2],\n [5, 5, -3, -6, 6],\n [-4, -5, 3, -3, 5],\n [-3, 3, 0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 5, 0, -4, 1],\n [4, 4, -1, -2, 5],\n [-3, 3, -6, -2, 3],\n [6, 3, 1, 1, 5],\n [-2, 3, -5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -1, -3, 2, 5],\n [-5, -2, 1, 5, -6],\n [-1, 1, 2, 0, -5],\n [-4, 6, 3, -6, 5],\n [-2, 1, 3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -5, -1, -6, -6],\n [6, 6, -2, 1, 5],\n [-4, 4, -4, -3, 6],\n [0, 0, 0, 2, 5],\n [4, 5, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, 5, 0, 3],\n [3, 5, 4, -3, -5],\n [4, 1, 6, -6, 0],\n [4, 1, -1, -1, -4],\n [1, -2, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -2, -6, 3, 2],\n [1, -2, -4, 5, 0],\n [-4, 3, 2, 2, -2],\n [3, -6, -6, -2, 1],\n [0, -4, -5, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 3, -6, 6, -2],\n [-1, 2, 2, -2, -5],\n [5, -3, -3, 0, 3],\n [2, 3, 4, 3, 2],\n [4, -2, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -4, 3, -4, 1],\n [-1, -1, 0, 2, -2],\n [-2, 5, -3, 4, 4],\n [6, -1, -1, -1, 3],\n [-6, 6, 4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -4, -3, -3, -5],\n [-3, -5, 5, -4, 5],\n [2, -3, -4, -2, 4],\n [-6, 0, 6, -3, 4],\n [0, 6, 0, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, -6, -6, 0],\n [5, -2, -4, 2, -3],\n [-6, 0, 5, 6, 6],\n [0, 0, -3, 5, -3],\n [-4, 4, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 4, -5, -4, 2],\n [2, -1, 0, 1, -3],\n [-1, -1, -3, 0, -4],\n [-3, -1, 0, 2, -6],\n [5, -3, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 2, 1, 6, -1],\n [5, -1, -3, -2, -2],\n [-4, 2, -5, 3, 2],\n [-6, 4, 6, -4, -5],\n [6, -6, -1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 1, 5, 6, -3],\n [-1, 1, -6, 6, 3],\n [0, 6, -1, 1, 3],\n [1, -5, -6, 6, -3],\n [2, -1, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 1, 4, -5, 5],\n [2, -6, 3, -3, -3],\n [1, -1, 4, 3, -5],\n [2, 4, 0, -4, -6],\n [-3, -3, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -3, -3, -4, 5],\n [6, -3, -3, -5, 5],\n [5, -3, -4, -5, 5],\n [0, -4, 5, 6, 6],\n [-5, -3, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 0, -2, 3, -2],\n [-1, 4, 0, -2, 4],\n [-5, 4, 6, -6, -2],\n [-4, 3, 4, -2, 3],\n [0, 4, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 2, 1, 5, 0],\n [6, -2, 4, 6, 5],\n [2, -6, 6, 1, -3],\n [1, 0, -4, -3, 3],\n [4, 1, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 5, 3, -5, -2],\n [5, -5, 1, -5, -6],\n [1, 4, -3, 0, 5],\n [-2, -1, 3, -5, 5],\n [3, -4, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 0, 2, -3, 6],\n [-2, 1, 0, -1, 5],\n [4, -1, 2, -2, 1],\n [1, 4, -2, 5, -3],\n [-4, -3, 5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 0, -1, -6, 0],\n [4, -2, -2, 6, -1],\n [6, -1, 0, -1, 4],\n [4, -6, 2, 1, 4],\n [-3, -6, 3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, -5, 6, 6],\n [2, 5, 0, -6, -1],\n [-6, 4, 5, -1, 6],\n [1, -2, 0, -4, -6],\n [4, 4, 4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -2, -1, -4, 0],\n [-2, -2, -3, 6, -2],\n [-1, -3, 3, -1, 2],\n [-1, -4, -3, 0, 2],\n [0, -1, -4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 1, 0, 5, -5],\n [1, -6, -6, 6, 2],\n [-4, 0, 1, -6, 4],\n [3, -6, -1, 6, -2],\n [4, -6, 6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -3, 5, 1, -2],\n [-1, 6, 0, -6, 5],\n [-3, 4, -5, -4, 5],\n [-4, 1, -2, 0, 2],\n [-2, -1, -1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -3, -1, -4, 4],\n [6, 1, -3, -6, 4],\n [-3, 3, -3, -4, 5],\n [-3, -1, 3, 6, 1],\n [1, -5, -6, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -6, 0, 4, 0],\n [-5, 0, -6, -4, 4],\n [4, -4, -5, -2, 3],\n [-6, -5, 4, 2, -6],\n [4, -2, -5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, -5, 4, 1],\n [-2, -2, 5, -2, -6],\n [0, 2, -4, 3, 1],\n [4, 4, -1, -5, -2],\n [2, -2, -5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 4, 5, 1, -6],\n [-4, 3, 2, 2, 4],\n [5, 5, 3, -5, -1],\n [1, -3, 4, 2, -1],\n [1, 0, -4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 3, -4, -6, -4],\n [2, -3, 3, 1, -4],\n [4, -5, -3, 3, -3],\n [0, -1, 4, 2, -2],\n [-1, 4, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 0, 6, -4, -3],\n [1, -5, 5, -6, 5],\n [5, 0, -1, -6, -2],\n [-4, -3, 2, 6, -2],\n [-6, -4, 5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -2, 5, 3, 0],\n [5, 2, -4, 4, -5],\n [-5, -2, -2, 0, 0],\n [-3, -2, 1, -1, -3],\n [4, 3, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -5, 0, -1, -6],\n [0, 5, 0, -5, -1],\n [-2, 4, -6, 6, -3],\n [-1, -5, -2, 3, -3],\n [-4, -3, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, -2, 4, -4],\n [-6, 2, 4, 3, 5],\n [-2, 4, 0, 3, -2],\n [-1, 6, -4, 3, -5],\n [-4, -1, -5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 5, -2, 2, 3],\n [6, -1, -4, 1, -5],\n [-2, 3, -2, 4, -1],\n [2, -3, -3, 5, -1],\n [-5, -3, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -4, -5, -1, -2],\n [5, 1, 0, -4, -2],\n [-6, -6, 0, -3, 5],\n [-1, 1, -2, 4, 6],\n [-3, 4, 3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -1, -4, -4, 5],\n [0, 6, 3, 5, 1],\n [-2, -6, -4, 3, 2],\n [5, 5, 2, 3, 4],\n [-2, -2, 5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, 1, 6, 4],\n [-5, -6, -6, 5, -6],\n [3, -2, 0, -1, -5],\n [4, -5, 6, 3, 0],\n [1, -4, -2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 2, -4, -2, -1],\n [5, 6, -6, 5, -4],\n [0, 0, -5, 5, -6],\n [6, 0, -4, -4, 0],\n [3, 6, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, 5, -1, 0],\n [6, -5, -4, 1, 3],\n [-4, 4, -5, -4, -2],\n [5, -5, 1, -3, 5],\n [1, 0, -2, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 1, -1, 3, -1],\n [2, 1, -3, 6, -5],\n [-1, 3, -2, -4, -3],\n [-4, -5, -3, -1, -4],\n [3, -2, -3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, -3, -6, -1],\n [4, 4, -1, 0, -1],\n [6, 3, -5, 3, 5],\n [0, -6, -6, -5, -5],\n [-2, 3, 5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 0, -3, -1, 0],\n [-4, -3, 5, 0, 1],\n [6, 5, 3, -2, -4],\n [1, 3, 3, 3, -1],\n [2, 5, -5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -2, 1, -4, 0],\n [1, 4, 6, -2, -5],\n [-4, 3, 2, 0, 1],\n [3, -5, -2, 0, 5],\n [-2, -3, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -1, -6, 3, -5],\n [4, 2, 1, 4, 3],\n [6, 5, 4, 0, 3],\n [-2, -5, 2, 6, -5],\n [2, -4, -4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 1, 3, 6, -4],\n [5, 1, -5, 4, 2],\n [-3, 5, 4, 5, -2],\n [4, -3, 6, -1, -6],\n [0, 5, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 4, -3, 6],\n [-6, -6, -1, -1, 1],\n [-2, 5, 2, -3, -5],\n [5, -2, -3, 0, 6],\n [6, 3, -4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -5, 1, 5, -3],\n [-4, 3, -6, -2, -5],\n [5, -6, -2, 0, -1],\n [-5, 6, 0, -2, 1],\n [4, 1, -6, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -2, -2, 5, -6],\n [-4, -1, 4, 0, 3],\n [-2, 0, 5, 2, -5],\n [-3, -5, -1, 5, -1],\n [3, 0, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 1, 2, -2, -5],\n [-5, 4, -6, -4, -6],\n [-6, 5, 4, -3, -2],\n [0, 1, 6, 3, -4],\n [0, -2, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, 5, 1, -6],\n [-2, -2, -3, 1, -2],\n [-4, -3, 1, 0, 1],\n [1, 4, -2, 2, 4],\n [1, -5, -3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -1, 5, 6, -4],\n [6, 1, -6, -3, -6],\n [2, 2, -1, -4, -2],\n [-6, -6, 4, 6, -2],\n [-3, 3, -3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 3, 5, -4, -6],\n [-1, 0, -5, 1, 3],\n [-3, 3, -6, 4, 2],\n [6, 5, 5, 1, 5],\n [-6, 3, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 1, 0, 3, -1],\n [5, -1, 2, 5, 3],\n [-2, -6, 4, 1, -3],\n [2, -3, -5, 6, 2],\n [3, -5, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, -4, 5, -2],\n [-2, 6, -4, -5, 5],\n [6, 0, 2, -6, 0],\n [-6, 5, 5, -4, -4],\n [-4, 6, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 5, 2, 6, 5],\n [1, -6, 3, -4, -1],\n [-6, 6, -5, -6, -4],\n [-5, -5, -6, 0, 6],\n [-3, -4, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -4, -5, 5, 6],\n [-2, 3, 6, -4, 3],\n [2, -2, -3, -5, -1],\n [3, -4, -2, -6, 5],\n [-2, 0, 5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 0, -4, 5, 5],\n [1, -4, -3, -2, 2],\n [-3, 3, 1, -6, 3],\n [4, -2, -6, -4, 4],\n [-5, 6, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 0, 1, 6, -2],\n [6, 5, 2, 6, -1],\n [-3, 6, 4, -5, -4],\n [1, -2, -2, -5, -5],\n [2, 2, -4, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 3, -6, -2, -6],\n [-2, -4, -2, 6, -6],\n [-6, -4, -5, -4, 4],\n [-1, -1, 3, -5, 1],\n [4, 4, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -1, -5, 1, -6],\n [-3, 5, -2, 2, 2],\n [-6, -4, 5, 6, 2],\n [5, 4, -5, 5, 2],\n [-2, 6, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 0, -6, -3, -1],\n [4, 6, -3, 0, 0],\n [-3, 3, -1, 5, -3],\n [-5, -4, -5, -1, -5],\n [5, -1, 1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 5, -4, 4, 5],\n [4, 0, 2, -5, 4],\n [4, 5, 4, 3, 5],\n [-1, 0, -4, 3, -3],\n [-3, -2, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 4, 0, 2, 0],\n [3, 1, 2, -5, -5],\n [2, -3, -3, -2, -5],\n [6, -6, -2, 6, 0],\n [4, 4, -2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -3, 3, -5, -1],\n [-3, -5, -6, 4, -5],\n [-3, -4, 0, -4, -6],\n [-2, -2, -5, -2, -5],\n [-2, 3, -2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -6, -6, 3, -6],\n [0, 4, -2, -6, -3],\n [1, -3, 1, -3, -3],\n [5, -1, 3, 6, -5],\n [-5, 3, -5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -1, -1, -1, 5],\n [6, -6, 2, -6, 3],\n [4, 4, 0, 6, 0],\n [4, 6, 2, -6, 5],\n [-6, -4, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -3, 1, 4, -4],\n [3, -6, -1, 0, 4],\n [-6, 1, -5, -3, 3],\n [-3, 0, 6, -1, 6],\n [-5, 1, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -6, 3, -2, -4],\n [1, -4, -4, -3, -2],\n [-2, 2, -3, -3, -2],\n [4, 3, -4, -6, -2],\n [-1, 4, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 4, 4, 4, 4],\n [-3, -2, 5, -3, 6],\n [-5, -5, 6, 3, -1],\n [3, -3, -4, -6, -2],\n [-1, -6, 0, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -1, 6, -2, 5],\n [0, -5, -5, 3, -4],\n [0, 1, 0, 3, 4],\n [4, -3, 4, 4, -2],\n [1, 0, -3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -5, -2, 2, 6],\n [3, -5, 1, 3, 0],\n [-5, -1, 3, -2, 4],\n [6, 1, -5, 3, -2],\n [3, 4, 3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 0, 6, -4, -1],\n [-3, -6, -4, -2, 2],\n [2, 3, -2, -6, -5],\n [3, 3, 1, -1, -2],\n [0, -4, 6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -6, -2, 3, 1],\n [5, 0, -3, -2, -2],\n [0, 0, -5, -2, 0],\n [-4, -3, 4, 2, -1],\n [3, -3, -3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -4, 2, 4, -2],\n [6, 1, 5, 6, 3],\n [5, -2, -3, -5, 1],\n [6, 4, 6, -5, 4],\n [-4, 1, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 4, 5, -4, -5],\n [4, -2, -5, 3, -2],\n [3, 0, -2, 1, -5],\n [-2, -6, 0, -4, -5],\n [4, 2, 2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 5, -1, -4, -5],\n [-6, 3, 4, -4, 2],\n [-5, -4, -2, 6, -1],\n [5, -3, 6, 4, 5],\n [4, 5, 3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 5, -3, 1, -1],\n [-4, -5, -5, -2, -2],\n [6, -3, -4, 6, 4],\n [3, 0, 1, 5, -3],\n [0, -1, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -5, 5, -3, 3],\n [-1, 5, 5, 2, -5],\n [5, -4, -1, 0, 3],\n [2, -6, 3, 0, 1],\n [3, 2, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, 2, -4, -6],\n [-3, -5, -6, -5, -2],\n [0, -3, 5, -5, 0],\n [-3, 2, -4, 6, 2],\n [-5, -6, -1, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 5, -3, -3, 0],\n [-5, -1, 4, 5, -1],\n [1, -3, 5, -1, 0],\n [-3, 6, -6, 5, 2],\n [4, 0, 2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -4, -2, -1, -6],\n [1, 4, 4, -5, -3],\n [0, -3, -1, -2, 3],\n [-1, -6, 0, -6, 3],\n [-1, -6, 4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 3, -6, -6, -3],\n [-6, 6, 4, 0, -6],\n [4, 5, 3, 6, 0],\n [1, -3, 0, 1, 1],\n [6, -2, 6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, 4, -4, 5],\n [1, 2, -1, 5, 3],\n [-6, -4, 2, -2, 1],\n [-1, 0, 6, -2, -1],\n [6, 0, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 2, 1, -1, 6],\n [2, 3, -2, 4, 6],\n [-5, -5, -2, 6, -1],\n [0, 5, 2, 3, -1],\n [-6, 2, -1, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -1, 5, -5, -2],\n [6, -6, -1, -2, 3],\n [-6, 2, -1, -1, -1],\n [-6, -6, 0, 3, 1],\n [-5, -2, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 4, -4, -4, 6],\n [-3, -1, 2, 6, -5],\n [-1, 0, 0, -2, -2],\n [-1, -1, 2, 0, -3],\n [5, 3, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 5, -1, -4, 1],\n [4, -5, -1, 3, -3],\n [5, -6, -4, 4, 4],\n [6, 1, -5, 3, 4],\n [-1, -6, 0, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 1, -4, -3, 0],\n [3, -2, -6, 0, 2],\n [5, 5, 6, 2, -3],\n [-6, 2, 6, -3, -5],\n [0, -4, 0, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -6, 3, -2, 0],\n [3, 5, 5, 2, 3],\n [0, -1, 5, 4, 5],\n [5, -6, 6, 5, -6],\n [5, -4, 5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -2, -2, -6, 5],\n [-1, 2, 5, -6, -1],\n [4, 5, -2, 0, -5],\n [4, 3, -2, -6, 3],\n [-1, -3, -5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 4, -1, 4, 6],\n [2, 6, 0, -2, 5],\n [-2, 6, 6, -4, 6],\n [-2, -1, 6, -1, 0],\n [6, 4, -4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -5, 1, -4, -5],\n [-4, -6, -5, 2, 6],\n [-6, -1, 5, -3, 5],\n [2, -4, 1, -3, -5],\n [0, 6, 1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, 2, -2, -2],\n [5, -4, -5, 1, -3],\n [-2, 0, 5, -4, -3],\n [3, -2, 3, -1, 2],\n [6, 6, -6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 5, -2, 4, 0],\n [4, 3, 5, -1, -1],\n [0, 5, 5, 0, 4],\n [5, 5, 3, 1, 4],\n [5, -5, -5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 1, 6, 2, -3],\n [-1, 3, 1, -5, 5],\n [3, -4, 0, 0, 6],\n [0, 2, -4, -3, 5],\n [4, -5, 2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 1, -4, 3, -1],\n [-5, 4, 4, -5, -1],\n [-4, -6, 5, 2, -4],\n [-4, -5, -5, 1, 2],\n [3, -6, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -3, 0, -2, -4],\n [1, 5, -3, 3, 6],\n [-3, 0, -5, 1, 6],\n [4, 2, -6, -5, -1],\n [0, -2, 5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, 5, -4, 6],\n [0, -2, -2, 2, -6],\n [2, 3, -5, -6, -6],\n [4, 6, -5, -6, -1],\n [6, 6, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 4, 4, 0, 3],\n [-2, -3, 6, 1, 3],\n [-5, -5, -4, 2, 5],\n [-6, -5, 1, 3, 0],\n [5, 3, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 3, 6, 3, 6],\n [-4, -4, 6, 4, 4],\n [2, -6, 3, -5, 3],\n [3, -5, -2, -4, 0],\n [-1, 0, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 6, -1, -1, -4],\n [-3, -1, 5, -1, -2],\n [3, -6, 4, 1, -3],\n [3, 4, 5, 2, 3],\n [6, 0, 1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -5, 6, 2, -5],\n [5, 2, 5, 2, 0],\n [-4, -2, -1, -5, 2],\n [2, -3, -4, 2, 1],\n [-6, 5, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -6, 6, -4, -2],\n [-5, 5, -5, 6, 1],\n [0, 6, 0, 6, -6],\n [1, -6, 4, 6, 0],\n [6, -6, 5, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 6, 6, -3, -2],\n [-3, -3, -2, 0, 3],\n [2, 6, 5, 1, -6],\n [2, 6, -2, 3, 4],\n [-5, 5, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 3, -3, -1, -3],\n [2, 1, -5, -3, 2],\n [2, -4, 1, 0, 5],\n [5, 5, 5, 1, 3],\n [-1, -5, -4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, -1, 4, -1],\n [1, 1, 3, 2, -3],\n [-2, 0, 4, -5, -6],\n [-4, 5, -5, -6, -4],\n [1, -6, -2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 6, -5, -5, -3],\n [3, -2, 4, -2, -1],\n [0, 2, 0, -3, -4],\n [-3, -2, 1, 2, 1],\n [3, -6, 3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 6, 4, 3, 5],\n [-3, -2, -5, -4, -6],\n [-3, 2, -1, 5, -2],\n [2, 4, 2, -3, 0],\n [-2, 5, 1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 1, 0, 1, 6],\n [3, -6, -4, 0, -1],\n [3, 2, -1, 6, -2],\n [-3, 5, -3, -5, -5],\n [5, 4, -2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, -6, -2, -6],\n [-3, 3, -1, 5, 6],\n [2, 4, -3, -6, 2],\n [6, -3, -3, 5, -4],\n [-5, 2, -3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -6, 4, -2, 2],\n [-6, 4, 0, 0, 1],\n [-2, 4, -1, 6, 0],\n [-1, -4, 1, 6, -1],\n [-3, -1, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -3, 0, -3, -2],\n [6, -3, -2, -5, -6],\n [3, -4, 2, 2, -3],\n [-4, -3, 4, 3, -6],\n [3, -6, -6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, 6, -5, -4],\n [0, 6, 4, 6, -5],\n [4, -6, 6, 3, -4],\n [4, 6, 2, 3, -5],\n [-3, 0, -3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 5, 2, -5, 5],\n [-1, 6, -5, -6, 0],\n [1, -2, 0, -4, 3],\n [2, -4, -1, -3, 3],\n [-2, -6, -4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 4, 0, 5, -5],\n [3, 2, -3, 5, -5],\n [-6, 3, -6, -6, 1],\n [-6, -2, -6, -1, -2],\n [-2, 4, 6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, -4, -3, 3],\n [1, 3, -3, 4, 5],\n [4, -4, 1, 5, 6],\n [2, 6, 2, -3, -3],\n [3, -3, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, -3, -1, -2],\n [1, 1, -1, 4, -2],\n [4, -6, 3, 2, 6],\n [0, -4, 4, -6, 0],\n [-1, -2, -6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 5, -4, -2, -2],\n [-2, 6, 3, 2, -2],\n [-6, 2, 3, 2, -6],\n [-5, 3, 1, 2, 5],\n [1, 5, 2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, -5, -1, -2],\n [-1, -5, 2, -5, -1],\n [-4, 4, 2, 3, 4],\n [1, 6, 4, -5, 6],\n [-5, 5, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 1, -4, 3, -2],\n [4, 2, 1, 0, 5],\n [6, 3, 5, -5, 2],\n [6, -4, 1, 4, 5],\n [-1, -2, 6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 0, -2, 0, 5],\n [6, 2, -5, -3, -3],\n [-1, 3, -1, -1, 3],\n [-5, 1, -3, 2, 1],\n [2, 2, 6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 3, 2, 0, -1],\n [2, 2, 6, -6, 2],\n [-2, 3, -3, -2, -2],\n [-4, 2, 1, -3, 1],\n [-1, -1, 6, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 5, 2, 4, 5],\n [4, -5, 2, -5, -6],\n [6, 4, -6, -6, -2],\n [-2, -5, 0, 0, -1],\n [5, -2, 3, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -6, -3, -6, 6],\n [4, 5, -3, -5, -4],\n [-3, -3, 6, -6, -3],\n [-2, -1, 3, 4, -3],\n [-3, -2, -2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -4, 0, -6, -2],\n [-3, 4, 5, 1, -1],\n [-1, -1, 2, -5, -2],\n [-5, -5, 2, 5, -5],\n [-5, -5, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 4, -6, -1, -6],\n [4, 1, 1, 6, -4],\n [4, -5, 4, -5, 3],\n [-5, -6, 3, 1, 0],\n [2, 2, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 5, -3, 0, 5],\n [-1, -3, 5, -3, -6],\n [-5, -5, 6, -5, -4],\n [-1, 5, -2, 4, -5],\n [-4, 2, -6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, 4, -6, 1],\n [-3, -2, -4, -6, -4],\n [-5, 0, -4, 4, 5],\n [-3, -1, 6, 2, -1],\n [3, 1, -6, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 5, 5, -2, 6],\n [6, 0, 2, 6, 3],\n [-1, 3, -1, -3, 2],\n [4, 3, -2, -5, 0],\n [5, 3, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -3, -6, -6, -3],\n [-1, -3, 6, -6, -3],\n [-1, 5, 6, -6, 3],\n [6, 5, 2, 0, 6],\n [1, 6, 3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 5, 1, -2, 0],\n [-5, 4, 1, 5, 1],\n [-6, -2, 2, 2, 6],\n [1, 6, 6, 0, 3],\n [3, 3, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 5, -1, 2, 2],\n [-4, -2, 0, -3, -2],\n [-5, 3, 3, -3, -4],\n [-4, 0, 2, 6, 0],\n [-1, -2, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -3, 2, -3, -3],\n [-6, 1, -4, 4, 0],\n [-5, 0, -5, -6, 0],\n [0, 4, -4, -2, -2],\n [-2, 1, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 6, 2, 3, -6],\n [2, -3, 1, 2, 5],\n [5, 6, 3, -1, 0],\n [-1, -4, -4, 4, 6],\n [6, -5, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -4, 1, -2, -6],\n [5, -4, -2, 2, -6],\n [-1, 1, 6, 2, 4],\n [-5, 3, -5, 0, 3],\n [1, -6, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, 1, 2, 3],\n [4, 1, 4, 4, 1],\n [5, -2, 5, -5, -2],\n [0, -1, -5, 4, 3],\n [4, -3, -3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, 5, 6, -5],\n [-6, -4, 6, 5, -3],\n [1, 0, -3, -6, -3],\n [-2, -1, -6, 0, -2],\n [4, 1, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 5, 0, -4, 5],\n [-1, -6, 1, 6, -3],\n [-3, -5, 2, 4, -1],\n [4, 1, 4, 4, 6],\n [-1, -1, 0, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 2, 0, 5, 2],\n [-1, 2, -5, 3, -1],\n [-3, 0, -1, 6, -4],\n [3, 6, -5, -3, 2],\n [5, -2, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -1, 2, -5, 4],\n [2, 0, -4, 5, -3],\n [-5, 5, 3, -5, -6],\n [4, -5, -1, -1, 2],\n [-5, 0, 0, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -1, 6, 0, -6],\n [2, -5, 2, 6, -3],\n [6, -1, -2, 1, -2],\n [0, 1, 2, -4, 6],\n [2, -4, -3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, -1, 5, 4],\n [2, -5, -6, 5, -4],\n [-4, 0, -5, -3, 5],\n [2, 1, -1, 1, -2],\n [-2, -5, -5, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -6, 3, 0, 0],\n [-5, 0, 3, 5, -5],\n [-2, 1, 3, -6, -6],\n [-2, 2, 6, -5, -1],\n [4, -5, 5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -5, 2, -6, 0],\n [5, -6, 5, 5, -2],\n [1, 3, 0, -5, -6],\n [2, 3, 4, -3, 0],\n [4, -2, -6, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 0, -4, -4, 4],\n [2, 1, 1, 3, 0],\n [5, -2, 3, 5, 4],\n [-2, -2, 6, 3, 6],\n [-1, -3, 6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 5, 0, 3, 2],\n [-2, 4, 0, 1, -2],\n [-3, 2, 0, -1, 5],\n [-6, -5, 3, 2, -3],\n [-3, -4, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -1, -4, -4, -6],\n [3, 4, -2, 3, -5],\n [-6, -1, -4, 5, -4],\n [5, -2, 3, 6, 3],\n [-4, -2, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 3, 3, -4, 4],\n [-4, 2, 6, -6, -3],\n [-3, -5, -6, 4, -2],\n [2, 2, 1, 5, -6],\n [-1, -5, -2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 6, -4, 0, -2],\n [-2, -3, 0, -6, -5],\n [-3, -4, -5, -5, -6],\n [3, 0, 5, 4, -3],\n [0, 0, 5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, 0, -3, 4],\n [-6, 4, 4, -1, -1],\n [3, 0, 1, 2, 1],\n [-1, -6, -2, -4, 4],\n [-6, 3, -1, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -5, 0, -5, 5],\n [-6, 5, -6, 0, 2],\n [1, -4, -2, 1, -2],\n [-4, 1, 1, 2, -4],\n [4, 3, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -4, -6, 1, 0],\n [-1, 6, 2, -5, -2],\n [6, 5, 4, -6, -6],\n [-6, 4, 0, 1, -3],\n [-3, 4, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -1, 5, -2, -1],\n [2, -4, -4, -1, 0],\n [3, -5, -4, -1, 1],\n [-6, -3, 6, -1, -5],\n [2, -2, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -4, -5, 0, 4],\n [-4, 2, 5, 4, 3],\n [-4, 5, 2, 5, -4],\n [-5, 0, 1, 2, -1],\n [5, -1, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, 4, 6, 3],\n [-5, 2, -3, 5, -5],\n [4, -4, -4, 4, -2],\n [-5, -5, -4, 5, 0],\n [0, -6, 4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 1, 5, -1, -6],\n [-1, -4, -2, -4, 6],\n [-4, -3, 2, 6, 2],\n [4, 0, -6, -1, -5],\n [1, 4, 4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -6, 3, -6, 1],\n [-5, 0, -2, 1, 5],\n [-5, -6, -4, -5, 5],\n [3, 0, -4, 5, -1],\n [2, -5, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -4, -4, -6, -6],\n [-4, 0, -6, 1, 5],\n [-1, 2, -6, 6, -3],\n [-1, 6, 1, -5, -2],\n [6, 1, 4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, -1, -5, 0],\n [-4, -4, 2, -2, -2],\n [4, 3, -1, 1, 3],\n [4, -1, -5, -5, -3],\n [6, 5, 1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 4, 4, -4, 0],\n [0, -1, -6, 6, 2],\n [1, -5, 0, -4, 1],\n [-3, 5, 3, 3, 6],\n [2, 3, -5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 0, 4, -6, 1],\n [-5, -3, 3, -3, 2],\n [2, -1, -1, 1, -1],\n [6, -6, -2, -3, -3],\n [-5, -3, -6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 4, 2, 4, 1],\n [4, -1, -3, 5, 2],\n [-6, 4, 4, -2, 2],\n [6, 6, -3, 6, 2],\n [-6, -6, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 5, -6, -6, 4],\n [-2, -4, -5, 0, 4],\n [3, 5, -6, 6, -2],\n [5, 1, 4, -4, 5],\n [-5, 6, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 0, 6, -1, -4],\n [-2, -2, 1, -5, 5],\n [3, 5, 6, 0, 1],\n [2, -2, 1, 0, -6],\n [3, 0, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 3, -1, -1, 3],\n [-1, 0, 1, -3, 1],\n [4, 2, 5, -3, 0],\n [5, 3, 5, 0, -3],\n [1, -3, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, 4, 4, 2],\n [4, 6, -1, 4, 0],\n [-2, 2, -3, 5, -6],\n [0, 3, -1, 3, 6],\n [-2, -3, -6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 0, -5, 5, -5],\n [4, -1, 5, -2, 4],\n [-6, 6, 4, 0, 3],\n [-4, 5, 1, 0, -4],\n [6, 4, 0, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 2, 1, -6, -6],\n [6, -1, 4, -2, -3],\n [1, -2, 2, -2, -6],\n [3, 2, -6, 3, 5],\n [-4, -3, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, 6, 4, 5],\n [4, 4, 1, -1, -6],\n [-4, -4, 0, -1, -2],\n [6, 4, 0, 2, -2],\n [-1, 1, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 2, 4, -3, -4],\n [-5, 6, -2, -1, -1],\n [-4, -3, -3, 1, -3],\n [-3, -6, 2, 5, -1],\n [4, 4, -6, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, 3, 6, -5],\n [-3, 4, 2, 6, -6],\n [-5, 2, -2, 0, -3],\n [-1, 0, 1, -5, -1],\n [1, 1, 6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 2, 1, -4, 0],\n [0, -4, 2, 3, 0],\n [0, 6, -4, -5, 0],\n [5, 6, 2, 2, 2],\n [-1, 6, 3, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 5, 4, 0, 6],\n [3, 1, 0, -1, 1],\n [-1, -6, 4, -4, 5],\n [5, -2, -2, -5, 6],\n [-4, 5, 1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 1, 2, 4, -5],\n [0, -3, 2, -3, -6],\n [2, -6, -5, -2, 3],\n [-4, -2, -1, 0, 5],\n [-3, -6, 4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, 6, 3, 2],\n [3, -3, 2, -5, 4],\n [5, -3, 4, 2, -5],\n [1, 2, 2, -1, 3],\n [3, -3, 6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 0, -5, -3, 1],\n [0, 4, 6, -4, 3],\n [2, 5, -3, 0, -1],\n [-3, -2, 5, -1, -2],\n [-6, 0, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -4, 2, 4, 0],\n [2, -2, 0, -1, -6],\n [-2, 2, 4, 2, 2],\n [-4, -1, 1, -3, -5],\n [-4, 5, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -1, 2, -3, 4],\n [-1, -5, -1, 1, -3],\n [1, 4, 3, 6, -3],\n [3, -1, -6, 5, -6],\n [5, 1, 6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 4, 2, -1, -3],\n [4, -3, -2, 1, 0],\n [1, -4, -6, 0, -5],\n [4, 4, -3, 2, 4],\n [1, 4, 6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, -1, -1, 2],\n [0, 1, 4, -5, 4],\n [-6, -1, 5, -6, 5],\n [-5, -5, 6, -2, -6],\n [6, 2, 6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 1, 5, 3, -5],\n [6, 1, 6, 4, 1],\n [4, -3, 5, -6, 0],\n [6, 0, 5, 4, 1],\n [-5, 3, 4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 2, 1, -4, 3],\n [-4, 1, -5, 4, 3],\n [3, -3, 5, 6, 6],\n [-3, 4, 0, -2, 1],\n [2, -1, 0, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 6, 3, -4, -1],\n [2, 1, 5, 2, -6],\n [4, -1, 3, -5, 0],\n [-5, -5, 2, -6, 3],\n [1, -5, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 3, 4, -4, -5],\n [4, -1, 0, 6, 5],\n [-1, -3, -3, 3, 0],\n [-3, 6, 2, -4, 4],\n [5, -1, -6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -2, 4, 3, 2],\n [2, -6, -4, 0, 4],\n [0, -1, 4, -5, -4],\n [6, 1, 0, 2, 4],\n [-4, 6, 1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -4, 1, -3, 0],\n [3, -3, -2, -1, -2],\n [-4, 6, -3, 4, -5],\n [5, -2, 4, -3, 1],\n [2, 2, 6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -2, -4, 5, 3],\n [-3, 4, -2, 1, 6],\n [3, -4, 1, 4, 1],\n [0, 0, 0, -2, 4],\n [-6, 5, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -4, 5, 2, -1],\n [-6, -6, -3, 1, 0],\n [3, 5, 5, -3, 0],\n [6, 6, 0, 3, 1],\n [1, -3, -3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 0, -6, 0, -3],\n [2, 1, 3, 2, 6],\n [-5, -2, -1, 0, -3],\n [-4, -2, -1, 1, -6],\n [4, 5, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 2, -2, 5, 5],\n [-5, 3, -6, 0, -4],\n [5, -4, 4, -6, 6],\n [3, 1, -6, 3, 1],\n [0, 1, 5, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -3, 2, 4, -6],\n [-5, -1, -3, 2, 3],\n [6, 3, 4, 6, 4],\n [-3, 1, 1, -2, 6],\n [-6, 1, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 3, -2, 6, 3],\n [0, 5, 0, 5, 0],\n [-6, -4, -3, -2, 0],\n [-1, -1, 3, -4, -3],\n [-3, 6, 5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, 3, 4, -6],\n [-1, 2, -5, -5, 3],\n [0, 5, -5, -2, 5],\n [3, -4, 0, 4, 0],\n [-2, -4, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -4, 6, -5, 3],\n [-2, 2, -6, 5, 1],\n [-2, -3, 6, -4, -6],\n [4, 6, 1, -2, 1],\n [0, -3, 3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -5, 6, -6, -1],\n [-6, -4, 0, -5, 5],\n [-3, 6, -1, 4, 6],\n [5, -4, 0, -1, -5],\n [-5, 5, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 0, 1, -5, -2],\n [0, 3, -5, 0, 3],\n [1, -2, -3, -5, -5],\n [-3, 4, 0, 5, -6],\n [0, -2, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 3, 1, 1, 1],\n [-5, -4, -2, -3, -4],\n [-5, -5, -3, 5, 6],\n [-5, 5, 3, 4, -1],\n [0, -1, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -3, 1, 5, -1],\n [5, 2, 3, -3, 1],\n [4, 5, -4, -3, -6],\n [-1, 3, -3, 1, -4],\n [-2, 5, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -2, -3, 6, 4],\n [-6, -5, -6, 4, 4],\n [0, 5, 6, 4, -2],\n [3, 6, 4, -3, -5],\n [1, 2, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 0, 6, -1, -1],\n [-2, -3, -3, -6, -1],\n [4, -3, 4, 4, 3],\n [-4, 4, -5, -1, 4],\n [3, -3, 5, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 1, 0, -3, 6],\n [-1, 5, 5, -6, 2],\n [-4, 3, 3, -5, 6],\n [0, 5, -3, -3, 6],\n [-6, 3, -6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -3, 2, -2, 0],\n [-5, -2, -5, 6, -1],\n [1, -2, 4, -1, 3],\n [-5, 0, 6, 6, -3],\n [-2, -3, 5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -1, 4, -2, 6],\n [-3, 0, -5, -6, 4],\n [1, -3, 5, -5, -2],\n [5, -5, -1, 0, 4],\n [-6, 4, 4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 4, -5, 6, -2],\n [-3, -2, 1, 4, 2],\n [6, -4, 3, -5, -3],\n [-6, 0, -3, 4, 1],\n [4, 1, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 6, -1, 2, 3],\n [3, 0, 1, -6, -2],\n [5, -1, 2, -4, -1],\n [0, 3, 3, -1, -2],\n [-5, -3, 5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 4, 1, 2, 4],\n [-2, 3, 5, -5, -4],\n [-4, 3, 3, -4, -6],\n [0, -4, -3, 6, -4],\n [-2, -3, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -6, -6, 5, -6],\n [3, 2, -1, 4, 5],\n [5, -4, -6, 5, -6],\n [-1, 2, -5, -5, -3],\n [3, -6, 6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -2, -4, 1, -2],\n [-1, -2, 6, -1, -3],\n [-3, 3, -6, 0, -2],\n [-2, 5, -1, 1, -6],\n [0, -2, -3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -1, 3, 0, 2],\n [-1, -3, -4, 3, -4],\n [0, 2, 2, -1, 1],\n [1, 3, 6, 3, -1],\n [6, -2, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, -2, -6, 2],\n [-1, 0, 3, -5, 6],\n [-6, 1, -3, -1, 5],\n [0, 0, -5, -5, -1],\n [0, -2, 1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 0, 0, -4, 0],\n [-1, -1, 1, 4, 1],\n [-3, 6, 5, -2, -3],\n [-2, 2, 3, -5, 0],\n [-6, -1, 2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 3, -2, -2, -6],\n [5, 4, -1, -5, -3],\n [3, 2, 3, -1, 0],\n [-4, -2, 3, -4, 5],\n [-6, 1, -5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, -2, 4, 6],\n [3, -6, -4, 2, -5],\n [6, 5, 4, -2, -2],\n [-4, 4, -3, -6, 1],\n [3, 3, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 2, 5, -6, -4],\n [-5, 5, -6, -1, 6],\n [-1, -2, -1, -2, -6],\n [-5, -2, 1, -2, 3],\n [-2, -4, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -3, 4, 2, 6],\n [-4, -1, 0, 6, -2],\n [4, 5, 1, 1, 4],\n [-3, -2, -3, -5, -3],\n [1, 1, -3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -2, 1, 1, 6],\n [4, -4, 4, 5, 3],\n [-3, 0, -5, 3, 2],\n [0, 6, 0, 0, 1],\n [6, 3, 3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -3, 1, 2, -5],\n [-2, -1, -5, -1, 5],\n [-3, 2, 2, 1, 5],\n [5, -6, 3, -5, -3],\n [-6, -4, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 5, -1, 0, -1],\n [0, 2, -6, -4, -4],\n [-1, -3, 1, 1, -6],\n [-5, -5, 6, 4, -2],\n [-3, -1, 2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -5, 3, -2, -1],\n [-6, -6, -4, 0, 6],\n [4, 5, 2, -6, 5],\n [4, 5, -1, -5, 2],\n [-6, -5, 1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 1, -1, -2, 5],\n [-1, -3, -3, 6, 3],\n [0, 3, -3, -1, 2],\n [1, 6, -6, -2, -5],\n [2, -6, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 5, -5, -3, -4],\n [6, -4, 5, 0, -3],\n [0, 3, 3, 2, 3],\n [2, 6, -4, 6, 2],\n [-3, 0, 5, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, 1, 1, 4],\n [5, -5, -4, 6, 5],\n [3, 4, -3, 4, -4],\n [-2, -6, 4, 6, 3],\n [-3, 4, 6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 2, -6, -5, -3],\n [-2, -2, 2, -4, -1],\n [5, -2, 5, -6, -6],\n [0, -3, 6, 1, 3],\n [-2, -1, -6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, 3, -5, 3],\n [4, -4, 5, 3, -6],\n [1, 0, 0, -1, 6],\n [4, 1, 5, -4, 5],\n [-2, 3, 6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 2, -4, 5, 3],\n [-2, 0, -3, 2, 5],\n [-4, -1, -1, 4, -6],\n [-6, 4, -1, -6, -1],\n [-2, 5, -4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -4, -2, 2, 1],\n [4, 6, 3, -3, 0],\n [-5, 0, 5, 0, -2],\n [5, -4, 5, -6, 5],\n [3, -3, -2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 4, -4, -6, -2],\n [2, -2, 2, -3, 4],\n [2, 1, -6, 5, -5],\n [1, 6, -1, -3, -5],\n [3, -1, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -1, 0, 3, 3],\n [4, -4, 4, -1, -5],\n [-4, 4, 1, -2, 4],\n [2, -4, -3, 1, 4],\n [2, 2, 3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, -3, 1, -1],\n [-3, 6, 0, -1, -2],\n [2, 1, 0, -3, -2],\n [5, -1, -5, 6, 3],\n [-3, 5, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 6, -6, -6, -1],\n [-5, -3, 4, -3, 6],\n [2, -3, 5, -4, 5],\n [-4, 3, 2, 0, 2],\n [-5, -5, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -2, -2, -4, 4],\n [-3, -4, 3, -2, -3],\n [-2, 1, -4, 3, -2],\n [4, 1, -5, 5, 5],\n [0, 6, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -5, 4, -5, 6],\n [4, 1, -4, 6, 6],\n [-1, -5, -5, 0, 5],\n [-2, -1, -5, 2, 4],\n [-6, -2, -3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 3, 3, 0, 0],\n [-6, -6, 6, -6, -4],\n [-3, 1, 3, 2, 2],\n [-5, 2, 2, -5, -3],\n [4, -6, -5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -6, -6, 5, 0],\n [-1, -2, 0, -4, 6],\n [-3, 1, -3, 6, -2],\n [-6, 3, -4, 1, 2],\n [-3, 5, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -6, -3, 4, 3],\n [4, -6, -1, -6, -4],\n [2, -4, -4, 3, -2],\n [4, -6, 3, 6, -5],\n [1, 0, -4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -6, 6, 4, -2],\n [0, 1, 5, -3, 2],\n [-2, -2, 3, 4, -3],\n [-5, 1, 2, -2, 0],\n [-6, -6, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 5, 2, 1, -4],\n [-6, -6, 5, 0, 4],\n [-3, 6, 5, 6, 2],\n [-3, 3, 6, 4, 1],\n [1, -3, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -5, 5, 4, -3],\n [-6, -2, 2, 1, 3],\n [-6, 0, 0, -4, -2],\n [0, -6, 4, 1, -4],\n [-5, -6, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 6, 6, -4, -6],\n [5, 3, 0, -4, -5],\n [1, -3, -1, 4, -6],\n [-1, 2, 6, -4, 0],\n [-4, 3, -3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -5, 4, 6, -2],\n [-1, -3, -5, -3, -1],\n [-1, -1, 4, 0, 6],\n [6, 1, 4, 1, -3],\n [6, -4, -5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 6, -6, -6, 5],\n [5, 5, 2, -1, 4],\n [-6, 2, -6, -3, -1],\n [6, -2, 0, 1, -1],\n [0, 1, 2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 6, -3, 5, -3],\n [5, -6, 1, 3, 2],\n [4, -1, 5, 5, -5],\n [5, 2, 6, -1, -5],\n [-5, -4, 4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -4, -5, 5, 5],\n [6, -1, 5, 3, 2],\n [0, 4, 5, 5, 3],\n [-6, -6, 1, -3, 1],\n [-5, 5, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 3, 6, -1, -1],\n [-2, -2, -6, -3, -1],\n [4, 1, 6, 1, 0],\n [2, -2, 0, -3, 1],\n [-6, -3, -3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, 3, -3, -4],\n [3, 1, 3, 2, 4],\n [-6, 0, 3, -4, -1],\n [-3, 5, 3, 4, -5],\n [6, 6, 4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -2, 5, 3, -5],\n [-3, -3, -4, -4, 0],\n [1, 0, 1, 6, -3],\n [-6, -2, 5, -5, 2],\n [-6, -5, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 1, -2, -6, 4],\n [-1, 3, 1, 0, -4],\n [2, 2, -6, -1, -6],\n [2, 3, -5, 5, -4],\n [-4, -2, -4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -4, -5, 2, 1],\n [2, -4, -4, -5, 4],\n [-1, 5, -6, 3, 3],\n [0, 5, 3, -6, 2],\n [-2, 6, -2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -1, 6, 3, -2],\n [-4, 3, 0, 5, -3],\n [6, 5, -5, 5, -5],\n [-2, -5, 1, 0, 6],\n [0, -1, 0, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 2, -5, 6, 6],\n [-5, -2, -4, 3, -1],\n [0, 1, 6, 1, 0],\n [-1, 5, -5, -3, 6],\n [2, -2, 3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 6, 2, -5, 4],\n [-4, 2, 5, -6, -4],\n [5, 5, -5, 2, -6],\n [-5, -5, -5, 6, 0],\n [-2, 5, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, -6, -3, 1],\n [-6, 4, -1, 1, 4],\n [-2, -4, -3, 3, -5],\n [-6, -3, -2, 5, -1],\n [0, -2, 3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -4, -1, -5, -1],\n [-3, -1, 6, 4, -1],\n [5, 4, 1, 0, 3],\n [-5, 5, 4, 6, -6],\n [-2, -1, -2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -5, 1, -6, 6],\n [-2, -3, 0, -4, 2],\n [-5, -2, -5, 5, 0],\n [3, -5, 2, -6, -4],\n [-5, -1, -3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 1, -5, 1, 3],\n [1, -6, -3, -6, 0],\n [1, 6, 1, -2, 5],\n [4, -5, -6, 1, -4],\n [0, 5, -5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 6, -5, -3, -3],\n [3, -2, -5, -2, -3],\n [0, -4, 4, -1, 4],\n [5, -4, 4, 3, -6],\n [-5, 6, -1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 6, 1, -4, 6],\n [6, -2, -4, 4, 0],\n [-4, -5, 6, 0, 3],\n [6, -2, 1, -1, -3],\n [0, 4, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -6, -1, -3, 6],\n [0, 3, -5, 0, 3],\n [-2, -5, -6, 4, -5],\n [-4, 4, -4, -1, -5],\n [2, -4, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 6, 4, 0, -1],\n [-4, -2, -4, 0, -6],\n [5, 5, -4, 5, 6],\n [4, -4, 3, 5, 0],\n [-1, -1, 4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 3, -3, 4, 4],\n [5, 2, -5, 0, 6],\n [-2, -2, 2, -2, 1],\n [-1, 3, 2, -3, 1],\n [6, -4, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -1, 1, -2, 3],\n [-2, 1, -3, 2, 4],\n [5, -5, 6, -6, 3],\n [-3, 5, -6, 4, -6],\n [-1, 0, 3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -3, 6, 1, -2],\n [4, -6, 5, 4, -3],\n [2, 1, -2, 4, -5],\n [-1, 2, -2, -1, 1],\n [1, 6, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 3, -3, 5, 2],\n [3, 2, 0, 5, -4],\n [0, -5, 6, -6, -2],\n [2, -3, 4, -5, 4],\n [-3, -4, 5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, -5, 4, -3],\n [-4, 2, -1, 2, 1],\n [2, -4, -4, 1, 6],\n [2, -5, -1, -3, -4],\n [-5, 4, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -3, -6, -2, -6],\n [-1, 5, 6, -5, 1],\n [0, -6, -3, -6, 0],\n [-2, -2, 2, -2, 0],\n [-5, 4, 5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 1, 0, -6, 4],\n [5, -6, 5, -1, 1],\n [-4, 3, -1, -3, -2],\n [2, -5, -3, 0, 5],\n [-1, 4, 3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, 5, -2, -5],\n [6, 4, -6, 4, 1],\n [-1, 4, -5, -3, -6],\n [-3, 0, -5, 0, -3],\n [-3, 0, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 1, -6, 0, 6],\n [1, -2, -2, 6, 2],\n [-4, -5, 2, -5, 5],\n [-3, 1, 2, -3, -4],\n [1, 5, -3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 0, 5, 4, -5],\n [4, -1, -5, 4, 5],\n [4, -4, -1, 0, 1],\n [6, 3, 5, 5, -6],\n [-3, -4, 6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -6, 0, -5, 6],\n [3, -1, 2, 3, -6],\n [-5, 1, 3, 2, 0],\n [-2, -2, -5, -2, -2],\n [-4, -6, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -1, 1, -4, 0],\n [-5, 4, 5, 4, -5],\n [5, -4, -5, 2, 3],\n [-4, 6, 4, 4, 0],\n [-3, -6, -3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 1, 4, -3, -3],\n [4, -1, -4, 3, 5],\n [1, 4, 0, -4, -3],\n [4, 1, 3, 5, -4],\n [1, 6, -1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -2, 6, 1, -5],\n [3, 2, -4, 3, 5],\n [1, 3, 5, -1, 1],\n [-2, -2, 0, 2, 1],\n [0, -3, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -3, -5, -6, -2],\n [-1, -4, 3, -6, 3],\n [3, -4, -6, -5, 2],\n [-6, -5, 2, -1, -3],\n [4, 2, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -6, -5, -1, 4],\n [-6, 0, -1, 6, 5],\n [2, 3, 0, 0, -5],\n [3, -2, -6, 1, 5],\n [3, 0, -5, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 2, 1, -6, 2],\n [-1, -3, 3, 5, -4],\n [-3, 6, -3, -4, -2],\n [5, 4, 2, 4, -1],\n [2, 1, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 6, 1, -6, -3],\n [6, 1, -5, 3, 1],\n [4, 0, -5, 6, 1],\n [6, -3, -4, 5, -5],\n [2, -1, 0, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 1, 3, 6, -1],\n [0, 6, 0, 3, -4],\n [-5, 0, -5, -4, 3],\n [-6, 6, 3, -4, 5],\n [-5, -4, 0, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 4, 6, 0, 0],\n [5, -4, 3, 0, -2],\n [-2, 5, -5, -5, -3],\n [4, 2, 5, -1, 2],\n [-3, 2, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -5, -5, 2, -5],\n [5, 6, 0, -1, 2],\n [5, -3, 6, -5, -2],\n [0, 4, -3, -1, 3],\n [-6, 2, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 0, -5, 2, -3],\n [-2, 4, -1, 6, 0],\n [6, -5, -5, 6, 6],\n [1, -6, -2, -5, 2],\n [-2, 1, -3, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -6, -4, 3, 6],\n [5, -4, 6, -3, -4],\n [-4, 4, -6, -6, -6],\n [-3, 5, -4, -5, -5],\n [-4, 4, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 0, 3, -5, 3],\n [-2, 2, 4, 2, 4],\n [-3, 1, -2, -2, -6],\n [3, -4, 4, 2, 1],\n [-4, 1, -1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -5, -4, 1, -3],\n [1, 0, -6, 5, -4],\n [6, 5, 2, -4, 4],\n [-6, 4, -2, -6, 5],\n [1, -5, 2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -5, 2, 0, -5],\n [-4, 3, -4, 6, 1],\n [2, -5, -2, -3, -3],\n [-4, -6, -6, 1, 4],\n [0, -3, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -4, -6, -3, -5],\n [6, 5, 0, 1, 6],\n [4, -3, 2, 4, 6],\n [3, 1, -2, 5, 3],\n [3, 1, 4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 5, 5, -1, 5],\n [-1, 6, 1, -5, 0],\n [3, -6, 3, -1, 4],\n [-1, 4, 0, 5, -6],\n [-5, -4, -1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 6, -1, -1, -5],\n [-4, 5, -2, 6, -4],\n [-3, -3, 4, 6, 4],\n [4, 1, 3, 1, -4],\n [2, -6, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 1, -6, 6, -3],\n [-2, 6, 6, -5, 3],\n [0, -6, 2, 6, 6],\n [-1, -6, 5, -3, -6],\n [6, -5, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -1, 2, -4, -5],\n [2, -2, 6, -2, 0],\n [4, -6, -4, -1, 0],\n [-3, 0, -6, -3, 6],\n [0, -5, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 3, 4, -4, 6],\n [6, 1, -1, 3, -6],\n [4, -1, -2, 4, -4],\n [3, 6, -1, -1, 3],\n [6, 6, -1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -4, 2, -5, -3],\n [-1, -1, 0, -3, -4],\n [5, 6, -4, -6, 2],\n [2, 6, -5, 3, 0],\n [1, -6, -2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 6, 2, 6, 6],\n [-4, 6, 6, 5, -2],\n [3, -2, 2, -5, -4],\n [3, 4, 2, -4, -3],\n [5, -2, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -4, 3, 3, 6],\n [-4, -3, -4, -6, 3],\n [4, -1, -2, 2, -1],\n [3, 2, 3, 3, 6],\n [-5, 5, 3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -3, 4, -4, -5],\n [0, -2, -5, 2, -2],\n [3, 3, 2, -2, -6],\n [-6, -3, -5, -5, 4],\n [1, 1, 6, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 3, -4, -6, 3],\n [-6, 1, 5, -2, -3],\n [6, 0, 5, 6, -1],\n [-1, 0, -3, 0, -4],\n [-4, -6, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -5, 5, 6, 3],\n [-1, 0, -6, 1, 0],\n [-6, 4, -6, -5, 4],\n [2, -3, 2, 3, 2],\n [4, -1, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 5, 4, -2, 2],\n [-2, 4, 0, 1, -3],\n [0, 1, -5, -2, -5],\n [3, -4, 4, -5, -5],\n [-1, -2, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -6, -6, 0, -4],\n [2, 3, 4, -2, 3],\n [-2, -3, 1, -1, -4],\n [2, 3, -5, 3, -4],\n [4, -2, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 5, 0, -5, -2],\n [0, 6, 3, -4, -6],\n [2, 6, 3, -6, 5],\n [0, -6, -1, -6, -2],\n [5, -2, 5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 2, 3, 5, 3],\n [6, -2, -3, 0, -2],\n [5, 3, 2, 6, -6],\n [-6, -1, 3, 5, 4],\n [-3, 4, -5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -3, 1, 1, 5],\n [-5, 3, -6, -4, -4],\n [4, 6, 6, -2, 0],\n [-1, 0, -1, -6, -1],\n [5, -2, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, 6, -6, 1],\n [2, -1, -6, -5, 2],\n [0, 5, -1, 0, -1],\n [3, 0, -5, 0, 2],\n [-3, 2, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -3, 5, -3, -4],\n [6, 1, 0, 5, 0],\n [2, -4, -1, 4, 4],\n [-6, 2, 0, -1, 5],\n [-5, 4, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -3, -6, 2, -3],\n [-5, 5, 6, 4, -1],\n [-3, -2, 6, 6, -4],\n [5, -6, 5, 3, 4],\n [-4, 6, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -2, -4, -1, 0],\n [4, -2, 5, -2, 5],\n [-4, -5, -1, 1, -1],\n [0, 3, 4, -2, 3],\n [4, -4, -1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 3, -5, -6, -5],\n [3, -5, -6, -6, -6],\n [-4, -4, 3, 4, 0],\n [3, -5, -6, 6, 0],\n [-4, -6, 5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 2, -1, -1, 4],\n [-3, -6, 0, 2, -3],\n [2, 3, -2, -3, 1],\n [-3, 2, -3, -4, 3],\n [0, 1, -3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, -2, 5, -2],\n [2, 5, 4, -4, 4],\n [-2, -1, 6, 3, 3],\n [-2, 2, -3, -6, -3],\n [5, 2, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 3, 2, 2, 2],\n [-2, -1, 6, -3, 1],\n [-3, 3, 6, -4, 0],\n [-5, 6, 2, 5, -6],\n [5, 6, 0, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -2, 1, -3, -5],\n [4, -2, -6, -5, 4],\n [-4, 4, 0, -1, -3],\n [-3, 1, 2, 0, 3],\n [-2, -6, -3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 4, 4, -3, -3],\n [-5, 0, 6, 5, -1],\n [0, -3, 5, 2, -6],\n [3, 4, -1, 1, 3],\n [-1, -3, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -4, 3, 5, -4],\n [4, 6, -3, 4, 0],\n [6, -1, -1, -1, 3],\n [-2, 4, -1, -2, 5],\n [6, 6, -2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 6, 5, 6, -1],\n [-4, 6, -5, 5, -4],\n [-3, 3, 1, -1, -6],\n [4, 1, 0, -2, 6],\n [-3, 5, 6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 5, -6, -6, -4],\n [-2, 6, 2, -4, 6],\n [1, 1, 3, 3, -1],\n [-3, -5, 2, -1, -6],\n [-2, -6, 5, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, 5, 6, -3],\n [2, -1, 4, -4, -2],\n [-3, -3, 5, -1, -5],\n [3, 4, 3, -5, -6],\n [-4, 5, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -6, 5, 1, 5],\n [1, -2, -2, 3, 5],\n [0, 6, 1, -3, -6],\n [0, -5, -4, 4, -4],\n [2, 4, 5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 3, 6, -3, 2],\n [5, 0, 0, -5, -2],\n [6, 0, 1, -4, 2],\n [-1, 6, 0, 6, 3],\n [-6, 3, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, -2, -4, -4],\n [-3, -2, 3, 0, 5],\n [-2, 1, 1, -4, -3],\n [-1, -6, 5, -6, 0],\n [1, -1, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -3, 5, 0, -4],\n [0, 1, -6, 2, -1],\n [-4, -3, 3, -4, 1],\n [-6, -1, -5, 3, -6],\n [2, 4, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -3, -5, 2, -4],\n [-2, -4, 2, -2, 0],\n [5, 3, -4, 5, -1],\n [2, 0, 3, 0, 5],\n [-3, -6, 4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, 0, -5, -2],\n [-2, -1, -4, -3, 2],\n [4, -5, 6, 2, 1],\n [5, -6, 5, 0, 4],\n [-1, 1, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -4, 2, -6, 2],\n [3, -3, -5, 6, -5],\n [-3, 4, 4, 3, -3],\n [2, -4, 0, 4, 2],\n [3, 2, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 1, -3, -6, 1],\n [-5, 3, -4, 6, 0],\n [1, -3, -2, -1, -3],\n [-6, -5, -2, -2, 4],\n [-6, -2, 2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -5, -4, 4, -2],\n [-3, -6, -5, 6, -3],\n [3, 3, 2, -2, 4],\n [-4, 4, -5, -2, -1],\n [0, -4, -2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -2, 5, 3, 3],\n [5, 1, 1, 5, -6],\n [-1, -5, 0, -4, 3],\n [2, 0, 6, -3, -6],\n [3, 3, -3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 3, -4, 5, 5],\n [4, -6, -4, -4, -5],\n [6, 1, 4, -6, 6],\n [6, -4, 5, 0, 0],\n [3, -3, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 3, 6, 5, 6],\n [2, 1, -1, 4, -5],\n [-3, -3, 1, -1, 0],\n [-3, 6, -3, 1, 2],\n [-6, 5, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 0, 0, 3, 4],\n [-2, 4, -3, 0, 1],\n [2, -5, 0, 1, -2],\n [1, 6, 4, -5, -4],\n [0, 2, -6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -1, -6, 5, 1],\n [2, 4, -4, -6, 6],\n [-2, 0, 5, 4, -4],\n [5, 0, 0, -4, -5],\n [2, -5, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -4, 2, 0, -2],\n [6, 4, 5, 1, -2],\n [0, 1, 3, 1, -2],\n [4, -2, -5, 4, -3],\n [5, -2, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, -4, 1, -1],\n [4, -1, -2, -2, 5],\n [-3, 1, 5, -2, -4],\n [-4, -4, 0, 4, -4],\n [5, -1, -6, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -1, -1, 6, 2],\n [5, 4, 5, 5, -2],\n [4, 3, -1, 3, 0],\n [6, -5, -6, -2, -4],\n [-1, 6, -4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -6, -1, -6, -3],\n [-6, 0, -5, 0, -4],\n [2, -2, -2, 2, 1],\n [-4, -4, -3, 0, -3],\n [5, -5, -2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -1, -6, -4, 5],\n [5, -4, 6, -5, -1],\n [-1, 6, 2, 4, 5],\n [3, -3, 6, -3, 1],\n [1, -1, 5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -1, -5, 1, 2],\n [-6, -6, -3, -1, 5],\n [-6, 2, 5, 2, -3],\n [4, 0, -4, 5, 0],\n [-6, 5, 5, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 0, -6, -5, 4],\n [2, 5, -6, -3, -1],\n [6, -5, 3, 0, -3],\n [-1, -4, 4, -1, -5],\n [4, -3, -1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -5, 1, -4, 3],\n [-4, -2, -3, 1, -5],\n [6, 5, 4, -2, -6],\n [4, 2, -3, 5, 1],\n [-2, 3, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -5, 6, 3, 2],\n [-6, -5, 5, 4, -5],\n [3, 4, -2, 1, 3],\n [-4, -5, -3, -4, 1],\n [6, 2, -5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 6, 0, -4, 3],\n [-4, -4, 1, 0, -5],\n [-2, -5, 6, 2, 0],\n [0, -3, -5, 3, -6],\n [-3, 0, 3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, 1, 0, 1],\n [-1, -3, 6, 0, 5],\n [-6, 3, 3, 2, -1],\n [-5, -2, 2, -1, 3],\n [-4, -4, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -4, -2, 5, -3],\n [4, -5, -6, -4, -1],\n [-4, -3, 3, 3, 5],\n [4, 4, 3, -3, -2],\n [-1, 2, 0, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 5, 2, -2],\n [-4, 5, -4, -1, 0],\n [-3, -6, 3, 1, 1],\n [0, -1, -6, -2, -2],\n [-6, -2, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 4, 1, -2, -4],\n [-1, 0, 2, 2, -5],\n [4, -4, -5, 4, 0],\n [-6, 5, -2, 5, 2],\n [-2, -1, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 3, 6, 1, 5],\n [1, 3, -3, 6, -6],\n [0, 0, 1, 4, 6],\n [2, 1, 3, -6, -2],\n [-5, 3, -6, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 5, 2, 3, 6],\n [0, 6, 3, 6, 5],\n [-3, 3, 4, -3, -1],\n [1, 5, 1, -4, 5],\n [-1, 2, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -6, -4, 3, 2],\n [-2, -5, -3, 5, -5],\n [5, 0, 0, -4, 3],\n [-2, -5, 3, -6, 1],\n [1, 6, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, 3, -5, 3],\n [-6, 1, 0, 4, 3],\n [6, 3, -4, -5, -2],\n [-3, -3, -2, 5, -5],\n [-3, 3, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -3, 2, -2, -2],\n [-4, -4, -4, 5, -3],\n [-4, 2, -3, -5, 5],\n [3, -6, 6, 4, 4],\n [-6, 3, 6, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 0, 1, 4, 3],\n [4, -1, -4, -1, 0],\n [2, -5, 6, -6, 0],\n [4, 6, -5, -4, -4],\n [-5, -4, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, 5, -1, 2],\n [0, 2, -2, 2, 4],\n [2, -4, -2, -3, -2],\n [3, -4, 1, 1, 3],\n [4, -3, -6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, -3, 0, 3],\n [2, 5, 4, -2, -4],\n [4, -6, -3, -6, 5],\n [3, -5, 4, -3, 4],\n [1, 2, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -5, -5, 6, -4],\n [-3, -1, 2, -5, 1],\n [-3, -3, 5, -2, 6],\n [6, -5, -5, -3, 6],\n [4, 6, -6, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -3, -2, 1, 1],\n [1, 4, -1, 3, 0],\n [-5, 0, 4, -1, -2],\n [-4, -2, -2, -5, -3],\n [3, -4, -1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -6, -3, -1, 1],\n [-1, 1, 3, 6, 2],\n [4, -1, 6, 2, 4],\n [-6, -3, -4, 4, 4],\n [3, 1, 0, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -2, 6, 1, 5],\n [-5, -1, -6, 1, 1],\n [0, -6, -5, 1, 4],\n [6, 4, 3, -4, -4],\n [4, -3, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -4, -1, -2, -3],\n [1, -6, 3, 5, 3],\n [-6, -3, -6, 2, 1],\n [1, 1, 5, -5, 3],\n [-1, -5, 4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, 2, 6, 5],\n [1, 4, 0, 1, -4],\n [0, 1, -4, -2, 1],\n [-4, 2, 5, 0, 3],\n [-1, -4, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 5, 3, -2, 2],\n [-4, 3, -1, 4, 4],\n [-3, 4, 3, 2, -5],\n [0, -5, -2, 2, 1],\n [-6, -1, 3, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 4, 4, 0, -1],\n [4, -3, 3, -3, 5],\n [5, 5, -5, 2, 3],\n [-3, 5, 4, 3, -2],\n [-4, 1, -3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 3, -5, 0, 3],\n [-3, 2, 3, -5, -2],\n [-3, 0, 5, -3, -1],\n [-1, 3, -2, -6, -6],\n [-1, 5, -4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 4, 4, 2, 4],\n [-5, -4, 2, -3, -2],\n [-5, 0, 6, 5, -5],\n [-2, 5, -5, 5, 5],\n [3, 2, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, -3, -6, 2],\n [3, 1, 2, -1, 5],\n [-6, -3, -3, -6, -5],\n [6, -3, 6, 3, -6],\n [-4, 0, -5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 1, -4, -1, 4],\n [-3, -2, -2, 6, -4],\n [2, 0, -3, 4, 2],\n [0, 1, 4, -3, 3],\n [-2, 6, -4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -1, -2, -1, 6],\n [-1, -5, 0, 0, -3],\n [-2, -5, -6, 4, -2],\n [-5, 1, -3, -1, 5],\n [2, -2, -1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 2, 0, 4, -6],\n [-2, 2, 0, -5, 2],\n [2, -5, 6, -5, -3],\n [6, -4, -2, 2, 1],\n [0, -2, 4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 2, -2, 4, -2],\n [3, -5, -3, -1, -5],\n [0, -6, -1, -2, -1],\n [-5, 4, -3, 3, 2],\n [-1, -4, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -5, 0, 0, 6],\n [0, 0, -5, 0, 2],\n [-4, -3, 1, 1, -4],\n [-3, 4, 6, 2, 5],\n [-4, 2, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 6, -4, -2, -5],\n [-6, -4, -6, -2, -6],\n [-6, -6, 0, -5, -5],\n [5, -5, 3, 0, 2],\n [4, -5, 5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 0, 4, -5, 6],\n [3, -2, -2, 2, -3],\n [-4, 0, -3, -6, 3],\n [-1, -4, -2, -3, 3],\n [6, 4, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -5, 5, 3, 0],\n [5, -2, -5, 1, 5],\n [0, -1, 2, 4, 6],\n [-5, 5, 3, 1, 2],\n [6, -3, -5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, 1, -4, 1],\n [1, -3, 6, 4, -1],\n [-1, -6, 4, 5, 0],\n [4, -4, -1, 4, 3],\n [-2, -3, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, -6, -3, 0],\n [-3, -4, 1, -2, 4],\n [-3, 1, -3, 1, 5],\n [2, -6, -2, 6, 2],\n [-6, 2, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 6, 4, 4, 4],\n [1, -4, 5, 2, -3],\n [-6, -2, 0, 1, -2],\n [-1, -5, 5, 2, 0],\n [-5, -1, 3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -2, -5, 2, 0],\n [-1, -6, 0, 2, -6],\n [-5, -6, 5, 5, 0],\n [4, -6, 0, 5, 2],\n [-1, -6, -2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 0, -6, -6, 2],\n [3, -6, -3, -4, -5],\n [-5, -4, 6, 3, 0],\n [0, 5, 0, 5, -1],\n [3, 0, 0, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 1, -2, 2, -5],\n [6, 6, -4, -6, 6],\n [0, -5, 5, -4, 3],\n [-4, 4, 1, 4, -2],\n [-1, 2, 1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -1, -5, -3, 1],\n [5, 3, -1, -1, -4],\n [-5, -4, 3, 6, 6],\n [-6, -2, -5, -6, -3],\n [-6, 0, -6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -1, 2, 2, 1],\n [3, -4, -6, 4, -2],\n [-4, 1, 4, -5, -1],\n [-3, 6, 4, 5, -4],\n [-2, -6, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 0, -2, -6, 3],\n [3, 3, -1, -1, 5],\n [5, -5, 3, -2, 0],\n [-3, -2, -3, 4, 0],\n [1, -1, -5, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -6, 1, -2, 5],\n [1, 5, -2, -1, 2],\n [-5, 6, 4, 4, -2],\n [-4, -1, -4, -6, 4],\n [5, 0, 4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, -4, -3, -2],\n [1, -1, -3, 1, 0],\n [-4, -6, 3, 2, -4],\n [-4, -2, -3, 1, -1],\n [6, -2, 1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, 1, 6, 0],\n [-6, 6, -2, 6, 1],\n [-3, -2, -2, -6, 3],\n [-4, 5, -6, 0, -6],\n [6, 1, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -5, -4, -2, 4],\n [-2, 5, 4, -3, 1],\n [3, -2, 0, -2, 3],\n [-4, -6, 3, 5, 3],\n [-4, -5, 6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, -5, -4, 6],\n [4, -1, 2, -1, 3],\n [1, 0, 0, 6, -1],\n [-4, -3, 6, 2, 6],\n [-5, 4, -5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -1, 5, 2, 5],\n [4, -6, 2, -1, -3],\n [0, -6, -6, 2, 0],\n [-6, 3, -1, -3, 0],\n [4, 5, 6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, 2, -2, 1],\n [3, -4, 5, -1, 0],\n [3, 4, -2, 5, -3],\n [6, -4, -5, -1, 2],\n [3, -5, -1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 4, 0, 0, -2],\n [4, -1, 3, -5, -1],\n [-2, 3, 1, 6, -4],\n [-1, 1, 2, -2, -1],\n [5, 4, -5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -2, -3, -1, -5],\n [-3, 0, 3, 2, 4],\n [-5, 5, 4, 1, 6],\n [-1, 6, 4, -6, 0],\n [1, -6, -2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 5, 3, 4, 3],\n [2, 2, -5, -4, 6],\n [3, 6, -6, 3, -3],\n [1, -4, -6, 6, 5],\n [3, -4, 1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -6, 5, -6, 0],\n [1, 6, -3, 1, 0],\n [3, -4, 4, -2, 2],\n [5, 3, 1, 2, -4],\n [3, 4, -2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -5, -3, -3, 2],\n [5, 5, 2, -4, 3],\n [0, -4, 2, 0, -1],\n [5, 0, 4, -1, -1],\n [-5, -5, -5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 2, -3, -5, -5],\n [6, -4, -4, -6, -4],\n [-6, -3, 5, -1, -6],\n [2, -3, -6, 0, -1],\n [5, 3, -5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 2, -2, 0, 1],\n [-5, -2, -4, -2, -3],\n [3, 1, 0, 2, -3],\n [-6, -6, 3, 6, 4],\n [-1, -6, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, -2, 2, -6],\n [-4, 6, -4, 2, 2],\n [-5, 6, -4, -1, -4],\n [-1, -3, 0, -2, 1],\n [0, 3, 4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 5, 6, -4, -3],\n [1, -1, -5, -4, -3],\n [2, 5, 3, 2, 4],\n [3, -2, -6, -4, 4],\n [3, -5, 0, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -3, 6, -5, -5],\n [-4, -6, 0, 3, -5],\n [-6, 2, 3, -4, 1],\n [-4, -2, 6, -5, 3],\n [-6, -4, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, -5, -4, -6],\n [-3, 1, -1, -6, 0],\n [-4, -3, 0, 2, 3],\n [-5, -1, -5, -1, 0],\n [-6, -5, 1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 3, -2, 4, -1],\n [-6, 3, -4, -3, 3],\n [-5, -2, 0, 5, -3],\n [6, 2, 3, -1, 1],\n [4, -5, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 1, -4, 1, 6],\n [1, 2, 3, -6, -4],\n [3, 2, -5, -2, -3],\n [2, 4, 3, 1, 3],\n [0, 2, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -1, 5, -2, -6],\n [5, 5, 1, 4, 1],\n [6, -3, 4, -2, 4],\n [-6, 3, -5, 6, 6],\n [-3, 1, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 0, -3, -3, 1],\n [5, 0, 1, 4, -3],\n [-3, 5, -2, -6, 6],\n [3, -5, -1, 1, -1],\n [-2, -4, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -1, -4, 3, 1],\n [1, -5, 2, 6, -3],\n [-6, -6, -6, -2, -4],\n [5, -3, 3, 4, 2],\n [-2, -6, 0, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 4, -1, 5, -6],\n [0, -5, 5, 0, -6],\n [-1, 2, -3, -5, 0],\n [1, -6, 6, 0, 5],\n [-5, -5, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 6, 1, 4, -3],\n [-5, 5, 6, -5, 3],\n [1, -4, 2, -4, -5],\n [2, 0, 2, 3, -1],\n [1, 0, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, 4, 2, -2],\n [-6, 5, -6, 0, 0],\n [2, -2, 6, -2, -1],\n [3, 0, 3, -2, 0],\n [6, 2, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -4, -2, -1, 3],\n [1, -6, -4, -1, 0],\n [0, 2, 1, 5, -2],\n [-1, 2, 2, -1, -6],\n [5, 5, 5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -4, -1, -4, 1],\n [-2, -4, 1, -5, 5],\n [-3, -6, 3, 1, 5],\n [2, -5, 1, 5, 0],\n [-2, 6, -2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, -5, 5, 5],\n [3, -1, -3, 6, 4],\n [-6, 4, -3, -1, -5],\n [2, -3, -4, 5, 6],\n [5, 3, -1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -2, -6, -6, -4],\n [-6, 2, -1, 6, 0],\n [2, -2, -1, -6, -4],\n [-1, 1, 2, 0, 0],\n [-3, -6, -1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -5, 5, 0, 6],\n [5, -1, -3, 1, 1],\n [-5, -5, 5, 4, 1],\n [-3, 0, 5, 5, -4],\n [-3, -4, -4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 6, 4, 3, 1],\n [2, 2, 2, 6, -1],\n [-4, 2, -4, -4, 4],\n [0, -6, 6, -3, -2],\n [1, -3, -1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -5, 5, -2, 4],\n [2, 2, -5, -1, -4],\n [-1, 3, 4, 3, -6],\n [-4, 6, 0, 2, 6],\n [-1, -6, 3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 3, 0, -6, 2],\n [3, -6, -2, 4, 5],\n [-3, 6, -2, -1, -3],\n [-4, -1, 4, -1, 0],\n [-1, -1, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -1, 4, 5, -2],\n [2, 5, 4, -5, 0],\n [2, 5, -5, 4, -2],\n [0, -6, 0, -5, -6],\n [-6, 1, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -3, -6, -1, -2],\n [2, 5, -1, 2, 1],\n [4, -3, -3, -3, -4],\n [-2, -3, -2, 0, 4],\n [4, 4, -6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -1, -1, -3, -3],\n [0, -1, 4, 1, -5],\n [2, -5, -3, -4, -3],\n [-4, 3, -1, 5, -1],\n [-5, 5, -4, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 4, 1, -6, 2],\n [-4, -4, 4, 0, -1],\n [-4, 6, 0, -4, -3],\n [1, 1, 2, -6, 2],\n [-6, -4, 3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -1, 1, -6, 6],\n [2, -6, -6, -5, 3],\n [5, -4, 3, -6, 6],\n [3, 0, -5, 5, 6],\n [-5, -3, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 2, -5, -3, 3],\n [4, -1, 3, -2, -1],\n [-3, -3, -6, 0, 0],\n [-3, -1, -5, -5, -6],\n [0, -6, -2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -4, 2, -6, 4],\n [5, 1, 3, -2, -1],\n [-6, 0, -1, -6, 4],\n [-6, 0, -2, -6, 4],\n [-4, -3, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 2, -6, -6, -1],\n [-6, 0, -5, -6, -1],\n [2, 1, 4, 2, 1],\n [0, -3, 2, -6, 4],\n [-3, 1, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 0, 5, -2, 6],\n [-1, -4, 1, 6, -1],\n [-4, 1, -3, -3, 6],\n [-6, 0, 5, -2, -3],\n [-2, -4, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -4, -1, -1, -2],\n [-6, -2, 5, -5, -5],\n [5, -5, 1, 1, 6],\n [4, -1, 3, 0, -6],\n [-2, 2, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, 4, 5, 5],\n [-6, -1, 0, -1, -4],\n [-5, -6, -2, 1, -6],\n [-1, 5, 5, -2, 3],\n [-4, 0, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -6, -5, -3, -2],\n [4, 0, 6, -5, -4],\n [2, 6, -3, -5, 3],\n [-5, -6, 3, -6, -6],\n [-6, 6, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -3, 5, -5, -6],\n [-1, -6, 2, 4, -4],\n [0, -1, -6, -1, 2],\n [5, -2, -4, 4, 3],\n [3, 1, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 3, 6, -2, 5],\n [3, 5, 2, -4, 0],\n [3, 5, -2, 4, -2],\n [-5, 2, -3, -5, 6],\n [0, -4, -1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, 4, 0, 0],\n [1, -1, 4, -3, 4],\n [3, -4, 5, 4, 4],\n [6, -4, -4, -4, 4],\n [0, -5, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 4, -4, 3, -6],\n [-6, -5, 1, 6, -6],\n [1, 2, 4, -4, 2],\n [5, 5, 2, -6, -5],\n [0, 4, -3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -1, 5, 4, 1],\n [1, 1, 0, -2, -3],\n [-4, -3, 4, 5, 4],\n [-4, 2, 5, 3, -5],\n [-3, 2, -3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -1, -4, 4, -4],\n [6, -1, 5, -1, 2],\n [-5, -1, 5, 4, 5],\n [2, 4, 6, 4, 6],\n [-2, -6, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 4, 3, 1, -3],\n [-3, -3, -4, 3, -5],\n [-5, 4, 5, 2, -2],\n [-2, 4, 0, 1, 3],\n [-1, 3, -6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 2, 2, 1, -1],\n [-5, 1, 6, 2, 1],\n [-4, -1, -5, 5, -3],\n [2, -4, 1, -4, 5],\n [4, -4, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 3, 3, -6, 4],\n [5, -1, 3, 5, -5],\n [0, 4, -2, 5, -3],\n [0, -5, 5, -3, -4],\n [3, 3, 3, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -4, -3, 3, 1],\n [3, -1, 2, -6, -2],\n [-5, 2, -2, -1, -6],\n [4, -2, -4, -3, 1],\n [1, 1, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -6, 4, -2, -1],\n [2, 1, -3, -1, 1],\n [6, -6, -4, -4, -5],\n [-1, -6, -6, -1, 5],\n [-5, 3, -4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, 3, -2, -3],\n [-1, 6, -1, 6, -4],\n [5, -6, -2, 4, -3],\n [4, 6, 6, 1, -2],\n [4, -4, 1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -3, 0, 5, -5],\n [0, -3, 2, 2, -4],\n [1, -4, -2, 0, 5],\n [6, -3, -1, 1, -1],\n [1, 2, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 2, -5, 0, 0],\n [-2, -5, -5, 2, 2],\n [1, 2, 6, 4, -5],\n [3, 2, 4, 4, 6],\n [5, -4, -3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -3, 2, 5, -6],\n [0, 6, 2, -4, -6],\n [0, -3, -3, 1, 4],\n [-4, -5, 3, -1, 2],\n [5, 1, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -6, 1, 2, 4],\n [-4, 3, -4, 2, -4],\n [-5, -5, -4, 5, -3],\n [4, 2, -3, 5, 0],\n [-5, 0, -5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 6, -1, -1, 0],\n [-6, -5, -5, -2, 5],\n [6, -6, 6, -4, 3],\n [1, 3, -1, -5, -6],\n [4, -5, 6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 4, 3, 4, -3],\n [-5, -1, -5, -6, 0],\n [-5, -5, -2, -5, -4],\n [-5, 0, -3, -4, -2],\n [-4, 1, -5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, 6, 3, 1],\n [-4, 6, 0, -4, 1],\n [-2, -5, 3, -2, 1],\n [5, -5, -2, 4, 3],\n [2, -3, 5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -4, -5, -1, 1],\n [1, 6, 6, -1, 5],\n [6, 2, -4, 5, -5],\n [5, 4, 5, -2, -1],\n [-1, 1, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 4, 5, 1, -3],\n [1, 5, 4, 6, -6],\n [-2, 3, -5, 4, 0],\n [1, 0, 5, 3, 0],\n [-6, -1, -4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -3, 2, 6, 6],\n [-1, 0, -2, -1, -5],\n [-4, 5, -5, 3, 5],\n [5, 6, -1, 4, 3],\n [2, 5, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 6, -3, -2, -4],\n [3, -1, -4, -3, 3],\n [-6, 3, 5, -3, 1],\n [0, -5, 0, 6, 4],\n [5, -3, 3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 6, -4, 2, -5],\n [6, 3, 4, 6, -6],\n [4, 0, 3, -6, 6],\n [-1, 2, 3, 3, -1],\n [-1, 4, -5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 4, 2, -3, -6],\n [2, 6, -5, 0, -6],\n [3, -1, -3, -2, 4],\n [-4, -3, 0, 4, 5],\n [-4, -3, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 6, -5, 6, -4],\n [4, -2, -5, -6, 1],\n [-6, 4, -1, -6, 3],\n [4, -3, 6, 6, 4],\n [-2, 5, -3, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 4, 4, 4, 6],\n [-6, -3, -1, -1, -3],\n [-3, 3, 5, -2, 1],\n [-5, -5, 4, -1, -2],\n [1, -3, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 4, 0, 0, 4],\n [4, -2, 5, -4, 1],\n [-1, 4, 3, 4, -2],\n [5, -4, 4, 0, -2],\n [3, 5, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 2, 2, -6, 2],\n [2, 6, -5, -1, -2],\n [2, -6, -4, -5, 3],\n [-6, 0, 6, 6, -4],\n [-1, -3, 1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -3, 2, 3, 0],\n [3, -2, -1, 5, -1],\n [6, 6, -4, 1, -2],\n [6, -4, 5, 5, 3],\n [-3, -3, -6, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 2, -5, 1, 0],\n [3, 0, 4, -4, 5],\n [-5, -5, -6, 1, 0],\n [6, -4, -6, 6, 1],\n [2, 4, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -2, 4, 5, 3],\n [-3, 6, 5, 2, 2],\n [6, -4, -3, 1, 5],\n [3, -3, 3, -6, -2],\n [2, -4, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -2, -5, -2, -2],\n [-4, -1, -3, 3, -3],\n [0, -1, 6, -4, 3],\n [1, 3, -2, -6, -4],\n [1, 1, 6, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 2, 2, -4, -3],\n [1, 6, 4, 6, 5],\n [5, 3, -4, 3, -1],\n [5, -3, -3, 2, 5],\n [-2, 3, -3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 4, -5, -6, 5],\n [5, 1, -4, -6, 6],\n [-1, 5, -2, -1, -4],\n [2, -3, -6, -4, -6],\n [6, 0, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 1, 2, -1, -4],\n [2, 4, -6, 2, 3],\n [2, -6, -3, -3, -2],\n [3, 4, -6, -1, 1],\n [6, 2, 4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 5, -1, -5, -4],\n [6, -5, 1, 6, 1],\n [6, 3, -3, 6, -4],\n [-1, -5, -1, -2, -1],\n [-6, -4, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -4, -6, 6, -1],\n [6, 3, -1, -4, 5],\n [-3, 1, -6, -1, -5],\n [-2, -6, 6, 5, 5],\n [5, 2, -2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 0, 4, -3, 0],\n [1, -2, -5, 4, 0],\n [6, -4, -1, 4, 1],\n [0, 2, -1, 4, -5],\n [1, 0, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 0, 5, 0, -3],\n [4, -2, 6, -5, -5],\n [-3, 2, 0, 1, 5],\n [0, -3, 5, 5, -1],\n [-5, -3, 3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -6, 4, 6, 5],\n [4, -4, 6, 4, 6],\n [6, -3, -3, 6, 2],\n [-6, -3, -2, 4, 0],\n [-2, -5, -6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, -1, -1, 2],\n [6, 2, 0, 4, 2],\n [0, -2, 1, 3, 2],\n [5, 3, 0, -5, -2],\n [2, -6, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 6, 4, 0, -4],\n [1, 5, 3, -3, -4],\n [-5, 5, 0, -3, -6],\n [-6, 4, 2, 0, 4],\n [-4, -2, 5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, -6, -6, 4],\n [1, 5, 5, -1, 4],\n [0, 0, 6, 1, 2],\n [1, -2, 3, 0, 6],\n [1, -2, 1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 1, -1, -5, -3],\n [-6, -1, 0, 4, -5],\n [-4, 2, 2, 2, 0],\n [-4, 3, 1, 2, 0],\n [-6, -4, 5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 6, 3, 1, 5],\n [-1, -6, -1, 5, -6],\n [-4, 3, -6, 2, 3],\n [4, -4, 5, -6, 3],\n [-5, 0, 1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 2, -3, 1, -1],\n [5, -6, 2, 2, 4],\n [0, -6, 2, 0, 4],\n [-3, -5, -1, 6, 4],\n [-4, -1, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -1, 6, -4, 6],\n [2, 5, 0, -5, -5],\n [-6, 3, -5, 4, 4],\n [-2, 4, -4, 5, -2],\n [2, 0, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, -2, 0, 2],\n [2, 2, 6, 0, -3],\n [-6, -4, 6, -3, 0],\n [-2, -3, -3, 4, 4],\n [6, -4, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 6, -6, 0, -5],\n [-1, -2, -4, -1, 1],\n [-4, -5, 1, -5, -2],\n [0, -5, -1, 6, 2],\n [0, 0, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -4, 3, 4, -5],\n [3, 5, 1, -6, -5],\n [0, 0, -4, 2, -6],\n [4, 4, -2, -4, 2],\n [6, -5, 2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 5, -6, 1, 3],\n [3, -2, 4, 1, 6],\n [-3, 4, -4, -4, 2],\n [1, 0, 5, -6, 2],\n [-1, -3, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -6, -6, -4, -1],\n [1, 2, -1, -5, -5],\n [-2, 1, 2, 4, -4],\n [1, 2, 2, 2, 5],\n [4, 2, -6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 3, 0, 2, 4],\n [1, -4, 4, 4, -6],\n [-6, 6, -6, 1, -1],\n [3, -4, -3, -2, 2],\n [0, 0, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 0, 3, 6, 5],\n [3, -2, -6, -5, 5],\n [5, 5, 5, 6, 0],\n [3, 0, 2, -1, -1],\n [2, 2, -3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -6, 5, -4, 1],\n [-1, 5, 4, -6, -2],\n [6, 5, 2, -2, 2],\n [6, 1, -2, -5, 6],\n [-4, 2, -5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -6, 4, -1, 6],\n [-1, 1, 2, -5, 5],\n [-6, 3, 5, 6, -2],\n [6, 6, -3, -1, 3],\n [6, 6, 5, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -1, 1, -2, -6],\n [6, -6, -1, -3, 3],\n [-2, 0, -5, -1, -5],\n [3, -3, 4, -5, 4],\n [-2, 1, -6, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -1, 1, 1, -6],\n [-6, 1, -5, -2, 4],\n [2, -5, -4, -5, 5],\n [5, 5, 5, 1, -1],\n [0, 3, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, -2, 1, -6],\n [5, 0, 4, -5, -5],\n [6, -4, 2, -6, 2],\n [-6, -1, 1, -1, -2],\n [-2, -4, -1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -5, -5, -2, -2],\n [-4, -1, 6, 5, -4],\n [5, 6, 0, 3, -5],\n [3, 1, 2, -6, 3],\n [-4, 4, -2, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -4, 4, -2, 3],\n [-6, -3, -4, -5, -3],\n [6, 0, -5, -2, -5],\n [5, 3, 5, 2, -5],\n [-2, 6, 6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 3, -6, -2, 3],\n [-3, -1, 2, -6, 3],\n [3, 6, 0, -5, 5],\n [-2, -1, 4, 1, 3],\n [0, -4, 1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 6, 0, -3, -1],\n [6, 5, 2, 5, 3],\n [5, -6, 3, -3, 0],\n [6, -6, 2, 6, 5],\n [-6, -5, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 0, 0, -1, -5],\n [3, 2, 6, -2, -5],\n [3, 4, 0, 5, 2],\n [-5, -1, -6, 3, 6],\n [-1, 1, 5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 1, 3, 6, 5],\n [0, -2, -3, 0, 2],\n [1, -5, -2, 2, -3],\n [6, -4, 0, -4, 5],\n [2, -1, -1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 5, -5, -2, -6],\n [6, 5, -5, -6, 3],\n [6, 6, -6, -6, 4],\n [-6, -2, 5, -5, -2],\n [-4, 3, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -2, 5, 6, -1],\n [2, -6, -2, -1, 1],\n [3, -5, 5, -5, 6],\n [-1, 4, 4, -4, 3],\n [4, -6, 4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 1, 4, 0, -1],\n [-4, 1, -6, 3, 5],\n [0, 5, 3, -1, 5],\n [-4, 5, 2, 4, 4],\n [2, -1, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -6, 4, -3, 4],\n [-5, -4, 4, -1, 6],\n [-1, 1, -2, -2, 4],\n [1, -1, -3, -5, -2],\n [6, -3, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -1, -6, 0, 5],\n [-5, 1, 1, -2, -3],\n [-6, 6, 4, -3, -1],\n [-2, -3, 0, -2, 2],\n [-3, -5, -4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -6, -5, -5, 2],\n [1, -1, 6, 4, -3],\n [0, -5, 2, 6, -4],\n [-6, -6, 3, -6, -2],\n [0, -5, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -4, -5, 1, -6],\n [0, -1, -3, -5, -2],\n [-6, 6, -5, -1, 5],\n [-2, 2, -6, -2, 2],\n [4, -1, 5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -6, 1, 5, 5],\n [2, 3, 2, 4, 4],\n [-4, -2, 3, 6, -2],\n [-3, 1, 3, -6, -3],\n [4, 0, -4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, 5, -3, 6],\n [6, -1, 1, 1, -6],\n [5, -1, 3, -6, 6],\n [-5, 0, 3, 5, -1],\n [-5, -2, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, -4, -2, 1],\n [-5, 1, 4, 5, 5],\n [3, 6, -5, 3, 2],\n [-5, -2, 4, -3, 1],\n [0, -2, 6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 1, 5, -5, 2],\n [-6, 5, -3, 3, 3],\n [4, 3, -6, -3, 4],\n [-5, 4, -1, -2, 4],\n [-6, -3, -2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 3, 2, 3, -3],\n [-2, 3, 4, 2, 0],\n [-4, 3, 2, -6, -6],\n [-5, -3, 0, 1, -3],\n [4, -6, 6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 1, -2, -2, 2],\n [-2, -3, 3, -4, -4],\n [-2, -1, 0, 1, -1],\n [-6, -4, 2, -2, 2],\n [-2, -2, 6, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, 1, -4, 1],\n [-2, -3, 4, 3, 5],\n [-4, -5, 2, -4, 3],\n [4, 1, -1, 3, 1],\n [5, 5, 2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -6, 2, 4, -3],\n [6, -3, 1, 4, -1],\n [0, -5, -3, 1, -6],\n [0, 3, -4, 4, -1],\n [4, -4, -5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -6, 0, 5, -3],\n [4, -3, 0, -3, 1],\n [-3, -5, -6, -1, -4],\n [-6, -2, 1, -2, 5],\n [-6, -4, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -4, 1, 3, 6],\n [-1, 1, 5, 5, 4],\n [-2, 6, -6, 4, -2],\n [-6, -5, -4, 2, 1],\n [0, -1, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 6, -5, -4, 3],\n [4, -3, 3, 0, -5],\n [5, -6, -1, 0, 2],\n [-3, 1, -3, 0, 2],\n [4, 1, 1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -6, 3, 5, 5],\n [-2, -3, -4, -1, -3],\n [6, 4, 3, 4, -1],\n [-3, 6, -5, 1, 6],\n [4, -1, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 6, -4, 0, -3],\n [-5, -5, 0, 3, -5],\n [0, 1, 5, 1, 4],\n [-5, -3, -3, 3, -5],\n [-3, 2, 2, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 0, 3, -5, 0],\n [1, -3, -1, 3, 0],\n [-4, -3, 2, 2, -3],\n [3, 2, 5, 6, -1],\n [0, -5, -5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 4, 2, -6, 6],\n [-1, 5, 1, 0, 1],\n [3, -3, 5, 4, -3],\n [-3, 0, -2, -4, -5],\n [3, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 3, -2, -4, -5],\n [4, -4, -3, -2, -6],\n [1, -2, 4, 0, -3],\n [6, 5, -3, -2, -2],\n [-4, -2, -3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, 0, -3, -3],\n [1, -4, -5, -5, -1],\n [-6, 1, -1, -3, 2],\n [5, -2, 0, 3, 3],\n [3, 4, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, 6, 0, -2],\n [2, -6, -5, -2, 3],\n [-6, 4, 2, 2, 5],\n [-1, -3, 0, -3, 3],\n [-6, -6, -2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -5, -3, 3, -4],\n [4, -6, -5, 2, -1],\n [-2, 2, 1, -6, -4],\n [6, -6, 6, -4, 5],\n [-5, 5, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -5, 5, -6, 0],\n [-3, -6, 3, 3, 0],\n [-3, 5, -3, 3, 5],\n [1, 6, 2, -1, -2],\n [6, -2, -2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 0, 2, 2, -2],\n [0, -4, 2, 2, 0],\n [5, 4, 3, -2, 2],\n [1, 3, 0, -6, 6],\n [-6, 5, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -2, -2, 1, -1],\n [0, -1, -1, -2, 1],\n [3, -3, -6, 2, -5],\n [5, 5, -2, 1, 6],\n [4, -1, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -5, -3, -4, 1],\n [-5, -5, 2, -3, -6],\n [6, 3, 0, -2, 3],\n [1, 5, 5, -6, 0],\n [-5, -5, -3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 0, -1, -1, -5],\n [3, -2, -6, 3, -6],\n [1, -1, 2, 0, -1],\n [-3, 5, 3, -3, -6],\n [-4, 5, 6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 4, -4, 3, -5],\n [-4, 5, 6, 1, 5],\n [3, 5, -3, -4, -4],\n [5, 2, 6, 0, -3],\n [5, 6, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -4, -6, 0, -6],\n [-1, 1, 5, 6, 6],\n [0, 3, 2, 0, 2],\n [-2, 0, 0, 0, -1],\n [-5, -6, 4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 5, 0, -4, -4],\n [-2, -4, -2, 4, 0],\n [2, -1, -6, -6, 2],\n [6, 3, 3, 2, 5],\n [3, -3, 4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -4, -2, -4, -2],\n [-1, -6, 1, 4, -5],\n [-3, 4, 2, -5, -1],\n [5, 1, -5, 0, 0],\n [-5, 1, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -4, 2, 1, -4],\n [-2, 4, -3, 2, 1],\n [4, 6, -5, -6, 5],\n [-6, 2, -2, 5, 6],\n [-1, -6, 0, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -4, 6, -1, 5],\n [2, 6, 5, 0, 6],\n [-2, -4, -2, -5, 0],\n [4, -1, 1, 6, -2],\n [0, 6, 3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 5, 0, 5, -2],\n [3, 4, -6, -2, 1],\n [6, 4, -1, 1, 6],\n [2, -2, -5, -1, 6],\n [4, 2, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -6, -3, -3, -2],\n [0, -3, 3, -3, -6],\n [2, -1, -6, 3, 0],\n [5, 3, 2, 0, -3],\n [3, -1, 3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, -2, 4, -4],\n [3, 3, 0, 0, -2],\n [4, 6, 6, -1, -2],\n [4, -4, -4, 2, -5],\n [5, -3, 4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, 4, 0, -2],\n [3, -3, 1, 5, -3],\n [6, -3, 1, 4, 0],\n [-5, 1, 2, -2, 6],\n [-3, 5, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -3, 6, -5, -6],\n [-1, 4, 4, 4, -2],\n [-1, 3, -6, 0, 0],\n [-1, 6, -4, -6, 1],\n [-4, 2, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -1, 3, 6, -2],\n [-3, 3, 5, 4, 2],\n [5, -6, 0, 6, -6],\n [-3, 4, -2, -6, -2],\n [5, -4, -3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 3, 0, 2, -4],\n [-2, 6, -4, -2, -5],\n [-4, -4, -3, 1, 6],\n [-1, 2, -2, -3, -3],\n [-1, -1, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -6, -3, -6, 6],\n [0, -4, -5, 1, -1],\n [-2, -6, -2, -1, -5],\n [-5, -1, -6, 6, -1],\n [-1, -1, -5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, -4, 2, 6],\n [-4, -3, -6, -4, -5],\n [-1, 5, -2, -6, 6],\n [-6, -2, -2, 1, -1],\n [-4, -4, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -4, -1, 4, 2],\n [5, 5, 3, -3, 0],\n [4, 5, -2, 1, -2],\n [-4, 1, -2, -5, -3],\n [6, 0, 6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 5, -6, -4, 1],\n [2, 6, 4, -6, 3],\n [2, 4, -1, -2, -4],\n [2, 3, 4, 1, 2],\n [-5, -6, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 0, 3, 4, 5],\n [6, -5, -2, 1, -5],\n [1, -2, 1, 1, 6],\n [-5, 1, 0, 6, 4],\n [-1, 6, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, -2, 3, -4],\n [-1, 1, 1, 1, 3],\n [1, 1, -2, 1, 0],\n [4, -1, 5, 0, 0],\n [-1, 0, 6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 2, 0, -4, 0],\n [1, -6, -1, -5, 0],\n [-2, 3, -3, -5, -2],\n [1, 1, 1, 3, 3],\n [-5, 0, -3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 5, 4, -3, 1],\n [-1, 2, -1, 6, 1],\n [2, -1, -6, -4, 4],\n [-1, -1, 5, 0, 2],\n [5, 5, -4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -3, -4, 1, 1],\n [0, -6, 4, 5, -2],\n [2, 0, -5, 6, 5],\n [-1, -1, 0, 6, -5],\n [4, -4, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -1, -2, -5, -6],\n [-4, 0, 1, -4, -2],\n [3, 1, -2, 6, 5],\n [-5, 3, -5, 2, 5],\n [5, -6, 5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -4, -1, 4, 0],\n [4, -2, -6, -3, -3],\n [2, -2, 5, 4, 5],\n [-3, -4, 6, -5, -5],\n [1, -4, 1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 3, -4, -4, 4],\n [-1, 1, -2, 6, 5],\n [1, 0, -3, -2, -5],\n [6, -6, 1, 0, 1],\n [4, -1, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 3, 4, -4, -2],\n [2, 1, -2, 5, -4],\n [-3, 6, -6, -1, 0],\n [-4, 1, 2, 5, -1],\n [0, 5, 1, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 6, -4, 1, -3],\n [-3, 6, -5, -6, 1],\n [3, -3, -6, 1, 2],\n [2, -6, 4, 2, 5],\n [-3, 4, 2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 0, 3, 1, 1],\n [1, -4, 4, -5, 2],\n [0, -6, -2, 1, 1],\n [-6, -5, 3, 2, 1],\n [0, 3, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 2, 0, -5, 4],\n [-5, 2, 1, -3, 6],\n [1, 6, 4, -5, -6],\n [6, 5, 4, 0, 1],\n [-2, -2, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 4, 3, 1, -4],\n [6, 6, 5, 1, 2],\n [-4, 5, -6, -4, -1],\n [-3, 6, -6, 5, 5],\n [-4, -1, -3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -6, -2, -6, 2],\n [3, 0, -6, 4, 2],\n [1, -5, 6, 2, -3],\n [-2, 0, -6, -5, 5],\n [-2, 4, -4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 0, 0, 1, 6],\n [5, -6, -6, 4, 3],\n [4, -3, 6, 5, 2],\n [0, -5, 2, -1, -2],\n [-4, 5, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -4, 5, -4, 1],\n [-5, 6, 0, 5, 0],\n [0, -1, -2, -3, 4],\n [3, 4, -2, -6, 5],\n [0, -5, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 2, 2, -4, 2],\n [-1, -6, -3, 6, 5],\n [-1, -6, 4, 2, -6],\n [-2, -2, 5, 5, -4],\n [4, 5, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 4, 5, 1, -6],\n [0, 0, 2, 3, -4],\n [-4, -1, 4, 2, 1],\n [-2, 1, 0, -5, 0],\n [-1, -3, -4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -6, 3, -3, 0],\n [-6, 4, -2, -6, 1],\n [6, -4, -3, 6, 6],\n [6, 6, 0, -5, 0],\n [1, -1, -6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 2, 6, -3, 3],\n [5, -4, -2, 6, 2],\n [-2, -2, 1, -3, -4],\n [-2, -4, 4, -5, 6],\n [-1, -2, -1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -1, -6, 1, 5],\n [1, 1, 3, -3, 6],\n [-1, 6, -5, 2, 5],\n [5, 6, -3, 2, 4],\n [5, -6, 1, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -4, 1, 2, -4],\n [2, -6, 0, -5, 0],\n [3, 2, -4, -3, -3],\n [5, -3, 0, -6, 6],\n [2, 4, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 1, 0, 5, -2],\n [5, 6, -3, 4, -2],\n [-1, 5, -1, -2, 6],\n [1, -3, 2, -3, 2],\n [-3, 4, 5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -3, -4, 6, -1],\n [0, -4, 2, 0, 1],\n [-3, -4, -3, 5, 5],\n [5, -6, -3, -2, -6],\n [4, -3, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -4, 2, 1, -6],\n [-2, -4, -2, -3, -4],\n [-4, 6, 0, -1, 2],\n [6, 2, 2, 1, -2],\n [-3, -1, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -2, -4, -5, 1],\n [-3, -2, 2, 5, 3],\n [-4, -2, -3, -2, -2],\n [-1, 6, -5, 2, 6],\n [-3, -4, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -1, -6, 5, -4],\n [5, 3, -3, 5, 2],\n [-6, -5, 2, -6, 1],\n [-6, -3, -3, -6, 6],\n [0, -4, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, 2, -4, -6],\n [2, 1, -6, -3, 6],\n [-6, -3, 3, 1, -2],\n [0, 1, -3, -1, -6],\n [1, 2, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -5, 5, 5, 4],\n [1, 1, 1, 6, 6],\n [-2, 2, -5, 6, -4],\n [-1, 3, 2, -2, -6],\n [-6, 5, 6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 2, -5, 0, -3],\n [4, 2, -3, -6, -5],\n [-1, 2, 6, -6, -3],\n [1, 2, -6, -3, -4],\n [1, 5, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -6, 2, 0, 5],\n [3, -2, -4, -2, 6],\n [5, 4, -5, 5, -4],\n [5, 4, -2, -6, 3],\n [-1, 4, 5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 0, -4, 2, -3],\n [-4, -1, 0, -6, -1],\n [1, -2, 5, 1, -2],\n [-3, 2, -6, 0, 3],\n [-5, -5, -1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, -2, 3, -4],\n [5, 4, 3, 0, 1],\n [1, 1, 2, 3, -4],\n [1, -3, -4, 1, 2],\n [2, 4, 4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -4, -2, 2, -5],\n [5, 6, 0, 6, 5],\n [-1, -1, -1, 6, 1],\n [-1, -6, -2, -6, 4],\n [-6, 6, 6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 6, -4, -3, 3],\n [-1, 6, 0, -5, -1],\n [-4, -1, -1, 4, 3],\n [1, -3, -4, -1, -2],\n [-4, 4, 1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, -4, -3, 2],\n [-2, 0, -1, -2, 2],\n [-2, -3, 1, 6, -4],\n [-6, -2, 0, -4, 1],\n [-4, -5, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 0, 1, 5, -2],\n [3, 0, 0, -3, 0],\n [-2, 2, 4, 3, 3],\n [-5, 5, 4, 3, 3],\n [0, -3, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 4, -5, -4, 1],\n [-3, 1, -6, -5, -6],\n [1, 6, -1, -2, 6],\n [-5, 3, -4, 6, -6],\n [-5, 0, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 6, 0, -5, -4],\n [-3, -3, 0, 3, 2],\n [2, 6, -6, -3, 0],\n [6, -5, 1, -6, 5],\n [-1, -6, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 0, 1, -4, -2],\n [-5, 1, 2, 4, 3],\n [2, 0, 3, -3, 5],\n [4, -1, 4, 3, -5],\n [0, 2, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 5, 4, 1, 3],\n [5, 3, 4, 4, 3],\n [6, 0, -6, 3, -3],\n [3, 5, -1, 1, 6],\n [-5, 3, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 0, 4, -6, -2],\n [4, -4, 4, -1, 5],\n [-6, -3, 4, 5, 1],\n [0, 5, 4, -6, 4],\n [1, -6, 1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 0, -2, -2, 5],\n [4, -1, 6, -4, -5],\n [5, 1, -1, 0, -5],\n [3, 0, 5, 1, 2],\n [-6, 4, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -5, -2, 0, -3],\n [-3, -5, 6, -2, -5],\n [-1, -1, -6, -3, 3],\n [3, 5, -5, -3, -4],\n [-6, 2, -3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 5, -2, 0, -5],\n [-1, -1, -3, -4, -1],\n [-6, -1, -6, 4, 2],\n [5, -2, 2, 5, 1],\n [1, 1, 0, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -1, -5, 1, 0],\n [-4, -6, 3, 4, 6],\n [-6, -5, -2, 5, 1],\n [-1, -4, -3, -3, -2],\n [-2, 5, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, 4, 3, -4],\n [-6, -6, 3, -5, 2],\n [-1, -2, -4, 0, 2],\n [-4, 0, 6, -2, 1],\n [-2, 4, -3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 6, -3, 6, 4],\n [-3, -4, -6, 5, 2],\n [6, -1, -6, 0, -3],\n [-3, 6, 1, 2, 1],\n [1, -3, 0, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -3, 4, -5, 4],\n [-6, 6, -1, 4, 3],\n [-4, 5, -6, -4, -4],\n [-2, 2, 1, 1, -4],\n [5, 2, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 3, 2, -1, -1],\n [2, 0, -3, -5, 0],\n [1, -4, 1, 2, 5],\n [-5, -5, -1, 4, 5],\n [6, 5, -1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -5, -6, 3, -3],\n [-1, 3, 6, 5, -1],\n [1, -3, -2, -3, 0],\n [-3, 4, 4, 3, 2],\n [-5, -4, 0, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, 1, -4, 5],\n [4, -2, -5, 1, -5],\n [1, -3, -3, -4, 3],\n [-1, -2, 3, 5, -1],\n [0, -4, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -3, 6, 5, 4],\n [3, 3, -4, 0, 4],\n [4, -3, -3, 0, 3],\n [0, -1, -6, -4, -2],\n [4, -1, 4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -2, -5, 6, 4],\n [-1, -3, -6, -4, -3],\n [-1, -1, -5, 5, -5],\n [-2, -5, -2, 0, -1],\n [-4, 3, 3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 6, 0, 6, 0],\n [-6, 6, -5, 6, 1],\n [5, 6, 2, 6, -3],\n [5, 4, -6, 5, -5],\n [6, 4, -4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -5, 0, 5, -1],\n [3, -4, 0, -6, -2],\n [-6, -2, 6, 2, -4],\n [-4, 1, 3, 2, -3],\n [-1, -5, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 2, -4, 2, 3],\n [-3, -4, 6, 2, 3],\n [6, -2, 4, 4, -3],\n [4, -1, -1, -3, -6],\n [3, -1, 6, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 3, -2, -5, 0],\n [1, -1, -1, -6, -3],\n [-6, -2, -6, 5, 2],\n [-3, -1, 5, 2, 5],\n [5, -6, -4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 1, -6, 3, -2],\n [-3, 4, 1, 4, 2],\n [-5, -5, -6, 0, 6],\n [4, -3, 4, -4, 4],\n [5, 1, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, 6, -2, 4],\n [4, -6, -1, 5, -4],\n [-6, 0, 1, -2, 4],\n [0, -1, -3, -1, -4],\n [-2, 5, -5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -5, -1, -1, 2],\n [4, -2, 2, 5, 2],\n [-6, -4, 3, 6, -2],\n [-3, -2, -3, 6, 1],\n [6, 3, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -6, 1, 2, -1],\n [0, -3, 3, 5, -2],\n [4, 6, 1, 2, 4],\n [-4, 3, -4, -5, 2],\n [6, -5, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, -2, -1, 4],\n [-3, -4, 0, -4, -1],\n [4, -6, -1, 2, 1],\n [-5, 0, -5, -2, 2],\n [-3, 0, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 5, 6, -3, 5],\n [1, 3, 3, 5, 5],\n [-1, 5, 4, -4, 6],\n [6, -1, 1, -2, 5],\n [4, -3, 4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 4, 4, 6, -3],\n [2, 1, 6, -5, 3],\n [-4, 3, 5, 4, 2],\n [-3, 6, -6, 2, 3],\n [-1, 4, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 3, 1, -5, 6],\n [4, 0, -6, 3, -5],\n [-6, 2, 5, 5, 0],\n [-4, -5, 2, -1, -1],\n [3, 0, -2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, -3, -6, 6],\n [0, 6, -1, 2, 6],\n [0, -3, -2, -4, -5],\n [-5, 3, 5, 0, -2],\n [2, 1, 1, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -1, -5, -5, 6],\n [0, 1, -5, 2, 4],\n [-1, 3, -4, -4, -6],\n [1, -2, 2, 4, -3],\n [0, 6, 0, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -2, -5, -3, -1],\n [-3, 5, -6, 6, 3],\n [6, 1, -2, 2, 4],\n [0, -4, 6, 4, -6],\n [-6, 2, 3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -3, -6, -1, -1],\n [-4, 2, 0, 4, 1],\n [-2, 5, 2, -2, 2],\n [-5, 4, 5, 0, 2],\n [0, -2, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, 6, 1, -3],\n [-2, -4, -3, -4, -5],\n [3, -2, -3, -6, 0],\n [4, -1, -6, 6, -5],\n [4, 2, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, 6, -6, 4],\n [2, 5, -1, -1, 3],\n [-2, 4, 2, 4, -1],\n [-5, -1, 6, 3, -4],\n [2, -5, -5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 6, -1, -4, -6],\n [0, 3, 3, -2, 2],\n [-6, 5, -1, -6, 0],\n [-2, 1, 2, 2, 0],\n [3, 6, 5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 6, -3, 5, -1],\n [-3, 6, -5, 1, 0],\n [4, -1, 1, 5, 3],\n [4, 4, 0, 1, 5],\n [-6, 6, -4, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -3, 6, 1, -6],\n [6, -5, 3, 3, 5],\n [1, 6, 3, -3, 1],\n [-3, 1, 2, -2, 6],\n [3, -6, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 4, -1, 4, -2],\n [6, 6, 3, -4, 6],\n [-1, 2, 3, 3, 5],\n [-1, 3, 6, -2, -1],\n [-1, -6, -1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 1, 0, 3, -2],\n [2, -6, 5, -4, 5],\n [-6, 5, 6, 1, -3],\n [1, 5, 1, 2, 0],\n [-4, -5, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -3, 1, -1, 6],\n [-3, -2, -4, 4, 0],\n [1, 2, 4, -2, 5],\n [2, 2, -3, 2, -2],\n [-2, 6, 6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -4, -3, -6, -2],\n [-2, -4, 3, 5, -2],\n [0, -1, 1, 2, 1],\n [-4, 4, 0, -6, 3],\n [4, 5, -6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -2, -1, -2, -1],\n [-4, -3, 6, -6, 2],\n [6, -5, 3, 4, 6],\n [0, 3, 6, -2, -1],\n [2, -4, 3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, -1, -2, -4],\n [5, 6, 1, -2, 2],\n [1, -4, 2, -4, -6],\n [1, 1, 1, -1, -1],\n [-1, -1, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 4, 6, 0, 5],\n [6, 5, 5, 1, 0],\n [-4, -6, 5, -4, -3],\n [6, 2, -5, 0, -1],\n [4, 6, 4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 6, -2, -4, 1],\n [2, 0, 3, 4, -4],\n [2, 3, 4, -6, -6],\n [6, -1, 2, 6, -5],\n [5, -1, -1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 3, -6, 2, 5],\n [2, 4, 3, -1, -1],\n [-4, 0, -2, -4, -6],\n [0, -4, -6, 4, 6],\n [-3, -6, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 2, -3, 6, 0],\n [-4, 4, -5, 2, 5],\n [-6, 4, -6, 3, -5],\n [-5, 5, -2, -3, 3],\n [0, -5, 1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -2, 3, 0, 6],\n [-6, 1, 1, -3, -6],\n [3, 0, 6, -6, 3],\n [0, -3, 6, -5, 4],\n [4, 1, 5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 3, -3, -3, 6],\n [0, -3, -5, -2, -2],\n [4, -3, -4, -6, 0],\n [-3, 3, -5, -4, 5],\n [-4, 1, -6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 5, -4, 0, -6],\n [1, 5, 2, 2, 3],\n [0, 3, -3, 6, -4],\n [-3, 3, -5, -6, 5],\n [0, 0, -2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 4, -3, 6, 3],\n [4, -3, 6, -5, -5],\n [3, 1, -4, 1, 6],\n [6, 2, 6, -6, 3],\n [-1, 2, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -3, 4, -6, 1],\n [1, -1, -2, -3, -3],\n [4, 5, -6, 2, 1],\n [-6, 5, -6, -6, -1],\n [4, 3, -3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 3, 5, 5, -6],\n [-2, -6, -1, 1, 4],\n [6, 0, 0, 5, 6],\n [-5, 2, -4, 3, 2],\n [3, 0, 4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 0, -3, 6, 6],\n [1, -1, -1, -1, -5],\n [4, -6, 2, 5, -3],\n [-1, 0, 2, 2, 0],\n [3, 3, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, 2, -4, 0],\n [0, 6, 2, 3, -4],\n [6, -4, -4, 0, 0],\n [1, -4, -5, 6, 3],\n [-2, -2, -6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 6, -4, 0, -6],\n [5, -6, -5, 3, 4],\n [2, 0, 3, -5, -6],\n [-2, -5, -6, 3, 4],\n [-1, 3, 4, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 5, 6, -2, -5],\n [-1, -6, 0, -2, -1],\n [-1, 5, -6, 4, 4],\n [-4, 6, -1, -4, 2],\n [-4, -3, 3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -5, 5, -1, 5],\n [-1, -4, 4, 1, 1],\n [6, 5, -4, -2, 5],\n [-4, 2, -4, 2, -2],\n [-6, 4, 3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -4, 6, -6, 1],\n [-5, 4, 5, 5, 5],\n [1, -3, -5, 2, -5],\n [-4, 2, 2, 4, -4],\n [-1, -5, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 5, 3, -5, 0],\n [5, 3, -1, 2, -2],\n [1, 5, -5, 3, -1],\n [1, -3, 3, 6, 3],\n [-4, -1, 2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 1, 2, 1, -3],\n [5, 5, -5, -6, -4],\n [2, -4, 6, 6, -1],\n [2, 1, -1, -6, 3],\n [-6, 4, 3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -2, 5, -1, 2],\n [-2, -1, 1, -1, -6],\n [0, 1, 5, 5, 5],\n [-5, -6, 5, -3, 3],\n [2, -5, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -2, -2, -3, 1],\n [-5, 4, -5, -1, -6],\n [-2, 3, 6, 3, -2],\n [0, 0, 5, -1, 5],\n [4, 4, 4, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -2, 6, -4, 6],\n [6, -6, 5, 2, 1],\n [5, 0, 6, 2, 0],\n [5, 2, -6, 0, -5],\n [0, 6, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -3, 5, 5, -1],\n [2, -1, 4, 1, 5],\n [2, -6, 6, -4, 1],\n [-1, 2, -5, -5, 0],\n [6, -6, -2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -3, -1, -1, 3],\n [-3, -5, 3, 4, 2],\n [-2, 0, -6, 6, -3],\n [-6, 5, -4, 6, 1],\n [-5, -4, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -6, -3, 2, 0],\n [3, -3, -4, 0, -6],\n [4, -4, 1, 3, 6],\n [6, -5, -6, 1, 0],\n [4, -2, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 4, 2, 5, -3],\n [2, -1, 0, 2, 5],\n [-5, -4, -5, 5, 3],\n [4, 3, -5, -2, 5],\n [-4, 5, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, -6, -3, 0],\n [0, -6, 4, 0, -2],\n [1, -3, -3, -5, 6],\n [4, -2, -5, -4, -3],\n [-4, 0, 2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 3, -6, 4, 2],\n [-6, -3, 0, -2, 3],\n [-3, 1, 5, 2, -1],\n [5, -2, -3, -4, 4],\n [3, 5, -3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, -6, 0, -5],\n [4, -4, -5, 5, -4],\n [5, 6, 1, -6, 2],\n [0, -2, 3, -4, 0],\n [3, 0, 5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 1, 2, -6, 4],\n [-5, -3, 2, 3, 2],\n [0, 2, -2, 3, -4],\n [-6, 5, 4, 3, 0],\n [3, -5, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -2, -1, 3, 5],\n [2, 3, -5, -4, 5],\n [4, 5, 5, -4, 6],\n [-4, -4, -4, -3, 6],\n [-4, -2, 5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -6, 0, -3, 2],\n [-1, 2, -5, 1, 0],\n [-2, -5, -1, 5, 0],\n [6, 5, 2, 0, 6],\n [-1, 0, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 1, 4, 6, 5],\n [-4, -5, 4, -4, 6],\n [3, 6, -6, -2, -2],\n [2, 6, 1, 3, -5],\n [1, 4, 5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 3, -2, -6, -3],\n [0, 0, 1, 4, 1],\n [3, -4, -2, 1, -1],\n [-5, 2, -4, -6, -6],\n [-6, 2, -1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -6, -5, -6, -3],\n [3, 1, 6, -1, 6],\n [3, 1, 3, 0, -6],\n [-1, -4, -5, -2, -6],\n [-3, 5, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -1, 0, 4, 3],\n [5, -1, 2, -6, 1],\n [-1, 3, -4, 3, 6],\n [1, -3, 1, -4, -1],\n [1, 5, -3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -1, 0, 2, 4],\n [-5, 2, -2, 4, 2],\n [3, -3, 2, -2, 0],\n [0, 0, 1, -1, 4],\n [0, 3, -6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 4, -2, -4, 4],\n [0, -1, -1, 3, -3],\n [-5, -1, -6, 3, 1],\n [3, -6, -1, -1, -4],\n [4, -2, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 6, -3, 4, -2],\n [2, 3, 4, -5, 3],\n [0, -5, 1, 4, 4],\n [3, -2, -6, -1, 1],\n [-5, -4, 1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 3, -6, 3, -5],\n [0, -5, -6, 1, 2],\n [-1, -4, 0, -5, 2],\n [3, -4, 3, 5, -5],\n [6, 1, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -4, -3, 1, -5],\n [-6, -3, -6, -4, 5],\n [-3, -5, -4, 5, -3],\n [-1, -2, -2, 5, -2],\n [-4, 0, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 3, -4, 4, -1],\n [0, -1, 6, 6, -6],\n [1, 3, 4, 6, 0],\n [6, 0, 6, 2, 1],\n [-3, 3, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -4, 4, 3, 3],\n [-1, -1, -2, 3, 6],\n [-1, 5, 2, -2, -1],\n [-1, 5, 2, -1, -5],\n [6, -5, -5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 6, -1, 4, 5],\n [-6, -4, -5, 4, 1],\n [4, 2, -4, 2, -4],\n [0, 4, 3, 5, -5],\n [-4, 0, 4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 4, -3, 4, -2],\n [-4, -2, -4, 3, 2],\n [0, -4, -6, 3, -2],\n [-2, -3, 3, 1, -5],\n [6, -4, -4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, 2, 1, -4],\n [-2, 0, 1, -6, -5],\n [-2, 3, -1, 4, 1],\n [5, -3, -6, 3, -6],\n [2, -1, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 6, -5, 6, 1],\n [-3, -6, 2, -6, -6],\n [0, -5, 4, -3, -1],\n [6, -5, 2, 0, -4],\n [0, -6, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 4, -2, -3, 6],\n [1, -5, 2, 4, -5],\n [-6, -4, 3, 5, 6],\n [3, -4, -4, -1, -6],\n [-5, -2, 6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 3, -5, 2, -6],\n [6, 2, 4, -3, 5],\n [-1, 6, -3, -5, 3],\n [-4, 0, -6, 0, 3],\n [2, 5, 5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 2, -2, -5, 4],\n [6, 6, 0, 5, -4],\n [6, -2, 1, 5, -3],\n [3, -5, -5, -6, 5],\n [5, 2, -3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 4, -2, -3, -6],\n [-4, 2, 3, -3, 3],\n [-4, -3, -3, -1, -5],\n [-3, 0, 3, -2, -6],\n [4, 1, -3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 2, 2, 0, 5],\n [0, 5, 4, 3, 3],\n [-3, -2, 6, -2, -3],\n [3, 0, 6, -6, 4],\n [-1, -5, 3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -6, -6, -3, -3],\n [2, -2, -1, -2, 0],\n [2, 1, 1, -4, -6],\n [3, -5, 0, -5, -4],\n [-2, -3, 3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, 5, 6, 3],\n [-5, -4, 6, -3, 5],\n [-2, 1, 0, -2, 0],\n [-1, -3, -2, -2, 4],\n [-3, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 3, -1, 5, 3],\n [0, 3, 2, 4, -2],\n [4, 5, 6, 2, 1],\n [1, -5, 2, -3, -5],\n [-4, 4, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 3, 4, 0, 3],\n [0, 2, 2, -2, 0],\n [3, 6, 5, -3, -1],\n [-1, 1, 0, -5, 1],\n [-4, 4, -2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -4, 4, -3, -1],\n [-3, 0, -6, 6, 2],\n [-4, -4, 5, -5, -5],\n [0, 1, 5, 0, -4],\n [-6, -4, -3, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -2, 4, 3, 1],\n [1, -1, -2, 4, 2],\n [-4, 0, -2, 6, 1],\n [1, -5, -1, -6, -4],\n [4, -2, 6, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -5, -2, -1, 1],\n [-3, 6, -5, 3, 1],\n [1, -4, 2, 0, 0],\n [-2, 3, -5, 2, -2],\n [2, -2, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -6, -1, -1, 2],\n [1, 1, -1, -6, -2],\n [1, 1, 3, 5, 6],\n [-1, 3, 5, 5, 4],\n [2, -4, -6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 6, -6, -2, 0],\n [-2, 5, -3, -2, 0],\n [5, -4, -2, 3, 6],\n [3, 0, 6, -3, 0],\n [4, 5, -4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 6, 2, -1, -1],\n [1, 2, -5, -1, -2],\n [-3, 6, 4, -2, -3],\n [-2, 0, 5, -1, -3],\n [2, -1, 5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 2, 0, -6, 3],\n [6, 6, 0, -3, -4],\n [4, 2, 5, -3, -5],\n [3, 1, -6, -6, -6],\n [-6, 2, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 4, 3, 6, 2],\n [2, 3, 3, -1, 3],\n [1, -1, -6, 0, 5],\n [-1, -2, 6, 4, 0],\n [-1, -4, -5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, 5, 0, 5],\n [6, -3, 2, -1, -6],\n [2, 3, -5, 6, -4],\n [-1, 3, -4, 2, -1],\n [-3, -5, 5, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -4, 3, -6, 4],\n [-1, 1, -3, 2, -6],\n [-6, -4, 1, 1, 5],\n [-4, -4, 4, -6, -1],\n [-4, -2, -5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -6, -4, 6, -2],\n [-5, 6, -3, -3, 1],\n [1, -2, 1, 1, 0],\n [1, 3, 3, -4, -5],\n [1, 1, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 3, -6, -6, 4],\n [-4, 0, 0, -3, 5],\n [0, 2, 0, 5, 0],\n [4, 2, -3, 2, 2],\n [3, -5, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 5, -6, 3, -6],\n [1, -2, 5, 6, 0],\n [-1, -5, 1, 4, 4],\n [-5, 5, 0, 4, 2],\n [5, -6, 1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -3, 2, 3, -5],\n [-4, 3, 1, -5, -4],\n [0, 0, -4, 2, -6],\n [5, -1, -6, 3, 1],\n [3, 3, 4, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -6, -5, -4, 0],\n [2, 5, -4, -5, 3],\n [1, -2, -3, 1, -5],\n [-2, -3, -5, 5, -3],\n [-2, -6, 6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -2, 3, -1, 5],\n [-2, -5, -5, 0, -3],\n [6, 3, -1, 3, -6],\n [6, -5, -4, -4, 5],\n [1, 3, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 2, 6, -4, -2],\n [5, 1, -5, 4, -5],\n [6, 1, 3, 0, 0],\n [3, -2, 5, -3, 5],\n [6, 2, -1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -6, 2, -1, -4],\n [-6, 6, 3, -4, 5],\n [-1, 4, 4, -2, 3],\n [-1, 2, 5, 6, -4],\n [1, -4, 4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -2, -3, -5, 6],\n [-6, -3, 4, -1, 2],\n [3, 3, 6, -1, -4],\n [1, 5, -2, 4, -3],\n [-6, -6, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 4, -5, -5, 4],\n [-3, -5, 3, 1, 6],\n [6, 3, 3, -5, 6],\n [-5, 5, 0, 4, -3],\n [1, 5, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 3, 2, -2, -3],\n [-5, -6, 5, -2, 0],\n [0, 2, -6, -2, 0],\n [2, 4, -1, 4, -5],\n [2, 0, -1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -2, -1, 1, 4],\n [-5, 1, 6, 3, -6],\n [4, 3, -3, -3, 0],\n [-1, -2, 0, -4, -2],\n [-5, 2, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, 3, 4, 2],\n [4, 1, -1, -3, -2],\n [1, 0, -1, -5, -6],\n [-2, 2, 6, -3, -1],\n [-1, 0, -1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -4, 1, 6, -3],\n [-1, -5, 2, -4, 6],\n [2, -4, -4, 3, -1],\n [-5, -4, 6, 6, -1],\n [-6, -3, 3, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -2, 6, 2, 3],\n [1, -1, 4, 1, 6],\n [0, -3, -2, -6, 6],\n [0, -2, -5, 0, 3],\n [2, -3, 3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -5, -3, 5, -1],\n [-2, -4, -3, -1, -2],\n [1, 3, -4, -6, 6],\n [5, -2, -4, -1, 4],\n [-5, 3, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -6, 0, -1, 4],\n [-1, -1, 0, -2, 2],\n [-3, -2, -6, -4, 2],\n [-6, -5, -4, 6, 0],\n [-6, -5, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -4, 6, -6, -2],\n [5, -3, -6, 2, -4],\n [-1, -4, -6, -3, 4],\n [4, -5, 3, 2, -5],\n [-4, 2, 1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -6, -1, -4, -1],\n [-2, -3, -2, -5, -1],\n [-3, -2, -2, 1, -2],\n [-2, -3, -6, -5, -2],\n [4, -4, -5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -1, -4, -3, -1],\n [-2, 0, -1, 1, -3],\n [-4, 0, 4, 0, 1],\n [-5, -1, -2, 2, -4],\n [5, -1, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -3, -4, -4, 0],\n [4, 3, 1, 6, -5],\n [5, 2, 0, -2, -2],\n [5, -3, -6, -1, 3],\n [-4, -6, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -4, 6, 2, -6],\n [-1, 6, -1, 0, 0],\n [1, -4, -6, -6, -4],\n [0, -2, 6, 6, -2],\n [5, -6, 5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -3, -2, 3, -2],\n [-2, 5, 4, 1, 1],\n [-6, 6, -5, 5, 0],\n [2, 6, -6, 3, 4],\n [2, 3, -2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 2, -5, 0, -1],\n [-4, 1, -4, -1, 6],\n [-3, 3, 4, -4, 4],\n [1, -3, -6, 6, -3],\n [1, 5, 2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -1, -2, 1, -2],\n [-3, 0, 6, -2, 1],\n [1, 4, 1, 3, -1],\n [-3, 6, 6, 1, 2],\n [-6, 2, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, 1, 1, 4],\n [-2, -3, -6, 1, 1],\n [-6, -6, -3, -2, 5],\n [-6, 3, -4, -5, 5],\n [6, -6, -2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 1, -4, 4, -4],\n [-1, -4, 0, 3, -1],\n [-2, -6, 5, -5, -4],\n [-3, -2, -1, 4, 6],\n [5, -2, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 3, -6, 1, 1],\n [5, 2, 1, 4, -3],\n [5, 6, 3, 0, -2],\n [6, 5, 5, -2, 4],\n [-2, 6, -1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -6, 6, 5, 0],\n [4, -5, 4, 6, 0],\n [5, 4, 0, 3, 1],\n [1, 5, -4, 6, 1],\n [5, 0, -4, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -3, -5, 3, -3],\n [-3, -1, 4, -3, 3],\n [6, 6, -6, -1, -2],\n [0, -5, 1, 3, 6],\n [0, 1, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -1, 1, -5, 0],\n [-3, 0, 1, -3, -2],\n [-3, -1, 3, 6, 6],\n [-1, -6, -4, 4, -6],\n [-4, -2, -5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, 5, 5, 3],\n [0, -1, 5, -1, 4],\n [-3, 6, 4, 0, -1],\n [3, -3, -2, 1, 5],\n [1, -3, 1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 6, -4, -5, 1],\n [-4, 6, -2, 5, 2],\n [4, -5, -6, -2, 2],\n [2, 6, -5, 3, -1],\n [-2, 6, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 2, -3, -2, 4],\n [0, 4, 3, -2, 2],\n [-5, -1, 2, 6, 2],\n [2, 2, 1, 3, -2],\n [-1, 5, 6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 6, -6, -6, 0],\n [-2, -4, -2, -4, 6],\n [-3, -4, 4, 3, 6],\n [-5, 1, 6, 4, 2],\n [-5, -1, -1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -2, 1, 1, -1],\n [4, -6, 2, 6, 4],\n [2, -1, -5, -6, 6],\n [-1, -4, 6, 2, 6],\n [-5, -3, 0, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 6, 4, -2, 1],\n [6, -5, -2, -4, 3],\n [4, 6, 1, -1, 6],\n [1, 5, -6, -6, 4],\n [-2, -2, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 6, -1, -6, 6],\n [2, 6, -6, 6, -6],\n [6, 1, 2, 1, -6],\n [-5, 5, 5, 3, 1],\n [5, -2, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 2, 1, 6, -4],\n [-6, 0, 6, -1, -4],\n [-2, 1, 4, -6, -1],\n [4, 2, -4, -3, 5],\n [-3, -4, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 3, 0, 5, 1],\n [0, 6, -5, 0, 6],\n [-5, 6, -6, 1, -4],\n [-4, 2, -1, 5, 3],\n [4, 6, 4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -4, 5, 6, -6],\n [6, 5, -6, -1, -2],\n [1, 0, -2, 5, -1],\n [-6, -6, 3, 3, 6],\n [-1, 0, -2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 6, 0, -1, 3],\n [5, 5, -6, 4, 0],\n [3, -1, 0, -4, -5],\n [0, -4, 2, -3, 3],\n [-5, -5, -2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 0, -3, 4, -2],\n [1, -5, 0, 0, 5],\n [2, -6, -3, -3, 1],\n [3, -5, -5, 2, -5],\n [2, -1, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -4, -5, 5, 6],\n [-5, -2, 1, 4, 6],\n [5, -4, 5, 6, 3],\n [4, -5, 6, -1, 6],\n [-2, -3, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, -2, 5, -3],\n [5, 5, -1, 2, -1],\n [5, -1, -5, 6, 6],\n [-2, 4, 4, 2, -6],\n [-6, -1, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -4, -3, -6, -6],\n [-3, 3, -1, 0, 3],\n [4, -3, -2, 0, -4],\n [-6, -5, -3, -3, 6],\n [-3, 2, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 2, -4, 3, 5],\n [6, 3, 5, 6, -5],\n [-3, 6, 0, -3, -6],\n [-6, 6, 5, -3, 0],\n [4, 1, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -3, 0, 4, 2],\n [-3, -1, -5, -6, 1],\n [2, -3, -3, 0, -2],\n [-3, -6, -3, 3, 2],\n [0, -3, -4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 4, -3, 4, -3],\n [0, 3, 3, -1, -2],\n [-2, 5, 6, 2, 6],\n [0, 2, 1, -2, -1],\n [2, -3, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, 3, 5, 3],\n [6, -5, 1, 1, 0],\n [0, -3, -1, 3, -2],\n [-6, -6, 5, 2, 6],\n [4, 4, -6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, 6, -2, -4],\n [5, -6, -2, 3, 3],\n [4, -3, 0, 5, 5],\n [-4, -6, 4, 4, -3],\n [5, -4, 1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 1, 4, 1, 0],\n [-6, 0, -5, -5, -4],\n [-6, -1, 6, -2, 4],\n [5, 0, 5, -1, 6],\n [4, -6, -5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 2, 0, 3, -5],\n [-2, 3, -3, 2, -2],\n [-5, -6, 0, -6, 6],\n [3, 6, 1, -2, -3],\n [-3, -3, 1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, -5, -3, 4],\n [-1, -6, -5, -3, -4],\n [-3, 3, -6, -5, 3],\n [-2, -5, -1, 0, 1],\n [5, 6, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -4, 5, 3, -1],\n [6, -3, 2, -1, -4],\n [4, 6, -1, 0, -5],\n [5, -3, 3, 6, 0],\n [-1, 2, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 6, 5, 4, 0],\n [-2, 3, 5, -2, 3],\n [-3, 3, 2, -5, 2],\n [-6, -4, -1, 4, 6],\n [2, 1, -6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -5, 4, 5, 2],\n [-3, 1, 6, -4, 3],\n [-5, 1, 4, -4, 4],\n [-5, -1, -1, 0, -6],\n [-2, 3, -2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 4, -5, 5, 1],\n [0, -4, -4, -2, 6],\n [6, -6, 0, -3, -2],\n [6, -3, -1, -2, -3],\n [-2, 5, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 4, -6, 4, -2],\n [0, -6, 5, 1, -4],\n [-4, 4, -3, 6, 5],\n [6, -2, 4, -4, 2],\n [5, 0, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 4, -5, -5, -1],\n [3, -6, -4, -5, -6],\n [5, 1, -2, 4, 2],\n [1, 3, 6, 1, 4],\n [2, -6, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -6, 2, -4, 5],\n [1, 4, -5, 5, -4],\n [0, -1, -6, -2, 5],\n [4, 5, -6, 4, 1],\n [-2, 0, -5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 4, -1, 4, -1],\n [0, 2, -2, 1, -1],\n [-2, 1, 6, 5, -1],\n [-3, 6, 0, 1, 1],\n [-1, -2, 5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 3, -4, 2, -3],\n [-5, 2, -5, 3, 4],\n [5, 1, 6, -5, 3],\n [-5, 4, -2, 5, -2],\n [3, -5, -5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -5, -5, -1, 3],\n [-6, 6, -3, -6, 3],\n [-5, -2, -6, 1, 0],\n [0, -1, 6, -3, -1],\n [6, 2, 3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -4, 2, 3, -3],\n [-2, -1, -1, -2, 3],\n [3, 6, -6, -6, -2],\n [3, -5, -4, 4, 6],\n [-3, 3, 0, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -6, -2, -2, -5],\n [2, 0, 3, -3, 1],\n [-2, 0, 6, 4, 2],\n [0, 6, -1, 5, 4],\n [3, 6, 3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -3, -1, 2, -3],\n [-2, -5, 4, 2, 6],\n [6, 2, 6, 0, 5],\n [2, -3, 3, 1, -1],\n [-3, 4, -6, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 5, 0, 3, -2],\n [-4, 4, -3, -1, 1],\n [-4, 0, 3, -6, 1],\n [5, 2, 0, -5, -6],\n [-1, -6, 2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 6, 5, 0, 3],\n [1, 5, 0, 3, 1],\n [1, 3, -6, 2, -3],\n [-4, 4, -1, 5, -5],\n [-3, 2, 3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -5, -2, 6, -6],\n [-2, 0, -3, 6, 2],\n [2, 1, 5, 6, 6],\n [1, -5, 2, -5, -4],\n [1, 2, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 2, 1, 3, 6],\n [0, 0, -6, 2, 1],\n [-3, 1, 4, 4, 4],\n [-5, -5, -3, 3, -2],\n [0, -4, -5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 1, 5, -5, -3],\n [5, -4, -2, -4, -2],\n [-2, 1, 1, 6, -6],\n [4, 2, 3, -4, 2],\n [-5, 4, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 2, 0, -2, 6],\n [-4, -3, -3, 2, -6],\n [6, 4, -2, 3, 6],\n [-4, -5, -3, -1, -6],\n [4, -5, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 5, -3, -3, 5],\n [-1, 4, 6, 5, -4],\n [5, 6, -6, -3, 0],\n [1, 6, 3, 3, -2],\n [6, 6, -6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 2, -5, 6],\n [2, -3, 4, 6, -4],\n [3, 0, 3, 3, 5],\n [-6, 5, -2, -4, -6],\n [6, 5, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 1, 6, 2, 6],\n [2, -5, 4, -3, -2],\n [1, -3, 5, 3, -5],\n [1, 4, -1, -3, -6],\n [-3, -4, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 1, -1, -1, 2],\n [1, -4, -2, -2, -6],\n [-6, -5, -2, 4, 0],\n [5, 0, 6, -5, 6],\n [-1, 6, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 6, 4, -5, 6],\n [4, -3, 5, 3, 6],\n [6, 6, 1, -1, 4],\n [-2, -2, 6, 5, -1],\n [4, 3, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 5, -5, 2, 4],\n [4, 1, 5, -5, 2],\n [2, 4, -1, 6, -5],\n [-2, -2, 3, -5, 1],\n [2, -5, 6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -6, -4, -2, 3],\n [3, 1, -6, 2, 5],\n [3, 2, 4, 5, 0],\n [-1, 0, 3, -6, -2],\n [6, 3, -1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -5, 1, -4, 3],\n [5, -3, 3, -5, 3],\n [5, 4, -3, 5, 3],\n [5, 5, -4, 0, 4],\n [2, 6, 3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -2, 4, 3, -3],\n [4, 4, 1, 4, -4],\n [3, 1, 1, -3, -2],\n [3, -1, 4, 6, -3],\n [3, -5, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 0, 5, 6, 0],\n [2, 5, -3, -4, -6],\n [-3, -4, -5, -3, -6],\n [6, -6, -3, 6, -4],\n [6, -1, -3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -3, -5, 5, -3],\n [-4, -1, -4, 6, 3],\n [6, -4, 0, -1, -6],\n [-6, -1, 4, -6, 1],\n [4, -2, 3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -4, 0, 6, -3],\n [1, -4, 1, 5, 3],\n [-5, 0, 1, 1, -3],\n [-3, 4, -5, 1, 1],\n [-5, 4, -5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -3, 4, 4, 2],\n [-6, -5, -5, 6, 0],\n [-5, 0, 3, 2, -1],\n [0, 0, -6, -4, 6],\n [3, -6, -6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 3, -3, -5, 0],\n [3, 3, -1, -6, 1],\n [-4, 5, 6, 3, -3],\n [-6, -4, 6, -5, -1],\n [-6, 3, 0, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -5, -3, -5, -6],\n [-2, 1, -5, -6, -2],\n [-2, -6, -6, 5, 5],\n [0, -5, -5, -4, 2],\n [-3, 2, -1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 0, 3, -4, -1],\n [2, 0, 5, -5, 6],\n [-3, 2, -4, -1, -3],\n [-2, 3, 0, 5, -5],\n [-5, -2, 5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 1, -6, -1, 6],\n [5, -2, 0, 0, 2],\n [-2, 0, -3, 4, -6],\n [2, -2, -1, 3, -4],\n [-2, 0, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -3, -1, 2, 1],\n [-6, 6, 3, 6, 3],\n [3, -2, -6, 5, -6],\n [3, -3, 5, -1, -3],\n [0, 6, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 4, -1, 5, -1],\n [-5, -1, 2, -4, -2],\n [6, 6, -4, -5, -5],\n [4, -5, -2, 0, 4],\n [-5, 3, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -4, 3, 2, -4],\n [4, 5, -3, 4, 1],\n [0, -1, -4, -3, 4],\n [-1, -3, 5, 1, -1],\n [1, -3, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 1, -4, -3, -5],\n [-3, 6, 5, -2, -4],\n [-5, 1, -1, 5, -2],\n [2, 0, -5, 4, -5],\n [-6, -6, -3, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 2, 0, 3, 1],\n [1, -2, -3, 4, -3],\n [5, 4, -3, 3, -2],\n [5, 3, 5, 5, 3],\n [6, 6, 6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 2, -5, -6, 2],\n [6, 4, -6, 6, 1],\n [0, -2, 6, -6, 3],\n [-1, 3, -3, 4, -6],\n [-4, 5, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -1, -5, -1, 3],\n [-6, 5, -4, -6, 1],\n [-5, 1, -4, -5, -3],\n [5, 1, 0, 1, -4],\n [-1, 1, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -4, 2, -3, 2],\n [-1, 0, 4, 1, -3],\n [-1, 3, 6, 2, -1],\n [-6, 3, -4, -3, -6],\n [-6, -1, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 2, -1, 4, -3],\n [4, 3, 6, 4, 4],\n [3, -4, 3, 1, 4],\n [-2, -5, 0, 5, -1],\n [-5, -1, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 1, -6, 2, 0],\n [-3, 1, 1, 5, 3],\n [-2, -5, 4, -4, -6],\n [3, -5, -6, 6, 6],\n [3, 0, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 6, -2, -6, 5],\n [1, 5, 6, -6, -1],\n [-1, 5, 4, 5, -5],\n [4, -1, 0, 1, -3],\n [0, 2, 3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 4, 1, -5, -2],\n [5, 1, -4, 3, 0],\n [0, -4, -4, -1, -2],\n [4, 4, -6, -1, 4],\n [1, -3, 5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -2, 0, -5, -5],\n [1, -4, 1, 6, 1],\n [-1, -5, 0, 3, 3],\n [5, -3, 4, 4, -5],\n [3, 1, 6, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 1, -6, -1, -6],\n [1, 1, 2, -6, -6],\n [0, -1, -2, -3, -5],\n [-5, -6, -1, -2, 5],\n [6, 0, 3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -4, 4, 4, -4],\n [5, 3, 3, -4, -1],\n [1, -4, -1, -2, 5],\n [3, -3, -3, -3, -4],\n [6, -3, 0, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -5, -6, -6, 0],\n [1, -2, 1, 3, -4],\n [6, 1, 4, 2, -4],\n [-2, 5, 5, 3, -6],\n [-4, 5, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -2, 5, 6, -4],\n [-4, -5, 5, 2, 1],\n [-3, 2, 0, 5, 0],\n [-2, -1, 6, 5, 4],\n [-4, -4, 1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 3, -1, 3, 1],\n [2, 2, -3, 2, -5],\n [6, 6, 6, -1, -1],\n [-2, 0, -2, 6, 3],\n [-5, -4, -3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -6, 3, 6, 3],\n [-4, -1, -4, -3, 2],\n [2, 3, 5, 4, -3],\n [6, 3, 3, -3, 3],\n [6, -3, -4, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 3, 5, -6, 6],\n [5, 1, -3, 0, -3],\n [5, -6, 6, 5, -3],\n [0, -5, -2, 3, -1],\n [0, -2, 4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -5, 4, 1, 6],\n [1, -1, 1, -3, 0],\n [-1, -6, -3, 3, 3],\n [-4, 5, 1, 0, 1],\n [1, 2, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 0, -4, -6, 0],\n [1, 1, -4, -3, -3],\n [0, -3, 0, -1, -3],\n [6, -6, 6, -3, 6],\n [5, -5, 4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -3, -4, -5, 2],\n [0, 3, 4, 1, 4],\n [0, 0, -4, 5, 0],\n [-2, -3, 2, -6, -6],\n [0, 1, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -5, 0, 2, 0],\n [-1, -1, -1, 5, 0],\n [4, -4, -3, 1, -2],\n [-6, -2, 0, 6, 4],\n [0, -3, -3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 6, -2, -6, 2],\n [4, 1, 5, 4, 2],\n [-2, -3, -5, 3, 2],\n [3, 1, 6, 0, 0],\n [1, 1, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -2, -2, -1, -6],\n [1, 5, 3, -2, -2],\n [3, -4, 6, 2, -5],\n [5, 3, 4, -3, -2],\n [-4, -1, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 4, 6, -3, 0],\n [4, 4, -4, -6, 6],\n [5, 6, 3, 6, -3],\n [-2, 5, -5, 0, 0],\n [-2, -2, 5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 2, -5, 3, 0],\n [-1, 2, 2, 6, -6],\n [-2, -4, 6, -5, 1],\n [4, -2, -2, -3, -5],\n [-2, 1, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 3, -6, 6, 2],\n [6, -2, -3, 6, -2],\n [5, 2, 3, 0, -5],\n [1, 3, 5, 6, -1],\n [4, 3, 5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -6, -5, 0, 6],\n [5, 5, -6, -3, -4],\n [6, -5, -6, 0, -3],\n [2, -5, 6, 6, -6],\n [-1, 0, 5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 0, -4, 4, -3],\n [1, 1, -6, -1, 6],\n [3, 4, 1, 6, -1],\n [1, -5, 1, 1, 0],\n [-2, -4, 5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 1, -4, 3, -2],\n [-3, 3, -5, 6, -1],\n [-6, -3, 1, 1, 3],\n [-1, 1, -3, -3, -4],\n [6, 4, 3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 2, 2, 4, 0],\n [-4, -1, -1, -4, 3],\n [-3, 2, 2, 5, 6],\n [4, -6, -1, -2, 1],\n [4, 1, -6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 5, -3, 4, -1],\n [4, -1, 6, 1, -4],\n [-1, -4, -4, 6, 6],\n [-1, 0, 0, 2, 6],\n [-3, 5, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 5, 5, 5, 6],\n [-6, 0, 5, 5, -1],\n [6, 1, 6, 0, -2],\n [5, 1, -2, -1, -5],\n [1, -4, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -4, 6, 4, 4],\n [-6, -5, 4, 2, 6],\n [0, 0, -3, 6, 3],\n [-2, 1, -6, -5, 5],\n [-2, 6, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -2, 0, 1, 3],\n [3, 4, -2, -2, 6],\n [6, 1, -5, 2, -5],\n [-1, -5, -6, 5, -5],\n [5, 6, 2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 1, -6, 6, 4],\n [-4, -3, 1, -3, 3],\n [-1, 6, 6, -6, 6],\n [-2, -2, -6, -1, -5],\n [5, 1, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -5, 0, -6, 6],\n [-6, 1, 4, 2, -1],\n [0, -4, 6, -6, 1],\n [-4, -2, 1, 1, -4],\n [6, 2, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 6, 3, -5, 0],\n [5, -1, -3, -1, -3],\n [1, -2, 5, 6, -2],\n [-2, 2, -1, 1, -1],\n [3, -2, 0, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -6, 6, -5, 3],\n [-5, -3, -1, -5, 1],\n [-2, -3, -1, -1, -1],\n [-1, 0, 4, 6, -5],\n [2, 6, 1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -3, -3, -6, 6],\n [3, 2, 4, 2, -6],\n [0, -2, 0, 1, 1],\n [3, 2, -1, -5, 4],\n [-1, -1, -3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, -6, -1, 4],\n [0, -5, -3, 4, 1],\n [2, 5, 1, -3, 5],\n [-6, 1, -4, 1, 3],\n [-2, 5, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -5, 2, -6, 2],\n [-5, 6, -4, 0, 3],\n [2, 6, 4, -2, 4],\n [1, 5, 6, -2, 2],\n [-3, -6, -1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 3, 0, 3, 6],\n [-5, 0, 3, -4, -4],\n [5, -1, -6, -6, 6],\n [4, 5, -3, 4, -4],\n [6, 0, -5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 3, 3, -6, 4],\n [3, -4, 0, 1, -4],\n [-1, 5, 1, 4, 3],\n [3, -1, -5, 4, -5],\n [-1, -5, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 0, 3, -6, -4],\n [6, 4, -1, 0, 4],\n [6, 0, -3, 6, 3],\n [6, 2, 0, 1, 0],\n [-3, -3, -3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 0, -3, -2, 5],\n [-3, -1, 4, -5, -5],\n [2, 0, 2, -5, 0],\n [-6, 1, -3, 4, 6],\n [6, 0, -1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, -6, 6, -6],\n [-2, 0, -2, -6, -4],\n [5, 6, 3, -5, -5],\n [4, 2, 4, -5, 3],\n [6, 2, -5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 1, -3, 6, 1],\n [-1, 2, 3, 1, 3],\n [4, -3, -2, 6, 0],\n [0, -4, 3, 3, -5],\n [-2, 4, 0, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 0, 2, 5, -5],\n [-6, -5, 2, -6, -4],\n [2, -4, -4, 1, -2],\n [-6, 6, -1, -4, -3],\n [4, -1, -3, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -4, -1, 1, 3],\n [4, 5, 3, -6, 5],\n [2, -1, 5, 3, 3],\n [0, -4, -3, 6, 0],\n [-5, 4, 3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, -3, -4, -2],\n [-2, -2, 4, 2, 6],\n [-1, -4, 3, -3, -6],\n [5, 5, 0, -2, 0],\n [5, 6, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -5, -3, 5, -5],\n [-4, 3, 3, -6, 6],\n [1, -3, 5, -5, 0],\n [6, -4, -4, 6, 6],\n [3, 4, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -3, 5, 5, 1],\n [2, 6, -6, 2, 4],\n [-3, 1, 4, 1, 0],\n [1, 6, -3, 4, 4],\n [-2, 4, -2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 3, -6, -4, 3],\n [5, -5, 5, -6, 3],\n [2, -5, -3, -6, 3],\n [-3, -6, 0, 2, -1],\n [-3, 0, 1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 0, 4, -3, 0],\n [2, 6, -2, -3, -5],\n [3, -6, 3, -1, 4],\n [4, 2, -6, -6, 5],\n [-6, -5, 6, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -3, 3, -3, -6],\n [6, 3, 3, 1, 2],\n [-1, 4, -1, 5, -4],\n [3, -2, -5, 6, -4],\n [-4, -5, 2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 2, 2, 1, 5],\n [-2, 1, 3, 0, 5],\n [-6, 4, -5, 6, 0],\n [3, 6, 5, -6, 3],\n [-1, 5, 1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -1, 0, -2, -6],\n [-4, 1, 1, 6, 1],\n [3, -5, 5, 0, -3],\n [2, -4, 2, 0, 5],\n [4, 2, -3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 2, -4, -4, 6],\n [-4, 6, 2, 6, -1],\n [-2, 5, -2, -4, 4],\n [0, -3, -6, 5, 0],\n [4, 3, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -1, 1, -1, -3],\n [-4, -3, -6, 6, 3],\n [1, 4, 3, 6, 5],\n [-5, 3, 4, 3, -2],\n [-6, 1, 1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 3, 3, 0, -3],\n [5, 1, 6, -2, 4],\n [5, 0, -4, -3, 2],\n [-5, 1, 3, -1, 1],\n [-3, 4, -3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, -2, -5, 3],\n [-3, -6, 3, -4, -6],\n [-5, 5, -5, 5, 3],\n [5, -6, 0, -4, -2],\n [-1, -1, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 2, -6, 1, -2],\n [2, 1, 3, -4, 0],\n [6, 2, 3, 0, 6],\n [6, -2, -6, 3, 1],\n [5, -5, 2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -4, 6, -6, 3],\n [1, 1, 0, 5, 6],\n [4, 1, -2, -6, 0],\n [-6, -3, 6, 4, 6],\n [-2, 6, 3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -6, 0, 4, 6],\n [-4, 5, 1, -6, -2],\n [2, -4, -3, 1, 3],\n [-1, -1, 6, -5, 0],\n [6, -1, 3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 4, -5, 3, 6],\n [5, 6, 4, 0, 4],\n [0, 2, 3, -1, -5],\n [2, -1, 5, -6, -2],\n [-5, -1, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 4, -4, 2, 1],\n [1, -4, 3, -6, 3],\n [-6, 6, 0, 6, -5],\n [-2, -2, -2, -2, -2],\n [1, 6, -5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 6, 5, -1, 0],\n [-6, -2, -6, 5, -4],\n [1, 5, 1, -4, -1],\n [-1, -1, 5, -1, -2],\n [4, 1, -4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -4, -5, 1, 4],\n [-4, 1, -1, 3, 2],\n [-1, -3, 5, 0, -3],\n [6, -4, -6, 5, 0],\n [-5, 1, -5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -6, 3, 0, 0],\n [6, 3, 6, 2, -1],\n [-2, -2, 5, 6, 2],\n [6, 6, 4, -3, -5],\n [6, 6, 6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -2, 6, -1, -3],\n [4, 2, -3, -6, -6],\n [-6, 4, -6, 5, 6],\n [3, 5, -3, -6, 1],\n [-6, 2, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, 5, -5, 1],\n [-3, 3, 4, -5, -2],\n [3, -2, 1, -3, -5],\n [-6, 5, 4, -4, 4],\n [0, -2, 1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 3, -1, 6, -5],\n [2, 5, -6, 0, -3],\n [2, -1, -6, -1, -6],\n [0, -3, 5, -1, -2],\n [5, -6, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 3, 1, 5, 2],\n [1, 0, 3, -4, 6],\n [6, 4, 4, -2, -3],\n [-1, -6, -2, 2, -2],\n [1, -5, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 6, 4, -4, 0],\n [2, -3, 6, 2, 2],\n [-4, -5, -4, -2, -3],\n [4, -2, 1, -1, 5],\n [4, -6, -6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -4, 4, -3, -1],\n [3, -1, 1, -6, -4],\n [-2, -3, 0, 4, -1],\n [0, 6, 2, 4, -4],\n [5, -6, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 2, -4, 0, 2],\n [-2, 0, -3, -5, 3],\n [0, 1, 0, 2, -1],\n [0, -1, 6, 4, 0],\n [5, -4, 2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -3, 0, 4, -3],\n [6, -2, -5, -3, 5],\n [-6, 3, 5, 2, 2],\n [5, 1, 1, -4, -2],\n [-3, 1, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -3, -6, 3, -3],\n [-4, -2, -4, 2, 5],\n [0, -1, 3, -6, -1],\n [0, -4, 1, 3, -5],\n [1, -2, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -3, 5, 3, -1],\n [2, -6, -5, -4, -1],\n [6, -5, 4, 4, 2],\n [3, -5, -2, -6, 1],\n [-1, 1, 5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 3, 1, 0, -4],\n [-2, 0, -2, 3, -4],\n [2, 6, 5, 0, 4],\n [-3, -3, 1, 0, -5],\n [-6, 1, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 3, -1, 2, -4],\n [-2, -4, -6, -2, -5],\n [-5, -5, 2, -6, 1],\n [3, -3, -1, -4, 6],\n [-2, -2, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 6, 0, 0, -4],\n [-2, 0, 4, -3, 3],\n [-3, 6, -6, 1, -1],\n [1, -1, 6, 4, 6],\n [5, -3, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 5, 2, 4, -4],\n [-4, 5, -4, 6, -2],\n [1, -6, -6, 0, 6],\n [-2, -3, -6, 3, -2],\n [2, 3, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -1, 5, -4, 4],\n [3, 2, -4, -6, -5],\n [-1, 5, -5, 4, -3],\n [4, -1, -4, 3, 4],\n [-3, -2, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -6, -3, -4, -4],\n [-6, -2, 4, 6, -1],\n [-1, 5, 1, 5, 6],\n [-1, -1, -3, 6, 4],\n [3, 5, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -3, -1, -6, 0],\n [-3, 5, -6, -4, -3],\n [1, -1, -4, 5, -1],\n [-2, 0, -2, 0, 3],\n [0, 0, 4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -1, 0, 2, -3],\n [-3, 5, -5, -3, 3],\n [4, 1, 6, 4, -2],\n [0, 4, -3, 3, 0],\n [5, -1, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 0, 1, 3, 4],\n [6, -3, -4, -6, -2],\n [3, 3, 2, 4, 0],\n [-5, -4, -6, -5, 6],\n [3, 3, 1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 6, 6, -3, -1],\n [-1, 5, -3, 4, -2],\n [-2, 4, 2, -1, 0],\n [-5, -1, 0, 1, 1],\n [5, -6, -3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -4, -6, 2, 1],\n [-2, 4, -5, -2, -5],\n [6, -1, 2, -5, 5],\n [3, 0, -3, 2, 5],\n [3, 1, 3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -3, -1, -1, 5],\n [-6, 2, -5, 6, -5],\n [-2, 3, 1, -3, -3],\n [1, 6, -6, 5, 6],\n [0, -2, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 6, 4, -3, -1],\n [4, 2, -3, -3, 2],\n [3, -4, -6, -2, 4],\n [-2, -3, 0, 4, 5],\n [-1, -1, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 0, 2, -5, 0],\n [2, 4, -1, 0, 6],\n [-5, -5, 0, -6, 1],\n [3, 4, 3, -2, -1],\n [-4, 1, -6, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 6, 0, 4, 6],\n [1, -4, 3, -5, 5],\n [1, -3, 3, 6, 4],\n [-1, -5, -2, -6, -4],\n [-6, -4, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 0, 2, 4, 5],\n [4, 2, 5, -1, 1],\n [5, 2, 1, -6, 0],\n [4, 0, 2, -5, 4],\n [5, 4, -6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -1, 2, -6, 6],\n [0, 1, -4, -5, -2],\n [4, 5, -2, 1, 3],\n [-1, 3, -4, -1, -4],\n [-3, 0, -1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -3, -3, 6, 3],\n [5, -1, -4, 4, -5],\n [-4, -6, 4, 3, -2],\n [6, -4, 0, -2, 5],\n [6, -5, -5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -4, 1, 1, 1],\n [2, -1, -5, -2, -2],\n [5, -3, -3, -3, 5],\n [-1, -1, 4, -5, -1],\n [1, 2, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -1, 6, -6, 1],\n [-5, -1, -5, -3, 1],\n [-5, 4, -4, 3, 4],\n [-6, -6, -1, 2, 3],\n [-6, 0, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 4, 6, -1, -2],\n [-4, 2, -4, -1, -3],\n [6, 1, 3, 4, -1],\n [-4, -4, 3, -6, 0],\n [-5, -1, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -1, -1, -6, -2],\n [-3, -1, 2, -6, 3],\n [-1, -3, 4, -1, 3],\n [-1, -2, -2, -6, -2],\n [-2, 1, -6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 3, 1, -2, -2],\n [4, -1, -6, -5, -3],\n [-4, -6, 1, 4, -4],\n [4, 1, 5, 2, 6],\n [3, -5, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, -6, -6, 5],\n [-3, 0, -5, -2, 1],\n [-5, -1, -3, -3, 0],\n [1, -1, 4, -3, -2],\n [0, -2, 5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -3, -5, 5, -2],\n [3, -1, 2, -6, -2],\n [-4, 6, 5, -5, 2],\n [5, -6, 4, 0, 4],\n [3, 3, 2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -2, 2, -1, -5],\n [-4, -5, 6, -5, -3],\n [-2, 6, -2, 4, -5],\n [-3, -5, 5, 4, 4],\n [1, 5, 3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 3, 4, -3, 3],\n [6, -2, -3, -3, 6],\n [0, 0, 5, -1, -5],\n [-3, -4, -6, 6, -6],\n [-6, 3, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 5, -5, 6, 0],\n [1, -1, -6, -4, 0],\n [-5, 4, -5, -4, -2],\n [-1, -3, -4, -5, -2],\n [-2, 4, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -1, 6, -2, -6],\n [2, 3, -5, -4, -2],\n [-6, -3, -1, -2, 4],\n [2, 5, -6, 1, 0],\n [1, 2, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -5, -2, -6, 4],\n [2, -5, 0, 2, -4],\n [-2, 4, -4, 2, -2],\n [-3, 3, 2, -5, -6],\n [0, 2, 3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 4, -2, -5, -2],\n [6, 1, -5, -2, -6],\n [-1, 4, -6, 6, -2],\n [1, -1, 6, 0, -2],\n [2, 3, 6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 6, -5, -5, 1],\n [2, 6, 2, 3, 4],\n [0, -1, -6, 2, -3],\n [-2, 0, 4, 1, -6],\n [4, 1, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 2, -1, 3, 2],\n [5, 1, 6, -1, -1],\n [-4, -2, 1, -3, 4],\n [-6, 1, -1, 3, 6],\n [-3, 4, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 6, 6, 5, -4],\n [0, -1, 5, 2, 3],\n [-2, 6, 2, 5, 5],\n [-4, 2, -5, 3, 2],\n [0, -2, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 2, 1, -2, -3],\n [-2, -2, 0, -5, 1],\n [0, -6, -3, -3, 0],\n [-4, 0, 4, -1, -3],\n [-4, 6, -2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 6, -2, -2, 5],\n [5, 4, 1, 5, 1],\n [-6, -2, 1, 4, 1],\n [1, 6, 4, -4, -5],\n [6, 0, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -2, 2, 6, 3],\n [2, -1, 3, 1, 5],\n [5, -2, 5, 2, 6],\n [-1, 0, 6, 3, 4],\n [1, 1, -6, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -4, -6, 4, 5],\n [3, 3, -5, 0, 6],\n [-1, 5, 2, -5, 4],\n [2, 0, 0, -3, 3],\n [-3, -3, -1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -1, 6, -1, 6],\n [-1, 1, 0, 1, -3],\n [6, -2, -1, -4, 6],\n [1, -3, -6, 2, 4],\n [4, -5, 4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -3, 5, -1, 1],\n [1, -1, -6, -2, -3],\n [4, 1, -3, 2, -2],\n [4, -1, -1, 5, 2],\n [2, 5, 5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -1, -3, 5, -3],\n [-2, 5, 1, -4, -5],\n [-1, -5, -6, 6, 5],\n [-3, 0, 5, -4, 0],\n [2, 2, -5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 5, 4, 2, 4],\n [3, 1, 6, 4, 2],\n [5, -6, 6, -6, 1],\n [-6, -2, 6, -5, -4],\n [-4, 6, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 3, 2, -3, -1],\n [0, 1, 5, -4, -3],\n [6, 0, -1, 3, -1],\n [3, 4, -3, 3, -4],\n [-6, 0, -2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 4, -2, -1, 1],\n [-2, 4, -6, -4, -1],\n [6, 4, -1, -5, 4],\n [3, 3, 6, 5, 3],\n [-5, -4, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -4, 0, -1, 5],\n [3, 5, 1, 4, -6],\n [2, 4, 6, 4, -3],\n [-1, -5, -6, 6, 1],\n [6, 2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -3, -5, 1, 3],\n [-4, -5, 5, 1, 4],\n [3, -2, -5, -2, -5],\n [0, -4, -3, -2, 5],\n [5, -4, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 6, -4, 4, 0],\n [-4, -6, 5, -6, 4],\n [-2, -6, 2, -1, -5],\n [-1, 1, 5, 0, -6],\n [4, -2, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 4, -2, 1, 5],\n [-2, 0, 4, -1, 2],\n [3, -2, 0, 6, 2],\n [-5, 0, -4, -2, -4],\n [2, -6, -2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 1, -5, -6, 4],\n [6, 6, 3, 6, 1],\n [-3, -2, -3, 6, 3],\n [6, -5, 1, -4, 2],\n [4, -6, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -1, -6, -4, 4],\n [4, -5, 0, -1, -6],\n [-4, 0, -4, 4, 3],\n [1, 3, 0, -5, -6],\n [6, -2, -1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 1, -4, -1, -1],\n [3, 0, -4, -1, 5],\n [-5, 2, -5, -3, -4],\n [0, -3, -1, -2, 4],\n [-5, 0, 0, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 2, 4, -3, -2],\n [1, -5, -2, -2, 1],\n [-5, 4, 5, -2, 1],\n [-2, 4, 5, -6, -5],\n [1, 0, -1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, -3, -2, 1],\n [-3, 6, 1, -2, 2],\n [-1, -3, 2, -4, -2],\n [-1, -5, -4, -6, 4],\n [6, 0, 0, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -1, -2, 4, 0],\n [4, 4, 2, -2, -5],\n [2, -6, 5, -1, 1],\n [-6, -3, -4, -2, 3],\n [-6, -4, -5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 1, -4, -1, -6],\n [-4, 1, -4, -5, 2],\n [-4, 2, 2, 5, 4],\n [-1, 0, -3, -4, -3],\n [6, 1, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 1, 5, 3, 3],\n [-4, -2, -1, -6, 4],\n [-6, 0, 5, 2, 1],\n [-4, -1, 6, -6, 2],\n [-6, 4, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 4, -4, 3, 2],\n [5, -3, -1, -2, -1],\n [-4, 3, -5, 5, 6],\n [1, -1, 5, -3, -6],\n [-2, 0, -1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -6, -3, -6, 0],\n [-5, -2, -3, -1, 1],\n [-6, 4, -6, 2, -1],\n [6, -1, -1, 6, 6],\n [5, 6, 3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 1, 4, 6, 1],\n [-4, 4, 5, 1, 3],\n [1, 4, 5, -2, 3],\n [-6, 3, 5, 5, 2],\n [-3, -1, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 3, -6, 5, 1],\n [-5, -1, 2, 1, -2],\n [-6, 0, 4, -1, -4],\n [-2, -5, 2, 5, -5],\n [2, 4, 5, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -2, 2, -6, -1],\n [-1, -4, 3, -2, -6],\n [-4, 0, -2, 3, -4],\n [3, -3, -4, 6, -5],\n [5, -4, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -4, 2, -6, -2],\n [5, 0, 5, 5, -4],\n [3, -2, -6, 0, 1],\n [2, -6, 0, 4, -6],\n [1, -4, -1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 5, -6, -1, 5],\n [-3, 3, -5, -6, 0],\n [1, -3, 0, 2, -3],\n [4, 5, -2, 6, -2],\n [-3, -2, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -1, 1, -4, -6],\n [-3, 4, 2, -6, 5],\n [-6, -5, -5, -2, 1],\n [-2, 1, -2, 2, 2],\n [4, -6, -5, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 2, -1, -2, -4],\n [-2, 4, 3, -1, 4],\n [0, 6, 2, -2, 3],\n [-5, 3, 1, 1, -2],\n [0, 2, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -4, 3, 3, -6],\n [0, 4, 6, 5, -4],\n [3, 1, 2, 2, 5],\n [0, -6, 6, 0, 0],\n [-6, -4, 2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 3, 4, 5, -5],\n [-1, 3, 2, -2, -3],\n [-4, 0, -1, -5, 1],\n [6, -3, -2, 3, 4],\n [-2, 3, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, 6, 4, 6],\n [1, 5, -1, 5, -5],\n [2, 0, -2, 3, -4],\n [3, 5, 4, 6, -4],\n [-6, 3, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 1, 6, -6, -6],\n [3, 6, -5, -4, 4],\n [6, -2, -3, -2, 2],\n [2, -3, 0, -1, 3],\n [5, -3, -3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -2, 0, 3, -2],\n [-5, -4, -4, 1, -6],\n [-2, -5, 3, 2, -3],\n [6, 2, -6, -4, -1],\n [4, -1, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 3, 0, -1, -3],\n [-1, -6, 2, 1, 5],\n [-1, 2, 0, 3, 5],\n [1, -3, 3, -1, 2],\n [-6, 2, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -1, 0, 0, -2],\n [3, 6, -2, 4, -2],\n [-6, 1, -6, -5, -4],\n [3, -6, -2, -6, -1],\n [3, 0, 6, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -4, 3, 1, 3],\n [1, 4, 4, -1, 6],\n [-5, -4, 6, -2, -2],\n [-6, 6, 5, -2, 1],\n [5, 4, -3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -5, 6, 3, -6],\n [0, 6, 2, 2, -2],\n [5, 5, -4, -2, -4],\n [-1, -6, 1, -5, -3],\n [0, 4, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -4, 1, 2, 1],\n [2, 4, -2, 1, 6],\n [-4, 2, -6, 2, 2],\n [0, 5, -2, 5, -2],\n [-5, -5, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -6, -2, -4, -6],\n [1, 5, -4, 2, 4],\n [-1, 3, -1, -4, 6],\n [-2, 6, 0, -5, -4],\n [-1, 6, -5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 3, -3, -3, 5],\n [-4, -2, 2, 5, 4],\n [-4, 2, 3, 1, 1],\n [5, 4, 1, 0, 4],\n [-6, -1, 5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -6, 4, -4, -3],\n [5, 1, -5, 1, -2],\n [-6, -4, 6, 0, -3],\n [-6, 2, 6, -4, 5],\n [6, 4, 2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -6, 4, 2, 4],\n [1, -4, -2, 2, 5],\n [-6, -1, 2, 5, -6],\n [-6, -3, 1, -4, 0],\n [-1, 0, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -5, 1, -5, 6],\n [-4, 3, 4, 0, -5],\n [-4, 6, -2, -2, 5],\n [3, -1, 5, 6, -3],\n [-3, -6, 3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 4, -5, 5, -4],\n [-2, -5, 4, -6, -4],\n [-5, -4, 6, 1, 6],\n [2, 0, -6, -3, 3],\n [2, 3, -1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, -2, -2, 6],\n [2, 2, -2, 6, 0],\n [5, 1, 1, -1, -2],\n [-6, -4, -2, 5, 5],\n [-6, -2, 3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -6, 1, 6, 0],\n [-6, 3, 1, 1, 1],\n [-1, 4, 5, 1, -3],\n [6, -5, 5, 4, 5],\n [1, -1, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 6, -3, 5, 4],\n [4, -4, 0, 2, -6],\n [4, -6, -1, 2, 5],\n [-4, -5, 4, 2, 0],\n [5, 0, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 6, 4, 6, 0],\n [4, 6, 2, -2, -5],\n [6, 0, 4, 2, 2],\n [-6, 5, 2, 5, -4],\n [-1, 5, -3, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, 4, -2, -3],\n [0, 2, -6, -6, -3],\n [-5, 2, -3, -1, 0],\n [6, 1, 2, -5, 1],\n [5, -5, -3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, 1, -4, -4],\n [-5, -5, -5, 4, 0],\n [5, 3, 3, -2, 4],\n [-1, 6, 6, -4, -5],\n [-1, 0, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 4, 6, 0, 4],\n [4, -6, -5, -5, 4],\n [-3, 6, 5, -6, 6],\n [5, 2, -2, 3, -2],\n [0, -3, -2, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, -2, 4, 4],\n [1, 1, 0, -1, 4],\n [6, 3, -5, -2, -1],\n [4, -1, -2, 1, 0],\n [5, 1, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 6, 4, 0, 0],\n [-2, 2, -1, -4, -3],\n [-3, -3, 6, 2, -3],\n [-5, 1, 1, 1, 5],\n [6, -2, 4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 3, -6, 1, -5],\n [-6, -6, 2, 1, 0],\n [-6, -6, -5, -3, 1],\n [-6, 4, 4, 1, 6],\n [-4, 2, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -5, 5, -5, -2],\n [1, -5, 1, 1, 4],\n [3, 5, 3, 2, 3],\n [6, -1, 0, -5, -3],\n [0, -6, -5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -1, 2, -6, 4],\n [6, -3, -1, 1, 4],\n [-6, 1, 5, -4, -6],\n [-6, 0, 2, 6, -5],\n [-4, -4, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -3, 6, -3, 2],\n [1, -4, 2, -4, -5],\n [-5, 5, 2, 6, -2],\n [5, -6, 0, -3, 2],\n [-2, 4, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -6, 0, -5, 0],\n [4, -2, -6, -2, 3],\n [0, -4, 0, 4, 1],\n [0, 2, 1, 3, -1],\n [-3, -1, 0, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -3, 3, 0, 2],\n [4, 5, 3, 3, -5],\n [-4, -4, 4, -4, -3],\n [2, -6, -6, 6, -6],\n [-6, 2, 2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, 5, -1, -5],\n [-2, -2, -6, 5, -1],\n [-4, 2, 6, -3, 1],\n [4, 5, 5, -6, -1],\n [3, 4, 5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -4, -4, -3, 1],\n [-3, 3, -6, 1, -2],\n [3, -6, -4, -2, -6],\n [5, -1, 1, -1, 5],\n [-2, -6, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 2, -4, -1, 1],\n [-4, -4, 2, 2, 6],\n [1, -4, -1, 0, 5],\n [-4, 5, 2, 4, 5],\n [-6, -3, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, 4, 6, -6],\n [-2, 6, 3, -1, 5],\n [-4, 4, 4, -1, -2],\n [-6, -4, 1, 5, 6],\n [0, 0, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 6, 5, 0, 1],\n [-6, 1, 6, -2, -6],\n [-1, -1, 5, 1, 6],\n [1, -3, 0, 0, -5],\n [3, 0, -2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -5, 1, -1, 6],\n [6, 3, -3, -4, 4],\n [-5, 0, -2, 6, 4],\n [-3, -5, -6, 6, -4],\n [0, 2, 6, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 2, 1, -1, -5],\n [0, 5, 4, 6, -1],\n [-4, 3, 0, 5, 1],\n [-6, -2, -6, -2, 2],\n [-5, 0, -6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 4, 5, -4, 6],\n [-5, -1, 0, 6, -2],\n [2, -4, -2, 0, 5],\n [5, -3, -2, 5, 4],\n [-6, 2, 6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -1, 5, 0, -6],\n [-5, -6, -4, -3, 0],\n [3, -4, 0, -6, -6],\n [1, 4, -3, 0, 6],\n [4, -1, -2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -1, 4, -5, -5],\n [-4, -1, 4, 1, 0],\n [-1, -6, -4, 6, -1],\n [-1, 6, 1, -4, 6],\n [-3, 2, 4, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 6, -5, 4, -2],\n [-6, 3, -4, 4, 2],\n [2, -6, 0, -6, 5],\n [3, 4, 6, 2, -5],\n [5, 4, -6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -4, 3, -6],\n [3, 6, -4, 2, -3],\n [-2, -5, -2, 1, 0],\n [-4, 2, 6, 4, 2],\n [2, -1, -3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 4, 0, -3, -4],\n [-3, -3, -5, 0, 5],\n [2, 6, 5, -5, -2],\n [1, 3, 0, -1, 4],\n [-6, 6, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -6, 3, 3, -4],\n [3, -6, -6, 6, 3],\n [3, 0, 3, -4, -6],\n [5, 2, -4, 2, -3],\n [-4, 2, 6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -5, -4, -6, -1],\n [-6, -2, 4, 4, -2],\n [3, 3, 1, 2, 2],\n [-6, 4, 5, -1, 6],\n [5, -3, 1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 4, -1, -4, 0],\n [3, -4, -4, 0, -5],\n [-6, 4, 0, -2, -6],\n [0, 5, -4, 2, 5],\n [-4, -2, 2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, -2, 3, -5],\n [-2, -2, 1, 5, 4],\n [4, 6, 2, -4, 1],\n [3, 5, 6, -1, -3],\n [1, -2, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 4, -2, -1, 1],\n [0, -6, 6, 0, 1],\n [4, 0, 1, 2, -4],\n [3, 5, 0, -6, -6],\n [-1, -5, -5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 5, -2, -2, 6],\n [-4, -4, 5, 6, 5],\n [3, 3, -3, 0, -1],\n [-6, -6, 5, -5, -2],\n [3, 2, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 5, 3, 3, 2],\n [-4, 4, -5, 6, -1],\n [6, 1, 4, 0, 0],\n [2, 0, -1, 4, 5],\n [5, -4, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -6, 0, 5, 5],\n [4, -3, -2, 0, 4],\n [-3, -2, 6, -6, -1],\n [3, 3, -4, 1, 3],\n [-4, 4, 6, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, 2, -2, -1],\n [4, 0, -1, -4, -1],\n [0, 0, -1, 5, -6],\n [-3, -1, 4, 3, -6],\n [-4, -2, -5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, -2, 3, 5],\n [0, -3, -6, 5, 6],\n [-1, -5, 5, -6, 4],\n [6, -1, -4, 6, 4],\n [2, -4, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -4, -2, 4, 4],\n [-6, 1, -1, 3, 3],\n [4, -5, -5, -6, 6],\n [2, 6, -1, 0, -4],\n [-6, -4, -6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 4, -3, 0, -5],\n [-4, 3, -4, 1, -6],\n [5, -1, -4, 3, 0],\n [-1, 2, 1, -5, 1],\n [-5, -1, -1, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -2, -3, 2, -6],\n [2, -1, 6, 5, -1],\n [-5, 4, -3, 6, -6],\n [-6, -2, -6, 3, 3],\n [3, 3, -2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 0, -5, -1, -5],\n [3, -5, 5, 2, -4],\n [1, 6, 0, -3, 1],\n [3, 3, 4, 2, 1],\n [2, 1, 1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 6, 5, 6, 0],\n [-6, 5, -1, -3, 1],\n [-3, -2, 0, 5, -2],\n [0, -3, -2, -4, 1],\n [-2, -2, 0, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, 4, -3, 2],\n [-2, 3, -3, 4, 3],\n [5, -1, 3, -6, -6],\n [-2, 1, 6, 4, 5],\n [2, -5, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -2, -5, 3, -6],\n [-1, -6, -5, -2, 0],\n [-2, -1, 4, 2, 2],\n [-1, 0, 5, -1, -1],\n [-2, -3, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 0, -5, 3, -6],\n [3, -1, -2, -5, 1],\n [-3, -6, -4, 0, 4],\n [-1, -2, 6, 5, 3],\n [-3, 0, 5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 2, -2, -3, -4],\n [-5, -4, 2, -6, -1],\n [2, -5, 4, 3, 0],\n [6, 4, 2, 5, -2],\n [-4, 5, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 0, -3, 5, 3],\n [3, -3, 5, -3, -4],\n [4, -4, 3, -2, -2],\n [-2, 2, -3, 2, -2],\n [-5, 4, 1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 3, -3, -5, -6],\n [-3, 1, -5, 4, 6],\n [-4, 2, 1, -1, 0],\n [-3, -6, -2, -5, 2],\n [2, 5, 1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -4, -5, -2, -6],\n [-2, -5, -2, -4, -6],\n [-2, 6, 2, 2, 5],\n [6, 6, -2, 3, 4],\n [2, -3, -1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -5, -5, 6, 2],\n [-3, -4, 4, 2, -2],\n [-1, 5, -6, -6, 6],\n [1, 4, -5, -2, 4],\n [-3, -4, -1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, -2, -4, 6],\n [5, 4, 0, -2, -3],\n [-5, 2, -5, -6, 1],\n [-4, 2, 4, -3, 2],\n [6, 0, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -2, -1, 4, 0],\n [2, 1, 4, -2, 1],\n [2, 6, -1, -2, 0],\n [3, 1, -4, -2, -1],\n [-2, 1, -6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -4, -2, 1, -4],\n [5, 4, 3, 2, 2],\n [4, 4, -6, 6, 5],\n [-6, -5, 5, 6, -4],\n [-3, 5, 0, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -5, 0, 6, 5],\n [-1, -4, 2, 6, -3],\n [3, 6, 2, 1, 3],\n [-1, 6, -1, -1, -3],\n [6, 3, 3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, 1, -2, 3],\n [3, -4, -6, 4, 0],\n [-3, -3, 2, 1, 4],\n [4, -3, 4, 2, -4],\n [0, -1, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, 1, -3, -6],\n [-4, 0, 0, -1, -2],\n [3, 1, 0, -2, -4],\n [-5, -4, 2, -4, 4],\n [5, -2, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, 0, -2, -2],\n [-1, 1, 2, 6, 5],\n [1, -5, -5, -2, 0],\n [-1, 2, 0, -1, 2],\n [4, -1, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 4, -1, -3, -4],\n [5, -2, -3, 4, 4],\n [3, -3, -3, 0, -3],\n [5, 0, 6, 4, 2],\n [4, -3, 2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -4, -1, -4, 0],\n [-4, -5, 3, 6, -6],\n [2, 6, -3, 4, 0],\n [-1, 3, 2, -3, 1],\n [1, -3, 1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 2, -3, -1, -6],\n [4, 2, 2, -2, -5],\n [-3, 5, -2, 1, 4],\n [3, -1, -5, -2, -1],\n [3, 2, -5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 1, 5, 2, 5],\n [-3, -4, -6, 5, 6],\n [1, 0, -1, -3, -6],\n [-3, -1, -3, 2, 0],\n [-6, 6, -1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -5, 2, 5, -5],\n [1, -3, -4, 2, -6],\n [-2, -1, -1, 6, -3],\n [2, 1, 1, 5, 0],\n [-1, -4, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 6, -6, 5, -2],\n [6, 4, 2, 0, -6],\n [-1, -6, -2, -1, -6],\n [-4, 4, -4, -1, -2],\n [-3, 1, 5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 6, -4, -3, 1],\n [6, 6, -6, 0, 1],\n [-2, -6, -2, 2, 5],\n [-3, -1, 1, 0, -5],\n [-5, 5, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 6, -3, 2, -5],\n [4, 2, 1, 3, -6],\n [-6, -3, -2, 0, -2],\n [0, 3, -5, 3, -1],\n [-4, 2, -4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 4, 6, 6, 6],\n [0, -3, -2, -1, 3],\n [-2, 4, -3, -4, 0],\n [-3, 6, 1, -4, -1],\n [5, 6, -6, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 4, 5, 1, 1],\n [3, 4, 6, -6, 3],\n [-1, -6, -2, -3, 4],\n [-4, 3, -1, 4, -3],\n [2, 2, 0, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 3, 5, 3, 3],\n [-4, 4, 1, 3, 5],\n [2, -4, 0, -1, -4],\n [3, 5, -1, 0, 1],\n [-3, 1, -5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, 1, 5, -5],\n [-1, 0, -1, -6, -2],\n [-6, 1, 0, 1, -3],\n [-2, -6, 2, 2, -6],\n [-6, -5, 5, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -3, 6, -4, -1],\n [5, 2, -3, -3, -1],\n [-6, 3, -5, -4, -5],\n [0, -1, -3, -1, 6],\n [3, -2, 3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, -1, 0, -4],\n [-5, 3, -3, 4, -5],\n [1, 0, 5, -6, 4],\n [-5, -6, -2, 6, 5],\n [-2, 4, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -5, 4, -3, 5],\n [-6, 2, -6, 5, -4],\n [-6, 3, 4, -6, 1],\n [-3, -5, 4, 4, 5],\n [2, 6, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -5, -2, -6, -4],\n [-1, -1, 5, -1, 4],\n [-1, 3, 0, 1, 0],\n [1, 2, -6, 0, -1],\n [-1, 2, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -4, -4, 6, 4],\n [5, 4, 3, 1, -4],\n [4, 1, -2, 6, 5],\n [-1, -6, -3, -5, 6],\n [-3, 2, -6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 3, 6, -6, 1],\n [-1, -3, -3, 1, 0],\n [1, 4, -4, 0, 2],\n [2, 1, 5, 1, 3],\n [6, -1, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 1, -5, -2, -2],\n [-6, -6, -4, 4, 4],\n [-2, 5, 3, -3, -5],\n [-2, 2, -1, 0, -6],\n [-1, 6, 2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 3, 2, -3, -6],\n [-5, 0, 6, 1, -4],\n [2, -4, -2, 3, -1],\n [-5, -2, 6, 4, 5],\n [0, 1, 0, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 1, -3, 5, 0],\n [1, 5, 5, -5, -6],\n [4, 6, 0, -3, 0],\n [3, -6, 4, 1, -1],\n [-6, 2, 1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -2, -6, -4, 6],\n [2, -5, 3, -3, 6],\n [1, 1, 0, -6, 3],\n [-2, 6, 0, -3, -6],\n [-1, -5, -6, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -1, -2, 3, 0],\n [-1, 6, 5, -3, -2],\n [-2, -1, -6, 6, 5],\n [-2, 6, -4, 2, -2],\n [1, 3, -6, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 0, -4, 6, 2],\n [0, 3, 4, 0, -6],\n [5, -4, -3, 3, -1],\n [3, -4, -4, -2, 0],\n [3, -6, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, 1, -2, -2],\n [6, 3, -3, 3, 0],\n [2, -1, -4, -4, 2],\n [4, -6, -2, 3, -5],\n [4, -6, 4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -2, 4, 0, -2],\n [6, 1, 0, 6, -5],\n [6, -3, -6, 3, -4],\n [0, 4, -4, -4, 4],\n [-1, -1, -4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -2, -1, -3, 0],\n [-1, -2, -6, 3, 1],\n [6, 0, 6, 6, 2],\n [-1, -6, -2, -6, 2],\n [-4, 2, 2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 3, 6, 0, -6],\n [-3, -1, 5, 6, 6],\n [6, -2, 2, -2, 6],\n [-4, 2, -4, 0, -2],\n [-1, 3, -5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -6, 4, -5, -5],\n [5, 5, 2, 2, 2],\n [5, -6, -3, 0, -1],\n [-1, -6, -6, -5, -1],\n [-2, 1, 3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 3, 3, -2, -5],\n [2, 3, 0, 2, 4],\n [-1, 1, 0, -4, -4],\n [-5, -6, 6, 3, -3],\n [-2, -3, 5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 1, -6, -5, 1],\n [-3, 0, 6, -1, -5],\n [-5, 6, -6, 6, 3],\n [-6, -2, 6, -5, 3],\n [-5, -5, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 2, -5, 0, -5],\n [3, 6, 5, 5, -4],\n [6, 3, 4, 4, 6],\n [-3, 4, 5, 3, -5],\n [-6, -1, 2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 2, 1, -3, 0],\n [4, 2, 2, -4, 4],\n [4, -2, -3, -2, 0],\n [6, 2, -5, -5, 6],\n [4, 1, 3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 2, 4, -4, 3],\n [-6, 5, -6, -5, 4],\n [4, 0, 1, 6, 1],\n [-6, 3, 4, 6, 4],\n [2, -4, 0, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -5, 4, 2, 4],\n [-5, -1, -1, 1, 3],\n [-2, -4, -6, 4, 2],\n [4, -2, 3, 3, 1],\n [-4, -5, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, 2, 4, 2],\n [0, 3, -5, -1, 1],\n [3, -3, -6, -3, 6],\n [-6, -3, 6, 3, -6],\n [1, -6, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -2, 1, -4, 2],\n [0, 2, 3, 2, -5],\n [1, -6, 5, 3, 2],\n [-1, 2, 3, 6, 3],\n [5, 6, -6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 2, -1, 5, 6],\n [-6, 0, -3, 0, 3],\n [-4, -2, 0, 4, 6],\n [-6, 5, -5, -1, 4],\n [1, -1, 5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -6, -5, 5, 3],\n [-5, -3, 6, -5, 6],\n [-1, 5, 0, 1, 3],\n [-6, -1, -5, 3, -4],\n [-2, 4, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 2, -4, -4, -1],\n [2, 0, -1, 1, 2],\n [-6, -2, 5, -6, 6],\n [-6, -4, -5, 4, -5],\n [-3, -4, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 0, 1, -3, -2],\n [-2, 4, 2, 4, 1],\n [4, -3, 3, 1, 3],\n [0, -1, 1, 6, -3],\n [3, 6, -3, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 0, 3, 5, -5],\n [6, -3, 4, 0, -2],\n [1, 6, 6, -6, 6],\n [1, 6, 6, 3, 1],\n [-3, 1, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -5, 4, 2, 1],\n [-3, 6, -4, -6, -6],\n [1, -6, -4, 3, 3],\n [-6, 2, -2, 3, -6],\n [5, -6, 2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 5, 1, -3, 2],\n [-2, -4, 0, -5, 6],\n [2, -1, -4, 0, 6],\n [1, -2, 1, -5, 5],\n [6, -6, 3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 5, 0, -1, 3],\n [-4, 0, -4, 6, -2],\n [-6, 1, 6, 3, 1],\n [-5, -5, 1, 5, -4],\n [-5, -3, -4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 3, -2, -1, -4],\n [4, -5, 6, -2, -3],\n [-4, -4, 6, -5, 0],\n [1, 1, -4, 3, -6],\n [5, -3, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -6, 0, -4, 3],\n [3, 6, -1, -2, 1],\n [4, -4, -3, 0, 1],\n [5, -6, 3, 5, 2],\n [-6, 1, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 6, -6, -1, 6],\n [-4, -3, -1, 6, 2],\n [-4, -3, 2, -3, 6],\n [-4, -5, -3, 0, -6],\n [4, -5, -5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, -5, 5, -5],\n [-2, 3, -2, -4, -5],\n [-5, 5, -2, -6, -5],\n [-3, -3, 1, 1, 2],\n [-2, -3, 6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -1, 6, 0, -4],\n [6, -3, -6, -6, 6],\n [1, -3, 5, -6, -3],\n [1, 5, 2, -4, 3],\n [3, -3, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -5, 1, -2, 3],\n [-4, 3, -4, 3, -2],\n [1, 4, -4, -2, -4],\n [5, 3, 1, -1, 4],\n [-3, -5, 4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 3, 4, -3, 4],\n [-3, 4, -4, 2, 0],\n [1, 1, -2, -2, -4],\n [5, -1, 1, -3, -3],\n [2, 5, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, 5, 1, 5],\n [1, -5, 0, -1, -6],\n [-5, -6, 2, 2, 6],\n [5, -3, -5, -4, 5],\n [4, -4, 6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, -2, 4, 5],\n [4, 0, 4, -5, -2],\n [2, -6, -1, 3, -1],\n [-3, 1, -3, 6, 5],\n [6, 5, 0, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 2, 4, -1, 3],\n [6, 2, 5, -6, 6],\n [-4, 4, -2, -1, 6],\n [-3, -5, -6, 0, 5],\n [4, 6, 3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 0, -6, -2, -2],\n [3, 5, -2, -3, -5],\n [-5, 5, 2, 6, 6],\n [-3, 4, 4, 5, 1],\n [-4, -5, 6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 2, 3, 1, -2],\n [6, 4, -1, -4, -5],\n [6, 3, -3, -6, 2],\n [-2, -6, -4, 6, 4],\n [-1, 2, 3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, -3, -5, -2],\n [4, 3, -5, -2, -2],\n [-3, 0, 6, 5, 2],\n [0, -2, 3, -4, 2],\n [0, 6, -6, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 1, 6, -6, 4],\n [1, -3, -4, 1, 5],\n [0, -3, -1, -1, -6],\n [4, 6, -1, -4, -5],\n [-3, 1, 1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, 2, 1, -3],\n [-5, -4, 4, -2, 6],\n [4, -6, 0, 1, 3],\n [6, 5, 4, 3, 6],\n [-2, -5, 1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 5, 1, 4, -6],\n [-3, 1, -3, 1, 2],\n [5, 1, -5, 2, 2],\n [-2, -1, 0, 2, 3],\n [5, -5, -6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, -5, 2, 3],\n [0, -1, -4, -5, -3],\n [2, -3, -1, 1, -1],\n [-5, -5, -5, 3, -6],\n [-1, 5, 6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -4, -6, -4, 3],\n [-5, 1, -1, -1, 1],\n [5, -1, -4, -2, -2],\n [-2, -1, 6, -5, -1],\n [2, 0, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -1, -3, -3, 1],\n [-6, 6, 2, -5, 2],\n [0, -2, -3, 2, -4],\n [-1, -2, 1, 0, 5],\n [2, 0, -3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -1, -1, 4, -6],\n [-1, -4, 4, 5, 1],\n [0, 3, -1, -5, -4],\n [-3, 3, -5, 2, 1],\n [5, 0, -6, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 6, -1, -4, 5],\n [5, -2, -4, 6, 3],\n [-5, -4, 3, -1, 6],\n [1, -5, 6, -4, 6],\n [-2, 2, -4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -2, 2, 3, -5],\n [6, -5, -5, 5, 2],\n [-3, 5, -1, 6, -2],\n [-5, 6, 6, -1, 5],\n [3, -5, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 6, -3, 3, 3],\n [3, -2, -3, -5, 1],\n [-3, 2, -3, -4, 5],\n [4, 1, -3, -4, -1],\n [1, -3, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -3, -2, -4, 2],\n [6, -5, -3, -5, 1],\n [-2, 4, 2, -6, -4],\n [6, -3, 0, 2, 2],\n [0, 3, -6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 0, 3, 1, -2],\n [6, 2, 4, 4, 1],\n [-3, -2, -3, 1, -2],\n [1, 4, -5, 5, 0],\n [4, -4, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -1, 4, 5, 5],\n [-2, -2, 0, 6, -1],\n [-6, -1, 2, 2, 4],\n [-1, 6, -4, -5, 5],\n [5, 0, 3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 4, -3, 3, 2],\n [1, -6, 2, -6, -5],\n [-3, -3, -5, -5, -2],\n [-3, -5, -3, -6, -1],\n [-1, -6, -6, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 3, -5, -5, 4],\n [-2, 6, -5, 5, -2],\n [1, 1, 3, -6, 1],\n [-1, -6, -2, -1, -3],\n [-4, 5, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 1, -1, -4, 1],\n [4, -1, 2, 4, -5],\n [-5, -3, -1, 5, 4],\n [-6, 6, -2, -5, -1],\n [-4, 6, -3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 6, 5, 3, 6],\n [0, 3, 0, -6, 3],\n [4, 0, -5, -4, -3],\n [-6, -3, 4, -2, 2],\n [-4, -6, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 4, 2, -4, 2],\n [-2, 1, -3, 3, 0],\n [5, -3, -6, -4, -4],\n [-4, 5, 1, -3, -4],\n [1, -1, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, 5, 6, -4],\n [-4, 0, 5, -2, 6],\n [-4, -1, 0, 3, -5],\n [-4, 0, -2, -2, -3],\n [3, 0, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 4, 1, -1, -2],\n [-4, 3, 0, 3, -1],\n [0, 4, 2, -6, -4],\n [-3, -5, -1, 3, 1],\n [-4, 5, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 3, -6, 1, -5],\n [3, -4, -2, -6, -1],\n [1, 4, -4, -4, 5],\n [-5, 5, 1, -5, 1],\n [-5, -4, 5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 4, 1, 4, -1],\n [4, 3, -4, -1, 5],\n [-6, -2, -1, 0, -5],\n [-4, -2, -6, 1, 4],\n [5, 1, -2, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 4, 3, 1],\n [-5, 3, -1, -1, 6],\n [-5, 6, 4, 6, 4],\n [-1, 6, 6, -6, 5],\n [6, 5, 0, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 5, -2, -3, -4],\n [0, -1, 4, -5, 4],\n [5, 1, -4, -5, -6],\n [-4, 4, 0, -1, 3],\n [6, 1, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -5, -3, 1, 0],\n [-3, -4, 4, -5, 0],\n [3, -1, -2, -2, 0],\n [3, 5, -5, 3, -5],\n [0, -1, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -1, 4, 3, -3],\n [6, -3, 6, -3, 5],\n [-1, 2, 3, -6, 5],\n [-5, 3, 6, -5, 4],\n [2, 0, 2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 3, 5, 0, 3],\n [-5, 5, -4, -5, -2],\n [-1, 2, 6, -5, -4],\n [4, 1, 1, 2, 0],\n [6, 0, -3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, -2, -2, -6],\n [6, -1, -1, -1, 0],\n [-2, -2, 6, -2, 1],\n [-2, 4, -5, -5, -2],\n [-5, 1, 5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 5, -5, -4, 4],\n [3, -2, -2, 1, -4],\n [2, 4, -2, -3, -3],\n [6, 3, 6, 6, 4],\n [2, -4, 3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, -4, -1, 4],\n [2, -6, -1, -4, 6],\n [-6, 1, 5, -2, 0],\n [-2, 6, 5, -1, 6],\n [-3, -3, 1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 0, 5, -6, -5],\n [-2, 0, 0, -3, 0],\n [-4, 5, 4, 5, 6],\n [-4, -1, -5, -2, 4],\n [-5, 6, 5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 3, -3, 0, -3],\n [-1, -2, -2, 0, 4],\n [0, -1, -1, -6, -1],\n [3, 2, 6, -2, -5],\n [1, -4, -5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -4, -5, 4, 1],\n [6, 5, -2, -4, 3],\n [-2, 3, 0, 5, -4],\n [-2, -6, 3, -1, 0],\n [1, 3, 1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 0, -4, 1, 0],\n [-2, -6, -6, -4, -3],\n [1, 4, -2, 6, 6],\n [-6, -6, -4, -1, -5],\n [-4, 1, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -1, -4, -5, -2],\n [2, -4, 1, 1, -2],\n [2, 5, 4, 6, -5],\n [3, 3, -2, 1, -5],\n [3, -5, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -3, -3, -2, 3],\n [5, -2, 2, 4, 0],\n [6, 3, 2, 4, 6],\n [-1, -2, 4, 4, 3],\n [-6, 4, -3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 0, -6, 3, -3],\n [-4, 0, 2, 1, 0],\n [-6, 3, -6, 4, 0],\n [-4, 4, -4, 0, 2],\n [2, 2, -2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -4, -1, 5, 3],\n [4, 6, -3, 1, 4],\n [5, 0, -4, -3, 6],\n [-3, 1, 6, 2, -3],\n [-2, -1, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 2, -1, -2, 6],\n [1, 5, -3, 6, -4],\n [0, -2, -4, -2, 1],\n [0, -1, 3, 5, -2],\n [-6, -6, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 4, -4, 0, -3],\n [2, -6, -5, -1, 1],\n [1, 2, 6, 4, 0],\n [3, 3, 0, -1, 4],\n [-4, 2, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -1, -4, 4, -1],\n [-6, -2, 2, -6, -4],\n [-4, -6, 4, -6, 4],\n [-1, 1, -2, -5, 0],\n [-1, 0, -1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, 1, -1, -5],\n [5, 5, 3, -2, 6],\n [1, 5, 4, 2, 4],\n [-6, 5, -5, -5, -4],\n [2, 3, 5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -1, 2, -3, -5],\n [-3, 1, 0, -3, 4],\n [4, -4, -2, 1, -6],\n [2, 1, -4, 1, 1],\n [2, 1, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 1, -4, 3, 6],\n [-4, -5, -2, -6, 3],\n [0, 5, 3, 0, -5],\n [3, 0, 5, 2, 2],\n [-5, -1, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 5, 3, -6, 4],\n [5, 6, 4, -1, -5],\n [-4, 6, 3, -2, -6],\n [0, -5, 0, -5, -2],\n [-5, -6, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -4, 4, 0, 3],\n [4, 3, -4, -6, 5],\n [2, 2, 5, -1, -2],\n [-2, 4, 5, 1, -4],\n [0, 3, 1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 2, 3, 5, 2],\n [-4, 2, -3, -2, 5],\n [4, -3, 0, 5, -1],\n [-2, -1, 0, -6, 4],\n [-3, -1, -4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -2, -3, -3, 5],\n [5, 0, 0, -5, 2],\n [6, -1, -5, 1, -5],\n [-2, 5, -5, -1, 5],\n [-1, 0, 6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -3, 0, -4, 4],\n [0, 5, -1, -3, 0],\n [-3, 2, 0, -6, -5],\n [2, -3, 4, 2, 5],\n [4, -6, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 1, 0, 5, -1],\n [0, 2, 3, -4, 0],\n [-6, -5, -3, -4, 2],\n [4, 5, 5, 2, -2],\n [-4, 6, 5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 5, -1, 2, 1],\n [0, 2, 1, 1, 2],\n [-3, -3, 6, 6, -1],\n [1, -4, 0, -3, -5],\n [-2, 0, 6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -3, 1, 4, 4],\n [5, 4, 2, 1, 0],\n [-3, 5, 6, -3, -4],\n [2, -5, -6, 4, 5],\n [-6, -1, -5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -6, -1, -5, 2],\n [4, 5, -3, 1, 4],\n [-3, 3, -6, -2, -3],\n [1, 3, -5, -3, 3],\n [2, -1, 6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 4, -3, 3, -6],\n [-4, -5, -4, 0, -2],\n [-1, -6, 1, -3, 4],\n [-2, -3, 0, -4, 2],\n [0, 3, 3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -6, -3, 4, -4],\n [-5, 6, 4, 6, -4],\n [-2, -6, 1, -2, -5],\n [0, 0, 1, -4, 0],\n [-3, 1, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 5, -2, 6, 4],\n [-2, -3, 6, -4, 3],\n [0, 0, -3, 4, -2],\n [2, 4, -2, 3, 4],\n [2, -3, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -5, -3, -6, 5],\n [0, 3, -3, -3, -5],\n [2, 1, 4, 3, -4],\n [2, -1, -3, -3, 4],\n [-6, -4, 2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 0, 0, -6, 0],\n [1, -4, -5, -6, -5],\n [3, -6, -4, 3, -4],\n [-6, 3, -5, 0, -4],\n [-5, 3, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, 2, 1, 5],\n [-3, 2, 6, 3, -3],\n [-5, 4, 2, 1, 3],\n [4, 4, 3, -1, 3],\n [-4, -2, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -1, -6, 6, 6],\n [0, -1, 4, 3, 1],\n [-1, 1, -4, -3, 6],\n [5, -1, 0, -6, -5],\n [-1, -3, 0, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -2, 0, 4, 2],\n [2, 5, -2, 6, 4],\n [-5, 5, 4, -6, 0],\n [3, 2, -3, -6, 2],\n [5, -4, -1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 0, 2, 6, 0],\n [0, 4, 5, 2, 6],\n [-5, 5, -5, -2, 0],\n [-1, -6, -1, 2, -2],\n [2, -6, 4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -4, -5, -3, 1],\n [1, -4, -3, -1, 0],\n [1, 6, 4, 3, 1],\n [-1, 2, 4, 1, 4],\n [-3, 4, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 5, 5, -6, 2],\n [4, -1, -6, 2, -5],\n [0, -3, 5, -3, -3],\n [-6, 0, -1, 6, -3],\n [5, 2, 5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 2, -2, 5, -6],\n [-4, 1, -6, -2, 0],\n [-4, -6, -5, -5, 5],\n [-5, 4, -1, -1, -5],\n [0, -1, -4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -1, 4, -3, -1],\n [-5, 5, -6, -5, -4],\n [-6, 1, -4, 1, 4],\n [-4, -5, 3, -2, -6],\n [0, 4, -3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 0, 4, -4, -6],\n [3, -5, 6, -1, -2],\n [5, -5, -4, 1, -6],\n [2, -2, 0, -1, 3],\n [1, 6, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, -5, -6, 4],\n [4, 0, -1, 1, 1],\n [-3, -5, 6, -4, -1],\n [-2, 3, 0, -4, -4],\n [-3, -6, -4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 4, 2, -4, -3],\n [0, -4, -1, -4, 1],\n [6, 2, 5, 6, -1],\n [4, 6, 1, 4, 0],\n [4, 4, 2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 3, -3, 1, 4],\n [5, 4, -5, -1, 3],\n [-4, 3, 4, 0, 2],\n [-3, -3, 6, 1, 1],\n [5, -2, -5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -5, 0, -1, 6],\n [1, 4, 6, 2, -1],\n [4, 4, -2, 6, 0],\n [1, -2, 6, 1, 3],\n [-4, 4, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 6, 1, 2, 3],\n [-5, 0, -3, -2, -5],\n [1, 0, -3, -1, -4],\n [2, -5, 5, 1, 4],\n [6, 4, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -5, -4, 0, 1],\n [-5, -4, 0, 6, 4],\n [-1, 6, 0, -3, 4],\n [3, -6, -6, -3, 0],\n [0, -1, 1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, 3, 0, 3],\n [3, 0, 3, 4, -5],\n [-4, 0, -2, 4, -4],\n [3, -4, 2, -5, 0],\n [0, 3, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 6, 3, 2, 5],\n [-2, 1, -4, 0, 5],\n [-3, 0, 6, -2, 2],\n [3, -5, -4, -5, 5],\n [1, 1, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, -6, -5, 2],\n [3, 6, 4, -3, -4],\n [2, 4, -3, 0, 2],\n [0, 5, -4, -1, 6],\n [3, 0, 2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 3, -3, -3, -5],\n [6, 3, -1, -6, 2],\n [3, -1, -2, 6, -4],\n [0, 5, 4, 6, -1],\n [4, 3, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 3, 6, 4, 5],\n [2, 0, -2, -3, 4],\n [1, 2, -3, -2, 6],\n [0, 6, 1, -1, -3],\n [-2, 1, 5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -5, -2, -4, 0],\n [-6, -2, 1, -3, -4],\n [-5, -2, 5, -5, -4],\n [-5, 0, -4, 6, 3],\n [4, -1, -6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -1, -5, 2, 1],\n [1, 4, 0, 0, 1],\n [4, 2, 5, -5, -4],\n [-4, 1, 2, -2, -4],\n [0, 4, 6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 6, -5, -2, -1],\n [-6, 6, 0, -2, -1],\n [-1, 4, 4, 6, -4],\n [3, 4, -1, 0, -6],\n [-1, 0, -3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, -1, -3, 1],\n [-4, -3, 6, 1, -4],\n [2, 2, 1, 1, -6],\n [0, -3, 6, -4, -3],\n [-4, 4, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -3, -3, 6, 1],\n [2, 4, 4, -6, -3],\n [-6, 3, 0, 2, 6],\n [0, -2, 6, 5, -3],\n [-5, -2, -5, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -3, -4, 1, -4],\n [-3, 2, -1, 1, -6],\n [-1, 3, 5, 3, -5],\n [2, 4, -5, 4, 6],\n [5, 2, -1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -3, -5, -1, 1],\n [4, -3, 0, 4, -4],\n [2, 4, -5, 2, -1],\n [-3, 0, 4, -5, 1],\n [0, -4, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -2, -4, 4, -6],\n [-5, 6, -5, 1, -3],\n [-1, 1, 1, 5, 1],\n [2, 5, -1, -2, 6],\n [4, 1, 5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, 0, -3, -4],\n [3, 6, 5, -3, -6],\n [-4, 2, -3, 0, -1],\n [-2, 2, 1, 2, -3],\n [1, 1, 6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 1, 6, -4, -2],\n [-4, 0, -5, -5, -3],\n [-3, -1, 2, -6, 0],\n [-2, 4, 2, 0, -5],\n [5, 1, -4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -3, -5, -6, 4],\n [-6, 2, 4, -5, -3],\n [-5, 2, 0, -1, 2],\n [1, -6, 0, -6, -4],\n [-1, -1, 1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -6, 2, 1, -4],\n [4, -6, -5, -2, 5],\n [-2, -2, 4, -5, -3],\n [-5, 1, 3, 0, -1],\n [5, -2, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 0, 3, 6, 6],\n [6, -2, -6, 5, -2],\n [-4, -1, -4, -2, -4],\n [-6, 5, 6, 2, -3],\n [6, -5, 1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 4, 1, -5, 6],\n [1, -6, 4, 0, 0],\n [2, -4, 4, 1, -3],\n [3, 4, -5, -1, -2],\n [1, 6, -5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 6, 0, -2, -3],\n [1, -4, -5, 6, 3],\n [-6, 1, 4, 0, -1],\n [6, 2, -6, -1, -5],\n [3, -2, -5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -2, -2, -4, 6],\n [-5, 2, 6, 6, -4],\n [-6, 1, 5, -1, -2],\n [4, -4, -1, -4, -2],\n [-5, 2, -5, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 6, 1, 0, 3],\n [-3, -4, -6, 0, 4],\n [-5, -5, -3, 4, -5],\n [1, -3, -3, 0, 2],\n [6, 4, -5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -4, -1, 2, -2],\n [-2, 2, -4, -1, 6],\n [1, 0, -6, 6, -2],\n [5, -4, -5, 1, 5],\n [6, 1, -1, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -2, -1, 2, 6],\n [-6, 6, 1, 5, 1],\n [5, -6, 5, 2, 6],\n [2, 2, -6, 1, -1],\n [4, 0, -6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -5, 0, -1, 6],\n [-3, -4, 3, 4, -3],\n [3, -6, -2, -4, -1],\n [-4, -5, -4, 6, 4],\n [-6, 3, 2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 6, -2, 5, 4],\n [-1, -1, 3, 2, -6],\n [4, -2, -4, -2, -6],\n [4, -4, -1, -4, 2],\n [3, -3, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 4, -1, -5, -4],\n [-4, -4, -6, -6, 1],\n [1, 1, 1, 3, -3],\n [3, -5, 6, 4, 1],\n [5, 3, -6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 5, 1, 2, -5],\n [0, 1, 2, -1, -5],\n [0, -3, 3, 1, -4],\n [3, 0, -3, -4, 2],\n [-6, -2, 6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 0, -4, -3, -4],\n [0, -2, -6, 0, 1],\n [-2, 3, -3, 6, 5],\n [6, -5, 4, 1, -3],\n [-4, 6, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 2, -2, 6, -1],\n [6, 3, 0, 3, -1],\n [-4, -5, -1, 1, -5],\n [-1, 3, 3, -3, -5],\n [-1, -3, 1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -3, -4, 0, -2],\n [-4, 0, -2, -1, -1],\n [-5, -2, -2, -4, -5],\n [-4, -1, 5, 2, -3],\n [5, -3, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 1, -5, 1, 5],\n [0, 6, -3, 3, 6],\n [-1, 4, -1, -5, -2],\n [4, 1, 4, 0, 3],\n [-1, -3, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 6, -6, 2, 1],\n [-4, -4, 3, -3, 5],\n [-5, -6, -4, 4, -6],\n [2, -1, -3, -6, -3],\n [-6, 5, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -6, 0, -3, 3],\n [0, 4, -1, -2, -3],\n [-5, 0, -6, 0, 5],\n [4, 0, 1, -2, 2],\n [-3, 5, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 4, -3, 2, -4],\n [2, 5, 5, 6, -3],\n [6, 6, 2, 1, -3],\n [-4, 6, 1, -5, -5],\n [4, 1, 1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -1, -5, 0, 4],\n [6, -3, 6, 6, -3],\n [-6, 3, -3, 2, -3],\n [-1, -6, -4, -3, 2],\n [5, 5, -5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -6, -2, -3, -3],\n [5, 3, 1, -5, -6],\n [-2, -1, -2, 0, 2],\n [5, 0, -5, 6, -3],\n [4, -5, 3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, -3, -6, -3],\n [-5, -2, -5, 2, 6],\n [6, 6, 3, 2, -4],\n [-4, 5, -5, 2, -4],\n [6, 3, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -5, 4, -4, -4],\n [-5, -1, 4, -2, -4],\n [-6, -4, 2, 5, 1],\n [-6, -3, -5, 0, 2],\n [3, 6, 0, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -2, -3, -5, 6],\n [-5, 3, 2, -3, -3],\n [-6, -1, -3, 0, 2],\n [2, 3, -5, 4, -6],\n [-2, -2, 5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, 6, 5, -6],\n [3, 2, -2, -3, -5],\n [-4, 2, -5, -4, -6],\n [6, -4, 0, -5, 4],\n [-1, 0, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 2, -5, -5, 3],\n [-1, -2, -2, -5, 0],\n [-2, 1, 1, 3, -3],\n [0, 5, -5, -5, -3],\n [2, -6, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 5, -4, 6, 1],\n [-5, -3, -2, 5, 0],\n [2, -1, 6, 6, 3],\n [1, -5, 3, -5, -6],\n [-3, -6, -3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, -2, 5, 1],\n [5, 4, -6, -4, 2],\n [1, -4, -5, 6, -6],\n [3, 6, 1, 2, -4],\n [-5, -2, 6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -6, 6, -6, 4],\n [4, -4, 1, 6, -2],\n [-3, -1, 0, 0, 2],\n [-4, 1, 6, 3, 2],\n [3, -4, 4, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 6, 5, 5, -1],\n [1, 3, 1, 5, 3],\n [-4, 2, 0, -2, -2],\n [2, 6, 1, -5, 3],\n [3, -3, -5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, 2, -6, 6],\n [-2, -4, -1, 6, -4],\n [5, 1, 2, -1, 2],\n [-2, -6, 0, 2, -2],\n [-5, 6, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, 1, 3, -5],\n [-3, 1, 3, 3, -1],\n [-6, 6, 3, 6, 6],\n [-4, -5, 1, 1, -5],\n [3, -2, -2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 3, 5, 0, -2],\n [1, -6, 4, 0, -6],\n [0, 1, 3, -4, 4],\n [5, 0, 4, -3, 5],\n [-6, 3, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -1, 0, 4, 0],\n [-3, -1, -5, 4, 0],\n [5, -4, -1, -6, 0],\n [2, 4, 1, 5, 5],\n [2, 0, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 5, -1, 6, -3],\n [4, -6, -1, -6, -5],\n [3, 6, -4, -2, -6],\n [2, -4, 4, 4, -5],\n [3, 3, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 6, -2, -3, 5],\n [2, -1, -2, 3, 2],\n [5, 2, 2, 0, -1],\n [-6, 3, 2, -5, -5],\n [-5, -4, -5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 2, 1, 2, -4],\n [-3, 1, -5, -6, -1],\n [2, 6, -6, 0, 5],\n [-2, -1, 1, 1, -6],\n [-6, 2, -3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 5, 6, 4, -3],\n [2, 5, -6, 5, 0],\n [-4, -4, -3, -3, 4],\n [4, -5, 5, 5, 1],\n [3, -5, -3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -1, 0, -3, 6],\n [4, -2, -5, -3, -6],\n [2, -1, 2, 5, 6],\n [-2, -5, -4, -3, 5],\n [4, -6, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -6, 1, 1, -5],\n [4, 2, -5, -5, 3],\n [4, -1, 2, 5, -1],\n [-4, -1, -6, -3, -5],\n [6, -5, -3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 2, -5, 0, -3],\n [4, 3, -6, -3, -1],\n [3, -6, 1, -5, 3],\n [2, 2, -6, 0, -5],\n [-1, 1, -1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -4, 4, 6, 4],\n [1, 0, 1, -3, 2],\n [-5, 3, 6, 0, -3],\n [-5, 5, 6, 0, 0],\n [-2, -5, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, 2, -6, 4],\n [6, -5, -6, -5, 4],\n [-3, 5, -5, -2, 2],\n [4, 5, -2, 6, 3],\n [-6, 3, -3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 5, 1, -3, 3],\n [-5, 0, -4, -3, -2],\n [0, -1, 0, -5, -2],\n [0, -4, -3, 1, -6],\n [-5, -3, -6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 0, 5, -5, 4],\n [-6, -4, -4, 6, -2],\n [1, 3, 6, 2, 5],\n [-3, 3, -2, 1, 5],\n [3, 6, -5, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -2, -5, 1, -1],\n [4, -2, -1, 4, 0],\n [-1, -2, -3, 5, -4],\n [-4, -2, 1, -3, -2],\n [-4, 4, -5, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 2, -3, -2, 1],\n [-2, 6, 6, -2, 5],\n [0, 5, 5, -1, -2],\n [-2, -3, -4, 1, 5],\n [-2, -3, -3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 3, 0, 4, 2],\n [-2, 4, -3, 4, -4],\n [1, 6, 6, 3, 1],\n [-6, 4, 4, 6, 0],\n [-2, 1, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 5, -3, 0, -2],\n [2, -2, 4, -2, -4],\n [-1, -5, 1, -1, 4],\n [0, 2, -2, -2, -2],\n [-5, 6, -6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -3, -4, 3, 3],\n [-6, 4, 5, -4, 5],\n [-5, 6, 2, 2, 5],\n [2, 2, 1, -6, -4],\n [0, -2, -6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -4, 3, -2, -3],\n [-6, 5, 6, -3, -1],\n [-1, 6, -3, -6, -3],\n [-2, 0, -4, 1, -4],\n [0, -1, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -5, -3, -3, 3],\n [0, -3, -3, 0, 1],\n [2, 1, 1, 0, -1],\n [-3, 1, -1, -6, -2],\n [-3, -1, -3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 2, 5, 1, 2],\n [6, 0, 4, 6, -1],\n [-2, -1, 1, -3, 0],\n [-1, 1, -5, -5, -2],\n [0, -3, -6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 0, -3, 5, -4],\n [-1, 1, 1, -2, 4],\n [6, 2, 6, 3, 4],\n [5, -2, 4, -2, -2],\n [-3, -1, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 6, 5, 6, -6],\n [4, 2, 0, -1, 2],\n [3, -3, 2, -2, 2],\n [0, 4, 0, 5, 0],\n [0, -5, 6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, 5, 0, -1],\n [6, -4, -2, 5, -2],\n [-4, -6, 6, 5, -4],\n [-4, 6, -2, 1, -3],\n [-5, 1, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 5, -6, -1, -3],\n [-2, 3, 0, -4, 6],\n [3, -1, -1, -4, 0],\n [-6, -3, 6, -1, -5],\n [-2, -4, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 3, 3, 4, 3],\n [-5, -2, -4, 5, 6],\n [-2, 6, 2, -6, 6],\n [-5, -2, -1, -4, -1],\n [-2, 5, -3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -2, 5, 6, -3],\n [4, 3, 3, -1, 0],\n [2, 3, 1, -6, 0],\n [-4, -3, -3, -2, -2],\n [1, 1, -5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 4, 5, -1, 4],\n [1, 4, 6, 0, 4],\n [4, 4, 3, 0, 6],\n [6, -6, 4, -2, 4],\n [-3, -6, 4, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 6, -6, 6, 3],\n [6, -6, -1, 4, -4],\n [6, -3, -5, -5, 0],\n [-1, -3, -1, 2, 5],\n [-2, 5, 1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -5, -5, -1, 1],\n [-3, -2, 3, 0, -6],\n [4, -1, 5, -1, 2],\n [1, 6, 2, -4, 4],\n [-1, 3, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, 1, 3, -1],\n [1, 3, 0, 4, 3],\n [-2, 6, 3, 6, 6],\n [3, 3, 1, 0, 3],\n [-6, -5, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, -4, -3, 5],\n [2, 5, -6, -2, -3],\n [2, 6, -4, 6, -2],\n [2, -1, 0, -2, -2],\n [0, -2, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 0, -1, -2, 6],\n [5, -5, -2, 2, 4],\n [-2, -3, 2, -2, 0],\n [3, 1, 6, -2, 2],\n [-3, 6, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, -5, 0, 4],\n [-3, -3, -6, 4, 1],\n [5, 5, 0, -6, -4],\n [0, -3, 3, -5, 0],\n [-3, 0, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 6, 2, 0, -6],\n [-1, 4, 2, -1, 5],\n [0, 5, -1, 4, 4],\n [1, 3, 2, -5, 6],\n [-2, -3, 5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 1, -2, -5, -6],\n [2, 2, -2, -3, 3],\n [-1, -1, -6, -1, 4],\n [-1, -5, 5, -6, 5],\n [0, 0, -2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 5, -5, 1, 4],\n [-4, -4, -5, 4, -3],\n [1, 3, -5, 1, 5],\n [1, -2, 2, 1, -1],\n [-1, 0, 2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -1, -4, 0, -5],\n [6, 5, -6, -5, -2],\n [2, -5, -4, -3, -2],\n [-4, -3, 3, 2, 6],\n [-4, -2, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -6, -5, -3, -3],\n [-3, 2, 0, 3, -1],\n [4, 3, -1, -5, -4],\n [6, 6, 6, -1, -4],\n [2, 1, -6, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 6, 2, 6, -2],\n [-3, -5, 3, 4, 5],\n [1, -5, -2, 3, -2],\n [-1, 4, -2, 0, 3],\n [3, -4, 5, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 1, 6, 3, 3],\n [0, 4, -2, 4, -6],\n [3, 6, 2, -4, -3],\n [-1, 4, 0, 6, 4],\n [-4, 2, -4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 3, -6, 6, 2],\n [2, 4, -2, -1, 4],\n [5, 0, -2, 5, 0],\n [1, -2, 6, 4, -2],\n [-6, -2, 6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 6, 4, 0, -3],\n [3, 6, 2, 2, 5],\n [-5, 6, -5, -4, -2],\n [5, -6, -2, -4, 0],\n [-4, -2, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 0, 5, 3, -6],\n [-1, 3, 3, 2, -3],\n [-1, -3, 2, 5, -3],\n [-1, 3, 5, 0, 1],\n [2, 3, -5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 1, 1, -5, 2],\n [3, 2, -4, -4, 1],\n [0, -2, -5, 4, 6],\n [-6, -2, -3, 0, -4],\n [2, 5, -2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, -3, 4, 0],\n [-5, 5, 5, -2, 5],\n [-5, -5, -5, -4, -6],\n [4, -1, -1, 5, 4],\n [1, 3, -3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 5, -2, 6, 1],\n [-4, 0, 3, -2, -2],\n [-5, -2, -4, 1, 2],\n [-3, 0, -6, -3, 2],\n [-2, 4, -6, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -6, 2, 2, 6],\n [-6, 0, 1, -2, 5],\n [4, -5, -2, 2, 3],\n [-6, 4, 1, -3, -1],\n [3, -5, 5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, -3, 3, 3],\n [-2, 6, 4, -4, 1],\n [4, 4, 4, 4, -2],\n [-4, 4, 2, -6, 2],\n [-2, 3, -1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 6, 2, 0, -2],\n [2, -5, 1, -1, -3],\n [2, 3, -4, -5, 5],\n [-1, 1, 3, -6, 2],\n [-2, 3, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 2, -6, -1, 2],\n [0, 4, -4, -6, 4],\n [3, 0, 6, 4, 5],\n [-1, 1, 5, -3, 3],\n [-1, 0, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -1, -1, 1, 4],\n [2, 5, -5, 4, 2],\n [2, -2, 5, 1, 0],\n [5, 1, -2, -2, -2],\n [-1, -4, 5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -3, 2, 0, 4],\n [-3, 6, -4, 1, 1],\n [0, 0, -6, 1, 6],\n [-2, 5, -5, 6, -4],\n [2, -6, -5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -4, 4, -5, 1],\n [3, 0, -1, -6, 4],\n [-5, -1, -2, -3, 3],\n [6, -2, -5, -6, -1],\n [-3, -1, 2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -4, 3, -5, -4],\n [4, -6, 3, 5, -3],\n [-3, 3, -6, 1, 6],\n [-3, 0, -6, -5, 2],\n [-3, -5, -4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 0, 2, 3, 3],\n [4, -1, 4, 5, 2],\n [3, -4, 4, -4, 2],\n [-6, -2, 0, 2, -4],\n [0, 5, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 6, 4, -1, 3],\n [-1, -6, -5, 1, -5],\n [2, 1, 4, 1, 6],\n [3, -4, -3, 0, 2],\n [-6, -4, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 4, 3, -3, -3],\n [2, 2, 3, -1, -6],\n [3, -2, 6, 1, 4],\n [-3, -4, 5, -3, 6],\n [-2, -1, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -2, 6, 6, 6],\n [2, -5, -6, 4, -2],\n [0, -4, -5, -5, 1],\n [-6, 1, -4, -1, 2],\n [3, -1, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 0, 0, -4, 6],\n [6, 4, 2, -6, 0],\n [-6, 6, -4, 3, 2],\n [5, 0, -3, 1, -3],\n [-4, -4, 4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -2, -2, 2, -6],\n [0, -4, -5, 0, 1],\n [4, -4, 1, 5, 1],\n [1, 2, 2, -5, -6],\n [-6, -5, 3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -4, -2, 5, 6],\n [3, -3, -2, 6, 0],\n [4, -5, -2, 3, 5],\n [-6, -1, -3, -6, 4],\n [4, -2, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -6, 6, 0, 1],\n [1, 4, -3, -5, 4],\n [3, -1, 3, 0, 0],\n [0, -1, -1, 4, 6],\n [-6, -3, 4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 1, 1, 3, 5],\n [3, -3, 6, -3, 0],\n [-4, 1, 0, -2, 0],\n [-4, -3, -1, 2, -4],\n [2, -1, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, 0, -2, -4],\n [2, -4, 3, 2, 1],\n [-3, -2, -3, -6, -1],\n [-6, 4, -1, 5, -5],\n [3, 4, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -6, -6, 4, 2],\n [6, -2, 3, 5, -3],\n [3, -6, 4, 3, -3],\n [-6, 0, -3, -4, 4],\n [-3, 4, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -3, 1, -1, 3],\n [-1, 0, 2, 6, -3],\n [3, 0, 6, 5, -2],\n [-1, 3, -3, -6, -6],\n [3, 5, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 1, 0, -1, 1],\n [-5, -5, 4, -2, -1],\n [-3, 6, 2, 2, 3],\n [0, 0, 4, 5, -6],\n [3, -4, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -5, 3, 0, -1],\n [5, 0, -1, 3, 6],\n [-2, 2, -2, 2, -1],\n [5, -6, -4, -5, -6],\n [-6, 1, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 0, -5, 6, 2],\n [4, 5, -3, 0, 0],\n [3, -6, -4, 4, 3],\n [4, -6, 1, 3, -4],\n [4, -4, -3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -1, -5, -4, -3],\n [-3, -4, -2, -1, 6],\n [1, 5, 1, 6, 0],\n [-4, 4, -6, 3, -1],\n [2, 3, -1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, 4, -5, -6],\n [-6, -1, 6, -6, -5],\n [0, -2, 5, 3, -3],\n [1, -2, -2, 4, -1],\n [5, 5, 3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -1, 4, -6, 6],\n [1, 5, 4, -3, -2],\n [-2, -2, -1, 2, 4],\n [-4, -4, -3, -6, -2],\n [6, 3, 4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -2, 1, -5, -4],\n [1, -1, 2, -3, 5],\n [-6, -1, -6, 1, -4],\n [5, -2, -5, 5, -6],\n [2, 2, 5, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -5, 6, -5, 5],\n [-1, -5, 1, 3, 6],\n [2, -1, 3, 4, -6],\n [0, -2, -1, -4, 1],\n [0, 5, 5, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 3, 4, -1, -5],\n [1, 5, -3, 4, 3],\n [0, 1, -6, -6, -3],\n [-3, 5, -4, -5, -5],\n [-5, 2, 1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 2, -5, -5, -5],\n [0, 1, -1, 5, -1],\n [-6, 3, 6, 1, 0],\n [-3, 2, 0, 2, 4],\n [1, -1, -1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -3, -3, 1, 6],\n [2, 0, 0, -6, -4],\n [-1, 1, 5, 2, -5],\n [2, -6, 4, -3, -4],\n [2, 0, 4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 5, 5, 6, 0],\n [-6, 5, 5, -4, -3],\n [2, -6, 5, -5, -3],\n [5, -1, 6, -5, -3],\n [5, 3, 3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 0, 3, -1, -1],\n [-4, 4, 2, -3, 0],\n [-5, -1, 5, -4, 1],\n [-6, 1, 3, -4, 0],\n [-4, -1, 6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 6, 6, 6, 2],\n [5, -6, 3, 5, 4],\n [-6, 5, 6, -4, 1],\n [0, -3, -2, -5, 4],\n [-4, -4, 4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 5, 1, 0, 5],\n [1, -5, 2, 1, 0],\n [3, 3, -6, -5, 6],\n [-2, -1, 3, 0, -6],\n [2, -2, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -4, -6, 2, 0],\n [6, 1, -3, -5, 6],\n [-1, 1, -1, 1, 1],\n [2, 4, 2, -5, -6],\n [5, 5, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 1, 1, -1, -2],\n [3, 5, 6, -5, -6],\n [4, 5, 6, 6, 6],\n [6, -4, 1, 3, 6],\n [5, -2, 6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 0, 2, 2, 0],\n [5, 6, 4, 6, -6],\n [-5, -3, 3, 6, 2],\n [-5, -4, 3, 0, 5],\n [-5, 0, 4, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 3, -4, 2, 6],\n [6, -4, -1, -2, 4],\n [3, 5, 2, 6, 2],\n [-1, -1, 6, -3, 5],\n [2, -3, -4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -4, 1, 2, -3],\n [-5, 3, 2, 6, 6],\n [-3, 0, -2, 5, 1],\n [3, 3, 2, -2, 4],\n [1, 2, -1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -4, -3, -2, 5],\n [5, -6, -4, 4, 0],\n [2, -3, 2, -5, 0],\n [-3, -2, 0, 1, -5],\n [2, 3, 5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 1, 6, -1, 4],\n [4, -6, 1, -3, -1],\n [1, 4, -2, 0, -4],\n [1, 3, 4, 2, -1],\n [2, 0, 5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -1, 0, -5, -1],\n [4, 6, 2, 1, 5],\n [6, -1, -3, 5, -5],\n [-2, -5, -2, 0, -3],\n [-5, -5, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 3, -5, -4, -4],\n [-6, 2, -4, 2, 4],\n [1, 0, 2, 3, 4],\n [6, -4, 6, -3, -1],\n [-6, 3, 3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 0, -5, 1, -6],\n [-2, -5, 2, -4, 0],\n [-5, -5, -2, -3, -3],\n [-6, 3, 4, -4, -2],\n [5, 5, -5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 5, -6, 2, 3],\n [1, -3, -1, -2, 2],\n [6, 4, 4, -4, -2],\n [4, -3, 3, 6, 5],\n [1, -4, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, -5, 2, 3],\n [-1, -5, -4, -4, -6],\n [1, -6, -2, 1, 2],\n [2, -2, -4, -3, -6],\n [1, 6, 0, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 5, -5, 5, 1],\n [-2, -1, -1, -4, -5],\n [-2, -2, -6, -5, 3],\n [-2, -6, 0, -4, -1],\n [5, 4, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 4, -6, -5, 3],\n [-2, 6, -4, 0, 2],\n [1, -3, -4, 2, 2],\n [6, 5, 3, -4, 3],\n [0, 2, 6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -6, 4, 4, 6],\n [-1, 4, 1, 2, 6],\n [4, -1, 2, 5, -5],\n [4, 1, 4, -1, -1],\n [5, -3, -3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -4, 4, -6, -6],\n [-4, 3, 6, -1, -2],\n [2, 6, 1, 1, 1],\n [1, 5, 2, -5, -1],\n [-4, -6, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 2, 6, -1, -6],\n [3, -2, 5, 5, -4],\n [2, 6, 1, 2, 6],\n [-1, 2, 5, 5, -1],\n [-3, -3, -6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 2, -1, 4, 1],\n [-4, -5, -2, 0, 3],\n [6, -6, -2, 1, -5],\n [-1, -5, -5, -3, -4],\n [3, 2, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 4, -1, -1, 3],\n [-3, 6, -1, 0, 5],\n [1, 4, -3, 6, -3],\n [-6, -3, 5, -4, -6],\n [6, -1, -3, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -5, -5, 6, -2],\n [-3, -5, 1, 6, 5],\n [-1, -2, 2, 6, -4],\n [1, 3, -2, 0, 3],\n [6, -6, 6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 0, 0, -6, -6],\n [-4, -2, -6, 0, 6],\n [-4, -5, -4, -5, 6],\n [3, 5, 2, -4, 5],\n [-3, 0, -5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, 0, 2, 6],\n [5, -5, -2, 6, 4],\n [6, -3, -2, 3, 2],\n [-6, -6, -1, 6, 6],\n [4, 6, 6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 2, -5, 2, -5],\n [-4, -5, 4, -2, -1],\n [-3, 5, -4, 4, -1],\n [-4, 4, -6, 6, -6],\n [-2, 6, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -1, -5, 0, 5],\n [-1, -6, 6, 4, -4],\n [-1, -5, -6, 0, -5],\n [0, 3, 1, -3, 6],\n [-1, 1, 1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 2, -4, 1, -2],\n [-3, 0, -3, -4, -3],\n [-2, -4, -1, 5, 4],\n [-2, 2, 0, -3, 4],\n [3, -6, -3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -3, -4, 0, 3],\n [-4, 1, 6, 3, 6],\n [-6, 6, 3, -3, -1],\n [4, 3, -6, -4, 0],\n [1, 6, -1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 5, 3, -4, 2],\n [-6, 2, -3, -4, -3],\n [4, 6, 4, 0, -2],\n [0, 3, -5, 4, 3],\n [-1, 0, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 0, -1, 2, -4],\n [4, 3, -3, 3, 0],\n [-3, 3, -2, -1, 4],\n [4, -3, -4, -1, 4],\n [4, 0, 0, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -1, -6, 3, -2],\n [0, 2, 5, 4, -6],\n [5, 1, 2, 1, -1],\n [-1, 1, 5, 2, 3],\n [3, 5, 2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, 1, 2, -4],\n [4, 5, 6, 5, -6],\n [-6, -3, -5, 4, 2],\n [-1, 4, -2, -5, -6],\n [4, -6, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -4, 2, 5, 1],\n [3, 1, 6, 3, 3],\n [1, 4, -6, -1, 4],\n [-4, -4, -1, 3, 4],\n [2, 5, -6, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 3, -5, -6, 1],\n [0, -6, -3, 5, 0],\n [-2, -6, 4, 2, -5],\n [0, 6, 1, -4, -2],\n [3, -3, -5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, 0, 2, 2],\n [5, 6, 3, 3, -6],\n [-1, 4, 5, 4, 5],\n [5, -4, 1, -1, 5],\n [-4, 2, -1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 2, 6, -2, 5],\n [3, 6, -5, -6, 1],\n [6, 6, -1, 4, 6],\n [2, 1, -4, -4, -1],\n [3, -4, 3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -5, -5, -2, -6],\n [5, -1, 5, -1, -4],\n [2, -5, 3, -2, -1],\n [-6, -1, -3, 3, -4],\n [1, -2, 6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -1, -3, 5, -6],\n [4, -3, 1, 0, -3],\n [-5, 5, 2, 6, 6],\n [-2, -2, -5, -1, -3],\n [-3, -4, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -4, 5, 6, 5],\n [-3, 4, -4, 3, 3],\n [1, -3, -2, -2, 3],\n [-2, 4, 2, -2, 4],\n [0, 6, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 1, 3, 2, -2],\n [-4, 3, -3, -5, 2],\n [1, 5, 4, -4, -4],\n [4, 6, 1, 5, -3],\n [2, 0, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 1, 2, 5, -4],\n [-2, -5, -3, -4, 5],\n [-3, 4, 2, -3, 6],\n [0, 3, 0, 3, -6],\n [-2, -2, 1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 4, -2, 1, 6],\n [3, -6, -5, -3, -5],\n [5, -3, 2, 3, -5],\n [5, -5, 6, 6, -4],\n [-5, -2, 0, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -5, 3, 3, 2],\n [3, -2, -5, 6, -6],\n [0, 1, -2, 4, -6],\n [1, 3, -2, -5, -2],\n [-4, -5, 6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 5, 2, 6, -4],\n [2, -2, -1, 5, 4],\n [4, 4, 2, 5, 0],\n [2, 1, -6, 1, 4],\n [0, 2, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, -5, 3, -3],\n [-2, -1, -5, 1, -2],\n [3, 2, -1, -1, 1],\n [1, 3, 4, -4, 0],\n [-1, -6, 5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -2, -5, -4, 3],\n [-5, -4, -5, 6, 0],\n [5, 5, -3, 4, -1],\n [6, -4, 2, 5, -2],\n [-1, -4, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, -6, -1, -1],\n [4, -3, -4, -6, 2],\n [4, -2, -2, 5, -3],\n [5, -4, -4, -2, -1],\n [-4, 4, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -4, -6, -6, -2],\n [4, 4, -2, 1, 6],\n [5, 5, 5, -6, -5],\n [-3, 0, 1, -1, 3],\n [-4, 4, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, -2, 0, -6],\n [4, -2, 6, 6, 1],\n [-5, 3, 0, 0, -6],\n [0, 6, 5, 5, 1],\n [-3, -2, 6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -2, -5, 1, -2],\n [3, 1, -3, 5, 0],\n [-5, 6, 5, 0, 6],\n [-1, 2, 0, 3, 6],\n [6, 5, 5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 4, 0, -6, -3],\n [-4, -6, 0, -1, 0],\n [-3, 5, -5, 1, -4],\n [6, -4, -3, 1, 2],\n [2, -5, 6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -3, -6, 5, 5],\n [5, -4, 3, 6, 0],\n [-4, -2, -3, -3, 0],\n [-3, -5, 6, -5, 6],\n [1, 6, 3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -2, -5, 1, -6],\n [-6, -3, -6, 4, -2],\n [-5, 0, 1, -5, 5],\n [-3, 2, -4, 2, -6],\n [4, 1, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 0, -3, -1, -3],\n [0, 4, 0, 5, 3],\n [4, -5, 0, -5, 6],\n [-1, -2, -5, -5, 4],\n [-3, 6, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -6, 0, -6, -5],\n [6, 6, -2, 2, -6],\n [3, -2, -1, 3, 4],\n [1, -3, -4, 4, -5],\n [-1, -5, 0, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 0, -3, 6, -6],\n [-1, -6, -5, -6, -4],\n [6, 3, -4, -4, 0],\n [6, -6, -4, 0, -3],\n [-3, -6, 0, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -5, -3, 3, 6],\n [4, -1, -4, -1, 3],\n [1, -6, -4, 0, 0],\n [2, 4, -6, -1, 6],\n [-4, -2, -3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -2, 3, -1, 1],\n [-2, -5, -1, -6, -6],\n [-4, 3, -3, -2, -1],\n [0, -5, 4, 0, -1],\n [-5, 1, -1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 6, 5, 3, 0],\n [6, -4, 0, -6, 4],\n [-1, -5, 5, 4, 3],\n [0, -5, 2, -4, 3],\n [1, -2, 6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -5, -4, 6, 1],\n [2, -4, 5, 5, 6],\n [-1, 1, -3, 4, -6],\n [5, 4, 2, 3, 0],\n [5, -2, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -5, 5, -3, 1],\n [-5, -2, -6, 1, 0],\n [5, -3, -4, 4, -5],\n [3, 0, 1, -4, -4],\n [6, 4, -1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -5, 2, -5, -3],\n [3, 6, -6, 3, -6],\n [-4, 5, 0, 2, -5],\n [-6, 4, -4, -5, -6],\n [-2, 1, -5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -3, 1, -5, -5],\n [-1, -2, 5, 2, 4],\n [-6, 5, 0, -4, -5],\n [-3, 4, -5, -5, -6],\n [6, -3, 3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 4, 3, 1, 0],\n [5, 1, -6, -6, -3],\n [2, 1, 3, 4, 1],\n [2, -3, -5, 6, 5],\n [2, 6, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 3, 5, -1, 6],\n [6, -3, 5, 4, 4],\n [-4, -3, 3, 0, 4],\n [6, 3, -3, 5, -6],\n [-1, 4, 0, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 5, 5, -6, 4],\n [3, 2, 0, 1, 3],\n [-5, 3, 1, 6, 2],\n [-4, 0, -1, 6, 0],\n [5, 3, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -2, -2, -2, 5],\n [-1, -5, -5, 6, 6],\n [-5, 5, 2, 2, 0],\n [6, -4, -1, -2, -4],\n [4, 5, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 3, 3, -5, -6],\n [-1, -5, 0, -1, -2],\n [-3, -6, 0, 1, 0],\n [2, -6, -3, 2, 4],\n [4, -1, 5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 2, 1, -6, -4],\n [-3, -6, -5, -2, 6],\n [0, -6, 3, 3, 5],\n [-3, 2, -4, -4, -6],\n [-3, 2, 2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, 4, -4, -3],\n [-5, 5, -4, 2, -4],\n [1, -3, -1, -2, 3],\n [-4, 3, -2, 1, -1],\n [-4, -2, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 4, -1, 2, -2],\n [3, -5, 0, 6, 3],\n [-6, 3, 5, -1, 4],\n [3, -4, -1, 6, 6],\n [-4, 0, 5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 1, -6, -6, 4],\n [-3, -1, -3, -2, 6],\n [-4, 5, 2, 4, 1],\n [-2, 2, 6, -6, -5],\n [-5, 1, 2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 5, 6, -4, -2],\n [0, 2, 1, -4, 1],\n [-1, 3, 6, 3, 6],\n [0, -6, -5, 6, 4],\n [5, 4, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, 5, 4, -2],\n [2, 1, 1, 3, -6],\n [-6, 5, -4, 4, 1],\n [-2, -5, -6, 5, 2],\n [-6, 6, 5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 4, -6, -1, -1],\n [6, 0, -1, 5, -3],\n [3, 2, 6, -4, 3],\n [1, -6, 1, -6, -4],\n [1, 5, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 3, -5, 5, 6],\n [3, -3, 0, -3, 2],\n [-3, 5, 5, 1, 0],\n [-3, -5, 5, 2, 3],\n [1, 2, 5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 4, -2, -6, 2],\n [-4, 3, 3, 5, 2],\n [1, -5, -5, 5, 6],\n [-3, 5, -3, 1, -4],\n [-2, 5, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 1, -2, -4, 5],\n [-1, -1, 0, 0, -4],\n [1, 2, 0, -5, 2],\n [-1, 1, 6, -5, 2],\n [1, -6, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 5, 0, -1, -5],\n [5, 2, -5, -6, 4],\n [-1, 6, 4, 2, -1],\n [1, 2, 4, -3, 2],\n [3, 6, 6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 3, -5, -6, 6],\n [-1, 3, -4, 5, -2],\n [-5, 0, 5, -4, 1],\n [-3, 2, 4, -2, -1],\n [-5, 2, 3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -6, -3, 5, 0],\n [0, 2, -2, 1, 6],\n [2, 6, -2, -6, 5],\n [5, 2, 0, 0, -6],\n [5, 5, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, 1, -6, -4],\n [2, -5, 0, 4, -4],\n [0, 4, 3, 6, 4],\n [-6, 3, 1, 6, -1],\n [-4, 3, 6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 3, 6, -4, 5],\n [-6, 1, 0, 4, 2],\n [-3, 1, 0, 3, -2],\n [2, -1, -3, 3, -3],\n [0, -1, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 1, 3, 6, 5],\n [5, -5, 5, 3, -4],\n [4, -5, 5, 6, 2],\n [0, -3, 3, -3, 0],\n [-5, 0, -5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -2, -1, 2, 1],\n [-1, 3, 4, 0, 1],\n [4, -4, -5, -4, -1],\n [4, -6, -3, -5, 0],\n [5, 1, -4, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 1, -2, 6, 3],\n [0, 3, 4, -4, 1],\n [-5, 3, -3, 2, -6],\n [-6, 3, -2, 6, -2],\n [-5, 4, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 2, 1, 1, -5],\n [4, -4, -2, -3, 5],\n [5, -2, 0, 0, -3],\n [2, -3, 3, 3, -3],\n [2, 3, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -1, -1, 6, 5],\n [-2, -5, 5, -5, 5],\n [3, 4, -1, -5, -3],\n [-5, -6, 0, -1, -6],\n [-5, 1, 1, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 6, -6, 5, -5],\n [-1, -1, 0, -3, 4],\n [-1, -5, -5, 1, 2],\n [3, 2, 4, -5, -6],\n [-6, -3, 2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 5, 6, 1, 5],\n [-4, -3, -3, 2, 1],\n [-2, 4, 5, -6, 2],\n [2, 1, -6, 6, -6],\n [3, -2, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 1, 0, -5, 4],\n [0, 2, -3, 2, -3],\n [-2, 4, 2, -1, 5],\n [5, 2, 2, -3, -5],\n [-1, 0, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -5, -4, 4, 3],\n [-2, 4, -2, 6, 4],\n [2, 4, 6, -3, -1],\n [0, -4, -4, 4, -4],\n [-1, 5, 2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 3, -1, 0, -2],\n [-5, 5, 0, 5, 6],\n [-1, 0, 2, -4, 2],\n [-5, 4, 3, 2, 6],\n [-1, 3, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -3, -2, -5, -3],\n [-3, 3, 3, -4, -3],\n [-4, 4, 5, 2, -4],\n [-2, -3, 2, 5, 0],\n [-3, -6, -5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, 4, 0, 0],\n [6, 2, 3, 2, 3],\n [-3, -6, -6, -2, 3],\n [4, -1, -3, 6, -4],\n [4, -3, 3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -5, 0, -1, -3],\n [-4, -1, -6, 3, 4],\n [4, -2, 2, 3, 1],\n [-4, 0, 4, 6, 1],\n [3, 0, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -1, 4, 1, 2],\n [0, -6, 2, 6, 4],\n [-5, 3, -5, 6, -6],\n [6, -2, 5, 0, 2],\n [2, -4, -2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 4, 2, 6, 2],\n [-1, -6, -2, 6, 6],\n [1, -4, 0, -4, 5],\n [-6, 3, -5, 5, 4],\n [-1, 4, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, 6, -5, 1],\n [6, 6, 3, 0, -6],\n [3, -1, -2, -5, 5],\n [3, 0, 6, 4, -1],\n [-2, -6, 1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -1, 2, -2, 1],\n [-3, 4, -3, 2, 5],\n [6, -6, -4, 1, 3],\n [-6, -2, 6, 5, 6],\n [-4, -3, -3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 1, -3, -5, 0],\n [5, 0, 1, 2, -3],\n [2, 6, 6, -1, 6],\n [-5, -5, -5, -6, -1],\n [1, 6, -5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 4, 2, 6, -6],\n [6, 3, 2, 3, 5],\n [3, -2, -5, 4, 3],\n [-5, 2, -4, 3, 5],\n [5, 1, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -3, 5, 1, 4],\n [1, -3, -4, 5, 6],\n [2, 5, 6, -2, 1],\n [-2, 4, -1, 4, -6],\n [-3, 2, -5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -2, 2, 6, -4],\n [3, 5, 2, -1, -1],\n [-1, 4, 0, -1, -5],\n [-3, 5, 5, 4, 0],\n [-5, -1, 0, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -1, -4, -6, 1],\n [-4, 4, 1, -1, -2],\n [-1, -5, 4, -4, -2],\n [6, -2, 3, -2, -2],\n [3, -5, -1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -2, 5, -1, -6],\n [-5, 1, 1, -5, -1],\n [-5, -4, 2, -2, -2],\n [5, 1, 1, -5, -3],\n [3, 2, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -4, 3, -3, 6],\n [0, -5, 4, 4, -6],\n [-4, 1, 0, 0, -1],\n [-2, -6, -3, 0, 6],\n [-6, 3, -1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 5, -3, 5, 6],\n [-3, -5, -2, 6, -5],\n [1, 2, 3, 4, -4],\n [0, -5, -1, -6, 4],\n [3, -6, 4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -2, -6, 3, -4],\n [-1, 3, -4, 6, -1],\n [4, 2, 3, -5, 2],\n [-5, 2, -4, -5, -2],\n [-3, -6, -5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -2, 2, -4, 3],\n [0, 2, -5, -6, 4],\n [4, 4, -4, 2, 3],\n [5, 3, -2, -3, -4],\n [-2, -2, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 2, -2, 3, 4],\n [0, 4, -5, -1, -5],\n [1, -4, -5, -1, 6],\n [-1, -3, 3, 6, 0],\n [-2, 1, -2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 2, 0, -2, 3],\n [1, 6, 0, 4, 6],\n [3, 0, -3, 3, 4],\n [3, 5, -2, 1, -2],\n [1, 0, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 0, 2, -2, 4],\n [-5, 6, 1, 5, 2],\n [5, 3, 5, 6, -4],\n [-4, -1, 6, -1, 5],\n [-6, 0, -3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 0, 6, -3, 1],\n [-3, 0, 1, 5, -4],\n [-1, -2, 5, 4, 1],\n [0, -4, -5, 0, -6],\n [-5, -6, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 2, 4, 5, -1],\n [2, -2, -6, -2, 0],\n [-5, 4, 4, -5, -4],\n [2, -1, 2, -2, -4],\n [4, 4, -3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -6, -5, 6, 2],\n [2, -1, -1, -6, 1],\n [-2, -5, 6, 4, 3],\n [0, -4, 0, -4, -6],\n [-3, 3, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -2, -1, -1, 1],\n [3, -3, -5, -2, -2],\n [-6, -5, 5, -1, -6],\n [4, 6, 6, 6, 4],\n [-2, -3, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -4, 1, 4, 6],\n [2, -5, 4, -4, 4],\n [3, -1, -4, 3, 6],\n [0, -4, 6, -4, -4],\n [0, -3, 2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -2, 3, 6, 3],\n [6, -3, 0, 0, -1],\n [5, -1, 2, 3, 6],\n [4, 4, -3, -4, 2],\n [-1, 6, -3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -6, -4, -4, 2],\n [2, 6, -6, 6, 0],\n [-3, -4, -6, -3, 5],\n [-1, -3, 0, -1, -4],\n [-3, 2, -2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 6, 5, 1, -4],\n [2, 1, 4, -1, -3],\n [1, -1, 4, 0, 6],\n [-6, 2, 3, 3, -6],\n [-2, 1, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -1, 6, -3, 3],\n [-1, 2, 5, -4, -1],\n [3, 4, 6, 4, -1],\n [-2, 2, -1, 0, 0],\n [6, -6, 6, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 6, 6, 0, -1],\n [0, -3, -3, -4, 4],\n [-6, -5, 6, 6, 5],\n [3, 2, -5, -5, -4],\n [3, -5, 4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 6, 1, -1, -1],\n [3, 1, 6, 4, 4],\n [-4, 2, 0, -3, -1],\n [6, -4, 2, -1, 6],\n [0, 2, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 1, 0, -6, -6],\n [4, -5, 3, 2, -2],\n [3, -4, -2, 0, -5],\n [-6, -6, 1, -1, 4],\n [-3, -5, 1, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 6, 6, 4, -5],\n [1, -4, 1, 3, 5],\n [4, -3, 2, 3, 0],\n [-2, -5, 6, 5, -5],\n [0, -6, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 5, 2, -5, 1],\n [1, 1, 6, 3, -6],\n [0, -2, 0, 2, -5],\n [5, 4, 6, 3, -4],\n [-3, -1, 5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 3, -2, -3, 4],\n [4, 3, -6, -3, -1],\n [-2, 4, 2, 5, -1],\n [-6, -4, 3, 2, -3],\n [1, 3, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -2, 4, 2, -5],\n [5, -5, 5, -3, -4],\n [-5, -2, 5, 6, 1],\n [-6, -3, 0, 3, -5],\n [-6, -4, 2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -2, -2, 5, 6],\n [-3, -3, 2, -3, -5],\n [3, 2, 5, 3, 4],\n [-6, -4, -2, 2, -2],\n [4, 3, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 2, -4, 3, 2],\n [-5, -6, 6, -2, 5],\n [1, -2, 0, -6, 1],\n [2, -2, -6, -4, 2],\n [0, 6, -3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 3, 1, -4, -6],\n [-2, -6, 1, -1, -4],\n [-5, -4, 3, -4, 3],\n [2, 0, -3, 5, -5],\n [-4, -3, -5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -1, -4, 5, -2],\n [6, -5, -6, -4, -2],\n [-1, 3, 1, -2, 3],\n [-6, -3, -1, 6, -4],\n [-6, 4, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 0, -1, -4, -3],\n [3, 3, -3, -6, -6],\n [-5, 0, -1, 1, 3],\n [1, 4, -2, 4, -2],\n [-2, 0, -5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -2, 4, 3, -4],\n [6, 1, -1, 2, -3],\n [2, 1, 5, 1, -6],\n [-5, 3, 4, 5, -1],\n [4, -1, -1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -5, -6, -3, -2],\n [1, -3, 5, -4, 6],\n [-4, -2, -6, -4, -5],\n [-1, -2, -4, -4, 1],\n [3, 4, -2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 1, -1, 3, 6],\n [3, 5, -1, -4, 0],\n [-3, 5, 5, 5, -2],\n [1, 3, -3, -5, 3],\n [2, -4, 1, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 4, 0, 3, 6],\n [0, 1, -2, -4, -2],\n [-4, 0, -3, 6, 5],\n [-1, -3, 6, -5, -5],\n [6, 6, 5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, 1, 6, -6],\n [-3, -5, 6, 6, 5],\n [5, -2, -2, 1, 3],\n [-1, -6, -1, -6, 1],\n [-2, 3, -1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 1, -3, -1, 3],\n [-6, -4, -3, -4, 2],\n [-5, -1, -5, 1, 0],\n [-3, 3, -6, -5, -4],\n [6, -5, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 6, 3, 1, 0],\n [-2, 0, -2, -6, 1],\n [1, -4, 2, 3, -6],\n [3, 1, 6, 1, -4],\n [-1, -4, 1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, -2, 0, -6],\n [-6, -6, -5, -3, -5],\n [-1, 2, -4, 0, -5],\n [-6, -3, 2, 2, 3],\n [0, -5, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 5, 6, -1, 3],\n [0, -6, 1, 3, 6],\n [-5, 1, -2, 3, 4],\n [3, 2, -3, -2, 5],\n [0, 1, -4, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -3, 1, 3, 5],\n [3, 5, -2, 5, -5],\n [6, 6, -6, -6, -1],\n [1, 5, -6, -6, 3],\n [2, 2, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 0, -2, -2, -3],\n [6, 0, 0, -1, 0],\n [4, -4, -3, 2, 5],\n [4, -2, 4, -6, 0],\n [6, -1, -6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, -5, -6, 2],\n [-3, -4, 4, -1, 4],\n [1, -1, -5, 0, 2],\n [2, -5, -1, -5, 2],\n [2, 3, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 1, 3, 3, 0],\n [-4, 6, -6, 4, 0],\n [1, 3, 5, 3, 1],\n [2, -3, 3, -6, 5],\n [-5, 4, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, 2, -5, -5],\n [1, 6, 0, 2, -4],\n [0, 4, 5, -2, -2],\n [-4, 1, 3, 0, 1],\n [0, 6, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 6, 4, 5, 5],\n [6, 1, -2, -3, -2],\n [-4, 2, 2, -1, 0],\n [-3, -6, -5, 4, 0],\n [-4, 2, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 1, 1, -1, 3],\n [-3, 2, 2, -5, -5],\n [5, -2, -5, -2, -2],\n [0, -3, 4, -5, -1],\n [-6, 3, 2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -2, -2, -4, 5],\n [4, 2, -1, -3, 3],\n [4, 3, 0, 3, 1],\n [-1, 2, 5, -4, -5],\n [-3, 2, 2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 0, 3, -1, -2],\n [6, -1, 5, -5, -3],\n [2, -6, -1, -1, -4],\n [-2, 0, -2, 2, -5],\n [-4, -6, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -6, -2, 6, 5],\n [-5, 6, 2, 2, -2],\n [-6, 5, -3, -3, 4],\n [6, 5, 1, -2, -3],\n [5, 1, 6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 5, 3, -2, 0],\n [2, -2, 6, 4, -2],\n [5, 0, -5, 3, 2],\n [4, 4, 6, -5, 3],\n [-5, -6, 6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 1, 3, 2, 2],\n [-3, -5, 5, 2, -1],\n [4, -5, 2, 3, 4],\n [-6, -6, 0, 5, 5],\n [-3, 4, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 4, -2, 2, -1],\n [4, 3, 5, 6, 0],\n [2, 0, -1, -4, -5],\n [-2, -5, 4, 2, 0],\n [-2, -1, -1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 1, -4, 2, -3],\n [4, 0, 0, -1, 0],\n [-5, -1, -5, -2, -3],\n [-6, 6, 2, 2, 1],\n [-2, 5, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 5, -1, -2, 1],\n [3, 6, 2, 6, -4],\n [6, -4, -4, 0, 1],\n [-6, -4, -2, 0, 1],\n [-3, -1, -3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -4, 1, -1, -2],\n [-6, -1, 1, 4, 1],\n [-5, -6, -3, 5, -2],\n [4, -4, -1, -5, 6],\n [6, -2, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -2, -3, -4, -1],\n [4, -5, 6, 5, 5],\n [-2, -1, -6, 3, 5],\n [-6, -5, 5, -4, 1],\n [-3, 2, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 5, 0, 0, -1],\n [0, 4, 0, -4, 3],\n [-3, -1, -1, 3, 1],\n [-4, 1, -6, 6, -6],\n [0, 2, -6, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -4, -2, -5, 6],\n [5, 3, 6, 6, -5],\n [2, -4, -4, 0, 5],\n [5, 1, -6, 1, -2],\n [6, 6, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -6, 1, -2, 2],\n [-3, 2, -4, -1, -6],\n [-5, -1, -1, 6, -1],\n [-1, 6, 5, -5, 0],\n [-6, 2, 2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 3, 2, -2, -1],\n [-6, -2, -6, 1, 2],\n [3, 2, 6, 6, -3],\n [-4, -2, 3, -3, 0],\n [4, 1, 3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -3, 3, 3, 3],\n [5, 2, 1, 0, 0],\n [1, 1, 4, -1, 4],\n [2, -6, 1, -1, -2],\n [-5, -2, -3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 5, -2, 2, 3],\n [1, 1, -5, 4, 6],\n [4, 3, 2, -2, -1],\n [-3, -2, 5, 6, -2],\n [5, 0, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 0, 5, 2, 5],\n [3, -3, 1, 2, -5],\n [-2, 1, -6, 6, -5],\n [-3, 6, 6, 3, 4],\n [-4, -4, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 0, -3, -1, -3],\n [-3, 3, -6, -1, -4],\n [-6, -2, 0, -4, 6],\n [-2, -2, 6, 5, 3],\n [6, 1, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 1, 6, 0, -2],\n [-5, 4, 3, 6, 2],\n [-1, 3, 3, 0, -6],\n [-1, 3, 6, -1, 1],\n [-6, -2, -2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 0, -3, 5, 1],\n [6, -3, -5, -5, 2],\n [1, 6, -5, 1, 0],\n [6, 6, 1, -5, 0],\n [0, 0, -5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, 0, 1, 1],\n [6, 0, 2, -2, 4],\n [-3, -1, -1, 1, 3],\n [-6, -2, -3, 2, 3],\n [-3, -4, 1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -3, 3, 3, 1],\n [-2, 5, -6, -3, -2],\n [-5, -1, -6, -3, 4],\n [3, -6, -6, 5, -4],\n [-5, -5, 6, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -4, -5, -1, 5],\n [0, -5, -2, 1, 4],\n [2, 6, 0, 3, -4],\n [-1, 5, 0, 1, 2],\n [-4, 5, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 4, -4, -1, -2],\n [-3, -5, -3, -5, 5],\n [-5, 6, -4, -1, -4],\n [0, 6, 2, -3, -2],\n [6, -5, -5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 3, 4, 4, -6],\n [1, 3, 0, -1, -3],\n [-3, -4, 6, -6, 5],\n [-6, 5, 0, -5, -6],\n [5, 0, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, -2, 5, -3],\n [2, 5, 2, 0, 6],\n [0, -1, -2, 4, 3],\n [-2, 4, -4, 5, -1],\n [4, 5, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 1, -5, -1, 6],\n [6, -3, 1, 5, 3],\n [-4, -6, -4, -1, 6],\n [-6, -4, 1, 1, -6],\n [3, 2, 0, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -1, -5, -6, -2],\n [-5, 6, 0, 2, 4],\n [-4, -4, 1, -2, 4],\n [-4, 4, -1, 1, -6],\n [3, 2, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, -2, -3, 0],\n [3, 5, 2, -4, 2],\n [-1, 2, 5, -3, -4],\n [2, 1, 1, -1, -2],\n [-1, 0, 4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -4, -1, -6, 3],\n [3, 2, -1, 3, 0],\n [3, 5, -3, 0, -4],\n [6, -6, -3, -1, 4],\n [1, -6, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -5, -4, 1, 2],\n [3, -1, 3, -4, -4],\n [4, -5, 1, 6, -2],\n [-1, -4, -6, -5, -1],\n [-1, -1, -5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -5, 2, 3, -3],\n [-6, 0, 0, -5, -5],\n [3, -6, -5, 6, -3],\n [-3, -5, -3, -3, 2],\n [-6, 2, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 4, 2, -2, -4],\n [-2, -4, -5, -5, -6],\n [-6, 0, -3, 5, -4],\n [-6, -1, 3, -3, -5],\n [4, 4, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 0, -5, -5, 4],\n [1, 6, 3, -2, 4],\n [-1, 0, -6, -3, -1],\n [-2, 4, -5, 3, -1],\n [-6, -3, -6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, 3, -2, 6],\n [4, -1, -1, -5, -5],\n [2, 5, 0, -1, -1],\n [2, 4, -6, -3, 5],\n [4, -1, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 0, -3, 5, -5],\n [-2, -2, -3, 1, 1],\n [4, 4, -2, 0, 2],\n [-3, 1, 4, 4, 0],\n [-6, -4, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -3, -2, 1, -6],\n [-2, -3, -1, 1, -1],\n [-2, 4, 1, 3, -6],\n [-4, -1, -1, 0, 3],\n [-3, -3, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 6, -2, 1, 5],\n [0, -3, 6, -2, 4],\n [0, 5, -4, -2, -3],\n [-3, 6, 0, -4, 2],\n [-4, 4, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -3, 0, 4, -6],\n [5, -1, -1, 6, -3],\n [5, -4, 2, 3, -6],\n [-1, -5, 3, -3, 0],\n [-3, 2, -6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 2, -3, -3, -6],\n [6, 3, -3, -5, 2],\n [0, -2, 4, 0, -3],\n [3, 3, 3, -3, 4],\n [-1, 5, 0, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -6, 3, -6, 2],\n [-5, 0, 6, 3, 0],\n [-4, 2, 2, -5, -1],\n [6, 6, 3, 3, -5],\n [5, -3, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -4, -5, -4, 1],\n [-5, -2, 2, -4, -6],\n [0, -6, -5, 6, 4],\n [5, -1, -6, 3, 5],\n [4, -5, -1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 5, 2, 5, -1],\n [6, -2, -4, -3, -3],\n [-2, -1, 0, 0, -4],\n [-3, -3, -2, -4, -2],\n [-4, -3, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -4, 5, -5, 5],\n [-3, 4, 6, 1, 2],\n [2, -2, 6, 1, -5],\n [-4, 5, 3, 5, 3],\n [3, 4, -6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 5, -2, -4, -4],\n [2, -4, 5, -2, 0],\n [-4, 3, 3, -4, 6],\n [6, 2, 2, -6, 5],\n [-5, -2, 0, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 3, 3, -2, 6],\n [1, -6, 6, 4, 1],\n [-5, 1, -2, 1, -1],\n [3, -2, -5, 6, 5],\n [5, -3, 2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 6, 4, 1, -2],\n [-6, 0, -2, 2, 2],\n [0, -4, 3, -5, 5],\n [4, -4, -1, -2, -4],\n [6, 3, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -6, -5, -6, 1],\n [2, -3, -6, 5, -4],\n [2, -5, -2, 6, 5],\n [-3, 1, 0, 2, 5],\n [-1, 3, -1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 5, 6, 5, -4],\n [3, -4, 4, -4, -3],\n [5, 2, 2, -5, 1],\n [-3, -4, -3, -5, -4],\n [-2, -4, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -4, -6, 3, -2],\n [6, 1, 1, -4, 5],\n [3, -1, -4, 0, 0],\n [-3, 1, -3, 1, -6],\n [5, 5, 1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -4, -3, 5, 1],\n [-4, -1, 1, 0, -6],\n [-1, 4, -3, 5, -4],\n [6, -1, -2, 6, -4],\n [-6, 5, -2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 1, -1, 4, 2],\n [4, 2, 2, 2, 3],\n [1, 6, -5, -4, 2],\n [4, -1, 0, -5, 0],\n [-1, -6, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -2, 0, 6, 5],\n [-3, -2, 3, 2, -3],\n [5, 5, 6, 6, 3],\n [-2, 5, 6, 4, 0],\n [0, -3, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 1, -6, -6, 3],\n [-1, -4, -1, -1, 4],\n [-3, 4, -4, -2, -3],\n [-4, 5, 3, 3, 3],\n [-3, 3, -3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 2, -4, -6, -6],\n [0, 5, -5, -1, -4],\n [6, -4, 3, 3, 6],\n [4, -6, -6, 3, -1],\n [1, 6, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 3, -2, 2, 0],\n [-5, -5, 6, 0, 0],\n [-5, 4, 0, -6, -6],\n [1, 5, -4, 6, 0],\n [5, 2, -1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, 1, 4, 1],\n [-4, 2, -5, -5, 5],\n [4, 3, 1, 0, 3],\n [-6, 4, 6, -3, 4],\n [6, -3, -3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 5, 1, 5, 3],\n [6, -5, -5, -4, -2],\n [1, -2, 2, 2, -5],\n [-2, -2, -2, 3, 6],\n [-4, -3, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -4, 3, -1, -5],\n [-3, -5, 4, 1, -1],\n [-2, -3, -6, 6, 3],\n [-5, 1, -1, 5, -4],\n [3, 6, 2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -3, 6, 5, 1],\n [-2, 6, -5, 4, -6],\n [-4, -5, 2, 4, -2],\n [-4, 0, 3, 0, 2],\n [-1, 1, -2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -4, 3, -6, -1],\n [-6, -5, 4, 3, -5],\n [-4, -3, -2, -6, -3],\n [-1, 1, 2, 6, -3],\n [-4, -5, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -6, 4, 6, -4],\n [1, -6, -2, -6, 6],\n [1, 3, -4, -4, -5],\n [-1, -3, -3, 0, 6],\n [0, -1, 5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 5, 5, 6, 2],\n [5, 5, -6, 6, 4],\n [-3, 1, 3, -2, -1],\n [3, -6, 1, -5, 1],\n [-4, -4, 3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 4, -5, -5, -1],\n [1, 0, 0, -4, 3],\n [-1, -1, -1, 5, 5],\n [6, 6, -1, -3, -3],\n [-4, -4, -2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 6, -5, 0, -2],\n [5, -5, 1, 2, -3],\n [2, 1, 6, -3, -5],\n [6, 2, -5, 2, -3],\n [-4, 5, -3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -6, 5, -2, 1],\n [0, 1, 3, 0, -4],\n [3, -6, -2, 3, 0],\n [4, 2, -2, -3, 2],\n [6, -5, -5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 3, 3, 1, -2],\n [6, -4, -1, 3, -6],\n [2, -1, 2, -5, 3],\n [6, 4, -5, 0, -6],\n [3, 0, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -2, -2, -4, -5],\n [-6, -5, 4, -4, 6],\n [-6, 5, 3, -3, 2],\n [5, 0, 6, 0, -5],\n [-3, 5, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -6, -6, 5, 5],\n [-5, 4, -4, -2, 3],\n [-4, -5, 3, 6, -6],\n [5, -6, -5, -5, 6],\n [-5, -1, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -5, 5, -3, 2],\n [-1, 1, -4, 5, 4],\n [-5, 0, 0, 3, 5],\n [1, 0, -6, 3, 1],\n [2, -1, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -5, 6, 6, 6],\n [0, -6, -5, 4, 2],\n [-1, -4, -4, -3, 6],\n [0, -5, 3, 0, 3],\n [-1, 6, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, 0, 5, -3],\n [1, 5, -2, 3, 5],\n [5, 5, 6, 1, -1],\n [-1, -4, -6, 2, 4],\n [-6, 4, 2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 5, -4, 1, -1],\n [-2, 0, -4, 0, 5],\n [-1, 4, -2, -6, -2],\n [-4, 5, 1, -3, -3],\n [-3, -1, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, 2, 5, -3],\n [-5, -3, 1, 6, 6],\n [3, -1, -1, 3, 1],\n [-6, -2, 6, -2, -4],\n [-1, -1, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 1, -2, -5, 5],\n [-5, -6, 1, 4, -3],\n [2, -1, -5, 3, -5],\n [4, 3, 0, -4, 1],\n [6, -5, 3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, -2, -1, 1],\n [-2, -3, 3, -5, -4],\n [0, 2, -2, -5, 4],\n [-5, -4, 0, -3, 1],\n [4, 3, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -6, -2, -6, 0],\n [3, 1, 1, -1, 3],\n [-3, 0, -2, -2, -1],\n [6, -4, 2, -3, 2],\n [2, 3, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 3, -6, 2, -6],\n [-2, -6, 6, 0, -6],\n [-5, 1, -5, -3, 6],\n [0, 1, 0, 3, -4],\n [-6, -4, -4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, -2, 0, 4],\n [6, -2, 0, -2, 5],\n [1, -1, 1, -4, 4],\n [-2, -4, 5, -6, 5],\n [0, -5, -2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -1, 6, -5, 4],\n [-5, 0, -6, -6, 0],\n [-4, 1, 2, 0, -4],\n [3, -4, -5, -5, 0],\n [-6, 5, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, -5, -1, -3],\n [6, 6, -4, -3, 2],\n [5, -3, -1, 0, 5],\n [-4, -5, -3, 3, 6],\n [-1, 0, 1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 1, 6, -6, 2],\n [2, 2, -3, 1, 5],\n [-6, 5, -6, 5, -3],\n [5, 4, -4, -5, -4],\n [0, 6, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 2, -4, -6, 1],\n [0, -6, -1, -1, -4],\n [3, -2, -1, -2, 0],\n [1, -3, 6, -3, -5],\n [-2, -6, 3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, -6, 1, 0],\n [3, -3, -4, -1, -3],\n [3, 6, -2, 1, 0],\n [-4, -5, 4, 3, -2],\n [1, -4, 5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -5, 3, 4, 0],\n [0, 2, -3, -4, -2],\n [6, -6, -3, 0, 6],\n [1, 3, 6, -3, 3],\n [-2, 2, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -5, -1, -5, 4],\n [1, -5, -4, 4, -5],\n [-3, 5, -2, 4, -2],\n [4, 4, 4, -1, -1],\n [4, 4, 6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 3, 3, 4, 5],\n [2, 6, -3, 3, -3],\n [4, -1, -5, -6, -5],\n [-2, 3, 3, 2, 5],\n [-5, -4, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -5, 3, -6, 6],\n [5, 3, -5, -2, -5],\n [5, 2, -4, -5, -5],\n [-3, -5, -3, -3, 5],\n [1, -4, -5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -2, -6, 5, -1],\n [4, -1, -6, -5, -3],\n [-3, 0, 6, 6, 0],\n [4, 6, 1, -3, 4],\n [-2, -6, -3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -5, -6, 4, -3],\n [6, -4, 5, 5, 1],\n [4, 4, -3, 1, 4],\n [-2, 6, 1, -2, 3],\n [2, -6, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -4, -4, 0, 5],\n [-6, -6, 3, -6, -4],\n [-1, 2, 1, 0, 4],\n [5, 6, -4, 1, 6],\n [1, -2, 3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -5, 3, -3, 4],\n [-1, 6, -4, -3, 6],\n [-6, -1, -3, 0, 1],\n [-4, -5, -6, 6, 6],\n [-2, 0, -1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 5, -1, -6, 3],\n [-3, -1, 4, 6, 6],\n [0, 3, 2, -6, 1],\n [6, 0, -6, -2, -4],\n [4, -3, 4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 0, -4, -2, 3],\n [3, 5, 5, 4, 5],\n [1, 6, 2, 4, 1],\n [1, 5, -5, -4, 1],\n [-3, 0, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 4, 4, -4, 5],\n [5, -6, -2, -3, -1],\n [6, -2, 5, 3, 0],\n [3, -3, 4, -6, 6],\n [3, -6, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 1, 1, -2, 1],\n [-5, -6, 1, -4, -3],\n [-2, -6, 0, -6, -5],\n [-3, -4, -4, -5, 5],\n [0, 4, 3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 4, 0, 4, 3],\n [-5, -2, -3, -6, -2],\n [2, -1, -4, 4, 6],\n [-4, 5, -1, -2, 6],\n [3, 0, 0, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 6, -4, -6, -6],\n [-3, -3, 1, 0, -5],\n [-5, -1, 2, -4, -5],\n [1, -2, -4, 0, 2],\n [0, 3, -5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -2, 3, 4, -2],\n [-3, 2, 6, 5, -6],\n [0, 3, 0, -4, 4],\n [-3, -1, 2, 4, 5],\n [2, -4, -6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -6, -6, 5, -6],\n [-1, 5, -1, 6, -2],\n [6, -3, 1, 1, -2],\n [-5, 1, -2, -4, 4],\n [-5, 0, 0, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -3, -3, -5, 1],\n [-4, 2, -3, -5, -2],\n [3, -1, 2, 4, -6],\n [3, 4, 1, -5, 6],\n [-4, 0, 6, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, 0, 0, 2],\n [-6, 1, -3, 6, 1],\n [5, -5, 6, 2, -6],\n [0, -2, -1, -4, -5],\n [-4, -1, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -5, -4, 4, 2],\n [2, 0, 0, 1, 1],\n [4, -4, 6, 5, -3],\n [-1, -3, 3, -4, -5],\n [-6, 4, -4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -4, -4, -4, 6],\n [0, -4, -4, -3, -3],\n [4, 0, -4, -1, 0],\n [0, 4, -6, 1, -6],\n [3, 4, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 4, -5, -1, -2],\n [1, 6, 3, -6, -1],\n [1, -4, -6, -1, -5],\n [3, -1, -6, -5, 0],\n [-3, -5, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -4, -1, 2, 4],\n [-3, -2, -2, -1, 0],\n [-1, -3, 6, -4, 0],\n [-5, 2, 6, 5, 4],\n [6, 5, 3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -3, 4, -5, 5],\n [3, -6, -4, 4, 0],\n [-3, -4, 4, 4, 1],\n [-6, -6, -1, 6, -4],\n [-6, -2, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 1, -1, -3, 6],\n [0, -5, -6, 0, -5],\n [4, -5, 1, -2, 2],\n [2, -6, -3, 4, -6],\n [0, -4, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 4, -1, -4, 1],\n [-5, -6, -2, 2, 4],\n [-3, 0, -1, 5, -1],\n [-5, -4, -6, -6, -3],\n [-3, 3, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 6, 3, 5, 1],\n [-1, 6, 2, -6, -5],\n [-5, 0, 3, 0, -2],\n [-5, 3, -4, -2, -1],\n [0, -4, 6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -6, 0, 5, -2],\n [-4, -3, 0, -1, -1],\n [-4, -6, -2, 2, 2],\n [-4, -6, -1, -4, -2],\n [-4, -5, -1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 4, -4, -2, -2],\n [2, 4, 1, 6, 4],\n [4, 4, -3, -5, 3],\n [-1, 0, 2, 0, 4],\n [-3, 4, 6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, -3, -3, -3],\n [-5, 1, 4, 4, 6],\n [-5, 5, 3, -4, -1],\n [0, 1, -5, 6, -1],\n [-3, 2, 6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 3, -4, -5, 5],\n [-4, -4, 3, -5, -5],\n [6, 5, -1, 1, -2],\n [-2, -3, -1, -4, -4],\n [4, 5, -6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -4, 6, 2, -1],\n [4, 2, 5, -4, -1],\n [1, 6, -1, -6, 3],\n [5, 0, -1, 5, -6],\n [4, 3, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -6, 4, -1, 5],\n [6, 6, -5, -2, 4],\n [6, -3, -5, -4, -2],\n [5, -4, 1, 0, 4],\n [1, 1, 6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 1, -1, -2, 4],\n [1, -5, -4, 6, 3],\n [2, -1, 6, 0, 1],\n [-4, 6, 6, 3, 1],\n [-3, -6, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -1, 0, -3, 4],\n [-1, 3, 0, 2, -3],\n [-1, -6, -3, -5, -4],\n [0, -4, 4, 0, 3],\n [5, 3, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -4, 5, 4, -1],\n [2, 4, 5, 6, -5],\n [-3, 3, -4, 5, -6],\n [-3, 6, -2, -5, -4],\n [-4, 0, -2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -3, 2, 0, -2],\n [1, 3, 6, 0, -5],\n [-3, 1, 3, 5, 0],\n [-3, -6, 3, 6, -4],\n [0, 6, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -4, -5, -1, 4],\n [5, 6, 4, 1, -6],\n [2, 1, -4, 5, -3],\n [-4, 5, -6, 6, -1],\n [6, 6, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 6, 2, -2, 3],\n [4, -5, -1, -4, -4],\n [2, -1, 2, -3, -2],\n [6, -6, 5, -2, 1],\n [-6, -5, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 5, 1, 1, 5],\n [1, -2, 0, 4, 4],\n [-4, 0, 1, 2, 3],\n [-3, -4, 0, 6, -2],\n [-1, 1, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 1, -3, 3, -5],\n [-5, -3, 6, -6, -2],\n [-5, 0, -4, 0, -2],\n [-1, -2, 1, 0, -3],\n [-2, 1, 4, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -6, 2, 6, 4],\n [-2, 6, 3, -2, -5],\n [-4, 4, -3, 6, 6],\n [-5, 2, -6, -5, -6],\n [0, 2, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 5, -4, 1, -1],\n [-4, 5, 1, -1, 6],\n [-4, -6, -2, -5, 1],\n [-1, -2, 4, -2, -3],\n [1, -1, 0, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -1, -2, 6, 3],\n [-2, 0, 6, -1, 6],\n [-2, 3, 1, 2, 6],\n [-2, -1, -3, 2, -2],\n [0, -4, -6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -6, -1, -5, -3],\n [-1, 5, 4, -6, -1],\n [3, 4, 3, -1, -5],\n [1, -2, -2, 5, -5],\n [-6, -2, 1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 5, 1, -1, -1],\n [-5, 3, 1, -2, -2],\n [5, -6, 1, -6, 2],\n [-3, 1, 2, -6, -5],\n [-6, 1, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -4, -2, -5, 3],\n [6, -6, -4, 6, 0],\n [-4, 1, -2, 6, 6],\n [3, 4, 3, -4, 3],\n [5, -3, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -6, -3, 6, -1],\n [4, 0, 1, -2, 1],\n [-3, -3, 5, 6, -3],\n [-6, 1, 6, -5, 6],\n [-2, -5, 5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 6, -6, 3, 6],\n [5, -4, -5, -3, 4],\n [-2, 6, -3, 4, -3],\n [0, -6, -4, 0, 6],\n [-3, -5, -3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 0, 0, 1, 2],\n [-1, 3, -1, 3, -3],\n [-1, -6, -4, -6, 6],\n [0, -5, -4, -1, -3],\n [5, -4, -2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, 6, -3, 4],\n [2, -2, -6, 5, -3],\n [-3, -4, 6, 4, 6],\n [-2, -3, -3, 2, 1],\n [6, 0, 3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 5, 4, 1, 4],\n [-6, -4, -1, 6, 0],\n [-1, 5, 5, 0, 5],\n [5, 1, 6, 2, 5],\n [-1, 5, 3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -4, 4, 4, 4],\n [-4, 6, 0, 1, -6],\n [5, -3, -2, 0, -4],\n [2, -6, 6, -3, -1],\n [1, 5, 4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -3, 5, -3, -5],\n [4, 4, -6, -4, 1],\n [-6, -2, -4, -4, -3],\n [0, -5, -3, 3, 6],\n [-5, -5, -5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, 2, 4, 2],\n [0, -5, -2, -2, -3],\n [-6, 6, -4, 3, 6],\n [4, 0, -4, 2, 1],\n [-6, 1, -6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, 1, 1, -4],\n [2, 5, -2, 0, -1],\n [0, -4, 4, 5, -1],\n [1, -3, -3, -6, 2],\n [0, -5, 3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -2, 0, 3, 3],\n [0, 0, -3, 4, 0],\n [-3, 4, -3, -6, 3],\n [4, 1, 1, 4, -3],\n [-5, -1, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 1, -4, -4, -2],\n [5, -2, 6, -1, -3],\n [1, 2, -2, 5, 4],\n [2, -5, -6, -6, -5],\n [-2, 2, 2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 3, 3, 0, -4],\n [5, 1, 3, 0, -6],\n [-4, 6, -4, 6, -4],\n [-1, 5, -1, -5, 3],\n [1, -2, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, -5, 0, 2],\n [3, -2, 1, 5, 0],\n [6, 1, 2, -3, 3],\n [1, -5, 4, 0, -3],\n [-1, 6, -6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -2, -5, 5, 2],\n [-3, -3, -1, -2, -4],\n [-5, -3, 6, -5, -6],\n [5, -1, 2, 2, 5],\n [6, 5, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 2, -1, 4, 4],\n [-3, 4, 2, 0, -3],\n [-3, -3, -3, -5, -2],\n [-2, 6, -3, 0, -2],\n [4, -6, 4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, -5, 1, 1],\n [2, 6, 3, 6, -3],\n [-2, 2, 0, -3, 1],\n [6, 5, -4, 1, 4],\n [-4, 1, 5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 1, -2, 3, -1],\n [-3, -6, -1, -5, 1],\n [-5, 2, 5, -1, 2],\n [4, 4, -3, 5, 4],\n [2, 5, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -5, 2, -2, 6],\n [-3, -3, -3, -5, 3],\n [2, 1, -4, -6, -4],\n [5, 0, -1, -3, -4],\n [-5, 3, 6, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 5, 2, 1, 0],\n [-5, -3, 0, 2, 1],\n [-5, 5, 2, -5, 5],\n [-2, -2, -2, -4, -6],\n [3, -4, 2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, 4, 5, 6],\n [-4, -2, -4, -3, -3],\n [-1, -3, -4, -5, -6],\n [4, 1, -3, 1, 5],\n [3, -3, -3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 3, 1, 0, 0],\n [2, 6, 3, -3, -1],\n [0, 1, -4, 4, -6],\n [2, -4, -5, -1, -1],\n [0, -4, -6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -5, 2, 1, 6],\n [-2, 6, 0, 5, -1],\n [-6, -1, -1, 5, -5],\n [-2, -1, 1, -3, -5],\n [0, 1, -3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -5, -3, 1, -3],\n [-5, 0, -2, 3, -5],\n [6, -1, -2, -5, -5],\n [5, 1, -4, 5, 6],\n [1, -2, -4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 5, 2, 5, 6],\n [0, -2, -5, -6, -6],\n [-6, 3, 0, 6, -5],\n [0, -6, -2, 0, 4],\n [3, 5, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -2, -2, 5, 6],\n [3, -3, 4, 1, -5],\n [-4, -3, 3, 5, 2],\n [-2, 6, 3, 0, -2],\n [6, 1, -6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 6, -2, 5, 2],\n [-3, -6, -6, 6, 4],\n [-2, 3, 4, 1, 3],\n [1, -6, 5, 2, -4],\n [6, 4, 0, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 6, -1, 5, 5],\n [0, 6, 2, -2, -4],\n [0, -5, -3, -4, 3],\n [-1, -2, 1, -3, 4],\n [0, 4, -3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 4, 6, 6, 2],\n [6, -2, -4, 5, -1],\n [2, -2, 6, 3, -5],\n [1, -1, -4, 5, -4],\n [5, 4, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -2, 4, -1, 1],\n [-3, 3, 3, -2, -1],\n [4, -5, 2, -3, -2],\n [3, -4, 5, -3, 0],\n [-4, 4, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -5, 2, -6, 4],\n [5, 6, 4, 6, -1],\n [-1, 4, 3, -1, 3],\n [-4, 2, 5, 6, 3],\n [-4, -3, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, 4, 5, -5],\n [-3, -3, 6, -2, 5],\n [1, 5, 3, 4, 1],\n [6, 2, -3, 2, 2],\n [0, -4, -1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, 0, -5, 4],\n [1, -2, -3, -2, 3],\n [-5, 4, -4, -5, 1],\n [1, -5, 0, -4, -5],\n [-4, -3, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 0, -5, -6, 5],\n [-5, 0, -6, -5, 5],\n [-4, -2, -5, 1, -1],\n [0, 6, -2, 4, -4],\n [5, 2, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 2, -5, 1, 0],\n [4, -3, -4, -4, 4],\n [6, 0, 2, 6, -1],\n [3, -6, -2, 3, -4],\n [6, 0, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -5, 4, 2, -2],\n [0, 4, 4, 6, 5],\n [-5, -2, -3, -1, 5],\n [0, 6, -2, -3, 5],\n [4, 6, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 1, -4, 3, 6],\n [1, 3, 0, 0, -6],\n [3, 3, 1, 3, 6],\n [1, 4, 0, 0, 3],\n [-6, 1, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 5, -3, -2, 5],\n [1, -2, 0, 4, -2],\n [1, -1, -5, -4, 6],\n [0, 3, -5, 2, -2],\n [2, 1, -1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -5, -2, -5, 6],\n [1, -6, 0, 0, 2],\n [-4, -3, 4, -6, 0],\n [-6, -1, 2, 3, 1],\n [-1, -4, -2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 1, -5, 0, -6],\n [5, -5, 6, 5, -2],\n [6, -3, -2, 0, 6],\n [0, 0, -5, -1, -2],\n [3, -4, 5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 1, 5, 6, -2],\n [-6, -4, -1, 4, 1],\n [2, 0, -2, 4, -3],\n [-1, 0, 5, -2, -1],\n [2, -3, -1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 0, 3, -6, -6],\n [-5, -6, 3, 1, -4],\n [3, 5, -6, 3, -4],\n [-4, -6, -1, 0, 0],\n [-6, 6, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -3, 3, 1, 0],\n [-5, 0, -3, 3, 0],\n [-6, 6, -1, -1, -2],\n [-6, -3, 6, 4, -1],\n [1, -5, -3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -3, -2, -4, -2],\n [4, -6, 4, 6, -4],\n [1, 0, 1, -1, -1],\n [0, -3, -5, -4, -5],\n [6, 4, -3, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, 1, 3, -5],\n [3, -2, 5, -3, 6],\n [-3, 3, 1, -4, 1],\n [3, 2, 5, -5, 0],\n [0, 4, -3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -4, 2, -6, -1],\n [-3, 6, -5, 5, 3],\n [-1, 1, -2, 6, 5],\n [5, 1, -6, -6, 3],\n [-4, 6, 1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, 6, 2, 0],\n [2, 1, 5, 0, 4],\n [-6, 4, 1, -4, -1],\n [4, -3, -2, 2, -2],\n [-5, 1, 5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 6, 6, -3, -2],\n [-4, -2, 3, 2, 6],\n [5, -1, -1, 3, -3],\n [-1, -1, -3, 1, 0],\n [-6, -5, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -6, 6, 6, 5],\n [1, 1, 3, 0, 5],\n [6, -6, -3, 5, 0],\n [-2, 2, 5, -2, -6],\n [-3, 3, -3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 2, 3, 4, -6],\n [2, 5, -5, -6, 3],\n [4, 3, 4, -4, -4],\n [6, 4, 6, -2, 3],\n [1, -3, 5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 6, 4, -1, -1],\n [0, 6, 1, 4, -3],\n [1, -3, -6, 1, 4],\n [-3, 0, 2, -4, 2],\n [3, 3, -3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -6, -1, -1, 6],\n [-2, -4, 3, 6, 4],\n [4, -5, -6, 5, 6],\n [5, 6, -6, -3, -1],\n [-5, 2, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -5, -2, -2, 3],\n [1, -3, 5, 4, 1],\n [-6, -1, 6, 0, 2],\n [-4, 3, -2, 6, -3],\n [-3, 5, 5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -3, 0, -5, -4],\n [0, 1, 4, -6, -3],\n [5, 4, 5, -2, 4],\n [-2, 6, 0, 5, 0],\n [-5, 3, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 4, 6, -5, 6],\n [6, -1, -4, 6, 0],\n [6, -2, 2, -6, 1],\n [-5, -4, 4, 6, 4],\n [-2, 3, -6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 5, -1, -5, 2],\n [-1, -4, -1, 4, -3],\n [4, -2, 1, -2, 6],\n [4, 6, -2, -3, -6],\n [-6, -6, -2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 2, 2, -6, 2],\n [1, 3, 4, 1, -6],\n [4, 1, -6, 3, 1],\n [1, -4, 2, 5, -6],\n [-1, -5, 6, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -2, -5, -3, -2],\n [0, -4, 3, -4, -4],\n [-6, -6, 3, -4, -2],\n [0, -1, -1, 0, -4],\n [-5, -2, 3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 0, 1, -2, -1],\n [-3, -3, 6, 6, -1],\n [4, 5, -1, 2, -6],\n [-2, 2, -4, 1, 3],\n [-5, 3, 6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -2, 0, -4, -6],\n [3, -3, -1, -4, -1],\n [6, 6, 3, 4, -4],\n [6, -2, -1, -2, -6],\n [0, -3, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -3, -6, 3, -5],\n [6, 5, 5, 3, 0],\n [0, 5, -5, -6, 6],\n [2, 1, 1, -4, -6],\n [4, 6, -2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -5, -6, -4, -3],\n [0, 5, -2, -4, -2],\n [-3, 0, -5, 1, 2],\n [-6, 5, 0, -4, 6],\n [5, -4, 5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 5, -2, 2, 5],\n [-6, 6, 6, 0, -6],\n [4, -1, 6, 5, 3],\n [5, -2, 1, -6, -6],\n [-4, -2, 0, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 1, -3, 2, 6],\n [2, -2, -1, 6, 6],\n [-6, -5, 5, 4, 1],\n [-2, -6, -1, 6, 3],\n [0, -3, -5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -2, 3, 6, 4],\n [-6, 5, -6, 6, -1],\n [-1, 3, 0, 1, 6],\n [-5, -1, -3, 0, 3],\n [2, 6, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -4, -1, 0, -2],\n [1, 5, -6, 3, 6],\n [-4, -4, 4, -6, -3],\n [4, -4, -3, 2, -3],\n [-1, -1, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -6, 4, 2, 2],\n [1, 3, -4, 5, 6],\n [-1, 2, -1, 1, -5],\n [4, -5, -4, -1, 4],\n [6, 3, -6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -4, 3, 6, -6],\n [3, 5, 6, 1, -6],\n [-2, -2, 2, 1, 6],\n [0, 6, 5, -4, 0],\n [-3, 2, 1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 0, 4, 4, -4],\n [0, -3, -4, -6, -5],\n [1, 4, 4, 4, -3],\n [4, -4, -3, 0, -2],\n [-5, 3, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -2, 1, 4, 6],\n [4, 6, 3, 0, 3],\n [5, 0, 1, 5, -4],\n [-2, 2, 2, 3, 6],\n [-6, -4, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 2, 6, -2, 5],\n [2, -6, -2, -5, 0],\n [-1, 1, -3, -6, 6],\n [-5, -1, 0, -6, 5],\n [-6, -3, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -3, 4, -1, -4],\n [2, 5, -2, -4, 6],\n [-4, 2, -4, -1, -1],\n [-5, -3, -3, 0, 2],\n [2, -3, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -5, -4, 1, -3],\n [2, 0, -4, -5, 1],\n [5, 4, -5, 6, 4],\n [-6, -3, -2, 0, -2],\n [6, -3, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 2, 6, -1, 6],\n [3, -2, 3, -3, -6],\n [6, -3, -2, 0, -1],\n [-4, -2, -3, 3, 3],\n [-4, 3, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 6, 4, 5, 0],\n [-1, 5, -5, -6, -3],\n [4, 5, -3, 2, -5],\n [-5, -6, -2, -3, -3],\n [-6, -2, -5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -2, 4, -4, -2],\n [-6, 6, 3, 5, -4],\n [-2, 1, -3, 0, 4],\n [-6, -1, 6, -4, 4],\n [-6, -6, 1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, 5, -4, 0],\n [4, 2, 5, 3, -4],\n [-6, 5, -3, 0, -2],\n [2, 1, -2, -2, -1],\n [-6, 0, -6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 3, 3, -2, -5],\n [1, -3, -3, -4, -3],\n [-3, 2, 0, 2, 0],\n [-6, 4, 5, 6, 4],\n [6, -2, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -6, 4, 0, 6],\n [-1, -6, -6, 3, 0],\n [6, 2, -2, 2, 5],\n [2, -5, 3, 6, 5],\n [6, -1, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 2, 4, 4, -5],\n [-1, 1, 4, -5, -5],\n [-5, 4, -2, -4, -6],\n [6, 6, -1, 0, -3],\n [-5, -6, -5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, -3, 3, 3],\n [4, 6, -6, 4, -5],\n [-2, 1, 2, 6, 1],\n [5, -4, 4, 0, 4],\n [3, 1, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -3, -2, 0, 4],\n [5, -5, 2, 6, 3],\n [6, 4, 3, 1, 6],\n [-2, 3, 1, -4, 6],\n [2, 2, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -5, 5, -3, -5],\n [-4, -1, 5, 1, -6],\n [5, 6, -1, 2, 3],\n [-5, 6, 0, -1, -4],\n [6, 6, -5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 5, -6, -4, 6],\n [4, 6, 6, 5, 3],\n [-3, 5, -2, -1, -1],\n [-3, 6, 3, -2, -4],\n [-3, -5, -3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -4, -3, -6, 6],\n [-4, 1, -5, 0, 5],\n [3, 3, -2, -6, -6],\n [6, -2, 2, -2, 4],\n [-4, -4, -5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 3, 1, 0, -6],\n [-6, 3, 4, 4, 6],\n [2, -3, -3, 4, -5],\n [6, 3, 3, 3, -1],\n [-2, -5, -6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -3, 4, -1, -3],\n [4, -2, -6, -4, -4],\n [3, 4, -2, 3, -2],\n [6, -1, -3, 3, 1],\n [4, 2, 3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 4, -6, -2, 3],\n [0, 1, 1, 1, 5],\n [-2, -6, 3, -6, -2],\n [2, 6, 1, -1, 5],\n [5, -1, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 4, -3, 4, 3],\n [3, 6, 0, 4, -4],\n [3, 3, -6, 2, -2],\n [-2, -6, 6, 5, -4],\n [4, 3, -5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -6, 3, 6, -2],\n [1, -2, -5, -2, -4],\n [-2, 5, 6, -4, -1],\n [-3, 1, -6, 6, 0],\n [1, 3, -5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, 5, -5, -6],\n [3, -5, 3, 6, 0],\n [-6, 3, -1, -3, 2],\n [5, -6, -1, -3, 2],\n [-6, 4, 0, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 0, 5, -2, 4],\n [-6, 1, -6, 3, 2],\n [-5, -6, 0, 1, -2],\n [-6, 1, 4, -6, -1],\n [4, -5, 5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 6, -5, -6, 0],\n [2, -1, 4, -6, -3],\n [3, -5, -1, -6, -5],\n [-1, -4, 4, -2, -5],\n [-6, 6, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, 3, -2, 0],\n [1, -6, -4, -6, -6],\n [-5, -1, -4, 3, -3],\n [1, 5, -3, -5, 2],\n [-3, -6, 4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 1, -4, -4, -5],\n [2, 5, 3, -4, -1],\n [3, 4, -4, -3, -1],\n [-5, -5, -4, 2, -5],\n [-2, -4, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -3, -6, -5, -6],\n [3, 0, 2, 5, 6],\n [2, 0, -5, -5, 1],\n [6, -1, -4, -2, -6],\n [4, -1, -2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, -3, 1, 3],\n [1, -6, 2, 2, -2],\n [3, 6, 4, -6, 6],\n [3, 6, 1, 0, 0],\n [-6, -3, 1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 6, -6, -1, -6],\n [5, 0, -1, 6, 5],\n [-4, -3, 1, -2, -2],\n [-6, 3, -3, 0, -4],\n [2, 6, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -4, 6, -2, -5],\n [-5, 6, 0, 2, 1],\n [-2, 2, -4, 1, -2],\n [-2, -2, -1, 4, -6],\n [-4, 2, 5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -4, 1, 4, -3],\n [1, -2, 5, 0, -5],\n [1, 4, 2, -5, 0],\n [-6, 0, 1, 6, -3],\n [-5, 6, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 0, -5, -5, -3],\n [6, 6, -3, 3, 5],\n [1, 6, -1, -3, 3],\n [-1, -6, 3, 5, 4],\n [-1, -1, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -5, 4, -2, 6],\n [-1, 6, 2, 6, -6],\n [-2, 2, 0, -2, -4],\n [-6, 6, -2, -2, -6],\n [4, -1, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -5, -4, -5, -1],\n [-2, 0, 6, 2, 1],\n [2, 6, -3, -3, -2],\n [0, -2, 2, -5, 0],\n [1, 2, -6, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -2, 6, -5, -4],\n [-1, -3, 0, -3, 4],\n [-6, -6, 3, 1, -3],\n [6, 5, 5, 5, -1],\n [-1, 6, 4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -2, 5, 3, -3],\n [3, 0, -4, 3, 5],\n [5, -3, 1, 4, -4],\n [-3, -3, 5, -6, -2],\n [4, -2, -2, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 6, 2, -6, -1],\n [3, 0, -4, -3, -5],\n [-5, 6, 0, 3, 6],\n [5, 5, 3, -2, 4],\n [-3, 4, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 1, 4, 0, -1],\n [1, -2, 0, -6, 0],\n [2, 2, 2, 1, 5],\n [6, -3, -6, 3, 2],\n [1, -2, 6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, 1, 3, -4],\n [-4, -2, 0, 5, -2],\n [3, 5, 5, 5, 6],\n [2, -1, 3, 0, 4],\n [6, -1, 3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -5, 3, -3, 6],\n [2, -5, -1, -1, 3],\n [5, 1, 6, 0, -4],\n [2, 6, 4, -5, 5],\n [-1, 2, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 1, -1, 3, 2],\n [-3, 5, -3, -5, 5],\n [5, -6, -3, -4, -1],\n [5, 1, -2, 0, -5],\n [-3, 3, 3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -5, 0, 3, 2],\n [3, -1, 6, 0, 0],\n [-6, 0, 1, 6, -6],\n [0, 1, 5, 6, -6],\n [4, -2, 5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, -5, 1, -5],\n [-6, -3, 3, 2, 1],\n [0, 4, 6, -6, -4],\n [2, 1, 6, -6, 3],\n [6, -2, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 3, -5, -5, -6],\n [2, -3, 4, -6, -6],\n [-3, 3, 2, 4, 0],\n [6, 2, 3, 4, 3],\n [5, -6, -6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -3, -4, -2, 6],\n [3, 2, 3, -1, -2],\n [6, 5, -3, -2, 3],\n [-5, 5, 5, 1, 0],\n [5, 3, -6, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 4, -1, 1, 0],\n [3, -2, 0, 0, 0],\n [1, 6, 1, -2, 2],\n [3, 1, -2, 1, -6],\n [1, -2, 5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -2, -6, -4, 5],\n [2, -5, 4, -1, 4],\n [-6, -1, 4, 2, 3],\n [5, 6, -3, 6, -5],\n [-5, -1, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 1, -5, 5],\n [-2, 3, 6, 0, 0],\n [-3, 6, 1, -5, 2],\n [3, 4, 0, -6, -4],\n [3, -2, -3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 3, -1, 2, 5],\n [3, -6, 3, -6, -6],\n [5, -2, -6, -4, -4],\n [-1, 3, 1, 3, 1],\n [-3, -2, -6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -1, 4, 1, 2],\n [-2, -6, 3, 4, -4],\n [-3, -1, -6, -6, -1],\n [-1, -4, 0, 0, 4],\n [2, 0, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 4, 4, 0, -5],\n [4, -5, -3, -4, 6],\n [5, -4, 3, -3, 5],\n [-2, 3, -1, 4, 4],\n [-1, 3, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -5, -1, -4, 5],\n [-2, 1, -3, 2, 6],\n [1, -6, -3, -3, -2],\n [6, -2, 2, 6, -1],\n [-3, -2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 6, 6, 2, 6],\n [-5, 6, 5, -6, 0],\n [4, -2, -1, 2, 6],\n [3, 4, 0, 1, 1],\n [-3, -2, -5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, -2, -3, 6],\n [2, 4, 5, 3, 2],\n [3, -1, 6, -1, 0],\n [4, 2, -3, 4, 5],\n [4, 0, -4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -1, -3, 6, -5],\n [5, 5, -3, -3, -4],\n [-5, 6, 3, -2, 0],\n [3, 1, 1, -6, 1],\n [-1, 4, 6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 0, 4, -4, 0],\n [-2, -3, 1, 4, -3],\n [2, 1, -4, -6, 4],\n [-4, 6, 0, -5, -4],\n [0, -3, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 4, 5, 2, 3],\n [-5, -4, -4, -3, 3],\n [-6, -5, -3, -2, 0],\n [-3, -4, 1, 3, 3],\n [-3, 4, -4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -6, -6, -1, 5],\n [6, 1, 6, -4, 0],\n [1, 2, -4, 5, 6],\n [3, 3, -5, 2, 0],\n [-1, 3, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -2, 4, -4, 5],\n [-5, -5, -5, -3, 6],\n [3, 4, 1, 2, -3],\n [1, -3, 3, 6, 4],\n [5, -3, -4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 2, 2, -4, -3],\n [1, -6, -2, -5, 5],\n [2, -3, -5, -1, -3],\n [-1, -4, -5, -5, -2],\n [1, 2, 5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -4, -5, -5, -3],\n [0, -6, 1, -1, 6],\n [1, -4, 0, 6, 4],\n [6, 1, 0, 2, 5],\n [-6, -6, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, 1, 1, -4],\n [4, 4, -4, 1, 2],\n [-3, -4, -1, -2, -4],\n [4, -1, -5, 6, 6],\n [-3, -4, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 1, 5, -6, -2],\n [-1, 4, 6, -4, 1],\n [-2, -6, 4, -3, -5],\n [6, -1, 2, -6, -4],\n [-2, -4, -5, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -1, 4, -6, 2],\n [6, -4, 2, 4, -1],\n [-4, -4, 6, -3, -4],\n [-6, 0, -2, 1, -6],\n [-2, 2, 4, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 1, -6, 6, 2],\n [3, -6, 4, 6, -6],\n [1, 4, 2, 5, 1],\n [5, 0, 3, -4, -6],\n [6, 0, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 4, 1, 1, -1],\n [0, 6, 2, 4, 3],\n [-4, -1, 6, 6, -1],\n [3, 4, 4, 1, 6],\n [2, -2, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -3, 5, 4, 3],\n [-4, -5, 0, 3, -2],\n [-6, -3, 3, 0, 3],\n [5, -3, -3, 2, 4],\n [-3, 4, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -4, -4, -6, -6],\n [1, 3, -5, 3, 4],\n [2, -4, 1, -3, 6],\n [0, 4, -6, -1, -5],\n [-5, 4, -3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -3, -4, 6, -6],\n [4, 0, 6, 4, -2],\n [-4, -4, 3, 0, -2],\n [-5, -1, 3, -2, 5],\n [-2, -4, 5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -1, -1, 6, -6],\n [-3, -5, -1, 4, 2],\n [3, -5, -6, 5, 0],\n [-2, -1, 3, -4, -3],\n [-4, -2, -3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -1, -6, -6, -3],\n [4, 5, -6, 4, -2],\n [-6, -2, 3, -1, -6],\n [0, 0, -2, 3, 6],\n [-2, -5, 4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -2, -3, -6, 1],\n [-6, -1, -1, 2, -2],\n [-2, 0, 2, 3, 1],\n [-5, -3, 0, 1, 3],\n [-4, -2, 2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 6, 1, 0, 1],\n [2, -4, -1, -2, -4],\n [-2, 3, 3, 3, -4],\n [5, -5, 4, 2, 5],\n [-1, 6, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -1, 1, 4, -1],\n [-4, 6, -1, -2, 1],\n [-6, -2, 1, 2, 2],\n [3, 3, 5, 6, 6],\n [-4, 6, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 1, 0, -2, 2],\n [-2, 5, 2, 6, -1],\n [6, 5, 1, -4, -4],\n [-6, 3, -5, -6, 6],\n [-2, 0, -5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 2, 3, 4, -3],\n [-5, 1, -3, 6, -2],\n [-5, 3, -2, -6, 5],\n [-3, 1, 1, 2, -1],\n [-3, 6, -5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -5, -2, -1, -6],\n [-4, 2, -2, -5, -2],\n [5, -6, 4, -3, 5],\n [1, -2, -5, -3, -5],\n [4, 5, 5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, 5, 2, -5],\n [-6, 0, 5, -5, -6],\n [3, -6, 4, -5, 1],\n [4, -6, -3, -4, 2],\n [0, -3, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 2, 5, 2, -5],\n [3, 2, -4, 1, -3],\n [4, -3, 5, 6, -3],\n [-3, -6, -5, 5, -5],\n [-2, 2, 5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 6, 1, 0, -2],\n [-4, 2, 0, -2, 6],\n [-6, -2, 5, 6, -1],\n [0, 2, -2, -3, 1],\n [0, -4, 3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 5, 2, 5, 6],\n [1, -1, 0, -2, -4],\n [6, -1, -5, -1, 1],\n [2, -4, -2, 4, 4],\n [-4, -2, -1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -4, 0, 5, 4],\n [1, 0, 2, -1, 4],\n [2, -3, -5, 0, 0],\n [2, 2, 6, 0, -1],\n [2, -5, 3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -2, -2, -2, 1],\n [6, 3, 2, -1, -5],\n [-3, 2, -5, 5, 3],\n [2, -4, -1, 4, 1],\n [-1, 4, 5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 6, 5, 6, 4],\n [0, 3, 3, 5, 1],\n [-1, -6, 6, 1, -4],\n [-3, 5, 0, 5, -5],\n [-2, -6, 4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 6, 1, 0, 3],\n [-5, 4, -2, 5, -4],\n [-4, -1, -5, -4, -3],\n [3, 6, 5, 5, -4],\n [4, -5, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 1, -4, -2, 3],\n [3, -6, -1, -1, -6],\n [6, -3, -6, 1, 4],\n [-4, 6, 0, -3, 1],\n [5, -5, -4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -6, -2, 2, 1],\n [-6, 2, -6, 0, -6],\n [6, -4, -4, 5, -2],\n [-1, 4, 4, -4, -6],\n [-2, -3, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 5, -5, 4, 6],\n [-2, -6, 3, -1, -3],\n [-2, 0, 6, 4, -5],\n [-6, 5, -2, 4, -4],\n [-2, 5, 5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, 5, 6, -4],\n [0, -3, -3, -6, -4],\n [1, 6, 6, 6, 0],\n [-1, 4, 0, 1, 4],\n [5, -4, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -2, 6, 5, -6],\n [-5, -3, 2, -2, 4],\n [-2, -2, -6, -4, -2],\n [4, 4, 6, 5, 2],\n [-4, 5, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -4, 1, -4, -1],\n [0, 5, -6, 3, 5],\n [-4, -1, 1, -3, 2],\n [1, 3, 2, 5, 2],\n [-2, 0, -1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -5, -2, -1, -5],\n [6, 6, 4, -6, 4],\n [0, 0, 6, -5, -2],\n [-1, 2, -5, 5, 6],\n [0, 3, -6, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, -1, 1, 4],\n [-4, -6, 6, -3, 6],\n [-2, -4, -4, -6, 3],\n [-6, -1, 0, -2, 1],\n [-6, 1, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -6, 0, -1, -2],\n [3, 3, -1, 3, 0],\n [1, -2, 1, -2, 5],\n [-4, -5, -6, -4, -2],\n [-2, -1, 5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 1, 0, 2, 0],\n [-6, 5, -4, 1, -5],\n [-6, -4, -3, 4, -3],\n [4, 4, 1, -5, -5],\n [1, 3, 6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -5, -5, 1, -4],\n [4, 3, -3, -5, -1],\n [-3, 6, -4, -4, -2],\n [-6, 0, -4, 4, -2],\n [-5, 6, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 0, 4, -3, 3],\n [2, 5, 3, 0, -5],\n [6, -5, 2, 6, 3],\n [4, -6, 6, -4, -2],\n [-2, 6, -6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 0, -5, 0, 3],\n [3, 5, 1, 1, -1],\n [1, 0, 2, -2, -3],\n [-4, -5, -5, 5, -1],\n [-4, 3, 4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, -3, -3, -4],\n [5, -2, 4, 6, -5],\n [5, 6, 4, 4, 2],\n [-5, -5, -6, -2, 0],\n [6, 5, 6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 4, 0, 1, 5],\n [0, 0, 2, -6, 4],\n [-6, -5, -4, -4, 0],\n [2, -6, -6, 3, -3],\n [-2, 3, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -2, -6, -1, 3],\n [-1, -2, 4, -1, 2],\n [2, 3, 4, 1, 1],\n [-1, 3, -6, 6, 4],\n [1, 2, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -1, 2, -4, -2],\n [-4, 6, 4, 1, 2],\n [2, 4, 6, 4, 5],\n [-6, 1, -6, -5, 6],\n [5, -3, -4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -6, -6, 1, -4],\n [-2, 5, 3, 6, 2],\n [6, 4, 1, -3, 2],\n [-5, -2, 1, 1, 5],\n [0, 5, -1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 2, 3, 3, 0],\n [6, -1, -1, 0, 0],\n [-5, 1, -1, 1, -4],\n [3, 4, -5, 2, -3],\n [0, -3, 6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 1, -4, 5, 4],\n [5, -5, 2, -5, -5],\n [-3, 2, -2, -2, 2],\n [-2, -1, 4, 5, 4],\n [-2, -3, -3, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -2, 2, 2, 5],\n [-2, -3, -4, 5, 2],\n [-6, 5, -2, 3, -3],\n [3, 2, 2, 1, -5],\n [-2, -3, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -5, 3, 1, -3],\n [-5, -5, 1, -2, 5],\n [4, 6, 5, 0, 6],\n [-3, 5, 4, 6, -5],\n [-4, -4, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -2, 4, 0, 5],\n [-1, -4, -2, 0, -2],\n [5, 6, 5, -4, -3],\n [-4, 6, -5, -4, 1],\n [6, 0, 0, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 4, -2, 6, 1],\n [1, -6, 0, -4, -1],\n [-6, 1, 4, -1, -3],\n [-6, -3, -2, 3, -2],\n [-1, 0, -5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, 4, -4, -3],\n [-4, 1, 4, -6, -3],\n [-5, 2, -6, 5, -2],\n [0, -1, -6, 0, -1],\n [6, -1, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 5, 4, -2, 1],\n [4, 0, -5, -6, -1],\n [4, 4, 0, -5, 4],\n [5, 4, 6, 3, -6],\n [0, 1, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 5, -2, -3, 2],\n [4, -5, 2, 4, 6],\n [4, -5, 6, -4, 1],\n [0, 6, 0, -3, 1],\n [3, -5, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 0, 6, -6, -1],\n [6, 1, 3, 1, -1],\n [0, 2, 4, -6, -6],\n [-3, 5, -2, 4, -3],\n [-4, 1, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -5, 2, 6, 3],\n [-1, -2, -3, 3, -1],\n [2, 4, -3, 6, -2],\n [0, 5, 0, -3, 1],\n [3, 4, 3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 6, 2, 6, 1],\n [-1, 6, 3, 5, -6],\n [1, -5, -5, -6, 5],\n [4, -6, -1, 5, -5],\n [6, -2, -6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, -1, -5, 5],\n [-6, -4, 5, 6, -5],\n [4, 1, 3, -5, -1],\n [3, 3, 0, 0, -2],\n [-5, 6, 5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 6, 3, -2, 1],\n [2, 3, 6, -6, -3],\n [-6, -4, -4, -5, 2],\n [-4, 1, 0, -6, 0],\n [0, -3, 4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -4, 0, 6, -4],\n [0, -1, -6, 6, 5],\n [-1, 4, -4, 5, 6],\n [0, 6, 0, 1, -4],\n [3, 3, -5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 4, 2, 5, 5],\n [-1, -2, -1, 5, 5],\n [-4, 0, 2, -1, 5],\n [-4, -1, 4, 6, 0],\n [3, -1, -3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 4, 5, 5, 1],\n [-3, -5, 1, -5, -3],\n [1, -6, 0, -5, -1],\n [1, 4, -6, 0, 5],\n [4, -4, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -4, -1, -3, -2],\n [0, 3, -4, 3, 0],\n [-1, -1, 0, -2, 3],\n [4, -3, 4, -4, 6],\n [-2, -3, 3, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 3, -2, 4, -1],\n [-4, 6, 1, 4, 3],\n [4, 0, -3, -3, -1],\n [-1, -1, -5, 4, 3],\n [-4, -3, -5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -5, -2, -5, 1],\n [-4, -2, 5, -2, -4],\n [2, -5, 6, -6, -6],\n [1, 5, -5, -1, -1],\n [-3, -6, -6, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 2, -1, 5, -4],\n [-1, 2, 1, 6, 0],\n [-5, 3, -2, -3, -5],\n [-2, 0, -1, -5, -3],\n [1, -6, -1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 2, 2, 5, -5],\n [6, -4, 2, -2, 5],\n [3, -6, -4, 4, 1],\n [0, 5, 1, 2, -1],\n [-3, 6, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 1, -1, -2, -2],\n [6, 3, -5, 2, -2],\n [3, 4, -1, -1, 3],\n [1, 3, -4, -3, -3],\n [-6, 5, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 4, 4, -1, 2],\n [-5, 6, 1, 2, -3],\n [-5, 1, -1, -1, -6],\n [-2, -1, -1, -6, -1],\n [3, -4, 5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, -2, 4, -5],\n [1, -1, -5, -1, 5],\n [3, 1, 4, -4, -3],\n [-3, -3, 3, -5, 5],\n [-4, 3, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -2, -6, -6, -4],\n [2, 4, -2, -1, 6],\n [-1, 4, 0, 0, 6],\n [-3, -2, -6, 2, 2],\n [-5, -3, 6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 3, -5, 6, -2],\n [-5, 4, -1, 0, -4],\n [-1, 4, -5, 0, 1],\n [-1, -4, -4, -6, -5],\n [-5, 5, 6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, -2, 1, 3],\n [3, 3, -2, -4, 2],\n [2, 3, -6, -2, -5],\n [-6, 5, -2, 6, -2],\n [-4, 3, -6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -2, -5, 6, -6],\n [6, 0, -6, -6, -2],\n [0, 1, -4, 0, -6],\n [3, -5, -5, 2, -4],\n [3, -6, -6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, -3, 5, 1],\n [-1, 0, 2, 2, -3],\n [6, 5, 4, -5, 3],\n [-4, 6, 5, 5, -2],\n [1, 2, 4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -5, -1, -3, -4],\n [6, 1, 2, 3, -2],\n [-6, 0, -1, -6, -4],\n [2, -3, -1, -6, -4],\n [2, 0, 5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, 1, -4, -3],\n [3, -1, -1, 5, 4],\n [-2, -6, 0, -2, 0],\n [1, -5, -4, 0, 2],\n [-2, 3, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 6, -3, -2, 6],\n [4, -4, 3, -4, -4],\n [4, 1, 3, 6, -6],\n [-6, 0, 6, 1, 1],\n [4, -3, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -2, -6, 6, 2],\n [-3, -5, -2, 0, 1],\n [6, -1, -2, 3, -6],\n [-4, 2, 1, 0, -3],\n [0, -4, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -5, 1, -2, 5],\n [1, 5, 0, -6, 0],\n [-4, -4, -3, -1, -4],\n [-4, -3, 5, 3, -1],\n [3, -5, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -6, 4, 6, -1],\n [-1, 0, -6, 5, 2],\n [-1, 6, 1, -4, -6],\n [0, 3, 5, -6, 2],\n [-3, -3, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, 1, -1, -3],\n [-5, -5, 5, 4, 2],\n [-3, -4, 5, 0, -5],\n [2, -3, 1, -2, 0],\n [-5, -3, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -3, 3, 1, -5],\n [2, 3, -3, 3, -2],\n [-4, -4, 2, -4, -3],\n [1, 2, 5, 2, 6],\n [-6, -5, 2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 0, 6, -6, 1],\n [-3, 2, 2, 3, -2],\n [-5, -5, -6, -5, -5],\n [5, 3, 2, 1, -3],\n [-5, -6, -1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -1, -6, -1, 3],\n [-1, 0, -1, 5, 2],\n [5, 3, -2, -5, 5],\n [3, 2, 4, 1, 3],\n [3, -2, 3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 2, -1, 5, 6],\n [6, 0, -6, -6, 1],\n [-4, 4, 4, 3, 4],\n [0, 1, -2, 3, -1],\n [-3, 4, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 2, -2, 0, -1],\n [2, 5, 4, 4, -3],\n [1, 3, 1, 1, -4],\n [2, 0, -1, -4, 2],\n [-3, 4, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 6, -5, 5, 1],\n [5, -1, -6, 3, -3],\n [4, 6, -2, 1, -1],\n [-2, -4, 6, -1, -4],\n [-1, 5, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -2, -2, 6, -2],\n [1, -2, 1, -6, 5],\n [-2, 6, -2, -5, 5],\n [-1, 3, -4, -5, 6],\n [-4, 3, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, -2, -3, 6],\n [6, -6, -6, -1, -6],\n [-2, -1, 2, 2, -3],\n [2, 2, 1, 0, 0],\n [0, 1, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -3, -5, -6, -1],\n [-3, -5, -3, -2, 5],\n [-4, 6, -4, -3, -3],\n [-1, 4, -3, -2, 1],\n [0, 5, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 2, -3, -5, -5],\n [4, -4, 2, 3, 1],\n [2, 6, 2, -1, -5],\n [2, -5, -1, 3, -1],\n [-5, -5, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -5, -4, 5, 3],\n [4, 1, -3, 4, 5],\n [2, 2, -4, 5, 0],\n [-6, 2, -5, 1, 1],\n [-1, 2, 6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 0, 4, -3, -1],\n [-6, 6, 0, 4, 3],\n [-4, 6, -6, 1, -1],\n [-4, 5, -3, -4, -3],\n [1, -5, 1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 1, 1, 6, 0],\n [1, -5, -2, -6, -4],\n [-1, -3, -3, -4, 5],\n [3, 0, 4, -4, -5],\n [2, -4, 3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 5, 2, 3, 0],\n [6, -1, 2, 4, -4],\n [-4, -3, 0, 1, 3],\n [1, -1, 5, -5, -5],\n [0, 5, -2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -2, 1, 3, -5],\n [-5, 0, 2, -4, 2],\n [4, -5, 4, -3, -6],\n [1, -6, -2, 2, -4],\n [-6, 4, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -3, 0, 3, 6],\n [1, 6, -2, -2, -2],\n [2, -2, 0, 6, -1],\n [-2, -2, -1, -3, -4],\n [5, 5, -6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, 2, 1, 4],\n [-1, 2, -4, -4, 1],\n [-4, -3, 1, 1, 4],\n [-5, -5, -3, -4, -3],\n [-2, -4, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 6, -4, 1, 3],\n [-6, 6, 4, 6, -2],\n [6, 1, 1, -5, 1],\n [2, -1, -5, 1, 6],\n [0, -6, 6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 6, -4, -2, -6],\n [-5, -1, -1, 2, -2],\n [-5, -4, 6, 1, 1],\n [0, -2, -5, -5, -4],\n [5, 3, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 4, 0, 6, -6],\n [-6, 0, -6, 3, 5],\n [-3, -1, -6, 4, 5],\n [5, 5, -5, -3, 6],\n [2, 0, -4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 4, -6, 0, 1],\n [2, -4, 6, -6, 4],\n [1, 1, -1, 5, 3],\n [0, -2, 2, 0, 6],\n [-1, 1, 1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 6, 2, -6, -4],\n [5, -5, 3, -4, 4],\n [4, 3, -3, -1, -6],\n [-2, -3, 1, 6, 3],\n [-5, -4, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 5, -6, -6, 3],\n [-4, 2, 2, 1, 6],\n [-3, 3, -4, -6, -5],\n [3, 0, 3, 2, -3],\n [-2, -5, -5, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -3, 2, 0, -4],\n [-3, 4, -5, 3, -3],\n [-3, 6, 3, 2, 4],\n [-4, 4, 1, 1, -3],\n [1, -4, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -1, 5, 0, 4],\n [-3, 0, 4, -1, 5],\n [3, 1, 3, 2, -1],\n [0, 2, -3, 6, 1],\n [1, 0, -6, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, 6, 5, 1],\n [4, -1, 5, -1, 5],\n [-4, -2, -5, 2, 1],\n [6, -2, 6, 3, -6],\n [-4, 1, 6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, -2, 0, -3],\n [3, 2, 1, -6, -3],\n [-4, -6, -4, -1, 2],\n [0, -5, 6, -2, -2],\n [-2, 1, 0, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, -4, 5, 4],\n [1, -4, 0, 5, 3],\n [6, 0, 4, -1, 2],\n [-4, 0, 4, 5, 1],\n [1, 5, -4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 3, 4, -4, 3],\n [-4, -5, -5, -5, -4],\n [-3, -6, -6, 2, -1],\n [0, -4, -2, 0, 2],\n [2, -3, 4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -6, 3, 3, -6],\n [3, 0, 5, 4, 4],\n [6, -6, -6, 4, -3],\n [3, 2, -6, 5, -6],\n [3, 0, 0, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 0, -2, 2, 5],\n [0, -1, 1, -1, 0],\n [-5, -2, -1, 5, 2],\n [6, -1, -6, -5, -6],\n [6, 4, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -4, -1, -3, 1],\n [3, -2, 6, -1, 2],\n [6, -4, -1, -1, 0],\n [6, -4, 3, 0, 3],\n [-6, -5, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -4, 0, 6, 4],\n [-2, -5, 5, 3, 6],\n [3, 2, -6, 1, -5],\n [1, 5, -2, 6, -1],\n [-2, 1, -6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 3, -5, 0, -5],\n [2, 1, -3, 3, 2],\n [4, 0, -3, -5, 4],\n [-4, -2, 3, -3, -5],\n [-4, 2, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -3, 6, -3, 4],\n [-1, -3, 3, 5, 2],\n [4, 1, 2, -3, -4],\n [-5, -4, 1, -6, 0],\n [4, -3, -4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 0, -3, 0, -5],\n [-5, -4, -2, -2, -5],\n [-1, 0, 0, 0, 0],\n [-4, -6, 1, -3, -4],\n [-3, -3, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -5, 0, -2, 3],\n [-3, -1, -3, -4, 1],\n [6, 1, -4, 2, -6],\n [-3, -4, 6, 0, -4],\n [6, -3, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, -6, 0, -4],\n [-4, -2, -4, 5, -1],\n [-4, 3, 1, 2, -3],\n [-4, 6, -3, -4, 1],\n [-4, 3, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, 3, 4, 1],\n [-4, 1, 5, 1, 2],\n [1, -6, 6, -1, -5],\n [-6, -2, 4, 0, -3],\n [6, -5, -1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 3, 0, -5, 4],\n [1, -4, 2, 1, -1],\n [6, 0, 5, -4, 2],\n [6, 2, -5, 0, 2],\n [2, -1, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -3, 3, -3, 0],\n [1, 2, 4, 4, 4],\n [3, 1, -2, -6, 3],\n [1, -5, 2, 6, -3],\n [-1, 6, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -5, -4, 5, -1],\n [-2, 6, -3, -5, -5],\n [3, 5, 6, -6, -6],\n [-6, 5, 3, 1, -1],\n [-3, -6, 1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -3, 3, 4, 0],\n [-3, -2, -2, -2, -5],\n [4, -1, -4, 6, 0],\n [-5, -4, 5, -2, -2],\n [-4, 0, 3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, -2, 3, 6],\n [4, 5, 3, -3, -2],\n [6, 0, -5, 5, -3],\n [-5, -2, -5, 6, 6],\n [-4, 4, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -2, -5, -6, 6],\n [-3, -1, 0, -3, -5],\n [-6, -6, 3, -6, -2],\n [-6, -3, 0, 3, 3],\n [-5, -3, 1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -4, 1, -2, -6],\n [2, 3, 2, -1, -6],\n [1, 2, 4, 2, 2],\n [4, -5, 4, 6, -3],\n [-6, -2, 6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -4, -6, -1, -6],\n [-4, -2, 6, -2, 1],\n [3, 5, -3, 3, -2],\n [0, -5, 2, -4, -2],\n [5, 0, 4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -1, -4, 3, 5],\n [1, 2, -1, 6, -1],\n [-2, -6, -1, 2, 3],\n [2, -5, 2, -2, 5],\n [1, -1, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -6, 1, 5, -6],\n [6, -1, 4, -3, -5],\n [5, 5, 1, -4, 5],\n [4, 3, -1, -2, 1],\n [1, 5, 0, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, -6, -6, -5],\n [3, -1, -2, 6, 2],\n [6, 0, -5, -2, 2],\n [1, 6, 6, -1, 2],\n [1, 1, 4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 6, 2, -2, -5],\n [-5, 2, 0, -3, -1],\n [-5, 1, 6, -5, 0],\n [-5, 5, -4, 6, 2],\n [-2, 2, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 2, 6, 4, -5],\n [2, -4, 1, 5, -1],\n [-6, 6, 5, 3, 0],\n [4, -5, 5, 5, 2],\n [1, 5, -5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 4, -4, -4, -4],\n [-3, -6, -6, 2, -4],\n [6, 2, 5, -2, 0],\n [3, 2, -3, -2, -1],\n [-2, 5, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 0, 3, -5, -2],\n [-5, 6, 2, -3, -6],\n [6, -5, -4, -2, 6],\n [5, -1, 0, 2, 1],\n [-1, -4, 1, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -5, -2, 4, -3],\n [-3, -6, 4, -2, -3],\n [-6, -5, 2, 3, 2],\n [5, 4, -1, -2, 0],\n [3, -5, 6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 5, 1, -6, 4],\n [-2, 5, 1, 3, 4],\n [4, 5, 0, 6, 2],\n [-4, -1, 3, 2, -2],\n [-6, 1, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -5, -6, -4, 5],\n [-2, 6, -2, 6, 5],\n [0, 5, -5, -6, -4],\n [-4, 0, 2, 2, -3],\n [3, 4, 4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -3, -6, -6, 0],\n [6, 6, 2, 5, 1],\n [2, -4, 5, 1, 5],\n [4, -4, 2, -5, 1],\n [-5, 0, -3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -2, 6, 5, 4],\n [-2, 3, 0, 6, -1],\n [1, 0, 3, -2, -3],\n [-2, -2, 4, 0, 2],\n [5, -3, 1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 5, 2, 5, -4],\n [2, 5, -1, -1, -5],\n [-1, 5, 1, -2, -2],\n [-4, 4, -3, 2, 1],\n [-2, 6, 0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 1, 1, -1, -2],\n [-1, -1, -6, -6, -1],\n [1, -6, -5, -6, 0],\n [2, 2, -1, -4, 5],\n [-1, -4, -4, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -4, -3, 3, 2],\n [-2, -6, -1, 2, -3],\n [-5, 6, 0, 0, 2],\n [6, 0, -5, -4, -6],\n [3, -6, -6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -6, -4, -2, -1],\n [-4, 4, -1, 2, -6],\n [-6, -6, 4, 6, 2],\n [-3, 1, 4, -1, 6],\n [6, -1, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, 2, -3, -2],\n [2, -3, 2, -1, 2],\n [-6, 1, 4, 5, 5],\n [1, 2, 5, 3, -5],\n [-1, -3, 1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 1, 5, 6, 4],\n [-6, -4, 3, -4, 0],\n [-1, 6, 4, -6, -6],\n [2, 6, -2, 4, -2],\n [3, 6, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 6, -4, 3, -4],\n [0, 0, -3, 2, -2],\n [-2, 1, -1, 2, -3],\n [3, 6, 5, 4, 6],\n [6, 3, -5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 1, 3, -1, 6],\n [-2, 6, 6, 1, 5],\n [6, 6, -4, 1, -4],\n [0, 1, -1, 0, 3],\n [0, -5, 1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -6, 5, -6, -4],\n [-5, -5, 2, -5, 5],\n [-6, 5, -4, -5, 1],\n [0, 5, -2, -2, 2],\n [-3, -5, -1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -4, -3, 5, -3],\n [5, 1, 2, 2, 1],\n [5, 2, 2, -3, -4],\n [-6, 6, -1, 2, -3],\n [-2, -5, -6, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -3, 2, -3, 4],\n [6, 6, 6, 3, 2],\n [-4, 5, -1, -2, 2],\n [1, -5, -4, 1, 6],\n [-1, -6, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -6, -6, -2, 3],\n [-3, 3, -6, 2, -1],\n [5, -1, 0, 4, 5],\n [6, 1, 2, -4, -2],\n [-1, 5, 5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, 3, 0, -5],\n [3, -6, -2, -2, -2],\n [2, 5, 0, -6, 6],\n [-3, -1, 1, 4, -2],\n [-2, -3, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -1, -4, 2, 3],\n [-2, -2, -2, -5, -2],\n [0, -5, 4, -6, 1],\n [0, -3, 3, -2, 4],\n [-2, -1, -5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -6, 1, 4, 5],\n [5, -6, -6, 5, -5],\n [-2, -4, -2, -6, 2],\n [2, 2, -3, 2, 1],\n [2, 1, -2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 1, 0, -2, 2],\n [4, 5, -4, -6, -5],\n [-6, -3, 2, 2, -1],\n [-2, -3, 0, 4, -5],\n [5, 1, -6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, 0, 0, 5],\n [-2, -4, -5, 4, 4],\n [-6, 3, -5, 5, -3],\n [2, 6, 6, -4, 3],\n [3, -4, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -3, 0, -2, 1],\n [5, -3, 6, 5, -4],\n [5, -1, -4, 4, -1],\n [2, 5, -2, 3, 1],\n [0, 0, -3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -5, -1, 4, 0],\n [1, -4, 4, -4, 3],\n [-1, 2, 4, -5, -5],\n [0, 4, -2, 6, -6],\n [-3, -3, 2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 5, 0, 1, 3],\n [-6, 1, -1, -1, 1],\n [-2, -5, 5, 1, -4],\n [-2, 3, 0, -4, -6],\n [-1, -2, 2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 5, -1, 3, -2],\n [4, -2, 0, 6, -1],\n [4, 4, 1, 6, 5],\n [-6, -6, -5, -6, -1],\n [2, 5, 5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -2, 1, 3, 4],\n [-6, 0, 4, -1, 4],\n [0, 1, 4, 0, -2],\n [1, -5, 4, 1, 5],\n [3, 5, 0, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -1, 4, -5, -2],\n [1, -6, 1, 1, -5],\n [-3, -4, -4, 3, 0],\n [2, 5, -6, 6, 4],\n [-6, -6, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, -3, 6, -4],\n [1, -6, -2, 4, 6],\n [5, 1, -1, -3, -6],\n [4, 1, -6, -5, 2],\n [4, 4, -2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, -1, 6, 6],\n [-3, 6, -1, -5, 5],\n [-1, -5, -1, 6, 3],\n [-2, -2, -5, 2, 2],\n [1, 4, 4, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 0, 4, 1, 0],\n [2, 5, 2, -6, -2],\n [-1, 3, -2, 0, 5],\n [-4, 4, -3, 2, 0],\n [4, 0, 5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 6, -2, -5, 3],\n [4, -5, -4, 1, 5],\n [-3, -5, 5, 0, -3],\n [-6, 2, -6, -3, -2],\n [2, -4, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 4, 5, -3, -5],\n [2, 5, 0, -6, -5],\n [1, 0, 5, 6, -1],\n [2, -4, 2, 6, 4],\n [-6, -2, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -1, -1, 5, 3],\n [1, -5, -2, -6, 2],\n [5, -1, 5, 1, 1],\n [2, 5, 5, 0, 3],\n [4, 3, -6, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, -4, -3, -6],\n [2, -5, -3, 1, -4],\n [5, -6, -2, -4, -4],\n [6, 5, -5, 1, -3],\n [2, 0, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 2, 4, -1, -6],\n [5, 3, -5, 3, -1],\n [1, 4, -3, 5, -5],\n [0, 0, -5, 4, 5],\n [0, -5, -6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, 6, -6, 2],\n [6, 3, 6, -4, 3],\n [5, 5, 1, -1, -1],\n [6, -6, -3, -5, -3],\n [-2, 6, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -1, 4, -1, -3],\n [-6, -3, -6, -4, -6],\n [-3, -5, 6, -5, 4],\n [0, 1, 4, -3, -4],\n [-6, 3, 2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -5, 0, 0, 2],\n [-4, -4, 4, 6, -4],\n [-4, 0, 4, 5, 0],\n [-4, 5, -4, 6, 3],\n [-3, 6, -4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 4, 4, 2, 6],\n [-5, 3, 6, -3, 4],\n [-4, 3, 5, 6, -4],\n [-4, 1, 1, 4, 3],\n [-1, 1, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -5, 4, 3, 4],\n [3, -3, -3, -6, 4],\n [-4, 3, -2, 4, 0],\n [-1, -4, 5, -5, -5],\n [-3, 3, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 6, 3, 1, 0],\n [4, -6, -5, -3, -4],\n [-2, 4, 2, -1, -3],\n [-6, -5, 6, -3, 1],\n [1, -5, 6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -1, 3, 4, -5],\n [-3, 0, 5, -2, -4],\n [-1, -6, 6, 3, -4],\n [-4, -2, -1, -6, -3],\n [-5, 3, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, 1, -3, 5],\n [-5, 0, 0, -1, -2],\n [1, -3, 5, 3, 5],\n [4, 5, -2, 0, 0],\n [-2, -3, 0, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 0, -1, 1, -5],\n [-3, 3, -4, -6, -6],\n [3, 0, 3, -5, 4],\n [4, -6, 0, -2, 3],\n [5, 5, 5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -2, 6, -3, 5],\n [-3, 6, 0, 0, -4],\n [-1, 5, -6, 5, -3],\n [-6, -3, -4, -1, 1],\n [4, -4, -6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, -2, 5, -6],\n [2, -5, -4, 3, 4],\n [-1, 4, 1, -6, -6],\n [0, -6, -3, -4, 1],\n [5, 3, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -3, 2, 3, 5],\n [-6, 0, -2, 4, -3],\n [-5, 6, -1, -6, 0],\n [-2, 1, 1, -3, 5],\n [5, 1, 3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -1, 4, -6, 6],\n [1, 0, 6, 2, -4],\n [5, 5, -5, -1, -1],\n [-2, -5, -5, -4, 6],\n [-2, 2, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 0, 5, -6, 3],\n [0, 5, -1, 5, -1],\n [2, 6, -2, 6, -2],\n [-2, -2, 1, 4, -2],\n [-1, -4, -3, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 6, 5, 3, -2],\n [0, -3, -3, 6, -4],\n [2, 2, -3, 3, 4],\n [-5, 4, 5, 0, 2],\n [-1, -2, -3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 2, -5, -3, -1],\n [3, 0, 4, 3, -2],\n [0, -4, 6, 1, 0],\n [0, 4, 6, -5, -1],\n [-1, 4, -3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -1, 1, -5, -4],\n [-6, 5, -5, 0, 0],\n [5, 1, -1, 4, 2],\n [6, -1, -3, -4, -1],\n [-4, 3, -1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -2, 5, 0, -4],\n [2, -6, -5, 4, -3],\n [-2, -2, 2, -5, -1],\n [4, 0, 0, 1, -6],\n [4, -5, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -5, -6, -3, -3],\n [4, 2, -3, 1, 1],\n [0, -4, 2, 3, -4],\n [-6, -1, -5, 3, -6],\n [-6, 6, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -4, -6, 4, 3],\n [1, -2, 4, -2, -4],\n [-2, 0, 4, -6, -1],\n [-6, 1, -3, 4, 6],\n [-3, 0, -1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -1, 4, -2, 4],\n [-4, -5, 2, 4, 4],\n [5, -4, -1, -5, 2],\n [-2, 4, -6, -1, -3],\n [1, 5, 1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 4, -2, 0, -5],\n [6, 4, -6, -6, 3],\n [4, -2, -2, -6, -6],\n [3, -4, -5, 0, 3],\n [2, -4, -3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 0, 3, -5, -1],\n [-1, 5, -2, -2, -3],\n [-1, 5, 6, -6, -4],\n [-6, 5, 1, 5, -3],\n [6, -4, 3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 3, -3, -5, -5],\n [-3, 3, -3, 5, 2],\n [1, 5, 6, 2, 6],\n [2, 4, -3, 2, 6],\n [-2, -5, -5, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 5, 6, 1, 0],\n [-3, 1, 2, 4, 4],\n [1, 6, -5, -2, 2],\n [-1, 2, -3, -6, -6],\n [4, 0, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 6, -2, -2, 0],\n [5, -2, -4, -5, 5],\n [-6, 4, 3, -6, -1],\n [-3, 5, 5, -3, 2],\n [2, 6, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -2, -1, -2, 0],\n [-6, -1, 0, -1, -1],\n [3, 4, 2, 1, -2],\n [-2, 3, -2, 4, -5],\n [2, 6, -4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 2, 1, -4, 5],\n [4, 2, -4, 5, 4],\n [-2, 3, 1, 3, -3],\n [5, -2, 2, 5, -5],\n [-1, 5, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -4, -4, -6, 2],\n [2, -5, 3, -6, -5],\n [-3, 0, -1, 1, 4],\n [0, 3, -6, -4, 5],\n [-3, -1, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -1, 2, -4, 2],\n [3, -3, 0, 6, -1],\n [-5, -4, -6, 4, -5],\n [3, 4, -1, 3, -6],\n [-2, -1, 2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 4, -2, 3, 0],\n [6, -5, -3, -5, 5],\n [-1, -4, 3, 5, -2],\n [-1, -6, 3, 5, -2],\n [3, -5, 2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 0, -3, 0, -3],\n [4, 5, -5, 3, -1],\n [-3, 0, 5, -5, -2],\n [-2, 6, -2, 4, 5],\n [1, 4, -5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, 2, 4, -1],\n [-6, 4, -2, -1, 4],\n [1, 2, 1, -1, -5],\n [-3, -4, -3, -2, 5],\n [-1, -5, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, -1, 2, 2],\n [6, 1, -4, 2, -2],\n [6, -1, 5, -3, 4],\n [6, 2, -4, 1, 2],\n [-1, -1, 2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -2, 6, -3, 4],\n [0, -1, -6, -3, 4],\n [0, 3, -5, -2, 3],\n [2, -1, 6, -2, 2],\n [0, 5, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 0, -3, -6, -2],\n [-6, 6, 4, -4, 5],\n [-6, 1, -1, 1, -4],\n [-2, -6, -3, 1, -5],\n [-1, 1, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 0, -1, 4, 3],\n [3, -1, 6, 0, 6],\n [-2, 4, -4, 1, -5],\n [5, -2, -6, -2, 2],\n [6, 0, 6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 3, 6, 5, 3],\n [0, -3, 6, -4, -1],\n [6, -3, 6, 2, 1],\n [6, 4, -1, 0, 3],\n [-6, 2, 5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -4, 4, 5, -1],\n [-5, 2, 6, -3, -2],\n [0, -3, 3, 5, 0],\n [-4, 6, 2, 1, -1],\n [5, 4, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 6, 2, -2, -2],\n [4, 4, -2, -1, 1],\n [3, 4, 2, -2, -1],\n [-4, 0, 1, -1, 6],\n [6, 2, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 5, 0, -6, 5],\n [-4, 3, 5, 2, 5],\n [1, -3, 6, -4, 4],\n [0, -4, -5, 1, -2],\n [4, 4, -5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -3, 6, 4, 3],\n [6, -4, -2, -1, 0],\n [5, 5, -2, -5, 0],\n [-1, -3, 4, -5, 5],\n [5, 0, 1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -4, 4, -3, -1],\n [6, 0, -5, 6, -6],\n [1, -5, -4, -6, 3],\n [-5, -2, -2, 4, 1],\n [-4, -3, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -6, 6, -1, -4],\n [6, -4, 1, -5, 5],\n [0, 3, -5, 4, 1],\n [4, 6, 5, 6, 2],\n [1, 0, -4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 2, -4, 0, -4],\n [-2, 6, -2, -1, -3],\n [3, 5, -4, -2, -4],\n [-6, 0, 6, -5, 6],\n [2, 3, -1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 3, 3, 4, 0],\n [0, 3, 3, 5, -5],\n [6, 5, 4, -5, -5],\n [2, 6, -5, 3, -5],\n [-1, 0, 1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -6, 6, -2, -5],\n [4, -6, -5, 1, -4],\n [3, 3, -3, -1, 0],\n [-2, -4, -2, 4, 1],\n [-5, -6, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -4, 1, 3, -6],\n [6, -4, 1, 5, -4],\n [-5, -5, 0, 2, 3],\n [3, -6, 4, -4, 2],\n [-3, 1, -1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -4, -3, -6, -2],\n [5, 0, 1, 0, 4],\n [-3, -5, 0, -4, 1],\n [6, -3, -1, -4, 1],\n [-5, 1, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 3, 2, -4, -3],\n [-5, -1, 5, 3, -5],\n [-5, 6, -2, 4, 6],\n [-3, -3, -1, 0, -6],\n [-3, 3, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 3, -6, -2, 2],\n [3, 2, 0, -4, 0],\n [-5, -4, 1, 4, 1],\n [1, -4, -5, -5, 3],\n [-2, 6, -6, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 0, -5, -4, -6],\n [-3, 4, 3, 1, 6],\n [-5, -3, -6, 0, 1],\n [-6, -2, 4, -4, -6],\n [-1, 6, -5, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 4, -5, -4, 3],\n [-5, 6, 1, -2, -6],\n [3, -1, 5, 6, -6],\n [6, -3, 5, 2, 0],\n [3, 4, 6, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 2, -1, 2, 4],\n [5, -4, 2, 1, 3],\n [6, 2, 1, 3, 5],\n [-2, 5, 2, 5, 5],\n [-2, 3, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -4, 3, -3, -2],\n [-3, 1, -4, 4, 1],\n [4, 5, -3, 0, 6],\n [2, 2, -2, 0, -4],\n [3, 1, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 2, 2, 6, 2],\n [-4, 2, -5, 3, -5],\n [5, 0, 1, -2, -4],\n [-3, 3, -5, -4, 1],\n [3, -3, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 1, 5, 0, 5],\n [-3, 1, 0, 1, 4],\n [-4, -6, 2, -5, -4],\n [-6, -3, -1, -3, -5],\n [-3, -2, 6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 6, 6, 5, -3],\n [3, 4, 6, 4, -3],\n [-5, -6, 3, 2, -3],\n [1, -3, 6, 1, -1],\n [-3, 4, 6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -6, 2, 3, 1],\n [4, 2, 5, 6, -6],\n [0, 4, -2, 1, -4],\n [2, 3, -4, 4, -4],\n [3, -1, 1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 1, -4, 1, 4],\n [-1, -2, -4, -1, -1],\n [-4, 0, -3, 3, -4],\n [6, 2, 3, -1, 5],\n [-5, -4, 3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -1, 2, -6, -4],\n [-2, -2, -6, 1, 6],\n [-6, 3, -4, 4, -1],\n [3, -1, -2, -3, -3],\n [-3, 2, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 4, -3, 5, 5],\n [-5, 2, 0, -4, -3],\n [-4, 6, -2, 0, 6],\n [-4, 2, 0, 5, 6],\n [3, 4, -1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 3, 2, -3, 3],\n [1, -1, 3, -1, 4],\n [-2, 3, -3, -2, 2],\n [4, 6, 1, -3, 6],\n [0, -5, 0, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 2, 0, 1, 0],\n [-4, 2, 0, 0, -1],\n [1, 6, -6, -6, -3],\n [1, 3, -6, -4, 0],\n [-4, 3, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -6, -6, 3, 3],\n [6, -1, 4, -6, 3],\n [3, 2, -4, 3, 2],\n [-6, -5, -4, -1, -4],\n [4, 3, 6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -4, 1, 3, 4],\n [-6, -5, -6, 2, -1],\n [0, -4, 0, 0, -5],\n [-5, 5, 0, 0, 1],\n [3, -2, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -4, 5, 4, -5],\n [-3, 2, -5, -2, -1],\n [2, 0, -3, 3, -1],\n [-4, 1, -2, -3, -1],\n [-1, 2, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 6, 2, 2, -3],\n [3, 5, 0, 2, -6],\n [1, 2, 0, 3, 0],\n [-6, -5, -5, 2, 2],\n [-3, 1, -1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 2, -2, 1, 2],\n [4, -1, 1, 2, 1],\n [-6, -4, -3, 3, 3],\n [6, 4, -1, 1, -4],\n [-2, -1, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 4, 0, -1, -5],\n [-1, -6, -1, -6, 0],\n [-4, -3, 2, -3, 1],\n [-3, -1, 3, -4, 2],\n [-4, -5, -4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 0, 1, 2, 1],\n [-3, -4, 6, 1, 1],\n [0, -6, 1, 4, 5],\n [4, -2, -1, 0, -2],\n [1, 6, 4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -3, -3, -5, -4],\n [0, 2, 2, -3, 1],\n [3, -1, -2, -6, 5],\n [1, -2, 6, -5, -1],\n [5, 5, 3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 3, 5, 5, 5],\n [1, 0, 2, -6, -2],\n [3, -2, 2, 6, -5],\n [1, -1, -2, 1, -3],\n [-3, 3, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 4, -6, 3, -5],\n [-6, 6, -5, -3, -1],\n [-4, 3, 1, 5, 0],\n [-2, -5, 1, 3, 3],\n [2, -2, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -3, -3, -1, -3],\n [-5, -1, -6, 2, 5],\n [0, 2, -4, 1, 0],\n [6, -6, 2, 1, 3],\n [-6, -6, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -2, -6, -1, 3],\n [3, -5, 2, 0, 4],\n [3, 2, 5, -2, 6],\n [0, -4, 1, -3, -3],\n [-2, -5, 1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 2, -1, 5, 1],\n [3, 2, 4, 1, 5],\n [-2, 5, -5, 0, 1],\n [-3, -4, 0, 6, -5],\n [-3, -6, 6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -5, -2, 0, -4],\n [-3, -1, 0, 6, -3],\n [-4, 4, 1, -6, -3],\n [-3, 2, 4, -1, -1],\n [0, 2, 5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -1, -4, 2, -5],\n [-3, -5, 6, -1, 0],\n [3, 3, -6, 2, 4],\n [-1, -1, 3, 4, -5],\n [-2, -5, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -3, -4, 4, -1],\n [2, 0, -5, -1, 6],\n [-4, -1, 0, -1, 5],\n [2, 4, 0, -5, 6],\n [3, -5, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -3, 3, -6, 2],\n [0, -5, -5, 0, 1],\n [-2, 5, -6, -4, -1],\n [5, -3, -3, -5, 1],\n [0, 3, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 5, -4, -1, -6],\n [1, -6, 1, 3, 1],\n [2, -4, -4, 3, -1],\n [3, 1, -1, 3, -5],\n [-2, -4, -2, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 2, 2, 2, 0],\n [-5, -3, -5, 5, -3],\n [-5, 6, -1, 0, -6],\n [5, 1, -3, 1, 1],\n [5, 3, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 1, 1, 4, 4],\n [-5, -2, 2, 5, 3],\n [0, 3, 4, -3, 0],\n [-5, -6, -5, -1, 4],\n [-5, -3, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 4, 6, 2, 2],\n [2, -1, -1, -3, -1],\n [4, 2, -6, 5, 4],\n [4, 2, 3, -2, -2],\n [1, 1, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -2, -3, 4, 0],\n [6, 1, 1, 2, -2],\n [6, 0, -3, 2, -1],\n [4, 2, 3, 2, 3],\n [-6, -3, -3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 4, 4, -4, -6],\n [3, -5, 0, -6, 1],\n [2, 1, -6, -5, 0],\n [0, 2, -3, -1, 0],\n [4, 5, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 2, -1, -2, 4],\n [0, -5, -1, -5, -6],\n [5, -5, 3, -1, -1],\n [1, 6, 3, -1, 2],\n [6, 0, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 3, -2, -4, -6],\n [5, 5, 0, -4, 6],\n [-6, 3, 1, -3, -1],\n [4, -1, -4, 3, -2],\n [-1, -1, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -3, -5, 1, -6],\n [-2, -1, 1, 6, -5],\n [-1, 6, 3, 5, 1],\n [3, -2, -2, -2, -1],\n [-1, 5, -5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 6, -5, -6, -1],\n [0, 4, 3, 0, 6],\n [-1, -2, -4, -6, -5],\n [0, 4, 1, 1, -2],\n [1, 4, 5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -3, 6, -2, -4],\n [-2, -6, -3, -3, -3],\n [2, -5, 4, -3, 1],\n [-2, -1, 4, 4, -1],\n [0, 1, -1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -3, 2, -4, 5],\n [0, -4, -4, 1, 3],\n [-2, -5, -4, 6, 1],\n [-1, -4, 6, -5, 6],\n [-6, -5, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 1, 5, -5, 6],\n [1, -1, 3, -4, -1],\n [2, 4, 4, 2, -6],\n [4, -1, -2, -4, 6],\n [1, 0, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 1, 6, -5, 0],\n [-2, 6, -3, -3, -2],\n [3, 6, 0, 5, 6],\n [-1, -5, 1, -1, 1],\n [-2, 1, 4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 0, 3, 3, 3],\n [2, -5, -4, 6, -4],\n [6, 2, -4, -3, 4],\n [2, 2, -6, 6, 3],\n [4, 0, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 0, 4, 0, -6],\n [-6, 6, 3, -6, 2],\n [-1, -1, 5, 3, -6],\n [1, -2, 4, 2, -4],\n [-5, -4, 3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 0, -2, -6, -3],\n [-4, -1, 4, 2, -1],\n [-4, -1, 3, 2, 6],\n [-1, -1, 5, 0, 0],\n [-4, -3, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 1, -1, 0, 6],\n [4, 2, 4, 1, 5],\n [2, 0, -1, -6, 0],\n [-3, -2, -3, -4, 1],\n [0, 6, 3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -3, -5, 4, -1],\n [2, 4, -6, 2, -4],\n [1, -3, 6, 1, -2],\n [-1, -4, 6, 0, 6],\n [3, 4, -4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -5, 3, 5, -2],\n [2, -1, 0, -2, 5],\n [6, -6, 5, -4, 4],\n [1, 1, -5, -1, 0],\n [-3, 0, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 6, 0, -3, 0],\n [4, 2, 0, -2, 3],\n [0, 1, 5, 3, -6],\n [-5, -6, 1, 4, -3],\n [0, 2, 5, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 3, 4, -4, 6],\n [-3, 4, -4, 2, -2],\n [-3, -5, -2, 4, 1],\n [0, -1, 4, -3, 5],\n [0, 0, 6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 3, 0, 1, 2],\n [2, 6, -4, 4, -2],\n [5, 1, -4, -6, 3],\n [6, -2, -5, 6, 1],\n [6, 0, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 5, 1, 6, -6],\n [-1, -2, 0, 3, -1],\n [-3, -4, 0, -4, 3],\n [-3, 1, 0, -3, 6],\n [-3, -3, 3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 3, -6, -6, -3],\n [3, 1, -1, -1, 0],\n [2, -4, 0, -2, 2],\n [-4, 0, -2, 6, -5],\n [-2, -2, -1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 2, 2, 3, 2],\n [0, 3, 4, 2, 0],\n [-3, 1, 5, -1, -6],\n [-2, 6, -3, -6, -4],\n [3, -2, 6, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 3, 6, -4, -2],\n [-4, 3, -2, 6, 5],\n [2, 2, -2, 3, -6],\n [6, -5, 1, -1, 6],\n [-1, -5, -5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -5, 4, 1, -3],\n [-4, -4, 5, 6, -5],\n [3, 0, -5, 3, -1],\n [-5, -3, 5, -3, -4],\n [4, 1, -2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 1, 4, 4, -2],\n [1, 0, 2, 2, -4],\n [-6, -4, -3, -1, -6],\n [-2, -2, 2, 6, -6],\n [-1, -6, -3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, -5, 5, 0],\n [0, 2, -4, 6, 4],\n [3, -5, 1, 3, -4],\n [-4, -4, 5, -5, -5],\n [6, 6, -3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 3, 6, 1, -5],\n [-5, -3, -5, -4, -4],\n [3, 2, 5, -4, -6],\n [6, 2, 3, 1, 4],\n [3, -1, -4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 2, -1, 0, 0],\n [0, -6, -1, 3, 0],\n [-5, 3, 1, -4, 0],\n [0, 1, -1, -6, -4],\n [0, 5, -1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 5, 1, -1, -5],\n [5, -5, 4, 0, 0],\n [-5, -3, 4, 4, -5],\n [-3, 1, 5, 0, -3],\n [-2, 5, -1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 6, -4, 0, -4],\n [3, -4, -4, 0, 1],\n [2, 3, 3, -4, 4],\n [3, 6, -4, -2, 2],\n [-3, -4, -5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 4, 6, 5, 2],\n [2, 2, -6, 4, 5],\n [-4, 0, -5, -6, -4],\n [-6, -1, -2, -5, -1],\n [-3, -2, -3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -6, -1, 5, 4],\n [-3, -3, 3, 3, -1],\n [4, 3, 3, -3, 4],\n [-2, 3, -5, 4, 2],\n [2, 2, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -4, -5, 2, 2],\n [-3, -3, -2, 0, 4],\n [-1, -1, -6, -6, 4],\n [0, 1, 1, 5, -4],\n [-6, -5, 5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 2, -2, 0, 5],\n [-6, 4, 2, -6, -4],\n [-6, 4, -6, -3, 6],\n [6, 2, 0, 6, 5],\n [-2, 2, 5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -3, -6, -6, 2],\n [-1, 6, 1, 5, -2],\n [0, 6, 2, 1, -3],\n [4, -3, 5, 2, 0],\n [6, 5, 6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -6, -2, 3, 6],\n [-4, 0, -4, -1, 6],\n [2, 3, 2, 0, -5],\n [-1, -2, 5, 6, 1],\n [1, -5, -1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, -2, 3, -4],\n [-4, -3, -4, 5, -6],\n [5, 1, 0, 2, -2],\n [-6, 2, -4, 4, 5],\n [5, 4, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 2, 1, 6, 0],\n [-3, -5, -4, 3, 5],\n [-5, 6, -5, 1, 3],\n [-3, 0, 3, -5, -6],\n [-4, -5, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, 1, 6, 3],\n [5, -2, -4, -3, 0],\n [0, -5, 1, -6, -3],\n [-6, -3, 1, -1, 4],\n [0, -5, 6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 4, 3, 4, -6],\n [0, 5, 2, -5, -6],\n [6, 6, -3, 1, 6],\n [0, -3, -1, 1, 2],\n [4, -6, -6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -4, -1, -4, -4],\n [-4, -5, 4, -1, 5],\n [0, -2, -4, 6, 0],\n [4, 2, -3, 3, -3],\n [5, 1, -1, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 6, 6, 2, 0],\n [-1, 1, 2, -4, -4],\n [1, 0, -3, -3, -4],\n [1, 1, 6, -1, 0],\n [4, -6, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -5, -3, 0, 0],\n [0, -5, -3, 1, 0],\n [2, 3, 1, -4, 4],\n [5, 4, -5, -2, 2],\n [-1, 0, -3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 0, 6, 1, 0],\n [5, 0, 6, 3, -6],\n [-2, 5, -1, -4, -1],\n [-3, -2, 2, 4, -1],\n [6, -3, 2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -2, -2, 1, -5],\n [3, -5, 4, 3, 0],\n [4, -1, -5, 5, 3],\n [1, 6, 6, 3, 3],\n [1, 6, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -5, 0, -2, 0],\n [5, -4, -5, 3, -6],\n [5, 5, 2, 0, -3],\n [0, -6, 1, -2, 3],\n [-4, -5, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 6, 4, 4, 5],\n [5, 0, -6, 4, -4],\n [2, -5, 3, -1, -6],\n [-5, -1, -6, -4, 0],\n [-1, 1, -6, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 4, 0, -2, -2],\n [2, 6, 0, 6, -6],\n [1, -4, 3, -5, -2],\n [3, -6, -1, 1, -2],\n [-1, 5, -2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -5, -1, -6, -2],\n [-5, -6, 5, -6, -2],\n [5, 4, 2, -3, -3],\n [-5, -4, 0, 2, 4],\n [5, -6, -3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 2, -2, -3, 3],\n [1, -1, -4, -5, 3],\n [0, 5, -6, -1, -2],\n [6, -4, -2, 5, -4],\n [-3, -2, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -6, 3, -2, -1],\n [1, -2, 6, 3, 5],\n [0, -3, 5, -5, -4],\n [-6, 2, -3, 0, -6],\n [5, -6, -5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, -6, 6, -1],\n [-3, -6, -4, -4, -6],\n [0, 2, 4, 3, 3],\n [-6, -1, 5, -5, 1],\n [-4, 2, -2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 6, 4, -3, 3],\n [-1, -5, -1, -5, 1],\n [1, -6, 0, 3, -5],\n [-2, 4, 6, 0, 0],\n [-2, 5, -5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, -6, -4, 1],\n [3, 6, 3, 4, 5],\n [4, -4, -2, -6, -2],\n [0, 2, 3, -1, -3],\n [4, 4, -4, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, 0, -5, 4],\n [4, -4, -4, -3, 1],\n [-1, 3, 0, -4, 5],\n [-2, 6, -3, 3, 0],\n [3, 4, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 4, -5, -4, -1],\n [4, 6, 6, 5, -1],\n [2, -3, -2, -4, -6],\n [2, -2, -6, 0, -1],\n [-6, 0, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 2, -5, -5, 5],\n [1, 6, -3, 1, 2],\n [1, 6, -1, 2, -1],\n [-4, -4, -5, 0, 0],\n [2, -1, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 3, 2, 4, 6],\n [-5, 2, -3, -6, 2],\n [5, 4, -4, -4, -1],\n [3, 4, -1, 0, 1],\n [-6, 6, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 0, 4, -5, 4],\n [2, 3, 0, -5, 3],\n [0, -5, -1, 4, -6],\n [3, -3, 2, 5, -1],\n [-5, 5, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, 2, -1, 6],\n [1, 4, -6, -1, 0],\n [4, 6, 3, -4, 2],\n [0, -5, 3, 2, 1],\n [-3, -1, -5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, 4, -5, -5],\n [-4, 6, -4, -4, -6],\n [3, 6, 6, -6, -5],\n [-3, -4, -1, -5, 5],\n [1, 0, -3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -4, 1, 5, 1],\n [3, -1, 6, -1, 4],\n [-4, 6, 0, -4, -2],\n [2, -2, 2, 4, -6],\n [1, -1, -4, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 1, -2, 1, -6],\n [-2, 1, -5, -5, 2],\n [-2, -6, 0, 0, 1],\n [-2, 1, -6, -1, 1],\n [1, -1, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -2, -2, -2, -1],\n [5, 5, -6, -1, 1],\n [-4, -1, -4, 1, 0],\n [4, 6, 2, -6, 4],\n [-1, -3, -2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -4, -4, -1, -1],\n [3, 0, -2, -3, -4],\n [-2, -3, -6, -2, 6],\n [-5, 4, 1, -6, 0],\n [6, 3, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -6, 0, 4, -6],\n [0, -2, 3, -6, -5],\n [0, 4, -5, 4, -1],\n [-5, 6, 1, -6, 1],\n [1, 5, -6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 4, 4, -2, 4],\n [5, 3, -6, -1, 2],\n [5, 3, -5, 2, -4],\n [-6, -5, -4, 2, 2],\n [0, 2, -6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 0, 4, -3, 0],\n [-1, 1, 6, 6, -1],\n [-1, 6, 2, -3, -4],\n [3, 4, -2, 0, -1],\n [-6, 6, -2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 3, 0, -5, 2],\n [-5, -3, -6, 1, 3],\n [-6, 6, 1, -3, -3],\n [-5, -3, 5, -3, 0],\n [-5, 6, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 4, 1, 5, -2],\n [0, 6, 6, -6, 1],\n [6, 1, -3, -6, -1],\n [3, -5, 3, 3, 5],\n [0, 6, 6, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 4, -3, 3, -1],\n [1, -4, 5, 3, -3],\n [4, 2, 3, -5, -4],\n [1, -2, 2, -3, 4],\n [-2, -4, 6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -3, 3, -5, 5],\n [-4, -1, -4, 6, -6],\n [0, -4, -3, 5, -6],\n [-1, -1, 6, 2, 4],\n [6, 1, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 0, -4, 1, -3],\n [-2, -3, -4, -6, -1],\n [3, 4, -3, 5, -1],\n [-4, -6, -5, 6, -4],\n [-2, 2, 5, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -3, 6, 2, 2],\n [-3, 0, -3, -3, -3],\n [0, -5, 6, -6, 4],\n [2, 1, -2, 2, -1],\n [5, 1, -3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -1, -1, -3, -4],\n [2, 3, -4, 3, -3],\n [-3, 6, 0, -1, 2],\n [-5, -3, -1, -3, 5],\n [-6, 4, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, -1, -3, 6],\n [-5, -4, -6, 2, -3],\n [-1, -5, 4, 6, -3],\n [3, 6, 0, 5, 4],\n [-6, 1, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -6, -4, -3, 0],\n [-5, -5, -3, -2, 6],\n [2, -2, 4, -5, -5],\n [5, -3, -5, 4, 1],\n [-2, -3, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -6, -5, 5, -2],\n [-1, -3, -5, 1, 1],\n [-4, 2, -2, 0, 2],\n [5, 2, -4, 3, -3],\n [2, 2, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -6, 4, 3, -3],\n [5, 2, -3, -2, -2],\n [-1, 3, -1, -3, 1],\n [1, 4, -5, -4, -4],\n [-5, -2, 3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -6, -4, 3, 6],\n [-3, -6, 0, 1, 5],\n [-6, -5, -3, -3, 4],\n [5, 0, 6, -4, 4],\n [-4, -3, 3, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 4, -4, -2, 0],\n [-4, 2, -2, 5, -1],\n [3, 4, 1, -2, 2],\n [0, 0, 3, -5, -5],\n [0, 6, 3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -5, -5, 0, -5],\n [6, 3, 4, -2, 3],\n [6, 2, -6, -2, 3],\n [6, -4, -3, 1, 3],\n [0, 1, 3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, 3, 3, -6],\n [-2, 6, 0, -4, 6],\n [-6, 2, -1, -2, 6],\n [-1, 3, -4, 0, 5],\n [0, -1, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 2, 4, 2, -2],\n [5, -2, 1, 2, 3],\n [-1, 0, 4, 5, 5],\n [-4, 0, -2, -6, 3],\n [-2, -2, 5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 0, -4, -3, -4],\n [-2, 6, 5, 6, -4],\n [1, 3, -3, -6, -3],\n [4, -2, 6, -4, -6],\n [1, 1, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 0, 1, 5],\n [4, -6, 6, -5, -2],\n [3, -4, 2, -3, -5],\n [-4, -4, 2, -2, -4],\n [5, -5, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 2, 3, 2, 2],\n [2, 1, 0, -5, 0],\n [-1, -5, 5, 3, 6],\n [3, -3, 0, 4, 6],\n [-2, -6, 3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -2, 3, 1, -2],\n [5, 3, 0, -4, -2],\n [6, -5, 1, -2, -2],\n [-6, -3, -4, 6, 2],\n [-6, 1, -1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -3, 4, 3, 3],\n [-6, -6, -5, -1, -3],\n [2, -2, -3, 4, 5],\n [5, -6, -2, 0, -6],\n [4, -2, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 5, -5, 0, -1],\n [3, 2, -6, -4, -1],\n [-1, -3, -4, 6, -5],\n [-4, -1, 5, -1, -3],\n [-1, 1, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -3, 2, 3, 6],\n [-3, 1, 1, 3, -5],\n [-6, 5, 0, 4, -6],\n [1, -4, 3, -3, 1],\n [3, -3, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 3, 5, -6, -4],\n [6, 2, 3, 0, -1],\n [0, -2, 1, 5, -5],\n [2, 2, 2, -1, -3],\n [-3, -2, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, -4, -5, 3],\n [-6, 5, -3, -1, 2],\n [-2, 6, -4, 2, 3],\n [4, -4, 1, 5, 5],\n [2, 3, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -6, 0, -6, 0],\n [1, -6, 6, 2, -2],\n [-4, -3, 2, -6, -5],\n [5, -2, -5, -2, -4],\n [-1, 0, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 1, 0, 4, -3],\n [3, 3, 3, 1, 5],\n [-5, 5, -5, -4, -6],\n [4, -4, 5, 5, 2],\n [5, 0, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 0, -6, -6, 1],\n [3, 0, -1, -1, 2],\n [-6, 6, 1, 0, 2],\n [2, -4, 4, -6, 6],\n [6, 4, 3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, 5, 6, -4],\n [0, 6, 4, 4, 0],\n [-6, -4, -4, -4, -6],\n [-4, -1, 2, 2, 1],\n [-1, 5, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 1, -3, -4, 1],\n [-3, -3, 1, -5, 1],\n [1, -6, 2, 0, -2],\n [0, 0, 4, 0, -6],\n [-3, -2, 3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, 4, -1, 5],\n [-4, -6, 2, 3, -1],\n [1, -5, -5, 2, 6],\n [-5, 5, -2, -5, 2],\n [-3, -1, 5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 2, 1, 5, 6],\n [3, 0, -3, 3, -4],\n [5, 2, 6, -3, 5],\n [-6, 5, 0, -2, 1],\n [-1, -6, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -4, -1, -4, 5],\n [-2, 0, -5, -2, -3],\n [3, 2, -6, 0, 2],\n [-1, 5, 1, -5, -2],\n [1, -3, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 0, -6, -5, 3],\n [-3, -1, -1, -3, 0],\n [-1, -1, -6, 3, -6],\n [-5, 4, 4, 0, 6],\n [-4, -4, -6, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -4, 4, -2, 4],\n [-2, 1, 4, -4, -6],\n [6, -1, 1, -4, -1],\n [-1, -4, 2, 5, 4],\n [6, 2, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 2, 4, -2, 0],\n [1, -1, 5, 3, 0],\n [1, -5, -5, -1, 1],\n [4, -1, 4, -3, 1],\n [-3, -6, 5, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -6, 4, 0, -6],\n [4, 5, 0, -3, 6],\n [-1, 0, -6, 6, 1],\n [0, -1, 3, -3, 0],\n [4, 5, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 5, -3, 4, 1],\n [-6, 1, -2, 0, 0],\n [5, 3, -2, 6, -1],\n [-5, -4, -1, 4, 3],\n [-6, 1, 2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -6, -3, -2, -6],\n [-3, -4, -4, -2, -4],\n [1, -1, -3, 2, -2],\n [1, 6, -4, -4, -2],\n [-1, -4, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 6, 4, 0, -2],\n [0, 4, 4, 0, 6],\n [-2, 3, -1, -3, -5],\n [1, -3, 6, 6, 1],\n [-3, 0, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -6, 6, -3, -6],\n [-5, -2, -5, -5, 4],\n [5, 5, -1, -1, -6],\n [4, 6, 6, 2, 6],\n [4, 6, -6, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 0, 2, -5, -5],\n [-4, 3, -4, -6, -3],\n [2, 6, -2, -2, -1],\n [0, 2, -4, -5, 4],\n [-4, 5, 6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, 6, 0, -5],\n [4, -3, 1, -5, 3],\n [2, -5, 3, -5, 4],\n [-6, -1, -2, -3, 0],\n [0, -6, 4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 1, -1, -2, -2],\n [-4, -2, 4, 0, 6],\n [-1, 3, -1, 2, 0],\n [-6, 6, -5, -6, 5],\n [3, -1, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 6, -2, 6, 2],\n [-1, -2, 1, -4, -1],\n [-1, 5, 5, 2, -3],\n [1, -3, -3, -1, -2],\n [6, -4, -1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, -2, 3, 1],\n [2, -1, 2, -1, -5],\n [4, 4, -1, -5, -3],\n [-2, 1, -1, -4, 5],\n [4, -1, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 6, -4, 6, -3],\n [0, 5, -4, -3, -1],\n [1, -6, 5, -2, -2],\n [3, 4, -5, -5, -1],\n [3, 5, -6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -5, -1, -5, 2],\n [-5, -5, 6, 1, -2],\n [3, 0, 6, -6, 5],\n [2, -2, 5, -1, 1],\n [3, 3, -5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -4, 2, -2, 2],\n [5, 0, 3, -5, 5],\n [-2, -1, 3, 3, 5],\n [0, 5, -1, -2, 3],\n [-5, 0, -6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -3, -2, 4, -2],\n [-1, 6, 4, 5, -4],\n [6, 4, 6, -3, 4],\n [-1, 5, -4, -2, 6],\n [6, 3, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 1, 1, -4, 0],\n [6, 4, 5, 0, 6],\n [6, 5, -6, -4, 2],\n [5, -3, 5, -3, 1],\n [-5, 2, -2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, -5, -1, 6],\n [5, 0, -5, 1, 4],\n [3, -5, 4, 6, 4],\n [1, 2, 5, -2, 6],\n [2, -2, -4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 3, 3, -3, 3],\n [6, 5, 4, 1, 5],\n [3, 4, 3, -2, 0],\n [-3, -6, 3, 6, -2],\n [1, 1, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 6, 0, 6, 4],\n [5, -6, -2, -5, 2],\n [6, -5, -6, 5, 4],\n [-1, 3, 2, 5, 2],\n [-3, -1, 6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 2, 2, 2, -2],\n [-3, 2, 0, 5, -3],\n [-4, 6, 2, -2, 5],\n [-2, 2, -6, 2, 5],\n [4, -1, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, -1, -4, 5],\n [-2, 0, -3, -2, 5],\n [-2, -2, 1, 1, -4],\n [2, -6, 2, -3, -6],\n [3, 2, 6, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -1, 1, -5, -1],\n [-3, -6, 5, -3, 3],\n [5, 4, 3, 6, 3],\n [2, 0, 5, 4, -1],\n [-5, -6, 5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -3, 6, 1, 6],\n [-4, -4, -6, -3, -5],\n [5, -3, -5, -6, -1],\n [0, 4, -2, -6, 1],\n [6, 0, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -5, 0, 4, -2],\n [2, -2, 1, 5, -4],\n [0, 5, -3, 5, -2],\n [1, 3, -3, 4, 0],\n [-3, 0, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -4, 5, 3, 6],\n [6, 4, 3, -6, -1],\n [0, 0, 5, 5, 3],\n [-3, 4, 3, -1, -5],\n [-4, 2, -2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 0, -3, -6, -6],\n [2, -5, 2, 6, 2],\n [-5, 2, -4, -4, 1],\n [0, 1, -1, 6, -6],\n [-1, -2, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -6, 3, -1, 3],\n [-6, -5, -6, -4, 3],\n [0, -1, 4, -1, 2],\n [-5, 5, 3, -6, -4],\n [3, 6, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 6, -1, 6, -2],\n [5, 0, 4, 4, 3],\n [3, 0, -3, 1, 4],\n [-1, -6, 3, -2, 6],\n [-5, 2, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -2, 1, -2, 1],\n [-3, 0, -4, 6, -5],\n [-6, -6, 2, 5, 6],\n [-5, 0, 6, -1, -1],\n [4, 5, 5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 4, 0, -1, -5],\n [0, -2, 1, -1, 1],\n [-1, -6, -5, -1, 0],\n [1, -4, -5, 2, -6],\n [-6, 0, -4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -1, 2, -1, -1],\n [-2, -4, 6, 6, -4],\n [1, -1, 5, 6, -1],\n [3, 5, 2, -1, -6],\n [3, -6, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -2, 3, -5, -5],\n [-3, -5, -2, 0, 2],\n [-2, -5, -3, -5, -2],\n [1, -4, 0, 6, -4],\n [5, -6, -2, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 6, -5, 1, -1],\n [-2, -1, -6, 5, 5],\n [2, 4, -2, -4, 3],\n [0, 3, 5, -6, 3],\n [5, 0, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -5, -5, -4, 6],\n [-3, -2, -4, 2, 6],\n [4, -2, -2, -4, 3],\n [-5, 0, -6, -6, -6],\n [-1, -2, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 2, 1, 4, 3],\n [3, -5, -6, 6, 5],\n [-5, 0, -1, -3, -5],\n [4, -6, -1, 1, 3],\n [6, -3, -2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 2, -6, 3, 0],\n [1, 4, -6, 3, 1],\n [4, -2, -5, -2, -6],\n [2, -2, -4, -5, -2],\n [3, 5, 5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 3, 3, 3, 6],\n [5, 1, 4, -5, 3],\n [-3, 3, -4, -3, 6],\n [3, 3, -2, -3, 2],\n [-2, 5, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 2, -3, -6, -4],\n [3, 5, 5, -1, 1],\n [5, -6, 2, -2, 4],\n [-4, -4, 5, 1, 1],\n [-1, 0, -5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -6, 4, 5, 4],\n [-2, 2, 4, 5, -4],\n [5, 4, -2, -4, 4],\n [-4, 0, 3, 0, -4],\n [6, -6, 6, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -4, 6, 0, -5],\n [6, -4, 1, 1, -3],\n [0, -2, 6, -1, 5],\n [-4, -5, 3, 5, 0],\n [-2, 1, -1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -4, -2, 5, -5],\n [3, -4, 1, 0, -4],\n [0, -5, -4, 6, -1],\n [1, 5, 3, -3, 2],\n [-6, -5, -6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -6, 3, -3, 4],\n [0, -4, 0, -2, -5],\n [-1, -6, 0, -5, -3],\n [6, 4, 3, -5, -6],\n [0, 1, 1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 6, 6, -6, -3],\n [-6, -2, -5, -5, 5],\n [1, 6, 4, 0, -4],\n [-4, 0, 1, -1, -2],\n [-4, 5, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -1, -1, -5, -1],\n [-2, -4, 4, 1, 2],\n [-4, -1, -5, -3, -1],\n [-4, 4, -5, -6, 6],\n [-3, 6, 6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -4, 2, 3, -6],\n [2, 2, 3, 4, -5],\n [-3, 2, 5, 4, -4],\n [-4, 2, 3, 6, 3],\n [0, 1, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 1, -2, 5, 4],\n [4, 2, -2, 0, -5],\n [-5, -3, -2, -1, -4],\n [2, -2, 6, 3, -2],\n [-1, -6, -2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -3, -4, -6, -4],\n [-4, -2, 5, -3, -2],\n [-2, 2, 3, 0, 6],\n [1, 1, -3, 0, 4],\n [-4, -1, 1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 6, 1, -4, 1],\n [-1, 2, -1, -6, 1],\n [-5, 1, -1, 2, -2],\n [6, 4, 0, -6, -4],\n [-2, 0, 3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 6, 1, -6, 5],\n [-3, -2, -5, 4, -6],\n [-6, 3, 2, 5, -4],\n [-3, -3, -2, -4, 6],\n [-4, 0, 2, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 2, -6, 0, 0],\n [1, 2, -3, 1, -1],\n [-4, -2, -4, 5, -1],\n [6, -1, 6, 6, -2],\n [6, 6, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 5, -2, 6, 5],\n [-1, 6, 2, 4, 5],\n [4, 6, -5, 5, -2],\n [-1, 6, -4, -4, -5],\n [3, 3, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -2, 6, 4, -2],\n [-2, 1, 0, 3, -5],\n [2, 4, 2, 5, -1],\n [-1, 0, -2, 0, -6],\n [-2, 3, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -3, -1, -2, 4],\n [-2, 4, -6, -5, -6],\n [-2, -6, 0, -6, -6],\n [-1, -3, 2, 0, 2],\n [-4, 0, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 4, 5, 2, -5],\n [-4, -4, 4, 2, -5],\n [-6, 3, 6, 6, 6],\n [-6, 2, 3, -1, -6],\n [-4, -5, -6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -1, -4, 0, -6],\n [-4, 0, 3, 3, -1],\n [3, 3, -5, 4, 6],\n [2, 6, 6, -1, 4],\n [0, -3, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 1, 3, -3, -5],\n [-4, -6, -6, -5, 6],\n [-6, 6, -2, -5, 6],\n [3, -5, -2, -5, -5],\n [-5, -1, -2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 1, 3, 0, -5],\n [-1, 4, -1, -3, -4],\n [2, 2, 5, -4, 5],\n [-1, 6, 5, 1, 0],\n [6, -5, 1, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 6, -4, -3, -4],\n [-2, 3, 1, 1, -1],\n [-1, -5, 4, -6, 6],\n [-3, -3, 0, -1, 6],\n [5, 2, -3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 5, 1, -5, -6],\n [3, -3, 6, -5, 3],\n [4, 1, -1, -5, 6],\n [-3, 0, 5, -1, 6],\n [0, 0, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -4, 4, -1, -6],\n [0, 4, 3, -2, -6],\n [-1, 0, 6, 3, -1],\n [1, 4, -5, 2, -3],\n [0, -3, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 4, -1, -4, 2],\n [-2, 2, -3, 5, -6],\n [-6, -3, 0, -6, 6],\n [-1, 6, 4, 0, -6],\n [-1, -4, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 2, -4, -3, -3],\n [6, -4, 0, 6, 6],\n [-5, 5, 2, -3, -4],\n [-5, -5, 2, -5, -5],\n [-5, -1, 6, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 3, -4, 4, 4],\n [5, 3, -1, 3, -4],\n [-3, -2, -5, -4, -5],\n [-4, -4, -2, -4, 4],\n [-5, -6, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -2, 6, -2, 3],\n [3, -4, -5, 2, 4],\n [-4, -2, -5, -3, 3],\n [-5, 4, -3, 5, 1],\n [5, -1, -1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 0, -4, 5, 5],\n [-2, 3, -3, 0, -6],\n [3, -4, -1, 6, -4],\n [-3, 0, 6, -6, 5],\n [4, -3, 4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 2, -3, -2, -4],\n [-6, 3, -3, -6, -5],\n [-4, -2, 6, -5, 2],\n [-2, 2, -6, 3, -4],\n [-3, 6, -4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 5, 0, -6, 0],\n [2, 2, 2, -5, 3],\n [-5, -5, -5, 0, 0],\n [-4, -5, -4, 0, 3],\n [1, 6, -6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -1, 3, -1, 5],\n [-5, 4, 3, 1, -1],\n [0, -6, 4, 4, -3],\n [-1, 5, -5, -6, -2],\n [-1, 0, 3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, -3, -4, -1],\n [4, 4, -4, 6, -4],\n [-3, -3, 2, 0, 3],\n [2, -1, 1, 4, -6],\n [2, -3, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, -4, -4, 0],\n [3, -6, 3, 4, 5],\n [4, 5, -6, 4, 2],\n [-6, 0, 2, -2, 5],\n [-3, -5, 3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -2, 0, -5, 5],\n [6, 1, 1, 2, -4],\n [-6, -2, 6, -5, -6],\n [-1, -2, -5, 2, -6],\n [-2, -2, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 6, -1, 4, -3],\n [-2, -1, -2, -4, -5],\n [6, -2, 4, 5, 5],\n [-1, 6, -6, -1, -2],\n [6, -3, 5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -1, -4, -3, 1],\n [0, 5, -3, -2, 2],\n [5, -4, -5, 0, -1],\n [-4, 0, -5, -5, -2],\n [-6, 4, -5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -3, 1, -3, 1],\n [-3, 3, 4, 0, 1],\n [3, 3, 4, 5, 0],\n [-5, 1, 3, -1, -1],\n [-1, -2, 4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -2, -1, -5, 2],\n [3, -1, 3, -2, -2],\n [2, 6, 5, -4, -4],\n [-3, 2, 4, -2, -4],\n [-6, -1, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -4, -5, -4, -3],\n [5, 4, 4, 5, 1],\n [-5, 1, 6, -2, -6],\n [5, 0, 1, -1, 0],\n [6, -4, 5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -2, 1, 3, -2],\n [-5, -3, -5, 1, 3],\n [6, -2, 3, -4, -2],\n [-4, 2, 1, 4, 2],\n [0, -6, -1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -2, 0, 1, 6],\n [2, 0, -6, 2, -2],\n [-5, -5, 1, 2, -4],\n [6, 5, 1, -4, -4],\n [-6, -2, 2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 2, -3, -4, -3],\n [1, -5, 2, 5, -4],\n [-3, -6, -2, 0, 2],\n [-5, 6, 5, 6, -2],\n [1, 3, 5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 6, 0, -3, -4],\n [-3, 6, 3, 0, -6],\n [5, -3, 4, -5, 0],\n [-5, -2, 2, 6, 0],\n [1, 6, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 4, 2, -6, -5],\n [-3, -5, 5, -4, 0],\n [3, 3, -4, 0, -2],\n [-3, 3, -5, 2, 1],\n [3, 1, -1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 5, 2, -3, -5],\n [-4, -2, -1, 1, -6],\n [-6, -5, -4, 2, -5],\n [6, 3, 2, 5, -6],\n [0, -6, -6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -4, -1, -3, -6],\n [-6, 1, -3, 4, 3],\n [-1, -4, -5, -3, -3],\n [-2, 5, 3, -3, -4],\n [-6, 5, -5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 6, 1, -4, 6],\n [2, 1, 2, -1, 3],\n [-3, 5, 5, -3, -4],\n [6, 3, -1, -3, 2],\n [-6, 1, -6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 3, -2, -3, 5],\n [-6, 1, 2, 1, 5],\n [5, 3, 0, -6, -1],\n [5, -1, 0, -2, -6],\n [-4, 6, 2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 2, 2, 5, -2],\n [-2, 0, -6, -4, -5],\n [-5, 2, -4, -6, -4],\n [-6, -5, 3, 2, 1],\n [5, -6, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -2, 3, -4, -4],\n [6, -5, -6, 2, 0],\n [4, -4, -1, 3, 6],\n [-6, -6, -2, 2, 3],\n [-3, -4, -3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 1, -6, 1, -5],\n [4, 3, 4, 4, -6],\n [-6, 3, 0, 4, -6],\n [6, 1, 6, 5, 2],\n [-5, -4, -6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -1, -1, 1, 6],\n [6, -5, -3, -4, 1],\n [0, 4, 0, 1, 2],\n [-2, -3, -4, -6, -2],\n [0, -1, 6, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 3, -6, 1, -2],\n [1, 2, 3, -3, 5],\n [-6, 3, 5, 2, 4],\n [3, 4, 0, 2, 5],\n [4, 6, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -4, -2, 2, 2],\n [4, 0, 5, -2, 1],\n [-2, -2, -2, -5, -5],\n [4, 2, -6, 6, -6],\n [-4, 6, 3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -6, 4, -2, -6],\n [-2, -1, 6, 1, -6],\n [-3, 4, -3, -3, 1],\n [0, -5, -1, 1, 3],\n [-5, -5, 6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 4, 5, 5, 0],\n [2, -6, 3, -1, 1],\n [-4, -5, -5, 6, -5],\n [-5, -5, 5, 6, 2],\n [-3, -1, 3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 2, -6, -3, -2],\n [-3, -1, -3, -4, 2],\n [0, 0, -1, -3, 2],\n [-2, 5, 3, 2, 3],\n [3, 1, 5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -5, -4, -6, 5],\n [-1, 4, 5, -4, -4],\n [-4, 0, 5, 2, -3],\n [5, -4, 3, -1, 5],\n [5, 4, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 4, 0, -3, -2],\n [-5, 5, 1, 0, -3],\n [-5, -1, -6, -5, -5],\n [-1, -6, -6, 6, 3],\n [3, -4, -3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -3, -4, 0, 3],\n [1, -4, -2, -3, 1],\n [1, 2, 5, -2, -3],\n [-1, -5, -3, -5, 5],\n [-5, -6, -3, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, 0, 6, 6],\n [1, -6, 1, -5, -5],\n [0, 5, -2, -6, 3],\n [-1, 1, -1, 1, -5],\n [-3, -3, -2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 1, -4, 3, 2],\n [5, 1, 6, 3, 2],\n [5, 0, -1, 3, -4],\n [2, 0, 5, -2, 4],\n [-2, 0, -3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -1, -3, -3, 3],\n [-1, 2, 2, 2, -5],\n [-2, -3, -2, -1, 4],\n [-3, -1, 4, 2, 3],\n [-4, -5, -5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -3, -4, 0, -1],\n [-2, 0, 1, -6, 4],\n [-3, 5, 1, 6, 3],\n [4, 5, 5, -2, -6],\n [-2, -5, -3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 5, -3, -5, -3],\n [-4, 4, 1, 3, -2],\n [6, -2, 6, 3, -2],\n [3, 2, 3, -5, -3],\n [-4, 2, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 0, 5, -5, 6],\n [0, 6, 6, -5, 2],\n [-4, -1, 4, -3, 6],\n [-2, -2, -5, -4, 5],\n [3, 6, -5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -6, -1, -5, -4],\n [5, -5, -2, -2, -4],\n [4, -1, -6, -5, 1],\n [2, 1, -6, -6, 6],\n [-3, 5, 1, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -3, -4, -4, -2],\n [2, 6, 4, 2, 0],\n [6, 5, -2, -6, -6],\n [-1, -4, -6, 4, -4],\n [2, 4, -5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -1, -3, 5, 6],\n [5, 0, -4, -1, -5],\n [-5, 5, -2, 0, -6],\n [-3, -2, -3, -3, -2],\n [0, 5, 5, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 4, 1, -1, 5],\n [-6, -2, -3, -1, -4],\n [1, -4, 6, 0, 0],\n [2, -3, 5, 1, -3],\n [5, -6, -4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -5, 0, 4, -4],\n [6, 3, -1, 2, 0],\n [-3, -3, -3, 0, -2],\n [-1, 4, 0, -4, -6],\n [5, -2, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, 6, -4, -5],\n [-6, 2, 6, 2, -3],\n [-6, -5, 0, 3, 6],\n [1, -6, 3, 5, -4],\n [-5, 5, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 1, 6, 1, 3],\n [4, -5, 5, 0, -1],\n [-6, 1, 3, 0, -5],\n [-6, -2, -1, 4, 4],\n [-1, 1, 6, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -5, 4, 0, -2],\n [4, -6, 6, -5, -2],\n [2, -5, 1, -4, 5],\n [5, 1, 6, 4, -3],\n [-6, -5, 6, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 4, -3, -5, 4],\n [4, 6, 1, 4, -1],\n [-3, -1, 1, -3, 6],\n [1, -2, 0, -5, -1],\n [0, 2, 2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 4, 2, -5, -5],\n [-6, 0, -2, -3, 5],\n [-5, 5, -5, -2, 1],\n [-4, 4, -5, 0, 4],\n [1, 1, 6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 4, -2, -1, 2],\n [-6, -3, 3, 2, 3],\n [4, -4, -4, -5, -6],\n [-5, 2, -6, 1, -6],\n [-5, -3, -1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -6, 6, 0, 5],\n [6, 6, 4, 0, 4],\n [-1, -1, 4, -5, 3],\n [0, 4, -5, -3, -6],\n [2, 0, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -5, -5, 4, -6],\n [4, -2, -3, -5, 1],\n [-3, 0, 6, -3, 0],\n [-2, -1, 5, 0, -2],\n [2, -6, 3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -1, -2, -4, -1],\n [6, -4, 4, 0, -3],\n [-5, 0, 1, -4, -6],\n [2, 4, -5, -1, -1],\n [-6, 6, 4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, -2, -5, 6],\n [-5, 4, 1, -4, 0],\n [3, -4, -5, -1, 6],\n [-2, -3, -3, 1, 6],\n [-4, -4, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 6, -2, -1, 0],\n [-1, 5, -3, -1, -5],\n [-5, 4, -5, 4, -2],\n [6, -6, -2, 4, 3],\n [-6, -6, -5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 4, 5, 5, -1],\n [3, 3, 2, -2, -3],\n [5, 2, -3, 1, 4],\n [4, 4, 0, -5, -6],\n [1, -4, 6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -2, -2, 5, 1],\n [-3, 1, -4, -3, 5],\n [-6, -5, 1, 0, 4],\n [-6, -4, 2, -4, 5],\n [6, 4, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -4, 5, -5, 2],\n [-1, 3, 6, 1, 0],\n [-6, -4, -2, 2, -5],\n [4, -6, -2, 1, 2],\n [-2, -2, -1, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, -5, -6, 4],\n [4, 3, 3, -4, -5],\n [-6, -6, 6, 0, 6],\n [6, -5, -2, 6, 5],\n [0, 5, -2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -2, 2, -3, -4],\n [-4, 5, 0, -3, 3],\n [-1, -1, -3, -2, -1],\n [-1, -6, 4, 2, -1],\n [-3, 3, -4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 4, 1, -3, 4],\n [-2, -2, -5, -1, -3],\n [-1, -5, 4, 2, 4],\n [-5, -3, 1, 0, -3],\n [-1, 1, 5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 1, -4, 3, 5],\n [5, 5, 6, -1, -6],\n [-3, 0, -1, 6, -3],\n [-5, -6, 1, -1, 3],\n [-1, -3, 4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 5, 0, 0, 1],\n [0, -6, -2, -2, -6],\n [2, 2, 2, 6, 0],\n [0, 4, -3, 2, 4],\n [-1, 6, -5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 0, 6, -1, -6],\n [-2, -3, -6, -1, 5],\n [5, 4, -4, -2, 1],\n [1, -3, 4, 1, 4],\n [-6, -6, 6, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -5, -2, -2, 3],\n [3, 4, -3, -4, 2],\n [-4, 2, 5, -4, 2],\n [-5, 4, 4, 0, -5],\n [4, -2, -3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 0, 0, 2, 2],\n [2, 4, -6, 0, 5],\n [5, 0, -4, -2, -3],\n [-1, 4, 0, 4, 6],\n [6, -6, 5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -4, 1, 1, 0],\n [0, 4, -1, 3, 1],\n [4, 3, 3, -6, 3],\n [5, 2, 3, 1, 6],\n [-4, -4, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 2, -1, -2, 1],\n [2, -4, 2, -3, -6],\n [-3, -3, -5, -2, -6],\n [-1, -5, -4, -3, 5],\n [-1, -6, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -1, 6, 2, 6],\n [-1, -5, -3, 6, -3],\n [0, 2, 6, 1, 6],\n [6, 1, 6, 1, 6],\n [-4, 0, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, -4, 2, -1],\n [6, 5, -3, -3, 5],\n [-2, -1, 0, 1, -6],\n [-2, -3, 4, -2, -6],\n [-2, -4, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -3, 4, 4, 1],\n [-4, 4, -3, -1, 5],\n [-3, -6, 1, -4, 6],\n [4, 4, 2, 2, -4],\n [-5, -4, -3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 1, 0, -2, 1],\n [4, 1, 4, -2, 5],\n [-1, -6, 0, 3, 3],\n [2, -3, -4, -1, 0],\n [4, 6, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 2, -1, 0, 3],\n [-6, -2, -6, 1, -6],\n [1, -1, 4, -3, -2],\n [6, -4, -3, 6, 6],\n [0, 0, -5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 1, -1, 5, 1],\n [-5, 4, 2, 1, -6],\n [5, 3, 6, 0, -3],\n [6, -6, 1, -2, 2],\n [1, 2, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -5, -3, 5, -2],\n [-2, 4, -1, 0, -3],\n [5, 6, 2, -5, 2],\n [1, 6, -2, 0, -3],\n [-5, -4, -1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -2, 0, 3, 0],\n [-2, 4, -3, 2, 4],\n [-4, 4, -5, -5, 4],\n [3, -3, 2, 5, -6],\n [2, 5, 2, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 5, -1, -1, -2],\n [-5, 1, 5, -5, 3],\n [3, 5, 1, -3, 1],\n [-2, -4, -5, -1, 4],\n [-5, -5, -5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 5, 1, 6, -2],\n [-2, 0, -3, -4, 0],\n [-2, 6, -3, -3, 5],\n [-6, -6, -3, 6, -3],\n [-4, -3, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, 0, -5, 4],\n [0, -4, -2, -6, 4],\n [-5, 6, 3, -3, -2],\n [0, 1, 6, 4, -1],\n [4, 0, -3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 5, -4, -2, -2],\n [2, -4, 2, -3, -3],\n [0, -6, 1, 1, 6],\n [-5, -5, 3, 2, 4],\n [-3, -5, 5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 2, 2, 0, 2],\n [-5, 4, -4, -4, 5],\n [4, 3, -1, 4, -2],\n [0, -2, 2, -1, -3],\n [-4, -2, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 1, 6, 5, -2],\n [-5, 4, 6, 3, 6],\n [3, -5, 5, 5, -1],\n [5, 1, -4, 4, 3],\n [-2, 0, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 3, 1, 5, 4],\n [-2, -2, 5, 5, -3],\n [0, 6, -1, -2, -4],\n [-4, -5, -1, 1, 4],\n [0, 5, 3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -3, 6, 0, -6],\n [1, -6, 6, -3, -2],\n [2, 4, 5, 4, 3],\n [-1, 4, -6, -1, 5],\n [-3, -5, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -2, 2, -6, 5],\n [4, 0, 4, -6, 2],\n [-4, 5, 4, -4, -2],\n [-5, -4, 5, 6, -5],\n [2, 4, -4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 5, -3, 4, 0],\n [-2, -4, -6, -3, -3],\n [6, 0, 3, 5, 0],\n [-4, 1, -5, 6, -1],\n [6, -3, -5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -4, 5, -3, -5],\n [-1, 0, -1, 4, 3],\n [-4, 6, 0, 2, -3],\n [-3, -6, -1, -6, -5],\n [5, 4, 1, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -6, 0, -3, -5],\n [5, 4, 5, 1, 3],\n [5, 6, -5, 4, -1],\n [-3, 1, 4, 6, -6],\n [1, 6, 4, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -4, 1, 4, 1],\n [-1, 1, 6, 4, 4],\n [6, -6, -5, 2, 0],\n [0, -5, -1, 4, -5],\n [2, -5, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -2, 3, -3, -2],\n [-3, -4, -2, -4, -2],\n [-5, 6, 2, 6, 6],\n [-6, 6, 0, 1, -1],\n [5, 4, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 0, -4, 5, 4],\n [-1, 2, 3, -4, 6],\n [3, 4, -2, 3, 3],\n [-2, -2, -3, 2, 0],\n [6, -3, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -2, 5, 2, -5],\n [-2, -2, 6, -1, 4],\n [-4, 6, 0, 6, -5],\n [-5, 2, 1, 6, -4],\n [-3, -4, 5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -3, 3, -2, -1],\n [4, -3, 2, -2, 6],\n [-3, 5, 0, -2, 2],\n [3, -6, -1, -4, 2],\n [6, -1, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 0, 0, 1, -6],\n [6, -6, 4, 0, 2],\n [1, 6, -4, 4, -6],\n [0, 5, -2, 2, 5],\n [0, -2, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -5, -1, 4, -4],\n [-1, -3, -1, 5, 1],\n [-5, 0, 2, 0, 4],\n [0, -3, 1, -2, 2],\n [-1, 2, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -1, 6, 1, -4],\n [4, 1, 2, 5, -2],\n [6, 1, 5, 0, 2],\n [4, -1, 4, 6, 2],\n [2, -5, -4, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -4, 3, -3, -5],\n [-4, -4, -4, 3, 2],\n [5, 5, 3, 2, -2],\n [-1, -1, -3, 6, -6],\n [5, -3, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 1, 3, 6, 4],\n [-2, 5, 2, -3, 4],\n [1, 2, 0, -2, 1],\n [1, 3, 1, 4, 1],\n [5, -2, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, -3, -2, -2],\n [-2, -3, -4, 3, 3],\n [2, 6, 3, -6, -5],\n [-5, -5, 2, 1, 2],\n [-3, -2, -6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -1, -2, 2, -4],\n [4, 5, -1, -4, -4],\n [6, -6, 4, -3, 0],\n [5, 6, -4, 4, 1],\n [-3, 4, 6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -6, 3, -3, -5],\n [5, 5, 3, 0, 4],\n [-1, 2, 1, 4, 5],\n [3, 0, -5, -6, 2],\n [5, -2, -5, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 5, -6, -5, 2],\n [0, 4, 3, 3, -5],\n [-5, 5, -3, -1, 3],\n [2, -3, -3, -6, 0],\n [-5, 4, -3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -4, 2, 6, -4],\n [-3, -3, 1, -4, -6],\n [-1, -4, 1, 5, -6],\n [2, 5, -1, 4, 1],\n [4, -1, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -2, -2, -4, -5],\n [-3, -1, 2, -1, 6],\n [1, 1, -5, 1, 2],\n [3, -6, -2, 0, 4],\n [6, 2, 0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -5, 0, -3, -4],\n [-5, -3, -5, 4, 1],\n [-6, 5, -2, -1, -2],\n [-4, -4, 5, 3, 4],\n [0, 2, 0, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -6, 1, 2, -4],\n [-6, 5, 0, -5, -3],\n [2, 4, 6, 0, 6],\n [-2, 3, 5, -4, -4],\n [-3, -3, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -1, -6, -6, 0],\n [-3, -2, 0, -2, 2],\n [5, 5, 4, -6, 2],\n [-2, -3, -4, -2, -2],\n [-2, -5, -5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -5, -2, 0, -5],\n [5, 5, -6, 0, 5],\n [-1, 6, 3, 5, -6],\n [-6, -3, -4, 6, 2],\n [-5, 3, 3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -4, -4, -5, -6],\n [-2, 6, 5, -4, -6],\n [-1, 5, -2, 2, 6],\n [3, 2, 6, -4, 3],\n [6, -5, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -2, 3, -3, -3],\n [-6, -6, -4, 1, 6],\n [-4, -2, -1, -6, -2],\n [-3, 2, 0, -6, 2],\n [2, -5, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 1, 6, 2, 5],\n [-5, 4, 2, 1, 1],\n [-1, -1, 5, 1, 0],\n [-2, 5, -4, 6, 2],\n [2, 5, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 6, 3, 3, 4],\n [-2, 1, -4, -4, 6],\n [-2, -5, 5, 4, 1],\n [-1, -3, -5, -2, 4],\n [2, 5, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 0, 0, 0, 5],\n [-1, 6, 2, 6, -5],\n [-1, 6, 3, -6, -2],\n [-2, 1, -1, 3, -6],\n [4, 0, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -4, 3, 6, 0],\n [1, 6, -2, -4, -2],\n [4, -1, -1, 3, -4],\n [-4, 3, 2, -1, 2],\n [2, 3, 2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -4, 3, -5, -3],\n [2, -3, 1, 2, 6],\n [-2, -6, 4, -5, 1],\n [2, -4, 0, 0, 3],\n [-1, -3, -2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -4, -1, -5, 2],\n [-6, 3, -3, 1, 0],\n [-3, -2, 0, 0, -4],\n [-6, 5, 0, 4, 5],\n [2, 3, -4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -3, 5, 3, -3],\n [-6, 4, 0, 6, 0],\n [-5, -6, -2, -2, 5],\n [4, 0, 3, 0, 6],\n [5, 0, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, 2, -4, -1],\n [0, 1, -2, -4, 1],\n [-4, -5, -5, -2, 4],\n [-6, -6, 0, -1, -4],\n [-1, 0, -5, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 0, -2, -6, 3],\n [-4, -4, -4, -2, -4],\n [-5, 5, 2, -6, 5],\n [5, 2, -4, 5, 3],\n [-2, 5, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 2, 1, -2, -3],\n [-3, 2, 3, -3, -1],\n [4, 1, -5, 0, 4],\n [-3, -2, 5, 5, -2],\n [6, 4, -6, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, 2, -5, 6],\n [1, 1, -3, -3, -3],\n [-1, 3, -3, 4, -3],\n [-6, -3, -6, -5, 0],\n [0, 2, 1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 1, 3, -3, 5],\n [2, 3, -6, -5, -1],\n [2, 3, -6, -5, 1],\n [1, 4, 6, -3, 5],\n [-4, -3, 3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 6, 1, 6, 5],\n [2, -3, 3, 2, -4],\n [5, -1, 4, -4, 6],\n [4, -3, 3, -1, 4],\n [-1, 6, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 6, -6, 1, 3],\n [5, 2, -2, 3, 2],\n [-3, 5, 4, 5, -6],\n [5, -4, 1, -2, 3],\n [-3, 5, 5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 3, 0, 6, 2],\n [4, 2, -1, -4, 0],\n [-4, 0, -1, -5, -6],\n [-4, 2, -2, 0, -1],\n [-5, 2, -1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 5, 0, 4, 4],\n [5, -1, 5, -5, 5],\n [6, 3, 2, 3, 5],\n [0, 4, 0, -2, 6],\n [3, -4, -1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -1, 6, 6, -1],\n [4, -5, 4, 3, -2],\n [1, -5, 0, -2, 5],\n [-4, 4, -4, 1, 5],\n [2, 6, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, 1, -4, -4],\n [5, 1, 3, 4, 0],\n [-6, 3, -5, -4, -3],\n [-5, -4, -2, 4, -3],\n [3, -1, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -4, -3, 6, 0],\n [5, -3, 2, -3, 1],\n [-3, -5, -4, -6, 1],\n [-3, 4, -5, -3, 5],\n [1, 3, -4, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -3, -1, 1, -3],\n [-1, 5, -2, 6, 0],\n [2, -6, 6, 5, 6],\n [4, 1, -2, 1, 2],\n [-2, 1, 6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 0, 1, 5, 4],\n [1, -6, 6, -5, 3],\n [4, 6, -6, -1, 3],\n [2, -3, 5, 4, 5],\n [-3, -3, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -6, 0, 5, 4],\n [3, 2, -6, -6, 1],\n [-1, 4, 6, 3, -1],\n [2, 1, 1, 0, -3],\n [-5, 6, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 0, 4, 3, -3],\n [-4, 5, 1, 6, 3],\n [1, -5, 4, 3, 1],\n [-6, 5, 5, -5, -1],\n [-6, 4, -1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -6, 6, 0, -2],\n [-4, 2, -3, -6, -1],\n [-4, 1, 1, 3, -3],\n [5, 6, 3, 5, 4],\n [-6, -2, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 0, 4, 4, -5],\n [-4, 2, 0, -5, -5],\n [6, -3, 6, -2, 4],\n [-4, -4, -3, -4, 3],\n [-1, 6, 1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -6, 6, 3, 0],\n [-3, 4, -6, 4, 1],\n [-6, 2, 1, 3, -1],\n [0, 5, -1, 0, 0],\n [-1, -3, 4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 0, 4, 2, 3],\n [1, 5, -6, 1, -2],\n [-6, -4, -6, -2, -3],\n [-4, -5, -6, 6, -2],\n [6, 5, 4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -6, -4, 5, 3],\n [2, -4, 3, -5, 5],\n [-6, -4, 4, -6, 4],\n [-5, -2, -1, 0, 1],\n [4, -4, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 3, -6, 1, -3],\n [-3, 3, 3, -6, -6],\n [6, -3, 0, -2, 4],\n [-2, -2, 0, -1, -1],\n [-1, -5, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, -4, -2, 1],\n [4, 0, -1, 1, 2],\n [5, -1, 4, -4, -2],\n [1, 2, 1, 0, -2],\n [-4, -1, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -2, -1, -2, 0],\n [0, -2, -4, 4, -5],\n [3, 3, -1, 6, -3],\n [1, -5, 0, -4, -1],\n [3, 2, 5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -5, -3, 1, -2],\n [4, 6, -5, 6, -1],\n [0, 0, -1, 2, 6],\n [0, -2, -1, 1, -6],\n [-2, -4, -3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 0, 0, 1, 0],\n [-6, -4, 1, 3, -2],\n [-2, 4, 1, 2, 2],\n [-4, 0, 3, 5, 5],\n [-6, 0, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, -4, -3, 3],\n [5, -5, -5, -3, -3],\n [-3, 6, -3, 2, 4],\n [-2, -3, 6, 5, -5],\n [0, -6, -3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, 4, -5, -5],\n [-3, -5, 5, -2, 4],\n [1, -1, 2, -1, -3],\n [2, 2, 4, -1, 5],\n [-4, 6, 3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, 2, -3, -4],\n [-1, -1, 0, 4, 4],\n [-5, 2, -1, -5, -4],\n [6, 3, 5, 0, -2],\n [0, -2, 3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, -6, 2, 5],\n [5, 0, 5, 0, -1],\n [3, -6, 5, -5, -1],\n [-3, -1, 4, 6, -2],\n [0, -1, 1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, 3, -3, 6],\n [-3, -2, 3, 6, 6],\n [5, -5, 5, -1, 5],\n [-4, -2, 6, 2, -3],\n [3, -4, -3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 2, 0, -6, -5],\n [5, 2, -5, 4, -3],\n [1, 2, 0, -6, 1],\n [-3, -1, -2, -6, -2],\n [-5, -3, 3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -6, -4, 3, 5],\n [0, -3, -6, -4, 5],\n [-4, -5, 3, -4, 2],\n [-5, -6, 0, 1, -5],\n [-2, 4, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, 4, 4, -6],\n [-1, 6, -4, 1, -4],\n [1, 2, -3, 2, 2],\n [2, -6, 6, 4, 5],\n [6, 6, -2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 6, -5, 2, 1],\n [1, -6, 0, 6, 4],\n [6, -6, 1, 0, -1],\n [5, 0, 1, -2, 0],\n [1, -3, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, -4, 1, 5],\n [2, -2, -3, 2, 4],\n [4, -5, -5, 5, 2],\n [3, 3, -2, 1, 0],\n [-3, -3, -4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -2, -1, 5, -5],\n [5, -3, -3, -4, 5],\n [4, -5, -6, 2, -4],\n [-2, 0, 1, -3, 4],\n [2, 3, 5, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -6, -3, 5, 5],\n [-4, -4, 4, 0, -3],\n [-2, 5, 3, 3, 5],\n [-2, 4, -2, 2, -1],\n [-6, -6, 4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 3, -1, 5, 1],\n [-5, 0, -6, 4, 4],\n [6, -6, 4, 1, -1],\n [-5, -5, -4, -4, -3],\n [-2, 2, 0, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, -2, -6, 2],\n [5, 0, -1, 6, -4],\n [-5, -2, -5, -5, -2],\n [0, -5, -3, -4, 0],\n [-4, -6, 5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 5, -5, 3, 6],\n [-3, -3, 6, -6, 6],\n [1, 0, 1, 1, -2],\n [4, -1, 3, 4, -6],\n [2, 6, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 4, 3, -6, 0],\n [-4, -3, -3, 4, 0],\n [-3, -4, 6, -2, -1],\n [-3, 2, -4, -5, -6],\n [0, 1, -5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, -5, 3, 5],\n [-4, 4, -6, 5, -3],\n [1, 6, -1, 4, -6],\n [-3, 6, -3, -6, -1],\n [-6, 6, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -2, 0, 3, 3],\n [-1, 6, 3, -5, 5],\n [-3, -4, 2, -3, -4],\n [-6, -6, 4, -4, 5],\n [4, 3, -2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 4, 1, -3, 1],\n [-1, 4, 6, -5, 6],\n [2, 2, 1, -1, 2],\n [-5, -3, -2, 0, -3],\n [-4, 6, 3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 4, 0, 5, -5],\n [3, -1, 4, 6, 4],\n [-5, 1, 2, 3, -6],\n [-5, 2, -2, -6, 4],\n [3, -6, 3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 3, 0, -6, -4],\n [2, 4, 1, -6, -3],\n [1, 0, 4, -5, 1],\n [-1, 5, 4, -5, -2],\n [-1, 2, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -3, 0, 4, 3],\n [4, -4, 6, 3, -2],\n [0, -2, 0, -5, 1],\n [-3, -1, -1, 6, -4],\n [-4, 4, 4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 4, 1, -2, 6],\n [-4, -3, 1, 6, 3],\n [-4, -2, -4, -4, -3],\n [-5, -2, -2, 5, 5],\n [0, 1, -1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, 5, -2, -2],\n [-5, 4, 6, -2, -4],\n [-2, 3, -4, -3, 5],\n [-5, 3, 1, -4, -6],\n [-6, -3, 2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, -6, -5, 1],\n [-4, -2, -4, 1, 5],\n [2, -6, 1, -4, -1],\n [6, 1, 1, 0, -3],\n [0, -1, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -1, -6, 5, 3],\n [-6, -5, -3, -2, 2],\n [-1, -6, 4, 0, -5],\n [1, 4, -3, -3, 1],\n [2, 6, 5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -4, -2, 0, -3],\n [-4, -3, 2, 3, 3],\n [2, -1, 1, -4, 6],\n [-5, -3, 2, 0, 1],\n [5, -1, 0, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -5, 5, -1, -3],\n [1, 4, -5, -6, 0],\n [-6, -5, 5, -6, 4],\n [0, 4, -1, 6, 3],\n [1, -4, 0, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -2, 4, -4, -5],\n [-1, -5, 6, -5, -5],\n [-6, -5, 4, 1, -4],\n [-4, -2, -3, -6, -3],\n [-3, 4, 2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, -1, 6, -6],\n [6, -6, -1, 1, -2],\n [6, -4, 1, -2, 0],\n [-4, -5, -3, -6, -4],\n [6, 2, 5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -4, 0, -1, -2],\n [5, 4, 0, 2, -5],\n [-5, 0, 5, 0, -3],\n [0, -5, -6, 6, 3],\n [-2, -6, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -1, 5, 4, 5],\n [5, -5, -4, 4, -1],\n [2, 3, -1, 0, 5],\n [-2, 6, 0, 4, 0],\n [3, 0, -3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -5, 0, 4, -3],\n [-6, 5, 5, 4, 3],\n [-3, 6, 3, -1, 4],\n [0, -2, 5, 0, -1],\n [-3, 1, 5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, 1, -4, -2],\n [-5, 0, 2, 5, 5],\n [6, -3, 2, 4, 6],\n [-1, 3, -2, -1, 2],\n [-4, -2, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -3, -2, -2, 5],\n [-6, 2, 5, 5, 0],\n [5, -5, -4, -4, 5],\n [-4, -3, -1, -1, -4],\n [-2, 0, -5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, 0, 0, 3],\n [-3, -6, -6, 5, -2],\n [5, -3, 6, -1, -5],\n [1, -2, -6, -3, -1],\n [-6, -2, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -6, -6, -5, -1],\n [2, 4, -4, -2, -6],\n [6, -5, 0, 6, -5],\n [-4, -6, 2, -5, 3],\n [2, 4, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 3, -2, -4, -6],\n [-5, 1, -1, 2, 3],\n [-6, -6, 6, 0, -1],\n [-3, 0, -4, -3, 5],\n [1, -1, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 0, 6, 2, 3],\n [6, -1, 4, 2, -2],\n [3, 0, -6, -4, -4],\n [3, 3, -4, -5, -1],\n [0, 6, -4, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -3, -1, -6, 3],\n [-1, 5, 1, 4, 2],\n [5, -6, -6, 5, 4],\n [-3, 2, -5, 0, -5],\n [0, 3, -3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -4, 5, 6, 2],\n [3, -1, -4, -1, 2],\n [-5, 1, -1, 4, -4],\n [0, 0, -3, 4, 2],\n [6, 1, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -3, -2, -6, -3],\n [-5, 5, 4, -6, 1],\n [-6, 4, 1, 1, 2],\n [1, 2, 1, 2, -3],\n [-3, 4, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -6, -3, -5, 5],\n [-2, -6, -4, 3, -4],\n [4, -3, -1, -4, 1],\n [-1, 4, 6, 1, 2],\n [-2, 5, 0, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -4, 3, 6, 0],\n [3, 6, 2, -4, 2],\n [-6, -5, 1, 0, -3],\n [-4, -4, 2, -6, 4],\n [-6, -6, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, -6, 5, 6],\n [-3, -4, -4, -5, -2],\n [3, 2, 3, -6, 6],\n [-2, -3, 1, -2, 2],\n [-6, 4, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 1, 1, 3, 2],\n [1, -6, 4, 1, -6],\n [-6, -5, 6, 0, -1],\n [1, 1, -2, 3, 1],\n [4, 3, -2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -1, 6, 4, -1],\n [2, -1, -3, 3, -5],\n [0, -2, 0, 0, -2],\n [2, -6, -3, 6, -6],\n [5, 2, -4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -6, 0, 1, -1],\n [0, 5, -6, 5, 2],\n [3, -5, -5, 0, -3],\n [3, 6, -6, -2, -4],\n [-5, -6, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -6, -5, -3, 3],\n [-6, 0, 1, 1, 2],\n [-2, 5, -3, -5, -1],\n [0, -3, -3, -1, -4],\n [-5, 6, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 5, -5, -5, -2],\n [5, 0, -1, 3, -4],\n [4, 0, 1, 6, -5],\n [4, -4, -5, 1, 6],\n [-1, -5, 5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 0, -6, -5, 5],\n [1, -6, -4, 6, 0],\n [4, -2, 4, -5, 0],\n [2, -3, 1, -1, 5],\n [4, 0, -5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, -4, 6, 3],\n [1, -4, -1, 6, 0],\n [5, -5, -1, -6, 0],\n [-5, -1, -6, 5, -2],\n [-4, 5, -4, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 6, 6, -5, 5],\n [0, -4, -2, 1, 1],\n [0, 1, 4, 0, -5],\n [2, 1, 3, -2, 6],\n [-4, -2, 0, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 3, 2, -1, -5],\n [-2, -3, 3, -5, 1],\n [-5, -3, 1, -3, 1],\n [-6, -6, 0, -4, -5],\n [-3, 4, -2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -5, 5, 4, 5],\n [2, -3, 2, 4, 2],\n [3, -5, -4, -2, -2],\n [2, -6, -5, -1, 3],\n [-3, 6, 3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -3, 6, 5, 5],\n [4, 0, -3, 2, 0],\n [-6, 5, 2, -4, 2],\n [-3, -5, 6, -4, 0],\n [-1, -2, -5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 6, -6, 2, 6],\n [-1, 1, 1, -4, -4],\n [-4, 4, 6, -5, 6],\n [-4, -1, -5, 6, 6],\n [-4, -2, 1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -3, 6, 2, 3],\n [1, 5, -4, -2, 4],\n [6, 2, 2, -5, -2],\n [0, -4, -3, -4, 1],\n [-6, 0, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 4, -5, -4, 3],\n [-1, 6, -6, -1, -3],\n [4, -2, 5, -5, 1],\n [-3, 1, 1, 1, 6],\n [3, 4, -3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -1, -5, -4, 6],\n [5, -4, -4, -2, -5],\n [-3, -3, -4, 5, 1],\n [-5, -6, 3, -1, 2],\n [-3, 4, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -2, -3, 2, -6],\n [-2, -6, 0, -4, 4],\n [4, 5, 3, -3, 0],\n [6, 4, -4, -2, 2],\n [3, 4, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 2, -4, -5, 2],\n [-4, 5, 2, -4, -5],\n [0, 4, 1, 4, 6],\n [-1, 6, 0, 2, 0],\n [0, -2, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -1, 1, 6, -6],\n [-1, 0, -3, -2, -4],\n [1, 2, -6, -2, -6],\n [2, 1, 6, -5, 6],\n [3, -2, -4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -2, 0, 2, -4],\n [-1, 1, 3, -2, 5],\n [-2, 0, 5, -5, 3],\n [-6, 4, 4, 1, 4],\n [-6, 6, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -1, 2, 6, -5],\n [6, -2, -4, -4, 4],\n [6, -4, -3, -4, 4],\n [0, 6, -2, 5, 0],\n [-5, 6, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -1, 0, -1, 5],\n [-1, -5, -2, -2, -5],\n [6, -6, 6, 5, 4],\n [6, -1, -5, 4, 4],\n [-5, -2, 6, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, 0, 6, 6],\n [-5, -2, -3, -2, 2],\n [-2, -6, 4, -1, -4],\n [5, 4, -4, -6, 4],\n [6, -2, 3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 5, 3, -6, 4],\n [-6, -1, 5, -5, 1],\n [-1, 5, -5, 2, -1],\n [0, -2, 2, -3, 2],\n [-6, -5, 4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 5, -6, -1, -6],\n [5, 4, -3, 3, 0],\n [-1, -2, -3, -3, 4],\n [4, -5, -4, -3, 5],\n [6, 3, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 3, -5, -4, -4],\n [5, -1, -1, -1, -3],\n [-4, -4, -1, 1, -4],\n [3, -6, -4, -5, -5],\n [1, 3, 1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -2, -1, 1, 6],\n [2, -2, -1, -3, 6],\n [3, 5, 6, -1, -1],\n [0, -3, 6, 2, -6],\n [-6, -3, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -6, 2, 0, -2],\n [-4, 0, 4, 2, -1],\n [-3, -6, -2, 6, 3],\n [-6, -3, 1, -3, -6],\n [4, -6, -5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -4, 5, 4, 0],\n [4, 3, -1, 1, 3],\n [4, 4, 4, -6, -2],\n [5, 5, -5, 3, 2],\n [3, -3, 6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 1, 0, -6, 3],\n [3, 0, 1, 2, -2],\n [-1, 1, 3, 0, -2],\n [5, -6, 2, -3, -5],\n [2, -5, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 1, 1, -5, -6],\n [6, 0, -5, 2, -6],\n [0, -5, -4, -2, -3],\n [3, -3, -2, 5, 5],\n [-4, -2, 6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 6, 5, -2, 6],\n [3, -5, -1, -3, 4],\n [5, -2, -5, -3, 0],\n [-6, 1, -6, -1, 1],\n [-2, -5, 6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 0, 1, 0, 2],\n [-5, -1, 4, 1, -4],\n [-6, -2, 1, 6, 0],\n [-4, -3, -6, 6, 1],\n [-5, 3, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, 0, 4, 5],\n [-4, 3, 5, 4, 1],\n [-2, -2, 5, -5, 5],\n [-6, -5, -6, 4, 2],\n [2, -1, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 0, -4, -2, -6],\n [3, -1, -1, 5, 6],\n [1, -1, 0, -5, 4],\n [-2, 5, 6, -4, -1],\n [4, -4, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -5, 0, 5, 1],\n [-5, -6, -4, -2, -2],\n [1, 5, -1, 6, -2],\n [-3, 1, -4, 0, 3],\n [5, -1, 2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 3, 1, -4, -4],\n [-4, -3, 5, 1, 1],\n [-1, -5, 4, 4, 2],\n [5, 5, 4, -1, 0],\n [0, 1, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -1, 1, 4, 0],\n [0, 3, 1, -3, 6],\n [2, -2, -5, 3, -4],\n [1, 2, 2, 0, 5],\n [0, -4, -4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 5, -6, -6, -6],\n [-4, -4, -6, -3, 0],\n [2, 1, -6, -6, -5],\n [-3, 6, 6, 2, 5],\n [-6, -6, -6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 0, 3, 1, 2],\n [3, -1, 5, -3, 5],\n [-5, -1, 1, 5, 6],\n [0, -5, -3, -1, -1],\n [-5, 1, 1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 3, -5, -5, -2],\n [3, 1, -4, 2, -4],\n [6, 4, 2, -2, -3],\n [-1, 5, -2, 2, -5],\n [1, -5, -5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, -2, 4, 0],\n [0, -1, 1, -2, 0],\n [6, 6, -6, 1, -5],\n [0, -5, -5, 4, 5],\n [6, 2, 6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -4, 6, -6, -1],\n [1, 0, 1, -6, -6],\n [-2, -6, 2, 1, 1],\n [2, 6, -4, 4, -6],\n [-4, -3, 4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 1, 5, -1, 3],\n [-1, -4, 3, 1, -4],\n [-3, 0, 0, -2, 6],\n [-3, 4, -3, 5, -6],\n [5, -3, 5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -1, 6, -1, -2],\n [1, 5, 0, 3, 1],\n [0, 5, -5, 1, 0],\n [5, -3, -6, -2, -5],\n [3, 2, -5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 3, 4, 6, -2],\n [-6, -3, -5, 6, -5],\n [-6, -3, 1, 2, -1],\n [-5, -1, 2, -1, 3],\n [-3, -5, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -1, 5, -4, 1],\n [-4, 6, -6, 4, 2],\n [-5, 4, 0, -4, 6],\n [2, -3, -3, 2, -5],\n [-6, 4, 0, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -3, 0, 1, -6],\n [-3, 6, -2, 1, 0],\n [2, -1, 3, 3, -6],\n [-2, 3, 3, 1, 5],\n [-3, -4, -3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -5, -1, 4],\n [4, -1, -4, -6, 3],\n [6, 4, 0, 4, 1],\n [-1, 3, -4, 5, -6],\n [-5, -5, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -4, 2, 6, 2],\n [-6, -6, 2, 3, 4],\n [-6, 4, 2, -2, -6],\n [1, 4, 0, -3, -4],\n [-4, -2, 1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -2, 1, 3, 1],\n [0, -2, -4, -2, -4],\n [2, -1, -1, 0, 6],\n [0, 6, 1, -5, -6],\n [3, -6, 5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 1, -5, -6, -6],\n [6, 6, 6, -1, -3],\n [-5, 1, 4, -5, 2],\n [-6, 5, 1, 6, 6],\n [1, -3, -1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 3, 1, 0, -3],\n [5, -1, 2, -6, 6],\n [1, 0, 6, -6, 1],\n [-4, 3, -1, -4, 0],\n [-2, 0, -5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -4, 5, 0, 1],\n [0, -1, 3, 5, 2],\n [-2, -1, -5, -3, -4],\n [0, 6, -4, 4, 4],\n [0, -4, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -3, -2, 2, -2],\n [6, 6, -5, 3, -1],\n [5, 2, -1, 1, 0],\n [4, 1, -5, 1, 4],\n [-3, 6, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 1, 5, -3, -5],\n [-1, 5, -2, 4, -2],\n [2, -6, 3, 1, -4],\n [-2, 3, -2, 2, 3],\n [-5, 3, -4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -3, 5, -2, -4],\n [6, 2, 2, 5, -5],\n [4, 2, 6, 5, -3],\n [1, -3, -2, 0, 0],\n [-2, 2, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, -4, -3, 0],\n [-6, 5, -3, -6, 5],\n [4, -1, -4, 1, 6],\n [-4, -5, 6, 4, 4],\n [-3, 2, 3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 1, 6, 3, -6],\n [4, 2, -2, 1, 4],\n [-1, -1, 1, -2, -1],\n [2, -4, 1, -2, -4],\n [3, -2, -1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, 0, 5, -6],\n [1, 5, -3, 6, 2],\n [-6, 6, -6, -3, 0],\n [-3, 5, -1, 2, -4],\n [-6, 0, -5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -2, -6, 4, -4],\n [-4, 4, 0, 5, 1],\n [3, -5, -4, 6, -2],\n [-5, 6, 1, 4, -4],\n [2, -1, 4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 5, 1, 3, -5],\n [6, 2, -1, -6, -1],\n [-3, -6, -2, 2, -2],\n [6, -2, 6, 2, 3],\n [-3, -1, -2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -1, -5, -2, 1],\n [5, 6, 5, 1, 1],\n [2, -5, -1, 0, -4],\n [2, -6, -1, 0, 6],\n [5, -4, 3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -2, -4, -5, -4],\n [-5, 4, -6, 4, -4],\n [3, -3, -3, 4, -3],\n [-5, -6, -4, 0, -5],\n [-2, -4, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 0, -1, -6, 1],\n [-4, -5, 2, 2, -5],\n [5, -3, 6, -1, 2],\n [-4, -6, 4, 2, 0],\n [-2, 0, -3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -5, 3, 1, -5],\n [-4, -4, 0, -3, -3],\n [-1, 3, -2, 6, 4],\n [-6, -5, 4, 5, -2],\n [-4, 6, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 2, -2, 4, 6],\n [0, 2, 3, -6, 6],\n [0, 1, -3, 4, 4],\n [5, 0, 0, 3, 4],\n [-5, 4, 1, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -5, 4, -3, 5],\n [2, 6, -5, 2, 6],\n [5, 2, 5, -5, 3],\n [-5, 3, -6, -3, -3],\n [2, -1, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -3, 6, -6, 6],\n [-3, 2, -3, -4, -6],\n [-2, -1, 3, 6, -1],\n [3, -1, 4, -6, -2],\n [2, 3, 3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, 0, 6, -1],\n [6, -1, -4, 3, 0],\n [-1, -4, 1, 5, 4],\n [-5, -3, 4, 2, 2],\n [-2, -6, -3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 0, 5, -1, 2],\n [-1, -3, -2, 1, 1],\n [0, 1, -6, 3, -6],\n [2, 0, 5, 5, 0],\n [-4, -4, -3, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 1, -6, 6, -5],\n [2, -1, 1, 6, -3],\n [-5, 1, -3, 4, -4],\n [-2, -1, -3, -4, -6],\n [-4, 2, 3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 6, 2, -3, -4],\n [5, -2, 6, -6, -2],\n [-5, -5, 4, -1, 5],\n [5, 3, -5, 6, 0],\n [-3, -4, 4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -6, 1, 5, 3],\n [1, 1, -3, -1, 4],\n [-5, -3, -5, 2, 3],\n [-6, -6, 0, -4, -6],\n [5, 5, 5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 5, 0, 0, -5],\n [0, -2, -3, -3, -3],\n [-5, -6, -1, 0, 1],\n [4, 4, -6, 2, 6],\n [0, 3, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 0, -3, -5, -4],\n [6, 0, 4, -4, 1],\n [-4, 5, 6, -1, -6],\n [-3, -6, -4, -6, 1],\n [-4, -2, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 3, 1, 1, -6],\n [6, 3, -6, 1, -5],\n [-2, -4, 3, 2, -3],\n [-1, -4, 0, 1, 4],\n [-2, -3, -3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 0, 1, 5],\n [5, -5, 0, -6, 3],\n [6, 4, 2, -4, -4],\n [5, 6, 6, 3, 0],\n [1, 0, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, 6, -2, 6],\n [2, 1, 1, -6, 2],\n [0, -4, 5, 6, 4],\n [-2, -6, -6, 0, -5],\n [6, -2, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 1, 5, 5, -4],\n [-1, -3, -6, -4, -3],\n [-5, -6, 2, -2, -3],\n [5, 1, 4, -4, 0],\n [-5, -4, 5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 6, 4, 6, 1],\n [4, 0, -4, 2, 0],\n [-2, 0, -1, -5, 3],\n [-3, -5, -5, 0, 4],\n [1, -1, 1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 1, -3, -4, 6],\n [-5, -5, -1, -2, 4],\n [-3, 3, 2, 5, 3],\n [-2, 6, -6, 5, 0],\n [3, -1, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -3, -4, -5, 5],\n [2, 2, 2, -3, -4],\n [2, 4, -2, 0, 4],\n [-2, -4, 2, -3, -5],\n [-5, 0, -1, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 0, -4, 4, 1],\n [-5, -1, -4, 6, -2],\n [-4, -6, -5, -5, 0],\n [2, -6, -6, -4, 4],\n [-1, -5, -5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, -1, 1, 2],\n [5, -2, 6, 4, -3],\n [-5, 3, -2, 5, -3],\n [4, -1, 1, 1, -5],\n [0, -1, -6, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 6, 5, 6, -3],\n [6, 6, -2, 6, -4],\n [4, -1, -5, -6, 3],\n [-1, -5, -2, 0, -6],\n [-2, 6, 5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 4, 6, 4, -4],\n [-2, -4, 6, 6, 1],\n [-4, 4, 1, 3, 5],\n [-3, 2, 0, 5, 5],\n [-5, 1, 5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 6, -4, 0, 1],\n [4, -2, -3, 6, 6],\n [-5, 0, 1, -2, 4],\n [-5, -3, 3, 3, -3],\n [1, 5, 1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -4, -5, 3, 6],\n [0, 0, -3, -4, -5],\n [5, -3, -2, -1, -6],\n [-6, -3, 6, 0, -3],\n [-2, -6, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 6, 2, 2, -5],\n [2, 5, 2, 1, 3],\n [1, -3, -4, 3, -6],\n [-3, 4, 3, 3, 5],\n [-6, 4, 6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -3, 5, 6, -4],\n [-4, 6, -1, 0, 5],\n [3, 1, -4, -2, 6],\n [1, 1, 0, -6, 3],\n [2, -4, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 0, -3, 1, 6],\n [1, 0, 5, -3, 6],\n [-3, 3, 4, 6, 6],\n [-6, 0, -4, 1, 2],\n [5, 2, -2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, -4, 6, 3],\n [0, -4, -3, -6, -6],\n [-4, 5, 3, 4, 6],\n [-2, -1, 3, -6, -5],\n [-3, 2, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -1, -4, 1, -1],\n [3, -6, -5, -5, 3],\n [6, -2, -2, -6, -1],\n [-5, 6, 5, 6, 3],\n [-4, -6, 5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 0, 3, -2, 6],\n [-6, -3, -3, 2, -6],\n [-1, -3, -3, -1, -4],\n [-2, 1, 4, -6, 5],\n [2, -4, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 5, 1, -1, 0],\n [2, -2, -1, -6, 5],\n [1, 3, 2, -6, -5],\n [-4, 2, 5, 5, 5],\n [-5, 4, -6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -4, -5, 3, -6],\n [-2, -6, -1, 4, 3],\n [-1, 4, -6, -5, 2],\n [3, 5, 4, 2, 2],\n [4, 3, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, -1, 2, -2],\n [5, -1, 4, 2, -3],\n [-2, -4, 5, -1, 0],\n [-5, 1, 2, -5, 1],\n [-2, -6, -1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 0, 5, -1, 2],\n [6, 5, 4, 5, 3],\n [2, 6, -1, 4, -6],\n [6, -2, 4, 0, 4],\n [3, -5, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -1, -6, -1, 6],\n [-1, -3, -6, 5, 3],\n [5, 3, -1, -4, -2],\n [-5, 1, -4, 3, -3],\n [0, 2, 5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 1, 3, 6, -5],\n [3, -3, -2, 2, 1],\n [0, -2, -4, -3, -1],\n [0, 6, -3, 6, 5],\n [1, 5, -3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -1, 4, 4, 0],\n [6, 3, -2, 1, -1],\n [-4, 6, 6, 3, -4],\n [-6, 3, 3, 1, 5],\n [-1, 5, -2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, 3, 0, 4],\n [-3, 2, 5, 6, 1],\n [-4, -1, 0, -2, -5],\n [-4, -3, -2, 4, 2],\n [4, -2, -1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 4, -2, 4, -6],\n [4, 3, 0, -5, 2],\n [5, -6, -2, -4, -5],\n [4, 1, -1, 4, 6],\n [5, 5, -5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 5, -5, -3, 1],\n [-1, 1, 5, 3, -5],\n [0, -1, 1, 1, -1],\n [5, -5, 0, 2, -1],\n [4, -5, 5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 5, -1, 4, 2],\n [1, 3, -1, -6, 3],\n [3, -5, -5, -3, -1],\n [-1, -2, 6, -6, -4],\n [3, 3, 2, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, 6, -3, -1],\n [-3, -1, 0, -3, -2],\n [-1, 1, -4, 2, 3],\n [-4, 3, 6, 5, 6],\n [5, 1, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -6, 3, 1, -5],\n [-2, -3, 6, 3, 1],\n [2, -4, -4, 1, 3],\n [0, 6, 3, 3, 0],\n [2, 2, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 2, -2, -4, -5],\n [3, -6, -4, -5, 0],\n [-6, 3, 6, 2, -5],\n [6, -5, -2, -3, 4],\n [-1, -4, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 3, 3, 2, 6],\n [-4, -4, -2, -6, 2],\n [-2, 0, 5, 0, 3],\n [-1, 5, -5, 2, 3],\n [-3, -2, 3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 1, -3, 6, 3],\n [1, 5, 4, -4, -3],\n [-6, 5, -3, -6, 0],\n [4, -6, 1, 2, 1],\n [2, -6, -4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -2, -6, -5, 2],\n [-6, -3, -4, 2, -2],\n [5, -4, 3, 2, 0],\n [-1, 1, -5, 1, 6],\n [-6, -1, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 5, 1, 2, 6],\n [-5, -4, 0, -1, 3],\n [0, -3, -6, 6, 0],\n [-5, 4, 5, -4, 4],\n [-5, 6, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -2, -6, -1, -4],\n [1, 5, -1, -4, 5],\n [1, 3, 5, -3, 0],\n [1, -5, 5, -1, 4],\n [0, 0, 3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -2, -1, 3, -5],\n [3, 5, -3, 0, 3],\n [-4, 1, 2, -6, -5],\n [3, -3, -6, 0, 6],\n [-5, -6, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, -5, 2, 6],\n [5, 2, 0, -6, 2],\n [6, -5, -4, -4, 0],\n [-2, 6, 6, 0, -3],\n [4, 4, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -4, 4, -5, 4],\n [-2, -6, -2, 3, 6],\n [-2, 3, -5, -2, 4],\n [4, 1, -6, 0, 1],\n [5, -5, 1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 0, 5, -4, 3],\n [-4, -5, -6, -2, 2],\n [4, -1, -1, 4, 6],\n [-6, 3, 3, 1, 5],\n [5, -3, -1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 0, -5, -5, -2],\n [-6, -4, -6, 1, 0],\n [-2, 2, 1, -6, -6],\n [-6, 2, -2, -1, 3],\n [1, 1, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -1, 0, 2, -6],\n [-4, -6, -2, -5, -6],\n [4, 2, -6, 2, -3],\n [5, 5, -3, -5, -2],\n [2, 1, 2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 6, 4, 1, 3],\n [6, -4, 1, 3, 3],\n [2, 3, 1, -6, 3],\n [6, 0, -4, -6, -3],\n [-5, -2, -4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 1, -5, 1, 3],\n [5, -2, 5, -3, -1],\n [5, 2, -5, -4, 5],\n [2, 1, 0, -4, 2],\n [0, 4, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, -4, -6, -1],\n [4, 3, -2, 1, 5],\n [5, 2, 4, 0, 2],\n [4, -6, -5, 6, -1],\n [0, -6, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 2, -4, -2, 4],\n [3, -3, 2, -2, 3],\n [-3, 5, -4, 1, -5],\n [-6, -3, 5, 1, -6],\n [5, -5, -2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, -5, -3, 4],\n [0, -2, 4, 2, -4],\n [0, -3, 6, 3, -2],\n [-1, -1, -5, -2, -5],\n [-4, 3, 2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -6, 2, -1, -4],\n [2, 5, -1, -5, 6],\n [-3, -3, -5, 3, -2],\n [3, 1, 1, -6, -6],\n [5, 5, -4, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 6, 2, -3, -3],\n [-1, -3, 3, 1, -6],\n [-5, -2, 6, 1, -3],\n [-6, -3, -2, -2, 5],\n [-5, 5, -2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 0, 6, 6, 5],\n [1, -1, 3, 6, -4],\n [-5, 0, -3, -3, 0],\n [2, -3, -5, 5, 1],\n [5, 3, 6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 1, 3, 4, -5],\n [5, 4, 1, -2, 0],\n [5, 0, -4, -3, 6],\n [4, 2, 2, 4, 2],\n [1, 6, 1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 2, 4, 1, -3],\n [-6, 6, 4, 2, -6],\n [2, 4, 1, 3, -5],\n [5, 0, 1, -1, -1],\n [3, -4, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 3, -1, 3, 5],\n [-5, -4, 2, 2, -5],\n [4, -6, 6, -5, -5],\n [-6, 3, -5, -2, 3],\n [6, -5, 5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 0, -5, -6, 2],\n [-3, -2, -3, -2, -5],\n [-5, -2, 5, 4, 3],\n [0, -3, 3, 6, 6],\n [1, 0, 1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 2, 0, -2, -2],\n [1, 5, -6, 3, -2],\n [0, 0, 3, -2, 3],\n [5, 2, -3, 4, 1],\n [-5, -1, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 1, -4, 3, 6],\n [3, 3, -1, -3, 4],\n [6, -1, 4, -5, 0],\n [6, -4, 6, 6, -4],\n [-4, -4, -3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -4, 5, -4, -6],\n [-3, 0, 6, -5, -3],\n [5, -4, -3, 0, -2],\n [4, -1, -5, 2, 0],\n [2, -3, -6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 6, 5, -5, 1],\n [-6, -4, 6, 4, -3],\n [-6, 3, 4, 6, -1],\n [5, 1, 4, 1, -4],\n [1, 6, 1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, 2, -3, 6],\n [3, 1, 1, -3, -5],\n [-2, 6, -4, 0, -6],\n [-1, -6, 4, -5, -3],\n [-2, 6, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 3, 5, 6, 4],\n [3, -3, -1, 4, -4],\n [4, -2, -2, 6, 2],\n [4, -2, -6, 1, 3],\n [-2, -3, -2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 2, -5, -4, 2],\n [0, 1, 5, -4, 1],\n [-4, 3, -3, 0, 5],\n [5, 3, 3, -5, -2],\n [6, -6, 1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -6, -5, -5, 1],\n [-3, 4, -2, 2, -5],\n [4, -5, 5, 6, -4],\n [-2, 0, 0, 3, 3],\n [-3, 5, 4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -6, 3, 0, 3],\n [2, -5, 5, -4, 4],\n [1, 4, 1, 3, 0],\n [3, -2, -3, -4, -5],\n [2, 0, -1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, 2, -2, -2],\n [-3, 1, -2, 2, 1],\n [-2, -3, -3, 0, 4],\n [-3, 3, 3, -5, -6],\n [-6, 3, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, 6, 1, -4],\n [-3, 6, -6, 2, 5],\n [5, -5, -5, 5, 1],\n [5, 4, -6, -3, 2],\n [5, 0, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -3, 1, -3, 2],\n [-5, 4, 2, 6, 2],\n [-3, 2, 3, 2, -1],\n [4, -5, -4, 5, 3],\n [5, 4, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 5, 0, 5, -6],\n [-6, 4, 1, -5, -4],\n [-2, 3, 0, 6, -6],\n [-2, -6, 6, 6, -1],\n [-1, -6, 5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -6, 4, 0, -6],\n [-5, 6, -2, -3, 4],\n [-3, 2, 6, -1, 4],\n [-2, 4, -6, -3, -2],\n [-4, 1, 5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -1, 6, -5, 2],\n [-3, 1, 1, 1, 5],\n [6, 0, 5, -2, -6],\n [1, 3, -4, -1, -5],\n [6, 1, 6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -1, 0, -1, 3],\n [2, -2, 0, -2, -4],\n [6, 1, -5, -2, 4],\n [5, -1, -4, 2, -4],\n [0, 1, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -1, -1, 2, -4],\n [5, 3, -5, -3, -5],\n [3, -6, 4, 2, 0],\n [0, 0, -3, -3, 1],\n [-2, 4, -6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -4, 2, 0, -1],\n [-2, 4, 3, -1, -6],\n [6, 5, 1, 4, 5],\n [-4, 6, 1, 4, 6],\n [-3, -6, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 5, 2, 4, -1],\n [0, 2, 3, -1, 6],\n [-5, -3, 0, -6, 2],\n [1, -3, 4, -2, 5],\n [-5, 4, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 5, -1, -1, 5],\n [2, 4, 3, 3, 2],\n [4, 1, 2, 5, 6],\n [2, -6, -6, -6, 1],\n [-1, 1, -6, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 1, -3, -1, 6],\n [0, 2, -6, -2, 1],\n [2, 5, 6, -2, -1],\n [-3, -4, -6, -1, -1],\n [-4, 2, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -2, -5, 2, 5],\n [4, -4, 0, 0, -6],\n [6, -1, -4, 6, -1],\n [5, -4, 0, 3, -1],\n [0, -3, -2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -1, -3, -5, -1],\n [-5, -3, 0, 4, -5],\n [2, 5, 5, -3, -2],\n [-5, -6, -6, -5, -1],\n [2, 2, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 5, 3, 6, 3],\n [3, -2, -3, -1, -2],\n [-1, 1, 5, 6, -5],\n [1, 1, 2, -1, 6],\n [3, -6, 3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 0, 1, -3, -5],\n [-5, 3, 3, -6, 6],\n [-3, 2, 4, -5, 4],\n [-3, 4, 2, 6, 0],\n [-5, 4, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -3, 1, -2, -6],\n [-4, 3, -1, -2, -2],\n [6, 2, -3, -5, 6],\n [5, 5, 0, 0, -3],\n [-6, 0, -6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 6, 3, 0, 2],\n [-4, -5, 4, -4, 4],\n [0, 3, -6, 4, 0],\n [-4, -2, -5, -3, -4],\n [-6, 4, 2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -1, 0, -1],\n [-2, 2, -6, -4, -4],\n [-1, -4, 2, -1, -2],\n [-5, -1, -1, -6, 6],\n [4, 6, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 0, -3, 4, 3],\n [6, 5, -3, 0, -4],\n [2, -1, -5, -1, 2],\n [-5, -1, 3, -5, 4],\n [-1, 4, -3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -3, 4, 2, -1],\n [-2, -2, 2, 0, -5],\n [2, 1, 6, 1, -2],\n [4, 6, -4, 0, 5],\n [6, -6, -2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -5, -5, -6, -5],\n [-1, 5, 6, 5, 2],\n [6, 4, -3, -4, 2],\n [0, 6, -3, -6, -2],\n [0, -6, 1, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -5, -1, 0, 5],\n [5, 3, -5, -2, -6],\n [-4, -6, -6, 2, 0],\n [-3, -1, -5, 0, 3],\n [3, 5, -3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -2, 1, -2, -5],\n [3, 0, -3, 5, -5],\n [-3, -1, 2, -2, -3],\n [-6, -3, -6, 3, 2],\n [-3, 1, 3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, 4, 6, 4],\n [-6, -2, -1, -2, 0],\n [-5, 5, 2, -5, -6],\n [-5, -1, 6, -4, -1],\n [-4, 2, -1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 3, -4, -5, -5],\n [-1, 5, 3, -5, -6],\n [1, 3, 2, 5, 1],\n [-2, -5, -2, 3, -1],\n [4, 0, -1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 2, 0, -5, 6],\n [6, 2, 2, -4, 1],\n [3, 0, 3, -6, 6],\n [1, -4, -1, 4, 6],\n [2, -2, -2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 0, -4, 1, 2],\n [1, 3, 2, -2, 1],\n [-4, 5, 3, -3, -4],\n [3, 4, 5, 3, -6],\n [4, -5, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -6, 6, 0, 4],\n [5, -5, 6, 0, -5],\n [-6, -1, 2, -4, -6],\n [-4, 1, -5, 3, 0],\n [6, -6, -4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -5, 5, -4, -2],\n [-6, 3, -2, 6, -6],\n [3, -2, 5, 5, 1],\n [-4, -5, 1, 1, -4],\n [5, 1, -3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, 4, 0, 4],\n [-1, -1, -3, -1, 6],\n [5, 1, 1, 0, -5],\n [-2, 6, 0, -5, 1],\n [5, 6, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 4, -1, 1, -5],\n [5, -1, 0, -1, 5],\n [0, 1, 2, -5, -2],\n [-1, -2, 0, -4, 5],\n [6, 5, 2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 0, -6, 5, 0],\n [0, -2, 0, -2, 3],\n [1, 2, -6, -5, 2],\n [2, -4, 6, -3, 3],\n [-6, 3, 5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -3, -5, 5, 3],\n [-4, -2, -1, 4, 4],\n [6, 4, -1, -1, 1],\n [-5, -1, -1, 3, -2],\n [-5, 6, 5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -6, -1, 3, -2],\n [2, 2, -4, 1, -5],\n [2, 2, -4, -2, -4],\n [1, 3, 6, 2, -6],\n [-1, -6, 2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, -5, 5, -1],\n [-6, 5, 4, 3, -4],\n [2, -5, 0, -1, -3],\n [6, 1, 2, -5, -2],\n [-3, -1, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 5, -1, -3, 4],\n [-4, -2, 6, -6, -6],\n [3, -4, -2, 0, -1],\n [-3, -3, 5, -4, -4],\n [-6, 3, -1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -6, 1, 2, 1],\n [-5, 2, -3, 3, -4],\n [-5, 3, -6, 4, -1],\n [6, -3, 4, 5, 2],\n [-5, 1, -5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -2, 6, 4, -6],\n [-3, -5, -6, 1, 0],\n [-2, -3, 6, -6, -5],\n [-2, 5, 6, 3, -3],\n [-1, 1, -4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 0, -4, -6, 4],\n [3, 5, 0, 3, -2],\n [-6, 6, -2, -4, 6],\n [-4, 4, -3, 6, -5],\n [6, 0, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 6, 1, -5, 5],\n [-5, 3, -1, 5, 2],\n [2, -5, 1, -6, 2],\n [4, 2, -1, 6, 6],\n [1, -3, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 6, -4, -4, 2],\n [-3, 4, -4, 4, 4],\n [3, 6, -2, 2, -1],\n [-4, -3, 0, -3, -2],\n [2, 6, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -6, 4, -3, -5],\n [2, 0, -1, 5, -1],\n [-3, 1, 2, -5, -6],\n [0, -4, -4, 3, -3],\n [4, 1, -4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -6, 2, -6, -4],\n [-6, 6, -2, 1, 3],\n [-6, 0, 3, -5, 2],\n [1, 5, -6, 2, 4],\n [-4, 4, 3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 5, 5, 4, -3],\n [0, 2, 5, 4, 6],\n [2, 0, 2, 5, 2],\n [0, 5, -2, 0, -6],\n [-5, 4, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, -3, 4, 1],\n [6, 3, 1, 0, 2],\n [-5, -3, 3, 0, 3],\n [2, -2, 6, -4, 1],\n [-1, -5, -5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 3, 1, 6, 6],\n [-5, 2, 6, 3, -4],\n [6, -1, -3, -5, 1],\n [-1, -6, -2, -6, 2],\n [-6, 4, 0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 3, 6, 4, 1],\n [-5, -2, 3, -5, -2],\n [5, 4, 5, 3, 6],\n [-2, -1, -4, 5, 5],\n [4, 4, -6, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -6, -2, 5, -2],\n [3, 1, 4, -4, -3],\n [3, -4, -5, 1, 4],\n [-2, 4, -1, -6, 5],\n [-1, -4, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -2, 2, -1, -3],\n [5, 2, 5, 4, 5],\n [6, -6, 4, -4, -4],\n [-5, 2, -2, -1, -1],\n [5, 3, 1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 0, 3, 0, -4],\n [-3, 2, 6, -1, 0],\n [2, -6, 0, -1, 5],\n [2, 6, 2, -4, 2],\n [5, -4, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 4, 5, 5, -4],\n [6, -5, 4, 0, 3],\n [4, -5, -4, 6, 4],\n [4, 1, 5, -3, -2],\n [0, -2, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -1, 2, -3, 0],\n [6, -6, 3, -4, -1],\n [-5, 0, -1, 0, 6],\n [-6, -5, 5, -1, 3],\n [-3, -4, -2, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -3, 2, -4, 3],\n [4, 5, -3, -1, 3],\n [1, 3, 1, -2, 0],\n [-1, -5, 5, 2, -1],\n [1, -5, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -4, -1, -2, -2],\n [5, -5, -3, 1, -6],\n [-4, 1, -1, 2, 1],\n [-4, -1, -3, -5, 1],\n [2, -4, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 0, 5, -4, 6],\n [-6, 5, -6, -1, 5],\n [-4, -5, 5, -1, 1],\n [-1, 5, 0, -3, -6],\n [3, -5, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -4, 6, 5, -5],\n [6, -5, -5, -3, -6],\n [-5, 0, -3, 1, 0],\n [4, -2, -1, 4, -1],\n [2, 4, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 0, 5, 6, 6],\n [2, 4, 0, 5, -1],\n [-5, 1, -6, -3, 3],\n [-2, -3, -3, 1, 0],\n [2, 6, -1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -2, -5, 3, 0],\n [-5, -6, -6, 5, 3],\n [-6, 0, -6, -5, 0],\n [5, -2, -4, 6, -4],\n [4, 1, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, -5, -1, -4],\n [5, 2, 3, -3, 2],\n [3, -5, 1, 1, -2],\n [4, 4, 2, 2, 1],\n [1, 1, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -1, 1, 5, -2],\n [-6, 5, 5, 6, -6],\n [6, 0, -1, 3, 5],\n [-3, -6, -1, 6, 6],\n [-1, -1, -6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -2, 3, -1, -6],\n [1, 3, 2, 1, 1],\n [4, 5, 3, 5, -3],\n [-6, 1, -1, -6, 2],\n [0, -3, 4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -3, 0, 4, -4],\n [1, -2, 3, 5, -3],\n [4, -4, -2, 1, 2],\n [4, 0, -4, 6, 3],\n [-2, -3, -3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -2, 0, -4, 5],\n [-6, -6, 2, -4, 2],\n [-4, 1, -6, -5, 6],\n [-1, -4, -4, -4, -3],\n [4, -1, -5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -2, -4, 6, -4],\n [-3, 4, 6, -3, -4],\n [-4, -2, 5, -5, 1],\n [2, -6, -4, -1, -5],\n [-4, -3, -5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, 0, 0, -5],\n [-3, 1, 2, -3, 3],\n [2, 2, -6, -5, 5],\n [-4, 2, -4, -2, 3],\n [2, -3, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 6, 3, -1, -3],\n [0, 0, 5, -4, -1],\n [5, -4, -2, -5, 3],\n [-5, -4, 5, 3, 3],\n [2, 3, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -2, 2, -1, 6],\n [2, 4, 5, 0, -3],\n [-4, -1, -3, 2, 0],\n [-1, 4, 4, 1, 2],\n [4, 3, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -4, 2, 4, -2],\n [-2, 3, 0, -2, 3],\n [1, 1, -4, 6, 0],\n [3, 4, -3, -2, 0],\n [6, 0, -5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -5, 0, -5, -3],\n [-4, -4, 4, 6, 2],\n [-5, 1, 1, 6, 0],\n [-6, 5, 1, -6, -6],\n [-4, -5, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -3, -6, -5, -6],\n [-4, -2, 2, -4, -1],\n [-5, -6, -2, -6, 4],\n [4, 4, 3, -2, 1],\n [2, 6, 0, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 5, -5, -4, 0],\n [0, 3, -1, 3, 4],\n [0, 3, 0, -4, -3],\n [-3, -2, 4, 0, 0],\n [4, 2, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -1, -6, -2, 1],\n [-3, -2, 5, 0, -3],\n [5, 6, -6, -4, -6],\n [4, -5, 3, 3, 6],\n [1, 2, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -5, 5, 1, -1],\n [-1, -2, 0, 6, 5],\n [2, 0, -4, 6, 2],\n [-2, -4, -1, 0, -5],\n [1, 3, 5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -1, -6, 3, 2],\n [-4, 5, -3, 3, -2],\n [5, 3, 5, -1, 2],\n [4, -2, -1, 0, -4],\n [6, -4, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 4, 0, -1, 0],\n [1, 1, 1, 3, 0],\n [-3, -1, 2, -4, 3],\n [-5, 2, -3, -4, 1],\n [0, -5, -5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, 1, 1, 4],\n [-4, 0, -5, 1, 4],\n [-6, -1, 3, -6, 6],\n [5, 0, 2, 4, 0],\n [1, -6, -1, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 4, 5, 6, 5],\n [6, -3, 0, 4, 6],\n [-1, -6, 0, 0, 5],\n [0, -5, -3, 4, -3],\n [4, 0, -2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -4, 5, -2, 2],\n [-2, 3, 3, -4, 2],\n [-5, -1, -5, -5, 6],\n [-1, -3, 0, -6, 1],\n [2, 0, -6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -3, 1, -5, -4],\n [6, -5, 5, -5, -6],\n [4, -4, -1, 5, 0],\n [-2, -1, -2, -1, 4],\n [-6, -6, 5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 5, 6, 3, 5],\n [-6, 3, -3, 6, -6],\n [-1, -6, -6, -6, 2],\n [-5, -3, -3, -3, 3],\n [-3, -2, -5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -4, -2, -5, -2],\n [-3, -5, -3, 2, 5],\n [2, 1, 4, 0, -6],\n [6, 3, 3, 2, 3],\n [-2, 3, 3, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, -2, -2, -3],\n [-6, 3, -2, 4, -4],\n [-2, -4, 2, 0, 3],\n [-6, -5, -4, -3, -3],\n [3, -2, 1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 2, 2, 4, -2],\n [-4, -5, -2, 2, 5],\n [5, -6, 3, -5, -5],\n [-5, 5, -2, 2, 6],\n [5, 5, -5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -5, -6, -1, 1],\n [0, 2, 2, 0, 1],\n [0, -6, -1, 2, 0],\n [-4, 6, 6, 2, -2],\n [-2, -4, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 4, -5, 1, 6],\n [-3, 2, 4, 2, -4],\n [0, -2, 3, 4, -6],\n [-1, 5, -3, -2, -4],\n [0, 2, 3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -3, 0, -2, 5],\n [4, 2, -6, -6, -5],\n [-6, 6, 4, 2, 4],\n [3, 4, 4, 1, 1],\n [5, -4, 5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 4, 3, 3, 4],\n [2, -5, -4, -2, -5],\n [-2, 3, -6, -6, 0],\n [5, -3, 3, -6, 5],\n [-4, 0, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -4, 1, -1, 5],\n [3, -1, -6, 1, 2],\n [1, -4, -6, 3, 3],\n [5, -1, -3, 3, 3],\n [1, -4, 2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -6, 2, -5, 1],\n [5, -2, -4, 6, 0],\n [0, -1, -1, 1, -3],\n [6, -5, -6, -5, -5],\n [4, 4, -4, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 6, -4, 1, -3],\n [-3, -1, 4, -1, -4],\n [-2, 3, -1, 5, -4],\n [-5, -1, 0, 0, 4],\n [-3, -4, -2, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -2, 1, 4, 5],\n [2, 1, -3, 3, -1],\n [-3, 5, -4, -1, 4],\n [2, -2, 3, -1, 0],\n [-4, -4, -2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -3, -6, -2, 3],\n [0, -5, 2, -1, -4],\n [4, -2, 2, -2, -6],\n [-2, -5, 0, -1, 5],\n [-4, 0, -1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 5, 5, 2, 5],\n [1, 5, -3, 4, 3],\n [1, -3, -6, -5, 5],\n [-4, -6, 2, -6, -4],\n [-1, 5, -6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 2, 2, -4, -5],\n [1, 3, -5, -5, -4],\n [1, -1, -4, 0, -1],\n [5, -5, 4, 5, -5],\n [-3, -6, 2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -5, -5, 5, 4],\n [3, 1, 3, 1, 6],\n [-6, 0, 4, -6, -3],\n [-5, 0, 6, 1, -1],\n [-5, -6, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -3, -4, 5, 5],\n [5, -4, 1, -2, 0],\n [2, -3, -6, 3, -3],\n [2, -2, -1, -5, -6],\n [1, 4, -6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 4, 0, -6, 0],\n [-1, 6, 1, 6, -6],\n [6, -6, 5, -2, -2],\n [2, 5, -4, 3, 2],\n [-2, 2, 6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -1, -6, 0, -4],\n [5, -2, -4, 3, -5],\n [-3, 4, 3, 6, 5],\n [2, 2, 1, 1, -6],\n [-6, 6, -3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 2, 4, 0, -1],\n [6, 1, 0, -3, 1],\n [4, -6, 0, -4, 2],\n [-1, 3, -1, 5, 3],\n [-5, -1, -5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -4, 5, 5, 5],\n [-1, 1, -4, 5, 1],\n [5, 4, -3, -6, -3],\n [-4, -6, 3, -3, 1],\n [-1, -1, 0, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, 1, 2, 5],\n [5, 2, -3, -6, -2],\n [-3, 1, -3, 3, -2],\n [6, -6, -1, -1, -5],\n [4, 2, 4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -6, -6, 2, 3],\n [-6, 1, 2, 5, -2],\n [-5, 0, 4, 5, 6],\n [-5, -5, 4, -4, -6],\n [4, -3, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -2, -3, 4, 6],\n [-3, 2, 4, -4, -1],\n [3, -3, -6, -1, -6],\n [5, -4, -6, 2, -4],\n [-2, -5, 0, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -3, 6, 5, -4],\n [1, 4, 6, 6, 6],\n [2, 5, 0, 0, -5],\n [5, -1, -4, 5, 6],\n [-1, 4, 2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 2, 6, -2, 1],\n [6, -4, 6, 6, 6],\n [-6, -1, 4, 4, -5],\n [-3, 3, 5, 1, 1],\n [3, 0, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 4, -5, -1, -2],\n [-4, -1, -3, 2, -3],\n [5, 2, -2, -5, -5],\n [-5, 0, -4, 0, 4],\n [-3, 4, -1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 6, -3, -6, 1],\n [4, 0, 3, 1, -1],\n [-4, -1, -2, 2, 5],\n [6, 5, 5, 2, 5],\n [6, 5, 1, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -5, 2, -1, 0],\n [3, -5, 3, -2, -1],\n [-6, 2, 6, 1, 4],\n [-2, 0, 0, 3, -1],\n [5, 0, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 3, -1, 2, 4],\n [5, 3, 5, 6, 0],\n [6, -2, 6, -1, -6],\n [-5, -4, -6, -6, -1],\n [-6, -5, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, -4, 2, 1],\n [1, -1, -5, -6, 1],\n [0, 5, -3, 0, 5],\n [-2, -2, -2, -1, 6],\n [-3, -2, 5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -1, -5, 1, -2],\n [0, 6, -2, -5, 2],\n [1, -1, 2, 3, 2],\n [3, 5, -4, -2, 0],\n [4, -5, 3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 2, -2, 4, 5],\n [-6, 0, -5, 6, -6],\n [-1, -1, 5, -1, 0],\n [-6, 4, -1, 0, 6],\n [0, 0, -5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 0, -1, -6, -3],\n [1, 2, 0, -6, -2],\n [-6, 4, -3, 5, 4],\n [-5, -3, 1, 1, -2],\n [-2, 5, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 1, 6, -2, -5],\n [-1, 4, -1, -4, 0],\n [-2, -2, 3, -5, -5],\n [5, -6, 3, -6, 0],\n [-3, -3, 4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 3, 5, 2, 5],\n [4, -2, 6, 6, 0],\n [3, -1, -6, -6, 4],\n [5, -3, 5, 2, -1],\n [2, -1, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 1, 1, -4, 1],\n [-2, 2, 2, 6, 1],\n [-4, 2, 5, -2, 6],\n [-1, 0, -4, 1, 5],\n [1, 1, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -1, 4, 6, -6],\n [3, 4, 5, -4, 6],\n [-5, -6, -4, 3, 5],\n [5, 1, 5, 1, 6],\n [-5, -1, -1, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -4, 2, -4, -6],\n [2, 0, 2, -4, 3],\n [3, 0, 4, -2, 2],\n [2, 0, 5, -3, -6],\n [0, 0, -1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -1, 5, 6, 3],\n [2, 3, -6, -2, -4],\n [0, -1, 1, 4, 0],\n [5, 1, -2, 3, 6],\n [-4, -5, -3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 1, -4, -5, -5],\n [6, -4, 3, 6, -4],\n [-1, 2, -1, -6, -1],\n [-3, 4, 1, 0, 2],\n [4, 3, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -4, 3, -3, 1],\n [-6, 4, -1, 5, -4],\n [-2, 4, -4, -5, -1],\n [-5, -4, -1, -5, -3],\n [-1, -4, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -4, 6, -3, 1],\n [-1, 5, -5, -6, -2],\n [5, 4, -5, -6, -6],\n [-6, -3, -5, 1, 0],\n [3, -6, -2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 5, 2, -1, -1],\n [-4, 3, 2, -2, -6],\n [-6, -3, -3, 5, 4],\n [2, -1, 5, -3, -6],\n [3, -3, 6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 2, -3, 4, -5],\n [-4, -4, -4, -5, 6],\n [5, -1, 4, 0, 5],\n [5, 3, -4, -3, -5],\n [4, -3, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -6, -3, -5, -5],\n [-5, -2, -6, -3, 2],\n [5, -2, -3, -6, -4],\n [2, -6, -3, 4, 6],\n [4, 0, -6, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -4, 4, -6, -3],\n [6, 4, -5, 1, 3],\n [-2, 5, 5, 0, 5],\n [1, 5, -5, -6, 5],\n [6, -3, -6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -4, 1, -1, 5],\n [-6, -5, 6, -5, 5],\n [-5, -4, 0, 6, 2],\n [0, 0, 1, 0, -6],\n [-4, -6, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -3, -5, 4, 2],\n [1, 6, -5, 5, -6],\n [-3, 4, 6, 2, -5],\n [-6, 1, -1, 5, 4],\n [-4, -6, 1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 0, 3, 2, 5],\n [5, -3, 3, -6, 2],\n [-1, 4, 5, 1, 0],\n [-6, 6, 4, 4, -1],\n [-2, 3, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 1, 0, 3, 6],\n [3, 5, -1, -6, 0],\n [5, 5, 3, -4, 5],\n [-1, -2, 3, -4, -2],\n [4, -2, 6, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 2, -3, 0, -1],\n [-5, 0, -4, 2, -5],\n [6, -2, 6, 0, 2],\n [2, 3, 0, 5, -3],\n [6, 6, 4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -2, -4, 1, -6],\n [5, 1, -5, 1, 2],\n [-6, 3, 1, -6, 3],\n [-5, 2, -1, 0, 2],\n [2, 6, -5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -4, -5, 4, -3],\n [-3, 0, 4, -4, 4],\n [3, 6, -2, 1, -1],\n [5, 2, 2, 1, 4],\n [-1, 1, -1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -1, -5, -5, -3],\n [2, 6, -6, 3, 3],\n [-6, -4, -6, 5, 0],\n [4, 5, 0, 5, -6],\n [0, 6, -4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -3, -5, -2, 5],\n [-5, -2, 0, 0, 3],\n [-1, -6, 6, 1, -6],\n [1, -5, -2, 3, -2],\n [-4, -2, 6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -1, -3, -3, -5],\n [1, 3, -2, 6, -5],\n [0, 3, -6, 0, -6],\n [5, 4, -3, -6, -2],\n [2, 6, -2, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -2, 5, 2, 2],\n [-2, 4, 3, 6, 4],\n [0, 0, 0, 2, 5],\n [-5, 4, -2, -2, -6],\n [-2, 6, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -3, -1, 0, 5],\n [2, -6, 0, 6, 6],\n [3, -6, 1, 2, 3],\n [-1, -6, -5, 6, 5],\n [-2, 4, 5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -1, -5, 4, 0],\n [6, 5, -4, -2, -3],\n [6, 2, 0, 1, -5],\n [-6, -4, 1, -3, -6],\n [-4, 4, 0, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 3, 3, -5, -5],\n [-4, -3, -6, -4, 5],\n [4, 5, -5, 0, -4],\n [-6, 6, -1, 6, -3],\n [0, -3, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -4, 6, 6, 4],\n [-4, -6, 0, -6, -5],\n [0, -4, -1, 0, 2],\n [-5, -3, -5, -5, -2],\n [-2, -1, -6, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 2, 0, -4, 4],\n [5, 1, 5, 5, 2],\n [-6, 5, 5, 1, -6],\n [-6, -1, 4, -6, 1],\n [-2, 2, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 2, 6, -5, -4],\n [-5, -3, -2, 2, 4],\n [-5, -6, 0, 4, -4],\n [1, -5, -5, 0, 5],\n [5, 2, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -1, 5, 3, 3],\n [3, 6, 2, -4, -2],\n [-2, 1, 2, -2, 0],\n [3, -5, 6, -3, 1],\n [-1, 3, -5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, 5, 2, 3],\n [2, 6, -5, -4, -5],\n [-4, -2, -2, -5, -4],\n [-3, -6, 3, -4, 5],\n [3, -3, 6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -5, -3, -6, 6],\n [-2, -1, 0, 5, -1],\n [-3, -4, 1, 3, -3],\n [0, -2, -1, -1, -4],\n [-3, 1, 1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -3, -5, -5, 1],\n [-2, 2, -5, -5, -5],\n [-2, 6, -5, -5, -3],\n [-3, -1, 4, -2, 1],\n [6, -5, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 5, 5, -1, 1],\n [1, 5, -5, 3, -5],\n [-5, -2, -4, 1, -2],\n [-5, -1, -4, -1, -5],\n [0, 0, 2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 1, -2, 4, -4],\n [-4, -6, -3, 2, 2],\n [-2, 6, -4, 6, -4],\n [-2, 3, 4, -4, 2],\n [6, 6, 6, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -2, -5, -4, 1],\n [3, 3, -4, -2, 1],\n [-3, 1, -3, -6, 1],\n [2, -6, -3, -1, -6],\n [4, -2, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 4, 5, 2, 1],\n [2, 1, 3, 0, -2],\n [-4, -1, 5, -3, 1],\n [-1, 2, -2, -3, 6],\n [2, -6, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 3, 6, -6, 5],\n [-1, 0, 0, 6, -3],\n [-5, -1, 3, 1, 3],\n [5, -6, 1, 6, -5],\n [-5, -6, 0, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 1, 2, 2, -3],\n [-1, 2, -4, -2, 0],\n [3, 5, -6, 0, 4],\n [-5, 5, 0, -5, -1],\n [-5, -6, 4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, 6, 2, 6],\n [3, -4, -5, 0, 3],\n [-4, 1, 2, -3, -6],\n [-2, 3, 2, -6, 3],\n [3, 2, 5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, -1, -3, 0],\n [-3, 5, -3, 4, -3],\n [2, -4, 6, -4, -1],\n [1, -6, -5, 0, -2],\n [5, 6, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 5, -4, -4, 5],\n [-2, -1, 0, -3, 1],\n [-1, 3, 2, 0, 1],\n [6, -3, 3, 0, 1],\n [-4, 5, 5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -2, 5, -2, 5],\n [0, -6, 0, 6, 3],\n [2, -3, -1, -2, -5],\n [-1, 3, -3, 2, 4],\n [-1, 6, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -2, 3, 5, -1],\n [2, -2, -3, -6, -2],\n [5, -1, 0, -4, -1],\n [-1, -3, -5, 1, -1],\n [-3, 4, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -1, 4, 2, -1],\n [-2, 0, -3, 1, -2],\n [3, -6, -3, -4, -4],\n [-4, -3, -2, -6, -5],\n [-4, 6, 6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -6, 0, 6, -4],\n [6, -1, 4, 6, -6],\n [3, -6, -2, -4, -5],\n [2, -4, 5, -2, 4],\n [1, 1, -5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -3, 3, 5, 1],\n [3, 0, 1, 5, 2],\n [-4, -3, 6, -4, 2],\n [6, 0, 6, -6, -6],\n [-6, -3, 4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 4, 3, 2, -6],\n [6, 5, 0, -3, 4],\n [-6, -3, -4, 6, -2],\n [4, 4, 2, 4, 2],\n [0, 3, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -3, -3, 3, -4],\n [2, 3, 0, -2, 1],\n [-3, -1, -4, -6, 0],\n [1, 0, -6, -6, -3],\n [-3, 0, 2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 2, -4, -1, -4],\n [0, 0, 2, -6, -3],\n [4, 5, -4, -4, -3],\n [6, 3, -4, -4, 6],\n [-4, -6, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 5, -6, -3, 2],\n [1, -3, 4, 4, 3],\n [6, -3, 1, 0, 4],\n [5, 5, -4, -3, 3],\n [1, 0, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -1, -4, -2, 4],\n [2, 3, 4, 0, -5],\n [3, 5, 5, 4, -1],\n [-4, 0, 6, 1, -6],\n [2, 6, -4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -2, -5, -5, -3],\n [-2, -6, 3, 2, 6],\n [2, -2, 3, 6, -6],\n [4, -4, -4, -4, -5],\n [-3, 3, -4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 2, -5, -4, -6],\n [3, 2, -1, 3, 0],\n [-5, 0, -3, 5, 6],\n [5, 5, -2, 3, 2],\n [4, -3, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 3, 6, -3, 6],\n [5, -4, -2, 6, -3],\n [-5, -2, 6, -2, -2],\n [-6, 4, -3, -1, 6],\n [3, 3, 4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 1, 6, -3, -1],\n [0, 0, -6, 5, -3],\n [0, -2, 5, 6, -6],\n [6, 2, -1, -2, 4],\n [5, 2, 6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 1, 2, 1, 3],\n [2, 5, 4, 0, 5],\n [-3, 0, 0, -2, -2],\n [3, -4, -3, -2, -2],\n [-3, 0, 6, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -3, -4, -2, 5],\n [-1, -2, 5, 4, 5],\n [6, -2, -3, 4, 4],\n [1, 3, 4, -3, -3],\n [3, -5, -6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -4, -2, -5, 1],\n [4, -5, 3, 5, 4],\n [-6, -1, 3, 5, 2],\n [0, 4, -4, 5, 0],\n [-5, 2, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -3, 2, 5, -5],\n [1, 4, 1, -5, -4],\n [0, 2, -4, -4, -4],\n [-4, 2, -5, -6, 1],\n [3, -4, 5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 6, -5, -3, 6],\n [4, 1, 2, 5, 5],\n [3, -1, -1, -4, -5],\n [0, 2, 2, -2, 5],\n [6, -4, -5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 6, 2, 5, -2],\n [-5, -3, 4, 1, 3],\n [-2, 4, -6, -5, -4],\n [-6, -4, 6, 6, 5],\n [5, 6, 5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, -6, 5, 1],\n [-6, 4, -3, -1, 6],\n [1, 0, -1, -5, 2],\n [-5, 3, 5, 1, 4],\n [2, 6, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 5, 1, 1, -6],\n [0, -4, -5, -4, 1],\n [-6, 4, 6, -1, 6],\n [-6, -5, 1, 5, 4],\n [2, 6, 6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -4, 4, 4, 6],\n [3, 3, -1, 1, -4],\n [-3, 5, -3, 5, 5],\n [-4, -5, 4, -2, 3],\n [-6, 5, -2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 0, -6, 2, -3],\n [-3, -1, 1, -3, 2],\n [-1, 2, 4, -1, 3],\n [6, 4, 1, -6, 0],\n [3, 3, 0, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 3, 4, 0, 4],\n [0, -1, 5, 6, -1],\n [-6, -4, -3, -5, 2],\n [-5, -6, 2, -4, -2],\n [6, 6, 1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -2, -3, -3, -3],\n [1, 1, 3, 0, 0],\n [-5, 1, 1, 3, 0],\n [4, 6, -4, 3, 6],\n [-6, -5, 5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -1, 3, 1, -4],\n [-5, 2, 0, 4, 0],\n [-6, 1, 5, 5, -4],\n [-2, 5, 4, 1, 4],\n [-4, 1, 5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, -3, 6, 4],\n [5, -5, 4, 3, -6],\n [-4, -5, 3, 1, -4],\n [2, 6, 2, -4, 6],\n [6, -4, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, -4, -4, 2],\n [2, -1, -4, 6, -3],\n [3, 5, -1, 2, -4],\n [-4, 5, -2, -1, 3],\n [5, -1, 1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -1, 0, -5, 4],\n [6, 5, 3, -5, 4],\n [-1, -5, 2, -4, 5],\n [4, -2, 6, 2, -5],\n [3, 3, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 2, 6, 0, -3],\n [-3, -5, -6, 1, -4],\n [6, -6, 6, 0, -6],\n [4, 3, 4, 3, 3],\n [-1, -4, -4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -2, -1, -4, -5],\n [1, -6, 3, -6, 3],\n [-2, 5, -4, 1, -2],\n [3, 5, -4, 0, 5],\n [-6, -6, 5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -2, 1, -4, -4],\n [3, -6, 5, 0, 0],\n [5, -3, 1, -6, 2],\n [2, -3, 4, 5, 5],\n [5, 1, -5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 6, 3, -3, 1],\n [-3, 5, 4, -6, -5],\n [-3, 0, 5, -1, -3],\n [3, 4, 1, 0, -3],\n [-4, 0, -2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 3, -5, 1, 0],\n [-3, 1, 3, 0, 6],\n [-4, 2, -3, -5, -5],\n [-6, 3, 4, 3, 0],\n [-2, 2, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 0, 4, -2, 2],\n [4, 2, -6, -5, -5],\n [-3, 3, 1, 2, 2],\n [-6, 1, -5, -5, 2],\n [1, 2, 5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -3, 3, 3, 6],\n [-1, 2, 3, 5, 6],\n [0, -3, 0, -5, -4],\n [1, 2, 6, -5, -1],\n [-4, 3, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 2, 3, -4, 4],\n [4, -6, -5, -3, -5],\n [-4, -5, -5, 3, -3],\n [5, -2, -6, -5, 5],\n [5, 5, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, 6, -2, 0],\n [-5, -5, -6, -1, -5],\n [1, -1, -2, 1, -3],\n [2, 4, -1, -5, 0],\n [-2, 6, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, -3, 6, -5],\n [-6, 3, 1, -1, 3],\n [5, 1, -2, 3, -2],\n [2, 2, 2, 5, -4],\n [0, 6, -3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -6, 6, 3, 4],\n [5, -1, 6, -6, 4],\n [3, -1, -6, -4, 3],\n [3, -2, -4, -5, -3],\n [2, 6, -6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -5, 3, 0, -1],\n [-2, -6, 6, 1, -2],\n [3, -1, 3, -1, 5],\n [-5, -3, -2, 0, -4],\n [-4, 4, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -6, 2, -1, 2],\n [1, -5, 0, -6, 1],\n [0, 6, 0, 6, 2],\n [6, 3, 2, 1, -1],\n [4, -6, 3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -3, -4, 3, 3],\n [-5, -6, 1, -2, -6],\n [6, 3, 4, 5, -2],\n [2, 5, -4, -5, 5],\n [2, -2, -3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 2, 3, -2, 1],\n [3, 3, -5, -6, -5],\n [4, 3, 5, -3, 1],\n [-3, -4, -5, -5, -1],\n [-2, 0, -1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -5, -1, 1, -3],\n [-4, -1, 3, -3, 5],\n [-4, 2, -6, 5, 5],\n [-5, 1, 4, 1, -1],\n [0, -4, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 5, -3, 0, 2],\n [-1, -4, -1, -3, -3],\n [-4, -1, 6, 5, 4],\n [-1, -2, 4, 2, 0],\n [-5, -5, 1, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 2, -4, 0, 4],\n [-5, -6, -2, 3, 0],\n [-5, -1, 3, 3, 1],\n [6, 6, -2, -2, -1],\n [-4, -3, -6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -6, 2, -5, 6],\n [4, 6, -6, 0, 5],\n [-6, 3, -2, -1, 3],\n [0, -5, -6, 3, -4],\n [-3, -1, -2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -4, -5, -2, 0],\n [3, -3, -4, -4, -3],\n [3, -2, 6, 1, 1],\n [-1, -3, -2, 1, 5],\n [5, -6, -5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -5, 6, 5, 5],\n [3, 0, 1, -6, -4],\n [3, 5, -4, 0, -1],\n [-6, -3, -6, 1, 2],\n [-5, 5, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 3, 3, 5, -1],\n [-1, -2, 0, -6, 6],\n [5, 0, 4, -4, 1],\n [2, -6, -3, 5, 5],\n [0, -4, 5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -4, -1, 6, -4],\n [-5, -4, -1, 3, 1],\n [0, 0, -2, 6, -1],\n [-4, -1, -6, 3, 1],\n [0, -4, -6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -6, 0, -6, -3],\n [-6, 4, 0, 2, 4],\n [-5, -6, 5, 6, 5],\n [-5, -3, -1, -6, -6],\n [4, 2, 1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -5, -5, 3, -2],\n [6, 1, 2, 6, -5],\n [0, -2, 4, 1, 3],\n [6, 0, -5, 1, -2],\n [-1, -1, 6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 0, 6, -2, -4],\n [-5, -1, 0, -6, -1],\n [-3, -3, 6, 2, -3],\n [-6, -1, -6, 0, 6],\n [-2, -3, -3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 1, 2, -6, -3],\n [-2, -6, 6, 5, -2],\n [-6, 5, 1, -6, 6],\n [0, -5, 6, -2, -1],\n [0, 3, 0, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 1, 5, -3, 6],\n [0, -4, 0, 1, 4],\n [4, -5, -3, 0, 0],\n [-6, -3, -4, 4, -4],\n [1, -4, -6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -3, 0, 0, 1],\n [0, 4, -3, -1, 2],\n [-6, 1, 5, -5, -6],\n [-6, -1, -2, 1, -5],\n [4, -5, 5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -5, -5, -2, 5],\n [-5, 2, 1, -2, 4],\n [-6, 4, -6, 0, -3],\n [0, -1, 0, 1, -6],\n [-2, 6, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -5, 5, -2, 3],\n [-6, -4, 0, -6, -4],\n [3, -4, -2, 1, 6],\n [0, 3, 0, 2, -2],\n [-1, 6, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, 1, 3, 2],\n [2, -4, -5, -6, 6],\n [3, 5, -1, 6, 2],\n [2, 6, -3, -2, 0],\n [-4, 1, 1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -2, 6, -6, 6],\n [-5, -6, 6, -2, 6],\n [-6, -6, -3, 1, 6],\n [-1, -4, 1, 6, 2],\n [-5, 2, 4, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 0, 4, -4, 2],\n [2, -1, 0, -1, 6],\n [-2, -4, 3, 5, 0],\n [6, -3, -3, -2, -1],\n [-2, 2, -5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -2, -5, 4, 1],\n [6, -2, -2, 3, -2],\n [-2, 6, -2, 5, -3],\n [3, -6, -2, -5, 6],\n [-4, 1, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -1, 3, -4, 4],\n [4, -1, -1, -6, -3],\n [5, 3, 1, 3, 5],\n [-2, -2, 5, 3, -4],\n [-4, 3, 1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -6, -3, 4, 3],\n [2, -3, 5, -4, 4],\n [-6, 4, 4, 6, -1],\n [-5, 1, 0, -3, -5],\n [5, 3, -3, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -1, 4, -5, -3],\n [-2, -6, 6, -2, -4],\n [-2, 0, -4, 5, -6],\n [5, -2, -1, 6, 4],\n [-2, -6, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 0, -4, 3, 6],\n [0, -6, -5, -4, -3],\n [5, -2, 4, 1, 1],\n [0, -2, 3, 5, 3],\n [-4, 0, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, -5, -2, -5],\n [-3, 4, 6, -2, 2],\n [0, 3, 2, -4, -3],\n [0, -4, 5, 2, 5],\n [-6, -4, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -4, -3, 5, 3],\n [-4, 5, 1, -1, 0],\n [3, 6, 3, -2, 1],\n [2, -3, -6, -2, -3],\n [3, -4, -6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -1, -2, 5, -6],\n [3, 3, -6, 5, 0],\n [4, -2, 4, -4, -1],\n [-2, -6, 0, -2, 6],\n [-5, -2, -4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -5, -6, -1, -6],\n [-5, 3, 1, 3, 1],\n [6, -3, -4, -4, -3],\n [-1, 6, -4, -2, -3],\n [-3, 2, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, 5, -5, 3],\n [-6, 0, -3, 4, -1],\n [-5, 2, 1, 5, 2],\n [-2, 5, 0, 3, 2],\n [-2, 0, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -3, -5, -4, -4],\n [-1, 4, -3, -6, 4],\n [-4, -3, -5, 4, -4],\n [-5, -2, 2, -2, -4],\n [-4, 2, 2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 6, -2, 2, -4],\n [-4, -2, -6, 0, -3],\n [5, -1, 0, -1, -5],\n [0, -6, -4, 3, 6],\n [4, 3, 4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 6, 0, -5, 3],\n [-1, -2, 5, -5, 0],\n [-4, -2, -2, 6, 2],\n [2, -5, -5, 2, -3],\n [-2, -1, 1, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -6, -6, 5, 2],\n [2, 2, 4, 1, 4],\n [6, 2, 2, -1, -4],\n [5, -6, -3, 4, 2],\n [-3, -1, 0, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -1, -3, 2, 6],\n [-6, 1, 0, -3, 5],\n [5, 1, -6, -6, -3],\n [0, -2, 5, 4, 0],\n [3, 1, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -6, -4, 5, -6],\n [5, -6, 4, 5, 5],\n [6, -6, -3, -1, 0],\n [-1, 6, 6, -2, -6],\n [0, 5, 4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, -2, -3, 3],\n [-1, -4, 5, 1, 3],\n [6, -5, -1, -1, -3],\n [-3, 2, 1, -4, 6],\n [-3, -3, -5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, 1, 5, -6],\n [1, 5, 2, 6, -4],\n [-6, -6, 0, -5, -1],\n [2, 2, -6, 2, 0],\n [-5, -1, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -6, -1, -4, -5],\n [0, 3, -2, 0, 1],\n [2, 2, -2, -1, 0],\n [6, 6, 5, 6, 6],\n [-2, -1, 5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -2, 6, -3, -2],\n [1, 4, -2, 5, 2],\n [-3, 1, -6, -6, 0],\n [5, -1, -5, -6, -2],\n [2, 4, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 2, 4, -2, 2],\n [-3, 0, 0, 2, 0],\n [5, -3, 6, -1, -2],\n [2, -1, -5, -4, 4],\n [-5, -6, -3, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 1, 6, -3, 3],\n [-2, -6, 6, 2, -5],\n [-3, 2, -5, 5, 3],\n [-2, 5, 4, 0, 4],\n [-5, -3, 4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -5, 2, -6, -2],\n [5, 3, 1, 5, -4],\n [1, -3, 0, -2, 2],\n [3, -3, -2, -4, -2],\n [-2, 2, 2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 4, 5, 4, 2],\n [-5, 5, 3, 2, -2],\n [2, -1, 6, -2, -5],\n [-3, -4, -3, -1, -6],\n [-2, -2, -5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -4, -1, -5, -2],\n [-5, -3, -3, 6, -2],\n [-3, 6, -4, 4, 5],\n [3, 3, -4, 1, 0],\n [-1, 4, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 1, 6, 3, -1],\n [-2, -4, -3, 2, -6],\n [1, 0, -6, 0, 4],\n [-1, 4, -4, -3, -5],\n [-1, -6, -4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 0, 4, -1, 1],\n [1, -2, 3, -2, -4],\n [-3, 4, -3, -3, 6],\n [-5, -2, 6, -5, -1],\n [-4, -3, -4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -4, 1, 1, 2],\n [2, 6, -5, -6, 6],\n [6, -2, 3, -4, -1],\n [5, 2, -6, -4, 4],\n [6, -2, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -5, -1, -6, 5],\n [-5, 3, 5, -6, -3],\n [-5, 4, -3, 3, -1],\n [0, -6, -2, 3, -5],\n [4, 4, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, 1, -5, 6],\n [-1, 4, -4, -1, -2],\n [-3, 6, 0, 3, -4],\n [-4, 5, -5, 1, -3],\n [-5, -3, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 5, 2, 1, 2],\n [0, 1, 2, -4, 0],\n [5, 1, -1, -4, 0],\n [4, -2, -5, 4, -3],\n [-4, 2, -2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -6, -4, -6, -6],\n [4, -5, -3, -3, -1],\n [-4, 2, -6, -2, -2],\n [3, 2, 6, 6, -1],\n [3, -1, -6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 6, -3, 4, 4],\n [3, 5, 4, 0, -2],\n [1, 2, 0, -3, -5],\n [5, 0, 4, 5, 3],\n [-1, 5, 5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 1, 4, -3, -5],\n [2, 4, -6, 6, 2],\n [-6, 0, -6, 4, 1],\n [-4, -3, -2, 0, 1],\n [5, -5, 6, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -5, -5, -1, 4],\n [2, 0, 4, 3, -2],\n [-3, -2, 0, -5, 2],\n [0, 3, 3, -6, 1],\n [-5, 4, -5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, -1, 6, -3],\n [4, 2, -6, -5, 4],\n [5, 1, 6, -6, -6],\n [3, 2, 1, 5, -6],\n [-2, 6, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 1, -5, 0, 6],\n [-5, 0, 4, 6, 2],\n [-1, 0, 5, 5, 0],\n [3, 1, -3, 4, 1],\n [3, -1, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -3, -4, 2, 3],\n [-6, 1, 5, 3, -2],\n [0, 3, -4, 5, 6],\n [6, 4, 5, -5, 4],\n [-3, -3, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 5, -3, -2, 5],\n [1, -5, 1, 6, 6],\n [-4, 1, -5, -3, -3],\n [-1, -6, 5, 1, -3],\n [2, -3, 1, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 4, -4, 4, 2],\n [2, 2, 3, 1, 6],\n [5, -4, 1, -5, -3],\n [-1, 3, -3, -6, 3],\n [6, 2, 3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, -1, -2, -2],\n [0, 6, -4, -6, 1],\n [2, -5, 5, -3, 2],\n [-5, 1, 0, 2, 4],\n [3, 6, -6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -5, -5, -6, -6],\n [-6, -2, -5, -2, -2],\n [2, -1, -2, -6, 1],\n [-3, -4, 5, -3, -6],\n [1, 1, 4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 0, 3, 6, -5],\n [2, -4, 1, 0, 3],\n [4, 1, 2, -3, 4],\n [-2, -4, -6, -3, -3],\n [-3, 6, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -3, -5, 1, 5],\n [5, 1, -1, -1, 0],\n [0, 6, 6, -4, -1],\n [2, -6, -3, 2, -3],\n [-3, -3, -4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -1, 1, -6, 3],\n [-6, 5, -2, 2, 1],\n [4, -1, 3, 0, 3],\n [5, -3, -6, 0, 0],\n [5, 3, -1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -5, 6, -3, -6],\n [-2, -5, 3, 0, 4],\n [6, 5, -4, -1, 2],\n [4, -3, 0, 2, -6],\n [2, 6, -2, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -1, 2, -3, 2],\n [-4, -6, -2, 0, -3],\n [6, 1, -5, 3, -4],\n [-2, -6, 6, 6, 4],\n [5, 5, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -5, -1, -3, 3],\n [6, 2, -5, -4, 6],\n [-2, 2, 5, -6, 3],\n [0, 6, -5, 3, 2],\n [-5, -3, 1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, -4, 0, -5],\n [-2, 2, -6, -5, -4],\n [-3, 4, 6, 0, -1],\n [-5, -5, -4, -2, -1],\n [6, 1, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -1, 5, -4, 1],\n [2, 4, 5, -3, 3],\n [-3, 5, -6, 5, 6],\n [0, 3, -6, -6, 0],\n [2, -6, 6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, 4, 0, -2],\n [4, 2, -2, 6, -5],\n [-4, 4, 1, -2, 4],\n [0, -1, 4, 2, 5],\n [2, 2, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -2, -6, -1, -4],\n [0, -1, -5, -1, -1],\n [2, 1, -6, 0, -1],\n [-2, 6, 1, -2, -2],\n [1, 5, 1, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -3, 4, 3, 4],\n [2, -5, -5, -4, 2],\n [6, 4, 4, 2, 4],\n [-2, -4, 2, 2, 2],\n [0, 1, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 3, 3, 4, -5],\n [2, -1, 5, -2, -5],\n [-5, -1, 0, 4, -2],\n [-5, 1, 4, -1, 4],\n [-5, -6, -2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 5, 4, 4, 3],\n [-4, 1, -2, 3, 1],\n [0, -4, 6, 0, 3],\n [-6, -5, -1, 0, 2],\n [-3, -3, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, -5, -5, -5],\n [-1, 4, 1, 6, 3],\n [-4, 2, 4, -6, -1],\n [2, -5, 5, -1, -1],\n [-5, -2, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, -6, 3, 0],\n [4, 4, 2, -5, -6],\n [-4, -6, -1, -5, -4],\n [1, 1, -4, 1, -6],\n [1, -3, -6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 4, -1, -5, 4],\n [5, -2, 5, -6, -5],\n [1, -1, -3, -1, 1],\n [3, -6, -5, 5, 4],\n [3, -4, 6, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -6, -1, 4, 6],\n [4, 2, 1, -4, -4],\n [3, 3, 4, -6, 4],\n [2, -1, -5, -4, 5],\n [-2, 1, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 4, 3, 4, -3],\n [2, -6, -3, 5, 6],\n [-4, -6, -4, -1, 4],\n [-1, 1, 2, 4, 1],\n [-3, 1, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -2, -5, -4, 5],\n [2, 3, 3, 1, 4],\n [-3, 1, 2, 6, 3],\n [-1, 5, 5, 0, -4],\n [-1, -2, -4, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 6, 4, 6, -5],\n [-4, -6, -6, 2, 5],\n [4, -6, -2, -5, -1],\n [-5, 3, 1, 5, 0],\n [5, 1, 5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -4, -1, 6, 2],\n [3, 5, -2, -5, -6],\n [0, -6, -2, 3, 3],\n [-2, 2, 2, -2, 4],\n [-2, 0, -6, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 4, -4, -6, 2],\n [-1, 2, -5, -2, -5],\n [1, -4, -3, 6, 6],\n [3, 3, 0, -6, 5],\n [0, 2, -6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -1, -6, -2, -4],\n [0, -5, 5, 1, -1],\n [3, 5, -1, 1, 2],\n [3, 0, -4, 4, -2],\n [4, 0, -1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -4, 6, 5, 5],\n [4, 6, 1, -2, 3],\n [0, 5, -4, 4, 0],\n [6, 0, 6, 1, 6],\n [4, 1, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, -4, -3, -1],\n [-5, 4, -6, 4, 5],\n [0, -2, 1, 0, 3],\n [0, 1, 2, -5, -3],\n [4, 6, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -5, -1, 4, 6],\n [-6, -5, 4, -4, 5],\n [-5, -5, 5, -4, 4],\n [-6, -5, 4, 0, -4],\n [0, 6, -2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 3, -4, 6, -1],\n [-6, 0, 0, -5, 4],\n [0, -3, -6, 4, -1],\n [-6, 2, -5, 3, 0],\n [-5, -2, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, 1, 5, 6],\n [-6, 2, 6, -5, -5],\n [-6, 1, -6, -5, -4],\n [2, -1, 5, 0, 3],\n [-1, 0, 3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 6, 3, -2, 6],\n [-4, -4, 3, 2, -2],\n [2, -4, 5, -6, 6],\n [4, 3, 0, -3, -6],\n [-5, 4, -1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -5, -2, -1, -2],\n [-6, -4, -3, -3, 2],\n [5, 5, 5, 6, 4],\n [6, -4, -2, -5, 0],\n [-6, -4, -6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -1, -5, 6, 3],\n [6, 5, -4, 1, 1],\n [-2, -1, -6, 2, 2],\n [-2, 4, 3, -4, -1],\n [2, 5, -6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 3, 6, -3, 6],\n [6, -1, -5, -3, 5],\n [3, 4, -5, 0, -6],\n [0, 1, 6, -1, 1],\n [1, 0, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 5, -2, 4, -2],\n [-5, 3, -2, 5, -5],\n [-1, -2, 6, -4, -3],\n [-2, 0, -4, -5, -5],\n [6, -3, -4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 4, -1, 3, 4],\n [-5, 3, 3, 4, -6],\n [2, 4, -5, -5, 2],\n [2, 3, 2, -5, -4],\n [4, -4, -1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -1, 0, 3, 2],\n [-1, -5, 3, -1, -3],\n [-4, 2, -6, 2, 0],\n [-5, 6, 6, -1, -4],\n [-5, -3, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 5, -3, -4, -1],\n [6, 1, -6, 1, -4],\n [0, -1, -4, -6, 6],\n [-4, 5, 0, 2, 2],\n [-1, 6, -6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -5, 1, 0, 1],\n [-2, -5, -4, -1, 3],\n [-1, 2, -5, -5, -1],\n [3, 4, -1, 5, 6],\n [5, 0, 6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 5, 5, -1, 3],\n [0, -1, -2, 0, 6],\n [-2, 5, 2, -6, -2],\n [-1, -4, -1, 3, -2],\n [-6, -3, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -5, -5, 4, 2],\n [0, 4, 1, -4, 0],\n [1, -3, -4, -1, 1],\n [-5, 3, 5, 6, 0],\n [0, 4, 2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -2, 2, -5, 0],\n [-2, -1, -6, 4, 4],\n [1, 6, 5, -5, -1],\n [-3, -5, 5, -5, -2],\n [0, 1, 6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 0, 5, -1, -1],\n [-1, 1, 4, -2, 2],\n [3, 6, -4, -5, 4],\n [-2, 4, 6, 4, -1],\n [3, 2, -1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -3, 6, 5, 5],\n [6, -6, 1, 6, 4],\n [1, 2, 3, 4, 2],\n [-6, 5, -4, 3, -5],\n [-5, -2, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 0, -3, -4, 0],\n [6, 6, 0, -4, 4],\n [-3, -1, -1, 2, 5],\n [2, 4, 2, -1, 5],\n [1, 1, 5, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, -3, -2, -1],\n [5, 4, 0, 5, 1],\n [3, -4, 1, -2, 4],\n [-4, 6, -2, 4, 4],\n [1, 2, 3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 6, -4, 5, -1],\n [-1, 5, -5, -6, 4],\n [-4, 3, -2, 5, 1],\n [6, -2, -3, 2, 3],\n [-6, -1, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, -1, 0, 6],\n [3, 2, -6, 1, 5],\n [2, -2, 2, -5, 6],\n [0, 2, 4, 1, -6],\n [1, 1, -6, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 2, 2, -4, 4],\n [4, -6, -3, -6, -4],\n [0, -6, 6, 3, 4],\n [3, 3, -2, -4, 3],\n [1, 5, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -6, 1, 3, 5],\n [-6, 4, -2, 1, 0],\n [-6, -4, 3, -4, -5],\n [5, 0, -6, 1, -4],\n [1, -2, 6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 6, 2, 5, 3],\n [4, -1, 4, -2, -1],\n [4, -5, 1, -6, -3],\n [1, 1, 2, -3, 6],\n [-2, 2, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 6, 2, -1],\n [-6, -2, -6, -1, 3],\n [2, 5, -4, -5, 3],\n [1, -3, -4, 4, -4],\n [-5, 2, 0, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 1, 4, -4, -3],\n [4, 4, -6, 6, -1],\n [-5, 5, 2, -1, 4],\n [6, 2, -2, 2, -2],\n [4, 4, -1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, -4, 1, -1],\n [6, 0, -5, 4, -3],\n [-1, 1, -5, 1, 3],\n [6, 1, 3, 0, -1],\n [-5, 0, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 4, 2, -3, 1],\n [4, 3, 4, 2, 1],\n [-5, 4, 6, 0, -6],\n [4, 4, -3, 1, 3],\n [-3, -3, 6, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 4, 4, 6, 5],\n [-5, -3, 0, 0, 6],\n [1, -2, -2, 6, -3],\n [-1, -1, -4, -2, 3],\n [-6, -6, -6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 1, 6, 0, 5],\n [-2, -3, 0, 6, -1],\n [-4, 4, 2, -6, -5],\n [0, 5, -2, -3, 4],\n [-6, 3, -3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -5, -2, 0, -5],\n [0, 3, 2, -3, -4],\n [1, -3, 3, 6, 6],\n [-1, -3, -1, -2, -6],\n [5, -3, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -4, 6, -3, -5],\n [0, 5, 6, 1, -1],\n [-4, -1, 4, -1, 5],\n [3, 4, 5, 1, -2],\n [2, -2, 3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -3, -5, -5, -2],\n [-3, -4, -6, 0, -6],\n [-2, -6, -1, 0, 0],\n [2, 1, 4, 1, 6],\n [3, 5, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -4, -6, 0, -5],\n [-4, 3, -3, 3, -6],\n [1, -1, -2, 6, 1],\n [4, -2, 6, -5, -6],\n [-1, 5, -6, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 2, -4, 3, 6],\n [6, -3, -5, -5, -4],\n [2, 6, 5, -1, 5],\n [2, 1, -2, -4, 6],\n [-6, -3, -5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, 5, -2, -6],\n [-3, 6, -4, -5, -1],\n [5, -6, -2, 6, 0],\n [-1, 5, 6, 3, 1],\n [5, 5, -6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -2, -2, 1, -4],\n [3, 3, 0, -4, -5],\n [-6, 6, 1, 5, -1],\n [0, -5, -1, -3, 2],\n [-2, 0, -5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -2, -6, 3, -2],\n [0, 4, -3, -6, -6],\n [1, 4, 2, 6, -5],\n [5, -5, 1, -6, 4],\n [3, -2, 3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, -4, -6, 4],\n [1, -4, -5, -3, -3],\n [-5, 6, 2, -3, 2],\n [1, -6, -6, 1, 2],\n [-2, -1, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 0, 4, 1, -5],\n [3, 2, 5, -6, -2],\n [-4, -5, 5, 3, 5],\n [4, -2, 6, 1, 5],\n [4, 1, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 2, -1, -4, 4],\n [1, 3, 2, 3, 5],\n [6, -5, -3, -5, 2],\n [4, -2, 1, 0, -2],\n [5, 4, 3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -1, -4, -3, -3],\n [-4, -2, 2, -1, 1],\n [4, -2, 0, 3, 1],\n [-5, 3, 3, 0, 2],\n [5, -4, -2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, 0, -1, 1],\n [3, -3, 4, 3, -5],\n [3, 2, -2, -3, 2],\n [0, 3, 3, 4, 4],\n [-1, 6, 2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -1, -6, -3, -2],\n [5, -4, -2, -1, 3],\n [2, -2, 1, 5, 2],\n [-2, -4, -6, 2, 0],\n [5, -6, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 1, 5, 5, 5],\n [0, 3, 2, 3, 2],\n [2, 4, 2, 4, 0],\n [-6, 5, -6, 6, 5],\n [5, 5, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -5, 2, -2, -1],\n [1, 6, 1, -6, -5],\n [-3, 1, 3, 0, 3],\n [2, 1, -2, -6, 5],\n [-1, 6, 3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -4, 5, 1, 0],\n [-2, -1, -6, 6, -4],\n [0, 4, 0, 2, 5],\n [5, -6, -5, -5, 4],\n [-2, 5, -5, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 0, -6, -2, 1],\n [-5, 4, -6, 5, 3],\n [-1, 2, 6, -4, 1],\n [5, 1, 0, 6, 3],\n [-1, -3, -5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, -6, 1, 4],\n [6, -1, -3, 1, 3],\n [2, 1, 6, 3, -5],\n [5, 5, 4, 2, -5],\n [4, -2, 2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -4, 1, 4, -4],\n [-2, -2, -1, -6, 3],\n [5, 5, -6, -1, -4],\n [3, 5, -1, 3, -2],\n [4, -3, -2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 3, -3, 1, 2],\n [5, 5, 3, 1, -4],\n [-3, -6, -1, -6, 1],\n [6, 3, -3, -6, -1],\n [-4, -4, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -6, 6, -3, 0],\n [0, 0, 0, -6, -1],\n [-5, -6, 5, -4, 0],\n [-1, -3, -6, -4, -5],\n [-6, 4, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -6, -1, 5, 2],\n [2, -6, -5, -3, -2],\n [-4, 2, -4, 6, -6],\n [5, -6, 0, 3, -6],\n [-1, 0, -3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 5, 5, 1, 6],\n [1, 6, -6, -6, -3],\n [2, 5, 4, 6, -4],\n [-5, 5, -5, 2, 3],\n [0, -6, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 0, 1, 5, -5],\n [0, -6, -2, -5, -3],\n [6, -6, -6, -5, -1],\n [2, -5, 4, 4, -5],\n [6, -5, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -2, 3, 3, 5],\n [2, 2, -3, 5, -2],\n [1, 5, 4, 1, -4],\n [-3, -4, -6, -2, 4],\n [5, -4, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -6, 6, -4, 4],\n [6, 4, -6, 0, 0],\n [5, -6, -4, -1, -5],\n [5, 6, 3, -1, -4],\n [5, -2, 1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, -3, 4, -2],\n [2, 4, 5, -2, 4],\n [1, 6, -3, 6, 5],\n [5, 5, -1, 2, -6],\n [-3, 6, -2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -1, 1, 4, 0],\n [-2, -3, 6, 3, -3],\n [-4, 6, 6, 3, -3],\n [2, 4, -1, -2, 4],\n [6, 2, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -2, 1, 0, -1],\n [1, 5, 6, 5, 4],\n [-3, -5, 0, 3, 4],\n [3, -3, 6, 1, -5],\n [-4, -5, 6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -3, 0, 5, -5],\n [-4, -6, -5, -1, 2],\n [1, 6, 0, -1, -3],\n [6, 5, 3, -2, 3],\n [3, -4, 4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 4, -5, -2, 5],\n [2, 3, 2, -5, 5],\n [-6, 4, 0, -3, 2],\n [1, -2, -2, -4, -4],\n [0, 6, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -5, -2, -2, 0],\n [-6, 6, -4, 6, 2],\n [-1, 5, 5, -6, 5],\n [3, 0, -1, 4, -1],\n [5, 6, -6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 4, -2, -5, -2],\n [4, 6, 4, 2, -1],\n [3, 2, -5, 3, 2],\n [-5, 6, 3, 6, -5],\n [-3, 2, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 6, 1, -1, 6],\n [0, 1, -2, -3, -5],\n [3, -1, -4, 6, -2],\n [-4, 2, 4, 1, 1],\n [2, 4, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 2, 3, 1, 1],\n [-2, -4, -4, -1, 5],\n [6, -4, -4, 6, 3],\n [-6, 2, -2, 3, 0],\n [-3, 4, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -4, 5, -3, -1],\n [-1, -3, -5, -3, 6],\n [-2, 2, -2, 0, 1],\n [2, -3, 5, 6, 1],\n [-6, 3, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 1, 3, -2, -5],\n [4, 0, 4, 2, -4],\n [0, 4, 0, -3, 1],\n [-1, 0, -1, -2, -1],\n [-1, -3, 1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -3, 2, -4, 1],\n [1, 2, -1, -6, -6],\n [-2, 4, -2, 6, -4],\n [0, -1, 5, -4, -6],\n [-6, -2, 1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -4, -6, -6, 6],\n [-4, 0, 1, 5, -5],\n [1, 4, -3, 2, -5],\n [-6, -2, -1, 4, 4],\n [4, 4, -6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -1, -5, 2, 1],\n [-2, -4, 3, 2, -3],\n [-4, -4, -2, 0, 4],\n [-6, -3, 0, -6, -3],\n [3, 5, -4, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 6, 2, 3, -4],\n [-5, 6, 2, -1, -6],\n [1, 1, -3, -1, -6],\n [-3, 1, 4, -3, -5],\n [2, -1, 1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -1, 5, -2, 5],\n [-6, 0, 6, 1, 4],\n [-5, 0, 3, -2, -1],\n [3, -1, -2, 4, 1],\n [0, 3, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 4, 0, -1, 4],\n [0, 5, -5, -6, 2],\n [6, -4, 1, 4, 3],\n [3, 5, -5, 1, 1],\n [6, -2, 3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -2, -6, 3, 1],\n [4, -6, 3, -6, -6],\n [-6, -5, 0, -3, -2],\n [5, 3, 4, 4, 4],\n [5, 2, -5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 4, 5, 3, 0],\n [0, 4, -5, 5, -2],\n [5, -3, 6, 3, 6],\n [-5, -1, 3, -3, -6],\n [-5, 2, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 2, -3, -1, -4],\n [-6, -4, 5, 4, 6],\n [3, -1, 0, 3, 0],\n [-3, -2, -1, 3, -4],\n [-6, -6, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -6, 2, 2, -4],\n [1, -2, 3, 4, 5],\n [-2, -5, -5, 5, 6],\n [3, -2, 2, -4, 5],\n [-1, -3, 3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, -3, -4, 0],\n [-3, -2, -5, 3, -4],\n [-5, -1, -1, 4, 1],\n [-1, 3, 5, 3, 1],\n [0, 5, 6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -6, -1, 3, -5],\n [-4, -6, -1, 0, -1],\n [0, -5, -5, 2, 4],\n [-4, 1, -3, -1, 1],\n [2, -1, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 4, 2, -1],\n [-4, -5, -2, -5, -2],\n [6, -6, 4, -4, -3],\n [0, -3, 5, -6, 0],\n [-3, -2, -1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, 3, 3, -4],\n [-4, -2, 5, 2, -1],\n [-1, 2, -4, -6, -5],\n [4, -5, -3, 2, -2],\n [-4, -5, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -2, -5, 3, 5],\n [-5, -3, -4, 2, -3],\n [4, -5, -1, 4, 0],\n [-5, 5, 6, -3, 5],\n [0, -2, 3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 4, -3, -6, -5],\n [-5, -6, -5, 6, -6],\n [-2, -3, 5, -2, -3],\n [2, -1, -3, 6, -5],\n [6, 4, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, 1, -2, -1],\n [6, -4, -3, 2, 3],\n [6, 2, 0, -6, 6],\n [6, 3, 1, 0, 1],\n [-3, -2, 2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 5, 3, 0, 2],\n [-6, 1, -2, -5, 6],\n [1, -6, -2, 2, -3],\n [-4, 6, 1, 6, 4],\n [0, -3, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 1, 6, -5, 1],\n [-1, -2, -2, 0, 1],\n [-2, -6, -2, -1, 5],\n [-1, 2, 2, 3, -6],\n [-3, 3, -6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -3, 0, 4, 3],\n [3, -3, 4, 4, -6],\n [1, -5, -5, -5, -1],\n [1, -6, 1, 1, -6],\n [-1, -2, 4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -4, 0, 3, -2],\n [4, -2, -5, -5, -4],\n [2, -4, 6, -3, -2],\n [-4, -6, 1, 2, -3],\n [3, 3, -4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -5, 4, 1, 2],\n [-1, 0, -4, -5, -4],\n [-5, 4, -6, -5, 3],\n [0, 0, -5, -1, -4],\n [-3, 3, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, 2, 4, 6],\n [0, 1, 2, -1, 0],\n [4, -6, -1, 2, -6],\n [-5, -6, -1, 2, 6],\n [-1, -3, -6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -3, 0, -6, -3],\n [-1, 2, 3, -3, 4],\n [1, -3, 0, 3, -3],\n [2, -2, -4, -4, -5],\n [-6, -6, -4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 3, -4, 0, 6],\n [6, 1, -5, -1, 3],\n [-4, 2, -2, 4, 3],\n [-1, 0, -4, 5, -2],\n [1, -1, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 6, -4, -2, 1],\n [-6, 5, -4, 4, -2],\n [-5, 6, -6, -5, -6],\n [-1, 4, 4, 5, 4],\n [-4, 4, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -6, 4, 3, 5],\n [-1, -5, -5, 1, 5],\n [-3, 4, 6, 2, 3],\n [-4, 0, -4, -3, -1],\n [-1, 1, -6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -5, 5, 1, 6],\n [-4, -3, -4, -5, 5],\n [-6, 5, -2, 4, 3],\n [-4, 5, -5, -4, 3],\n [4, -4, -1, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, 1, 3, 0],\n [1, 4, -4, -2, 2],\n [3, 6, -1, 4, 1],\n [0, 3, 0, 4, 3],\n [3, 6, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 6, 1, 2, -5],\n [2, -6, -5, 0, 4],\n [-4, -3, 3, 3, 6],\n [-1, 6, 3, 0, 2],\n [4, 1, 4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 1, 6, 0, 4],\n [6, -4, 1, 1, -5],\n [-2, 5, 0, -6, 4],\n [3, 2, 3, 5, 3],\n [3, -4, 3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -4, 4, 2, -4],\n [-4, 3, 4, 1, 1],\n [3, -5, 6, 6, -4],\n [-3, 2, 0, 5, -5],\n [6, 4, 5, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 5, -1, 1, -4],\n [1, 1, 0, 0, 5],\n [-1, -5, 4, 1, -4],\n [0, -5, 0, 5, 1],\n [2, 3, 6, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 1, 6, 3, -3],\n [5, 2, 4, -5, 3],\n [-3, 2, 6, -5, -2],\n [3, 3, 4, 6, 6],\n [-3, 1, 1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 3, -5, -2, 4],\n [-4, -2, 6, -6, -3],\n [6, 5, -5, -5, -1],\n [-1, -3, -2, 1, -1],\n [3, 0, -4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -6, -3, -2, 4],\n [-2, 1, 3, 0, 1],\n [-5, -1, -5, -3, 1],\n [-1, 6, -5, -4, -3],\n [0, 1, -5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 4, 3, 6, 4],\n [1, -2, 6, 2, -4],\n [-1, -1, 2, 6, 6],\n [-5, -2, -1, 6, -2],\n [-2, 3, -3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -2, 0, 5, -1],\n [-3, -5, -3, 1, 0],\n [5, -3, 2, -1, 2],\n [4, 2, -5, 4, 4],\n [-1, 5, 5, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -3, -2, -2, 0],\n [3, -6, 4, -5, 4],\n [-6, 4, 0, 4, -2],\n [5, -2, 2, -1, -5],\n [-5, -6, 3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 5, -4, -5, -5],\n [3, -2, 0, -5, 3],\n [-4, 5, 0, -4, -1],\n [1, 4, -5, 1, 0],\n [2, 6, -5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 2, 4, 6, -6],\n [0, 1, -6, -5, -4],\n [-6, 4, 4, -5, 3],\n [-6, 2, -5, -3, 0],\n [4, -5, 4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -1, 5, -6, 4],\n [6, 2, -6, 3, 5],\n [-6, 2, 6, 6, -1],\n [-4, 5, 6, 1, -6],\n [1, 0, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 4, 0, 6, 2],\n [2, 6, -6, 1, -4],\n [-2, 6, 0, 5, -1],\n [3, -5, -3, 2, -6],\n [-1, -2, 2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 0, 2, -5, 6],\n [-2, -1, 1, -5, -6],\n [2, 0, 3, 6, 6],\n [-6, -2, 6, -6, 4],\n [2, -4, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 0, -3, -1, 5],\n [-6, 5, -4, -4, -2],\n [2, -2, 1, -1, 2],\n [2, -1, 0, 3, 5],\n [2, -4, 1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 4, 1, -1, -5],\n [-2, 1, -1, 1, 6],\n [3, 6, 0, 3, 1],\n [-4, -2, 2, 0, -5],\n [4, -6, -6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -3, -1, -5, -4],\n [-2, 6, -5, -5, 3],\n [-4, -2, -3, -1, 3],\n [0, -6, 1, -3, -6],\n [1, -1, -5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 6, 2, 6, -6],\n [1, 1, 4, 2, 3],\n [4, -1, 2, -4, 1],\n [-4, 3, 2, 5, -3],\n [4, 5, 1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -1, -4, 4, -2],\n [1, 3, -2, 5, -1],\n [-2, 0, 6, -5, -2],\n [-2, 6, -3, -4, 1],\n [-3, -3, -3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 5, -4, -1, -4],\n [-6, 3, 3, 0, -1],\n [3, -1, 4, -1, -2],\n [4, -4, -4, 6, 1],\n [-3, -6, -2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -5, 5, 3, -4],\n [-3, 5, -3, 3, 0],\n [0, -5, 5, 2, 0],\n [-2, -4, -6, -1, 4],\n [-6, -6, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -3, -5, 2, 2],\n [-4, 2, -5, 5, -6],\n [1, 3, -2, -6, -2],\n [1, 0, -4, -4, 4],\n [2, 2, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 0, 2, 3, 2],\n [-2, -1, 5, 1, 5],\n [2, 0, 2, -5, 5],\n [-6, -6, 1, 4, -2],\n [-4, 2, -4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -1, -1, -1, 4],\n [6, -1, 2, -3, -3],\n [4, -5, 3, -1, 4],\n [2, -6, 3, 1, 4],\n [-6, 6, 5, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -5, 5, 1, 2],\n [3, 4, -2, 2, -6],\n [-1, -2, 5, 3, -1],\n [-3, -5, 4, -6, 3],\n [0, 4, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 3, 5, -5, -2],\n [6, -6, 4, 1, 6],\n [4, 5, -4, 6, -3],\n [6, -1, -1, -6, -1],\n [3, -1, -5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 1, 0, 5, -3],\n [-5, 0, 6, 1, 2],\n [6, -2, 0, 1, 5],\n [-1, 3, -1, 5, -3],\n [3, 0, -3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 5, -4, 0, 1],\n [-2, -5, -2, -5, 3],\n [6, 3, 1, -6, -2],\n [-2, 0, 2, 3, 4],\n [3, -1, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -3, 3, -2, 0],\n [6, 2, 3, -3, 6],\n [1, 5, 5, -5, -6],\n [-3, -3, 6, 4, -1],\n [-2, -1, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, 4, -5, 3],\n [3, -5, -5, 1, 1],\n [-4, 2, 5, 2, 0],\n [6, 2, 0, -6, 3],\n [1, -5, -3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -2, 5, -2, 4],\n [3, -5, 3, 5, -3],\n [-3, -6, -1, -1, -4],\n [1, 4, -1, -3, 1],\n [-1, -2, 3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -4, -6, 3, 5],\n [5, -2, -1, 0, -5],\n [2, -6, -5, -5, 1],\n [-3, -6, -2, 1, -1],\n [-5, -6, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -1, 5, -4, 6],\n [-1, 1, -2, 2, 2],\n [-2, -2, 5, 0, 5],\n [2, -2, 6, 2, -5],\n [4, 1, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 5, 4, 6, -3],\n [-6, 4, -3, 5, 4],\n [4, 0, 3, -6, -4],\n [-2, 5, -2, -4, 3],\n [-6, -2, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, 6, -3, 4],\n [-4, 3, 6, 1, 2],\n [-1, -1, 4, 4, -6],\n [-5, -5, -6, -4, -1],\n [3, -5, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, 5, 1, -5],\n [-3, 1, 3, 2, 5],\n [-6, -2, -3, -6, 1],\n [5, 1, 4, 0, 1],\n [1, 4, -4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 0, -4, 1, 4],\n [4, -3, -5, 3, 1],\n [-3, 0, 2, -6, 5],\n [3, 2, -6, -3, -6],\n [-6, -4, 3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 0, -3, -4, -6],\n [-1, -2, -2, -5, -4],\n [0, 5, -3, -6, -1],\n [1, 6, -4, -1, 1],\n [-4, 4, 4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, 6, -1, 3],\n [0, -2, 0, -3, 4],\n [-3, 2, 4, 0, 3],\n [-3, -6, -2, -4, 5],\n [-3, -5, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 4, -5, 4, 3],\n [4, -3, 4, -1, 5],\n [-5, -1, -5, -2, 4],\n [0, 2, -4, 2, -2],\n [-2, 5, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -5, 4, 0, 6],\n [-3, 5, 5, 2, -3],\n [0, -3, 3, -1, 6],\n [-5, -4, -5, -2, -4],\n [6, -5, 4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -2, -5, -3, -3],\n [6, 5, 0, 6, 2],\n [-4, -5, 6, -1, 1],\n [-5, 3, 2, 2, 6],\n [-5, 2, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 6, -4, 0, 4],\n [-4, 1, 5, -5, -6],\n [-4, 3, 4, 2, 4],\n [0, 0, 2, 5, 2],\n [-6, -4, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 3, 6, 1, 0],\n [-6, -4, 1, 0, 1],\n [-2, 6, -3, 6, -6],\n [-1, -2, -3, 5, -3],\n [4, -5, 6, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -3, 5, 0, 0],\n [-6, 6, 5, -1, 3],\n [4, -2, -2, 3, 5],\n [-1, -3, -1, -6, -3],\n [1, -1, -5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -6, -4, -2, 3],\n [0, 4, -1, 0, -4],\n [6, -5, 6, -1, -3],\n [-6, -1, 6, -6, -4],\n [4, -5, -2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, -4, 3, 0],\n [3, -5, 4, 3, 0],\n [0, 1, 1, 4, 1],\n [-2, -4, 1, -4, -3],\n [0, 0, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 6, 0, 5, 4],\n [6, -2, 2, -1, 2],\n [-3, -3, 1, -3, -4],\n [-4, -2, -4, 3, 0],\n [-4, 6, -6, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 2, -1, 6, -5],\n [0, -4, 2, -5, -3],\n [-6, -3, 3, 4, 6],\n [-4, -1, -5, -3, -4],\n [2, -4, 5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 0, -5, -3, -6],\n [4, -4, 2, 2, 3],\n [1, 4, 6, 5, -4],\n [-4, 5, 4, 0, 6],\n [2, 2, 6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 6, 0, -1, 0],\n [-4, -6, 6, -5, -1],\n [5, -5, 6, -6, -1],\n [6, 5, -6, -6, -3],\n [0, 3, -1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -2, 3, 0, 1],\n [-1, -5, -3, -4, -5],\n [3, 2, -2, -2, 4],\n [0, -2, -5, 6, -2],\n [-1, 2, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -5, -2, 6, -4],\n [2, 0, -2, -4, -6],\n [-1, -5, 4, 3, -1],\n [4, 1, 3, -2, 0],\n [5, 3, 5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -6, -6, -4, -1],\n [4, -4, -2, -3, -6],\n [4, 4, 4, -6, -3],\n [-3, 2, -2, -4, 6],\n [-6, 6, -1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 5, -6, 1, 3],\n [-3, -4, 4, -4, 4],\n [0, 5, -1, 4, 2],\n [1, 0, -1, -2, -6],\n [-5, 1, 6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -4, 4, -6, 6],\n [0, 4, -1, 2, 3],\n [2, 3, -4, 6, 3],\n [-3, -5, 6, -3, -6],\n [5, -5, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -6, 5, -4, 5],\n [2, 2, -2, 1, 3],\n [5, 2, 5, -5, 2],\n [-3, 1, 0, -1, 1],\n [2, 6, 1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -6, -3, -1, 4],\n [1, -6, 6, -6, -5],\n [6, -2, 3, 3, 2],\n [-3, -3, -4, 6, -5],\n [0, -3, 0, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 0, -4, 6, 5],\n [-4, 0, 2, -1, 2],\n [3, -1, -6, 0, -3],\n [6, -2, 4, 6, 3],\n [-3, -1, 0, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 4, -3, -2, 6],\n [5, 1, 1, -6, -6],\n [4, -6, -2, 6, -4],\n [-4, -3, 6, 3, 0],\n [-5, 3, -6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, 2, 6, -1],\n [2, -3, -2, 0, -2],\n [0, -2, 3, 5, 2],\n [-4, -6, 5, -3, 3],\n [5, -2, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -5, -3, -2, 3],\n [0, 3, 4, 4, -6],\n [-4, -2, -3, 4, 2],\n [2, 1, -5, -1, 3],\n [3, 6, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 6, -3, -6, -6],\n [0, 4, 5, 3, 6],\n [0, -3, 5, -1, -6],\n [-2, -3, -4, 1, -3],\n [5, 0, 3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 4, 3, 0, 3],\n [5, -3, -5, 3, -6],\n [1, -4, -1, 5, -6],\n [-1, -6, 6, 6, 3],\n [-6, 1, -4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -3, -5, -6, 5],\n [-2, -2, 4, -1, -6],\n [5, 0, -1, -4, 5],\n [-2, -1, -2, 4, -5],\n [-6, -6, -1, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 0, 0, 6, 2],\n [6, 5, -4, -5, 0],\n [-6, -2, 3, -4, 5],\n [1, -1, -5, 0, -5],\n [0, 3, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, 6, 6, 1],\n [2, -2, 6, -4, -2],\n [2, -1, -3, -4, -3],\n [-1, 3, 0, -5, -4],\n [-1, -1, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -5, -3, 2, -4],\n [-3, 6, 6, 0, 3],\n [-2, -5, -4, -6, 0],\n [-1, 2, 3, -4, 2],\n [-1, -1, 5, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 0, 6, -3, -5],\n [-2, -4, 2, -2, -2],\n [-4, -6, 3, 0, -4],\n [2, 3, -6, -5, -3],\n [4, 0, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 4, 4, 3, 0],\n [-4, -6, -3, 4, 2],\n [-2, -1, 6, 4, 1],\n [4, 0, -2, 6, 4],\n [-2, 1, -6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, 0, 0, 6],\n [2, -5, 1, -3, 1],\n [-5, 5, -1, 2, -6],\n [3, 3, -4, -4, 2],\n [3, 0, -6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -5, -2, 3, 3],\n [-5, -1, 1, 6, 5],\n [-5, -4, 5, 3, -6],\n [1, 0, -1, 2, -4],\n [0, -1, 3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -2, -5, -4, -1],\n [1, -3, -3, -3, -4],\n [0, -1, 0, 3, 1],\n [5, -2, 3, -4, 2],\n [-6, 2, -1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 4, -2, 0, 1],\n [-5, 3, -4, 5, -3],\n [1, -6, -6, 6, 2],\n [1, -6, -4, -2, -5],\n [5, 3, 4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -1, 2, 5, -6],\n [-3, -4, -6, -6, 4],\n [-6, 1, -4, 3, -4],\n [-4, 1, -4, -6, -2],\n [6, -3, -2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, -5, -5, -5],\n [4, 2, 2, -2, 0],\n [1, 0, 4, -1, -5],\n [6, -4, 2, -2, 3],\n [-5, -2, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -5, 5, -1, 4],\n [5, 6, 5, -3, -1],\n [-6, -6, 5, 0, 4],\n [5, 1, 6, -3, -6],\n [-2, 2, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 1, -4, -4, -1],\n [-1, 5, 0, -4, -1],\n [-3, 0, 1, 1, -4],\n [-3, 6, -1, 0, -3],\n [2, -3, -5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 5, 0, 5, 2],\n [-2, -1, -3, 2, -1],\n [-5, 4, -2, -6, 3],\n [-4, 2, 4, -6, 5],\n [5, -2, -2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, -6, -1, 2],\n [-1, 0, -1, -5, -5],\n [3, 4, -2, -1, -2],\n [3, 3, 2, -4, 1],\n [-3, -2, 5, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 1, 4, -3, 5],\n [5, 1, -3, 2, 3],\n [-6, 5, -3, 3, -4],\n [0, 2, -6, 0, -5],\n [3, 3, 0, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 1, -6, -6, 4],\n [0, -2, 0, 3, 5],\n [-3, 6, 0, -4, 5],\n [3, -3, 6, 6, -2],\n [4, 4, -1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 4, 3, 1, -2],\n [1, -6, -5, -2, 5],\n [4, 5, -2, 0, -3],\n [0, -2, -1, 5, -5],\n [3, -4, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -3, 3, 4, -1],\n [2, -3, -2, -3, -3],\n [6, -3, -2, -3, -2],\n [4, 5, 4, 1, -2],\n [3, 1, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -4, 1, 1, -6],\n [2, 4, 3, -2, 0],\n [3, 4, -6, -6, -4],\n [0, 5, -2, 5, 2],\n [-2, 2, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -1, 0, 2, 0],\n [-2, 2, 5, 5, 1],\n [0, -6, 2, 3, -3],\n [3, -6, -2, 1, -6],\n [-5, -1, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 3, -2, -5, 6],\n [-5, -6, -2, -1, -3],\n [0, -2, 0, -6, 0],\n [6, 1, 3, 1, -4],\n [-3, -5, 4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -6, -6, 1, 3],\n [3, -3, -6, -1, -4],\n [-1, -3, -5, -1, -1],\n [-5, -6, 3, -4, -2],\n [-1, 3, -1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -4, -6, 5, -4],\n [2, 6, 2, 6, 4],\n [-1, 4, 1, 3, 6],\n [-4, -5, 3, -5, -5],\n [6, 6, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 4, -4, -2, 0],\n [4, 6, 3, -3, 1],\n [3, 2, 4, 3, -3],\n [3, 0, -6, 6, -1],\n [2, 4, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, -2, -1, 5],\n [-4, -2, -4, 2, 4],\n [1, 0, 4, 5, -6],\n [3, 1, 0, -6, 4],\n [-4, 1, -1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 1, 6, -3, -5],\n [4, -3, 3, -1, -2],\n [1, -2, -2, -4, -2],\n [-3, -1, -3, 5, -1],\n [4, 6, 1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -3, 3, 3, 0],\n [-6, -4, 5, 5, 2],\n [4, -6, 3, -2, -4],\n [0, 4, -3, -6, -3],\n [-4, 2, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -6, 0, -2, 6],\n [1, -6, 4, -6, 1],\n [0, -4, 4, 6, 0],\n [2, 2, 0, 0, -2],\n [6, 4, 5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -2, -6, 6, 1],\n [2, -5, -6, -2, -2],\n [3, 4, 2, -1, -1],\n [-6, -6, 4, -5, -5],\n [-1, 0, -1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 6, 3, 3, -1],\n [-5, 5, -5, -2, 3],\n [-4, 4, 1, 2, -1],\n [6, 5, -6, -4, -3],\n [6, 2, 5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 5, 3, 4, 4],\n [4, 5, -4, -5, -3],\n [6, -3, -6, 1, -4],\n [5, -2, -5, -4, 5],\n [0, 3, -5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -6, 2, 2, -3],\n [2, -1, -2, -5, 6],\n [-3, 1, -6, -6, -1],\n [-6, 5, -2, 0, -1],\n [-1, 5, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 2, 1, 2, 0],\n [-2, 5, -6, -1, -1],\n [5, -2, -2, -5, 0],\n [4, 6, 1, -5, -2],\n [2, 6, -3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 1, 5, -5, 2],\n [0, 0, 6, -3, -1],\n [5, -1, 2, -4, 5],\n [0, 0, -6, 2, -2],\n [4, -3, -3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -1, -4, 3, 1],\n [3, -6, 0, -3, -2],\n [1, 6, 0, 2, 1],\n [2, -6, 2, 0, 0],\n [4, 6, 2, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -5, -6, -6, -5],\n [3, 6, 4, -4, 2],\n [5, 1, -3, 1, -1],\n [-4, 2, -6, 3, 4],\n [0, 2, 5, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 1, -4, 1, 3],\n [2, -1, -6, -3, -2],\n [0, 1, -5, 5, -1],\n [-1, -2, 6, -2, -1],\n [-6, 0, -6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 3, 0, 5, -1],\n [4, -3, -5, -1, -2],\n [0, 3, 1, -3, -6],\n [4, 6, -4, -2, -2],\n [1, -3, 5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, -2, 2, 1],\n [-6, 0, -2, 2, -1],\n [0, -5, -1, 1, -6],\n [-3, -6, 6, -3, -2],\n [2, 3, -6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, 2, 6, 1],\n [-2, -4, 6, 1, 6],\n [-4, -6, -4, 0, 2],\n [5, 4, 5, -6, -6],\n [6, -2, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 3, 1, 1, -6],\n [0, 5, -4, 4, 5],\n [5, -6, 6, -6, 6],\n [-4, 6, 2, -4, -4],\n [2, 2, -1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, -1, 1, -3],\n [4, 4, 5, -6, 3],\n [0, 4, -3, -5, 6],\n [2, 0, -3, 3, -4],\n [5, -5, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 3, -5, -5, 6],\n [-4, -2, -1, -1, 5],\n [1, 2, -1, 0, -4],\n [3, -1, -1, 5, 6],\n [4, 0, -5, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 0, 3, 4, 2],\n [-1, 3, 6, 1, -4],\n [1, -6, 3, 3, 5],\n [3, -4, -1, -5, -6],\n [-3, 3, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 2, 2, -1, -2],\n [-4, 1, -3, 3, -6],\n [6, 5, 3, 3, 1],\n [-5, 3, -3, 1, -5],\n [-2, -1, -5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -4, 4, 1, 4],\n [4, -2, -1, 6, -2],\n [-1, 2, 5, 6, -4],\n [0, 5, 5, -4, 6],\n [-6, 5, -6, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, -1, -1, -4],\n [0, -4, 6, 6, 3],\n [-1, -1, 3, -2, 1],\n [5, -2, 2, -6, 0],\n [6, 0, 1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 2, -3, -4, 3],\n [-6, -6, 2, 0, 3],\n [6, 6, -6, 3, 4],\n [-2, -1, 6, -2, 4],\n [2, -2, 3, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -2, 1, 5, 2],\n [-4, 6, 1, 1, 0],\n [1, -2, -2, -5, -3],\n [-6, 4, -3, 2, 4],\n [1, -1, -2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -2, 5, -6, 3],\n [2, 3, 0, -4, -5],\n [-4, -1, 1, 2, -3],\n [6, 1, -1, -5, 4],\n [0, 5, 2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -1, -2, 3, -1],\n [5, -1, 5, 0, -3],\n [-2, 2, 2, -4, -5],\n [1, -2, 3, -2, 3],\n [-2, 0, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 1, -1, -4, 3],\n [-5, -3, 6, 3, -5],\n [-3, 1, 1, -3, 0],\n [-5, 4, -5, 2, -6],\n [-3, 6, -5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 1, 3, -3, 3],\n [-4, -5, -4, 6, -6],\n [4, -2, 5, 3, -4],\n [6, -1, 5, 1, 1],\n [1, 2, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -5, -5, 5, -2],\n [-1, 2, -5, 1, 4],\n [3, 2, 3, -5, 0],\n [-1, -1, 4, -2, 2],\n [-3, -5, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 2, 5, 6, -2],\n [-2, 6, -4, 0, -2],\n [-2, -4, -5, 5, -2],\n [6, -6, -3, -1, 6],\n [2, -6, 5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, 5, 0, 1],\n [-3, 1, 6, -3, 6],\n [5, -3, -4, 6, 0],\n [-4, -4, -1, -4, 0],\n [0, 4, -6, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, 1, 4, 1],\n [0, 6, -6, 4, 1],\n [-1, 0, -5, 5, -5],\n [-3, -1, 6, 2, -2],\n [-1, 0, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -2, -2, -3, 1],\n [2, -5, 0, -6, -1],\n [-1, -1, -4, 3, 6],\n [1, -5, -3, -1, -4],\n [1, -3, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -1, -4, 6, -6],\n [2, 3, 5, 6, -4],\n [-4, -6, 4, -5, -2],\n [5, -5, 1, -2, -2],\n [-4, 4, -5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -1, 3, 6, -6],\n [-3, 2, 0, 2, 5],\n [5, 3, -2, 3, 4],\n [-6, 0, -6, -2, -3],\n [-2, 2, -6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -4, 5, -3, 6],\n [0, -3, 1, -4, -4],\n [5, 2, -4, -1, -3],\n [-1, -5, 3, -2, 5],\n [5, 5, 0, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, 1, -6, 2],\n [-6, -6, 0, 4, 3],\n [2, 4, 1, -3, -6],\n [2, 1, 4, -1, -2],\n [-2, 6, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -6, -5, 3, 2],\n [-1, -3, -4, 5, 5],\n [-3, 0, 1, -2, -3],\n [-2, -1, 1, -4, -2],\n [0, 2, 3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 1, -3, 3, -5],\n [3, 4, -5, -1, -4],\n [-3, 3, -2, -1, -2],\n [3, -5, 0, -2, 1],\n [0, -6, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 6, -3, 6, 6],\n [4, 2, 2, 2, 2],\n [4, 1, 2, -3, 1],\n [-1, 6, 4, -2, -4],\n [3, -4, 6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -3, 3, -1, -2],\n [2, -3, 5, -4, 4],\n [5, -6, -1, 2, -2],\n [-5, 0, 1, 0, 5],\n [-2, 0, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 5, -3, 1, 2],\n [3, -4, 6, -2, 0],\n [4, -5, 4, 0, 4],\n [-5, -4, -1, 5, 6],\n [4, -1, -3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 1, 6, 1, -4],\n [4, 1, 0, 4, 3],\n [-5, 3, 0, 4, 6],\n [0, 6, -6, 1, 5],\n [3, 0, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 4, 2, -5, 3],\n [-6, 2, -3, -2, -5],\n [-6, 1, -6, 0, -5],\n [-5, -2, 6, -2, 6],\n [5, -2, -4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, 3, -3, 3],\n [1, -5, -2, 1, 4],\n [5, -6, -3, 2, -2],\n [-5, 5, -4, 6, -2],\n [-2, -2, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 4, 0, -6, 4],\n [-5, 4, -3, 0, -6],\n [2, -4, 6, -1, 0],\n [-5, 5, 6, 3, 5],\n [0, -4, -6, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 1, 5, 4, -6],\n [-4, 6, -1, -1, 3],\n [5, 3, -1, 0, 3],\n [-5, 0, 6, -5, 6],\n [2, 2, 0, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, 0, -3, -2],\n [4, 3, -6, -3, -4],\n [0, 5, -1, 2, 4],\n [4, -6, -2, 6, 6],\n [6, 5, -1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 0, 4, -4, 3],\n [-1, 4, -2, 6, -5],\n [-3, -2, -6, -2, -1],\n [-5, -4, -3, -3, -4],\n [-2, 3, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 1, 2, -3, -6],\n [-2, 2, 4, 4, 0],\n [3, 3, -6, 1, 2],\n [-3, 1, 4, 1, 0],\n [-3, -4, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, -5, -1, 3],\n [3, 5, -6, -6, -2],\n [2, 3, -3, 6, -6],\n [-6, 3, 6, -6, -2],\n [-6, -3, -3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 6, 6, 0, 2],\n [5, 6, -4, -2, -1],\n [-3, 2, -4, 0, 0],\n [5, -5, -3, -5, 6],\n [4, -4, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 1, -6, -6, 5],\n [-1, 2, -5, 2, -2],\n [4, 5, 4, -4, 5],\n [0, -3, 5, -1, 6],\n [3, -5, -3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, 0, 4, -5],\n [1, 1, -5, 3, 4],\n [1, 3, -2, 5, 0],\n [5, 1, 2, -4, 1],\n [-4, 0, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -3, 6, 2, -2],\n [2, -3, -3, 2, 3],\n [1, -2, -1, -1, 4],\n [5, 5, -5, 4, -3],\n [-3, -6, 2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 4, 6, -3, 0],\n [1, 0, 3, 2, -4],\n [2, 3, -5, -4, -5],\n [-1, -3, 3, -4, -3],\n [-5, 3, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -5, -5, 6, -2],\n [5, -5, -5, -6, 2],\n [-2, -6, -6, 2, -2],\n [-6, 6, 0, 5, 1],\n [1, -1, -2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -1, 6, 3, -6],\n [2, 6, 6, 4, -6],\n [3, -4, 5, 3, -6],\n [3, -1, 6, 0, 1],\n [-2, 6, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, 2, 5, -3],\n [1, 5, 2, 6, 6],\n [4, 3, -3, -4, -6],\n [-5, 1, 6, 2, -3],\n [-1, -5, 3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 1, -5, -1, 2],\n [6, -6, 1, 1, -1],\n [1, 6, -6, 3, 5],\n [6, -3, 4, -5, -3],\n [5, 6, -5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, -6, 3, 5],\n [-3, -2, 0, 1, -4],\n [-4, -2, -1, -5, 1],\n [3, 1, 2, 6, 5],\n [4, 4, 3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 4, 0, -2, -3],\n [3, -4, -2, -2, 1],\n [-3, -3, -3, -2, -5],\n [4, 5, -3, 1, -3],\n [-1, -1, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 6, -5, -4, -2],\n [6, 3, 4, 1, -4],\n [-1, -3, 1, -2, 0],\n [-6, -3, 5, -4, -4],\n [-6, 2, 4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 1, -1, 6, -1],\n [-3, 3, 6, -6, -6],\n [-5, -3, 3, 2, 6],\n [-6, 3, 3, -2, 0],\n [-3, 6, -4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -5, 6, -2, -2],\n [0, -1, 1, 0, 0],\n [0, 2, -6, -6, -3],\n [1, 1, -4, -3, -4],\n [5, -2, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 5, -2, 1, -6],\n [-1, -2, 1, -6, -3],\n [-4, 6, 6, -5, -2],\n [-2, 1, 3, -1, 5],\n [-4, -3, 6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 3, 3, 3, 5],\n [2, -6, -6, -2, -2],\n [1, -2, 1, -6, 2],\n [4, 2, -5, 6, 4],\n [0, 4, -6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -3, 6, -3, -6],\n [-5, 3, 0, -6, 2],\n [4, -5, -1, 4, 4],\n [6, 0, 4, -6, 5],\n [-6, -5, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -1, 4, -5, 4],\n [-5, -2, 4, 4, 2],\n [4, 2, -4, 3, 4],\n [3, 0, 1, 6, -6],\n [6, -1, 5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -3, -1, -1, -1],\n [-2, 5, 3, 2, 1],\n [-4, -3, -2, 6, -3],\n [-4, -3, 4, -1, -1],\n [-1, 1, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, 4, 2, 2],\n [3, 6, -5, 0, 6],\n [1, 2, -1, -2, -4],\n [-5, 2, -5, 6, 3],\n [6, 4, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 5, 3, 0, -4],\n [6, -6, 2, 3, -4],\n [-4, -6, -1, -6, -1],\n [-1, 2, 5, -5, -2],\n [4, 6, -5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -4, 2, 3, -4],\n [-6, -5, 5, -6, 5],\n [-3, 1, 2, 1, 3],\n [4, -4, 1, -2, -1],\n [3, -2, 3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 2, 3, 6, 6],\n [2, -2, 2, -1, 4],\n [-2, -2, 0, 4, -1],\n [0, 2, 6, -2, 4],\n [5, 4, 5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -1, 0, -4, 6],\n [5, -5, -2, -2, -6],\n [1, -5, 2, -4, 4],\n [-2, 5, -4, 1, -5],\n [1, 1, 5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, 3, 4, 5],\n [4, -5, 0, 3, 3],\n [3, -4, -5, 5, 0],\n [-1, 3, -2, -1, -1],\n [1, 2, 0, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 4, 5, -3, 0],\n [0, 0, 2, 6, -4],\n [6, -6, -5, -4, 3],\n [4, 1, -5, 1, -6],\n [5, -4, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -4, -4, 1, 6],\n [-6, 4, 5, 0, 0],\n [4, 0, 1, 5, 6],\n [-5, -1, 4, -4, 6],\n [4, -2, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 3, 2, 2, 4],\n [-5, 5, 1, -1, -3],\n [6, 4, -3, 5, 2],\n [1, 5, 4, -4, 2],\n [-4, -1, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -2, -5, -1, 3],\n [-1, -3, -5, 2, -2],\n [5, 4, 1, 3, -4],\n [3, -6, 6, -3, -5],\n [4, -3, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 1, -4, 0, 3],\n [-1, 2, 0, 3, 5],\n [-6, -6, -5, 0, 5],\n [-4, -6, -1, 1, 3],\n [3, 2, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 3, 0, -4, 4],\n [-1, -4, 3, -1, 2],\n [-6, 4, -2, -4, -1],\n [-2, 1, -2, 2, 0],\n [3, -1, 1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -5, -4, 2, 6],\n [1, 0, 4, 6, 3],\n [-1, 3, 1, 0, -1],\n [0, 0, 2, -2, 4],\n [-3, 0, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 3, 4, -6, 4],\n [-1, -4, 1, -3, -4],\n [2, 4, 0, 2, 0],\n [3, -4, 1, 1, 4],\n [-6, -3, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 5, 4, 3, -1],\n [-3, 3, 6, -1, -6],\n [6, 5, 6, 6, -2],\n [-1, -2, 0, 4, 0],\n [-6, 6, 3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -2, -4, 6, 5],\n [5, -5, -5, 1, 4],\n [-3, -4, 3, 1, -2],\n [-3, -2, 2, 4, -1],\n [-5, 3, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 4, 3, -4, -5],\n [5, -6, 0, 6, 1],\n [0, -3, 5, -4, 1],\n [0, 5, 5, 6, 2],\n [-5, -3, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 5, -1, 2, 0],\n [-2, -6, -3, -6, 3],\n [6, -3, 3, 5, 3],\n [5, 5, 2, 0, 6],\n [1, -5, 5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 5, -3, 0, -5],\n [-1, 5, 2, -2, -3],\n [2, 4, 1, -6, -3],\n [-1, -1, -1, -5, 6],\n [-1, -5, 3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 2, 4, -6, -6],\n [6, 5, 6, -2, 0],\n [-5, 4, -3, -1, 1],\n [3, 6, -1, 3, -2],\n [-6, 4, -5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, 3, 6, 3],\n [6, -3, 6, -5, 5],\n [-4, 3, 1, -1, 4],\n [4, 6, 0, -2, -2],\n [1, -5, 1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -2, 3, 0, 2],\n [-4, -2, 4, 1, 6],\n [3, -3, 0, -3, -6],\n [3, 4, 2, 3, -5],\n [5, -3, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 5, 4, 2, 0],\n [-2, 5, -3, 2, 2],\n [-6, -3, -1, -4, -5],\n [-5, -3, 3, -6, 6],\n [-6, 0, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, -3, 2, -3],\n [-3, 4, 2, 1, 2],\n [-5, -3, -3, -3, -3],\n [6, -2, 3, 0, 4],\n [-3, 6, 6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 2, -2, 5, 5],\n [3, 0, 5, 6, 2],\n [-5, 6, 2, 1, 4],\n [-1, 5, -6, -1, -3],\n [6, -6, 3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 0, -2, 3, 5],\n [4, -5, -2, -5, -4],\n [5, 3, -5, -3, -2],\n [-4, -3, 3, -3, -6],\n [1, -6, 3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 0, -4, 0, -4],\n [-6, 1, -2, 2, -3],\n [-3, -4, -6, -5, -2],\n [0, 5, -3, -4, 2],\n [2, 1, -2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, -6, 0, 2],\n [5, 3, -1, 0, 6],\n [2, 6, -6, 0, 4],\n [-3, -1, 3, 5, 1],\n [3, -6, 5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -4, -4, 0, 2],\n [-3, 3, -6, -3, 0],\n [-4, 1, -1, 5, -1],\n [1, 2, 3, 1, -5],\n [6, 0, -1, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 2, 1, 3, -1],\n [-2, 0, 0, 2, -1],\n [-1, 6, 3, 5, 1],\n [-6, -1, 4, -6, -2],\n [0, -1, 4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 5, 3, 5, 2],\n [4, 5, -2, 2, 2],\n [4, -2, -4, 4, 6],\n [0, 3, 4, 1, -4],\n [4, 3, 4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -2, 5, 4, 3],\n [3, -4, -3, -5, 5],\n [-6, -4, -2, 1, -2],\n [-6, 0, 5, 2, 3],\n [0, 4, -4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -5, -1, 1, -1],\n [5, -2, -1, 6, 4],\n [6, -3, -2, -1, -3],\n [-4, 1, -6, 2, 6],\n [5, -6, -6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 6, -5, 6, 1],\n [6, 3, 0, -1, 6],\n [-1, 4, -3, -4, 0],\n [-4, 0, 4, -6, 3],\n [-1, 4, 5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 0, -4, -3, -2],\n [4, 1, 2, -1, 6],\n [-3, 0, 0, -2, 6],\n [-2, 3, 6, 2, -2],\n [5, 5, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 6, 0, -5, 5],\n [3, 1, -5, -6, 3],\n [-6, -1, -6, -5, -4],\n [0, -3, 3, 1, 2],\n [-4, 4, -4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 5, -5, 5, 6],\n [-4, -2, 5, -5, -4],\n [6, 5, -2, 0, 6],\n [5, -1, -5, 5, 5],\n [6, -6, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 1, 0, 3, -6],\n [1, 1, 3, -2, -1],\n [5, -1, 4, 5, 3],\n [6, -1, -6, 4, -6],\n [5, 4, -5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 1, 6, 1, 5],\n [-6, 6, 5, -3, -4],\n [-3, -5, 3, 4, 2],\n [6, -2, -3, -6, -3],\n [-3, 6, -6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 4, 4, -2, -4],\n [2, 2, -5, 2, -6],\n [-6, -3, -4, 2, -6],\n [1, 2, -5, 5, 6],\n [-6, -4, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 4, -1, -2, -3],\n [5, -6, 0, -6, 1],\n [-3, 5, 4, 4, -2],\n [2, 5, -1, -1, 0],\n [-3, -5, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -2, 5, 4, -6],\n [1, -1, -1, -5, 4],\n [-2, -4, -6, 6, 4],\n [6, -4, 1, 2, -2],\n [-6, -1, -5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -1, 4, 0, 4],\n [-4, -1, -3, 2, 4],\n [-2, 0, 6, 2, 2],\n [0, 0, 4, 5, 1],\n [-6, 0, -2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 6, 3, -3, 6],\n [6, 6, 5, 4, -6],\n [-5, 2, -1, -6, 6],\n [-3, -1, 2, 0, -6],\n [5, -2, 5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, 0, 6, -2],\n [-1, 4, -1, 2, -1],\n [1, -3, 3, -5, 0],\n [4, -3, -3, 6, -5],\n [-3, 0, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -1, 2, -4, 6],\n [-3, 2, 3, -6, 2],\n [5, 5, -5, -5, 3],\n [5, -6, -1, 4, 0],\n [2, -6, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 1, -2, 1, 1],\n [-5, 2, 0, -2, 4],\n [3, -2, 0, -5, 0],\n [4, 3, -2, 6, 0],\n [0, 6, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 3, -6, 1, -1],\n [2, 2, 6, 6, 0],\n [-6, 4, 3, -5, -2],\n [-3, 0, -1, -6, -2],\n [0, 3, -5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 6, 5, -6, 3],\n [-4, 1, -4, 0, -4],\n [5, -3, 2, 4, -6],\n [-3, 3, 2, -2, 2],\n [0, 6, -3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -2, 3, 5, -1],\n [1, -2, 5, 0, -4],\n [4, -6, 0, -4, 6],\n [-4, 4, 0, 0, -3],\n [5, -6, 6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -1, -3, -2, -4],\n [4, -2, 0, 6, -3],\n [-3, 6, 1, 5, -5],\n [3, 1, 6, 3, -3],\n [5, -3, -4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, 6, 1, -5],\n [-6, 3, -1, 1, 4],\n [-3, 3, 2, -6, -6],\n [6, 2, 3, -4, 3],\n [4, -4, 6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, 1, -2, 1],\n [-3, -5, 5, -1, -3],\n [-1, -4, 0, -4, 6],\n [-1, 3, -1, 3, -5],\n [-6, -3, -4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 5, -2, 6, 6],\n [-6, 5, -5, -1, 5],\n [1, 1, 3, 2, 6],\n [1, -6, 3, -6, 5],\n [6, 2, -1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 3, 5, 0, 5],\n [-2, 6, 4, 2, -4],\n [4, 6, -6, 5, -6],\n [-1, -3, 3, -6, 4],\n [-3, -6, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, 5, -3, 5],\n [6, 3, 0, -6, 6],\n [-1, 0, -5, -1, 0],\n [3, 5, -4, -4, 6],\n [-4, 0, -3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 4, 0, 4, 2],\n [-4, 2, -1, -3, 4],\n [-4, -3, -5, -2, 6],\n [1, -5, -2, 4, -2],\n [0, 2, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -5, 2, 2, -5],\n [-1, 3, 5, 1, -3],\n [0, -6, -4, -2, -3],\n [-1, 4, -5, -4, 4],\n [-1, 4, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -2, -3, -5, 5],\n [2, -3, 1, 0, 0],\n [-2, -5, 6, 1, 4],\n [0, -4, 4, -2, 3],\n [6, -5, -5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 6, -1, 3, -2],\n [1, 1, 0, 6, 4],\n [-6, 6, -6, 1, -1],\n [4, 3, 4, -6, -3],\n [-2, 4, -2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, 4, 3, 4],\n [-6, -5, 6, 6, 5],\n [-3, 2, 3, -5, -3],\n [3, 3, 2, -4, 1],\n [-1, 3, -1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, 4, 1, -4],\n [1, -1, 2, 2, 6],\n [-5, 6, 2, -2, -6],\n [-6, 6, 2, -2, 1],\n [-4, -5, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -3, -3, 4, 0],\n [4, 2, 1, -3, 6],\n [-1, -3, 6, 3, 6],\n [-4, -6, 3, 5, 2],\n [0, 5, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 3, -6, -1, 4],\n [-5, 5, -4, 5, 5],\n [5, 3, -1, -6, 1],\n [-1, 4, -5, 1, 2],\n [-6, 5, -4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -5, -5, -5, 1],\n [6, -4, -3, -6, -4],\n [4, 3, 2, -3, 3],\n [1, -2, 6, 0, -4],\n [6, 5, -4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -5, 5, -5, -5],\n [5, 3, 3, -5, -3],\n [6, 6, 4, -3, -2],\n [5, 2, -4, 6, 1],\n [-4, -3, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -3, 2, 6, 3],\n [2, 2, -5, 5, 0],\n [-2, -5, 1, 2, 2],\n [5, -2, -5, -6, 3],\n [-2, -1, 6, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 0, 1, -2, 1],\n [0, -1, -3, 2, -2],\n [-1, 2, 3, 5, 4],\n [-4, 2, 4, -3, 1],\n [6, -2, -1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 6, -3, 2, -1],\n [-6, -4, 0, -2, -5],\n [-2, -3, -2, 6, -1],\n [1, -5, 5, 3, -3],\n [1, 0, -5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -4, 0, -3, 5],\n [5, 5, 3, -2, -1],\n [4, -1, -4, -1, -1],\n [3, -4, -2, 1, 6],\n [5, 4, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -4, -6, -4, 0],\n [-2, 1, 3, -4, 0],\n [1, -3, 1, 5, -5],\n [3, 2, -3, -4, 3],\n [-4, -3, 3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -2, 5, 3, 0],\n [6, 0, 3, -3, 5],\n [1, -6, 4, 0, -6],\n [-2, -5, -3, -4, -6],\n [-2, 4, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 2, 3, 6, 6],\n [4, 4, 2, 4, -4],\n [-4, 2, 0, -3, -1],\n [-1, 0, -6, 0, -5],\n [4, 6, 6, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -5, 5, 3, 4],\n [-4, 5, 5, 2, 2],\n [3, -2, 0, 3, -6],\n [-1, -6, 0, 6, -4],\n [6, -2, -5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 0, 4, 5, 4],\n [0, -3, -6, -6, 3],\n [-3, 4, -2, -3, -3],\n [1, 4, 0, 6, -2],\n [0, 2, 4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -3, 4, -5, 3],\n [-3, 4, 6, -6, 2],\n [-5, 4, 5, 3, -6],\n [4, -3, 6, 4, -1],\n [5, 4, 6, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, 1, -1, 6],\n [-6, -5, -4, 4, 2],\n [-4, 2, -1, 1, -3],\n [5, -1, -3, 6, -1],\n [0, 5, 0, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 0, -5, -6, 5],\n [-1, 5, -6, -6, 2],\n [4, 1, -4, 4, -1],\n [4, 0, -1, -1, 5],\n [5, -2, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -2, 0, 2, 3],\n [-6, 4, -4, 3, 1],\n [0, 2, 2, 1, -5],\n [-5, 1, -1, -5, -3],\n [-1, -2, 0, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -6, 1, 1, 4],\n [0, -1, -5, 0, -3],\n [-4, 1, -1, 6, 0],\n [-6, -3, -5, -2, 6],\n [-6, 1, 6, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, 4, 0, -6],\n [4, 5, -2, 5, 1],\n [1, 6, 6, -3, -6],\n [-2, 6, 1, -5, -4],\n [-5, 6, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 2, -1, 5, -4],\n [1, 0, 4, 2, 2],\n [-1, -3, -2, -1, -2],\n [-1, 6, -1, 6, 2],\n [0, -6, 3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -3, -5, 1, 6],\n [0, -6, -5, 5, -3],\n [6, -1, 4, 4, -6],\n [-1, 4, 1, 6, -6],\n [-3, -3, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 0, -4, -1, 0],\n [3, -1, 2, 2, -3],\n [5, -4, 6, 0, -1],\n [-4, -5, 1, -2, 1],\n [0, 3, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 2, 6, 4, -3],\n [5, 1, 0, 2, 6],\n [-2, 4, 6, -4, 3],\n [2, 4, 4, 6, -3],\n [4, -5, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 4, 1, 2, 6],\n [3, 0, 2, 3, -5],\n [0, -3, -3, 5, -2],\n [5, -1, -1, -1, 3],\n [-2, -5, -4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 2, 3, -6, -4],\n [-5, 4, 1, 4, -1],\n [-2, -1, 2, 3, -6],\n [-5, -2, -1, 3, 2],\n [0, -5, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 3, 1, 2, 4],\n [3, -5, -4, -1, 6],\n [3, 2, -5, 0, -2],\n [5, 1, -3, -5, -4],\n [3, 6, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -2, 1, -5, 4],\n [6, 2, -4, -6, 0],\n [-5, 6, 1, 3, -3],\n [-1, 6, -5, 5, -1],\n [-6, -1, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -5, -4, -6, 5],\n [-5, 3, 5, -1, 3],\n [3, -1, -5, -2, 5],\n [2, 3, -2, -4, 1],\n [3, 3, 0, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 3, 3, -6, 5],\n [5, -4, 5, 4, -2],\n [3, 1, -4, -6, 3],\n [4, 2, -5, 4, 4],\n [5, 0, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 4, 6, -2, 2],\n [-6, -4, 6, 5, 2],\n [-6, 4, -6, -2, 4],\n [3, 6, 3, -4, 6],\n [-6, 0, 2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 3, 3, 6, 4],\n [6, 2, 5, -5, -4],\n [2, 6, 2, 1, 3],\n [-6, 3, 0, 5, 0],\n [-4, 0, -3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 3, -5, -3, -5],\n [4, -2, -3, 1, 5],\n [-3, -2, 0, -4, -5],\n [1, 3, -4, -2, 2],\n [-3, 0, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -5, -5, 2, 1],\n [1, -3, 6, -5, 1],\n [5, 0, 4, 6, -3],\n [4, -1, 6, 0, -2],\n [-4, -3, 3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -4, -4, -1, -6],\n [0, -2, -1, 1, 1],\n [1, 2, 1, -3, -4],\n [-5, 0, -2, 0, 4],\n [-3, 2, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -3, 3, 3, 2],\n [4, -3, 1, -3, 3],\n [-5, -1, -6, -3, -5],\n [-3, 0, -4, 4, 2],\n [4, 2, -6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 2, -2, -5, -5],\n [-1, 1, -3, -5, 3],\n [2, 2, -3, -4, 2],\n [-2, -4, 4, 4, 4],\n [-5, 6, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -6, 2, 3, -6],\n [-1, -5, -2, 6, 1],\n [4, -4, -3, 3, -5],\n [-6, 2, -3, -5, -4],\n [-2, -5, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, -3, 5, -6],\n [5, 2, -5, 3, -1],\n [1, -1, 1, -6, -3],\n [2, -1, 5, -3, 4],\n [0, 3, 1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 6, 1, -4, -6],\n [6, 3, -4, 1, 2],\n [4, 0, 0, -4, -5],\n [-4, 1, -2, 2, -5],\n [4, 5, -1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -3, -3, -4, 4],\n [1, -4, -6, -3, -3],\n [2, -4, -1, -5, 3],\n [1, 3, 5, -3, 0],\n [-6, -3, -1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 5, -5, -6, 6],\n [0, -2, -6, 6, -4],\n [-1, 5, -1, -5, 2],\n [5, -2, 2, 2, 6],\n [0, -6, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, -1, -2, -4],\n [-6, -2, -5, 4, -5],\n [-1, -2, -2, 1, -2],\n [5, -6, -2, 5, -1],\n [6, 6, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 5, -3, 5, -1],\n [-5, -1, -3, -6, -1],\n [4, -1, -6, -5, 5],\n [4, -5, 4, -6, -2],\n [3, 0, 6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 2, 6, 4, 6],\n [-1, -6, -6, -2, 3],\n [0, 0, -1, 3, -6],\n [-2, 2, -3, -4, -6],\n [0, -5, -4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 3, 1, 1, -1],\n [4, 4, -6, 3, 6],\n [6, -1, 6, 3, -4],\n [-6, 2, 2, -2, -3],\n [4, -4, 5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 4, -2, 5, 3],\n [-1, 0, -3, -5, 4],\n [3, 3, -5, 6, 5],\n [-5, 2, 2, 3, 4],\n [1, -6, -5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -3, -4, 0, -1],\n [2, -4, 3, 3, -2],\n [1, 6, -2, -2, 4],\n [2, 4, -1, -1, -5],\n [-5, -2, 5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -6, -5, -6, 6],\n [2, -4, -6, -2, 2],\n [0, 0, -4, -4, 1],\n [-4, 4, -5, -5, 0],\n [-4, 6, -6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 4, 4, 2, 6],\n [1, -3, -3, 5, -6],\n [4, -2, 3, 6, 1],\n [3, -1, -1, -2, 1],\n [5, -3, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -4, 1, 6, -1],\n [4, -3, 4, -6, -2],\n [5, -6, -2, -5, -3],\n [-6, 1, 2, -4, 2],\n [-3, -5, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 3, -5, 5, -4],\n [-6, 5, 6, -3, -1],\n [-6, -2, 2, 2, -4],\n [-1, 2, 3, 6, -5],\n [0, -2, 1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -3, -1, 6, -3],\n [-3, 2, -1, -6, 4],\n [1, 0, 5, -5, 5],\n [-1, 5, 3, -1, 3],\n [6, -4, 3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 2, 4, 1, 5],\n [-6, -5, 0, 3, 6],\n [2, 4, -4, -6, -6],\n [3, 0, 6, 0, 0],\n [6, 5, -6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -3, -3, -4, 6],\n [6, 3, -5, 2, 3],\n [-5, -2, 3, -1, 1],\n [-5, 4, -5, 2, -6],\n [2, 3, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -1, 5, -2, 5],\n [-5, 5, -2, -3, -4],\n [5, -2, 4, -5, -5],\n [-5, -2, -5, 6, 2],\n [1, 6, 3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -4, -2, -2, 2],\n [2, -6, -3, -1, -3],\n [-3, 6, 4, -4, -1],\n [-6, -4, 0, -3, -4],\n [-5, -5, 2, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -2, -6, -2, 0],\n [-2, 5, 6, 0, -4],\n [0, -4, 0, -3, 6],\n [3, 1, -3, 5, 4],\n [-2, -2, 5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 5, -6, -5, 0],\n [3, -1, -2, 1, -5],\n [-3, -6, -3, -1, -2],\n [4, -3, 4, 2, -5],\n [-1, -5, -1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -6, 5, 0, 2],\n [-2, 6, 1, 1, 4],\n [6, -5, -2, 5, 0],\n [-1, -6, 0, -2, -5],\n [5, -6, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 6, -6, 3, 3],\n [-4, 5, -5, 4, -6],\n [6, -3, 0, -3, 2],\n [5, 3, -2, 4, -5],\n [-3, 3, 4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -6, 5, 1, -2],\n [-1, 4, -1, -5, 3],\n [0, -2, -4, -2, -6],\n [-4, -3, 5, 3, 1],\n [-4, -6, 6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -2, 0, -3, 2],\n [2, 2, 2, -3, 0],\n [-4, -3, 2, -3, 2],\n [6, 3, -1, -5, 3],\n [6, 0, -3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 6, 1, 3, 3],\n [1, -6, 0, -2, -1],\n [-3, -2, 5, 3, -4],\n [1, 0, -5, -1, -6],\n [1, -2, 3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 3, -1, 0, -3],\n [1, -6, 0, -5, 5],\n [-5, 4, 1, -3, -6],\n [6, -6, -4, -5, 3],\n [-2, -6, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 4, -5, -6, 1],\n [-2, -2, 0, 4, -1],\n [0, -2, -5, -5, 0],\n [3, 4, 1, 3, -2],\n [4, -2, -6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 5, 2, -6, -3],\n [-5, 4, 3, -1, 6],\n [-1, -4, 1, 4, -3],\n [-2, 5, 3, -3, 5],\n [-1, -5, -3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, -6, 1, -1],\n [0, 6, -2, 1, 5],\n [0, 5, 6, 5, 2],\n [-5, -6, 3, -5, 0],\n [4, -2, -3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -3, -4, 4, -5],\n [-2, 3, -1, 5, -6],\n [-6, -4, -6, 0, 0],\n [-5, 6, -6, -5, 6],\n [5, 3, 6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 2, 4, 1, 2],\n [3, -2, -6, -6, 3],\n [-3, 5, -2, 4, -6],\n [-5, 6, 6, 2, -4],\n [6, -4, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -1, -1, 3, 1],\n [0, 0, -5, -2, 5],\n [1, -3, -6, 1, 2],\n [3, 6, 0, 6, 6],\n [4, 3, 2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -6, 4, 1, -1],\n [0, 2, -1, -2, 2],\n [1, -4, -3, -4, -3],\n [-3, 0, 0, 4, -5],\n [1, 2, -2, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -4, 4, 6, 3],\n [0, 2, -5, 3, -1],\n [2, 4, 2, 1, 1],\n [2, 5, 6, 5, -4],\n [-2, -5, 0, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -4, 1, -1, -6],\n [-4, -1, -4, -5, 1],\n [0, -4, 0, 0, -1],\n [-5, 0, -6, 6, 1],\n [4, 4, 6, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 1, -4, 3, 3],\n [1, 0, 0, -4, -1],\n [-1, -1, 4, -6, -4],\n [0, -6, -2, -2, -6],\n [0, 1, -4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -2, 1, 6, 3],\n [-5, -5, 6, 2, 1],\n [-6, 4, 0, 2, -6],\n [-2, -3, 4, -6, 4],\n [-6, 5, -6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 5, 1, -3, 3],\n [0, 5, -3, -5, 0],\n [1, -6, -1, -1, -6],\n [0, 1, -5, -6, 1],\n [-5, -2, 4, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -5, -5, 3, 5],\n [-1, 4, -4, 3, 1],\n [0, 4, 3, 3, -6],\n [-4, 6, 2, 6, -1],\n [2, 5, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -2, 3, -5, 4],\n [5, 1, -5, 0, -1],\n [5, -6, 6, 1, 4],\n [-4, -4, 3, 0, 2],\n [-6, -2, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 0, 2, -5, -1],\n [3, 6, 2, -5, 5],\n [-6, 4, 0, 1, 1],\n [0, 4, 3, 3, 1],\n [1, 4, -1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -3, -4, -2, 3],\n [-5, 2, 4, -5, -2],\n [-1, -5, -6, -4, -2],\n [-4, 5, -2, -2, -3],\n [-5, 4, -6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -6, 3, 0, 0],\n [0, 5, 0, 4, -1],\n [1, -4, -3, 4, 1],\n [-3, -3, 6, 3, -3],\n [5, 1, -5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -2, 3, -1, 6],\n [2, 5, 1, -2, -6],\n [-4, -2, -1, -5, 3],\n [5, 1, 6, -2, 5],\n [3, 0, -3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 3, -3, -5, -6],\n [5, 3, -4, 3, -2],\n [6, 3, 5, 4, 1],\n [-3, 2, 4, 2, -2],\n [-4, 6, 4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -6, 1, 2, 6],\n [3, 2, 3, -4, 2],\n [3, -2, 5, 4, -2],\n [-2, 5, 3, -4, -2],\n [-3, -6, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -6, 6, 2, -3],\n [-6, 5, -6, 0, -3],\n [1, 1, -6, -4, -5],\n [-3, 3, 0, -6, -2],\n [0, -5, 6, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, -4, -2, 2],\n [-6, -1, -2, 5, 2],\n [-4, 1, 6, 2, -2],\n [-3, 4, 0, -5, 0],\n [-4, 1, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -2, 0, -1, -2],\n [6, -5, 4, 1, -3],\n [4, 5, 1, -3, -4],\n [1, -2, -1, -5, -2],\n [-1, 0, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -5, -5, -4, 2],\n [6, 2, 2, -6, -3],\n [-5, -6, -5, -1, -4],\n [-5, 6, -4, -1, 2],\n [-5, -1, -3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, -4, -4, 0],\n [4, -4, -5, -2, -2],\n [4, -4, 1, 0, 5],\n [-1, -5, 0, -4, -3],\n [4, -2, 1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 6, 2, 6, 6],\n [6, -6, -1, 2, -1],\n [2, 0, -3, 3, -4],\n [6, -3, 3, -1, -6],\n [5, 6, 5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -3, -6, -3, 0],\n [-3, 3, 1, -1, 5],\n [1, 5, -3, 0, -4],\n [5, -5, -4, -3, -1],\n [0, -4, 2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 1, 2, 4, -2],\n [1, -2, 1, 0, -2],\n [4, 0, 4, 2, 3],\n [6, -4, 4, 1, -5],\n [6, 3, -4, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -2, 2, 0, 5],\n [6, 4, -1, 6, -2],\n [0, 6, -2, 0, -1],\n [4, -5, -1, 4, -5],\n [3, -4, -4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -2, -5, 1, -6],\n [-1, 4, -3, 3, 4],\n [2, 5, -2, -5, -3],\n [2, -5, 5, 3, -2],\n [2, 3, -2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, -5, -3, 1],\n [-2, 5, 4, -1, 3],\n [-6, -2, 6, -6, 2],\n [-5, -4, -4, 0, 0],\n [-4, 5, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -5, 5, -1, -6],\n [-2, 3, -3, 4, -1],\n [-5, 6, 4, -6, 2],\n [3, 1, -1, -5, -2],\n [-1, -3, 2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 0, 2, -1, -5],\n [-1, -4, 1, 5, -1],\n [-5, -6, 0, 0, 4],\n [-2, -1, 1, 2, -6],\n [6, -6, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 1, 5, -4, 3],\n [2, 5, -4, -2, 3],\n [-1, 0, -6, 0, -3],\n [-2, 0, -6, 3, -1],\n [-3, 6, -3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -3, -5, 5, 3],\n [-1, -5, -3, 1, -6],\n [3, -4, -2, 0, 3],\n [-3, -4, 2, 4, -1],\n [-3, 3, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, -1, -6, 0],\n [-3, 6, -4, 0, -4],\n [0, 6, 1, -6, 6],\n [-2, -3, -6, 0, -4],\n [-2, 5, -5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -3, 0, 5, 2],\n [2, 3, 1, 1, -3],\n [-2, -5, 4, -5, -3],\n [-4, -3, -1, 0, 4],\n [6, 6, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 6, -3, -4, -1],\n [3, 1, -2, -1, -4],\n [-6, 3, -6, 3, -1],\n [4, -4, 6, -5, 0],\n [-4, -5, 6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 2, 4, 2, 5],\n [5, -3, 2, -2, 5],\n [-3, 6, -1, 3, 2],\n [-4, 2, 4, -1, 4],\n [6, -5, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -3, 5, -4, 6],\n [2, -5, -6, 5, -6],\n [6, 6, 1, 6, -3],\n [4, 6, 4, -5, 4],\n [0, -5, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 5, -6, 2, 3],\n [5, -1, 5, 4, 3],\n [-6, 6, -6, 1, -1],\n [-3, -4, -1, -5, -1],\n [4, 1, 6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, 3, 1, -4],\n [5, -4, 1, -4, 4],\n [6, 2, -3, 2, 2],\n [3, 6, 6, -2, 5],\n [4, -2, -5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -2, 6, 5, -2],\n [-6, -3, 1, -3, -3],\n [0, 1, -2, 5, -1],\n [-3, -5, -5, -4, 5],\n [1, -5, 1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -5, -2, 2, -4],\n [-6, -5, 2, 1, 6],\n [6, -6, 5, 6, 5],\n [-2, -5, -1, -1, -5],\n [-2, 5, 3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 3, 4, -1, 1],\n [3, 3, -5, -3, 4],\n [-5, -1, 5, -4, -2],\n [-5, 2, -4, 0, -4],\n [4, 2, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, 2, -5, -2],\n [-6, -5, 6, -5, 5],\n [1, 6, 3, 5, 4],\n [-2, 0, -2, 1, -5],\n [6, -2, -5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 2, -4, 3, 0],\n [6, 4, 3, 3, 1],\n [1, -5, -5, -2, 3],\n [6, 0, 4, -6, -2],\n [-3, 3, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -2, 3, -4, -6],\n [-1, 6, -4, 4, 4],\n [-5, -4, -1, 2, -2],\n [-2, 2, 0, 6, 4],\n [5, -4, -4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 6, -3, 3, -4],\n [4, -5, -6, -3, 4],\n [-3, -1, 1, -2, 6],\n [-5, -5, 6, 4, -6],\n [-1, -6, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -6, 6, -4, -5],\n [-6, 2, -1, -2, 5],\n [-6, 3, 2, 5, 2],\n [-5, 0, 5, 2, -3],\n [-4, 3, -1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, 0, -6, -1],\n [-5, 1, 6, 2, -4],\n [-2, 6, 0, -3, 5],\n [-4, 4, -4, 4, 4],\n [2, 6, 1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 4, 0, -2, 2],\n [-5, 6, 2, 3, -6],\n [4, 0, -3, -2, -5],\n [6, -5, -5, 1, -1],\n [-3, -4, -5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 2, 4, -4, -4],\n [4, 4, -3, 5, 2],\n [-4, 0, 0, 1, -6],\n [-5, 6, 6, 1, 0],\n [0, -3, 4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 5, 0, 2, -2],\n [-1, 1, -5, -5, -1],\n [-5, -6, 1, -1, 1],\n [-3, 2, 6, -5, 1],\n [-4, -4, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 1, -3, -3, 3],\n [-4, 5, 4, 3, 5],\n [-5, 5, -3, 2, 2],\n [1, 3, 4, 2, 5],\n [-2, -1, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 1, -3, 3, -5],\n [1, 6, 1, -6, 6],\n [0, -2, -5, 4, 2],\n [-6, -4, 0, 6, 5],\n [2, -1, -6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 1, -6, -2, 3],\n [-3, -2, -5, -6, 2],\n [4, 6, 4, 2, 6],\n [2, 3, 3, -4, 5],\n [-6, 4, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 2, 1, 6, -6],\n [5, 1, 4, 3, -4],\n [-2, -1, 5, -3, -6],\n [3, -5, 0, -1, 5],\n [4, -5, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 5, -5, -4, 4],\n [-6, 6, 0, -4, 0],\n [-5, -6, -2, -6, 5],\n [3, 5, 2, 4, 3],\n [-4, 0, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -6, 3, -1, 0],\n [5, -3, 3, 3, -4],\n [-4, 6, -1, 6, 6],\n [-3, -4, -2, -4, -4],\n [5, 6, 4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, 2, -1, -5],\n [3, 5, -5, -6, -6],\n [6, 1, 1, -2, 0],\n [1, -1, -1, -4, 1],\n [-1, -6, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 0, 1, -6, 4],\n [-3, -1, 6, 0, -1],\n [-3, 2, 5, -3, -2],\n [6, -2, 6, -2, 0],\n [-2, 4, -3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 2, -6, 2, -5],\n [5, -1, -2, -2, 0],\n [6, 6, -5, -6, -1],\n [3, -5, -6, -5, 3],\n [1, -2, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -2, 4, -5, 5],\n [-1, 2, 1, 4, 2],\n [-3, 3, -6, -2, 1],\n [-5, -4, -5, -1, 3],\n [4, -4, -5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 0, 0, 6, 1],\n [1, -6, 6, 5, 4],\n [4, -5, 3, 3, 6],\n [-6, 0, 2, -1, 6],\n [-4, 6, -3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -3, -6, -3, -4],\n [-4, 4, 5, -1, 4],\n [2, -2, -3, 1, 3],\n [5, 0, -2, -1, -5],\n [2, -1, -3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -2, -3, -4, 0],\n [-2, 2, -1, 4, 1],\n [2, -6, 2, 6, 4],\n [3, 6, 1, 5, -6],\n [-5, -3, 0, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -5, 0, 6, -1],\n [2, -3, -3, 2, -2],\n [-2, 1, 5, -5, 2],\n [6, 0, -1, 1, -5],\n [-1, 6, -6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 0, 3, 2, -5],\n [-1, -1, 2, -6, -2],\n [5, 5, 1, 6, -5],\n [2, 2, 0, -5, -3],\n [-3, 3, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, 0, -5, 6],\n [6, 2, 1, -5, -5],\n [-6, -6, -3, 3, -1],\n [4, -6, -3, -5, 6],\n [5, -4, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 0, -6, -4, -2],\n [3, -3, 5, -2, -3],\n [-3, 3, 0, 2, 6],\n [4, -4, 1, -5, 3],\n [-6, 4, -1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 4, 1, -6, -4],\n [-5, 0, -5, -6, -6],\n [-6, -2, -4, -5, 6],\n [-5, -6, -3, -3, 2],\n [5, 1, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -2, -3, 0, 0],\n [-4, 0, 2, -5, 5],\n [-2, -3, 0, 5, 4],\n [3, 5, -6, -5, -3],\n [4, 0, -5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -3, -3, -5, 3],\n [-2, -2, -5, 0, -6],\n [0, 4, 6, -4, -1],\n [6, 1, -3, 1, 1],\n [-2, 5, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 1, 6, -3, 5],\n [-5, 6, -6, 1, 1],\n [-4, -4, 4, 2, 0],\n [-3, -4, 2, -4, 3],\n [6, -1, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -6, 5, -3, -4],\n [4, -4, -6, -5, 2],\n [0, -1, -1, 2, -5],\n [-4, -3, 4, 0, 4],\n [4, 3, 1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 3, 5, -2, -4],\n [3, 5, -2, 3, -6],\n [6, 3, -6, -1, 6],\n [5, 6, 5, 5, 0],\n [1, -1, 2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -2, 0, 6, 6],\n [-1, 6, 6, -1, -1],\n [-1, -1, -2, 4, -6],\n [4, 3, -2, -6, 4],\n [1, -4, 1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -4, 3, -6, 2],\n [-3, -6, -6, 5, 3],\n [-1, -3, -5, 3, -6],\n [3, 3, -2, -3, -3],\n [-3, 0, -3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -6, -6, -5, -6],\n [-1, 4, -1, 5, -3],\n [0, -4, 1, -4, 1],\n [3, 1, 5, -4, -2],\n [-4, -2, -1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -6, 3, 0, 4],\n [6, -1, 5, -6, 0],\n [-6, -4, -3, -1, -2],\n [0, -1, 1, -1, -5],\n [-3, 0, -5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 3, -4, -6, -1],\n [-5, 6, -1, -5, -5],\n [1, -2, 4, 0, 3],\n [6, -5, 2, -3, 0],\n [-2, 3, -1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -1, 0, 4, 2],\n [1, 6, -2, 2, 0],\n [-4, -4, -3, -6, 2],\n [2, 1, 0, 0, -3],\n [-3, -6, -5, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 2, 0, 4, 6],\n [-3, -2, 0, -3, -1],\n [5, -3, -2, 5, -2],\n [1, 0, 2, 0, 0],\n [3, 3, 6, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 5, 6, 0, 6],\n [6, 2, 2, -2, -2],\n [-4, 4, 0, -6, 6],\n [3, 0, 1, 6, -4],\n [-6, -5, -2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 3, -6, 5, -1],\n [-4, 4, 4, 4, 5],\n [1, -4, -1, -3, 6],\n [-6, 3, -5, 5, 5],\n [-6, 5, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 5, -1, -6, -5],\n [-6, 0, -1, -3, 1],\n [4, -6, -3, 3, -2],\n [2, 0, -1, -2, -6],\n [-6, 0, -2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 5, -2, -6, 2],\n [6, 5, 0, 3, 0],\n [1, -3, -2, -1, -4],\n [-1, -6, 3, -4, 5],\n [-5, -3, 3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, 0, -5, -1],\n [-5, 4, -3, -2, -6],\n [3, -4, 0, -1, 1],\n [-3, -6, 4, 1, -2],\n [2, -6, -4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 4, -6, 6, 4],\n [1, -6, 1, -2, -6],\n [6, 0, -6, 2, 2],\n [5, -1, 6, 0, 0],\n [-3, 1, -6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 5, -2, 6, -6],\n [-1, 3, -3, -3, 4],\n [5, 2, -3, 2, 1],\n [-4, 0, 0, 0, 5],\n [-6, 1, 6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 6, -5, -6, 6],\n [4, 0, 6, -2, 6],\n [1, 5, -1, 0, 0],\n [0, -1, -2, 6, -4],\n [-1, -5, -1, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 3, 4, 4, -4],\n [-1, 1, 3, -4, -4],\n [4, 1, 3, 6, -6],\n [-6, -6, 6, 2, 1],\n [-1, -4, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -2, 0, -5, 2],\n [4, -6, 4, -2, 2],\n [1, 0, 0, -6, -3],\n [4, 0, 2, 3, -3],\n [0, -4, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -5, -1, 4, -1],\n [0, 1, 3, -4, 0],\n [5, -1, 5, 6, 3],\n [-1, 4, 6, 3, -3],\n [-5, 5, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -5, -5, -3, 4],\n [1, 5, 1, -6, 5],\n [-5, 6, -6, 6, 1],\n [0, 6, -6, -6, 4],\n [3, -3, 6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -5, 1, 4, 0],\n [0, 3, 1, -3, 1],\n [-4, -4, -5, 5, -5],\n [1, -3, 3, 1, -3],\n [-5, -3, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -5, 2, 3, 5],\n [1, 5, 2, 4, 6],\n [4, 1, -6, -2, -3],\n [0, -5, 4, -5, 4],\n [6, -6, -5, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -3, -3, 6, 2],\n [4, 0, -6, -3, -3],\n [-3, -3, 6, 0, 4],\n [-1, 5, 4, 1, -1],\n [-3, 2, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, 1, -3, -2],\n [1, -5, -1, -6, -1],\n [6, -6, 3, -4, -6],\n [-5, -3, 1, -5, -6],\n [0, 5, -1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -4, 3, -1, -1],\n [3, 6, 2, 0, -4],\n [-2, 1, 6, -3, 1],\n [0, -2, 3, -6, 5],\n [5, -5, -5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 4, 1, -1, -2],\n [-6, 6, 2, 4, 0],\n [-4, 1, 3, 3, 5],\n [6, 5, 2, -2, 5],\n [4, -2, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -2, -5, -1, -2],\n [-6, 4, -5, -4, 1],\n [-6, 1, -4, -5, -5],\n [-3, 4, 6, -6, -4],\n [-6, -3, -1, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, -2, -5, 2],\n [-3, 3, 5, 1, 6],\n [-2, 4, -5, 2, -3],\n [-4, -3, -3, -5, -6],\n [-3, -2, -6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 4, -4, -2, 5],\n [3, -2, 1, 0, 3],\n [-6, -1, -2, 1, 3],\n [-2, -5, 3, -2, 3],\n [-3, -1, -1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 2, -4, -5, -4],\n [0, -2, 6, -4, -2],\n [1, 4, -4, -4, -2],\n [-6, -2, -3, -5, 6],\n [-6, -5, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, -4, 1, 2],\n [4, -2, 6, 1, 6],\n [-3, -3, 3, 1, 6],\n [-4, -2, 6, -6, -3],\n [4, 3, 4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 1, 6, -6, -3],\n [5, 4, 6, -5, 3],\n [-5, 0, 4, -4, 5],\n [-5, -4, 0, -4, -6],\n [2, 6, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 5, -4, 3, -6],\n [5, -3, -3, -2, -2],\n [4, -3, -4, 1, 5],\n [-3, -5, 2, 2, 4],\n [4, -4, 6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 0, -6, -1, 1],\n [5, -5, 4, 6, 6],\n [2, -5, 0, -6, 3],\n [-1, -1, 3, 0, 4],\n [2, 2, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 0, 3, 6, 1],\n [-6, -6, -6, -1, 3],\n [-5, -3, -3, 1, 6],\n [0, 1, 4, 2, -1],\n [5, 0, 6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 3, -4, 5, -5],\n [6, -3, -4, -3, -2],\n [5, 4, 3, -1, 2],\n [-1, -5, 0, -3, -1],\n [-1, -6, -1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 5, -1, 3, -6],\n [0, -6, 6, -6, -5],\n [0, -6, 1, -3, -3],\n [2, -6, -1, -3, -1],\n [-5, -6, -2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 2, 0, 6, 1],\n [-6, -1, -4, -5, 0],\n [3, 3, 2, -6, -1],\n [5, 2, 3, -5, -4],\n [2, 2, 1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 5, 0, 1, -5],\n [5, 5, -2, -5, 5],\n [-4, -5, -2, -2, 1],\n [1, -4, -3, 6, 6],\n [1, -3, -6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -5, -6, 5, 3],\n [-2, 1, -1, -6, -2],\n [-6, 2, -6, 3, 4],\n [-4, 4, -4, 3, -2],\n [4, -3, 3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 4, 1, 6, 4],\n [4, 1, -4, 6, 6],\n [5, 6, -4, 3, 1],\n [-1, -5, 0, 3, 3],\n [-6, 0, 5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 2, 1, 5, -4],\n [0, -6, 4, -5, -5],\n [4, 2, 2, 1, 2],\n [-4, -4, 4, -1, 2],\n [-3, 1, 0, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 0, 3, 3, 3],\n [-5, 1, 3, -6, 4],\n [0, 4, -6, 3, -5],\n [4, -6, -1, -1, -6],\n [-5, 2, -3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, -3, -3, 2],\n [1, 4, 4, -2, 5],\n [3, -3, 1, -2, -1],\n [0, -1, 0, 4, 3],\n [-2, 2, -2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 4, -4, -2, -1],\n [-2, -6, -1, 4, -4],\n [-2, 4, 0, 0, -6],\n [-6, 3, -1, 2, 0],\n [-4, 6, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -3, -3, 1, 2],\n [-2, 1, 3, -6, 2],\n [6, -3, 0, 2, 5],\n [2, -1, -4, -5, 1],\n [-4, -1, -3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 1, -1, -6, -6],\n [-5, -5, -1, -1, 0],\n [-6, 0, -3, 3, -1],\n [4, -3, -5, 2, 6],\n [-1, 5, -5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 2, 6, 5, -1],\n [2, -5, 1, -6, 0],\n [6, -6, -2, 2, 4],\n [6, 4, -3, -6, -2],\n [-1, 4, -5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, -4, 4, -2],\n [-2, -1, 2, 6, -4],\n [3, -3, -3, 0, 5],\n [-5, -3, -5, 6, -1],\n [6, 2, 1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 6, 0, -3, 5],\n [-5, -3, 6, 4, -2],\n [-4, -6, -3, 5, 5],\n [-2, -4, 4, 3, -3],\n [-4, 6, -1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 3, -3, -4, 1],\n [4, 1, -3, 0, -2],\n [2, -4, -4, 0, -3],\n [4, 3, -4, 6, 4],\n [5, 5, 1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -3, 2, 2, 5],\n [-5, -3, 4, -4, -4],\n [-5, -6, -4, 1, -4],\n [2, 5, -1, 1, 5],\n [-2, 3, 2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -2, 0, 6, 4],\n [3, 4, 3, -4, -2],\n [-6, 5, -5, 6, 5],\n [-4, -2, 6, 3, -3],\n [6, 1, -5, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -5, -3, -6, -6],\n [-6, -2, 0, -2, -2],\n [-5, -1, -1, -1, -4],\n [3, 5, -5, -5, 6],\n [3, 4, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -4, -2, 1, 6],\n [-2, 0, 0, 3, -2],\n [3, -3, 1, -3, 3],\n [4, 1, -5, -2, -6],\n [-2, -2, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 2, 0, 6, -1],\n [1, -5, 0, -4, 5],\n [-6, -4, -3, 4, -3],\n [-2, 4, -5, -2, 0],\n [4, -5, -5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, 0, -2, 3],\n [-6, -3, -6, 6, 0],\n [-1, 6, -4, -6, 3],\n [-2, -3, -2, -4, 4],\n [-4, -1, 0, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 1, -2, -4, -1],\n [6, -2, -6, -6, 6],\n [-2, 4, 1, 0, -6],\n [-5, 2, -2, 3, 4],\n [2, -5, 1, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -3, 0, 1, 4],\n [2, 0, -4, -2, 1],\n [-4, 3, -3, 0, -2],\n [-6, -5, 2, -5, 0],\n [2, -1, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -6, -4, -5, -5],\n [-2, 6, -2, 3, 4],\n [4, 0, 0, 3, 1],\n [5, -3, -3, 2, 6],\n [3, -2, -5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -3, 6, 3, 3],\n [2, 4, -4, 3, -3],\n [0, 5, 3, -1, 5],\n [-1, -4, -2, 3, 5],\n [-1, -3, -5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, 1, 4, -5],\n [-4, 0, 4, -2, -4],\n [4, 6, -2, 6, 0],\n [6, -1, 1, 5, 1],\n [-6, -1, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -4, -5, -6, 5],\n [4, -5, -5, 6, -4],\n [6, -3, 4, 1, -3],\n [-2, -4, 0, 1, -3],\n [-5, 0, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, 4, -6, -1],\n [1, 6, -2, -1, -2],\n [2, 3, 2, -6, -6],\n [6, 1, -4, 5, -6],\n [-4, -6, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -1, -4, -5, -4],\n [-4, -6, 6, 3, 0],\n [-5, 1, 4, 0, 1],\n [-5, -1, 5, 1, -3],\n [-2, 4, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -1, 0, -5, 4],\n [5, 5, 2, -6, 1],\n [-2, -3, 3, 5, -2],\n [2, -1, -5, -1, 6],\n [2, -1, 3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, -5, 1, 1],\n [-6, -3, -3, -3, 2],\n [2, 5, -1, -1, 2],\n [-6, 6, -4, -3, -1],\n [6, -4, -3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -4, -4, 1, 4],\n [6, 3, -1, 0, 1],\n [-1, -2, 6, 1, -1],\n [4, -1, -4, 3, 3],\n [-2, -2, -4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 3, -1, -6, -1],\n [-5, -6, 0, 1, 6],\n [-4, 0, 0, 2, 2],\n [-5, 5, 5, 4, -6],\n [2, -4, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 5, -3, -4, 3],\n [-5, 5, 5, 6, 3],\n [6, 4, -6, -3, 1],\n [-4, 0, 1, -1, -5],\n [5, 1, -4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -3, -2, -5, -6],\n [3, 5, 4, 5, -3],\n [-5, 2, 4, 6, -1],\n [1, 3, -5, 5, 2],\n [5, 2, -3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -1, 6, 3, 1],\n [1, 1, 4, -2, -2],\n [5, -3, 6, 6, 6],\n [-2, 2, -5, 4, -5],\n [-5, -5, -6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 1, -1, 6, -5],\n [-6, 3, -2, 6, 6],\n [-6, 6, 1, 4, 5],\n [-2, 2, -6, -1, -4],\n [-2, 5, 1, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, 3, -6, 3],\n [-4, -4, 1, 1, 6],\n [-2, -1, -3, 6, 0],\n [-2, 2, -1, -5, 6],\n [6, 6, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -5, 4, -6, 4],\n [-2, -2, -2, -4, -3],\n [6, -2, -4, 1, -4],\n [-4, 1, 5, -1, 3],\n [1, -3, 3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 4, -4, 1, -1],\n [-2, 1, 3, 6, -4],\n [-5, -3, -5, 0, 2],\n [-5, -1, -1, -6, 6],\n [0, 6, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 0, 3, 5, 2],\n [6, 4, 5, -4, 5],\n [-3, 2, -4, -2, -3],\n [5, 1, -6, -6, -5],\n [-6, 2, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -5, -3, -5, 3],\n [0, 4, -4, 5, 0],\n [3, 4, -4, 2, -5],\n [0, 5, -2, 6, -3],\n [5, -5, -6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -5, -5, 2, 0],\n [5, 3, -6, -4, 0],\n [3, -1, 4, 5, 2],\n [-3, 6, -5, 6, -4],\n [1, 4, 1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -6, 2, 3, 6],\n [6, 4, -1, 0, 1],\n [6, 6, -6, -5, -3],\n [3, 3, 2, 0, -6],\n [1, -3, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -4, 0, 5, -6],\n [-1, 5, 6, 5, 1],\n [4, -2, -4, 6, 3],\n [-5, -6, 0, 5, 4],\n [-1, 6, 4, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 4, -4, 4, -5],\n [5, -5, 4, -3, 5],\n [-3, -1, 1, 4, 1],\n [3, -5, -4, 2, -1],\n [-6, 5, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, 2, -4, 3],\n [-5, -2, -4, -3, 2],\n [-4, -6, -6, 4, -4],\n [0, -6, -6, -6, 4],\n [3, 1, 4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -2, -5, 5, 3],\n [-4, 0, -3, 3, -4],\n [-3, -6, -2, 3, 1],\n [3, 4, 2, 0, 5],\n [5, -5, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, -6, -5, 5],\n [2, -6, 0, 3, -3],\n [-2, -6, -2, 2, -2],\n [-2, -1, -4, 3, 2],\n [-6, 5, -5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, -2, -1, -1],\n [-5, 5, 3, -1, 3],\n [-3, -6, -3, 1, 6],\n [-4, -1, -6, 5, -1],\n [1, -5, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -1, -3, 0, 5],\n [4, 2, -1, -5, -3],\n [-1, 2, -6, -6, -5],\n [-5, -3, 4, 6, 5],\n [6, -2, 3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -3, 1, 0, 6],\n [-5, -1, 1, -2, 0],\n [3, 4, 6, -4, -4],\n [0, 1, -1, 0, 2],\n [2, 6, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 5, 6, 5, -6],\n [-5, -1, -1, 2, -3],\n [-2, -3, 3, -5, 5],\n [2, 4, -3, -2, 2],\n [0, 6, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 0, 1, -6, 6],\n [3, -2, 2, 6, -5],\n [-6, 5, -1, 1, 4],\n [6, -1, -1, 0, 3],\n [1, 3, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 4, 5, -4, 1],\n [2, -5, 5, 6, -6],\n [-5, -6, -3, 1, 1],\n [-4, -1, -3, 5, -4],\n [0, 5, -5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 2, 4, -1, 2],\n [-1, -1, -3, 4, 3],\n [1, -4, 6, 5, -4],\n [6, 6, -2, 5, 3],\n [4, -3, -3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 6, -4, 3, 3],\n [2, -2, 0, 1, -5],\n [-3, -4, -6, -3, -5],\n [2, -4, -5, -2, -4],\n [1, -4, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -6, -4, 5, -1],\n [-5, 4, -2, 2, -3],\n [-2, -4, 1, -6, 1],\n [-1, 3, 2, 0, -3],\n [-2, 0, -1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 3, 4, 2, 5],\n [6, 3, 1, -6, 0],\n [4, 6, -1, -4, -2],\n [-5, 4, -6, 3, -1],\n [-3, 6, 0, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -2, -4, -2, 1],\n [0, 2, 3, 6, 2],\n [-4, 2, -5, -3, -3],\n [0, 3, 0, 6, 6],\n [5, 1, 4, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -6, -3, 6, 6],\n [6, 6, -6, 1, -6],\n [-5, 6, 5, 1, 4],\n [-5, -2, -4, -6, 6],\n [-1, 4, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 6, -3, 6, 5],\n [4, 0, -6, 4, 2],\n [-6, -2, 5, -6, 5],\n [3, -1, 6, -3, -2],\n [-3, 3, -6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 6, 1, -6, -5],\n [1, -1, 1, 1, -3],\n [6, -4, 0, -4, 1],\n [2, 1, 1, 2, -1],\n [6, -6, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 0, 5, -6, 4],\n [-4, 3, 6, 6, 6],\n [6, 4, 1, -5, 0],\n [1, 5, -2, 3, 1],\n [-3, 6, 1, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -5, 1, 3, -5],\n [-3, -2, 5, -6, -3],\n [5, 3, -6, 6, 4],\n [0, -3, 3, -5, 3],\n [-1, 6, -2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, -4, 0, -5],\n [1, -3, 6, -2, 5],\n [-1, 3, -2, 2, 3],\n [5, -1, 0, -1, -3],\n [3, 3, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 1, -6, -1, 2],\n [4, 2, -1, -4, 2],\n [5, 2, -2, -2, -1],\n [-3, -6, 2, 0, 0],\n [2, 3, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 6, 4, 5, 3],\n [-1, 5, 3, -6, 6],\n [-6, -4, 0, 4, 1],\n [3, -2, 3, 5, 2],\n [1, 4, -3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 3, 6, 6, -3],\n [2, -6, 2, -1, 6],\n [-3, -3, -6, 4, 6],\n [-6, -5, 1, 0, 2],\n [-5, 1, -5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -1, 1, -4, 0],\n [5, 5, 4, 4, 3],\n [5, -3, 4, 5, -1],\n [1, -6, 0, -5, 6],\n [-5, 4, 1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 3, 6, -4, -6],\n [5, 4, -2, 5, 5],\n [6, -1, 0, 6, 1],\n [-4, 3, -3, -5, 5],\n [4, 4, 3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 5, 6, -5, -2],\n [2, -5, 4, 2, 3],\n [4, -2, 4, 0, 5],\n [-1, 2, -1, 6, -1],\n [1, -4, 4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 3, 5, 6, 4],\n [-5, -6, 0, 2, 6],\n [4, 4, 5, 1, -6],\n [2, -1, 2, -5, -2],\n [-4, -5, -6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 1, 0, -4, 1],\n [-5, 5, 6, 0, 3],\n [1, 0, 2, -3, 4],\n [6, 3, -1, 0, -2],\n [4, 0, -6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -5, -1, 2, -5],\n [-1, -1, 0, 6, 1],\n [6, 2, -3, 2, 2],\n [5, 5, -4, 0, 3],\n [-3, -5, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 1, 5, 5, 5],\n [-5, -3, 2, 2, 4],\n [-2, 0, -1, -4, -6],\n [-6, 5, 3, -4, -6],\n [-5, 0, 4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 4, 1, 2, 3],\n [1, 2, -4, -6, -1],\n [6, -2, -5, -4, 6],\n [0, -6, -1, 6, 1],\n [0, 6, 3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -1, -5, -4, 0],\n [-5, 1, -4, 2, 6],\n [4, -1, -2, 3, 3],\n [4, -2, -1, 1, -6],\n [4, 0, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -2, -6, -6, 0],\n [-6, -6, 5, -1, 1],\n [0, -2, -5, 6, -3],\n [-1, -4, 3, 6, -4],\n [-5, 1, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -2, -6, 2, -5],\n [-5, -3, -5, 5, -6],\n [6, 2, -5, -4, -4],\n [4, 6, -1, 0, -2],\n [1, 2, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -2, -5, 3, -3],\n [5, 2, 6, -2, -3],\n [1, 5, -3, -2, 1],\n [6, 2, 2, -1, 3],\n [-4, 4, -6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, 5, 1, -3],\n [3, -1, 0, 0, 1],\n [-6, -3, -1, 2, -3],\n [0, 2, -1, 1, 6],\n [-4, -5, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 4, 5, -2, 6],\n [0, 0, -2, 4, 1],\n [4, -6, -2, 1, -4],\n [-5, 3, 1, 3, 5],\n [-6, 6, 1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -1, -2, 0, 3],\n [-2, 3, -1, 3, 0],\n [2, 6, 4, -4, 3],\n [4, 2, 5, 6, -5],\n [1, 1, -5, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -6, -4, 1, 2],\n [6, -2, 3, -4, -1],\n [-3, -4, -2, 1, 4],\n [-6, 5, 0, -2, -4],\n [-1, -4, 4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -3, 1, 3, 6],\n [5, 5, 6, 0, 3],\n [-3, 6, 0, 4, 4],\n [5, -4, 4, 1, 2],\n [1, 0, -1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -2, -1, 4, 6],\n [0, 6, 5, 4, -3],\n [-3, 6, 0, 1, -5],\n [-2, -5, -1, 3, -6],\n [0, 0, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 6, 1, 2, 0],\n [4, 5, 3, -4, 2],\n [2, -4, -4, 2, 5],\n [4, 0, 5, -3, -6],\n [2, -3, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 6, 2, -6, 1],\n [-3, 6, -3, 1, -4],\n [0, 0, 6, -3, 0],\n [-1, 4, 5, 5, 4],\n [5, 4, -1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 5, -3, 4, 6],\n [-1, -1, 4, 3, 2],\n [2, -5, 1, 1, 3],\n [1, 0, -1, -5, -4],\n [-5, 5, 2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 3, 0, 6, 4],\n [0, -6, 6, 6, 5],\n [0, -2, 5, -1, 5],\n [3, 5, -2, 6, 6],\n [-3, 6, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 3, 5, -3, 3],\n [-5, -5, 2, -3, -4],\n [0, 5, -2, -6, 3],\n [-4, -2, -5, 1, 5],\n [2, 0, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, 1, 2, 0],\n [2, 1, -6, 3, -1],\n [-4, 6, -5, 6, -4],\n [3, 6, 1, 2, -6],\n [2, 1, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 0, -2, 4, 4],\n [-6, -5, 4, -3, 0],\n [-6, -4, 5, -5, 3],\n [-4, 4, -3, -2, -3],\n [0, -5, -6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, -2, 3, -6],\n [1, 5, 4, -2, 6],\n [-4, 5, 0, -6, 2],\n [4, 4, 1, -4, -5],\n [0, -1, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 6, 3, -1, -3],\n [-2, 3, 4, 5, -4],\n [-4, -1, 3, -1, -2],\n [-4, -6, 3, -2, 0],\n [-3, -3, 2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, 6, 5, 5],\n [-4, -6, 1, 4, 6],\n [-1, -6, 6, -3, -6],\n [-3, 0, -5, -2, -5],\n [-1, -5, -3, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 2, -2, 5, 5],\n [-5, -2, -6, 2, -2],\n [0, 6, -6, 6, 2],\n [-5, 6, -6, -2, -3],\n [-4, 0, 5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -5, 4, -2, 3],\n [-4, 5, -3, 3, -1],\n [1, 3, -3, 1, 2],\n [0, 5, 6, -4, -6],\n [-3, 1, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -1, -5, -3, -6],\n [-1, -1, -1, -5, 4],\n [-3, 2, 3, 0, 6],\n [2, -2, 6, 4, 1],\n [-4, 2, 1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -4, 2, -1, 0],\n [2, 4, 5, 4, -1],\n [5, 2, -6, 6, 1],\n [0, 2, 5, 4, -1],\n [-6, -2, 6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 5, -4, -2, -4],\n [-6, -2, -5, -3, -2],\n [1, 1, 5, -3, -1],\n [-1, -5, -1, 1, 0],\n [5, -3, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -3, -6, 1, 1],\n [-1, -3, 5, 0, 5],\n [6, 1, 3, 5, -5],\n [1, 3, -4, -3, 5],\n [3, 4, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, -4, -2, -5],\n [-3, -4, 0, -1, 3],\n [-5, 2, 2, -5, 1],\n [1, 4, -4, 0, -2],\n [0, -3, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 0, -5, -5, 5],\n [3, 2, -1, 3, 1],\n [-4, -1, -3, 4, 6],\n [2, -5, 0, 5, 0],\n [-6, 5, -6, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -5, -2, 0, -5],\n [0, 0, 6, -2, 0],\n [2, 5, -4, 3, 2],\n [1, -1, -2, 5, -6],\n [4, 0, -6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 5, -4, -2, 2],\n [3, 5, 2, -1, -5],\n [2, -3, 0, -2, 3],\n [-4, -3, -4, -3, 0],\n [1, 1, 3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 4, -6, -6, -1],\n [-5, 6, 5, 5, -3],\n [-2, 5, -3, 4, 6],\n [-4, -6, -3, 0, 5],\n [-3, 0, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -2, -3, 1, 5],\n [6, 6, 0, -4, 6],\n [-2, 5, 3, 2, 0],\n [5, -6, 4, 6, -5],\n [6, -4, 3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -6, -5, -4, -2],\n [-4, 6, -3, -3, 6],\n [-5, 4, -3, 2, 0],\n [4, -6, 5, 3, -6],\n [-2, -2, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 0, 6, -5, -1],\n [3, 6, 1, 5, 5],\n [-4, 5, -5, -6, -3],\n [-5, 4, 2, -2, 4],\n [-4, 0, -6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 5, -1, -4, -3],\n [-6, 2, -5, 2, -2],\n [-2, -6, 6, 3, 1],\n [-4, 1, 2, 0, 1],\n [-2, 5, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -4, -5, 0, 2],\n [4, 0, 6, -2, 0],\n [1, -3, 4, -3, 0],\n [-6, 1, -4, 1, 5],\n [0, -3, 5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, 4, 2, 2],\n [-3, 0, 4, -5, -2],\n [2, 4, 2, 5, -5],\n [1, -3, 0, 3, 0],\n [1, -5, 6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 6, 5, 3, 4],\n [-3, 6, 5, -6, -1],\n [3, -3, -4, -3, 1],\n [-6, 1, -5, 4, -4],\n [5, 6, 2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 5, 0, 2, 4],\n [1, 4, 0, -4, -5],\n [-6, 3, 4, -6, -1],\n [1, 4, 1, -4, -4],\n [-2, -1, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -5, -2, -5, 5],\n [1, -5, 4, -4, -5],\n [6, -4, 1, 6, 3],\n [-4, -3, 6, -4, 2],\n [3, -2, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -2, -1, 5, -1],\n [3, 1, -2, -3, -4],\n [2, 4, 4, 3, 3],\n [-4, 5, -2, 4, -3],\n [5, 3, 3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -5, 1, -5, -6],\n [-6, 5, -3, 3, -2],\n [2, -3, -2, 3, 6],\n [1, 4, 1, 0, 2],\n [-2, 4, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 0, -6, -3, -5],\n [4, -1, 6, -2, 0],\n [-3, -6, -2, -1, -2],\n [-4, 4, 3, 6, -4],\n [6, 0, -6, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 6, -4, -2, 4],\n [-4, -5, -6, -4, 5],\n [5, 5, 6, 4, 4],\n [4, 5, -1, -1, -2],\n [1, 2, -6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, -3, 6, 1],\n [6, 0, -4, 1, -4],\n [-2, -1, -1, 4, 5],\n [3, -4, -5, -1, -6],\n [5, -3, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 5, -2, -4, 1],\n [-3, 3, 2, 5, -5],\n [0, 3, 5, -1, -3],\n [1, 6, -1, 1, -2],\n [-1, 3, -5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 0, 1, 1, -6],\n [4, -1, -3, -1, -6],\n [5, -5, 0, 0, 1],\n [-5, 2, 0, 4, -6],\n [-4, -5, 0, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 1, 2, -6, -4],\n [-2, 6, 6, -3, 4],\n [5, 3, 4, -3, 3],\n [5, 5, -4, -1, 5],\n [2, -2, -3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -6, -6, 1, -3],\n [1, -4, 2, -6, -5],\n [-3, -1, -6, -2, 2],\n [-4, -2, 1, 6, 2],\n [-2, -5, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 2, 0, 2, -1],\n [-5, 5, -1, 2, -4],\n [6, -6, 3, 3, 3],\n [-2, -6, 4, 4, 4],\n [5, 2, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -1, -5, 2, 3],\n [-4, -5, 3, -5, 1],\n [2, 2, -3, 4, 0],\n [4, 1, -5, 4, 3],\n [-2, -6, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 6, -6, 4, -5],\n [-1, 0, 5, 2, 4],\n [2, -4, -4, 3, 1],\n [-5, 1, -5, 0, 5],\n [3, 3, 2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 4, -6, -1, 4],\n [3, 0, 5, 0, 1],\n [-2, -4, -3, -1, -6],\n [-3, -3, -3, 1, 1],\n [0, -3, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 1, 4, 0, 2],\n [-2, 5, -1, 2, 4],\n [1, -3, -5, 6, -2],\n [3, 0, -6, 0, 6],\n [-2, 1, -5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 4, 5, 3, -4],\n [3, -1, 1, -6, -5],\n [-4, -4, -3, 5, 2],\n [6, 3, 5, -1, 0],\n [-3, -1, 4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 1, 5, 6, 3],\n [-4, -6, -5, -1, 5],\n [0, 3, 3, 1, 2],\n [-1, -6, -1, 5, -1],\n [5, -3, 4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -3, -3, -3, -4],\n [2, 6, -3, -6, -3],\n [-2, 3, 5, 3, 0],\n [-2, 3, 3, 6, -4],\n [-4, 1, -6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -6, 5, 1, -1],\n [6, 5, 4, -5, 4],\n [-3, -6, -4, 5, 1],\n [-1, 6, -6, 0, -4],\n [-4, -1, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, -1, -4, 2],\n [-1, -3, 0, 0, 4],\n [0, -5, 6, -2, 4],\n [1, 2, -2, 4, 0],\n [6, 6, -5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 1, 3, -1, -3],\n [-3, 1, 0, 3, -5],\n [5, -1, -4, -2, 1],\n [-1, 3, -6, -1, 6],\n [-5, 0, 1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 2, -6, -2, 3],\n [-1, 4, -4, -6, -1],\n [5, 5, -1, -6, -2],\n [-1, 2, -5, 3, -2],\n [-6, -6, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -3, -2, 1, -4],\n [0, -6, -1, -1, -5],\n [-3, 1, -3, 1, 2],\n [0, -6, -3, 0, 3],\n [-4, -1, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -3, 6, 0, -6],\n [1, 4, -3, -4, 5],\n [0, 3, 6, -5, 3],\n [-3, -6, 0, -2, -3],\n [0, -6, 0, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, -1, -1, -5],\n [2, 2, -6, -3, -6],\n [-5, 4, -6, 6, 4],\n [5, -3, -4, -2, -4],\n [5, -1, 5, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 5, 3, -6, -4],\n [5, -6, -3, -5, 2],\n [-3, -5, -6, -4, -5],\n [-4, 4, -1, 4, 3],\n [4, -5, 6, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -3, 3, -6, -4],\n [4, 0, 2, 5, -4],\n [2, -1, -3, 4, -5],\n [0, -6, 4, 1, 0],\n [-6, 6, 3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -5, -6, -4, -4],\n [-1, 6, -5, -4, -1],\n [3, 1, -6, 4, -3],\n [-3, -1, 0, -1, 1],\n [6, -2, -2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 2, -1, 3, -4],\n [5, 0, -1, -1, 1],\n [-5, 5, -6, -4, -3],\n [4, 6, 4, 4, 3],\n [5, -5, 5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -4, -3, -1, 6],\n [-4, 2, 1, 4, 3],\n [-1, -1, 0, 0, -4],\n [3, -5, 5, 4, -1],\n [2, -1, -3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 2, -2, 0, 0],\n [2, 2, 1, 6, 2],\n [4, -5, 1, 2, -3],\n [-4, 1, 0, -2, 3],\n [-3, 2, 0, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -3, -4, 3, -3],\n [3, -4, 2, -1, -5],\n [3, 6, -5, -1, -3],\n [6, 3, 2, 6, 6],\n [-5, 5, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 6, 4, -4, 5],\n [2, -6, -6, -4, 6],\n [5, 2, 3, 6, -6],\n [-6, -4, -6, 0, 1],\n [-1, 5, -5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -3, 1, -4, -6],\n [-4, 6, 6, -1, -5],\n [6, -6, -1, 0, 2],\n [6, -3, -3, -4, -5],\n [1, 0, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, 5, -6, 3],\n [5, -1, 1, 2, -6],\n [5, 6, 4, 2, -1],\n [1, -3, 5, 1, 5],\n [5, 0, 6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -4, 3, -6, 2],\n [-3, -1, 1, 5, 2],\n [1, 2, -6, 6, 4],\n [-3, 3, -3, 2, -4],\n [-6, -2, 2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -6, -2, 0, 3],\n [-4, 3, -2, 1, -5],\n [3, 1, 6, 4, -1],\n [-6, 1, 5, 6, 2],\n [-5, -5, 2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -1, -6, 5, 3],\n [-4, 5, -2, 3, 5],\n [-1, 0, -5, -6, 1],\n [0, -1, 0, -2, 2],\n [5, 2, 0, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -6, 5, -1, -3],\n [-1, 5, 3, 3, -4],\n [-1, -4, -2, 1, 0],\n [-5, -2, 0, 2, 0],\n [2, 3, -5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -1, 3, 3, -4],\n [4, 6, -4, -5, -1],\n [-4, 0, 0, -3, -3],\n [2, 5, 4, -3, -3],\n [-4, -4, -6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 1, -2, -3, 1],\n [1, -4, -2, -2, 4],\n [2, 1, -1, -6, 6],\n [-2, 2, -5, -5, 6],\n [0, -4, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -6, 0, 6, -4],\n [-1, 0, -3, -3, 3],\n [4, 2, -5, 5, -1],\n [-4, -1, 2, 1, -4],\n [0, 1, 5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -6, 5, -2, -3],\n [4, -1, 1, 4, 3],\n [1, 3, -6, -1, 4],\n [-4, -1, -4, -2, 4],\n [0, 2, -3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 2, 6, -6, -6],\n [5, -5, -2, -6, 4],\n [-1, -6, -1, 1, -5],\n [-3, 5, 1, 2, 2],\n [2, 6, -3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -4, 2, -2, -6],\n [1, -6, 6, -4, 3],\n [0, 3, 6, 2, -2],\n [-5, -3, -1, -2, 1],\n [0, 5, -6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -6, -3, 4, -4],\n [-1, 6, 1, 1, -4],\n [5, 2, -2, 6, -2],\n [1, 5, 1, -4, -2],\n [-5, 2, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -3, 4, -2, -2],\n [4, 6, 0, -3, -2],\n [-5, 1, -5, 5, -5],\n [3, -4, -5, -4, 5],\n [-6, 4, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 2, -4, -5, -5],\n [4, -1, -2, 4, 1],\n [1, 0, -2, 2, 3],\n [-5, 0, 5, 1, -3],\n [1, -6, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -1, 5, 1, 0],\n [-1, -3, 4, -6, 2],\n [-3, 4, -5, 4, 3],\n [2, -1, 3, 6, 3],\n [0, 0, -3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -3, 6, -6, 1],\n [3, 0, -3, 5, -2],\n [5, -2, 5, 6, 4],\n [6, 5, 0, -6, 6],\n [6, 1, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 6, -2, -3, 1],\n [2, 1, -6, 5, -4],\n [-4, -1, -2, -5, -2],\n [6, 3, -1, 4, -6],\n [-4, -5, 1, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, 0, -3, -2],\n [6, 1, 0, -5, 2],\n [-2, 1, 6, -3, -4],\n [-2, -6, -1, 5, -3],\n [6, -2, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -4, 4, 1, -6],\n [6, -4, 1, -1, 6],\n [3, 4, -4, -3, 2],\n [3, 0, -4, -1, 6],\n [-3, -1, -3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 2, -1, 4, -5],\n [2, -1, -4, 0, 1],\n [6, 3, -6, -3, 2],\n [3, 5, -6, 6, -5],\n [6, 1, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 4, -1, 2, -1],\n [-6, 2, -1, 3, -6],\n [0, 6, 2, 2, -2],\n [6, -4, -3, 3, 1],\n [3, -1, -3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 2, 6, 4, 6],\n [6, 6, -3, 3, -1],\n [-3, -6, 5, 4, 1],\n [6, 0, -2, 1, -1],\n [3, -2, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 0, 1, 1, 3],\n [3, 0, 1, -2, 6],\n [-4, -5, 2, -3, -2],\n [2, -2, 1, 3, 3],\n [-1, -3, 2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 6, 6, -4, 0],\n [4, 3, -5, 1, 0],\n [4, -3, -2, 0, -4],\n [-1, 4, 4, -3, 2],\n [1, -6, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -4, 2, 2, 3],\n [0, -5, 5, -2, -2],\n [-6, -4, 0, 2, 2],\n [3, -2, -5, -6, -4],\n [4, 3, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 2, -2, -3, 6],\n [0, -1, -2, -2, 3],\n [-5, 2, 0, 0, -4],\n [4, 1, 2, -3, 0],\n [-6, -3, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -5, 1, 3, 0],\n [0, -6, -6, 1, -1],\n [-2, 6, -1, -3, -3],\n [0, -3, 4, 5, -6],\n [2, -2, -2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, -3, 2, 0],\n [4, -2, 6, 4, -1],\n [-1, -1, -5, -1, 4],\n [2, 5, 0, -3, 2],\n [0, -3, 5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, -6, -4, -1],\n [3, 5, -2, -4, 1],\n [0, 2, 3, -4, 4],\n [-3, 1, -6, 1, 1],\n [6, -6, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -2, 6, 3, -4],\n [-4, 6, -5, 1, -4],\n [0, 0, 0, 0, 3],\n [6, 2, 6, -2, 6],\n [-4, 4, -2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 2, 2, 5, 0],\n [-1, -3, 4, 4, 2],\n [-6, 4, -5, -2, -5],\n [-1, -5, 2, -6, -4],\n [3, -3, 6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -1, -3, -5, -3],\n [-1, 2, -1, 6, 3],\n [-6, -2, 2, -1, -3],\n [0, -4, 6, -6, 0],\n [3, 5, 6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -5, 2, 5],\n [6, 5, 5, 5, 3],\n [4, 2, 5, 5, -4],\n [-5, 0, -6, -4, 2],\n [3, -3, -6, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 0, 6, -2, 4],\n [-2, 5, -6, -3, 6],\n [-1, 3, -5, -3, -6],\n [-5, -6, 4, 5, -2],\n [2, -4, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 4, -1, 6, 2],\n [-1, -4, -4, 0, -5],\n [3, -3, -5, -3, -6],\n [-2, -2, 2, -3, -2],\n [-1, 3, 3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, 6, 6, 5],\n [-3, -2, 6, -5, -5],\n [-1, 6, -1, -4, 2],\n [6, 0, 0, 5, 6],\n [6, 4, 1, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 6, 1, -3, -1],\n [-5, 3, -3, 6, 3],\n [3, -3, -5, -2, 0],\n [-4, -5, -3, 5, -2],\n [-5, -4, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -3, -2, 5, -6],\n [0, -1, 2, 1, 1],\n [6, 5, -4, -5, 6],\n [4, 3, -2, 0, 6],\n [4, -3, -1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 1, 3, 3, 6],\n [1, -2, -5, -2, -5],\n [4, 0, 2, -1, 5],\n [4, -2, -6, -1, 1],\n [-3, 5, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 4, -5, 2, 0],\n [6, 5, -1, 1, 3],\n [-3, -1, 3, -3, 6],\n [-4, -2, 6, -2, -3],\n [0, -6, 0, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, 4, 0, 4],\n [2, 0, 0, -5, -5],\n [-1, 0, 0, -4, -5],\n [-2, 1, -5, 5, -5],\n [4, -2, 6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -2, 3, -5, -4],\n [5, 3, -2, 1, 1],\n [6, 4, 5, 3, 5],\n [0, -2, -2, 2, -6],\n [-4, -5, -1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 5, 5, -1, -5],\n [-3, -5, -6, -4, 6],\n [6, 5, -3, -6, 1],\n [-3, 4, -4, -4, 5],\n [1, 2, -1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 5, 5, 1, -1],\n [-5, 3, 5, -3, -4],\n [6, -6, -1, 1, -5],\n [-4, -1, 1, -2, -6],\n [-4, -5, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 5, 0, -3, -4],\n [1, 5, 1, -5, -4],\n [5, 0, -4, -1, 4],\n [-6, 0, 5, 3, 1],\n [1, -6, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -4, -1, -6, -5],\n [5, -5, 2, 0, 1],\n [6, 2, -3, -4, 6],\n [-4, 2, 1, 2, 1],\n [-6, 2, -4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -5, -4, 4, 4],\n [0, 4, -5, 0, -3],\n [4, -5, 4, -3, -6],\n [-5, -1, 4, -6, -6],\n [2, 0, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 4, 0, -5, 5],\n [4, 3, 3, -6, -1],\n [-4, -2, -5, 3, 0],\n [6, 2, -3, 3, 5],\n [-4, 3, -4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 3, 3, -4, -1],\n [5, 0, 5, 4, -4],\n [-3, -1, -3, -1, -6],\n [-3, 1, -1, 1, -1],\n [-6, 6, 4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -5, -4, 4, 6],\n [6, -2, 2, 6, -2],\n [-5, 4, 1, 1, 1],\n [5, 1, -5, 3, 5],\n [-3, 2, -3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, -3, 2, -3],\n [-6, 1, 3, -2, -6],\n [0, 6, 4, 2, -6],\n [-6, -6, -2, 0, 4],\n [-1, -2, -3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 6, -5, 3, 1],\n [-5, 6, -6, -2, -4],\n [5, 3, 6, -6, 5],\n [-2, -6, -5, 6, 2],\n [-2, -4, 6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 6, 1, -1, 1],\n [5, -4, 0, 4, 0],\n [4, -3, 5, -6, -5],\n [-1, 4, 4, -3, -4],\n [4, -3, -4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 3, -3, 6, -6],\n [4, 3, 0, 0, 4],\n [-1, 2, 0, 6, -4],\n [-1, -3, 6, 5, -5],\n [4, -1, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -2, -4, 3, 6],\n [1, 2, -5, -5, 0],\n [4, -6, 6, -5, -4],\n [-4, 4, -5, -5, 6],\n [-4, 1, 6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 1, 0, 3, -3],\n [4, 0, 4, -1, 3],\n [-1, 5, 1, -6, -4],\n [-3, -6, 2, -6, -6],\n [-3, -4, 5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 5, -6, -2, -5],\n [-4, 0, -3, -1, 1],\n [-2, -3, -6, -1, 2],\n [-2, 1, 3, 4, 4],\n [0, 0, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 0, 1, -4, -4],\n [6, 4, 4, 6, 2],\n [-3, 3, 0, -1, 6],\n [1, 1, 0, -4, -1],\n [6, -2, -5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 5, 6, -1, 1],\n [0, 0, -5, 5, 6],\n [4, 4, -1, 2, 5],\n [4, 0, 3, -6, -6],\n [6, 1, 5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -6, 6, -6, -3],\n [2, -5, -6, 0, 1],\n [0, 0, -1, 4, -5],\n [-1, 6, 6, 2, -4],\n [-5, -2, -4, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 1, -1, -4, 1],\n [6, -1, -2, 6, -4],\n [-3, 2, -5, 2, 3],\n [3, 5, 0, -1, 6],\n [1, -4, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 5, -3, 6, 0],\n [-2, 1, -4, 0, 0],\n [-1, -4, 0, 4, 6],\n [3, 0, 3, 6, 1],\n [-2, 6, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -6, 0, -3, 1],\n [-2, -2, -4, 4, 3],\n [-3, -5, 2, -4, -5],\n [5, 1, -4, -3, 5],\n [6, 5, -5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 0, 0, 2, -4],\n [0, -3, -6, -3, -2],\n [4, -2, 3, 6, -3],\n [-2, 2, 4, -6, 2],\n [2, -6, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -3, -3, -4, -4],\n [-6, 3, 5, -2, 4],\n [-1, 5, -6, -5, -1],\n [5, -4, -6, 1, 3],\n [-4, 1, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 2, 5, 4, 4],\n [4, -1, 5, -1, -4],\n [-4, -5, 0, -5, 2],\n [6, 0, -2, -6, -1],\n [-5, 3, -5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -2, 3, 5, 0],\n [5, 5, -3, 1, 0],\n [0, -3, -4, 0, 1],\n [4, -3, -3, 0, -4],\n [4, 3, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 1, -6, -4, -3],\n [-3, -1, -5, -3, 4],\n [-4, 6, -4, -6, -2],\n [-1, 1, 4, -5, 2],\n [-1, 0, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -4, -5, 1, 6],\n [2, 2, -6, 4, 3],\n [-3, -1, -4, 2, 5],\n [-4, -6, 1, -2, -1],\n [-3, 4, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -2, -5, -4, -5],\n [2, 0, -4, 2, -1],\n [-3, 1, 0, 3, 4],\n [4, -4, -5, 6, -5],\n [1, 1, 0, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -4, -1, -1, 4],\n [3, 3, -1, 5, -5],\n [4, 0, 1, 1, 1],\n [-1, 1, -4, -1, 6],\n [-1, 4, -5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 0, -6, -5, 5],\n [6, 5, -2, 4, 5],\n [0, -6, 6, 4, -1],\n [4, 0, 1, -2, 5],\n [-4, -2, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 1, 2, -4, 1],\n [-1, -5, 2, -6, 3],\n [3, -2, -6, 0, 6],\n [-5, 0, -5, 5, 1],\n [-6, 2, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 2, 5, -2, -1],\n [-6, -1, 3, -5, -5],\n [4, 5, -1, -5, -5],\n [-5, 0, -1, -4, 4],\n [5, -4, -2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -4, -2, -1, -2],\n [-3, -3, -2, -1, 3],\n [1, 3, 5, 0, -1],\n [5, -4, -5, 5, 5],\n [4, 3, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -1, -5, -2, 0],\n [2, 2, 2, -3, -6],\n [-4, 4, 4, 4, -2],\n [5, 0, 2, 1, -6],\n [-1, 0, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 0, -2, 2, 6],\n [2, -4, 3, -2, 5],\n [6, 5, 0, 4, -2],\n [-4, 5, -1, 0, -4],\n [2, 6, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 4, -5, -6, 6],\n [-2, -5, 4, -3, 3],\n [-4, 5, 5, -1, 3],\n [3, -5, 3, -1, 6],\n [2, 4, 0, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -3, -1, 6, -2],\n [4, 6, -6, -2, -5],\n [3, 6, 6, -5, 0],\n [-1, -2, 3, -2, 6],\n [5, -3, 1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, 4, -3, -1],\n [0, -2, 3, 1, 6],\n [-1, -1, 1, -4, 2],\n [5, -6, 6, 4, 6],\n [5, -4, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -3, 1, 0, 4],\n [-6, 4, 6, -5, 4],\n [5, 4, 1, -5, 5],\n [5, -6, -4, -3, -3],\n [-1, 1, -1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 1, -1, -4, -6],\n [2, 0, 5, 0, -2],\n [6, -1, -2, -5, -6],\n [-1, -6, -2, 2, -6],\n [-4, -5, -3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 1, 5, -3, 4],\n [1, 6, -3, -5, -6],\n [4, -5, -6, 4, -2],\n [4, -2, -5, -2, -2],\n [-1, 5, 4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -3, -1, 3, 3],\n [-2, 5, 3, 2, 3],\n [-5, -4, 4, -1, 0],\n [-2, -3, -2, -4, -5],\n [0, 2, 3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -6, 5, -3, -3],\n [-5, 2, 4, -2, 4],\n [-3, 5, 1, 5, -3],\n [0, 4, 4, 2, -6],\n [-6, 1, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 5, 6, -4, -6],\n [-4, -4, -1, 1, -1],\n [1, -3, -6, -5, 5],\n [-6, -5, -1, 5, 5],\n [4, 0, -2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 0, -6, -3, -2],\n [-6, 5, 6, -1, -4],\n [-1, 0, 5, -5, -5],\n [-3, 6, -3, 5, 2],\n [-2, 3, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, 4, 3, -4],\n [5, 6, 1, -1, 3],\n [5, -6, -2, -3, 3],\n [-3, 1, 5, 6, -3],\n [0, 4, 3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 4, 0, -2, 4],\n [6, -3, -5, -4, -4],\n [3, 2, 1, -5, 5],\n [4, 4, 5, 5, 2],\n [1, -1, 1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, -6, 4, 2],\n [3, -4, 3, 3, -1],\n [3, 0, 1, 2, 1],\n [-6, 1, -6, 0, 4],\n [3, -1, -1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -2, -1, 2, 0],\n [6, -6, -3, -3, 0],\n [-1, 4, 2, -4, 6],\n [2, -1, 2, 0, 3],\n [0, 5, -5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 0, 3, 5, -6],\n [-2, 5, 5, -3, -1],\n [-4, 5, 6, -1, 4],\n [-1, 6, 4, -2, 5],\n [-6, -1, -4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 3, -3, -2, -2],\n [2, -1, -3, -4, 0],\n [1, 3, 4, 4, 2],\n [3, 2, -1, 4, -1],\n [2, 3, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, 0, -6, -6],\n [0, -6, -6, -6, 4],\n [4, 3, 5, 2, -1],\n [2, -6, -6, 3, 1],\n [-5, -1, 1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, 3, 5, 5],\n [3, 6, -3, -3, 5],\n [-5, 3, 3, -1, 2],\n [6, 6, 5, 5, 6],\n [5, -5, -6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -2, -5, -3, -5],\n [5, 0, -6, 3, -1],\n [-4, -5, 5, -1, 0],\n [6, -6, 2, -3, 5],\n [-4, 4, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -1, 2, 0, -3],\n [4, 5, 0, 1, 6],\n [-1, 3, -1, 2, -5],\n [6, 1, -4, 4, 4],\n [-4, -3, 6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -5, 6, 2, 1],\n [1, 2, 1, 3, -2],\n [-1, 4, 2, 2, 4],\n [6, 0, -1, -1, 0],\n [-3, 3, 1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 0, 3, 1, 4],\n [-3, -3, -1, 1, -2],\n [5, -5, -3, -5, 0],\n [1, -2, -4, -4, -1],\n [1, -5, 3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -2, -5, -4, -5],\n [-2, -1, 5, 6, 2],\n [6, 3, -3, -3, 1],\n [6, -6, -5, 6, -1],\n [4, -6, 0, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, 1, -4, 2],\n [-4, 0, -4, 6, 0],\n [-1, -5, -4, 0, -4],\n [2, 0, 3, 5, -2],\n [6, -1, 6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, -1, 4, 3],\n [3, -1, 6, 0, 3],\n [1, 2, -2, -3, 4],\n [6, 3, 1, -3, -5],\n [-2, -4, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -2, 4, 6, -3],\n [5, 4, -2, 5, 5],\n [-6, -1, 3, -6, -5],\n [1, 2, 0, -1, 1],\n [-5, -3, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 0, 1, 0, 5],\n [-4, -5, -6, -4, -5],\n [-3, 3, -3, 5, -4],\n [0, -1, 0, 5, -1],\n [3, -2, -1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -6, -1, 4, -3],\n [-2, 6, 2, 4, -6],\n [5, 1, 5, 0, -3],\n [0, -1, 5, 1, 5],\n [3, 4, -5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -2, 3, 2, -3],\n [4, -6, -2, -3, 4],\n [-5, -5, 2, -2, 4],\n [-1, 0, 6, -1, 3],\n [6, 5, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -2, 2, -2, -1],\n [-2, -4, 3, 1, 0],\n [3, -6, 0, 5, -4],\n [2, -3, 3, -2, 1],\n [4, -6, -1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -2, 0, 0, 4],\n [-5, 2, 1, 2, -3],\n [-1, -3, 6, 6, 2],\n [-6, -3, 2, 0, -4],\n [-6, 4, 1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 2, -5, -5, 3],\n [-2, 6, -6, -2, -2],\n [-1, 4, -1, -5, -3],\n [-5, 2, 2, 0, 1],\n [3, 0, 1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 6, 1, -6, 0],\n [-6, -5, 0, 3, 0],\n [-4, -4, 6, -6, 6],\n [0, 1, -6, 5, 0],\n [-5, -5, 4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 5, -3, 3, -3],\n [2, -2, 1, 3, -2],\n [-1, -5, 1, -2, 6],\n [1, -1, 4, -2, 5],\n [1, -3, 3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -3, -6, 0, -4],\n [-4, 0, 4, -5, 4],\n [-3, 4, 1, -6, 2],\n [-5, 4, 4, 5, -2],\n [-3, -4, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, 3, 3, 1],\n [1, -4, -2, -1, -3],\n [3, -1, -3, -5, 1],\n [4, -2, -6, -5, 2],\n [4, 3, 4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 0, -5, -4, -2],\n [-2, -4, 0, 2, 5],\n [4, -5, 1, 6, 2],\n [-4, 0, 6, 5, -1],\n [2, -2, 6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -1, -4, -3, 2],\n [1, 2, 2, -3, -1],\n [-3, -4, 2, 1, -6],\n [-2, -4, 0, 0, 6],\n [2, 6, -5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, 3, 2, 4],\n [-4, -6, 3, -5, -3],\n [-4, 6, 0, -6, 3],\n [-1, -3, 5, 2, 0],\n [2, -6, -1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 2, -5, 1, -1],\n [-1, 4, 2, -3, -2],\n [-4, 1, 1, -5, -6],\n [5, -6, -3, 6, 0],\n [5, 6, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 2, -5, 3, -1],\n [0, 3, -6, 6, 5],\n [-4, -3, -1, 0, -5],\n [-6, 6, 1, 3, -1],\n [1, -3, 3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -5, -6, 4, -6],\n [-5, -2, -3, -6, -1],\n [-4, -5, -6, 0, 6],\n [4, 0, 4, 6, -2],\n [0, 6, -3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -1, -4, 2, -6],\n [-5, -6, 5, -6, -3],\n [-4, -1, 6, -1, -1],\n [3, 0, -3, 4, 3],\n [-2, -2, 0, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 3, -1, 0, -4],\n [6, -2, -4, 0, 3],\n [-2, 1, -1, 6, 1],\n [1, 0, -4, -5, 4],\n [5, 3, 5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -6, -1, 0, 6],\n [-2, 3, -1, -1, 6],\n [5, 4, -1, -1, 1],\n [5, 6, 4, -6, 1],\n [-1, 3, -3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 2, 4, -3, 0],\n [2, -3, 0, -3, -2],\n [-4, 2, 1, 3, -5],\n [-2, 6, -2, -6, -6],\n [2, 0, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 3, 1, -6, 1],\n [2, -5, 5, -4, -3],\n [1, -1, -2, 0, -6],\n [-4, -1, -6, 5, -5],\n [0, 3, 5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 2, 3, 3, 4],\n [4, -6, -5, -2, 2],\n [-3, -1, 3, 3, 4],\n [-2, -5, -4, 6, 6],\n [4, 4, 3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 3, 1, 3, -1],\n [2, -4, 6, 3, -5],\n [4, -1, 1, 4, -5],\n [4, -4, -3, 0, 4],\n [4, -6, 4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, 0, 0, -3],\n [3, -2, 5, -3, 6],\n [6, 0, 3, 1, -6],\n [0, 1, -4, 1, 4],\n [0, 0, -5, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -3, -4, -3],\n [3, 3, 6, 5, -3],\n [3, 6, -1, 6, 1],\n [-3, 2, -4, 2, 2],\n [1, 6, -2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 5, -4, 3, -3],\n [-3, 3, -4, -5, 2],\n [-6, 2, -2, 0, 5],\n [-6, -5, 3, 3, 6],\n [0, -5, 2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, -5, 4, 5],\n [6, 0, -4, -4, 5],\n [-4, 5, 0, 1, -6],\n [-2, 3, 2, -4, 4],\n [0, -4, -2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 4, -1, 6, 1],\n [-6, -2, -4, 1, 2],\n [0, -2, -3, -5, 0],\n [1, 0, -1, 6, 0],\n [4, 4, -5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 3, 4, -6, -1],\n [1, 0, 0, 5, -2],\n [-5, 1, -3, 3, -3],\n [4, -1, -6, -5, -4],\n [6, 1, -6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, -3, -3, -4],\n [0, -3, -4, -4, -3],\n [5, -5, -1, 5, 4],\n [0, -3, 6, -2, -3],\n [1, 5, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -6, 2, -5, -4],\n [5, 0, -1, -2, 6],\n [-1, -2, 3, 6, -1],\n [4, -5, -5, -1, -1],\n [-2, 5, 5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -6, 4, -1, -1],\n [3, 0, -5, -4, 1],\n [-3, 0, -4, -6, 1],\n [5, -5, -1, -4, 2],\n [0, -1, -5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 5, -5, 5, -3],\n [-6, 3, -1, -1, 1],\n [2, 6, 3, 3, 2],\n [-3, 1, -3, 4, -6],\n [6, 1, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -6, -5, 5, -4],\n [4, 6, 1, 5, 0],\n [1, -2, -1, 3, -6],\n [0, -2, 4, 6, -3],\n [-3, 2, 0, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -2, 4, -4, 2],\n [1, 1, 1, -4, 4],\n [1, -3, -4, -2, 1],\n [1, 4, -1, -4, 3],\n [6, -5, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -4, 1, 2, -2],\n [0, 5, -1, 3, -1],\n [6, 6, 5, -1, 5],\n [2, -4, 4, -4, 5],\n [3, -6, -1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 4, 1, 3, -4],\n [6, -5, 5, -3, -4],\n [4, 2, -5, -2, 4],\n [-6, -3, -1, -1, 1],\n [3, 0, 3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 4, -4, -3, 0],\n [2, 1, -2, 3, -5],\n [1, 4, -4, 2, -3],\n [6, -5, -1, -4, -6],\n [-4, -2, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 3, -4, 2, -4],\n [3, 6, 5, -6, -3],\n [-5, -2, -1, -3, -2],\n [6, -5, 0, -3, 6],\n [-4, -5, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 5, -6, -6, -6],\n [2, -3, -6, -6, 0],\n [-5, -1, -4, 3, -4],\n [-3, -5, -5, 4, 4],\n [-6, -3, -1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 4, 6, 6, 0],\n [-2, 2, -5, 3, -6],\n [5, 4, -6, 3, -3],\n [-1, -6, 5, 4, -3],\n [3, 0, -6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -3, 4, -4, 3],\n [-3, -1, 4, -1, 3],\n [-1, 3, 0, 2, 4],\n [-2, 0, -6, -1, 6],\n [1, -3, 0, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 4, 5, -2, -1],\n [0, 0, -6, 6, 3],\n [2, 2, 6, -5, 5],\n [-1, 1, -4, -6, 0],\n [2, -3, -5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -2, -2, -2, 2],\n [6, -5, 5, 0, -4],\n [5, -2, 1, -3, 5],\n [-6, -1, -3, 3, -2],\n [-2, -6, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 5, -1, -4, 4],\n [3, 3, 1, 5, -1],\n [-1, -6, 0, -3, -6],\n [-3, 0, -4, 0, 4],\n [4, 1, 2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 1, -3, 5, 5],\n [4, 3, -3, -6, 3],\n [3, -6, 2, -6, 0],\n [-4, -6, -6, -5, 0],\n [0, 2, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 0, -2, -2, -6],\n [-6, -2, 0, 1, -5],\n [-4, -4, 6, 5, -1],\n [-4, -4, 2, -1, -3],\n [0, -5, -2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 1, -4, 2, 6],\n [-5, 2, 6, -4, 0],\n [2, -4, -3, -6, -6],\n [-1, 4, 5, 4, -2],\n [1, -4, -2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 2, 3, -6, -5],\n [-3, -3, -4, -2, -5],\n [-3, -3, -3, 0, -4],\n [-2, -1, 4, 3, -2],\n [6, 3, -5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 0, -3, 3, -3],\n [-4, -2, 3, 6, -1],\n [-4, -3, 3, 2, -4],\n [1, -5, 6, -3, -6],\n [2, 4, 6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 6, 0, -6, 5],\n [-3, 4, 1, 0, 1],\n [5, 1, 0, -6, -3],\n [-4, 5, -5, 0, 5],\n [4, -5, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -6, 4, -5, -5],\n [-3, -3, -3, 1, -2],\n [3, 5, -2, -3, 5],\n [3, -3, -4, -4, -1],\n [-5, 1, -1, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -6, -3, -1, 4],\n [-3, -6, -6, -6, -4],\n [5, 2, 0, 1, 5],\n [1, 0, 1, 0, 2],\n [3, 4, -5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -2, -4, -6, -5],\n [-1, 2, 4, 0, -6],\n [-1, 0, -4, 1, -5],\n [-3, 4, -4, 0, 4],\n [5, -6, 3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 4, 3, -5],\n [-3, 5, -5, -4, 1],\n [-2, 0, 6, 6, 4],\n [-2, -3, 1, -2, 6],\n [3, 5, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, -5, 4, 4],\n [2, -2, 0, -5, 0],\n [-6, -3, 5, 4, 2],\n [-2, 6, 6, 4, -4],\n [4, -5, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -2, 4, -2, -4],\n [-4, -3, -5, 3, -6],\n [-1, 3, 3, -2, -2],\n [-1, -1, 2, 4, -2],\n [5, 3, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, -2, 6, 3],\n [6, -2, -2, -6, -6],\n [5, 6, 1, 3, -1],\n [3, -4, -5, 3, 4],\n [-1, 6, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 0, 4, -6, 0],\n [0, -6, 0, -3, -1],\n [6, 0, -5, 0, 2],\n [-5, -6, 6, 1, 3],\n [-4, -6, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -2, -4, 6, -3],\n [-6, -2, 2, 2, 0],\n [3, 2, 1, 1, -4],\n [-6, 2, 4, 6, 0],\n [-4, 6, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 0, 2, -6, 6],\n [-5, 4, 4, 1, 3],\n [-3, 4, 2, -3, 1],\n [0, 2, -4, -4, 4],\n [3, -4, 2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -1, 4, -3, -3],\n [0, 5, 2, 5, -5],\n [-4, 0, 3, -5, 3],\n [4, -4, 4, 1, 1],\n [-5, -1, -4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -5, 3, 6, 5],\n [0, 5, -4, -6, 2],\n [-1, -2, -3, 0, -6],\n [3, 3, 2, 4, 2],\n [1, 0, 6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 4, 4, 2, -2],\n [-6, 5, -5, 5, 5],\n [1, 4, 6, -3, 5],\n [1, 2, 5, -1, -1],\n [-4, 1, -1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 6, -3, 4, 1],\n [-2, 5, 6, -5, 2],\n [-1, 1, 2, 2, 2],\n [-1, -1, 0, -2, -5],\n [0, 1, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 4, -3, 4, 5],\n [-2, 2, -5, 5, 4],\n [1, 6, -1, -6, -3],\n [-2, 1, 2, 0, -1],\n [-5, 6, 3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 4, -5, 2, -2],\n [-1, 4, 1, -5, -6],\n [-6, -3, 6, -5, 5],\n [0, -3, -2, 0, -2],\n [3, -1, 1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -4, 5, 6, 4],\n [-5, -3, 4, 5, -3],\n [-4, 5, 5, 0, 2],\n [2, 6, -3, 2, 1],\n [-4, 1, -3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 6, -3, 6, -5],\n [-2, 3, 1, 3, 1],\n [2, -4, 6, 5, 3],\n [6, 2, -4, 5, 5],\n [-6, 6, -3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 1, 0, 0, 6],\n [2, 1, -2, -1, -1],\n [5, 1, -6, 4, 6],\n [5, 4, 3, -2, -3],\n [4, -1, -6, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 1, 3, 4, -4],\n [6, 5, -1, -1, 0],\n [0, -2, -3, 2, -4],\n [0, -2, 4, -6, 6],\n [-2, 6, 2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, 5, 4, 1],\n [2, -2, -3, 6, -1],\n [5, -3, 6, 0, -5],\n [6, -1, -4, 1, -2],\n [-6, 1, -1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -5, 1, -6, 0],\n [3, 1, -2, 6, 2],\n [5, -6, -3, 6, -5],\n [5, 5, -5, -5, 5],\n [4, 4, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -4, -1, 6, -5],\n [-4, 6, -5, 5, 0],\n [1, 4, -5, -2, -4],\n [-3, -5, 4, -3, 5],\n [3, 4, -1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 5, 0, 6, -5],\n [-4, -6, 4, 3, 1],\n [-6, -6, 1, -2, 6],\n [3, -5, 3, -4, -4],\n [2, 2, 5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 6, -3, -6, 4],\n [-3, 2, -3, 2, 0],\n [3, 2, 6, -5, -3],\n [3, 1, -5, -5, -4],\n [-5, 3, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 2, -2, 6, -4],\n [-5, -6, 4, 1, 3],\n [-2, 6, -6, -1, 3],\n [5, -6, -6, 4, 3],\n [-2, 0, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, 6, 5, 0],\n [-4, 5, 0, 2, 5],\n [2, 6, -3, -4, -3],\n [-4, 5, -6, 6, 3],\n [-3, 0, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, 6, -4, -5],\n [6, 5, -6, -5, 0],\n [-3, 0, -6, -2, -6],\n [-3, -6, -4, 6, -2],\n [2, 2, -3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 4, -4, 5, -1],\n [-2, 6, -5, -5, 6],\n [1, 0, -2, 4, -5],\n [2, -1, 0, 0, -5],\n [-3, 6, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 2, -5, 3, 3],\n [4, 1, 3, 6, 6],\n [2, 3, 3, -5, 6],\n [6, 0, -3, 1, 3],\n [5, 4, 5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, 0, 0, 3],\n [1, 2, -4, 2, 6],\n [5, -2, -1, -1, -6],\n [-5, -2, -6, 4, -3],\n [2, 2, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -3, -6, -2, 0],\n [-3, -6, -1, -3, 2],\n [4, -1, 4, 4, -5],\n [-4, 3, -2, 6, -2],\n [5, 3, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, -6, -2, 2],\n [-1, 4, 4, 4, -6],\n [-1, -1, -2, 3, -2],\n [5, 2, 0, 2, -2],\n [3, -5, 0, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -4, -2, -6, 4],\n [4, -3, 1, -1, 2],\n [3, -6, 6, 2, -2],\n [6, -3, 3, -5, 2],\n [0, -2, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -2, 0, -5, -3],\n [4, 0, -3, 4, 6],\n [-6, 5, 3, 0, 2],\n [5, -1, 6, 6, -6],\n [-6, 3, 2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 3, -1, -5, 0],\n [4, -1, 2, -2, -6],\n [1, -1, -3, 2, -3],\n [-5, -2, -1, 1, 5],\n [-6, 5, -6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -5, -1, 4, 1],\n [-3, -2, 4, -4, 5],\n [-3, 3, -1, 4, -2],\n [2, -4, 1, -4, -3],\n [-4, -1, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 5, -2, 0, -1],\n [-5, 0, 1, 1, -5],\n [-2, 0, -2, -3, 0],\n [1, -6, 0, -3, 3],\n [4, -1, -1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 2, -1, -4, 2],\n [-6, 5, 4, 0, 6],\n [1, 6, -5, 3, 6],\n [5, -4, 2, -6, 5],\n [5, -1, 0, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 2, -6, -1, 0],\n [-2, -3, -4, 3, -1],\n [-2, -2, -6, -2, 2],\n [-2, 4, 1, -4, 6],\n [4, -6, 5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -5, -6, 4, 3],\n [0, -3, -5, -4, -1],\n [-4, 0, 3, 4, -6],\n [5, 3, 3, 5, 2],\n [-1, -1, -6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -1, 3, -2, 3],\n [-2, 5, 0, -6, -5],\n [-1, 1, 2, -1, -4],\n [1, 1, 5, 2, 0],\n [3, -5, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 2, 3, 6, -2],\n [5, 2, 4, -1, -5],\n [3, 1, 3, -6, 4],\n [0, 6, 0, 2, -1],\n [1, -4, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -2, 2, -5, 1],\n [-6, -2, 3, 2, 0],\n [0, 6, 0, 4, -4],\n [-6, 0, -1, -5, -1],\n [4, 1, 4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -3, -1, 0, 4],\n [2, -2, 0, -3, -3],\n [-6, 1, 0, -5, 3],\n [-1, -2, -1, -6, 1],\n [-6, 2, -5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 1, -4, -3, 4],\n [2, 2, -1, 3, -6],\n [3, -1, -6, -5, -4],\n [5, -1, -2, -1, -4],\n [-2, -5, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 1, -5, -1, 0],\n [0, 5, -1, 5, -3],\n [5, -6, 1, 3, 1],\n [-4, -6, 4, 1, -4],\n [2, -6, -3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -3, 0, -5, -6],\n [1, 0, -2, 2, 0],\n [5, 4, 3, -1, 2],\n [-1, -6, -2, -2, 0],\n [3, 3, -4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 6, 1, -2, 1],\n [-4, 0, -5, 3, 3],\n [3, -3, 3, -5, 2],\n [-1, 4, 4, 5, -6],\n [5, 2, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -5, 2, -2, -4],\n [-5, 5, -2, -2, -5],\n [3, -5, 0, -1, 5],\n [-5, 0, -3, 0, 3],\n [1, 2, -1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, 0, 6, 4],\n [3, 0, 3, 6, -5],\n [4, 0, 3, -3, -3],\n [2, -6, 3, -2, 6],\n [-6, -4, -2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, 3, -2, 0],\n [0, 2, -1, 4, -1],\n [3, -4, -3, 4, 2],\n [-4, 6, 2, -4, 4],\n [-5, 0, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 4, 6, 6, 2],\n [5, 5, 0, 3, -1],\n [3, -1, -5, -5, 4],\n [0, 0, 0, 2, -5],\n [-4, 1, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -2, -2, -4, 0],\n [1, 3, 2, 3, -2],\n [-5, -5, 5, 3, 2],\n [-2, -5, 1, -1, 4],\n [-3, 6, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 0, 3, -1, 3],\n [-5, 6, 6, -5, -2],\n [-3, 0, 0, 0, -4],\n [-5, 4, 3, 4, 6],\n [-4, -4, -2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 1, -6, 1, 0],\n [5, 1, 0, -6, 0],\n [2, -3, 6, 5, -4],\n [2, 2, 0, 3, 6],\n [-6, 4, 2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -5, 3, -4, 5],\n [-6, 2, 0, 2, -2],\n [5, 1, -3, 0, 3],\n [1, -2, 1, -2, 6],\n [6, 2, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, 1, 6, -6],\n [4, 5, 2, 5, 3],\n [5, 1, -3, 4, 3],\n [5, 4, -1, -5, 2],\n [-3, 3, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 5, 5, 5, -3],\n [-1, 4, 2, 4, 1],\n [2, 2, 3, -5, 4],\n [3, -5, -3, 1, -4],\n [1, 4, 1, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 2, 5, -2, -1],\n [-5, -1, -5, -6, -2],\n [3, 5, -6, 3, -5],\n [-5, -6, 1, -6, -4],\n [3, -2, 6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -4, 4, 3, 5],\n [-3, 0, -6, 0, 1],\n [-4, -3, -4, -2, 4],\n [4, -4, 3, 5, -1],\n [5, 2, -3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 2, 0, 2, -2],\n [0, 0, 4, -5, 6],\n [2, 0, 5, -1, -6],\n [-6, 0, -3, 1, -3],\n [0, 3, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -6, 5, -5, 0],\n [4, -6, 2, 3, -3],\n [-3, 0, -4, 2, 3],\n [5, 6, -4, 3, 2],\n [-3, 6, -5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -3, 4, -5, -1],\n [-4, 6, -3, -3, -1],\n [0, 5, 3, -1, 6],\n [0, -2, 2, -2, -6],\n [4, 2, 6, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -6, 6, 6, 2],\n [-2, 0, 3, 5, -2],\n [2, -1, 1, 1, 1],\n [1, 5, -1, -1, -4],\n [-5, -3, 1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 5, 1, -3, -2],\n [-3, 6, -4, -3, -6],\n [1, -2, 4, -2, 5],\n [5, -2, 6, 4, 3],\n [-5, -4, 1, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 6, -3, -2, 5],\n [2, 6, 1, -6, -1],\n [-5, 5, -4, -2, 3],\n [3, 1, -3, 0, -1],\n [-3, -3, 3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 5, -3, -3, -4],\n [-4, -3, 3, 1, 5],\n [-4, -6, -6, 0, -6],\n [2, 1, 2, 1, 4],\n [2, 0, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, -3, 2, -1],\n [1, 6, -2, -6, 1],\n [-3, 3, 2, 1, -6],\n [-5, 5, 6, 0, -1],\n [-1, -5, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 1, 3, -3, 2],\n [1, 3, 4, 1, -2],\n [5, 3, -5, 5, 2],\n [6, 4, -2, -3, 3],\n [-2, -5, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 2, -3, -4, 0],\n [-3, 6, -5, 2, -4],\n [-4, -3, -3, 1, -6],\n [-5, -1, 4, -1, -6],\n [-3, 2, 5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -3, -4, 3, 2],\n [0, 5, -1, -6, -3],\n [-4, -1, -5, -2, 5],\n [0, -1, 6, -4, 1],\n [-6, 3, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 0, 2, -2, -2],\n [0, 2, -2, 0, -1],\n [2, 1, 6, 6, 3],\n [4, -2, -4, -4, 0],\n [3, -1, -6, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -2, -3, 1, -4],\n [5, -1, 0, 5, -6],\n [5, -4, -1, -4, -5],\n [-4, -2, 1, 5, -2],\n [6, 5, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 6, -5, 0, -1],\n [3, -2, -6, 1, -3],\n [-3, -2, -6, -3, 6],\n [4, -1, 1, 2, -3],\n [4, -2, -3, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 3, -1, 5, -4],\n [0, -4, -3, -4, 1],\n [-6, -6, 3, -1, 5],\n [1, 2, 1, 5, -3],\n [4, 3, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -6, 1, 0, 6],\n [6, -4, 2, 2, 0],\n [-6, 5, 2, 3, 5],\n [-1, -5, -3, -6, 1],\n [3, 1, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 5, -4, 5, 1],\n [-2, 3, -4, -5, -1],\n [-6, -6, 1, -5, -1],\n [3, -5, -5, 2, 0],\n [-1, -1, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -2, -2, -6, 3],\n [0, -6, 0, 4, 2],\n [5, 5, 3, 1, 4],\n [5, 6, -4, 2, -5],\n [-4, 3, 5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, -2, -3, 0],\n [-4, 3, -4, -5, 2],\n [-6, 0, 1, -6, -6],\n [4, 2, 4, 4, 5],\n [2, -5, 2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, 4, -3, -6],\n [-6, 2, 3, -5, 5],\n [2, -5, -1, 2, 3],\n [5, -3, 5, -4, 0],\n [-5, -1, -2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -3, 4, 1, 4],\n [-2, 0, -3, -1, -6],\n [3, -3, -2, 2, 6],\n [-1, -2, -1, -4, 6],\n [-6, 4, 3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -6, -4, -2, -1],\n [2, -5, 3, -6, -6],\n [5, 1, 2, 2, -6],\n [6, -2, -4, 6, 4],\n [2, 4, -1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -3, 1, -4, -6],\n [-4, 1, -3, -3, -4],\n [6, -5, 5, -3, -6],\n [6, -5, 4, -3, -3],\n [-1, -5, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 1, -5, 5, -2],\n [-5, 3, 0, 5, 5],\n [-4, -3, -1, -4, -6],\n [-5, 0, -6, 6, 5],\n [6, 4, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -6, 6, 5, -2],\n [2, -5, -5, 4, -1],\n [5, 3, -3, 3, -6],\n [2, -3, -3, 6, 0],\n [3, 6, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 0, -5, 4, -6],\n [-6, 4, 4, 6, -1],\n [-3, 0, 1, -6, -6],\n [3, -3, 1, 3, 5],\n [1, 4, 3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, -3, -4, -4],\n [6, 4, -3, 1, -5],\n [-3, 5, -2, -4, -4],\n [1, -5, 0, -6, 1],\n [5, 5, 1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -6, -5, 0, -6],\n [-1, 6, 6, -3, 0],\n [-5, -1, -6, 5, -1],\n [-2, 5, 4, 5, -2],\n [-6, 5, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -1, 0, 4, 0],\n [2, 6, -4, 1, -3],\n [-1, -2, 6, -5, 4],\n [0, 1, -4, 1, -3],\n [5, 2, -4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -4, 0, -3, -2],\n [-2, -1, -6, -4, -4],\n [-1, 1, -4, -1, -2],\n [-1, -5, -1, -1, 4],\n [1, 3, -5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 0, -5, -3, -4],\n [-5, -5, 0, -1, 6],\n [-4, 4, 5, 0, 0],\n [-4, -5, -3, 4, -1],\n [3, -6, -5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 3, -5, -4, 5],\n [-3, -1, 3, 0, 1],\n [6, -1, 5, -3, -1],\n [-1, -2, 0, -6, 1],\n [-5, -1, 6, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, 1, 1, -4],\n [-1, -2, 6, 2, 3],\n [5, 3, -1, -3, -3],\n [3, 4, -4, 4, 3],\n [6, -2, 3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -5, 4, 5, 1],\n [5, 4, 0, -1, 3],\n [4, 6, -6, 0, 2],\n [5, -2, -4, 6, -5],\n [3, 0, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 5, -3, 6, 1],\n [-6, 6, -1, -2, 2],\n [6, -3, 2, -4, 6],\n [-4, -3, 5, 6, 1],\n [6, 5, -3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, -2, 6, 3],\n [2, -3, 0, 4, -4],\n [0, -2, 1, 1, 3],\n [-5, -5, -5, 3, -1],\n [1, 1, 5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -4, -4, 2, 2],\n [2, 5, -3, 4, -4],\n [-4, 5, -5, -5, 6],\n [-1, 0, -4, -6, 2],\n [-2, 1, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 3, -5, 3, 5],\n [-3, 0, 4, 6, 1],\n [6, 2, -5, -6, -4],\n [-6, -3, -1, -6, -5],\n [2, -6, 6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 4, 2, -4, 1],\n [4, 0, -5, 1, 6],\n [2, -3, 1, 3, -5],\n [-5, 1, 6, -6, -1],\n [1, 4, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -5, 1, -6, 1],\n [-4, 6, -3, -6, -4],\n [0, -2, -3, -4, 5],\n [3, -3, 6, 6, 6],\n [6, -4, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -4, 3, 5, -3],\n [4, -2, -3, -5, -1],\n [-2, -6, 2, 6, -2],\n [3, -5, -2, 5, -2],\n [-1, -3, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -2, 6, 0, 1],\n [0, 5, 4, -1, 2],\n [-4, 0, 6, -1, -1],\n [-3, 4, 3, -5, 3],\n [2, -2, 5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 3, -3, 1, 0],\n [1, 4, 1, -5, 2],\n [-4, 5, 6, -4, 6],\n [-4, -1, -6, 0, -6],\n [3, -6, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 6, -4, -1, 4],\n [-2, -3, -1, -5, 5],\n [-6, -1, -2, 4, -1],\n [0, 0, -4, 0, -1],\n [4, -6, -2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 3, -6, -4, -4],\n [6, 3, 3, -3, -2],\n [-2, 3, -2, -2, -5],\n [-5, -3, -1, 2, -6],\n [-6, -2, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 6, -4, 1, 1],\n [4, -1, 1, -6, -1],\n [6, 6, -5, 4, -3],\n [-2, -6, -6, 4, 1],\n [2, 6, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 6, 4, 1],\n [-3, 2, -4, -6, 4],\n [-1, -5, 5, -3, 4],\n [-4, 0, -5, 4, 5],\n [-4, -3, -4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 0, -4, 2, 0],\n [6, 3, 5, 5, 5],\n [-4, 3, -4, 2, 0],\n [-1, 3, -6, 4, -5],\n [0, -1, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -6, 1, 2, 3],\n [-2, -6, -2, -5, -6],\n [-4, -5, -3, 0, 6],\n [6, 1, -1, 4, -6],\n [-5, 0, 5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 5, -4, 2, -3],\n [-1, -1, 6, -2, 4],\n [0, 3, -4, 0, 2],\n [-5, -6, 3, -4, 3],\n [-6, 5, -2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 3, 3, 4, -5],\n [-6, -2, -1, 2, 3],\n [-5, 3, -4, -2, 3],\n [3, 2, 6, 1, -6],\n [2, -3, -3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -2, -5, -5, -4],\n [-2, 6, 5, -1, 4],\n [-6, 3, -1, 0, -2],\n [-4, -5, -2, -4, -5],\n [2, -2, -5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 1, -1, -1, -2],\n [-6, 0, -6, 2, -4],\n [1, 5, -4, -1, 0],\n [-6, 5, 6, -4, -4],\n [-5, 3, 1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -1, -2, -6, -5],\n [-1, 3, -6, 1, 1],\n [0, 3, -1, -4, -6],\n [-2, 2, 3, 6, -3],\n [5, -4, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -4, -2, 6, -1],\n [-5, -4, -1, -6, -5],\n [2, 1, -2, 1, 3],\n [-6, 6, 1, 2, 6],\n [-5, 6, -6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 1, -1, 6, 1],\n [-1, -1, 6, 2, 2],\n [6, 1, 4, 2, -5],\n [5, 6, 2, -5, 4],\n [-6, 2, -4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -3, 0, 6, 4],\n [-3, 0, 3, 1, -3],\n [-5, -3, -2, -4, 0],\n [-2, 0, 5, 4, -5],\n [-4, -6, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 0, -4, -1, 4],\n [1, -1, 4, -4, 6],\n [-2, 5, -1, -4, -2],\n [5, 6, -6, 6, -4],\n [3, 2, -6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -4, 4, 0, 5],\n [-1, 4, -5, 6, 5],\n [-3, 0, -5, 3, 6],\n [1, -3, 6, -6, -1],\n [3, -2, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 1, 4, 4, -3],\n [1, -3, 5, 4, 5],\n [2, -5, 4, -6, 6],\n [5, 2, 0, 1, -4],\n [5, 0, 5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -3, 6, 1, -5],\n [3, -1, 5, 3, 3],\n [-3, 6, 2, 3, -6],\n [-3, 3, 1, 2, -1],\n [-2, -1, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -2, 1, 1, -3],\n [2, 5, 6, 5, 1],\n [-2, -6, 2, 1, -2],\n [2, 3, -6, 1, -1],\n [-2, 6, -4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -5, -3, 2, 5],\n [0, 1, 1, 5, -6],\n [-1, 6, -6, -5, 0],\n [5, 0, 1, -6, 2],\n [-1, -6, 6, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, -5, 3, -1],\n [6, 6, -5, -4, 0],\n [-2, 0, 6, -1, 0],\n [1, -6, -3, 3, 2],\n [1, 3, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -6, -6, 3, 3],\n [-5, 4, -1, -1, -4],\n [-4, 1, -6, 1, 3],\n [-6, 1, -3, 6, -5],\n [-5, 5, -5, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -2, 0, 2, -3],\n [-6, -2, 3, -1, -3],\n [-5, -4, 3, 6, 0],\n [0, 6, 6, 0, -2],\n [-1, 5, 6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 1, -1, -3, -6],\n [0, 3, 6, 1, -1],\n [-6, -2, 1, 3, -6],\n [6, 6, 4, 6, -2],\n [0, 4, 5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 0, 5, -5, 3],\n [-3, -3, 0, 3, 2],\n [0, -1, -4, 5, 5],\n [5, 6, 4, -3, -6],\n [4, -3, 3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 5, -1, -5, 0],\n [1, 2, 5, -2, 2],\n [-3, -4, 6, -5, 6],\n [4, 2, 1, 2, 3],\n [3, 6, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 0, -4, 6, -5],\n [-2, 5, 1, 5, -5],\n [-2, 5, -4, 0, -3],\n [4, -3, 3, 0, -6],\n [4, 6, 1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 6, 5, -5, -4],\n [5, -2, -2, 5, 3],\n [-4, -3, 4, 4, 4],\n [-5, -4, 1, 6, -3],\n [6, 4, -6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, -4, -5, 5],\n [6, -4, -4, 6, 2],\n [4, -4, -5, 6, 1],\n [6, 4, -6, -4, -2],\n [0, 4, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -4, 5, -6, -4],\n [4, -3, 1, 3, -4],\n [-6, 3, 3, -6, 5],\n [-1, 6, 0, -4, 4],\n [4, -5, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, 0, 1, 6],\n [5, 2, -1, -2, -3],\n [4, 2, 1, -4, -2],\n [2, 0, 5, -4, 0],\n [1, 1, 5, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -5, 6, -6, -1],\n [0, -6, -1, 4, 2],\n [-5, -4, -5, 5, -3],\n [-6, 3, 0, 5, 3],\n [6, -4, 1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 2, -3, 6, -3],\n [4, 3, 1, 4, 6],\n [-5, 2, -6, 0, 0],\n [-5, -4, -2, -1, 0],\n [5, 5, 5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -3, -1, 3, 5],\n [-3, -2, -1, 0, 2],\n [0, 1, 3, 1, 0],\n [6, -3, 1, -5, -2],\n [-4, 6, 2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -2, -3, -5, 3],\n [-2, -3, 3, -1, -5],\n [-3, -5, 1, 6, 4],\n [4, -1, 6, 2, 5],\n [1, -4, -4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 4, 2, 0, -4],\n [1, 6, 0, 6, -2],\n [5, -2, -1, -4, -4],\n [-6, -4, -4, 6, 4],\n [-1, 5, 2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -5, 0, -5, 1],\n [-3, -1, -3, 0, -4],\n [1, 4, 4, 6, -3],\n [-2, 1, 0, 6, -2],\n [4, -6, -4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 0, 5, 6, 3],\n [-3, -6, -5, -3, -2],\n [5, -4, 4, 3, 4],\n [2, -2, -5, 5, 5],\n [3, 0, -6, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 6, -3, -3, -1],\n [5, 2, 6, 0, -1],\n [6, 6, -4, -2, 0],\n [2, 6, -6, 6, 1],\n [2, -4, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 4, -6, -5, 2],\n [-2, 6, 6, 4, 2],\n [-1, -1, 0, -5, 1],\n [-5, -3, 1, -5, 6],\n [3, 2, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -4, 3, -3, -5],\n [-5, 6, 4, 3, 1],\n [3, 2, -1, 5, 3],\n [-6, -5, -2, -5, 0],\n [-2, -6, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 5, 3, 4, -2],\n [1, 6, -2, 3, -2],\n [-5, 6, 6, -2, 4],\n [-2, -2, 3, 1, 5],\n [-2, 1, 5, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 6, -2, 4, 4],\n [-1, 4, 5, 2, -1],\n [5, 0, -2, 6, -5],\n [-5, 6, -2, -1, 0],\n [-2, 0, -3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 5, 6, 4, 6],\n [-4, -1, -1, 2, 0],\n [2, -6, -4, -4, 6],\n [-4, 0, 2, 3, 1],\n [6, 3, 6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 3, 3, -3, 4],\n [6, 2, -1, -2, 3],\n [4, 1, 6, -5, -6],\n [-6, -5, -4, 6, -6],\n [1, -6, 5, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -6, 1, -6, -1],\n [5, -1, 5, 1, -2],\n [-6, -1, -2, 0, 6],\n [-3, 6, 4, -1, 3],\n [-6, 0, 4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 5, 3, 6, -4],\n [1, -5, -4, -3, -5],\n [5, 1, 5, 4, -4],\n [-5, 4, 4, 0, 4],\n [-6, -2, 1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -3, 5, 6, -5],\n [6, -2, -6, 4, 4],\n [3, 0, -4, 0, -1],\n [-3, 5, -3, 5, -2],\n [-1, -5, -1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 2, -4, 0, 0],\n [2, 0, 4, 3, -5],\n [0, 2, -2, 3, -5],\n [3, -4, -6, 0, 4],\n [0, 0, 0, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 0, -4, -5, -5],\n [-3, -1, -4, -6, 2],\n [-4, 1, -5, -5, -5],\n [5, 4, 2, -4, -5],\n [4, 1, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 2, 3, -2, 6],\n [-6, 3, -4, 3, -1],\n [-1, 4, -5, 0, -1],\n [-1, -4, -2, 3, 2],\n [-2, 5, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 4, -2, 5, 4],\n [0, -5, 3, 0, -1],\n [0, 2, 2, -1, -5],\n [-2, -1, 3, 0, -2],\n [6, 4, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -1, 6, 1, -6],\n [4, 3, -1, 0, 2],\n [6, 1, 4, 2, -6],\n [2, -6, 1, -1, 4],\n [2, 2, 4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -4, -4, 3, 3],\n [-6, 2, -4, 2, 3],\n [4, -1, 4, 2, 3],\n [0, 6, -2, 4, 2],\n [1, 0, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 2, -6, -5, 3],\n [5, 1, -3, 6, 1],\n [-1, 5, 1, 1, -2],\n [-4, 4, -2, 0, -6],\n [6, -3, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 3, 0, 1, 2],\n [2, -6, 6, 2, 0],\n [3, -5, -5, 4, -6],\n [5, -1, 1, 3, -2],\n [1, 0, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -2, 5, 0, -4],\n [-5, 5, -1, 3, -4],\n [5, -2, -3, -2, -6],\n [-1, 3, -6, -3, 4],\n [4, 3, -2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 3, 5, 3, 5],\n [3, -5, -1, 2, -3],\n [-2, 5, 0, -4, -2],\n [-6, 1, 1, -4, -4],\n [-2, 0, 1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 1, 1, 3, -4],\n [4, -2, 4, 3, 1],\n [3, -3, -4, -5, 2],\n [5, 2, 6, -2, 0],\n [1, -6, 1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -4, -2, -5, -6],\n [-3, 1, -2, -6, 5],\n [6, 3, -4, 4, 0],\n [-5, 4, -4, -3, -3],\n [-5, 4, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 2, -1, 0, -5],\n [3, -2, -4, 1, 4],\n [6, -5, -6, -2, 1],\n [-5, -6, 6, -4, 4],\n [3, 3, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -3, 5, 5, 0],\n [2, 0, -4, -4, 0],\n [0, -1, 2, 0, 2],\n [3, -1, 1, 5, 1],\n [-6, -3, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 1, 5, 1, -3],\n [2, 2, 0, -2, -4],\n [-6, 4, -2, -4, 5],\n [-2, -4, -6, -6, -3],\n [-4, -1, -1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, -5, 3, 1],\n [1, -5, 5, -2, -5],\n [6, 1, -3, 3, -6],\n [-3, -5, -5, -6, 1],\n [-2, 1, 6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -6, 2, 4, -4],\n [-2, -3, 4, -6, -6],\n [6, 5, 1, -6, 1],\n [-6, 0, 1, 6, 5],\n [-5, 5, 3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 5, -1, -3, -6],\n [-2, -5, 5, -3, -4],\n [-4, -4, -6, -2, -2],\n [3, 6, -1, 6, -3],\n [-6, -5, 1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 6, 4, 1, -3],\n [-6, 6, -1, 0, 3],\n [4, 3, -5, 2, 5],\n [5, 0, 1, 2, 3],\n [-5, -1, 2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 2, 6, 3, 4],\n [5, 6, -3, -5, 3],\n [-1, 3, 6, -4, 6],\n [-6, -3, 4, -3, 1],\n [-6, 4, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 1, -4, 0, 1],\n [5, 1, -1, 6, 3],\n [-1, 6, 2, 1, 4],\n [-2, 0, 5, -4, -1],\n [6, -1, -5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 1, -4, 5, 4],\n [-1, 1, -5, 4, -3],\n [6, 0, 0, 4, -4],\n [1, 2, -3, 0, -3],\n [-6, 4, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, -1, -5, 5],\n [-1, -2, 3, 2, -1],\n [5, -4, -1, -5, 6],\n [3, -2, -3, 4, 0],\n [-1, 2, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -2, 6, 6, -6],\n [4, 2, -1, 1, 1],\n [-5, -5, 5, -2, 1],\n [0, -2, 3, 4, -1],\n [0, -3, 5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 0, 5, 1, -4],\n [0, -4, 6, 3, 1],\n [2, -3, 5, 4, 2],\n [-1, -6, -4, -2, -3],\n [-2, -1, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 3, 5, -5, 3],\n [-1, -2, 3, -6, -5],\n [6, 2, -4, -4, 2],\n [6, -4, 5, -2, 0],\n [4, 3, -4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -2, 5, 2, 1],\n [0, -4, 2, -5, -6],\n [4, 6, 5, -4, 5],\n [2, -6, -4, -6, -2],\n [1, -4, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -1, 5, 4, 4],\n [-2, 5, 1, 1, -6],\n [6, 6, 5, -3, -5],\n [1, 4, -5, 3, -1],\n [-2, 2, 4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -2, 0, 1, 6],\n [0, 3, 1, 5, -2],\n [5, 6, -3, -4, 5],\n [0, 1, 5, 5, -5],\n [-5, -2, 0, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 0, 2, -3, 0],\n [0, -6, -5, -2, -3],\n [2, -1, -6, 4, -3],\n [4, 4, -6, -5, -6],\n [1, -2, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -3, 0, 1, -3],\n [-2, -2, 4, -4, 4],\n [-5, -6, -4, 6, 0],\n [0, -6, 1, 2, 1],\n [1, -1, 4, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 6, -1, -3, -5],\n [-1, -5, -5, 4, -5],\n [1, 4, 2, 4, 5],\n [0, 6, -4, 2, 0],\n [5, -4, 2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, 4, 6, 0],\n [-3, -3, 6, 2, -4],\n [-1, -2, -1, -5, 1],\n [5, 4, 1, -6, -6],\n [-5, -2, 5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, 0, 3, 5],\n [1, -5, 5, 6, 6],\n [-1, -3, -4, 0, 5],\n [-1, -3, 5, -6, 0],\n [5, -1, -6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -1, 4, 3, 6],\n [-2, 3, 2, 5, -6],\n [-6, -6, 6, 2, -6],\n [6, 4, 5, 5, -4],\n [-6, 3, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -4, 6, -3, -3],\n [-3, -2, 1, -3, 1],\n [-1, -1, 0, 6, 2],\n [-5, -6, -1, 6, -3],\n [-2, 3, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 1, 4, -6, -3],\n [4, -5, -2, 2, -4],\n [5, 2, 5, 1, -2],\n [-4, -1, 3, 0, -5],\n [6, -5, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 3, 3, -1, -2],\n [6, -1, -4, 4, -4],\n [-6, -1, 6, 1, -4],\n [6, -6, -5, -4, 4],\n [1, 0, 3, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 1, 5, 4, 5],\n [-2, 6, 4, -1, 5],\n [-4, 0, -4, 6, 5],\n [-1, 2, -1, 1, -2],\n [-3, 3, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -3, 3, 4, 6],\n [2, 1, -4, 5, 1],\n [3, 6, -2, -5, -1],\n [5, -6, 4, -1, 1],\n [2, -1, 0, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -4, -2, 6, -3],\n [3, -5, -6, 5, 6],\n [-1, -4, -4, 5, 1],\n [-2, 5, -6, 4, -6],\n [0, -4, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 0, 2, 1, -2],\n [-4, -1, 6, 6, -1],\n [2, 1, 3, -2, -4],\n [1, 5, 1, 0, 2],\n [0, 4, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 0, -1, 5, -6],\n [-2, -3, 4, -5, 0],\n [-4, -4, 4, 0, 6],\n [2, -2, 2, -4, 1],\n [-5, 1, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 2, 4, -6, -6],\n [1, -4, 3, 1, -6],\n [3, 4, 3, -2, 6],\n [-4, -3, 5, -5, -1],\n [1, 2, 0, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -4, -3, -5, -6],\n [0, 4, -5, -6, 5],\n [2, 3, 5, -3, -1],\n [-5, -4, -5, -3, 4],\n [-1, 6, 5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -6, -2, 2, -3],\n [1, 2, 0, 4, -5],\n [4, 4, 2, -5, -6],\n [4, -5, -1, 4, -3],\n [-6, -1, 1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 0, 0, 1, -3],\n [1, -4, -1, 6, -4],\n [1, -3, 5, 5, 3],\n [-6, -3, 1, -1, -3],\n [-6, 1, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -5, 1, 4, -5],\n [-4, 0, 0, -1, 3],\n [-5, -6, -1, -5, -4],\n [-5, -5, -4, -6, 5],\n [5, 1, 2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, 2, 1, 2],\n [1, -1, 4, 4, 4],\n [-5, -4, 6, -4, 0],\n [-5, -2, 6, -5, 5],\n [-2, -6, -6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 4, -3, -4, -3],\n [-5, 4, -4, -3, -6],\n [-4, 4, -5, -1, 6],\n [0, -3, 3, -6, -6],\n [-4, 0, 5, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, 2, 2, -4],\n [-2, -1, 0, 3, 4],\n [-5, -6, -3, 6, 6],\n [-5, 6, -3, 4, 0],\n [-1, 3, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -5, 0, 0, 2],\n [5, 3, 0, 3, 5],\n [1, 1, 2, -5, -4],\n [3, 2, 4, 5, -6],\n [-5, -4, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 0, -5, 0, -2],\n [-2, 3, 3, 3, 1],\n [2, 6, -4, -6, -4],\n [-2, -6, -4, -4, 3],\n [-5, 3, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, 3, -2, -1],\n [-2, 1, 4, -4, 6],\n [-6, -6, 4, -1, 5],\n [4, 5, -4, -1, -1],\n [4, 3, -3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -2, 3, 2, 0],\n [3, -3, -4, 0, 5],\n [-4, 4, -6, -5, 3],\n [-2, 5, 3, -6, -1],\n [-5, 5, -2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 0, -4, -4, -6],\n [-6, -4, -3, 0, 4],\n [-2, -5, 6, 4, -3],\n [-4, 0, -5, -3, 3],\n [4, 0, 5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, 0, 3, -3],\n [-6, 1, -4, 3, 3],\n [3, -4, -1, 2, -5],\n [-3, 6, -3, 4, -6],\n [-4, -3, 4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 6, 2, -3, 0],\n [6, -1, -6, 4, -4],\n [3, -2, -2, 0, -1],\n [3, -2, -5, 6, -4],\n [-6, 4, 3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 6, 2, 5, 5],\n [3, 6, 1, -6, -4],\n [-4, 6, -4, -3, 1],\n [-6, -3, -2, 1, -1],\n [-2, -1, 2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 0, 6, -5, -2],\n [1, -3, -5, -4, 2],\n [-4, 5, -6, 0, 6],\n [0, -3, 2, 2, -5],\n [3, 6, -2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 6, -3, 3, 6],\n [1, 4, 4, 5, -1],\n [6, -3, -5, 6, 6],\n [6, 3, -3, -1, -5],\n [5, 2, 3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, -6, 3, 1],\n [3, 3, 5, -5, 3],\n [-3, -3, 5, 0, 1],\n [0, 0, -1, -6, 5],\n [0, -1, 2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -6, -5, -2, -5],\n [-6, -3, -2, 5, 4],\n [1, -3, -5, 3, -4],\n [6, 4, -4, -6, -5],\n [-2, -3, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 4, -4, -3, 3],\n [1, 5, 4, 3, -2],\n [-1, 5, 1, -3, 2],\n [1, -2, 4, -5, -3],\n [3, 1, 2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, 3, 5, 4],\n [0, 5, 0, -2, -2],\n [5, -4, -3, -4, -4],\n [3, 1, -5, 5, 3],\n [5, -3, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -6, 5, 4, 1],\n [1, -4, 2, 3, 5],\n [5, 0, 0, 4, -1],\n [-2, 0, 0, -2, -5],\n [-5, 6, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -3, 6, 3, -6],\n [2, 5, -5, 6, 5],\n [6, 1, -6, -2, 5],\n [3, -1, -6, -2, -1],\n [6, -6, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -5, -4, 4, 4],\n [2, 6, -2, 6, 0],\n [-3, -3, 3, 1, 3],\n [2, -2, -2, 6, 2],\n [3, 5, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 6, 5, -1, -2],\n [-5, 1, -5, 3, 1],\n [-4, 3, 5, -5, 6],\n [1, 2, 5, 0, -3],\n [-1, 1, 3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 6, -4, -5, -4],\n [-2, -3, 4, -5, 0],\n [0, 3, 4, 0, -4],\n [-5, 4, 6, 2, 2],\n [-6, 4, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 3, -2, 2, 4],\n [-1, -5, 0, 2, -3],\n [2, -2, 4, 5, 2],\n [1, -6, -4, 4, 1],\n [2, 0, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -1, 5, 1, -3],\n [4, 0, -5, -5, 1],\n [-2, 4, 0, -1, 0],\n [4, 5, -5, -6, -2],\n [-1, -6, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -4, 0, 3, 2],\n [6, -1, -4, 4, 1],\n [3, -6, -3, -5, -5],\n [6, -5, -6, 5, -1],\n [-4, -3, 6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 1, -5, -6, -2],\n [3, -4, 5, -5, 4],\n [-3, -6, -2, 0, 2],\n [4, 0, 4, -1, -1],\n [6, -1, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 2, -6, 5, -4],\n [-5, -3, 6, 5, 5],\n [3, 5, 3, -4, 2],\n [-6, 0, -2, -5, 2],\n [5, 3, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 6, 1, -2, -4],\n [1, -5, -2, 3, -3],\n [1, 3, -4, -4, 6],\n [3, -4, -6, -5, -1],\n [0, -2, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 1, -6, -3, 0],\n [-5, 0, 6, -3, 2],\n [1, -2, 0, 4, -2],\n [0, 0, 3, 1, -6],\n [0, -1, -4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 2, -3, 3, 3],\n [-4, -3, 0, 4, 5],\n [-6, 4, -4, 5, -4],\n [-2, -3, -4, 5, 2],\n [-1, 6, 1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 1, -3, -1, -3],\n [-3, 0, 3, -3, -3],\n [-6, 3, 5, 5, 0],\n [-4, 4, 4, 4, 1],\n [3, -4, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, 5, 2, -1],\n [2, 4, 6, 0, -3],\n [-3, -1, -3, 3, -5],\n [4, 0, 0, 2, 1],\n [5, 2, 1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 6, -1, -1, 4],\n [2, 4, 1, 4, -4],\n [-3, -2, -1, 1, -3],\n [-6, -6, 6, 1, 2],\n [2, 4, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -1, 1, -2, 4],\n [-5, -6, 2, -6, -1],\n [1, -6, 2, -3, -5],\n [-2, -1, 2, 1, -2],\n [2, 6, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 3, 1, 2, 6],\n [-3, -2, 2, -5, -3],\n [-6, -2, -1, 6, 0],\n [4, 6, 6, -3, 5],\n [-1, 1, -4, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -1, 0, 4, -4],\n [4, 4, -1, 1, 4],\n [-1, -6, -4, 1, -1],\n [0, -4, 0, -2, -1],\n [6, 4, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -3, 5, 5, 5],\n [-1, 4, -1, -5, 5],\n [5, 6, 0, 5, -4],\n [2, 2, -4, 4, 6],\n [2, 1, -5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 3, -3, 2, -4],\n [-6, -6, -4, -1, -5],\n [1, 1, 5, -3, -5],\n [6, -4, 1, -2, 5],\n [2, 1, 3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -2, 3, 0, 3],\n [5, 3, 1, 1, 4],\n [1, 0, 3, 6, 3],\n [-4, 0, -6, -6, 1],\n [-6, -1, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 6, 4, 4, 6],\n [6, 6, 0, -3, -3],\n [-2, 3, -4, -3, -6],\n [-6, 4, -1, -1, 3],\n [-2, -6, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 1, 5, -2, -1],\n [2, -6, -6, -1, -1],\n [6, 3, -1, 3, 6],\n [-6, 4, -2, -6, 4],\n [-4, -2, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -6, 0, -6, -3],\n [0, -3, 5, 2, 2],\n [-2, -3, 3, 6, -4],\n [4, -6, 0, -3, -5],\n [-6, 2, 4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 3, -2, -1, 4],\n [1, 2, 3, 3, -4],\n [-3, -5, 1, 0, 2],\n [-3, 6, 6, 1, 3],\n [3, -1, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 6, 2, -6, 0],\n [-2, 0, -4, 4, -3],\n [-2, 0, 4, 5, -6],\n [-6, 1, 3, -6, 5],\n [3, -6, -5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -1, 6, -5, 0],\n [-3, 3, -1, 1, 0],\n [1, -2, 1, 2, 4],\n [6, 2, 1, 5, 5],\n [2, 5, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -2, 1, -2, -1],\n [3, 2, -5, 4, 6],\n [6, 0, -2, 3, 1],\n [3, -1, -6, -2, -2],\n [-2, 0, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 5, 2, -3, 2],\n [-3, -4, 1, 1, -5],\n [-4, 1, -2, 1, -2],\n [-6, 0, -5, -3, -3],\n [0, 1, 5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 5, 2, -5, -4],\n [5, -4, 1, 2, 5],\n [-5, -4, 2, 0, -2],\n [-1, 5, 2, -6, -5],\n [5, 5, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 3, 0, 1, -4],\n [3, -5, -6, 5, 6],\n [-6, -5, 2, -1, 6],\n [3, -3, 1, -4, -4],\n [1, 2, 5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, -3, -2, 3],\n [-3, 2, 2, -6, 2],\n [-3, 2, 4, -5, -6],\n [1, 6, 2, 1, 1],\n [-5, 4, -3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -6, 3, 3, -3],\n [4, 6, 1, -1, 2],\n [5, 1, -6, 5, 5],\n [4, 1, -5, 1, 1],\n [6, -3, -4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 6, 2, -5, -2],\n [4, 4, -6, -6, -2],\n [3, -4, -5, 5, 1],\n [-3, -3, 3, -4, -2],\n [-6, 6, -2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 1, 6, 3, 0],\n [3, 4, 2, -4, 4],\n [1, 6, -2, 0, -6],\n [4, 0, -4, 6, 1],\n [-4, 6, 0, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -3, 0, 4, -1],\n [6, -5, -3, -3, 4],\n [-5, 2, 1, 2, -6],\n [1, 6, 4, 0, -3],\n [-6, 2, 5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 6, 1, 2, -6],\n [-3, 2, -4, -5, 1],\n [3, -6, -2, -1, 5],\n [4, 3, -1, 6, -1],\n [6, -5, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 3, 6, -1, -2],\n [5, 2, 6, -5, -4],\n [0, -1, -5, -5, -4],\n [-3, -5, 6, 0, 6],\n [-2, -5, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 4, -2, -4, -2],\n [2, -6, 6, -1, 3],\n [-1, 4, -4, 5, 2],\n [-1, -6, 2, -4, -6],\n [5, 4, 3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, 3, -1, -2],\n [5, 0, 6, 4, -6],\n [-4, -6, -1, -1, -3],\n [0, 5, -5, -2, -4],\n [3, -2, 5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -2, -2, 5, -6],\n [0, -2, 3, 6, 1],\n [-6, -5, -5, 6, -4],\n [6, 1, 3, 1, 3],\n [5, -5, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 5, -6, 1, 5],\n [-3, 6, -3, 4, 2],\n [-6, 4, 4, -2, 3],\n [-3, -2, 1, -5, -3],\n [0, -6, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 1, 6, -6, -1],\n [4, -3, 6, 1, 5],\n [3, -6, 0, -3, 5],\n [-3, -3, 6, 5, -6],\n [-4, -2, -3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -5, 0, -4, -5],\n [4, 0, -3, 6, 6],\n [-6, 4, -2, 2, -3],\n [-3, -3, -2, -4, 3],\n [4, 6, -3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, 0, 6, 5],\n [-5, 3, 2, -3, -2],\n [-4, -6, -3, 5, 6],\n [0, 2, 6, -3, -6],\n [6, 0, 1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 6, 1, 2, 3],\n [6, -4, 2, 5, -6],\n [-2, -1, 5, -1, 2],\n [3, 6, -6, 2, -2],\n [0, -3, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, 3, -1, -6],\n [5, 3, -2, 3, 1],\n [6, -4, -1, 0, -5],\n [-3, 2, -1, 0, -4],\n [-6, -6, -6, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 4, -3, 6, 1],\n [1, -6, 4, 6, -2],\n [-3, -6, 2, 5, 4],\n [-6, -4, 5, 0, 5],\n [4, -6, 4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -5, -1, -2, 5],\n [6, 6, 3, 6, -6],\n [-3, 3, 6, -6, -6],\n [-2, 0, 1, -4, 0],\n [-5, 6, -3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, -6, -3, 1],\n [-5, 2, 5, 0, -3],\n [6, 5, -5, -1, -5],\n [-6, -4, -4, -3, 6],\n [4, 1, -1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 1, -3, -2, 1],\n [2, -4, 2, -4, -2],\n [4, 6, 1, -2, -1],\n [1, -1, -3, -5, 3],\n [3, -3, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 6, -6, 1, 1],\n [1, 2, -1, 3, 3],\n [-4, 6, -5, -6, -2],\n [-5, -6, 5, -3, 6],\n [4, -1, -4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -5, -4, 2, 1],\n [-4, -4, -5, 3, 0],\n [-3, 4, 4, 4, -3],\n [-6, -3, -5, -2, 3],\n [6, -2, 6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 2, 3, 5, -3],\n [-3, 2, -6, 5, 4],\n [-6, -6, 4, 3, -6],\n [6, 6, 4, 6, 5],\n [-6, 3, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 6, 2, -1, -5],\n [-5, 2, 2, -2, 3],\n [2, -4, -6, 1, 5],\n [1, -6, 0, 4, -5],\n [0, 6, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 4, -6, 3, 2],\n [-4, 1, 6, 6, -6],\n [2, 3, 6, -2, -2],\n [3, -5, -4, -6, 4],\n [-2, 6, -1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -4, 2, -2, -3],\n [-6, 0, 6, -4, -1],\n [4, -3, 5, 3, 3],\n [-3, 4, 2, -4, -2],\n [5, 2, 3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 6, -5, 2, 4],\n [5, 3, -2, 0, 5],\n [2, -5, -6, 6, -1],\n [-3, -3, -5, -5, 5],\n [6, 1, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -2, 6, 4, 6],\n [1, -5, 6, 4, 6],\n [5, 2, 4, -3, -3],\n [-4, -3, -3, -3, -5],\n [-4, 2, 2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 0, -1, -4, -3],\n [-1, 4, -2, -5, -4],\n [3, 5, -1, 1, -3],\n [6, 1, 6, -5, 6],\n [3, 5, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 6, 2, 1, -5],\n [6, -5, -1, -5, -6],\n [5, -5, 5, 4, 6],\n [-4, -6, 4, 0, 4],\n [6, 1, -3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -6, 5, 6, -3],\n [-4, 0, 3, 5, 1],\n [5, -3, 3, 6, -2],\n [-3, -3, 5, -4, 2],\n [3, 6, 5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 3, -6, 2, -5],\n [2, -2, -3, -6, 6],\n [6, -3, 6, 2, 5],\n [1, -6, 1, 6, -1],\n [-2, -2, -6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -6, 4, 5, 5],\n [-2, -5, 0, -6, 5],\n [1, 1, -6, 2, 2],\n [-4, -3, 1, 6, -5],\n [4, 0, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -6, 2, -3, 1],\n [3, -4, -5, 0, 2],\n [-1, 6, -4, -5, 6],\n [3, -2, 2, -4, 2],\n [-5, -4, 3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 1, 5, -5, 0],\n [3, -3, 2, 1, -3],\n [-3, 3, -3, -5, -6],\n [3, -6, -6, 1, -1],\n [-6, 1, 3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -3, 6, -2, 6],\n [-4, 2, -6, -2, -4],\n [2, -5, 0, 5, 3],\n [3, -3, 2, -2, 4],\n [1, 2, 6, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -6, -6, 0, -3],\n [0, -1, -6, 2, 6],\n [-3, 3, -3, 2, -3],\n [1, -6, -6, -1, -6],\n [-1, 0, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 1, 2, 5, 2],\n [1, 3, -6, -2, -1],\n [-3, -2, -6, -5, -6],\n [3, -4, 0, -3, -5],\n [-3, -6, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 1, 2, -6, -4],\n [-4, -3, 2, -1, -3],\n [-3, 0, 6, 0, 6],\n [1, 3, -4, -3, -3],\n [-2, 0, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, 5, 1, 3],\n [-3, -6, 3, 6, 6],\n [-2, -1, 1, -4, 1],\n [-2, 4, 2, -3, -2],\n [-6, 0, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -3, -2, 4, -1],\n [5, 3, -3, 3, 2],\n [-3, -6, -6, -1, -5],\n [1, 4, 1, 6, -5],\n [-1, -4, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 0, 4, 0, 5],\n [2, -4, 2, -5, -1],\n [1, 6, 2, 6, -2],\n [0, 2, -3, 2, 5],\n [2, 5, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 1, -1, 0, 6],\n [-3, 0, -1, 1, 0],\n [-4, 1, 5, -6, -6],\n [-3, -1, -1, 3, -2],\n [-4, 6, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -6, -1, -3, 2],\n [3, 2, -6, -6, -4],\n [2, 6, 1, 2, -5],\n [5, -4, -4, 5, 6],\n [5, 1, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, -6, 6, -1],\n [6, -1, -4, 2, 0],\n [-1, 5, 4, 4, 2],\n [6, 2, -6, 1, 4],\n [1, 4, 5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -2, -1, -4, -4],\n [-2, 2, -2, -1, -5],\n [-6, 6, 4, 1, -1],\n [1, 6, -4, -5, -5],\n [5, -1, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 6, 3, -6, -3],\n [-4, 1, 5, 1, 5],\n [-2, 6, -4, -5, 6],\n [-5, 6, -3, 2, 2],\n [3, -6, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 1, -1, 3, 6],\n [3, -6, 5, 1, -2],\n [-3, 3, 3, 4, -4],\n [-5, 6, 1, -4, 4],\n [1, -4, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -2, -6, -4, 5],\n [-1, 3, -5, 2, 5],\n [-1, 1, -4, -6, 0],\n [6, -3, 6, -2, -4],\n [-3, 0, -3, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -1, -4, -6, 0],\n [-1, -1, -3, -3, 0],\n [6, -4, 2, -3, -4],\n [-4, -1, -3, -2, -3],\n [-4, 5, 4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 4, -4, -3, -6],\n [2, -1, 5, 2, 0],\n [5, 4, 5, -6, 2],\n [-3, 4, -5, 6, -1],\n [-2, 0, 3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 1, 6, 4, 3],\n [-1, -1, 2, -4, 4],\n [-4, -6, -6, 4, 2],\n [-3, -3, 6, 6, 3],\n [-3, -3, 4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 6, 5, -5, 5],\n [0, -1, -4, 3, 2],\n [-5, 5, 5, 1, 3],\n [-5, 5, 1, -2, 2],\n [6, 1, 5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 6, 1, -3, 2],\n [2, 2, 0, 4, 1],\n [2, 3, 1, 6, -1],\n [0, 2, -5, 6, -4],\n [-6, -3, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -5, -1, 2, 4],\n [-4, 3, 5, 0, -1],\n [-5, 3, 1, 4, -4],\n [2, 4, 5, 5, 3],\n [-1, -6, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 4, 1, -3, 0],\n [-3, -2, -3, 4, -1],\n [2, 3, -2, 0, 5],\n [0, -5, 0, 1, -4],\n [-2, 0, -4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, -6, 0, 1],\n [0, -5, -5, 0, 6],\n [-5, -5, 3, -3, 3],\n [-5, 0, 1, -5, -1],\n [-4, 4, 6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 2, -5, -4, -4],\n [6, -4, 2, -2, -1],\n [6, 5, -6, 0, -1],\n [4, 4, 4, 4, 2],\n [2, 0, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 2, 4, -4, -6],\n [-2, 1, -3, -4, 2],\n [-4, 4, -5, 4, -1],\n [4, 2, 5, 3, -4],\n [-6, -6, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -1, 0, -3, -6],\n [2, 3, -6, 4, -6],\n [-3, -1, 6, 6, 3],\n [-6, -6, 1, -6, 5],\n [-4, 3, -5, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 1, -5, 5, 6],\n [-3, 1, 5, 4, -5],\n [-3, -6, -4, 5, 1],\n [-2, 4, 5, -4, -6],\n [-6, -4, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 1, 4, -6, -2],\n [4, 2, 6, -3, 5],\n [-2, 4, 6, 6, 0],\n [6, 2, 0, 5, -1],\n [3, 4, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 2, 2, 2, -6],\n [-1, 6, 3, 2, -6],\n [-3, -4, -4, 0, -5],\n [1, 2, -1, -1, -4],\n [5, 0, -5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 1, -2, -6, 1],\n [-3, -6, 3, 3, -4],\n [-1, 5, 1, -5, 4],\n [4, -5, 3, 6, 2],\n [-3, -5, -6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -1, 4, 1, 3],\n [-6, 0, 4, -1, -3],\n [0, -6, -5, -3, 0],\n [1, 6, -5, 6, 2],\n [-3, 6, 4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 2, 6, 3, -6],\n [4, -1, 0, -6, 0],\n [0, 2, 5, -6, -2],\n [2, 3, -2, 1, -1],\n [6, -2, -3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -3, -1, -2, -6],\n [2, 3, -1, 5, 3],\n [1, 5, 6, 1, 0],\n [3, 0, 2, -6, 6],\n [-1, -4, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -2, -1, -4, -3],\n [6, 5, 3, -4, -1],\n [6, 1, 0, -2, -1],\n [4, 0, -2, 6, 4],\n [-4, -6, -4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 4, -4, 5, 1],\n [-4, 3, -2, -6, 2],\n [2, 3, -4, 4, 0],\n [-6, -6, 6, 1, 5],\n [-4, -4, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 0, -5, -5, -4],\n [5, -5, 5, 5, 5],\n [3, -4, -2, 0, -3],\n [6, 2, 2, -2, 0],\n [6, -6, 3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, -6, -3, -1],\n [3, 2, -6, 1, -1],\n [-3, 2, 6, -4, 5],\n [5, -2, 1, 1, -1],\n [3, -2, -4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, 2, -5, 6],\n [3, -3, 0, -6, -1],\n [1, 3, 1, -6, 2],\n [-5, 5, -1, -5, 4],\n [-1, -2, -3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -1, -6, -2, 4],\n [-5, 5, -2, 4, -2],\n [2, -6, -3, 3, -4],\n [-5, 2, -3, -2, 4],\n [6, -3, 6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -3, 4, -4, 5],\n [0, -4, -1, 3, -3],\n [-3, 4, -5, 6, 2],\n [5, -1, 6, 6, 2],\n [6, 5, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 2, 3, 0, 1],\n [2, -5, -4, 1, -3],\n [5, -3, 4, -4, -6],\n [4, 1, 1, 2, 5],\n [4, 6, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 4, -6, -3, 4],\n [4, -3, 2, -2, -3],\n [-5, 5, 2, -5, -4],\n [-4, 6, 3, 5, 3],\n [-3, 0, -6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 1, -1, 3, 5],\n [2, 4, 0, 5, -5],\n [-4, -6, 0, -2, -1],\n [4, -1, 4, -1, -6],\n [-4, 4, -4, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 4, -1, -6, 4],\n [0, -6, -3, -1, -3],\n [4, 2, -1, 5, 6],\n [2, -1, 0, -6, 4],\n [3, 0, 6, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 6, 4, -2, 0],\n [-2, 6, -1, 0, -1],\n [4, 1, -3, -4, 6],\n [-3, -2, -5, -5, 0],\n [6, -2, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, 2, -4, -2],\n [-2, -6, 2, 6, 6],\n [-6, -2, -3, -2, -2],\n [-6, 0, 4, 3, 1],\n [5, 3, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -5, -1, -5, 1],\n [-6, 1, 4, 3, 6],\n [1, -6, -2, -6, -3],\n [-5, 4, -1, -4, 4],\n [-6, -2, 0, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, -4, -6, 4],\n [-5, 2, -1, 3, 5],\n [3, -1, -1, 1, -6],\n [0, -3, 4, 3, -1],\n [1, -1, 5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 0, 3, 1, 0],\n [-4, 5, 5, 3, 6],\n [3, 4, 5, -6, -4],\n [-2, -2, 4, 5, 1],\n [-3, 6, 5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 4, 5, -3, -2],\n [4, -3, -1, 5, -3],\n [-6, 3, -6, -4, -6],\n [3, -4, 5, -5, 5],\n [3, 6, -2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -5, 3, 6, -6],\n [0, 4, -3, 5, 5],\n [-3, 6, -5, -1, 1],\n [-6, -3, -1, 2, 5],\n [-1, -4, 5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -6, 0, -5, -5],\n [1, -6, -6, 6, -2],\n [4, 0, -4, 3, 3],\n [-2, 4, 3, -4, -3],\n [-5, 4, -6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 1, 5, 0, 4],\n [-4, -3, -5, 4, -2],\n [6, 3, -5, 6, 3],\n [-5, 2, 4, 3, -1],\n [1, -1, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, 2, -4, 1],\n [2, -2, 5, -5, 2],\n [2, 1, -1, -6, 1],\n [4, 2, 6, -6, 2],\n [-6, 5, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -1, -2, 2, -6],\n [6, -6, 5, 2, 4],\n [-3, 4, 0, -2, 4],\n [6, 3, -4, -2, 4],\n [-6, -1, -6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 3, -2, 2, -5],\n [4, 5, 6, 0, -5],\n [5, 6, -2, 0, -5],\n [-5, -1, -6, 4, -4],\n [1, -6, -3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -2, -6, -2, 3],\n [-3, 2, -1, -5, 2],\n [5, -5, -3, 2, -3],\n [-5, -6, -4, -3, 4],\n [4, 4, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 6, 4, -1, 6],\n [2, 0, 6, -6, 3],\n [-6, -2, -5, 3, 1],\n [5, 0, 6, -6, -2],\n [6, -6, 4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, -2, -3, 3],\n [2, -5, 3, -1, 6],\n [4, 1, 4, -3, -2],\n [-6, -2, 2, 6, -1],\n [-6, 2, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -6, 5, -5, -1],\n [2, -4, -5, -4, -4],\n [5, 6, 1, 5, 4],\n [-5, -3, 6, 5, -2],\n [-3, -5, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -6, -1, 5, 3],\n [-6, -1, 2, 6, 1],\n [-2, 6, 4, -4, 3],\n [4, -4, 6, -2, 1],\n [-1, -6, -1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 5, -2, -5, 4],\n [-2, -5, 4, -2, -6],\n [-1, 2, 5, -5, 5],\n [4, 4, -4, 6, 3],\n [-5, -1, 5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 6, 5, 1, 1],\n [-3, 2, -2, 2, 1],\n [-4, -1, -5, 5, -3],\n [0, -5, 4, -4, -1],\n [-4, -1, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, 3, 1, 0],\n [6, 0, 3, -2, -5],\n [4, -1, 4, -6, -3],\n [3, -6, -3, 1, -2],\n [-1, 4, -1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 3, -4, 4, 2],\n [5, -3, 1, 2, -1],\n [-1, -2, 4, 3, 5],\n [4, -6, 4, 3, -5],\n [2, -2, 6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 1, -4, -1, -6],\n [5, -6, 2, 6, 3],\n [-3, 2, 0, -3, 2],\n [-6, 0, 1, 3, 3],\n [-3, 2, 5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 3, 4, -3, 2],\n [-6, -1, 1, 2, -5],\n [-5, 3, -4, -3, -4],\n [-3, -1, 4, -1, -4],\n [3, 3, -4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 0, 2, 4, -3],\n [0, -1, -5, -6, -6],\n [-1, 4, 3, -2, 0],\n [4, 2, 2, 3, -1],\n [6, -3, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, 0, -2, -3],\n [6, -2, 6, -3, 1],\n [-2, -6, 6, -3, 4],\n [2, -6, 0, 0, 6],\n [6, -4, 1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -6, 1, 0, 4],\n [-3, -5, 3, -4, 6],\n [0, -4, 4, -4, 1],\n [-5, -1, -1, 1, -4],\n [-6, -3, -6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 3, 2, 1, 2],\n [-3, 2, -1, 1, 4],\n [-3, -3, 4, 2, 6],\n [-1, -3, -5, 3, -4],\n [1, -5, -1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -2, -1, -1, 3],\n [-5, 1, 5, 0, 1],\n [-5, 1, -4, -1, -1],\n [5, -4, -6, 2, -5],\n [5, 0, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -3, 5, -4, 3],\n [3, 4, -4, 3, 0],\n [4, -6, -5, 2, 4],\n [-3, -3, 6, -2, -4],\n [-1, -2, 4, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -3, -5, 0, 3],\n [1, -1, 3, 1, 0],\n [2, -3, -3, -4, 1],\n [3, -6, -5, 2, -6],\n [0, -2, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -4, 0, 1, 4],\n [1, 6, 0, -1, 5],\n [2, -4, 6, 4, -3],\n [6, -2, -1, -5, 0],\n [-4, -3, -1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 0, 3, 4, 6],\n [-1, -1, 3, 6, -5],\n [-6, -3, -6, 2, -2],\n [-4, 5, 6, 4, -3],\n [3, 0, -3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, 0, 2, -5],\n [2, -4, 3, -4, 5],\n [0, 0, 6, 6, -2],\n [-2, 4, -4, -4, 0],\n [3, 0, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -6, -3, -4, -2],\n [4, -1, -1, 4, 6],\n [-3, -4, 4, 4, 2],\n [1, -5, -5, 0, -2],\n [3, 3, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, 1, 1, 0],\n [3, -3, 2, 2, 5],\n [4, 6, -2, 2, 3],\n [4, -4, 2, 4, -2],\n [4, -2, 5, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -6, -6, -4, 1],\n [-4, 2, -1, 2, 0],\n [0, -5, 1, 4, 2],\n [-5, -1, 5, -2, 2],\n [0, 0, -5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 3, -5, -3, 5],\n [-5, -5, 2, 6, -2],\n [-5, 6, -2, -2, 4],\n [6, -5, 5, -1, 3],\n [5, 2, 2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -2, 6, -4, 4],\n [2, -2, -6, 6, 2],\n [-4, 2, -2, 4, 5],\n [-5, -5, 6, 1, 0],\n [-1, 0, -6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -1, -3, -2, 6],\n [-4, -3, 1, 4, 4],\n [0, 0, 0, -2, 0],\n [4, -3, -6, -2, 4],\n [-4, 3, -6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 6, -4, -5, -6],\n [6, -2, -6, 6, 4],\n [-6, 6, 0, -3, 0],\n [-4, 0, 0, 0, 2],\n [2, 5, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -5, -6, 5, 3],\n [3, -6, -5, 6, 0],\n [0, 4, 0, -1, 3],\n [-5, 4, -2, -5, -5],\n [-6, 0, 2, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 5, 3, 2, 4],\n [3, -4, -3, -3, 3],\n [0, -2, 4, 6, -3],\n [2, 3, 3, 6, 4],\n [6, -1, -6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 3, 3, 6, 5],\n [-4, -4, 1, -4, -5],\n [0, 0, 0, -4, -1],\n [-6, 2, -5, -4, 2],\n [4, 1, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -4, -6, -3, 0],\n [5, -1, -1, -1, 0],\n [6, 5, 3, 6, -6],\n [5, 4, -3, 6, -5],\n [-6, -4, -3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 5, -5, -3, -5],\n [-2, -5, -5, -2, -3],\n [6, -1, 3, 1, -4],\n [-4, 2, 4, -2, 4],\n [-4, -2, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -1, 5, 1, 0],\n [-3, -4, -5, 6, 5],\n [2, 4, 0, 3, 6],\n [-2, 0, 5, -2, -5],\n [-5, -5, -5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 4, 0, 2, 0],\n [-6, -5, 3, -4, -5],\n [6, -2, 2, 1, -1],\n [-4, 4, -5, 6, 3],\n [4, 0, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 6, -2, 3, -3],\n [-2, -1, -3, 1, 3],\n [2, -1, -4, 5, 2],\n [3, 2, -5, -3, 3],\n [-4, -2, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 6, 4, 3, -4],\n [3, 6, 3, 0, 2],\n [1, 3, -3, -5, 1],\n [6, -1, 2, -4, -5],\n [-6, -4, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -5, -1, 6, 0],\n [-1, 6, 3, -4, -4],\n [-5, 1, 1, 6, -1],\n [-5, 5, 2, 0, 4],\n [-5, 4, 5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, 6, -5, -2],\n [-3, 5, 3, -3, 2],\n [-2, -4, -5, -4, -4],\n [6, 3, -3, -4, 6],\n [-6, 4, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 2, 6, -1, 5],\n [6, -3, -2, -1, -3],\n [-2, -1, -2, 0, 0],\n [0, -5, -5, -6, 6],\n [-5, 3, -2, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -4, 1, 6, 0],\n [4, 4, -1, -3, 2],\n [-3, -4, 2, 3, 4],\n [-1, -5, -4, 5, -1],\n [2, -1, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -4, 6, 1, -6],\n [1, -6, 3, 3, -2],\n [0, 6, 3, 0, -2],\n [-2, 3, -4, 3, -4],\n [-2, -3, -5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 1, 5, 1, 4],\n [0, -4, -5, -2, -3],\n [-4, 1, 0, -3, -4],\n [-2, 6, 1, 1, -6],\n [-4, -5, 0, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 5, -3, -1, 5],\n [3, -5, 4, -1, 0],\n [5, 5, 5, -2, 6],\n [6, 4, -5, 4, -4],\n [-2, -1, 6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 3, -1, 1, 2],\n [5, 5, 2, 6, 2],\n [3, -5, 5, -2, 1],\n [-5, -3, -4, 1, -4],\n [-3, 3, -2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -3, -1, 1, -1],\n [-4, -6, -4, -1, -5],\n [1, 5, 4, 5, 1],\n [-6, 1, 6, 4, -2],\n [-5, -1, -1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -4, 5, 0, 3],\n [-3, -4, -2, -4, 4],\n [2, -1, 0, 3, -2],\n [4, -1, 2, -5, -1],\n [-4, -3, 2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -6, 2, -1, -5],\n [-4, 4, 4, 3, -4],\n [-6, 0, -2, -1, 5],\n [2, -1, -2, 1, 5],\n [-1, 6, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -4, 5, 1, -4],\n [-4, 0, 1, -3, -3],\n [3, 6, -1, 5, 0],\n [4, -5, -4, 0, -2],\n [4, 4, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 5, 3, -4, 4],\n [1, -1, -3, -2, 5],\n [6, 6, -5, 0, -3],\n [-3, -1, 2, 0, -6],\n [2, -6, 3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 6, 5, 3, 0],\n [-3, 6, -6, 6, 6],\n [3, -6, -1, 5, 6],\n [1, -2, -3, -4, 4],\n [-5, 5, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, 4, -3, 6],\n [-6, 1, -2, -2, -5],\n [3, -3, -5, 1, 2],\n [-6, 1, 3, 2, 1],\n [4, 4, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 1, 1, -1, 4],\n [6, 3, -4, 0, -2],\n [4, -5, -5, 5, -3],\n [-2, -2, -3, 3, 0],\n [-6, 3, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -2, 1, -6, 6],\n [-1, -5, -2, 3, -1],\n [-4, 5, 6, -2, -2],\n [-3, 4, -1, -4, 5],\n [-3, 5, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 3, 1, -5, 0],\n [-3, 1, -2, 3, 5],\n [-4, 1, 0, -4, -3],\n [5, 0, -2, -4, 4],\n [-5, -6, 4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -2, 6, 5, 3],\n [0, -5, 2, 2, -5],\n [2, 5, 0, -1, 4],\n [0, -6, 0, 1, 2],\n [0, -3, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 6, 6, -6, 1],\n [5, -6, -1, -5, -2],\n [-5, -1, -4, -1, 0],\n [3, 0, 6, 2, 5],\n [2, 4, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -5, -2, 3, -2],\n [-4, 3, 4, 1, -6],\n [0, 1, -4, -5, -3],\n [-2, -3, -2, -4, -2],\n [-6, -6, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -1, 1, -5, -1],\n [-2, -2, 1, -5, -1],\n [5, -1, -2, 4, 3],\n [0, 5, -1, -6, -6],\n [2, 4, -2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 5, 4, 5, 2],\n [-2, -4, 0, -3, -2],\n [1, -3, 3, 6, -3],\n [-6, 0, 4, -5, -4],\n [0, 5, 4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, 2, 3, -5],\n [-5, -5, 4, -6, -1],\n [-3, -2, 4, 2, 5],\n [-4, 3, 4, -5, 2],\n [2, 1, 5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 5, 1, 0, 1],\n [-5, 4, -5, 4, 3],\n [3, 3, -4, -3, -2],\n [5, -4, 2, 0, -4],\n [-2, 1, 5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -4, 6, -3, 6],\n [1, 6, -3, 5, -5],\n [3, -1, -3, 1, 6],\n [-6, -2, 6, -2, 1],\n [-1, -5, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 0, -1, 4, 2],\n [-3, -2, 5, 4, 5],\n [0, -5, -5, -3, 3],\n [-2, -3, -4, -1, 4],\n [-2, 3, 2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -4, 2, -2, 0],\n [4, -2, 1, 3, -3],\n [-1, -3, 4, 3, -1],\n [4, 5, 6, 5, 3],\n [-4, 6, 1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 5, 3, -2, -5],\n [-2, -5, 3, 0, -2],\n [-1, 6, -4, 5, 0],\n [2, -5, -3, 2, -2],\n [0, -6, 5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 0, 4, -3, -5],\n [5, 6, 0, -1, -1],\n [-5, 1, 0, -4, 3],\n [-4, -2, 6, -2, -6],\n [5, -4, 5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 1, 3, -3, -3],\n [-1, 3, -6, 5, 4],\n [4, -1, 5, 6, 6],\n [1, 5, 1, -6, -1],\n [-2, 3, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 4, -4, -4, 1],\n [6, 0, -4, -4, -4],\n [4, -2, 6, 5, 5],\n [-6, 3, -3, -5, 5],\n [-2, 5, -6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 5, -1, -5, 2],\n [6, -1, -6, 1, -5],\n [-5, -5, 1, 4, 6],\n [-5, 6, 1, -1, 3],\n [3, -3, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 2, 6, 2, -2],\n [-6, -2, 2, 1, 2],\n [-4, -1, 5, -1, 5],\n [-2, -6, 4, 0, 1],\n [-1, 2, -4, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 4, 1, -3, 6],\n [1, -1, 5, -4, -5],\n [0, 6, -6, -4, -1],\n [-1, 2, 4, -6, 2],\n [-1, 1, -1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -6, 3, 5, 1],\n [1, 6, -6, 5, -5],\n [0, 0, 4, 3, -5],\n [-3, 2, 5, -3, -5],\n [-6, -6, 2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 5, -6, 5, -6],\n [-4, -1, 3, 6, -3],\n [-6, -3, -2, -1, -4],\n [-1, 0, -2, 3, 3],\n [4, 6, -4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -4, 0, 1, 1],\n [-3, 4, 1, 0, -2],\n [1, 4, 3, 2, 0],\n [-3, -4, 1, 1, -1],\n [-1, -2, 3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, 6, 0, 0],\n [4, 3, 2, -1, 0],\n [5, 0, -2, 0, -5],\n [6, 1, -6, 6, 6],\n [-5, 5, -5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -3, 0, 0, -2],\n [1, -2, -2, 5, 4],\n [5, -2, -4, -5, -3],\n [-5, -1, -6, 2, -4],\n [-1, -6, -4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -2, 1, 4, 0],\n [4, 3, 6, 0, -1],\n [-1, -2, 1, -4, -6],\n [5, 5, 4, 3, 5],\n [5, 3, 1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 6, 3, 4, 5],\n [1, 2, -4, 4, 0],\n [-5, 2, -3, 2, 6],\n [-5, -3, 5, -3, 3],\n [1, 0, -2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 0, -1, -6, 4],\n [4, 2, 4, 5, 6],\n [-5, 5, 3, 1, -3],\n [-5, 0, -1, -4, 2],\n [0, 1, -2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 3, -3, -1, 0],\n [4, 0, -5, 6, -2],\n [-1, -1, -6, 4, 6],\n [6, -1, 2, 4, 6],\n [5, -6, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -6, 6, 4, 0],\n [5, 5, 4, 4, 3],\n [5, -4, -1, -1, 3],\n [-4, 2, 6, -2, 3],\n [-2, 2, -5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 3, -6, -5, -2],\n [-4, 4, -2, 6, 3],\n [0, 1, 6, -6, -3],\n [5, -5, 0, -6, 6],\n [-2, -4, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -2, -5, 4, 1],\n [1, 5, -3, -6, 1],\n [-4, 5, -4, 2, -6],\n [-3, -2, -1, 6, 3],\n [2, -4, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -3, 6, -4, 2],\n [-3, -5, 6, -4, -6],\n [3, 4, 3, 3, 6],\n [-1, 4, 3, -1, 2],\n [3, -3, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -1, -2, -6, 1],\n [-1, -2, 0, 1, -1],\n [5, 1, -4, -6, 5],\n [1, -2, 3, 6, 2],\n [5, -6, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -3, -2, -3, 3],\n [4, 2, 1, 4, 1],\n [-6, 1, 4, 0, 0],\n [1, -5, -1, -5, -5],\n [4, -1, -6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -3, -5, 4, 2],\n [2, -4, 1, 3, -3],\n [-5, -5, 0, -1, -3],\n [2, 6, 5, 0, -4],\n [-6, 4, 2, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -2, -4, 2, 0],\n [3, -6, 0, -5, -6],\n [-3, 5, -4, 2, 2],\n [-5, 5, 5, -4, 5],\n [6, 0, 2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 5, 4, 5, 1],\n [1, -6, 4, 3, 4],\n [5, 4, 4, 2, -5],\n [4, -2, 3, -3, -6],\n [4, 3, -3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -3, -6, 4, 0],\n [5, 5, 0, 2, -4],\n [-3, -3, -5, 4, -5],\n [-6, -1, -4, -5, 2],\n [1, -2, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 3, -5, 4, 1],\n [1, 0, 4, -5, 1],\n [-2, -5, -5, 2, -3],\n [2, 3, 3, 2, 2],\n [4, -4, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 5, -6, 6, 1],\n [0, 6, -6, 0, 2],\n [-6, -2, -3, -5, 4],\n [-3, -5, 0, 4, 2],\n [4, 4, -6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 3, -3, -4, -2],\n [4, 0, 5, 0, -2],\n [3, 1, 4, 4, -3],\n [2, -3, 3, 2, -6],\n [5, -4, 6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 3, -4, 3, 6],\n [2, 4, 5, -5, -3],\n [-1, 3, -6, -4, 0],\n [-6, -3, -2, -4, 1],\n [-2, -1, -3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 0, -6, -1, 4],\n [2, 6, -1, 6, 2],\n [1, 3, -5, -3, 4],\n [4, -5, -1, 5, -1],\n [5, 5, -1, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -6, -5, 0, -6],\n [-1, 5, -1, -2, -1],\n [-6, -6, -5, 1, -2],\n [5, -4, -4, 5, -6],\n [-3, 6, -1, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -2, -3, 1, 6],\n [3, -1, 6, 3, 5],\n [3, -3, 0, 3, -2],\n [5, -2, 5, -4, -3],\n [1, 3, -3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 3, -6, 6, -4],\n [5, -4, 0, -4, 5],\n [2, 2, 0, -3, -3],\n [-2, 1, -4, -6, -3],\n [-3, -3, 3, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, 4, -4, 6],\n [-5, 1, 4, 6, 4],\n [-1, 1, 5, 5, 4],\n [1, -5, -2, 5, -2],\n [4, -3, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 4, 6, 2, 6],\n [-2, 6, 5, 5, 3],\n [4, 3, 6, 6, -3],\n [3, -4, 3, -5, -4],\n [6, 6, -5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 1, -3, -2, 1],\n [3, -2, 0, 6, 5],\n [2, 6, 1, 1, -5],\n [4, -4, -4, 2, -6],\n [5, 6, 2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -2, -4, 2, -2],\n [-2, -2, 2, -5, 6],\n [6, -3, -6, 4, -5],\n [4, -3, -3, -1, 1],\n [-1, -2, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 6, -3, -1, -2],\n [5, -4, 3, 4, -1],\n [-5, 6, 5, -2, 4],\n [-6, 6, -6, 5, -2],\n [3, -1, -1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -3, -5, -1, -1],\n [-4, -3, -5, -1, 5],\n [6, -5, 3, -3, 0],\n [5, 4, -1, -5, 0],\n [-3, 4, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 1, -6, 5, -3],\n [2, -5, -1, 5, 3],\n [-2, -5, -1, -3, 6],\n [-6, 1, -5, -4, 4],\n [-6, 3, -6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 0, 6, 1, 1],\n [3, -5, 3, 1, -4],\n [-3, 3, 6, 5, -1],\n [4, 4, -5, 5, -1],\n [-2, -2, 5, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, -4, 6, -1],\n [6, -6, 0, -4, -1],\n [-4, 6, 6, 5, -6],\n [5, 6, 2, 0, -5],\n [-2, 3, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 4, -4, 4, 6],\n [-1, -3, -3, -5, 6],\n [6, -4, -6, -4, 3],\n [1, -3, 3, 1, 2],\n [-5, 1, 3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, -4, -5, -1],\n [1, 2, 3, -5, 1],\n [1, 6, -3, -6, 0],\n [2, 5, 0, 6, 6],\n [-6, -6, -1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, 0, 6, 3],\n [-4, -5, 3, 3, 4],\n [0, 6, 6, -5, -6],\n [4, 2, 3, -2, -6],\n [6, -3, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -4, -1, -1, -3],\n [-4, 2, 2, -6, -4],\n [-6, 5, 2, -6, -1],\n [-1, -2, 0, 1, -6],\n [2, -6, 0, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 0, 6, 5, -1],\n [-5, -4, -5, -2, -2],\n [2, 1, 6, -6, 4],\n [-6, -4, 3, -3, 0],\n [-2, 6, 5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 6, -6, 1, 0],\n [-2, 6, 3, -4, 3],\n [1, 5, -3, 2, 1],\n [-6, -1, 1, -6, 4],\n [-5, 6, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -4, 2, 1, 6],\n [5, -2, 5, 3, -6],\n [-2, -6, 0, -2, 3],\n [-2, -6, 5, 6, 2],\n [-2, -5, -3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -4, 0, 0, 0],\n [1, -4, -6, -4, 6],\n [5, 3, 4, 2, 2],\n [3, -5, -5, 6, -6],\n [1, -3, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -2, -2, -6, 2],\n [0, 0, -3, 3, -2],\n [6, 0, 6, -6, -3],\n [-1, -4, 5, 2, 0],\n [-2, 0, 6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 6, -4, -1, 2],\n [-3, -1, -5, -4, 2],\n [-2, 2, 0, 3, 0],\n [-5, 1, 2, 2, 1],\n [6, -5, -5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -3, -2, 0, -5],\n [5, -5, 6, 1, 0],\n [-4, 0, -2, -2, 4],\n [3, 1, 6, -1, 4],\n [-5, 6, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 0, -3, 4, -1],\n [-5, 0, 3, 4, -5],\n [3, -3, 0, -3, -6],\n [1, -4, 1, 3, 2],\n [4, -3, -5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -4, -1, -3, 0],\n [-1, 5, 6, -1, 4],\n [6, -3, 3, -6, -5],\n [-5, -3, -6, 1, 3],\n [-5, 1, 6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -6, 3, 0, 0],\n [0, 2, 4, -1, 2],\n [6, 0, 1, -2, 0],\n [1, -6, -1, 6, -4],\n [-4, 5, 1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, 3, -4, 6],\n [-5, -4, 4, -5, -5],\n [-2, -5, -6, 2, 3],\n [6, 0, -3, -5, -3],\n [-1, 1, 3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -4, -5, -5, -4],\n [-1, -3, -3, -6, 1],\n [6, -5, 1, 4, -6],\n [3, 2, 0, -4, -4],\n [3, 2, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -4, 2, 4, 5],\n [-5, 0, 6, -6, 1],\n [4, 0, 5, 3, -1],\n [-3, -4, 3, 4, 4],\n [-5, 1, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 5, 1, 5, -2],\n [-6, -5, -1, 1, 6],\n [1, -5, 3, -3, -2],\n [2, 1, -4, -4, 1],\n [-3, 1, 2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 2, -1, -4, 1],\n [1, -5, 1, 0, 1],\n [6, 3, -1, 0, -2],\n [-4, -1, -3, -6, -4],\n [5, -5, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -3, -5, -6, 1],\n [-1, 4, -5, -4, 1],\n [-2, 5, -3, 5, 6],\n [3, 1, -5, 0, 4],\n [-3, -6, 5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 3, -1, -4, -2],\n [-4, -3, 3, 6, -2],\n [1, 1, 5, 4, 0],\n [-5, 6, -2, 2, -4],\n [2, -1, -4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -1, 2, 2, 4],\n [6, 1, 5, 4, -5],\n [4, 6, 4, 5, -4],\n [4, -1, -4, -4, -6],\n [4, -1, 3, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -5, -6, -3, -1],\n [1, 2, -5, -3, 2],\n [-1, 4, 6, -1, 6],\n [-2, -3, 4, 6, 4],\n [2, 6, -2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -3, -2, -3, 5],\n [5, -2, 4, -3, 0],\n [-6, 5, 5, -2, 2],\n [-2, 5, -4, 6, 0],\n [0, 6, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, -4, -1, 6],\n [6, -2, 0, -5, 6],\n [2, 1, -4, 5, 1],\n [-4, 6, 4, 3, -6],\n [5, 1, 2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -4, 3, -4, 2],\n [0, -3, 5, 6, -5],\n [-5, -5, -1, -4, -1],\n [-1, 0, 1, 0, 4],\n [-1, 5, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 1, 5, -6, 2],\n [4, 3, 6, -3, 2],\n [0, -5, -3, 4, 2],\n [-4, -1, -5, 3, 0],\n [5, 4, -6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 0, 2, -2, 6],\n [1, 1, 2, 5, 3],\n [-6, -5, 6, 4, 4],\n [4, -5, -5, 6, 1],\n [-6, -2, -4, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 2, -4, -3, -6],\n [5, 4, -5, 5, -5],\n [-6, -5, 6, 6, -1],\n [3, -2, 1, 3, -6],\n [-4, -5, -6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, -3, -1, 0],\n [6, -5, 3, -1, 1],\n [2, 6, -4, 4, 2],\n [1, 0, 4, -6, -6],\n [-1, 5, -5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 2, 5, 1, 2],\n [-4, 1, -3, 2, 2],\n [0, -6, 4, -1, 2],\n [6, -3, 3, 6, 3],\n [1, 6, 2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 2, -1, -2, 1],\n [-6, 4, 2, 3, -3],\n [-6, 3, 0, 2, -4],\n [2, 4, 6, 5, 4],\n [1, 5, -4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 3, 6, 5, 4],\n [2, -4, 1, -6, 6],\n [-4, -5, -6, -1, -5],\n [3, 2, 3, 6, 2],\n [-2, 4, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 3, 0, -2, 4],\n [4, 3, -1, -1, 1],\n [3, 0, -3, -4, 6],\n [5, 6, 5, 3, 5],\n [-2, -2, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 2, -1, 3, 1],\n [3, 4, -1, 1, -4],\n [-6, -5, 4, 2, -5],\n [-3, -3, 1, -4, -3],\n [5, 0, -3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -5, 4, 1, 2],\n [0, 5, -6, 2, -3],\n [-2, -5, 4, 0, -5],\n [-6, 2, -5, 6, -6],\n [-6, -4, 4, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -2, -1, -1, 1],\n [0, 6, -2, 4, 3],\n [5, 6, 5, 2, -6],\n [0, 0, -2, 2, 6],\n [2, -4, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 6, 4, -2, 0],\n [-6, -2, -3, 6, -5],\n [1, 1, -1, -2, -1],\n [-5, 2, -1, 0, 3],\n [1, 2, 3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 3, 1, 6, -5],\n [3, 2, -1, -4, 0],\n [0, -6, -6, 4, 0],\n [2, -2, 2, -5, -3],\n [6, -3, -5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -3, -2, -2, -4],\n [4, 4, 6, 3, 6],\n [-3, 2, -1, 1, -5],\n [-6, -6, -6, -4, 3],\n [-5, -4, 6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, -1, -5, 1],\n [3, -3, 4, 6, -1],\n [2, 4, 4, -1, -5],\n [4, 1, -1, -5, 6],\n [4, -4, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, -3, 6, -6],\n [-5, -1, -2, 4, 3],\n [1, 3, -4, 2, -5],\n [0, -6, 5, 6, 5],\n [1, 4, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -5, -1, 0, -1],\n [2, 1, -4, -1, 4],\n [-5, -4, -3, -3, -2],\n [6, 3, 0, -4, 6],\n [-5, -1, 1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, -4, -5, -4],\n [6, -2, 3, -5, 3],\n [3, 2, -5, -5, -6],\n [1, -6, 6, -1, 5],\n [5, 5, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 0, 0, -3, 0],\n [3, -4, 3, -5, -6],\n [5, 5, -6, 3, 0],\n [-1, -4, -1, 1, 6],\n [-2, 5, 1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -3, 2, 1, 4],\n [1, 1, 6, -6, 5],\n [-4, -3, 6, -6, -2],\n [-4, 6, 6, 6, -2],\n [-4, 1, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 3, 2, 4, -5],\n [-6, 3, 1, -6, 1],\n [1, 2, 3, 3, 4],\n [5, 4, 2, -1, -1],\n [2, -5, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -4, 2, -3, 1],\n [-4, -2, 3, 6, -6],\n [0, -1, -4, 6, -3],\n [4, 1, -4, 0, -5],\n [-2, -1, 5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 0, 2, -3, -6],\n [4, -2, -5, 4, 6],\n [5, -2, -5, 1, 0],\n [0, 0, -5, 1, -5],\n [0, 1, 3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 4, 0, 1, -4],\n [4, -2, -1, 3, -1],\n [-1, -1, -3, -3, -6],\n [6, 2, 2, -1, 0],\n [3, 6, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -3, 4, 4, 0],\n [1, -1, 0, 6, 4],\n [5, -3, 4, -6, 6],\n [6, 0, 5, -3, -4],\n [-6, -6, 6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -1, 3, 1, 1],\n [-6, 0, 0, 6, 4],\n [5, 5, 6, -1, -4],\n [-1, 3, 2, 1, 5],\n [4, 6, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -5, -1, -5, -2],\n [-6, 6, 3, 5, 1],\n [2, -1, -2, 5, -2],\n [3, 4, -6, -2, -5],\n [1, 3, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -6, 2, 6, 6],\n [-2, -5, 2, 0, -5],\n [-6, 6, -5, 0, 0],\n [-3, -1, -1, 2, -1],\n [-6, 4, 3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 2, 1, -5, -6],\n [-4, 2, -5, 2, 0],\n [6, 0, -6, 0, -1],\n [-1, 1, 6, -4, 4],\n [0, 1, -5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 6, -2, -2, 2],\n [3, 6, -6, 3, 1],\n [-4, 1, 4, -1, -5],\n [-1, -5, 2, -5, 0],\n [-3, 0, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -4, 0, 0, -1],\n [3, 5, -6, -2, 2],\n [-2, -3, 6, 5, -3],\n [4, -6, -4, 1, -2],\n [-5, 6, 5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 5, -2, -3, -4],\n [1, 6, 2, -5, 3],\n [1, -1, 5, -1, 1],\n [-4, 0, 3, 3, 6],\n [-2, -5, 1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 1, 0, 2, 0],\n [5, 1, -3, -4, -6],\n [-6, -6, 6, 6, 3],\n [0, 4, -3, -6, 6],\n [-5, 6, -6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 4, 3, 2, 2],\n [-2, -5, -3, 0, -4],\n [-3, -6, 5, -1, 3],\n [-5, 3, -2, -2, 2],\n [0, -2, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 3, -3, 5, 5],\n [-2, 4, 1, 5, -3],\n [0, -6, -4, 2, -3],\n [-3, 0, 3, 2, 5],\n [2, 2, 1, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 1, 1, -2, 6],\n [-3, 3, 2, -3, -5],\n [1, 0, 2, 3, -4],\n [5, -5, 4, -6, 4],\n [-4, 0, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, -4, 1, -3],\n [-2, -2, -2, 4, 2],\n [-2, -4, 4, 6, 4],\n [-5, 6, -4, 1, -3],\n [-4, 1, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 1, -6, 4, -6],\n [-6, 0, 6, 4, -6],\n [3, -6, -4, -4, 2],\n [-4, -1, 5, 2, 6],\n [-6, 5, -1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 1, 1, 4, -5],\n [-3, 3, -2, 3, 3],\n [2, -4, -1, 3, -1],\n [1, 3, -2, -2, 0],\n [1, -2, -6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -6, 0, 5, 0],\n [3, -5, 6, -3, -2],\n [-3, -1, 1, -4, 2],\n [-2, 2, 2, -1, -3],\n [-3, -1, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 5, 3, 6, -1],\n [-2, 6, -4, -3, 6],\n [2, -1, -1, 5, -4],\n [3, -3, -6, 5, 5],\n [-2, 1, 1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, -5, 3, 1],\n [0, 2, -1, -1, -5],\n [-5, -4, -5, -6, 4],\n [2, 6, -4, 4, 3],\n [0, 5, 3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 3, 2, 0, -3],\n [-6, -2, 5, 2, 1],\n [-4, -5, 1, 2, 5],\n [1, 5, 1, -6, 0],\n [4, -6, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 3, -4, 6, 0],\n [-6, 1, 3, -6, 3],\n [5, -3, -2, -2, -2],\n [-6, -4, -4, 4, -3],\n [-5, -4, -1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -4, -4, 5, -5],\n [0, 3, -4, 2, 1],\n [-5, 6, 3, -6, 0],\n [5, -2, 6, 0, -4],\n [-1, 6, 4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, 0, -1, 3],\n [1, -3, -3, 2, 4],\n [-3, -1, 4, 3, 5],\n [-1, -5, -1, -5, 0],\n [-4, -6, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -5, -2, -2, -2],\n [-6, 6, -5, -3, 2],\n [-2, 0, 4, 6, 6],\n [5, 1, 6, 4, 3],\n [-5, -1, 5, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, 3, 3, 1],\n [2, 0, -2, 5, 1],\n [6, 2, 2, 5, -5],\n [-1, -4, 2, 2, 1],\n [2, -3, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -6, -3, -3, -4],\n [2, 0, -2, 3, 2],\n [-1, 0, 5, -4, -5],\n [1, -2, 2, -6, 2],\n [4, -5, 5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -3, -2, 1, 5],\n [-3, -5, -3, 4, 5],\n [-6, 2, 4, -2, 3],\n [0, -1, 0, -5, 2],\n [3, 2, -4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -4, -5, -6, 0],\n [2, 2, -3, -6, -3],\n [-2, 6, 2, -3, 1],\n [2, 4, -4, 6, 6],\n [3, -2, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 4, -4, -5, 1],\n [6, -2, -5, -5, 2],\n [-3, 4, -6, -1, -2],\n [3, 1, -5, -5, 3],\n [2, 3, 6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -6, -1, 3, -1],\n [6, -1, 2, 3, -4],\n [1, 6, -4, 3, 5],\n [2, -3, -2, 6, -2],\n [-1, -1, -3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 5, 6, 5, -2],\n [2, -5, 3, -1, -6],\n [5, 0, -6, -4, 0],\n [-6, 6, -3, -4, 5],\n [3, 2, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 0, -5, 1, -1],\n [0, 3, 3, 5, -5],\n [-2, 0, -1, 5, -6],\n [4, -5, -4, 6, 3],\n [3, -6, 2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -2, -2, 1, 4],\n [1, 3, 1, -5, 2],\n [-1, 5, -6, -5, -4],\n [5, 4, 5, -4, -6],\n [1, 6, 5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -5, -2, 0, -1],\n [-1, -1, 4, 1, -2],\n [-5, 3, -2, 2, -5],\n [5, -3, -3, 6, -4],\n [1, 2, -5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, 4, 2, 5],\n [0, 1, -1, 4, 6],\n [2, 4, 5, 5, 5],\n [0, -3, 0, 4, 3],\n [0, 4, -6, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -4, -4, -4, -4],\n [-3, 3, 2, 3, -4],\n [-5, 6, -4, -6, -2],\n [5, -5, 0, -3, -3],\n [3, -3, 6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 1, -2, -6, 2],\n [1, 5, 4, 3, -1],\n [4, -3, -5, 4, -5],\n [1, 5, 2, -6, -2],\n [4, 6, 5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -1, -3, 5, -3],\n [1, -5, 1, 0, -1],\n [-4, 5, -4, 0, -5],\n [4, 1, -1, 2, 5],\n [-2, 2, 5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 3, 6, -3, 3],\n [-3, 5, -2, -2, -1],\n [5, 3, 4, 5, 6],\n [-4, 0, -5, -4, 6],\n [-1, -6, 6, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 2, 2, -2, -2],\n [1, 5, -5, 5, 5],\n [2, 1, -1, 1, -5],\n [4, 3, 5, -4, 5],\n [2, -5, -4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 0, 4, 3, 0],\n [5, -6, -4, 4, 5],\n [4, -1, -2, 6, 6],\n [5, 1, -2, -4, 2],\n [5, -5, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, -6, 1, -2],\n [-1, 5, 4, -3, -3],\n [0, 6, -2, -6, 4],\n [-3, -4, 5, 2, -2],\n [-3, -5, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -4, -6, -2, -5],\n [-6, 3, -1, -3, -5],\n [5, 5, 4, 6, 5],\n [6, 6, -5, -6, -4],\n [5, 6, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 0, 6, 3, -6],\n [0, 5, -5, -2, -6],\n [-4, -6, -1, 1, -4],\n [0, -5, 5, -3, 4],\n [2, -4, -1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -5, -1, 1, -6],\n [5, 3, 1, 6, -1],\n [0, 2, 1, 2, -2],\n [-1, 6, -4, -3, 4],\n [-1, 0, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -3, -2, 4, -1],\n [1, -5, -1, 0, 6],\n [6, -5, -4, -2, 1],\n [-1, 4, -6, -1, -5],\n [6, 1, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -3, -3, -3, -4],\n [-6, 5, 6, 1, 1],\n [0, -6, 1, 6, 3],\n [-2, 3, -6, -3, -3],\n [3, 2, -5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 6, -5, -4, -5],\n [-3, 4, -1, -4, -6],\n [-2, 2, 6, -4, -6],\n [5, -5, -5, 2, -1],\n [3, 0, -5, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 1, -5, 5, -2],\n [0, -5, -6, -2, 2],\n [-1, 4, -3, 5, 1],\n [6, -1, -2, -6, -6],\n [0, 0, 6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 1, 4, -3, 1],\n [0, -2, -6, 6, 2],\n [-3, -1, -3, -3, 0],\n [-4, 2, -3, 4, 0],\n [-5, 3, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 2, -4, 3, 2],\n [5, -4, 0, 2, 4],\n [-5, 4, 3, -2, 5],\n [5, -6, -1, 2, 6],\n [-4, -6, 2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -2, -1, 5, -6],\n [3, 3, 5, -1, 1],\n [6, 5, 3, -5, -5],\n [5, 3, 3, 3, 0],\n [-3, 0, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -3, -6, -4, 0],\n [0, 1, 0, 5, -4],\n [-6, -5, 0, 0, -4],\n [1, -3, 2, -5, -2],\n [-4, 0, 5, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 5, 0, -1, -1],\n [6, 2, -6, -2, -2],\n [3, 0, 5, 4, -3],\n [-5, 4, -5, 6, -6],\n [5, -4, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -5, -6, -4, 0],\n [2, 0, -5, -1, 1],\n [-6, 3, -2, 1, -3],\n [6, -2, -2, 5, 2],\n [-6, -1, -2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, -2, -6, 3],\n [1, -2, -4, 5, 0],\n [-2, -4, 4, 4, -6],\n [-5, 3, 3, -1, -3],\n [-2, 0, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 4, 1, 1, -1],\n [3, -2, 4, 1, 4],\n [0, 3, -3, 5, 1],\n [-4, -5, 1, 1, 3],\n [4, -6, 2, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 3, 6, 5, -1],\n [1, 4, 1, -5, -1],\n [-1, -6, 2, -3, -4],\n [-6, -4, -1, -4, 4],\n [3, -4, 6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 0, 2, -4, -3],\n [3, -5, 2, -6, 3],\n [1, -6, -2, 5, 4],\n [0, 3, 0, 5, 0],\n [5, -2, -6, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -4, -1, 2, -3],\n [3, -3, 1, -3, -4],\n [-6, 5, 0, -6, -4],\n [-1, -2, 4, 3, 3],\n [-3, -6, 4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 6, 0, 1, 4],\n [5, 3, 1, 2, -3],\n [-2, 2, 1, 2, 1],\n [1, -1, 5, 0, 1],\n [-2, -5, 5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 5, -1, -4, 3],\n [-3, -2, 1, -6, -3],\n [-4, 5, -1, -5, 2],\n [-5, -5, 1, 6, 0],\n [1, 3, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -6, -4, -6, 3],\n [-5, 0, 4, -2, -2],\n [-6, -1, -3, -2, 0],\n [6, 6, 0, 0, -2],\n [3, -4, -2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 1, 1, -4, 4],\n [6, 3, 1, 6, 2],\n [-3, -1, 1, 6, -1],\n [-4, -4, 4, 2, -5],\n [4, 3, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -3, -6, -1, 1],\n [1, -6, 0, -5, -3],\n [-2, 5, 1, -1, -3],\n [2, 4, -3, -5, -6],\n [5, -6, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -1, -1, -5, -6],\n [5, -6, -2, 3, 5],\n [-6, -1, -5, 6, 1],\n [-1, 4, -3, 0, 1],\n [5, -3, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 6, 6, -1, -4],\n [5, 0, 5, 0, 3],\n [-6, 4, 1, 2, -5],\n [-6, -5, 3, 6, -2],\n [4, 3, -5, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 4, -6, 1, -5],\n [-1, -2, -6, 6, -5],\n [-6, -2, 4, 2, 5],\n [4, 2, -5, 3, 5],\n [-2, 4, 5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 0, 1, -6, 5],\n [-5, -2, -4, -5, 0],\n [0, 5, 4, -4, 4],\n [-6, 6, 0, 4, 3],\n [3, -5, -4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 2, -4, -3, 1],\n [6, 4, 3, 6, -6],\n [2, -3, -1, 6, 6],\n [-1, -2, 5, 6, 0],\n [2, -3, -2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 4, -4, -5, -1],\n [-4, -1, 3, 5, -5],\n [-3, 3, -4, 1, -6],\n [-4, 3, 1, 0, -5],\n [-3, -2, 2, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 4, -1, 1, 0],\n [-3, -3, 2, 2, 1],\n [1, -6, -3, -4, 0],\n [-4, -2, 1, -2, -5],\n [-6, 5, 5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 2, 2, 1, 2],\n [-6, -3, -3, -5, -1],\n [6, 3, -3, -4, -3],\n [-2, -1, -1, -6, -3],\n [4, 1, -3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 4, -5, -5, -3],\n [2, 4, -2, 6, -5],\n [-5, -4, 3, 5, 1],\n [2, 1, 0, -2, -5],\n [6, -6, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -5, 2, 1, 0],\n [-3, -3, -4, -6, 5],\n [-5, -2, 6, 3, 0],\n [5, -4, -6, 6, -6],\n [-2, 1, -5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 4, -6, -1, -1],\n [2, -3, -1, 0, 1],\n [6, 5, 0, -3, 0],\n [4, -6, 1, 3, 3],\n [-2, -5, 4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 5, -4, -6, -2],\n [3, 5, 6, 3, -3],\n [1, -6, -2, 4, 0],\n [-1, 0, 6, -2, 4],\n [3, 3, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 5, -5, 5, 4],\n [-5, -1, -4, 3, 4],\n [-1, -4, -1, 3, -3],\n [-3, 3, -2, 1, -4],\n [3, 5, 3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 5, 5, -2, -1],\n [-5, 2, -5, 3, -5],\n [6, 2, 2, 6, -3],\n [-1, -5, 2, -5, 0],\n [0, 6, -2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -4, 3, 3, -5],\n [5, 6, 2, 6, 5],\n [-3, 3, -5, -1, 4],\n [-5, 4, -1, -6, 3],\n [-1, -5, 6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 0, -6, -5, 2],\n [3, 4, 2, 0, -4],\n [4, -1, -3, 5, -4],\n [6, 3, -5, -4, -6],\n [-6, -1, -6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -6, -5, -5, -3],\n [-4, -1, 3, 1, -4],\n [-2, 1, 0, 5, 1],\n [-5, -2, -3, -6, 3],\n [-2, 4, -3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, -5, 0, -4],\n [3, 2, 1, 1, -6],\n [2, -3, -1, 6, -1],\n [3, 3, -2, 3, -5],\n [4, 1, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 5, -3, -6, 3],\n [0, 1, 2, -3, -4],\n [5, 4, -5, -3, 6],\n [-6, 3, -2, 3, -5],\n [-4, -2, -5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 1, 1, -3, 0],\n [0, -5, 0, 0, 0],\n [1, -3, -5, 3, 0],\n [-2, 4, 5, -2, -2],\n [-2, -2, -4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -4, -5, 0, -2],\n [-4, 3, 2, 1, -1],\n [0, 4, -1, 3, -1],\n [0, 3, 3, -5, 2],\n [-4, -4, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 6, 1, -6, -5],\n [6, -5, 2, -4, 3],\n [-3, 2, 1, 0, -1],\n [1, -3, -1, -3, 5],\n [-2, -1, 6, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -2, 1, 0, -6],\n [-4, -4, 0, 3, 2],\n [-5, 0, -5, -3, 2],\n [5, -6, 0, -4, -3],\n [1, -4, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 3, 4, -6, 6],\n [-4, 0, -6, 3, -1],\n [-2, 1, -5, -6, 1],\n [3, -3, 5, 3, -1],\n [-6, 2, -4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 6, 2, -4, 2],\n [-1, 2, -4, 1, -5],\n [-4, -3, 5, -5, 0],\n [3, 1, 5, -6, 6],\n [-5, 6, 1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -3, -4, 2, -3],\n [-1, 0, -5, 2, -1],\n [2, 0, 3, 0, 3],\n [-5, 1, -6, 1, 3],\n [-4, 2, 5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, -2, 5, 0],\n [2, 6, -1, 2, -1],\n [-4, -1, -3, 4, 2],\n [4, 3, 0, 5, 1],\n [1, 2, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 2, 3, -6, 3],\n [-3, -1, 6, -6, 2],\n [5, 4, 5, 1, 5],\n [-1, 5, 2, -1, 6],\n [-5, 3, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 4, 1, 4, 1],\n [2, 4, -6, 1, -5],\n [3, 2, -1, 1, 6],\n [3, -1, 3, 2, 0],\n [-1, 1, 1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, 0, 6, -1],\n [5, 2, -3, -5, 3],\n [2, -5, -4, 0, 6],\n [-3, 4, -1, -6, 5],\n [1, -5, -5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 2, 0, 2, 2],\n [4, 6, -1, -6, -1],\n [0, -1, 5, -4, 1],\n [5, -3, -3, -4, 2],\n [3, 4, 3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 4, -6, -3, -1],\n [0, 2, 2, -6, -5],\n [-5, 1, 3, -1, -3],\n [-3, -2, 3, 1, -3],\n [-5, 4, -2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 3, -3, -5, -5],\n [3, 3, 4, -3, -3],\n [6, 1, 5, 4, -1],\n [0, 3, 3, 3, -1],\n [0, -5, -5, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -2, -6, 1, 4],\n [-6, -6, -6, -6, 6],\n [3, 2, -2, -5, 6],\n [-1, 0, -4, -4, 4],\n [3, -6, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -4, -6, -4, 2],\n [-6, 4, -1, -4, -1],\n [-2, 4, 5, 3, -1],\n [-6, 3, -1, 6, 5],\n [-1, 0, 5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 6, 1, 3, -6],\n [-4, 0, 6, -6, 6],\n [1, 0, 2, -5, 6],\n [5, -2, 2, 5, 3],\n [-5, -4, -2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, 5, -4, -2],\n [2, -5, 2, -5, 3],\n [3, -1, 1, 3, 6],\n [-4, 4, -6, -5, -3],\n [4, -2, -4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -3, 6, 4, -5],\n [-3, 3, 1, -6, 6],\n [2, -3, 2, 3, -2],\n [3, -2, 5, 4, 0],\n [-6, 1, 0, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 5, 2, 2, -1],\n [-1, -1, 6, 5, 6],\n [-4, 3, 6, -4, 0],\n [2, 3, 6, 4, 0],\n [-5, 0, -5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -5, 3, -1, 3],\n [-6, 1, 6, -4, -2],\n [6, 1, 0, -3, 0],\n [1, 5, 4, 0, -4],\n [6, 6, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 6, -2, -4, -1],\n [1, -2, 5, 0, 1],\n [3, 3, 5, 0, 6],\n [5, 3, 3, 4, 6],\n [2, -5, -4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 5, 2, 1, -3],\n [-1, 5, -6, -6, -2],\n [-2, 5, 3, 0, 0],\n [3, -6, 5, -1, -5],\n [-4, -3, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 4, -2, -1, 6],\n [2, -4, -1, 6, 4],\n [1, 4, 2, 2, -1],\n [-6, 1, -1, 6, 5],\n [5, -4, 3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 2, -4, -5, 6],\n [3, 0, 3, -6, 0],\n [-2, -5, -5, -2, 0],\n [6, 6, 2, 0, -3],\n [2, 1, -2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -3, 5, 2, -3],\n [1, 2, -5, 3, 4],\n [-4, -6, -2, -4, 1],\n [2, 3, -1, -6, 4],\n [-5, -4, 6, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 3, 1, 3, -6],\n [-2, 5, -2, 2, 5],\n [6, 3, 2, -1, -4],\n [0, 1, -4, -2, 2],\n [4, 2, -5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -1, 2, -6, 4],\n [0, 5, -4, 5, 4],\n [0, -2, -1, -6, 1],\n [-2, 1, 3, 6, -6],\n [3, 1, 3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -6, 6, -3, 3],\n [5, -4, 1, 1, -4],\n [0, -1, 6, 1, 4],\n [4, -2, -6, -2, -1],\n [5, -5, -5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 4, 5, 2, -1],\n [-6, -6, 6, 1, 6],\n [0, 0, -6, -5, 4],\n [0, -6, -6, 4, 3],\n [-4, 3, -1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -5, -5, -3, 5],\n [3, -5, 3, -5, 4],\n [0, -4, -1, 6, -5],\n [6, 4, -3, 5, -3],\n [-2, -6, 5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -1, 6, -5, 4],\n [5, 0, 2, -4, -1],\n [-2, -3, 4, 5, 1],\n [4, -1, 1, 0, 1],\n [0, 4, -4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 3, -5, 1, -5],\n [4, -1, -4, 2, 4],\n [-2, 3, 6, 5, 0],\n [-2, 4, 3, -5, -6],\n [-1, 4, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -5, 1, -2, 0],\n [0, -3, 3, -1, 0],\n [-4, 5, 1, 0, 0],\n [-2, 0, 5, 6, -3],\n [1, -3, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 2, -3, 4, -2],\n [0, -3, -1, 3, -5],\n [0, -4, 1, -3, 6],\n [6, 6, 5, -1, 1],\n [-6, 2, 4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -6, 0, 3, -2],\n [-6, -2, 4, 0, -6],\n [1, -3, 0, -3, -4],\n [-2, -1, -2, -1, 4],\n [6, 2, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -2, 3, -6, 3],\n [5, 0, 4, -1, 4],\n [2, -4, 5, -4, -5],\n [-6, 0, 5, 4, -6],\n [-3, 4, 2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, -1, -4, 4],\n [-1, -2, -4, 4, 0],\n [0, -2, 1, -6, 2],\n [3, 3, -3, -3, -3],\n [6, 6, -6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 3, 3, -3, -1],\n [4, -1, 3, -1, 5],\n [2, 6, 3, 0, 0],\n [-5, 4, 4, 5, 1],\n [-2, 0, -2, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 0, -2, -3, 4],\n [1, 4, 0, -2, 3],\n [-3, 1, -3, 3, 3],\n [-2, -6, 1, 1, 1],\n [2, 6, -4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 5, -5, -2, -2],\n [2, 0, 0, 2, -2],\n [4, 1, -5, 2, -1],\n [4, 3, 1, 5, 1],\n [5, -6, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -5, 1, -6, 3],\n [5, 6, 0, 2, 3],\n [3, -5, -1, -1, 6],\n [-4, 5, 1, -4, -3],\n [4, -4, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, -2, 3, 6],\n [-2, -1, 3, 4, -3],\n [2, 3, 2, 5, 4],\n [-2, 3, 1, -5, 5],\n [0, 6, -3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 6, 2, 1, 2],\n [-1, 6, 1, -1, -5],\n [3, -4, 0, -6, 3],\n [2, 5, -1, -5, -2],\n [-3, 2, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 6, 0, -6, -2],\n [-2, 4, 2, 3, -2],\n [5, -4, 3, 6, 2],\n [2, 0, -5, -4, 5],\n [6, -4, -6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 1, -6, 0, 1],\n [-4, -5, 1, 5, -4],\n [1, 1, 1, 4, -2],\n [-5, -6, 2, 6, 0],\n [5, 2, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 0, -5, -5, 5],\n [3, -5, 6, -5, -6],\n [1, -4, 0, 3, -6],\n [-6, 6, 3, -6, -5],\n [3, -3, -2, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -6, -3, -2, -4],\n [-4, 3, -1, 2, 1],\n [2, -5, 5, 2, -1],\n [3, -4, -5, 2, 2],\n [-3, 5, 1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 0, 3, 1, -2],\n [-2, -1, 3, 5, -2],\n [-1, 0, 2, 4, 6],\n [-1, 4, -1, 5, -3],\n [3, -2, 0, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -6, 4, 2, 3],\n [5, 0, 2, 3, -2],\n [-5, -4, 1, -2, 6],\n [-2, -4, -5, 3, 5],\n [2, 0, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, 5, -3, 4],\n [2, -4, -5, 2, 6],\n [-3, 1, 6, -6, -2],\n [-4, -1, 6, 6, -4],\n [-6, 6, -5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 0, -6, 0, -4],\n [-3, 3, 2, -5, 5],\n [-2, 3, 6, -6, -2],\n [5, 3, 0, -1, 4],\n [-2, 4, 1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 3, 2, 4, -6],\n [-4, -2, 4, 2, -2],\n [-3, 0, 5, 3, -2],\n [0, 2, 5, 2, 6],\n [-6, -2, -1, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -1, 3, -3, 5],\n [-3, 4, 6, 3, -1],\n [-4, -5, -4, 5, 4],\n [0, -6, -4, 6, -1],\n [1, 5, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -5, 2, 6, -4],\n [-3, -3, -1, 2, -1],\n [0, 0, -4, -4, -2],\n [6, 3, -3, 4, -1],\n [-3, -1, -5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -3, 0, -4, 6],\n [6, -2, -5, 1, 6],\n [3, 0, -1, 2, -6],\n [4, 5, 5, -2, 1],\n [-4, 1, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -5, 2, -1, -6],\n [-2, 0, -2, -3, -1],\n [-3, 6, -5, -2, 0],\n [4, -6, -3, -3, 3],\n [3, 6, 5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -3, -4, -1, -5],\n [2, 2, -1, -3, 1],\n [6, -2, 5, 3, -5],\n [0, 3, 5, -3, -4],\n [-6, 0, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 6, 0, -5, 3],\n [5, 1, 1, -3, 4],\n [0, 3, 3, -4, 3],\n [-6, -4, -2, 5, -2],\n [-5, -3, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 5, 2, -5, -3],\n [-1, 1, 4, 6, 0],\n [2, 1, 4, -3, -4],\n [4, -6, -5, 1, 4],\n [2, -4, -1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 4, 0, 6, 4],\n [5, 1, -6, 3, -4],\n [-5, 5, -1, -1, -4],\n [5, -4, 2, -6, 2],\n [1, -2, 4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -1, -3, -2, -5],\n [1, 5, -2, -4, 2],\n [0, -6, 6, 0, -4],\n [6, -1, 0, -3, 6],\n [6, 0, -6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, -2, -5, 0],\n [-1, -3, 1, 2, 0],\n [5, -2, -2, 2, -3],\n [0, 3, -2, 4, 3],\n [3, -2, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 4, -4, 2, 5],\n [0, -5, -4, 3, -5],\n [-3, 4, 4, 5, 3],\n [-3, -6, -6, -5, 3],\n [3, 4, -5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 2, -2, 5, -3],\n [3, 4, 5, 3, -2],\n [6, 1, 1, 0, -1],\n [4, -1, -6, 4, 0],\n [6, -3, -1, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 4, 4, -5, -3],\n [3, -2, -2, -5, -6],\n [1, 6, 0, 5, -2],\n [2, 3, -2, -5, 2],\n [-6, 0, 5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -3, -2, 6, 5],\n [-2, -3, -5, 1, -4],\n [4, -5, 5, -6, -4],\n [1, -5, -4, -5, -3],\n [1, 0, 4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 3, 2, -6, 1],\n [-6, 5, 2, 5, -4],\n [-3, -5, 5, -2, -3],\n [3, 5, -5, 0, 1],\n [-6, 5, -2, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -1, 4, 5, 1],\n [1, -1, 2, 3, 6],\n [4, -2, -6, -2, 2],\n [-2, -5, 2, 4, -2],\n [3, 3, 6, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 3, 0, -6, -1],\n [5, -5, 4, 3, 6],\n [-1, 3, -5, -5, -4],\n [-4, -1, 5, 4, 0],\n [1, 2, -4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -6, -6, 0, 0],\n [-5, 4, -6, 6, 2],\n [0, 0, 5, 1, 2],\n [3, -3, -5, 6, 0],\n [1, 4, -5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 4, -5, -1, 0],\n [6, 0, 1, 4, -5],\n [-1, -2, -5, 6, 4],\n [-4, 0, -6, 4, 4],\n [-5, -2, -1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 0, 2, -5, 4],\n [-1, 4, 5, 1, -1],\n [0, 1, 6, -2, 4],\n [6, 0, 1, 2, 1],\n [6, 2, 2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -1, -6, -4, -6],\n [2, -3, 5, 6, 6],\n [-3, 4, 0, 0, 6],\n [6, 3, 4, -3, 4],\n [-1, 6, -6, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 5, 5, 6, -5],\n [-1, -5, 4, 0, 6],\n [4, -5, 2, -1, -2],\n [3, -1, 3, -1, -6],\n [-1, -5, -6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, 1, 5, -2],\n [2, 4, 5, 3, -4],\n [1, 2, 1, 3, 5],\n [2, 5, 2, 3, -1],\n [-6, 1, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -4, 3, -5, -3],\n [-3, -5, -5, -3, 0],\n [3, -3, 6, 6, 4],\n [2, -4, -4, -6, -2],\n [2, -2, -6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 3, 1, 5, 0],\n [6, 0, -6, -4, 6],\n [6, -4, 2, -2, -5],\n [-2, 0, 5, 4, -2],\n [-4, 6, -6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 1, 6, 0, 3],\n [4, -1, -3, -1, -2],\n [0, -6, 6, 4, -3],\n [5, -2, 4, -1, 5],\n [2, -1, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -3, -3, 4, -3],\n [-3, 1, -4, 1, -1],\n [-5, 1, 0, -3, 3],\n [-3, 5, 3, -1, -1],\n [-2, -4, 6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -1, -4, 0, 0],\n [6, 2, -4, 3, -1],\n [-5, -6, -3, -5, 6],\n [2, -2, 0, -5, -6],\n [-6, 0, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -4, 6, 3, 4],\n [3, 4, 2, 5, -3],\n [-3, -3, -5, 4, -3],\n [5, 1, 0, 5, 1],\n [-3, -5, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -4, -4, 3, 0],\n [-3, 5, 2, 6, 3],\n [4, -4, -3, 1, -4],\n [-1, 3, -2, 4, -5],\n [0, 3, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -1, 4, 2, -6],\n [6, 5, 4, 1, 6],\n [-1, 6, 5, -6, -5],\n [5, -2, -1, -1, -4],\n [1, -2, 4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -6, 5, 3, -6],\n [-3, 0, 2, -1, -1],\n [-2, -5, -6, -3, 1],\n [3, -2, -4, -4, 3],\n [1, 6, -5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 6, 4, -1, -3],\n [6, -1, 1, 2, 1],\n [-3, 0, -5, -3, -3],\n [-5, -6, 6, 0, 2],\n [0, 1, -6, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -5, 0, -3, 0],\n [2, -4, -1, -1, 3],\n [-2, -2, 1, 1, 3],\n [2, -6, 6, -1, -4],\n [6, -6, -1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 5, 3, -2, 6],\n [-5, -4, 6, -2, -6],\n [0, 2, 5, 1, 2],\n [2, 2, -2, -4, 4],\n [-3, -4, -4, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -6, -5, 3, 1],\n [2, 4, -6, -2, -4],\n [2, -3, -3, 1, -4],\n [-1, 1, 6, -2, 3],\n [-4, 6, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 6, -4, -2, 2],\n [-2, -4, -2, 6, -2],\n [6, -5, -2, -1, 4],\n [5, -1, -5, 0, 5],\n [0, 4, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 5, -6, -5, 5],\n [4, -4, 3, 6, 6],\n [-6, -5, -1, -3, -3],\n [-3, 6, -3, -1, 1],\n [-3, -2, -6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -1, -1, 5, 0],\n [-2, 1, 6, -2, -4],\n [5, 3, 0, -5, 5],\n [-1, 2, -1, 6, -1],\n [-4, -4, -2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 3, 5, -1, -6],\n [-1, 2, 6, 2, -6],\n [6, -5, 6, 2, 3],\n [2, -2, 1, -5, 0],\n [3, 2, 3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 0, -2, 5, -2],\n [0, 3, -3, -2, -1],\n [5, -4, 6, -4, -3],\n [2, 3, 6, -3, -5],\n [1, 2, -6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -1, 0, 5, 3],\n [-5, 1, -2, 2, -6],\n [5, -3, 2, -3, -5],\n [3, 1, -2, 6, 5],\n [-2, -3, -1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 4, 3, -5, -3],\n [3, 1, 2, -4, -6],\n [-5, -1, 3, 1, 3],\n [-4, 0, 2, 4, 0],\n [-3, 3, -4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 0, -2, 5, 0],\n [-4, 6, -3, -5, 5],\n [5, 2, -2, 4, -4],\n [0, 0, 4, -1, -5],\n [-5, 6, -3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -2, -4, 0, -1],\n [1, 3, -3, -2, -5],\n [5, 4, 3, -2, 1],\n [-5, 0, -1, -2, 4],\n [-5, -4, 1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -5, -4, -3, 3],\n [4, -5, 0, -3, -4],\n [1, -5, 4, 6, 4],\n [0, 3, -1, 3, -2],\n [2, 2, 2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 4, -1, 2, -5],\n [-1, 5, -1, 5, 4],\n [3, -6, 2, 0, 5],\n [-3, -5, -2, 5, 0],\n [0, -4, 0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 1, -1, 1, 3],\n [-3, -5, -6, -6, 5],\n [1, -3, -5, 4, 5],\n [5, -2, -1, 0, 3],\n [2, 6, 3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 1, 5, 3, 1],\n [5, 1, -1, -3, 0],\n [-1, 4, 5, 4, 4],\n [-2, 6, -2, 0, 3],\n [0, -1, 0, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -3, 5, -6, -3],\n [-1, -1, 6, 1, -6],\n [3, 3, 2, -5, 2],\n [0, 6, 6, -4, 0],\n [6, 4, -3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -2, 1, 1, -2],\n [-6, 6, -5, -6, 0],\n [0, -2, -5, -5, -3],\n [4, 5, -4, 1, 6],\n [6, 3, -4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 3, -3, -2, -4],\n [-6, -6, 0, -5, -5],\n [4, 3, -1, 3, -1],\n [-1, 3, 3, -6, 2],\n [-3, -1, -2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, 2, 6, -2],\n [-6, -3, -4, 4, 0],\n [-5, -4, -4, 5, -2],\n [-6, 4, 1, -3, -5],\n [1, -4, -2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 1, -3, 4, -5],\n [1, 6, -6, -1, 5],\n [4, -4, -5, -6, -6],\n [4, 3, 6, 5, 2],\n [-1, 2, -5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 1, -5, -2, 1],\n [1, 0, 1, 6, 1],\n [-2, 4, -5, 5, -4],\n [0, 5, -1, -3, -5],\n [1, 5, -4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -2, 5, 0, -5],\n [6, 5, 6, 3, -1],\n [-4, 5, -4, 6, -5],\n [2, 6, -4, 5, 4],\n [4, 0, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -3, 2, 3, -4],\n [6, -2, 0, 0, -1],\n [-3, -4, -2, -1, -1],\n [2, 0, -2, -1, 5],\n [4, -5, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -2, 5, 2, 1],\n [-2, -2, 1, 4, -2],\n [-1, 1, 1, -1, -6],\n [-3, 1, 3, -3, 6],\n [-1, -3, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 1, -3, 4, -6],\n [5, -4, -5, 3, -2],\n [3, 3, -4, 6, 5],\n [4, -3, -6, -3, 2],\n [-5, -3, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -4, 6, 6, -4],\n [5, -1, -6, 3, 1],\n [-4, 3, -4, 3, 0],\n [5, 0, -1, -2, -1],\n [5, 4, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 6, -4, 3, 2],\n [3, -6, 0, 2, 1],\n [-1, 6, -4, 2, 0],\n [-1, 0, -1, -2, -3],\n [6, -2, -5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 1, 6, 3, 5],\n [5, 5, -4, 6, 4],\n [-3, -6, 4, -5, 5],\n [-6, -6, -6, 0, -5],\n [-6, 5, 0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 4, -2, -4, 5],\n [3, -2, 4, 1, 6],\n [-4, 3, 5, 6, 2],\n [-5, -3, 6, -1, 5],\n [-5, 3, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 4, 4, 6, 3],\n [-1, 2, 4, 0, 3],\n [1, 6, 2, 2, 0],\n [4, 3, 4, 4, -3],\n [5, 6, 1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 5, -2, 3, 4],\n [-2, 6, -5, -5, 4],\n [1, 4, 6, -2, -4],\n [-4, -3, 5, 6, -3],\n [-6, 1, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -5, 1, -5, 6],\n [1, 0, 1, -5, -1],\n [2, -3, 2, -1, 4],\n [-5, 6, -3, 2, 6],\n [-2, 0, 3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 0, 3, 4, -6],\n [-6, 4, 4, -6, 5],\n [5, 4, 6, 0, 2],\n [5, -5, -1, 0, 0],\n [0, 1, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -4, -4, 2, 3],\n [-3, -4, 5, -6, -2],\n [2, 0, 6, -1, 6],\n [6, 5, -4, -5, 5],\n [5, 2, 3, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, -4, 5, -2],\n [-4, -6, 1, 3, -4],\n [-3, 2, 3, -3, 6],\n [-2, 5, 5, 6, 0],\n [-5, 4, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 3, 1, 2, -5],\n [3, 1, -6, 4, 6],\n [-3, 5, 6, -5, -2],\n [6, -5, 5, 0, 5],\n [0, -2, 1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -1, 6, -4, -4],\n [-4, 3, -6, -2, -4],\n [-6, 4, -6, 4, -3],\n [6, -2, 4, 2, 5],\n [4, 1, 3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 5, -1, -2, 4],\n [-2, 0, 0, 6, -1],\n [-5, 5, -6, -3, -2],\n [2, -4, -4, 0, -2],\n [2, 5, -1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -3, -1, 1, -6],\n [-4, 2, 0, -5, 0],\n [-4, 6, 1, 2, -4],\n [-5, -2, -1, 3, -6],\n [-1, 5, 1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 5, 0, 3, -6],\n [4, -4, -6, 5, 1],\n [4, 6, -5, 6, -5],\n [2, -4, 4, -4, -4],\n [-6, 0, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -1, -6, -4, 2],\n [1, 1, -3, 6, -2],\n [-6, -1, -6, 2, -4],\n [-3, -6, 5, 3, -6],\n [-2, -5, 5, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 2, -6, -5, -5],\n [-6, -3, -3, -6, 2],\n [6, 1, 6, 4, -4],\n [1, 0, -4, 1, 1],\n [0, 4, -3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -5, -5, -1, 1],\n [5, 3, 4, 4, 4],\n [-6, 0, 6, 6, 0],\n [1, -1, -6, 6, 5],\n [-4, 6, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -2, -3, -5, 6],\n [-2, -4, -6, 4, -2],\n [0, -2, -1, 2, -4],\n [-4, -2, -3, -4, -4],\n [0, -5, 4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 5, -2, 3, -6],\n [-2, 2, -3, -6, 2],\n [3, 6, 4, 0, -6],\n [3, 5, 1, 3, 1],\n [-4, -1, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 2, -3, -6, 1],\n [3, 0, 5, 2, 4],\n [-6, 2, -3, -4, -2],\n [0, 4, 4, -2, -6],\n [-1, -1, 2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 1, 1, -4, 0],\n [-3, 4, -5, 6, 4],\n [-3, 0, -4, 6, -3],\n [5, -2, 0, 5, 1],\n [-6, 4, 5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 2, -3, -6, -1],\n [-3, -4, 3, -3, 2],\n [5, 1, 4, 4, -3],\n [6, 3, -3, 0, -5],\n [0, 1, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, -5, -1, -5],\n [-1, 1, -5, 6, -3],\n [4, -6, 5, 5, 0],\n [5, -6, -4, 1, 2],\n [-4, -6, -2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, 5, -1, -3],\n [5, 5, 1, -2, 6],\n [-4, -5, 5, -3, -3],\n [-3, -6, 6, 0, -6],\n [-4, 1, 1, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 1, -6, -4, 2],\n [2, 4, -4, 5, -6],\n [4, 4, -3, -4, -5],\n [1, -6, 0, -3, -2],\n [2, 0, -1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 1, -2, 4, 6],\n [-3, -1, 5, -4, 6],\n [-2, 2, -6, -4, 6],\n [1, 4, 2, 5, -6],\n [4, 2, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -6, 5, 3, -2],\n [-3, 6, 3, -1, 2],\n [4, -5, -5, -3, 1],\n [5, 1, -6, -1, -5],\n [4, 5, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 1, -5, 5, 4],\n [-1, 6, 4, 2, -4],\n [-3, 3, 2, 6, 5],\n [-2, 2, 4, 4, 6],\n [4, -5, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -2, -4, -1, 0],\n [6, 1, 4, 2, -5],\n [-5, 6, 3, 1, -1],\n [-5, 1, -5, -4, 5],\n [-4, -5, -4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -2, 0, -2, -4],\n [-4, 6, -1, 2, -4],\n [-4, 2, 3, -1, -6],\n [5, -6, -4, 0, 5],\n [5, -6, -3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 5, -5, -2, 0],\n [1, -5, 0, 6, 0],\n [-3, 2, -3, 1, 5],\n [-4, -6, 3, -4, -4],\n [-6, -2, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 4, 5, -6, -5],\n [-5, 4, -3, 0, 5],\n [4, -5, 3, 2, -1],\n [-1, -5, 0, 0, -5],\n [-1, 1, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 0, 3, 2, -1],\n [0, -6, -4, 3, 0],\n [0, -2, -1, 1, -2],\n [-2, -1, -5, 1, -5],\n [0, -6, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 5, 1, 3, -1],\n [-3, 3, -1, 4, -2],\n [2, -2, 4, 6, -5],\n [4, 6, -3, 0, -4],\n [5, -2, 5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -5, 0, 1, -1],\n [-5, -3, 4, -5, -3],\n [6, -6, 5, -2, 6],\n [3, -6, -2, 0, 1],\n [1, 4, -2, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 4, 2, -6, -5],\n [2, 3, -5, -2, 4],\n [0, 5, 2, -1, -3],\n [-1, -5, 3, -6, 4],\n [6, -4, 6, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -6, -2, -4, 4],\n [0, 2, -3, 1, 0],\n [2, 6, -5, 2, 6],\n [-2, -6, 3, -3, 5],\n [-4, -3, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 2, 4, 2, -2],\n [-4, 6, -4, 3, -5],\n [-5, -3, 4, -2, -4],\n [-6, 3, -6, 6, 6],\n [6, -2, -5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 5, -1, 1, 2],\n [-5, 5, -6, 3, -4],\n [-3, 4, 0, 2, -4],\n [-4, 5, -6, 0, -4],\n [2, -6, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, -4, 2, -2],\n [-1, -5, -3, -4, -5],\n [1, 5, -2, 0, -5],\n [5, -1, -3, -6, 6],\n [2, 0, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -2, -4, 6, -4],\n [-1, 5, -5, -4, 4],\n [3, 5, -4, 3, -3],\n [2, 1, -5, 6, 4],\n [1, 0, 6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 4, 3, 4, -2],\n [5, 1, 6, -4, -4],\n [5, -6, -3, 5, 3],\n [1, -2, 4, 3, -6],\n [-3, 1, 5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -4, 6, -1, 2],\n [3, -3, 3, -1, -6],\n [2, -6, -1, 3, 0],\n [-2, -3, 0, 2, -4],\n [4, -2, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -5, 0, 1, -5],\n [6, 5, -2, 6, 1],\n [-6, 2, -6, 4, 5],\n [-6, -6, -3, 1, -3],\n [4, 4, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -6, 2, -6, 0],\n [-3, -5, 1, 3, -3],\n [3, 1, 4, -6, -2],\n [2, 0, 0, 3, -6],\n [0, -6, 3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 6, -1, 2, -3],\n [5, -4, -3, -1, -6],\n [-6, 0, 2, -6, -1],\n [4, -2, -5, -6, 4],\n [-2, -1, -4, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, -6, -2, 3],\n [1, -1, 5, 5, 5],\n [-1, -2, -4, -5, 2],\n [-4, 6, -1, 5, -1],\n [5, 1, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -6, 1, 5, 6],\n [0, 0, 6, -4, 2],\n [1, -1, -2, -6, -1],\n [-5, 0, -2, -5, -2],\n [2, -1, -5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -5, 3, 2, 2],\n [-1, 6, 3, -5, 1],\n [-1, -6, 3, 5, 5],\n [6, 5, 0, 5, 4],\n [-1, 4, 5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -1, -6, 1, -3],\n [-4, 6, -6, -1, -3],\n [3, 5, 3, 1, -1],\n [4, -4, -6, -6, 4],\n [0, 1, 4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -4, 4, -2, -1],\n [-2, -5, 5, -4, 3],\n [2, 3, 5, 2, -3],\n [-6, -3, -1, 0, 3],\n [0, 4, -1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 2, 3, 3, 4],\n [-2, -6, -5, 3, 2],\n [-6, -3, 6, -6, 1],\n [2, 4, -4, 4, 4],\n [-6, 6, -1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 2, -4, -4, -1],\n [-6, -4, 0, 0, -1],\n [-6, -3, -2, 3, -3],\n [-5, 2, -4, 3, -5],\n [-4, -1, 1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 6, 2, 2, -3],\n [-6, -5, -1, 0, -2],\n [4, 0, 5, 1, -4],\n [4, 3, 6, 2, 2],\n [0, -1, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 6, 0, 6, -2],\n [1, -4, 2, 2, 5],\n [-1, -5, 4, -2, -2],\n [-5, -3, 4, 3, 3],\n [-6, 2, 1, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -3, -5, 6, -3],\n [-1, 2, 2, 2, 3],\n [-3, -1, 2, 5, -1],\n [-3, -4, 0, -6, 0],\n [-1, 4, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 4, -4, 3, -1],\n [3, 1, 4, -4, -1],\n [-5, 5, 4, 0, 0],\n [3, 6, 2, -6, -4],\n [1, -3, -6, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 4, -5, -1, 6],\n [-2, 5, 3, -3, 3],\n [1, -4, 5, 0, 4],\n [2, -6, -6, 5, 3],\n [-4, 4, 5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, -1, 5, -4],\n [-3, 6, 0, -1, -3],\n [2, -5, 4, -4, 0],\n [6, 6, 0, 3, -4],\n [0, 4, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 6, 6, 4, 3],\n [-3, -3, -4, 0, 1],\n [-6, -1, 2, 4, -3],\n [0, 2, 5, -1, 1],\n [3, 0, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 3, -5, 0, -5],\n [0, 6, 1, 0, -2],\n [0, -6, -3, -1, -1],\n [6, 0, -6, -3, -6],\n [-2, -3, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -6, 6, -2, 0],\n [-6, -2, -1, 6, -4],\n [-5, 5, 1, -1, -1],\n [4, 5, -2, 1, 0],\n [-1, -3, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 2, -6, 0, 1],\n [6, -1, 1, -3, 4],\n [-2, -2, -5, -5, -3],\n [5, -1, 5, -6, -1],\n [-5, -3, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -2, 6, 1, 6],\n [2, -6, 6, -3, -4],\n [-6, -3, -3, -1, -1],\n [5, -1, -6, 2, -4],\n [0, -6, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -1, -5, 3, 1],\n [3, 1, 1, -1, -5],\n [3, -6, 6, -3, -5],\n [3, 4, 1, 0, 2],\n [5, 4, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -2, -3, 5, -1],\n [-6, -3, 2, -1, 5],\n [-6, 6, 2, 0, -5],\n [4, 5, 6, 2, 0],\n [-3, -4, -6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -2, 6, -3, -2],\n [4, 3, -3, -1, -2],\n [-5, -2, -6, 1, 6],\n [0, -1, 5, -5, -6],\n [1, 4, -3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -2, 4, 1, -3],\n [-3, -5, -2, 6, 2],\n [0, -2, -3, 1, 0],\n [0, 1, -5, 2, 2],\n [6, -4, -5, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, -2, 0, 0],\n [3, 0, 6, -3, 2],\n [-3, 0, -1, 5, 2],\n [-6, 5, -3, -2, -3],\n [-5, -3, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -6, -5, -4, -3],\n [3, 4, 5, 2, 1],\n [2, 1, 0, -5, -6],\n [3, -1, 6, 3, -3],\n [-2, -1, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, 6, -4, -6],\n [5, -6, 4, 6, 6],\n [-1, 3, -5, 3, -4],\n [-5, -3, -2, 5, -6],\n [3, 5, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -6, -6, 1, 2],\n [-6, 2, -2, 6, 5],\n [-4, 5, 3, 6, -4],\n [-5, 1, 0, 1, 1],\n [1, 0, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -2, 3, -3, 0],\n [-3, 0, 3, 1, -1],\n [4, -6, -1, -4, 5],\n [4, 4, 3, -5, -4],\n [0, 5, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 6, 2, -5, -5],\n [-3, -2, 2, 6, -1],\n [2, 1, 2, -4, 6],\n [6, -1, 5, -3, 2],\n [5, -2, -4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 4, 5, -4, -6],\n [5, 5, 1, -4, 4],\n [-3, 3, -2, 4, 3],\n [-1, -3, 3, -2, 4],\n [-5, 3, 4, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 2, -4, 4, 3],\n [3, 4, -3, -2, -2],\n [0, 6, 6, 4, 4],\n [-5, 3, -6, -3, 2],\n [-6, -1, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -1, -2, 2, 5],\n [-1, -5, 5, -4, -5],\n [-6, -2, -5, -5, 5],\n [3, -1, -3, 4, 5],\n [3, 3, -1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -1, -1, -5, 6],\n [-4, -4, 6, 5, 1],\n [5, -6, -1, -1, -3],\n [-3, 0, -5, -1, 0],\n [-5, -2, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 3, 5, -4, -1],\n [3, -4, -5, -4, 6],\n [-2, -4, 5, 1, -4],\n [-2, -2, -2, 6, -6],\n [-5, -3, 1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -1, 6, 1, 1],\n [-2, 2, 6, -6, -2],\n [4, 3, 1, 0, -5],\n [6, 3, -5, 6, -1],\n [3, -4, -3, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 5, -5, 0, -1],\n [-6, -1, 6, -2, -6],\n [-6, 4, 2, -5, 5],\n [2, 1, 2, 1, -3],\n [-4, 6, -2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -4, 6, 4, 3],\n [1, -6, 2, 1, -2],\n [5, -4, 6, 6, 3],\n [-3, 6, 2, 2, -2],\n [4, 6, 1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, 5, -2, -2],\n [-4, -2, 6, -4, -4],\n [-6, 5, 1, -1, 3],\n [4, 2, 5, -3, -6],\n [4, 4, 2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 2, 0, 0, 2],\n [-5, 5, 3, 1, 3],\n [2, 4, 2, -1, 4],\n [3, 6, 1, -6, 3],\n [2, 4, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -1, 1, 2, -4],\n [-3, 2, -6, -5, 4],\n [-4, 0, -1, -4, 3],\n [1, 3, 0, 0, -6],\n [5, -1, 4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 0, 2, 5, -2],\n [-3, 3, -4, 6, 6],\n [-5, 0, -4, 0, -1],\n [6, -1, -2, -3, 1],\n [1, -6, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -2, 0, -1, 0],\n [-5, 4, -4, 2, -5],\n [-1, 2, -6, -5, 2],\n [0, 4, -3, -4, 6],\n [-6, -1, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 0, 6, 3, 1],\n [1, -3, 5, 4, -6],\n [-5, 5, -1, -3, 5],\n [-3, 6, -2, 1, -1],\n [3, 2, -5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 3, -4, -6, -2],\n [-4, 3, -2, 1, 2],\n [-6, -4, -4, 2, 3],\n [5, 2, -6, 5, -5],\n [3, -3, -6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -4, 3, 1, -4],\n [-6, 1, -4, 0, -4],\n [6, 0, 1, 3, -1],\n [-3, -5, -5, 5, -1],\n [4, -2, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, 1, -2, 3],\n [-5, 2, 6, -2, 5],\n [-4, -1, 0, 5, -1],\n [-2, 2, -4, 6, -1],\n [-5, -6, -6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 6, -2, 3, 2],\n [3, 0, -3, 5, 6],\n [-6, 1, 1, 5, -6],\n [0, 5, -6, -3, 0],\n [-1, -1, 1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -5, -6, -6, 5],\n [2, -4, -3, -2, 2],\n [-5, 3, 0, 3, -2],\n [5, 4, 0, 2, -6],\n [5, -5, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -6, -5, -6, -6],\n [2, -6, 0, 0, -6],\n [-5, 5, -2, -4, 6],\n [-1, 2, -4, -2, -3],\n [-4, 3, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -1, 0, 3, 1],\n [-3, -3, -6, 1, 3],\n [2, 4, -3, -4, -6],\n [6, 4, -3, 6, 4],\n [-3, -5, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 5, 0, -4, 2],\n [1, -3, -5, -5, 0],\n [3, -2, -1, -4, 6],\n [-4, 6, -6, -3, 4],\n [-2, -4, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, -5, 3, 2],\n [-2, 0, -4, 0, 0],\n [-1, -2, 4, 0, 2],\n [3, 1, 0, -5, -6],\n [1, -5, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -4, 3, 0, 2],\n [-5, 4, -1, 3, 0],\n [5, 5, 1, 3, 5],\n [-2, 6, -6, 1, -3],\n [-1, 0, 5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, 1, -2, 1],\n [-6, 2, 0, -1, -3],\n [4, 5, -1, -5, -2],\n [3, 5, 1, 3, -1],\n [3, -6, 6, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 1, -4, 3, -6],\n [-3, 6, 3, -4, -4],\n [2, -1, 5, 4, 1],\n [-4, 2, 5, 1, 6],\n [3, 5, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 4, -2, 4, 2],\n [-4, 3, 2, -2, 2],\n [1, -4, -1, 5, -3],\n [-2, -1, 0, -6, -2],\n [-4, 4, 1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -3, -5, -1, 6],\n [-1, -1, -5, -3, -2],\n [5, -5, -2, 1, 3],\n [-4, -2, 6, 6, 5],\n [-6, 0, -3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 3, 2, -1, 4],\n [5, 1, -4, -5, -3],\n [0, 2, -1, -2, 3],\n [4, -5, -4, 4, -1],\n [-6, 1, 5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 4, 6, -4, 0],\n [-1, -2, 6, -5, -3],\n [3, -2, -4, -1, 6],\n [-5, 0, 4, -5, -6],\n [-3, 1, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 5, -1, -3, -4],\n [-2, -5, -6, -5, 1],\n [4, -2, 5, 0, -6],\n [4, -5, 3, 1, 0],\n [0, 2, 5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, -6, 6, -3],\n [-5, 0, -4, -4, 4],\n [0, -5, -3, 4, -3],\n [-5, -3, 4, -4, 0],\n [6, 2, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 1, 0, -5, -5],\n [2, -4, 3, -4, -3],\n [3, 5, -3, -5, -2],\n [4, -3, -1, 1, 5],\n [6, -4, 0, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 1, -1, 5, 2],\n [-2, 5, 1, 0, 4],\n [-5, 3, 5, 4, -6],\n [3, 1, -4, 1, -2],\n [5, -1, 6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, -3, -3, 3],\n [5, -5, 4, 6, 1],\n [-3, 0, -6, 4, 6],\n [-6, 2, -1, -3, 6],\n [4, -2, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 1, -1, -3, -1],\n [-4, -4, -3, 2, 5],\n [-3, -4, 2, 4, 2],\n [-1, 6, 3, 1, -4],\n [1, 4, -5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -6, -3, 3, -4],\n [0, -6, -5, 4, 5],\n [-1, -5, 4, 3, 6],\n [0, -1, 1, 4, -6],\n [1, 1, -6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 5, -6, -3, 2],\n [-6, 0, 3, -1, 6],\n [-3, 6, 5, 0, -4],\n [3, 5, 1, 4, -2],\n [4, -5, -2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 4, 2, -6, 6],\n [-5, 6, 4, 2, 6],\n [4, 5, -5, 0, 4],\n [2, -5, -4, 5, 6],\n [-3, -4, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 4, 3, -2, -3],\n [3, -3, -4, 6, -5],\n [6, -2, -5, 0, -5],\n [3, 0, -6, 0, 1],\n [6, -4, -5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -2, 0, 3, 1],\n [0, 4, -4, -5, 3],\n [-6, 4, -3, 2, -5],\n [-6, 4, 3, 5, 4],\n [6, 6, -5, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -3, 2, -4, -4],\n [-2, 3, 1, -2, -3],\n [-5, 6, -6, 6, -1],\n [-6, 1, -3, -6, 4],\n [1, 0, 6, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 6, 5, 4, 3],\n [0, -2, -5, -2, 1],\n [-6, 4, -1, -4, -1],\n [6, 0, 5, 0, 5],\n [3, 3, -1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 1, 2, 2, 1],\n [-2, -4, 4, -2, -5],\n [-5, -4, -6, 6, 3],\n [-5, -6, 1, 2, -1],\n [-4, -4, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -4, 6, 5, 2],\n [-5, 4, -2, -1, -5],\n [-5, -6, 0, 6, 2],\n [0, 1, -2, 6, 0],\n [-1, 6, -3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 6, -1, -3, -1],\n [2, -2, 4, -4, -2],\n [2, -1, 3, -6, -5],\n [-3, -5, 4, 2, 3],\n [-5, -5, -5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -4, -5, 2, 3],\n [-1, -2, 0, -6, -5],\n [5, 5, -4, -2, 2],\n [-6, 2, 2, -6, -1],\n [1, -4, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 5, -6, 1, 6],\n [-5, 2, 0, 5, 6],\n [5, 2, -2, -3, 2],\n [-6, 3, 6, 4, 3],\n [-6, -5, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 6, -1, -3, -5],\n [-6, -2, -5, -3, 1],\n [1, 6, 6, -1, 1],\n [4, 3, -5, -5, -3],\n [-6, -2, 5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, -1, -4, -2],\n [6, -1, 0, -6, 6],\n [4, 0, 1, 2, -5],\n [-2, 0, 5, 1, -6],\n [-1, 3, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -6, 4, 0, 4],\n [-2, -3, -6, 6, 4],\n [5, -5, -6, -3, -2],\n [2, 5, -1, 6, 0],\n [4, 3, -6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -3, 5, -4, -4],\n [2, 3, -6, -6, 4],\n [-4, -1, 5, 4, -3],\n [4, -2, -6, -3, -6],\n [4, -3, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -2, -5, 4, -4],\n [-4, 1, -2, -2, -1],\n [-1, -6, -2, 5, -1],\n [-1, 3, -4, 6, 0],\n [5, -5, -4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 2, 3, 1, 5],\n [-1, -1, 3, -5, -4],\n [-3, 4, -5, 6, -1],\n [4, 2, 6, 3, 0],\n [-2, -2, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -3, 4, 6, -3],\n [-4, -1, 5, 3, 4],\n [-2, 1, -1, 3, 2],\n [4, 4, 6, -1, 0],\n [-1, 3, -4, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 6, 5, 4, -6],\n [2, -5, 5, -2, -2],\n [-6, 2, 3, 3, 4],\n [-6, -1, 1, -6, 4],\n [-6, 2, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 6, 1, 0, 1],\n [-4, 4, 2, -3, 0],\n [-4, 2, 5, -4, -5],\n [2, 0, 1, -5, 1],\n [1, -5, -4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -3, 2, 4, -2],\n [-5, -6, 0, -3, 3],\n [5, -3, -3, -2, 0],\n [1, 1, -6, 0, 4],\n [5, 4, 0, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -3, -3, -3, 1],\n [1, 5, 2, -1, -6],\n [-2, 5, 6, -6, 2],\n [-1, -1, 6, -4, 5],\n [-5, 3, 4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 1, 1, -4, 6],\n [5, -3, 2, -1, 5],\n [1, -3, 2, 4, -3],\n [-2, 2, 4, 2, -4],\n [-5, -1, 6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 3, -1, -1, 0],\n [5, -2, -3, -6, -5],\n [4, 4, 4, 4, 2],\n [2, 3, -1, -3, -3],\n [-6, 2, 5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -3, -1, -6, -3],\n [-6, 2, 5, 1, 3],\n [-4, -5, 4, -3, -1],\n [-5, -2, -5, -2, 5],\n [3, 1, -3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 1, 6, 6, 5],\n [6, -1, -2, 2, 4],\n [3, 0, 1, -3, 4],\n [4, -2, 2, 6, 3],\n [-3, 3, 0, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -5, 0, -4, 2],\n [-3, 5, -5, -4, -3],\n [2, 5, 4, -1, 4],\n [5, -4, -3, 1, 1],\n [5, -5, 2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -4, 3, -4, -6],\n [-3, -2, -3, 4, -5],\n [0, 1, 1, 0, 5],\n [3, 4, 5, -6, 2],\n [-4, 5, 3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 5, -2, -2, -6],\n [1, 6, 1, -1, -2],\n [-4, 2, -6, 1, -1],\n [5, -1, 1, 4, 5],\n [-1, -5, 2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -3, 4, -2, -5],\n [-5, -4, -6, -4, 5],\n [2, -5, 3, 5, 5],\n [4, 3, -3, -2, -6],\n [-2, 2, -4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -4, -4, 3, 4],\n [5, -1, -2, 2, 4],\n [3, 1, -5, 2, 5],\n [-1, 2, -6, 3, -1],\n [-6, -2, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 6, 3, 3, 1],\n [-4, 4, 3, 6, 4],\n [5, 2, 6, 1, -5],\n [4, 3, 5, -1, 1],\n [1, -4, -6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -3, -4, -6, 1],\n [0, 3, 4, -3, 0],\n [6, 3, 2, -6, -6],\n [-6, 2, -1, -1, -4],\n [6, -5, -4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -6, 6, 3, 3],\n [4, -5, 6, -5, -4],\n [4, 6, -5, 1, 6],\n [-6, 0, 2, 1, 0],\n [-1, 3, 6, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -1, 1, -1, -6],\n [-5, -3, 5, -6, 3],\n [-4, 0, -6, -5, 4],\n [-2, 0, -2, -3, -4],\n [3, 2, -2, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -2, -1, -4, -4],\n [4, -1, 4, 6, 0],\n [6, 6, -1, -1, -2],\n [0, -4, -2, 4, -6],\n [1, 2, -5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 1, 1, 4, -6],\n [3, 6, -3, -6, 2],\n [3, 4, -2, -4, 4],\n [-1, 1, -5, -2, -6],\n [-3, 5, 3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 3, 4, 2, -6],\n [4, -4, -5, -3, -5],\n [1, 1, 0, -6, 0],\n [1, -2, -3, 0, -4],\n [6, 0, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 0, -5, -4, 0],\n [-4, -2, -1, 3, 3],\n [5, 2, -3, 6, 2],\n [-5, 0, -5, 2, -6],\n [2, 0, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 0, 6, 1, -2],\n [4, 0, -4, 1, 0],\n [6, 0, -5, -5, 6],\n [-6, -1, 3, 4, 3],\n [-3, 4, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 1, -2, 5, 1],\n [5, -1, -3, 2, 3],\n [4, 0, 1, 2, 5],\n [6, 6, -5, 1, 3],\n [4, -1, -1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -3, -4, 6, -6],\n [-6, 0, -4, -5, -2],\n [4, -3, 0, 1, 2],\n [-4, 2, -5, 3, -6],\n [3, 3, 0, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 6, 6, -1, -2],\n [-5, 2, -2, -4, 1],\n [3, 5, -2, -5, 2],\n [-4, 1, -4, 5, 1],\n [-3, -2, -3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -5, 6, 2, 4],\n [6, 0, -4, -5, -3],\n [-3, 1, 3, 2, -4],\n [6, -3, 3, -3, 4],\n [-3, -4, 1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 4, -5, -6, 1],\n [1, -3, 5, 0, -3],\n [0, -4, -4, 6, 6],\n [5, 4, 1, -2, 1],\n [-4, 2, -5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 2, 5, 6, -3],\n [0, 0, 0, -1, 2],\n [5, -6, -5, 0, -1],\n [-3, -6, 6, 5, 3],\n [-3, -2, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -3, -5, -5, 6],\n [3, 2, -6, -6, -4],\n [3, 2, 1, 5, 0],\n [6, 0, 1, -2, 3],\n [-5, 4, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 5, -6, -2, 0],\n [0, -4, 5, 3, -6],\n [-6, -5, -3, -1, -6],\n [5, 4, -3, 5, 2],\n [-6, -1, -5, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 6, 6, 3, 4],\n [1, -3, 5, 0, -2],\n [-4, 5, -6, -5, -2],\n [6, 0, -4, 1, -4],\n [4, -2, 4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -5, -3, -5, -4],\n [1, 5, -4, 3, 0],\n [5, 0, -3, -5, 1],\n [-3, 6, -2, -2, -4],\n [-6, 4, 3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -6, 0, -2, 3],\n [2, -4, -4, -1, 0],\n [-5, -2, -4, 1, -3],\n [2, 6, -6, -1, -3],\n [-2, 4, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -4, -5, -3, 6],\n [1, 6, -2, -6, 3],\n [0, -1, 4, -4, 0],\n [-4, 2, -5, -5, 3],\n [-1, 5, 5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, 2, -1, -6],\n [-3, -5, 0, -6, 5],\n [-6, 2, -5, 5, 5],\n [6, -3, 2, 6, -6],\n [4, 0, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 1, -1, 3, 0],\n [1, 5, 4, 1, 6],\n [2, 1, 3, 0, 0],\n [-2, 6, -4, -2, 4],\n [2, 0, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -2, 0, -4, -3],\n [2, -6, 0, -5, 3],\n [-1, -2, 0, -6, 4],\n [-6, -1, -3, -4, 5],\n [-4, 1, -5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -1, 6, 0, -4],\n [6, -3, -6, 3, 0],\n [-4, 2, 6, 6, 0],\n [-2, 2, 1, 0, -1],\n [4, -2, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 0, -2, 4, 5],\n [4, 3, -3, -6, 3],\n [2, 5, 4, 4, -2],\n [-3, -1, -5, -5, 0],\n [4, -4, 3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -5, 5, -6, -6],\n [5, -4, 0, 1, 4],\n [-3, -6, -5, 1, -6],\n [1, 2, -5, 2, -5],\n [-2, 1, 5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 0, -4, -3, 3],\n [-5, -5, 4, 5, -1],\n [-6, 5, 3, 2, 4],\n [-2, 2, 3, 3, 0],\n [-5, 5, -6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, -6, 1, -2],\n [-4, 6, 3, -5, 3],\n [-3, 1, -1, -1, -5],\n [0, 6, 3, -5, -5],\n [-1, -4, 4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 4, 0, -6, -2],\n [0, 0, -2, -3, 2],\n [-4, -3, -5, 1, 2],\n [5, -3, -6, -6, 3],\n [3, 3, 3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 0, -4, 1, -1],\n [-1, -3, -3, -2, 5],\n [-6, 3, -2, 6, 0],\n [3, -2, -5, -6, -2],\n [-5, -4, 5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -2, 0, 0, -3],\n [-1, -5, -5, 5, -4],\n [-5, -4, 2, 5, 2],\n [-3, -4, -2, -1, -4],\n [-4, 2, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 3, 3, -4, 6],\n [-1, -1, -3, 0, 5],\n [-2, 4, -3, 1, -4],\n [2, 5, -6, -2, 0],\n [2, -1, -2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -5, 2, 5, 3],\n [1, 1, -5, 0, -4],\n [3, -4, 0, 2, 1],\n [-4, -5, -1, -4, -4],\n [6, -3, 3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 0, 5, 3, -3],\n [-1, -5, -4, -1, -3],\n [2, -4, 6, -1, -1],\n [4, 4, 4, -5, -3],\n [-1, 6, -4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -3, 3, -1, -1],\n [1, 5, -2, 1, 3],\n [-6, 4, 1, -3, -5],\n [-4, -4, 1, -1, -4],\n [1, -5, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 0, 3, 2, -3],\n [3, 0, -2, 6, 4],\n [0, -5, -6, 3, 2],\n [1, -4, -5, -3, 4],\n [-6, 5, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 4, 2, -3, 3],\n [4, -1, -5, -4, 1],\n [3, 6, 5, -5, -4],\n [1, 6, -3, 3, -6],\n [-1, -4, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -6, -4, -4, 3],\n [5, -3, -2, 3, 5],\n [2, 3, 0, -5, 2],\n [-2, 4, -6, 0, 6],\n [-4, -2, -1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -5, -6, 5, 5],\n [-4, 6, 2, 6, 3],\n [2, 3, -3, 2, 0],\n [3, 3, 6, 3, -2],\n [0, -2, -6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -2, -6, -2, 0],\n [4, -4, -4, -5, -2],\n [3, -6, 4, 6, 0],\n [4, -4, 4, -3, -2],\n [5, 0, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 6, -4, -5, 5],\n [4, 6, 4, -4, -1],\n [-6, 6, 5, -4, -3],\n [6, 1, 3, 3, 5],\n [5, -3, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, 3, -6, -6],\n [0, -1, -3, -4, -1],\n [-4, -3, 3, -5, -2],\n [-2, 6, 6, -6, -2],\n [-2, 5, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 0, -1, 0, 2],\n [5, -1, 1, 1, -4],\n [-6, 1, -1, 4, 3],\n [2, 4, 1, -4, 2],\n [-5, -1, -6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -2, 0, 5, 3],\n [3, 5, 0, -5, -4],\n [-1, 5, 3, -3, 0],\n [-3, 2, 5, 2, 5],\n [0, -5, 1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -6, -2, 0, 3],\n [-6, -1, 6, -1, 5],\n [2, 3, -5, -1, -4],\n [0, -3, 6, -5, -6],\n [6, 3, -6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 3, 1, -5, 3],\n [6, 1, 5, -3, 5],\n [5, 4, 2, 3, -5],\n [-5, 3, 2, -6, -2],\n [-3, -3, -6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 4, -3, 3, 1],\n [6, -4, 3, 2, 5],\n [4, 3, -5, -6, 5],\n [3, -6, 6, -4, -5],\n [5, 2, 2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 4, 1, 3, -2],\n [0, -2, -5, -5, 6],\n [-3, 4, 1, -4, -6],\n [-4, -2, -2, 0, 6],\n [-6, -4, -4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 2, 5, 3, 5],\n [5, 1, -2, 2, -5],\n [-3, -1, 3, 4, -3],\n [-3, -5, 6, 3, 0],\n [-4, 2, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 1, -3, -2, 1],\n [-3, 1, 0, 6, 5],\n [-4, 6, -3, 1, 0],\n [0, 4, 6, 5, 0],\n [-4, -4, 6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 5, 5, -6, 2],\n [4, -6, 0, -2, 1],\n [-1, 0, 3, 6, -1],\n [-3, -3, -1, 0, -4],\n [4, -1, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, 0, -1, 3],\n [0, -3, -2, 0, 0],\n [-6, -2, -6, -2, -3],\n [-4, 6, 0, -2, -1],\n [1, 5, -6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 0, 0, -2, -2],\n [-4, -5, -6, -2, -3],\n [0, 0, -6, 6, -2],\n [6, -6, 3, 4, -5],\n [0, 4, 3, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -2, -5, 1, 1],\n [-6, 5, 4, -4, 1],\n [3, -4, 0, 4, 6],\n [2, -6, 3, 5, -2],\n [-5, 1, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 4, 2, 4, -6],\n [3, 4, 6, -6, -4],\n [-3, 0, -2, 1, -6],\n [2, 6, -2, 6, 0],\n [4, -5, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 5, -3, 5, -5],\n [4, 4, 2, 1, 5],\n [4, 6, 3, -3, -2],\n [1, -6, -3, -5, -5],\n [-1, -2, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 1, -2, -6, 5],\n [3, 0, -3, 0, 6],\n [-5, 6, -2, 6, 0],\n [0, 4, 2, 3, -6],\n [6, -3, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 2, 1, 1, -4],\n [3, -4, -4, 5, 0],\n [6, 5, 6, 2, -4],\n [-3, 2, -5, -4, 5],\n [-6, -1, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -6, -2, -4, -5],\n [0, 6, -2, -2, -5],\n [-1, -1, -4, -5, -6],\n [5, 0, 5, 6, -5],\n [-6, -3, 2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -6, 0, -3, -6],\n [3, 6, -6, 1, 4],\n [6, 6, -1, 2, 1],\n [-4, 5, 5, 5, -1],\n [-4, 0, -3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -6, 5, -1, -2],\n [-2, -1, -5, 6, -1],\n [2, 0, -4, 4, -4],\n [3, 2, -6, -2, 6],\n [-6, 5, 1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 1, 1, -4, -5],\n [5, 6, -1, 6, -6],\n [3, -6, 6, 6, 3],\n [0, -3, -4, 4, -4],\n [6, 1, 1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -5, -5, 4, 0],\n [0, 3, 1, 3, 2],\n [6, 3, -3, -5, -2],\n [5, -4, -6, 4, -5],\n [1, 5, -4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -1, 5, -1, 0],\n [2, -6, -3, -2, -6],\n [5, -6, -6, 2, -4],\n [5, -6, 4, -4, -3],\n [-3, 6, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 2, 1, -2, -5],\n [5, 5, -6, -1, 6],\n [-1, 1, 0, -3, -3],\n [6, 4, 2, 0, 5],\n [-6, 0, -6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -4, -6, 5, 3],\n [-3, 1, 3, -4, -5],\n [0, -4, -5, -3, 4],\n [-2, 0, -5, 3, -2],\n [-5, -6, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 2, 6, 5, 4],\n [6, 3, -2, 3, -6],\n [-1, 0, -2, 4, -3],\n [5, 0, 6, -6, 3],\n [-2, -1, 6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -4, -3, 0, -3],\n [-1, 4, 3, -6, -6],\n [-4, -5, -4, -1, 2],\n [3, -4, -6, 5, 3],\n [-6, 6, -3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, -1, 5, -4],\n [3, 1, -6, 4, -5],\n [-5, 2, 4, -6, 1],\n [3, 3, -6, 0, 5],\n [-3, 3, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, -6, -4, -4],\n [-2, -2, 0, -6, 5],\n [3, 2, -6, 3, 4],\n [6, 4, 0, 1, 6],\n [-3, -6, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -4, -2, 5, 2],\n [4, 5, -4, -1, -1],\n [1, -2, 4, 4, -2],\n [1, -1, 1, -6, 1],\n [-5, 2, -3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, -5, 1, -4],\n [-3, 6, -1, -1, 0],\n [-6, 2, -6, 0, -2],\n [-1, 0, 1, 5, -2],\n [5, -4, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 5, 3, 5, -6],\n [6, -2, 3, -5, 3],\n [-5, 2, -4, 1, 3],\n [2, 0, 4, 2, 4],\n [-6, 4, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 2, -5, 0, -3],\n [-5, -6, -6, 1, 0],\n [5, 2, 4, -1, 2],\n [0, 5, -6, -2, -6],\n [6, -3, 5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -4, 6, 0, -2],\n [6, -5, 1, 5, 2],\n [1, -4, -6, -1, 5],\n [4, -3, -6, 4, -2],\n [3, 3, -5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -4, 1, 1, 1],\n [6, 4, -4, 0, -1],\n [-5, -5, 2, 2, -2],\n [-1, 3, 4, 5, -1],\n [-2, -3, -1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 1, 0, 1, -4],\n [4, -6, 4, -3, 6],\n [2, -3, 6, 5, 4],\n [5, 2, -5, 5, 3],\n [-4, 4, 1, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 3, -6, -4, -1],\n [-2, -1, -5, -6, -2],\n [6, -3, -2, -1, -4],\n [3, 2, -4, 5, 6],\n [1, 6, 1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 2, 1, -1, -6],\n [-2, 3, 2, 0, -1],\n [1, 6, -3, 2, 6],\n [1, 5, 3, 5, 2],\n [2, 5, 5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -3, 4, 2, 6],\n [-6, -2, -6, 0, 4],\n [3, -3, 3, 0, 1],\n [4, -6, 6, -6, 3],\n [4, 2, 5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 2, 5, -3, 6],\n [4, 2, 4, -1, -6],\n [6, -2, -6, 6, 6],\n [-2, 5, -4, -1, 6],\n [-3, -6, 1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 3, 2, -5, 4],\n [-4, 4, 2, 0, 4],\n [4, -2, -5, 1, -6],\n [-6, -6, -3, 3, 0],\n [-2, -3, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -5, -2, 5, 5],\n [-4, -6, -2, 0, 4],\n [1, -3, 0, 1, -1],\n [2, -1, -2, -3, -3],\n [0, 0, -5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -6, -2, 6, 0],\n [-5, 5, 2, -2, -6],\n [-3, 5, -2, -6, 2],\n [-4, 2, 5, -4, 2],\n [1, 6, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, 0, 4, -6],\n [5, -2, 1, -6, -3],\n [3, -1, -3, 0, -1],\n [-3, 5, -3, 2, 5],\n [3, 2, -5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, -6, 6, -3],\n [-6, -3, 2, 1, -5],\n [6, 6, -6, -4, 1],\n [4, -5, -2, -5, 5],\n [2, -5, 3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, -2, -3, -3],\n [-5, 4, 1, -4, -6],\n [4, -1, -5, 1, -3],\n [5, 2, 2, -3, 3],\n [-1, 3, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -1, -2, 3, -2],\n [2, 3, -5, 2, 5],\n [2, 1, -3, 5, -5],\n [-2, -4, -3, 1, -4],\n [-3, 4, 0, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 4, -3, -3, -3],\n [-3, 1, 4, -5, -3],\n [3, -5, 1, -4, -4],\n [5, -5, -6, 3, -2],\n [-4, 5, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -4, 6, 3, 6],\n [-3, 0, 0, -5, -4],\n [-1, -4, -5, 5, -5],\n [-2, 3, 0, 5, -2],\n [6, -6, -3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -5, 0, -1, 6],\n [1, -1, -4, 1, 5],\n [6, 3, 5, -4, 6],\n [-4, 5, 3, 3, -3],\n [2, -3, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 6, -5, -1, -6],\n [-3, -3, -1, 3, 2],\n [1, 3, -3, 0, -6],\n [6, 6, -2, 6, 2],\n [2, -4, 4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -3, -3, 5, -5],\n [-3, 4, -6, 1, 5],\n [-2, -2, -2, 0, 3],\n [-6, -2, 3, 1, 4],\n [-5, 4, 4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 2, 0, 6, -1],\n [-2, -1, -3, -5, 5],\n [2, -5, 6, -3, -3],\n [1, 6, 2, 4, 2],\n [4, 5, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -6, 5, -3, 4],\n [2, 5, -3, -1, -6],\n [6, 5, 2, 4, 1],\n [5, 2, 1, 1, 0],\n [6, -3, -2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -3, 3, -5, 3],\n [-3, -2, -6, -4, -3],\n [-3, -4, -4, -6, -5],\n [-3, -5, 3, -4, -1],\n [-2, 3, -2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 0, 5, 0, -1],\n [3, -3, 2, 4, -4],\n [-5, -5, 5, 6, 1],\n [1, 0, 6, 0, -6],\n [-2, -4, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 6, 6, -4, -6],\n [4, 0, -2, -5, -1],\n [-2, -1, -4, 3, -3],\n [3, -2, -3, 5, -3],\n [-6, 3, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 5, -1, 2, 2],\n [4, 0, -5, 5, -6],\n [2, 3, -6, 5, 0],\n [2, -1, -5, 1, 2],\n [-5, -2, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 2, -2, 6, 2],\n [2, -6, 0, -4, -6],\n [-1, -3, 6, 3, 6],\n [-4, 6, -2, -3, -5],\n [-5, 5, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -1, 5, -2, -5],\n [-1, -6, 3, 1, 3],\n [-1, 3, 4, -6, 2],\n [5, -5, 3, -6, 4],\n [6, 2, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, 6, -3, 4],\n [3, 0, -5, 2, -3],\n [-5, -5, 3, 0, 3],\n [-2, 4, 6, 0, 3],\n [-6, -5, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -4, -4, -1, 5],\n [-5, 5, 6, -3, 2],\n [-6, 4, 0, -4, 0],\n [1, -2, -4, 5, 1],\n [-4, -6, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 2, 1, -2, -1],\n [6, -5, 0, -5, 3],\n [0, 6, 1, -3, 0],\n [-2, -3, -6, 0, -4],\n [5, -2, -4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -4, 2, 4, -2],\n [-4, -4, 3, 2, 4],\n [-1, -2, -6, -3, 6],\n [-2, 3, -6, -4, 3],\n [-3, -4, -6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 2, 4, 5, -2],\n [-1, 4, 3, 2, 6],\n [4, -3, 0, 1, 1],\n [3, 3, 3, -5, 6],\n [-5, 5, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, -4, 3, 0],\n [4, 6, -6, 3, 1],\n [4, 6, 2, 6, 2],\n [-1, 2, 4, 3, 2],\n [0, -1, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 5, 5, 5, -6],\n [1, 2, -5, -4, -5],\n [4, 0, 3, 2, -4],\n [2, 0, 1, 3, -2],\n [6, 1, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, -6, 4, -6],\n [-3, 4, 0, -5, 4],\n [2, -3, 4, -3, -2],\n [-5, 2, 6, 3, 6],\n [5, -2, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -4, -5, -1, -6],\n [-5, 6, 1, -6, 0],\n [-6, -2, 3, 1, -6],\n [-4, -5, 0, -2, -2],\n [1, -2, 6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -2, 3, -3, 5],\n [-4, -6, 5, 2, -2],\n [-1, -5, -1, -2, -5],\n [2, -3, -5, 2, -2],\n [6, 4, 4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 0, -5, 6, -2],\n [-2, 6, 3, 6, 4],\n [6, 6, 2, 1, -2],\n [0, -2, 4, -6, -5],\n [-6, -1, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 0, -1, -5, 5],\n [-6, 4, 4, 4, 4],\n [-6, -5, -5, 6, 2],\n [4, 2, -2, -1, 6],\n [-1, 0, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -3, 3, 6, 6],\n [-6, 0, 1, -1, 4],\n [1, -4, 2, -5, 3],\n [1, 5, -4, 5, 3],\n [5, -1, -3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 6, -3, -3, 3],\n [-1, 4, -1, -3, 4],\n [1, -5, -1, 6, -4],\n [0, 1, -4, 3, -3],\n [-4, -4, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 6, 1, -3, 3],\n [-2, -3, 4, 3, -2],\n [3, 1, -4, -4, -3],\n [-6, -3, -5, 5, 2],\n [-3, -5, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, -6, -4, 1],\n [-6, -3, -6, -6, -6],\n [3, -6, -6, 5, -3],\n [-5, 4, 5, 6, 2],\n [-1, 0, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 1, 3, 1, 5],\n [-2, 2, -1, -4, -4],\n [-5, 4, 1, 3, 0],\n [1, -1, 0, -4, 3],\n [-5, 5, 4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 0, 3, 6, 6],\n [-4, 4, 0, 1, -1],\n [-3, -2, 0, -4, 4],\n [6, -1, 3, 2, -4],\n [-2, -2, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 6, -5, 5, -2],\n [1, 6, -3, 3, -4],\n [4, -6, 1, 6, -2],\n [-1, -2, -6, -1, -1],\n [-4, 0, 5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 0, -3, -6, 4],\n [-4, -6, -2, 2, -2],\n [-1, -2, 5, -1, -2],\n [1, -4, -1, -3, 1],\n [-2, 0, -5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -6, 1, 5, 4],\n [6, -5, -6, 1, -4],\n [-2, 2, 2, -4, 5],\n [1, 5, 5, -1, -5],\n [4, 6, -5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -1, 5, 3, -2],\n [2, -4, -1, 1, -3],\n [3, -5, 5, 6, -3],\n [3, -4, -6, 5, 0],\n [6, -4, 6, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 4, 5, 2, -5],\n [-2, -3, -5, -4, 0],\n [-6, -4, 5, 5, 4],\n [6, 3, 5, -6, 5],\n [-1, -6, 2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 5, -2, 1, -1],\n [-4, -6, 3, 1, 6],\n [-1, 3, 2, -4, 4],\n [-3, -5, -4, 6, 4],\n [1, -5, -5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 1, 6, -2, 0],\n [-5, 4, -5, 2, 3],\n [-4, -6, 2, 4, -6],\n [-2, -3, -2, -6, 5],\n [4, 6, 0, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -5, -6, 4, -6],\n [2, 3, -3, -5, -2],\n [5, 0, 0, 3, 1],\n [6, 3, -4, -3, 4],\n [2, 2, -3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -4, -5, -1, 4],\n [1, -1, 0, -4, -3],\n [-4, -2, -4, 4, 1],\n [1, 4, 2, -6, 1],\n [2, -4, -5, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, -1, 2, -4],\n [-4, -2, 3, 0, 1],\n [0, 3, 4, -4, 1],\n [0, -3, 6, -4, 0],\n [5, 5, 3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 4, -2, 3, 3],\n [3, 0, -6, -4, 3],\n [0, -5, 4, 0, 6],\n [0, 6, 0, -6, -2],\n [-5, 3, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 2, 3, 0, -3],\n [-5, 6, 3, 2, -1],\n [-2, 4, 0, -6, -1],\n [-1, 6, -1, -1, 5],\n [0, -4, -5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -2, 2, 6, -2],\n [1, 1, -5, 2, -6],\n [2, -5, -3, -2, 5],\n [5, 4, 6, -6, 3],\n [6, -3, -2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -1, 6, -1, 0],\n [-5, 5, -6, -2, 4],\n [-6, -1, 2, 6, 6],\n [1, -6, 1, -4, -5],\n [-2, -6, 3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -4, 2, -3, -2],\n [-4, -4, -5, -1, 4],\n [4, -4, 5, 0, 1],\n [-4, -4, 1, 5, -6],\n [6, -6, 2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 3, 0, 2, 5],\n [4, 0, 6, -6, -2],\n [1, 3, -6, 2, 4],\n [-2, 5, 1, 1, -3],\n [-1, 5, 3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -3, 1, -2, 3],\n [-6, -1, 2, -5, 1],\n [0, 4, 3, 2, -1],\n [-2, 5, -2, -2, 2],\n [5, 2, -5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 6, 1, -2, 4],\n [-1, -1, 3, -1, 6],\n [2, 4, -5, -5, -2],\n [-2, 2, 0, -2, -2],\n [-3, 4, -2, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -2, 5, 5, 3],\n [-3, -4, -2, -6, -2],\n [-5, 3, 3, 2, 3],\n [2, -2, -5, 1, 6],\n [-4, 0, 1, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -1, -2, 6, -2],\n [-4, 5, 6, 0, 3],\n [5, 2, 1, -5, -3],\n [-4, -1, -3, 1, 3],\n [-5, -6, -1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 3, 1, 3, -4],\n [2, -4, 6, 3, -5],\n [6, 4, -3, -3, 1],\n [2, 4, 1, 0, -5],\n [6, 4, 5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 5, -1, 3, 5],\n [6, -6, 3, 4, -3],\n [-1, -3, -3, -6, 2],\n [-6, -3, -2, -1, 0],\n [2, 3, 5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -1, 0, -5, -2],\n [-4, 0, 4, 0, -6],\n [-2, 5, 4, 2, 2],\n [-3, 3, 0, -2, 1],\n [4, 3, -5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -4, -4, 2, -4],\n [4, -3, -1, 1, -1],\n [-4, -1, 1, 1, -6],\n [5, -1, 0, -3, -4],\n [4, -4, -4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 5, 4, -1, 5],\n [3, -4, -6, -2, 1],\n [3, 1, 1, 3, 4],\n [0, -1, -6, 4, -1],\n [-5, 1, 3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 2, -1, -1, -5],\n [-2, -4, 5, 0, -3],\n [-3, -4, 3, -3, 4],\n [-6, -5, -5, 6, -1],\n [-4, -2, -2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 3, 4, 5, 6],\n [0, 6, -6, -4, -4],\n [3, 0, 4, 4, -1],\n [5, 0, -5, -4, -3],\n [3, -3, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, 4, -1, 3],\n [-1, 0, -2, 3, 5],\n [5, -3, -1, 1, 1],\n [3, 2, -6, 3, 0],\n [4, 6, -4, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 5, 4, 6, 4],\n [4, 4, 1, -6, 2],\n [6, -1, -5, 2, -6],\n [-6, 1, -2, 4, 3],\n [-4, -3, -1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 3, -6, -5, 0],\n [0, -3, 5, -4, 0],\n [-2, -3, -3, 1, 2],\n [0, -2, -3, 4, -3],\n [3, -4, 3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, 5, 3, 0],\n [4, -2, -1, 1, 4],\n [3, -1, -6, 2, 1],\n [4, -2, -2, 0, -4],\n [3, -4, -3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 2, -1, -2, -4],\n [6, -5, 4, -1, 3],\n [-1, -6, -1, -3, 6],\n [0, 3, -1, -3, 4],\n [6, 2, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -5, -1, -2, 3],\n [-1, 5, -6, 1, 1],\n [3, 3, 3, -6, 6],\n [-3, 5, -4, 0, 5],\n [0, -6, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -4, 3, -4, -1],\n [3, -1, 0, -1, 3],\n [1, 3, 5, 5, 5],\n [3, 2, 1, 6, 1],\n [0, -3, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 0, -2, 1, -2],\n [-1, -4, 0, 6, 6],\n [5, 3, 0, -4, 3],\n [-6, -1, -5, 3, 4],\n [-2, 1, -3, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -5, -2, -6, 0],\n [6, -5, -1, 0, 4],\n [4, -5, 0, 4, -3],\n [-5, 4, -3, -5, 4],\n [2, 6, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 3, -2, -5, -5],\n [-5, 0, -3, -6, -5],\n [1, 1, -1, 5, 4],\n [1, 0, -1, -3, 0],\n [-1, 3, 5, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, 0, 5, -4],\n [3, 3, 2, 1, 0],\n [-4, 3, -1, 0, -5],\n [-2, 2, -2, 6, 6],\n [0, -3, 4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, -4, 6, -5],\n [-2, -3, -2, -1, 5],\n [-6, -4, 0, -4, 3],\n [1, 6, 1, -2, -3],\n [-5, 3, 0, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 3, 1, 2, -2],\n [-2, 2, 3, 1, 3],\n [3, -4, 6, 0, 4],\n [-6, 2, -3, 0, 1],\n [-1, 4, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 0, -3, 6, -2],\n [0, 2, -4, 6, 5],\n [2, -4, -5, 2, 3],\n [5, -3, 5, 6, 5],\n [-6, -2, -5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 0, -4, 2, -3],\n [0, -2, -2, 0, -1],\n [2, -2, 5, -2, -6],\n [-2, -1, 5, 1, 1],\n [2, 5, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -3, 3, 5, 6],\n [1, 4, 1, 5, 4],\n [-1, -6, -3, -2, -5],\n [-6, -4, -6, 2, -4],\n [6, -5, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 4, -2, 1, -1],\n [-3, -5, 5, 2, -2],\n [4, 4, -6, -5, 2],\n [-3, -1, -3, 6, 6],\n [-4, 1, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -3, -1, -6, -2],\n [1, -4, -3, -4, 5],\n [-5, 4, 3, 5, 4],\n [-2, 4, -1, 2, 4],\n [-3, 2, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 2, 2, -5, -1],\n [6, 4, -1, -4, -4],\n [-3, -1, 4, -3, 2],\n [6, 1, 3, -3, 0],\n [-1, -3, 5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 0, 6, 3, -1],\n [-6, 2, 1, 4, 6],\n [1, 6, -3, -5, -4],\n [3, -4, 6, 2, 2],\n [4, 1, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 2, 5, 2, 1],\n [-6, -2, 0, 1, -1],\n [3, 4, -1, -6, 1],\n [0, -2, 2, -1, -6],\n [5, 1, -3, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -2, -5, 4, 0],\n [3, 3, 1, 6, -3],\n [0, 5, -2, 4, 2],\n [-3, 2, 3, 6, -4],\n [4, -2, 2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -3, 3, -6, 5],\n [-2, 3, 5, -4, -5],\n [-4, -3, 6, -2, 6],\n [6, 5, -4, 3, 3],\n [-5, 5, -6, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -4, 5, -5, -4],\n [3, 2, 1, -3, -6],\n [-3, -2, 0, 1, 3],\n [4, 3, 2, -2, 2],\n [1, 1, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, 3, -4, -4],\n [-4, -4, 0, 3, 4],\n [2, 2, 6, -3, 6],\n [-1, -5, 3, 2, -5],\n [6, 2, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 4, 1, -6, 3],\n [6, 1, -1, 2, 4],\n [0, 2, -4, -6, 0],\n [3, -2, 3, 3, 5],\n [1, -3, 5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 6, 3, 1, -3],\n [-5, 2, -5, -5, -1],\n [-5, -4, 4, 4, -4],\n [-4, -3, 3, 6, -2],\n [0, 5, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 1, -1, 0, -1],\n [-6, 6, -1, -5, 1],\n [6, -5, 5, 6, 5],\n [-5, -4, 2, 3, 0],\n [4, 4, -5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 0, -6, -1, -6],\n [0, -3, 2, 6, -6],\n [4, -1, -2, -3, -2],\n [6, -6, 3, 1, -5],\n [5, -6, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 6, -4, -3, -5],\n [-5, -6, 1, -2, 1],\n [-2, 6, -3, 3, -5],\n [6, 2, -6, -4, 6],\n [-3, 4, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 4, -6, 6, -6],\n [4, 3, 1, 3, -4],\n [-2, -3, 2, 2, 1],\n [4, -4, -6, 3, -5],\n [-4, -2, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 0, -3, -3, 6],\n [4, 5, -2, -5, 3],\n [-4, 1, -3, -6, 3],\n [1, -3, 0, 3, 3],\n [-2, -3, -5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 2, 2, -2, -6],\n [-4, -4, -1, 3, -3],\n [-5, 3, 2, 3, 4],\n [5, 0, -3, -4, 2],\n [0, -3, 0, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 1, 2, -2, 4],\n [4, -3, -2, 5, -3],\n [5, 3, 0, -1, 6],\n [1, 3, -4, -1, -3],\n [2, 2, 5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -4, 6, -2, 2],\n [0, -1, -4, -6, -1],\n [6, -4, 3, -6, 0],\n [-2, -4, -3, 2, 4],\n [3, -3, -1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -3, 5, 6, 1],\n [2, 1, 4, 5, -3],\n [3, -2, 3, 6, -6],\n [3, -1, 3, -5, -2],\n [-4, -5, 0, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 3, -1, -2, -3],\n [-1, 1, -3, 4, -2],\n [2, 2, 3, -4, 0],\n [-4, -3, 5, 5, 4],\n [4, 1, -3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -4, 5, 2, 0],\n [-4, -4, 4, 1, -4],\n [-6, -4, -6, 0, -3],\n [5, -2, 6, -6, -5],\n [-5, -4, -5, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 3, 1, -2, -2],\n [6, -5, 2, 4, 1],\n [-4, 3, 6, -6, -1],\n [-1, 0, -3, 3, -1],\n [2, 1, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 5, 1, -5, -3],\n [-4, 1, 0, -1, 4],\n [-6, -3, 6, -2, -4],\n [6, 6, -5, 3, 5],\n [-3, -5, -5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, -3, 5, -6],\n [-3, -1, 1, -2, -3],\n [-2, -5, 3, 1, 6],\n [-2, 6, 2, -1, -4],\n [-3, 4, -5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -1, 5, -5, 4],\n [4, 6, -3, -2, -2],\n [4, 6, -6, 3, 5],\n [4, -4, -4, 0, -1],\n [-4, -4, 5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -6, 3, -1, 4],\n [6, 2, -3, 6, 3],\n [3, 0, -3, -2, 6],\n [2, -1, 0, -3, 1],\n [4, 0, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -2, -6, 5, 6],\n [-3, 3, 0, 1, 1],\n [3, -4, 0, -5, -5],\n [1, 2, 6, 5, 6],\n [4, -6, -6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 4, -3, 2, -1],\n [-2, 0, -1, 5, -5],\n [6, -6, -4, 1, -5],\n [5, 1, 1, 4, -1],\n [-3, 3, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -2, -4, -5, 5],\n [4, -3, 1, 3, -6],\n [1, 4, 4, -4, -3],\n [6, 6, 5, -2, -5],\n [-3, 0, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -5, -5, -2, 1],\n [6, 0, 6, 2, 5],\n [-5, 0, -2, 3, 2],\n [1, 2, 4, -6, -3],\n [-6, 0, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -5, 3, 3, -4],\n [-3, -6, -3, -5, -6],\n [6, 3, 2, -6, -5],\n [2, 3, -5, 4, 4],\n [3, -3, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, 5, 1, 0],\n [-5, 2, 0, 4, 0],\n [0, -1, 2, 2, 4],\n [2, -5, -4, 6, 2],\n [1, 5, -1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 1, 4, -1, 3],\n [5, 5, 4, 3, -4],\n [-4, 5, -1, -3, 4],\n [2, 5, -3, 3, 5],\n [-3, 0, -2, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 2, -5, -3, 3],\n [6, -4, -1, -3, 0],\n [3, -2, 3, -4, 5],\n [-4, 5, -2, 5, 0],\n [-5, -1, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 3, -4, -2, 4],\n [4, 5, -5, 2, 3],\n [-5, -5, 5, -1, 5],\n [-2, 6, -6, -5, 3],\n [-3, 0, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 0, 4, -1, -6],\n [-5, -1, 1, -6, 4],\n [5, 4, 0, 6, -2],\n [2, -2, -6, 0, -3],\n [3, 1, 6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -3, 5, -1, -4],\n [-5, -4, -5, 5, -2],\n [5, -6, 2, 5, 4],\n [2, 5, -5, -5, -2],\n [4, 6, 3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -1, 4, 1, 5],\n [1, 5, 2, -5, 3],\n [-2, 1, 2, 3, 5],\n [1, -4, 5, -2, -1],\n [4, 1, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 0, 1, -3, -2],\n [-1, -5, 1, -4, -4],\n [4, -5, -3, -5, -5],\n [6, -3, 0, 1, 0],\n [-1, -5, -1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 0, -6, 0, -3],\n [1, -2, 3, -2, 6],\n [-6, -3, 0, 4, -1],\n [-2, -6, 2, 4, -2],\n [0, 4, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 6, -3, 5, 1],\n [0, 1, 4, 0, 6],\n [1, 6, 2, -3, -5],\n [4, 2, -1, -6, 3],\n [2, -2, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, 1, 2, -4],\n [-6, 1, -4, 1, 1],\n [-3, -4, -1, 4, 0],\n [0, 3, -1, -1, 4],\n [6, 1, 6, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 0, 1, 2, -3],\n [6, -2, -1, -2, -5],\n [0, 6, 2, 4, -6],\n [-4, 1, 5, 3, 3],\n [5, -5, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 5, -5, 4, 6],\n [-1, -2, 2, -6, 6],\n [-3, 6, 3, 0, -2],\n [4, 3, -4, -4, -5],\n [5, 3, -3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -2, -5, -2, 3],\n [0, 5, 3, 2, -6],\n [1, -2, -4, -4, 2],\n [2, 2, -5, -2, -1],\n [0, -5, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -2, 4, -2, -3],\n [3, 3, 1, 5, 1],\n [4, -5, -2, -4, 0],\n [-2, -5, 1, 6, -3],\n [-6, 5, 5, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 0, 6, 0, 2],\n [-2, -6, -2, -2, 0],\n [-6, 2, -1, 4, 4],\n [-3, 4, -4, -1, 6],\n [-6, 1, -1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, -6, 2, 5],\n [-1, -6, -4, -5, 2],\n [-1, 5, -5, 0, 3],\n [5, -1, -5, 3, 2],\n [-3, -2, -3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 5, 6, 5, 3],\n [-6, 3, 4, 4, -4],\n [4, 6, 0, 0, -1],\n [3, -2, -2, -3, -1],\n [-2, -2, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -5, 3, 2, -5],\n [-5, 0, -4, -3, 5],\n [1, -6, 1, 0, 1],\n [-4, -2, 4, 6, 4],\n [0, 2, 1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -3, 5, -5, 5],\n [-1, 2, 3, 3, -4],\n [-2, 5, -2, 6, 4],\n [-6, 5, -4, -5, -1],\n [-5, -5, 0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -6, -4, -1, 5],\n [3, 1, -2, 0, 5],\n [5, 2, 0, -3, 5],\n [1, 5, 1, -6, 1],\n [-6, 6, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 1, -3, -3, -1],\n [-6, 6, 6, -2, -3],\n [-4, 6, -1, 4, 1],\n [0, -2, 1, 4, -1],\n [-3, 6, -6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -4, -3, -5, 6],\n [2, -2, 1, 2, -3],\n [3, -4, -4, 4, 5],\n [6, 1, 4, 5, 6],\n [0, -2, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 5, 5, -1, -2],\n [3, 1, 6, 1, 3],\n [-5, -5, 2, 5, 3],\n [6, -3, -5, 2, 0],\n [-2, 2, -3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 6, -2, -3, -3],\n [-5, 0, 3, -5, -6],\n [1, 0, -3, -5, -5],\n [-2, -1, 1, 5, 6],\n [4, -5, 0, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 2, 1, 5, 2],\n [-4, 0, -1, 2, -1],\n [1, 1, 3, -3, -2],\n [-5, 0, 1, -2, 6],\n [1, 0, 3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -3, -2, 5, -5],\n [0, 6, -1, 5, 4],\n [2, -5, -6, 5, 2],\n [6, 0, -6, -2, -5],\n [0, -3, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -1, -6, 1, -1],\n [1, 0, -4, 3, -4],\n [-6, 1, -6, 5, 2],\n [6, -1, -1, -4, -2],\n [-6, -1, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 5, 2, 5, 2],\n [6, -6, 1, 4, -4],\n [0, 4, 3, -2, 1],\n [5, 5, 2, 1, -5],\n [0, 5, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 6, 4, -2, 3],\n [-2, -4, 5, 0, 0],\n [6, -1, 5, -6, 2],\n [-6, 6, 3, -3, 1],\n [0, 1, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -6, 4, -4, 3],\n [6, -5, -6, -1, 6],\n [-4, 2, -6, -2, -6],\n [2, 6, 0, -1, 2],\n [-2, 5, 6, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -4, -4, 2, 0],\n [1, 0, -2, 6, 6],\n [-1, -4, 4, -2, -2],\n [3, 2, -4, -1, 6],\n [-6, -6, -6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, -1, -2, -5, 2],\n [1, 1, 2, -3, -5],\n [-4, 3, -6, 0, 5],\n [-1, -3, -4, -4, -2],\n [5, 1, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 2, 4, 5, 0],\n [-6, -1, 0, -5, -5],\n [-1, -5, -5, 5, -1],\n [5, -1, 0, 3, 5],\n [-2, 2, -4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, -4, 1, 5],\n [3, -1, 0, 3, 4],\n [-1, 1, 3, 2, 0],\n [1, 5, -5, 1, -5],\n [-4, -6, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -6, 5, 0, -5],\n [-3, 0, -1, 2, -5],\n [-4, 3, -1, 1, 6],\n [0, 2, 0, -6, -1],\n [-5, 4, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -3, 3, 1, -1],\n [-6, -6, -3, -2, 3],\n [-5, 0, -5, -2, -6],\n [0, -3, -1, -1, -6],\n [1, -1, -5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -5, -2, -2, 6],\n [2, -6, -5, 2, 1],\n [2, 3, 3, -5, -2],\n [0, 6, 2, 6, 2],\n [4, 4, 3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -1, -4, 2, -3],\n [5, 1, -1, -2, -3],\n [1, -1, 0, -5, -2],\n [3, 6, 0, 3, -2],\n [5, -2, 2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -3, 1, -4, -4],\n [4, 3, -3, -4, 4],\n [1, -3, 5, -1, 1],\n [-6, 4, 1, 6, 4],\n [-3, -5, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, 3, -3, -2],\n [6, -4, -3, 2, -2],\n [-5, 1, 0, 3, 2],\n [-5, 4, 1, 6, -1],\n [-2, -4, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -6, -6, 0, 5],\n [6, -3, -3, -1, 0],\n [2, 0, 4, 6, 2],\n [-3, 5, -5, 4, 4],\n [6, 1, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, 1, 4, -4],\n [-5, 3, -1, 0, 1],\n [3, -2, 5, -6, -1],\n [2, 1, 4, 5, 6],\n [1, -2, -2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, 2, -5, 0],\n [0, -6, -3, -4, 6],\n [-4, 2, -4, 3, -4],\n [5, -5, 4, 4, -1],\n [6, -5, 4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, -3, -1, -3],\n [-6, 0, -2, -3, 5],\n [5, -4, -6, -5, 2],\n [1, 2, -6, -3, -4],\n [-1, 0, 6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 6, 3, -5, 1],\n [-4, 1, -6, -6, 6],\n [-6, -3, -4, -1, -3],\n [-1, -1, -5, -1, 3],\n [-5, -3, 1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 2, -4, -3, 3],\n [4, -2, 5, -4, -1],\n [6, 5, -1, -4, 3],\n [5, 1, -2, 5, -3],\n [6, 4, 6, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 6, -5, -3, 6],\n [-5, -5, 3, -5, -1],\n [-4, 2, 3, -4, -3],\n [6, 4, 4, -2, 3],\n [3, 6, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -4, 3, -4, 0],\n [1, 0, -4, 1, 5],\n [-2, 2, -6, -6, -5],\n [3, 1, 3, -3, 2],\n [3, 5, -2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -6, -6, -4, 0],\n [0, -2, 4, 0, -6],\n [-3, 3, -4, -6, -3],\n [1, -2, 6, -1, 4],\n [-5, -6, -4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 0, 4, -3, -4],\n [0, 4, -5, -4, -1],\n [5, -2, -3, -3, 1],\n [4, 1, 1, -3, 5],\n [-1, 5, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 6, 5, 6, 3],\n [-1, -2, 3, 5, 6],\n [-6, 5, 6, -5, 3],\n [3, -3, 2, -5, 6],\n [3, 5, -6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -6, -2, -6, 3],\n [3, -2, -2, 4, -5],\n [-3, 4, -1, -3, 3],\n [5, 4, 1, -1, 1],\n [0, -1, 5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 0, 2, -6, 1],\n [2, 0, -2, 5, -2],\n [6, 5, 5, 0, -4],\n [0, 6, -6, -3, -3],\n [2, 5, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -3, 6, -3, 6],\n [6, -4, -4, -1, 6],\n [-2, 2, 4, -5, 4],\n [2, -3, 3, 4, -2],\n [4, -5, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -5, 3, -6, -3],\n [-1, 6, -3, -2, 0],\n [5, -6, -3, 3, -5],\n [-4, 0, 0, -1, -2],\n [-6, -5, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 1, 2, -3, 1],\n [6, 1, 3, 5, 1],\n [4, -3, -4, -1, 1],\n [-2, 5, 1, 6, 1],\n [4, -4, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -1, -2, 6, -4],\n [-4, 0, 0, 2, -5],\n [3, 0, 0, 5, -1],\n [3, -2, -4, 3, 5],\n [-5, -3, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 1, -3, 6, -2],\n [5, 6, 6, 1, 2],\n [-6, -3, 4, -5, 6],\n [-6, -4, -6, -4, -6],\n [-6, -3, 4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -3, -1, -5, -2],\n [1, -4, 0, -4, 4],\n [3, -6, 4, -5, 5],\n [2, -4, 4, 4, 3],\n [-1, 3, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, 2, -5, -3],\n [-5, -1, -6, 2, 5],\n [2, 1, -6, -1, -2],\n [-1, 2, 2, 5, -6],\n [-5, -3, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 3, -2, -4, 4],\n [5, -5, 4, 2, -4],\n [4, 4, 1, 3, 0],\n [6, 5, 0, 1, 3],\n [5, -6, 2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 5, -4, 0, -1],\n [3, 4, -5, 4, 1],\n [-1, 2, 6, -2, 1],\n [4, 4, -6, -4, 4],\n [-3, -6, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 5, 6, 6, 1],\n [-1, 5, 0, -3, 1],\n [-5, -1, -1, 3, 3],\n [-4, -4, -2, 1, -1],\n [1, 6, 2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -1, -5, 4, -6],\n [-5, 3, -4, 5, -6],\n [6, 6, -2, -2, 0],\n [5, 0, 6, -4, 1],\n [-6, 1, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 5, -2, 0, -6],\n [6, 6, -3, -6, 3],\n [-3, 0, 4, -6, 4],\n [3, 4, -4, -2, -1],\n [1, -5, 0, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 3, -2, 3, 3],\n [-3, -1, -6, 3, 1],\n [0, -5, 1, 4, -5],\n [1, -4, 6, 2, -3],\n [2, -1, 2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 4, -5, 1, -2],\n [0, 4, -1, 4, 4],\n [-3, 1, -6, -3, -3],\n [-1, 4, 1, -1, 0],\n [-1, 5, 2, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, -4, -3, -1],\n [-4, 1, 4, 4, 5],\n [0, -2, 2, 6, 1],\n [-1, -4, 4, 2, 2],\n [-1, 4, 1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 6, -5, 2, 5],\n [5, 5, 1, 2, -1],\n [5, 1, -4, -4, 4],\n [1, 2, -1, -5, -4],\n [-5, -5, -4, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 4, -3, 5, -4],\n [2, -2, -3, -5, 2],\n [-1, 1, 2, -1, 6],\n [5, -4, 3, 4, 3],\n [-1, -6, 0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 0, 2, 3, -3],\n [5, -5, 5, 4, 2],\n [-4, 3, 3, 1, 0],\n [3, -3, -4, 1, -1],\n [1, 1, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 0, -6, 4, -6],\n [3, 6, -4, 3, 0],\n [-5, -3, -5, 6, -6],\n [-3, -5, -1, 1, 1],\n [-5, -2, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 4, 2, 3, -1],\n [-6, 1, -4, 4, 5],\n [3, -5, 1, 4, -6],\n [3, -1, -4, 2, 6],\n [-1, 5, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -4, 2, 6, 1],\n [-6, -2, 2, -5, -1],\n [-5, 0, 6, 4, 4],\n [-6, -4, 6, -6, 4],\n [1, -3, 1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -5, 2, 3, -3],\n [-6, -1, 5, 6, -3],\n [4, -1, 6, 6, 3],\n [-4, 6, -5, 4, 4],\n [5, 1, 5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -1, 2, -4, 5],\n [5, -1, -5, 5, 1],\n [-2, 4, -1, 5, 1],\n [6, 2, 0, 1, 2],\n [0, -3, 5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -1, 6, -2, -2],\n [-4, 3, 5, 1, 6],\n [-5, -4, -2, -1, 6],\n [2, 6, 1, 3, 2],\n [-4, 6, 1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 2, 6, 0, 6],\n [0, -1, 5, -6, 3],\n [-5, -1, -5, 5, -1],\n [2, -5, -2, 3, -4],\n [-4, -5, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -3, 6, 1, -5],\n [2, 3, -4, 2, -4],\n [5, -1, -3, 6, -1],\n [4, -2, 2, 2, 2],\n [4, 6, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -3, 1, 2, -6],\n [-3, -6, 1, 2, -6],\n [-4, 1, 0, 3, -4],\n [-3, 1, 2, 2, 2],\n [5, 5, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, -4, -1, -4],\n [-1, 5, -6, 5, 3],\n [4, 6, -5, -4, -2],\n [3, -5, -2, -5, -2],\n [3, -6, 3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -5, -6, -2, -3],\n [2, 2, -1, -4, -3],\n [-3, -4, 2, -6, 6],\n [-6, -3, -2, 0, -2],\n [-3, -5, 3, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -6, 5, 0, 6],\n [2, 2, -2, 3, 4],\n [5, 3, 4, -4, -6],\n [3, -3, 5, 1, 0],\n [5, 5, 4, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -5, 0, 6, 5],\n [-3, -1, -5, 4, 0],\n [1, -4, -1, -2, -5],\n [4, 1, -3, -4, -2],\n [2, -4, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 5, 6, 3, -6],\n [0, 1, 5, -2, -3],\n [-3, -3, 4, 0, -2],\n [-1, 1, 1, 3, 0],\n [-6, 2, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -3, -3, -3, -6],\n [6, -4, 1, -5, 1],\n [0, -1, 4, -5, 3],\n [2, -6, -5, -5, 1],\n [6, 4, 5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -1, -3, 4, -6],\n [-3, -3, 5, 2, 6],\n [-3, -3, 0, -6, 2],\n [5, -2, 6, 6, -3],\n [-4, 6, 6, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 0, -6, 1, 1],\n [-1, 4, 1, -1, -3],\n [3, 4, -3, -5, 5],\n [3, 2, -2, 4, 1],\n [6, 5, 1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 4, 2, 0, 2],\n [-6, 5, 3, 0, 5],\n [-2, -1, 3, 6, -5],\n [0, -1, 3, 6, -4],\n [3, -6, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -6, -6, -6, 4],\n [-5, 4, 6, 0, -1],\n [0, -2, -4, 6, 5],\n [-2, 5, -3, 1, -1],\n [3, -6, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 0, -6, -5, -1],\n [-1, 2, -4, 4, 2],\n [-6, 1, -6, 2, 2],\n [-3, 1, -4, -5, 6],\n [1, -6, 5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, -6, -3, -3],\n [-2, -6, -2, 4, 3],\n [-1, 6, 1, -5, 3],\n [4, -2, 4, 5, 3],\n [0, 1, 5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 5, 6, 0, 0],\n [-2, 3, -6, 6, 2],\n [2, 0, 2, 3, 2],\n [-5, 2, -4, -2, -3],\n [-6, -1, -5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 2, -6, 5, -5],\n [5, -6, -3, -2, 0],\n [0, -6, 1, -1, 6],\n [5, 3, 0, 2, -6],\n [-5, 4, 5, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 0, -6, -6, 3],\n [-3, 5, -5, -1, 6],\n [-3, 6, -6, 3, -6],\n [3, 4, -3, 3, 0],\n [-3, 5, 0, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 1, -3, 3, 6],\n [-4, -2, -1, 2, -2],\n [-5, 0, 3, 3, -5],\n [-6, 5, -5, -6, -5],\n [-6, -5, 6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 2, 0, -6, -4],\n [4, -6, 1, 3, 4],\n [2, -6, -2, 1, 1],\n [3, -1, -5, 2, 6],\n [0, 3, 3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 3, 4, -6, 1],\n [6, -6, 3, 4, 5],\n [-4, 5, -3, 3, -3],\n [3, 5, 3, -4, -1],\n [-6, -4, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -1, 6, -3, 3],\n [4, -2, -6, 3, -4],\n [-6, 3, 4, -3, 5],\n [5, 0, -5, 1, -2],\n [-1, -5, 1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -4, -1, -2, 0],\n [-6, -4, -5, -1, 3],\n [1, -6, 5, 2, -2],\n [-5, -1, 2, 3, 6],\n [-4, 6, -4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -5, -1, 5, -3],\n [-6, 3, 0, 4, 2],\n [3, 5, -3, -6, 1],\n [3, -2, 2, -1, -6],\n [-1, 3, 4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 6, -4, 6, -1],\n [-2, -1, -5, 5, 3],\n [-3, 0, 4, 5, -1],\n [-3, 2, 3, 3, -3],\n [5, 0, 5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -3, 5, -4, 5],\n [3, -3, -6, 3, 2],\n [-5, 4, 6, 3, 1],\n [5, -5, -2, 4, -4],\n [1, -5, -6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 6, -6, 1, 3],\n [6, 4, 2, -1, -6],\n [-6, -2, 1, -4, 1],\n [-2, -4, -4, 3, -4],\n [4, -1, -4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -6, 1, 0, -3],\n [-6, 2, 0, 3, 5],\n [4, -6, 3, -4, -4],\n [-3, -1, -3, 5, -3],\n [-3, -1, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, -3, -6, -2],\n [-5, 0, 3, -3, 1],\n [-5, 4, -3, -6, -4],\n [2, -5, 2, -3, -5],\n [3, 5, -3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 5, -6, -5, 3],\n [4, 5, 5, -1, -1],\n [4, -5, -6, -2, 1],\n [-1, -5, 3, -6, 0],\n [-6, 0, 4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 4, 4, -1, 5],\n [-1, 1, 5, -2, 3],\n [5, -4, 1, 5, -6],\n [3, -6, 6, -2, -2],\n [2, -3, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -3, 1, 1, -6],\n [-4, -3, -5, -4, -4],\n [1, -2, -1, 5, -2],\n [3, -4, 1, 4, -2],\n [-3, 1, -3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 4, 3, -2, -5],\n [3, 1, 6, -6, -6],\n [-3, 6, 1, -4, -2],\n [1, -6, 4, -3, -1],\n [-4, 1, -3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 0, 5, 6, 4],\n [5, 4, 1, 2, 4],\n [1, -6, 5, -2, -1],\n [5, 1, 2, 3, 1],\n [3, 5, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 6, -5, -6, 2],\n [-3, -6, 2, 6, -4],\n [6, 2, 2, -1, 4],\n [-2, -5, 6, 2, 0],\n [4, -2, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 3, -4, 0, 0],\n [-1, 4, -3, -5, -2],\n [3, -1, -6, -2, -4],\n [4, 5, 1, -4, -5],\n [6, -5, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 1, -6, -1],\n [-4, -2, 6, -6, -6],\n [0, 1, 0, 3, -5],\n [-1, 2, 1, -5, -1],\n [-1, -4, -2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 3, -3, 2, -3],\n [6, 1, 5, -5, 1],\n [-1, -5, -1, 3, -1],\n [6, 2, -2, -2, -1],\n [-1, 2, 2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 1, 5, 0, 0],\n [6, -6, -2, 0, -6],\n [4, -2, 1, -1, 4],\n [-1, -3, 0, 3, -1],\n [-1, -5, -4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, 3, 0, 5],\n [-5, -3, 2, 5, -2],\n [-5, -3, -2, 5, 6],\n [4, 0, -6, -4, 2],\n [-4, 1, -2, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 6, -3, 5, 1],\n [1, 1, 4, 1, -1],\n [0, 1, 0, -1, 5],\n [-6, -5, -1, 1, 3],\n [1, -2, 6, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 1, -6, -5, -5],\n [0, 1, 4, -6, 4],\n [4, -1, -5, 0, 6],\n [-5, -5, -1, -5, -5],\n [3, -5, -3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 0, 1, 1, -3],\n [0, -2, 4, -2, 0],\n [0, -2, 4, -3, 4],\n [1, 6, 1, 5, 0],\n [0, -2, -6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 6, 0, 3, 2],\n [-6, 5, 4, 3, -5],\n [3, -2, 3, -3, 1],\n [-1, -1, 1, 6, -1],\n [5, -5, 6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -6, -6, -4, -5],\n [0, 0, -5, -3, 4],\n [0, 6, -3, 2, -6],\n [5, -3, 4, 2, 0],\n [4, -2, -1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -6, 1, 5, -2],\n [-1, 5, 5, -5, 1],\n [-6, 4, 3, -5, 1],\n [6, 6, 5, 1, 1],\n [1, 0, -2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -4, 3, 1, 5],\n [-5, -6, 3, -6, 3],\n [-4, -6, -2, -4, 0],\n [6, -3, -5, 2, 0],\n [5, 0, -5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -3, -2, -1, 3],\n [0, -3, 0, 2, -6],\n [-1, 4, -3, 4, 0],\n [0, 1, 0, -3, -5],\n [-6, -3, -6, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -5, -3, 1, 3],\n [-4, 4, -1, 0, 6],\n [-6, 4, 3, 4, 2],\n [-3, 1, -1, -4, 1],\n [-1, 6, -2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 4, 6, 2, -3],\n [-3, -2, -5, 6, -2],\n [0, 2, 0, 4, 4],\n [-3, -6, -5, -2, 2],\n [2, -4, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -1, -2, -2, -4],\n [-6, -3, -1, 6, 4],\n [1, -5, -3, -3, 0],\n [2, 0, 2, 2, -5],\n [-2, -2, -3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -6, -4, 4, 6],\n [1, -4, -6, 4, 0],\n [-4, 6, 3, -3, -3],\n [3, -2, 0, -1, 3],\n [-5, -6, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 3, 0, -1, 4],\n [-3, 0, 5, 0, 2],\n [-5, -5, -2, -4, -3],\n [-2, -2, -4, -2, -4],\n [3, 0, -4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -4, 0, -6, -4],\n [-4, -4, 6, -3, 6],\n [0, -6, -2, -3, -5],\n [6, 3, -3, -2, 4],\n [-4, -1, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 0, -2, -6, -4],\n [2, 3, 0, -2, -1],\n [-3, -6, 5, -6, -5],\n [-3, 1, -4, -3, 6],\n [1, 5, -5, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -1, 6, 6, -1],\n [-4, 0, 6, -3, 3],\n [6, 0, 6, 1, 6],\n [3, -6, 3, -6, 6],\n [-1, 3, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -6, 5, 3, -1],\n [1, -2, 6, 2, 2],\n [6, 4, 6, 6, -5],\n [5, -6, 0, -4, -1],\n [3, 6, -1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 5, 0, 1, 3],\n [-6, -5, -5, 5, -4],\n [-3, 1, 4, 0, 2],\n [-3, 5, 1, -5, -5],\n [2, -1, 3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -4, -2, -4, 0],\n [-5, -1, 6, -6, 3],\n [3, 0, 2, -1, -5],\n [-5, 2, -3, -3, -1],\n [0, -3, 3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -4, 5, 6, 5],\n [-2, 0, -2, 3, -5],\n [-5, -1, -6, -5, -4],\n [-2, 3, -4, -3, 1],\n [-4, -2, -3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -6, 1, -3, -5],\n [-4, 6, 1, -2, 5],\n [6, -2, -2, -2, -2],\n [-3, 3, 2, -2, 2],\n [5, 5, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, -3, 5, 3],\n [-3, 0, 5, -3, -2],\n [-4, 3, -2, 4, -2],\n [2, -2, 2, -4, -1],\n [4, -4, 1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -6, -5, 6, -2],\n [2, 0, 2, -4, 3],\n [-6, 5, -5, 0, -3],\n [2, 1, -1, 6, -3],\n [-5, 5, -3, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -6, -3, -1, 0],\n [-1, -5, 3, -1, 1],\n [-5, 1, -3, 1, -4],\n [5, 0, 1, 1, -3],\n [0, 1, -4, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, 0, 3, -5],\n [5, -3, -5, -5, -1],\n [-5, -6, -5, 0, -6],\n [4, -4, 2, 6, -4],\n [0, -5, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 3, -2, 1, -3],\n [-6, 4, -4, -5, -6],\n [-2, 5, 5, 2, 3],\n [1, 1, -2, 2, 6],\n [4, -2, -2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 1, -6, 2, 5],\n [3, 0, 1, -5, -6],\n [4, 4, -2, -2, -4],\n [-5, 4, 6, -2, 1],\n [3, -2, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 0, -1, 1, 2],\n [2, -4, -1, 0, -4],\n [-2, 6, -6, -1, -5],\n [-4, 0, -6, 3, -1],\n [1, 2, -6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -4, 1, -5, 5],\n [4, -5, -5, -2, -4],\n [0, -6, -4, 4, 1],\n [-4, -5, -3, 6, -1],\n [3, 0, 1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 6, -4, 3, -4],\n [-3, 3, 3, 3, -6],\n [-5, 3, -5, -6, 1],\n [2, 6, 5, 3, 4],\n [-4, 5, -6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 2, 2, -5, 0],\n [4, 6, 3, 2, 0],\n [0, 4, 1, -5, -5],\n [6, 0, -5, 3, 5],\n [3, -3, -6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -2, -5, 4, 1],\n [0, -3, 2, 3, -2],\n [-6, -5, 5, 5, 2],\n [1, 2, 4, -5, -6],\n [6, 0, -5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 2, 0, -1, 0],\n [3, 5, -4, 0, -2],\n [3, 6, -6, -5, 4],\n [-1, -4, -4, 2, 6],\n [-4, -2, -6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -1, 6, -5, 1],\n [-5, 6, 0, 1, -4],\n [2, -3, -3, -6, 3],\n [-1, 3, 4, 5, 5],\n [-3, -2, 1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -6, 3, 3, -6],\n [2, -1, 1, -4, 5],\n [0, 5, 6, 4, 6],\n [6, -2, 4, -1, 2],\n [-4, 6, 1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -5, 2, 1, 5],\n [-2, 3, 1, -1, -3],\n [-1, -6, -3, -6, 4],\n [4, 3, -4, -4, -4],\n [0, -3, 4, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -4, 6, 4, 1],\n [-4, 1, -3, -3, 1],\n [-1, 6, -2, -2, -3],\n [-2, -1, -1, 6, 5],\n [-4, 0, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 6, 5, -5, -1],\n [3, 0, -6, 1, 5],\n [2, 2, 4, 3, 5],\n [-4, 2, 0, -6, -1],\n [4, 3, 3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 1, 4, 1, 6],\n [-1, 2, 5, -1, 1],\n [6, -2, 2, 0, 6],\n [4, 1, 6, 6, -6],\n [-3, -5, 5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -5, -4, 6, -5],\n [3, -5, -3, -3, -2],\n [-5, -2, -6, -6, 5],\n [5, 4, 5, 2, 6],\n [0, -6, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 5, -4, 5, 1],\n [-5, -6, 0, -3, -4],\n [-1, 3, 4, 3, 6],\n [2, 4, 6, -4, 2],\n [0, 5, 5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 0, -4, -5, -6],\n [5, -5, -2, -2, 2],\n [-2, -5, -3, -4, -6],\n [0, 4, 3, -3, 3],\n [-1, 5, -6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -1, 0, 4, 4],\n [-4, -5, 3, 0, -1],\n [-3, 1, 1, 1, -2],\n [-2, -5, 2, 6, 1],\n [6, -4, 5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -1, 2, -3, -5],\n [-3, 6, -2, -6, -5],\n [0, 6, -1, 1, -5],\n [1, -1, 3, -2, 2],\n [-5, -2, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, 6, 0, -3],\n [2, 3, 3, -1, 0],\n [1, 0, -1, -3, -4],\n [0, -6, -4, 4, -5],\n [2, 3, -5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 2, 5, -4, -4],\n [-3, -5, 6, -5, 6],\n [4, 6, -2, 1, -1],\n [5, -3, -1, 2, 4],\n [1, 0, -6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, -5, 3, -6],\n [6, -5, -2, 5, 4],\n [6, 3, -6, 4, -3],\n [6, -3, 3, -2, -1],\n [-2, 4, -2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 1, 6, 4, -4],\n [4, -3, -1, 1, 1],\n [1, 5, 5, 4, -5],\n [-5, -6, -1, -6, 1],\n [3, -4, -5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -5, 1, 6, -5],\n [-6, 2, -5, 6, 3],\n [6, 4, 5, 6, 2],\n [5, -4, 5, 1, 6],\n [0, -3, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 3, -4, 5, 2],\n [2, 3, -3, 6, 2],\n [-5, -2, -6, 3, 4],\n [-5, -3, -4, 0, 3],\n [-5, 1, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 2, 6, -6, 0],\n [4, 3, -2, -6, 5],\n [1, 5, -4, -5, 6],\n [-4, -1, 3, -1, 5],\n [-4, -4, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, 0, -2, 0],\n [-5, 6, -6, 0, 0],\n [0, -5, -1, -4, -3],\n [-5, -4, 6, 2, -5],\n [6, 2, 0, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 3, 5, 4, -4],\n [3, -2, -2, 0, -6],\n [5, 3, 0, 4, 0],\n [3, 0, -2, 0, -1],\n [-4, -5, 0, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -4, 5, 2, 4],\n [-4, 6, -6, 5, -2],\n [6, -2, 6, -1, -5],\n [-4, -4, 6, -2, -5],\n [0, 2, 1, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 6, -6, 0, -2],\n [5, -1, 4, 5, -3],\n [6, 1, 0, -4, -6],\n [-6, -1, -4, -1, -6],\n [4, 5, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -4, 2, 1, -1],\n [-5, 2, -4, 2, 2],\n [-2, -3, 3, 3, 1],\n [-1, 0, -6, 3, 1],\n [6, 5, -2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -3, 2, 0, -2],\n [6, 5, -6, 0, 1],\n [-6, -5, -5, -4, 1],\n [-1, 2, 1, 2, -1],\n [1, -4, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 6, -1, -4, 5],\n [5, 3, 5, 3, 4],\n [-5, -6, 1, -6, -1],\n [5, -6, 3, -6, -2],\n [0, -6, -5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -2, -4, -1, 3],\n [-2, -5, -3, 2, 0],\n [-5, 6, 0, 0, -5],\n [-6, -4, -6, -4, -2],\n [-4, 5, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -3, 0, 5, -2],\n [-2, 3, -2, 6, 5],\n [-3, 6, -4, 1, 1],\n [-3, -5, 2, 5, -4],\n [0, -4, 1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -6, -5, -1, -2],\n [0, -6, 0, 5, -4],\n [2, 6, -1, -1, 0],\n [1, 6, 4, 4, -6],\n [-6, 3, 3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 1, -4, 2, -1],\n [5, 6, 6, -3, -6],\n [-5, -6, 5, 4, 3],\n [0, -6, 0, -4, -1],\n [6, 4, -1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 2, 1, 3, 4],\n [-2, -6, -6, -1, 1],\n [-4, 1, 2, 1, -4],\n [-3, -6, 1, 2, -1],\n [-6, 5, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, 2, 6, 3],\n [-2, 0, -6, 3, 0],\n [-5, 1, 3, 0, -2],\n [4, -6, -1, -1, -2],\n [-1, 1, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 2, -3, -3, 0],\n [0, 5, 4, 0, 5],\n [5, -1, -4, 6, -4],\n [-6, -1, -3, -3, -6],\n [-3, 3, -6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, -5, -5, 3],\n [-2, 5, 2, 6, -5],\n [6, -5, -4, 1, 6],\n [-5, -1, -6, -3, 0],\n [-1, -1, -5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 2, 4, -2, 3],\n [6, -5, 0, -6, -6],\n [-5, -5, -4, -3, -2],\n [-2, 0, 1, -3, 2],\n [2, 6, 1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -6, 5, -2, 3],\n [-2, -4, 4, -1, -3],\n [-4, -4, 1, -3, -4],\n [-1, 3, -3, -3, 1],\n [2, 5, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 6, 0, 4, 1],\n [1, -6, 6, -5, 2],\n [0, -2, -5, 6, -5],\n [1, 5, 5, -4, 2],\n [0, 2, -1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -2, 0, -2, 5],\n [1, 1, 5, 5, 6],\n [-2, -1, -4, -1, -2],\n [4, 4, -4, -6, 6],\n [-3, -2, -6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 1, 0, -1, 2],\n [3, 0, -2, -3, 2],\n [6, 6, 1, -1, 5],\n [6, -3, -4, -2, 6],\n [-6, 4, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -3, 4, 0, 3],\n [-2, -1, -2, 1, 4],\n [-5, 1, -2, 0, -2],\n [-4, -5, -6, -1, 3],\n [0, 5, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -4, -4, -3, -5],\n [-6, 1, 1, 5, 1],\n [1, -2, 0, -2, 2],\n [-6, -4, 1, 6, 6],\n [1, -4, -1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, -2, 2, 0],\n [0, -4, -4, -3, 4],\n [2, -3, -5, 2, 4],\n [-5, 3, 5, -4, -4],\n [5, -1, 3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -4, -5, -6, 0],\n [6, -2, -1, 4, 4],\n [-4, -2, -3, -2, 2],\n [4, -2, 1, 4, 3],\n [-1, -5, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 0, 1, 2, -5],\n [-3, -4, 6, -4, 2],\n [-1, 0, 3, -2, -5],\n [3, 3, -2, -2, 1],\n [1, 2, 1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 1, -1, -4, 0],\n [-3, 5, -4, 3, 4],\n [3, 6, -2, -5, 2],\n [2, -2, -2, -6, 4],\n [2, 4, 4, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 2, 1, 1, -5],\n [1, 1, -5, 0, -5],\n [-6, -5, -2, -1, -1],\n [-1, 4, 2, 3, -6],\n [3, 5, -1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 4, -1, 5, -4],\n [0, -5, -6, -2, -3],\n [0, -3, 3, 4, -6],\n [5, 5, 0, -4, -3],\n [2, -6, -5, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -3, -3, 6, -5],\n [-3, 1, 4, 6, -4],\n [4, -5, 6, 0, 1],\n [3, -5, -1, 2, -6],\n [1, -5, -1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -2, 1, 4, 4],\n [0, 1, 4, -1, 3],\n [2, -2, 0, 4, -4],\n [6, -4, -2, 5, 2],\n [4, 3, -5, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 0, -1, 6, 4],\n [4, 5, -4, 5, 3],\n [-1, 2, -5, 4, -6],\n [2, 2, 4, 6, 5],\n [1, 2, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 4, 5, -1, 1],\n [-3, 3, -6, -4, 6],\n [-4, -6, 2, 2, 5],\n [-2, 5, -6, 2, 4],\n [2, 2, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -3, -4, 3, -4],\n [-6, -6, 0, -1, -5],\n [-2, 0, -4, -5, 6],\n [-5, 0, 4, -4, -2],\n [6, 2, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -5, 5, -1, 2],\n [1, 0, -5, 0, -2],\n [-5, 6, -3, 0, -5],\n [3, -4, -1, -1, 1],\n [6, -3, -6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -2, 5, -2, -5],\n [-3, -4, -5, -4, 5],\n [-6, -4, 2, -5, -5],\n [-2, 0, -3, -5, 2],\n [5, -6, 4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -5, -3, -3, -1],\n [-6, 6, -1, -4, -3],\n [-6, 6, -1, 2, 0],\n [3, 6, 3, 6, 5],\n [-5, 0, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 4, -4, 2, -2],\n [6, -4, -1, 5, 1],\n [-1, 1, -3, -1, 6],\n [0, 6, 3, 4, -6],\n [-2, -2, -1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 3, -4, -5, -4],\n [-6, 0, -1, 4, 4],\n [-3, 1, 6, -6, -4],\n [-6, 6, 6, -5, -3],\n [6, 2, 5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, -1, 6, 1],\n [2, 4, 0, -4, -6],\n [-3, 5, 2, -1, 2],\n [6, -2, -2, -5, -1],\n [1, -6, 5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -3, 4, 5, -2],\n [-2, 6, -3, -2, -4],\n [4, 1, 3, -4, -5],\n [2, -3, 0, -6, 0],\n [-6, 3, 0, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 3, 4, 2, 5],\n [-6, 3, -6, -4, -5],\n [2, 6, -1, 4, -4],\n [-5, -6, -2, -5, 2],\n [-3, 5, -4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, 6, -6, 6],\n [6, 1, 4, -6, -4],\n [-5, 0, -3, 0, 3],\n [-2, -4, -4, 2, -5],\n [-2, 5, 6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 3, 2, -1, 6],\n [-4, 5, -5, -2, -1],\n [-1, 2, -6, -5, -3],\n [1, 6, 4, -2, 5],\n [-1, 2, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -1, 1, -1, 0],\n [6, -6, -2, -5, 5],\n [6, -4, -2, 1, -1],\n [-1, -1, -1, 4, -4],\n [-4, 4, 5, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 0, -2, -2, -4],\n [1, 1, 4, 0, 6],\n [-5, -3, 0, -6, -1],\n [4, -4, -1, -6, 1],\n [0, -4, 5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 1, -4, -5, 2],\n [0, -5, 6, -5, -2],\n [4, -4, -4, 6, -6],\n [-4, 6, -5, 5, 3],\n [3, -4, -5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 5, 3, 3, 0],\n [6, -2, -2, 6, -5],\n [5, 4, -4, 6, 5],\n [6, 4, 0, -4, -1],\n [1, 5, -6, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -4, -6, -6, -4],\n [3, 4, 3, 6, -6],\n [6, 3, 0, 5, 0],\n [5, 1, 3, -2, 6],\n [6, 1, -1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 3, -3, -2, -5],\n [5, -2, -5, 5, 0],\n [-4, 3, 1, -1, 6],\n [2, 3, -6, 3, 3],\n [-4, -2, -5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -6, 6, 5, 2],\n [5, 5, -5, -6, 0],\n [1, -5, 4, -4, -6],\n [1, 3, 6, -5, 2],\n [3, -5, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, -3, -2, 3],\n [-5, -4, -3, -3, 4],\n [-4, -2, 5, -3, 3],\n [3, -6, -1, -2, 4],\n [-4, -1, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -5, 5, -1, 1],\n [-1, 5, -3, 2, 3],\n [-5, -6, 0, 1, 0],\n [-4, 6, 2, -4, -4],\n [-2, 6, 1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -6, 5, 2, 6],\n [4, 5, 4, -5, -1],\n [-2, -6, -5, 6, -1],\n [-3, 2, -1, 2, -3],\n [-6, 5, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 5, -5, 6, -2],\n [-3, 2, 2, 5, 6],\n [0, -5, 1, -4, 4],\n [-4, -1, -6, 1, -3],\n [-3, 3, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 1, 1, 4, -6],\n [6, 2, -4, -3, 6],\n [3, 5, 5, 0, -2],\n [1, 0, -1, -4, 6],\n [-6, -4, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 6, -5, 6, -6],\n [-5, 4, -5, -6, 1],\n [-6, 0, 1, 6, 3],\n [3, 1, -3, -5, -4],\n [0, -5, 5, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 4, 4, -1, -5],\n [3, -5, 6, -5, -3],\n [5, 5, 6, 3, -2],\n [-1, 3, 3, -2, 6],\n [0, 2, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 5, 1, 5, 1],\n [-3, 1, 6, 4, 4],\n [-4, -4, -6, 5, -6],\n [2, 5, -5, 2, 3],\n [-4, -2, 0, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 0, 6, 4, 1],\n [-4, -2, -3, 3, 3],\n [-2, -6, 0, -5, -4],\n [1, -4, 1, 6, -5],\n [-3, 1, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 5, -2, -5, 3],\n [5, 4, -2, 4, 6],\n [2, -4, 0, -2, 4],\n [-3, 2, 4, 4, 4],\n [4, -3, -5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 6, -1, -5, -4],\n [3, -2, 3, 0, -6],\n [-6, -5, -1, 4, 6],\n [-1, 5, 1, -1, -2],\n [2, -5, 1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -6, -6, -3, -5],\n [4, 6, -3, -5, -4],\n [-4, -3, -1, 0, -3],\n [-3, 4, -3, 6, 2],\n [-6, -6, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 3, 4, 5, -4],\n [6, -4, -1, -2, -4],\n [-1, 6, -1, 2, -1],\n [-2, -1, 3, -4, -3],\n [3, -5, 2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 5, 2, 2, -1],\n [-3, -1, 4, 1, 4],\n [-2, 2, 2, -4, -6],\n [4, -3, 1, -2, -4],\n [-3, 4, -1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 5, -4, 3, -2],\n [-1, -2, -3, -3, -3],\n [-5, -1, 3, 4, -2],\n [-1, -3, 0, 3, -1],\n [3, -6, -6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, -3, 2, -3],\n [-4, -5, 0, 5, -2],\n [0, 4, 4, 3, -3],\n [4, 3, 2, 0, -5],\n [2, 5, 4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, -2, -2, 2],\n [4, -3, -5, 4, -3],\n [0, -6, 0, 6, -2],\n [-2, -4, -5, 1, 2],\n [2, 0, 5, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 3, 3, 6, 4],\n [-6, 0, -4, -4, -5],\n [-3, -1, 4, -3, 6],\n [-6, -4, 2, 1, 4],\n [1, -1, -2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 0, -2, -2, 2],\n [-3, 5, 2, -1, 0],\n [-4, 4, 1, 5, 0],\n [-5, 6, 3, -4, -5],\n [-1, -3, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, 3, 2, -2],\n [-3, 2, -5, -1, 6],\n [2, 6, 0, 5, 2],\n [-2, 0, 6, -1, -6],\n [0, 0, 3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 4, 0, -6, -5],\n [-3, 6, 0, 0, 4],\n [2, 1, -1, 4, -6],\n [0, -2, 2, 0, 6],\n [4, -3, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, 0, 1, 6],\n [-1, -1, -1, 2, -3],\n [3, 2, -3, -2, -4],\n [-3, 0, 1, -4, 4],\n [6, -6, 1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 6, -4, -5, -5],\n [3, -6, -4, -6, 3],\n [-5, 3, -4, 0, 5],\n [0, -1, 2, -5, -6],\n [-3, -5, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -2, -2, 3, -3],\n [-1, 0, -6, -2, -2],\n [0, 6, 2, -6, 1],\n [1, 5, 2, -6, 1],\n [-4, -1, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, 0, -1, 6],\n [4, 5, 0, -1, -4],\n [1, -2, 4, -6, -4],\n [-4, 1, -3, -4, -5],\n [-4, -4, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 3, 4, 4, -3],\n [-3, 5, -3, -2, 2],\n [2, 0, -4, 5, -6],\n [0, 5, 4, -6, 2],\n [-6, -6, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 2, -2, 4, -5],\n [5, 0, -6, -5, 5],\n [-3, 1, 1, 2, 6],\n [3, 4, 4, -6, 1],\n [4, -1, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -3, 4, -5, 3],\n [-5, 3, 3, -6, -6],\n [3, -4, 0, -5, -1],\n [1, 1, -6, 1, -1],\n [4, -4, -6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 3, 5, -3, 2],\n [5, -6, 3, -1, 2],\n [-3, 6, -6, -6, -5],\n [1, -2, -4, -1, 2],\n [4, 0, 6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -3, -1, 2, 6],\n [1, -5, -3, -6, -3],\n [-2, -6, -5, 4, -1],\n [3, 1, 6, 0, 0],\n [-3, 0, -3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 2, 0, 4, 4],\n [-4, 6, -1, -3, 5],\n [-5, 1, 3, 5, -2],\n [4, 6, 0, -6, -5],\n [-2, -6, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 4, -1, -6, -4],\n [-5, 2, -3, -3, 3],\n [0, -5, -1, 2, -1],\n [-3, 2, 4, 3, -3],\n [0, 6, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 5, -1, -3, 4],\n [0, 2, 3, -5, -1],\n [-5, 3, 0, 5, 5],\n [-5, -5, 4, 2, -1],\n [-4, -4, 4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 4, 1, -5, 3],\n [-2, -5, -6, 4, 2],\n [4, -1, -5, -4, -3],\n [-6, -6, 1, 1, -6],\n [-2, -6, -6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 3, -3, -5, -2],\n [-3, 3, 2, 4, -5],\n [-4, 4, 1, 1, 3],\n [5, -1, -1, -3, -1],\n [6, -3, 2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 0, -5, -4, 5],\n [1, -3, 2, 4, -6],\n [0, 2, -1, -3, 3],\n [3, -3, -2, -4, -6],\n [2, -2, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, 5, 1, 0],\n [4, 5, 0, 2, -2],\n [-5, 3, 6, 4, 1],\n [-2, 5, 4, 0, -2],\n [3, -6, -1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 1, 3, 4, 3],\n [-4, -6, -2, -5, 6],\n [-1, 2, 0, 4, 0],\n [3, 4, 1, 5, -5],\n [0, 6, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -2, 1, 3, 5],\n [-4, -4, 6, 6, 3],\n [4, -6, 3, 4, 5],\n [3, -5, -5, -4, -6],\n [-4, 0, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 4, 4, 4, -4],\n [0, 3, 5, -6, 4],\n [6, 6, 1, 6, -4],\n [6, 6, 1, 4, -3],\n [-3, 4, -5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 5, -2, 1, -5],\n [-1, 6, 2, -6, -2],\n [-6, 1, 6, 0, 3],\n [5, 1, -1, -4, -3],\n [-6, -3, 2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, -1, -2, -5],\n [-6, 6, -5, -6, -3],\n [5, 4, 0, 6, 1],\n [-1, -5, 0, -2, 5],\n [4, -6, -5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -2, -4, -3, -3],\n [6, 6, -1, 3, 0],\n [-2, 4, 3, -6, -6],\n [-6, 4, -3, 6, 4],\n [5, 3, 5, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -2, 6, 3, 1],\n [2, 1, 1, 1, 3],\n [-4, 6, 0, -2, 5],\n [5, 4, -4, -2, -1],\n [-4, -2, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, 1, -5, 1],\n [1, -3, 0, 3, 3],\n [-3, -4, 2, 1, 0],\n [-6, -4, -5, 5, 6],\n [3, -2, -1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -6, -4, 4, 0],\n [-6, -1, -1, -3, 6],\n [-5, 2, 1, 3, -5],\n [-5, 0, -3, -6, -3],\n [-3, -3, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -2, 3, 4, 1],\n [3, 6, 4, -4, 2],\n [-1, 0, -1, -6, -6],\n [3, -3, -1, 4, 3],\n [-2, -3, -5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -1, 4, -1, -6],\n [0, -4, -1, -6, -5],\n [-6, 2, 5, 1, 3],\n [1, 6, 0, -2, 0],\n [-1, -6, -5, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -5, 6, 6, -3],\n [3, 2, -6, 3, -5],\n [-2, -6, -5, -5, 3],\n [3, 1, -1, 3, 5],\n [-3, -2, 1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 0, -6, -5, 4],\n [-6, -4, -1, 5, -2],\n [-1, -3, -6, 6, 3],\n [3, 4, -2, -6, 1],\n [3, 5, 5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 2, -1, 5, 2],\n [-4, -4, 2, 5, -5],\n [-5, 5, -6, -4, 1],\n [6, 0, 2, 5, 3],\n [1, 3, 6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, 6, -2, 5],\n [5, -4, -1, 0, 4],\n [-3, -1, -3, -3, 2],\n [0, -1, -4, 2, -1],\n [-6, -2, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 2, 3, -6, -5],\n [-2, -5, 6, -4, 6],\n [-5, 1, 2, 4, -1],\n [0, -3, 6, -5, -5],\n [-3, 6, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 0, -5, 2, -3],\n [-3, -1, 0, 6, -5],\n [-3, 4, 1, 2, -3],\n [4, 3, -3, -5, 0],\n [-1, 1, -2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 4, 5, -5, -2],\n [-6, 0, -2, -1, -4],\n [-6, -6, -3, -3, 0],\n [1, 1, 3, 4, -2],\n [-1, -5, 4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -4, -4, -3, 3],\n [3, 3, -3, 5, 1],\n [6, -6, 5, -6, 5],\n [-1, 6, -3, -3, -3],\n [0, 6, -2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 3, 4, 1, -5],\n [-4, 1, 0, 4, 3],\n [3, 3, 4, 0, -4],\n [5, -1, 5, -4, -5],\n [-3, -6, 6, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 5, -6, -3, 2],\n [6, -6, 6, -2, 5],\n [2, 6, -6, 1, 2],\n [-3, -4, -6, 2, 4],\n [-4, 3, 5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -4, -5, -2, -4],\n [2, 2, -3, 1, -3],\n [0, -2, 3, 3, -4],\n [4, 3, 2, 4, -2],\n [-2, 4, 4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -1, -4, -1, 4],\n [3, -1, -2, -6, -3],\n [-4, -5, -6, -3, -3],\n [-6, 5, -3, -6, 6],\n [0, 6, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -6, -3, 2, -6],\n [6, 0, 6, 6, 5],\n [5, 0, -5, -5, 2],\n [3, 2, 0, 3, 5],\n [6, 1, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -6, -4, 3, -6],\n [-1, 1, -1, -3, -3],\n [0, -3, 1, -5, 4],\n [6, -6, -1, -3, 4],\n [-4, -3, -3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -3, 0, -2, 4],\n [-2, 1, 4, 0, -3],\n [3, 5, -4, -4, 2],\n [-4, -5, -5, -2, -1],\n [-3, -4, 4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 6, -6, 1, 0],\n [4, -5, 6, -2, 3],\n [0, 4, 2, 5, -3],\n [-4, 1, -3, 0, -2],\n [2, 6, 1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -2, -4, -4, 6],\n [6, 2, 1, -6, -6],\n [-4, 4, -5, 3, -3],\n [-5, -4, 6, -5, 4],\n [-6, 3, -1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 6, -2, 0, -4],\n [-4, -6, 0, -3, 0],\n [-2, 6, 5, 0, -3],\n [6, -5, 1, 3, -5],\n [6, -1, -5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -4, 4, -6, 3],\n [-6, 6, -5, -6, -4],\n [0, -2, 2, -5, 3],\n [-2, -2, -2, 1, 3],\n [2, 3, -5, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 1, -3, -5, -2],\n [-5, 1, -2, 2, -6],\n [2, 1, -6, -2, 6],\n [-6, -3, 0, 4, 1],\n [6, 2, 5, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 6, 2, -2, 6],\n [-2, 2, -4, 4, 0],\n [-2, -3, -6, -4, -2],\n [-6, 0, 6, 6, 5],\n [4, -1, -3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, 2, 4, 4],\n [-2, 4, 4, -2, -6],\n [-5, -3, -1, 4, -2],\n [3, -3, -4, 0, 2],\n [-3, 6, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -2, -1, 2, -6],\n [1, -5, -5, 1, 2],\n [-3, 5, -3, 3, -5],\n [5, 3, 1, -3, 2],\n [1, 6, 2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 4, 6, -6, -5],\n [-1, 6, -5, 3, -1],\n [1, 4, 0, 4, -3],\n [-5, 4, 5, -1, -2],\n [4, -6, -1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -5, 3, 1, -1],\n [-5, 2, 6, -6, 1],\n [6, 5, -3, -1, -6],\n [2, -4, 1, 6, -4],\n [-1, 6, 2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, 3, -1, 3],\n [3, 1, -4, -5, -4],\n [4, 0, 3, 6, 5],\n [-5, -1, 3, 5, 3],\n [-6, -5, 0, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 1, 1, -2, 4],\n [-1, -4, 6, -1, -1],\n [-6, 6, 0, -1, 2],\n [5, -6, -6, 3, 2],\n [4, 3, 1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -4, 3, -4, -5],\n [2, 3, -3, -2, 5],\n [-1, -2, 1, -1, -2],\n [4, -3, 3, 3, 6],\n [6, -4, 1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 0, 4, -3, -2],\n [-3, -2, 1, -5, 5],\n [0, 0, -4, -6, -4],\n [0, 6, 5, 2, 5],\n [5, -5, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -5, -4, 1, -1],\n [-5, 2, -3, 6, 4],\n [-2, 3, 6, -2, -5],\n [3, -6, -3, -3, 2],\n [-1, -6, -3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 0, -3, 1, 5],\n [6, 4, -6, -4, -4],\n [0, 1, 0, -2, 4],\n [-6, 4, -1, 4, 6],\n [-2, -3, -4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -6, 0, 3, 6],\n [6, -4, -4, -6, 5],\n [-4, 2, -2, -5, 6],\n [2, 5, -4, 2, 2],\n [-3, -3, -5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 4, -6, 5, -2],\n [6, -5, -6, -1, -6],\n [3, 5, -3, -2, 5],\n [6, 5, 4, 1, 3],\n [4, 4, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 0, 6, -5, -4],\n [-4, -6, 5, 6, 1],\n [-1, -4, 3, -3, -3],\n [1, -3, -4, 4, 2],\n [1, 2, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -2, -1, -4, -3],\n [6, 1, 3, -1, -1],\n [0, 5, -6, 2, 2],\n [1, -4, -2, 6, -3],\n [6, 4, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 4, 3, -4, -1],\n [-1, 0, 1, 0, 0],\n [-1, 4, 1, 5, -1],\n [-4, 1, -3, -3, 0],\n [6, -1, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, 6, -2, -5],\n [4, 3, 2, -5, -6],\n [-4, -4, -4, 3, 4],\n [-6, -3, -6, 4, -4],\n [0, -4, -1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -6, -1, 3, -4],\n [1, 1, 4, 1, 0],\n [1, -3, -3, -2, -6],\n [-2, -4, -2, -2, 0],\n [-3, 0, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -3, 6, 0, 3],\n [1, 1, -3, -2, 3],\n [2, -5, 3, 1, 2],\n [0, 2, -3, -6, 2],\n [-3, -1, -5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 4, -4, 3, -5],\n [4, 4, -5, 1, -5],\n [5, -3, 4, -4, -6],\n [-1, 3, -2, -3, -4],\n [-4, 5, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -3, 1, 3, -3],\n [-4, -1, -1, -6, 2],\n [-3, -3, 5, 4, 2],\n [3, 2, 5, 1, -1],\n [6, -2, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -2, 4, 0, 5],\n [-5, -6, 4, 5, 0],\n [-5, 0, 6, 1, -2],\n [0, -2, -1, 4, 5],\n [-4, -6, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 0, -6, 4, -6],\n [6, 2, 0, 0, 1],\n [-2, 5, -4, 2, 2],\n [0, 5, 0, -5, -3],\n [0, -2, -4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -6, 4, -1, 6],\n [-1, -1, -2, 5, 1],\n [-1, 5, -5, 1, -1],\n [-5, -3, -5, 2, 1],\n [-2, 3, 1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -3, -2, 6, -5],\n [2, 1, -4, -4, -1],\n [6, 3, 4, 0, 5],\n [-2, 2, -2, -6, 4],\n [-1, -5, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 1, 3, -2, 6],\n [5, 6, 3, 3, 0],\n [-3, -2, -6, 3, -3],\n [1, -4, 0, -4, -3],\n [6, 4, -5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 5, 4, -5, -4],\n [3, -1, -4, 2, -1],\n [4, -3, 5, 5, 4],\n [-3, -3, 3, 6, -3],\n [4, -2, 1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -1, -3, 3, 3],\n [-6, 2, -4, -5, 1],\n [-4, 3, 6, 3, -4],\n [5, 4, 4, -2, 3],\n [0, -2, -2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 4, -1, -3, 3],\n [0, -2, -5, 2, -4],\n [0, 5, 6, -6, 0],\n [2, 0, 5, 2, 4],\n [4, -4, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 5, 5, 3, -1],\n [-3, 3, -3, 6, 0],\n [6, 6, 0, 6, -1],\n [-5, 0, 6, -4, -3],\n [-5, -1, -3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 2, 3, 5, 4],\n [4, 4, 4, -2, 0],\n [5, 0, 2, -3, 6],\n [-6, -2, -4, -1, 2],\n [-4, 2, 0, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -6, 3, -3, 5],\n [-5, 2, 4, 6, 0],\n [-6, 1, 4, -5, 6],\n [0, 0, 0, -3, -2],\n [-1, 0, 0, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 3, 1, 0, 4],\n [-2, -6, 4, 2, 2],\n [-6, -5, -1, -2, -2],\n [5, -1, -6, -3, 4],\n [-6, 2, 5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -5, -1, 1, 1],\n [3, -2, -3, 1, -4],\n [2, 6, 3, -2, 4],\n [3, 6, 3, -3, -1],\n [1, 3, 6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -2, 4, -1, -2],\n [-1, 6, 1, 4, -3],\n [3, 0, -4, 3, 1],\n [1, 1, 4, 5, -5],\n [5, 0, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -4, 3, -2, 5],\n [4, 4, -4, 5, -6],\n [5, -1, 5, -6, -2],\n [6, -5, -5, -5, 5],\n [-4, -5, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 1, -6, 6, 6],\n [6, -4, -5, 0, -4],\n [0, 2, 4, -3, -4],\n [-2, -4, 5, -2, -6],\n [-5, -6, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 3, 1, 5, -6],\n [4, 2, 5, -3, -3],\n [3, 5, -1, -2, -4],\n [-6, 4, 4, -3, -6],\n [1, -2, 3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -1, -1, 4, -3],\n [-3, -1, -4, 5, 2],\n [-2, 1, -4, -5, -6],\n [-1, 0, 5, 6, 5],\n [-3, -6, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -1, 1, -5, -5],\n [5, 5, -6, -1, -1],\n [-4, 3, -3, -2, 4],\n [-1, -2, 1, 1, 4],\n [-3, 2, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 5, 6, 4, 6],\n [-6, -1, -2, 1, -3],\n [2, 2, 6, 2, -5],\n [-4, 1, -1, 5, -1],\n [1, 5, 4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -3, 3, 3, -1],\n [0, -5, 5, -1, -1],\n [0, -1, 5, 0, -4],\n [1, -4, -1, -4, -6],\n [-1, -1, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 5, 5, -1, -6],\n [0, 4, 6, 2, -4],\n [-1, 1, 2, -6, -4],\n [2, -2, 3, -5, -3],\n [4, -4, 6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 5, -4, 1, -1],\n [-1, -3, -2, -4, -4],\n [3, 2, 1, -5, 2],\n [-2, 0, -1, -1, 0],\n [-3, -5, -2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -1, -4, -5, -6],\n [-1, 0, -4, -3, 3],\n [1, 0, -5, -4, 1],\n [-3, 0, 0, -4, 6],\n [-5, -2, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -1, -3, -6, -5],\n [6, 5, -6, 1, 4],\n [4, 5, 4, 3, -2],\n [5, -6, -4, 3, -1],\n [0, -3, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -1, 0, -6, 4],\n [6, 1, 0, 6, 6],\n [4, -4, -4, 1, -3],\n [-5, 0, 2, -4, 3],\n [2, 1, -5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -5, -5, -2, -1],\n [4, 2, -6, -6, -2],\n [-6, 1, -2, -2, -5],\n [5, 3, 3, -6, 1],\n [-1, 3, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 0, 2, -4, 3],\n [5, 0, 6, -2, 3],\n [2, 1, -4, -2, 6],\n [-1, -5, 1, 3, -4],\n [-5, 3, 5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, 5, 1, -1],\n [-4, 0, 0, 4, 2],\n [2, 6, 5, -4, 6],\n [1, 5, 3, 1, 4],\n [-2, 5, -4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -2, 4, -1, -6],\n [-1, -2, -5, 2, 4],\n [2, -3, 5, -3, -4],\n [3, 4, 0, 4, 4],\n [-2, 0, -4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 0, 0, 0, -1],\n [-3, 6, 2, -2, -3],\n [-3, 3, -1, 5, 4],\n [0, -4, -3, 0, -6],\n [3, -4, -3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, -6, -6, 3],\n [2, 3, -1, 4, -6],\n [0, 2, 3, -4, -6],\n [6, -1, 2, -5, -1],\n [-2, 3, 3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -3, 0, 2, -4],\n [-2, 2, 2, -2, -1],\n [-2, -6, 1, 2, -3],\n [2, -5, -5, -6, 1],\n [-4, 6, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -4, 4, -4, -5],\n [6, -5, 6, -2, 0],\n [1, 0, -4, 0, -3],\n [6, 6, -2, -2, -3],\n [-3, -5, -6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 3, 6, 4, 6],\n [5, 1, -2, 5, -2],\n [6, 2, -1, -1, -2],\n [-2, 5, -6, -2, -2],\n [2, -6, -2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -1, -3, 0, 6],\n [4, 6, 5, 1, -5],\n [2, 1, 2, 6, 2],\n [3, 3, -5, 2, 1],\n [-6, 0, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 2, 5, -5, 4],\n [5, 0, -2, 3, 2],\n [1, -1, -4, -3, 4],\n [1, 2, 6, -1, -5],\n [0, -5, 1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 1, -1, 2, 3],\n [5, 6, 2, -3, 1],\n [-4, -6, -5, 0, 2],\n [1, 5, 3, 4, -6],\n [2, 4, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -5, -1, 4, -1],\n [2, -1, -6, -2, -3],\n [3, -6, 3, 4, -6],\n [-3, -3, -3, -4, 0],\n [1, -2, -3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -4, 5, 2, 3],\n [5, 2, -4, 1, 3],\n [-3, -6, 2, -5, -4],\n [6, 1, 1, -2, -2],\n [1, -3, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -3, -2, 4, -3],\n [-2, -1, 5, 4, 6],\n [2, -2, -6, 1, -3],\n [-4, 5, -1, 2, 2],\n [3, -2, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 5, 1, 1, -1],\n [-5, -6, -3, -5, 5],\n [6, -1, -2, 2, 6],\n [-1, -3, -1, 4, 3],\n [-1, -1, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, 6, -4, -5],\n [-4, 3, 4, -4, -2],\n [5, -4, -6, -6, 6],\n [6, 5, -5, 6, 6],\n [3, -6, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 2, 2, -5, -1],\n [-2, 2, -5, 2, 4],\n [6, 2, 1, -5, 4],\n [0, -6, -2, 3, -2],\n [2, -1, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -5, -2, -6, 6],\n [2, -4, -5, -1, -4],\n [2, 1, 1, 5, 1],\n [-1, 1, -3, 5, 3],\n [-4, -2, -5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 2, -4, -4, -3],\n [-5, -5, -6, -6, 4],\n [-4, -4, -4, 6, 4],\n [2, 0, 1, 0, 5],\n [1, -3, 6, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 2, -2, -1, -3],\n [-3, -5, -6, -6, 6],\n [-6, -6, 1, 1, 4],\n [-4, 4, 1, 3, -5],\n [6, 6, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 2, -6, -4, -6],\n [-5, -2, -1, -5, -2],\n [0, 3, -4, 3, 0],\n [-5, -6, 6, -6, 3],\n [-6, 0, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -4, -4, 2, 1],\n [6, -3, -5, -5, 2],\n [0, 0, -1, -4, 1],\n [-3, 0, -1, -5, 1],\n [1, 4, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -4, 4, 1, -4],\n [-2, 1, -1, 0, 0],\n [-2, 2, 5, 5, -2],\n [4, 3, -3, 0, -4],\n [2, -1, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, -1, -2, 3],\n [5, 6, 5, -5, -1],\n [-6, 4, -4, 6, 4],\n [1, 0, 1, 1, 4],\n [-3, 1, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 5, 2, 3, -2],\n [1, -1, -6, 6, 4],\n [-1, -2, -1, 4, -1],\n [-6, 4, 3, 5, 4],\n [6, 2, 4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -6, 0, -5, -3],\n [6, 3, 6, 6, -6],\n [1, 3, -2, 6, -1],\n [1, 2, -6, -5, 4],\n [0, 5, -2, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, 0, -1, 1],\n [4, 4, 2, 4, -6],\n [1, 0, -6, -2, -1],\n [4, 2, 5, 2, -1],\n [6, -5, 5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -6, 6, -6, 3],\n [-2, 1, 0, -6, -6],\n [4, 0, 1, 6, -6],\n [3, 3, 6, 6, 1],\n [-3, 2, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -5, -1, 3, 4],\n [4, -2, 4, 3, 0],\n [1, -5, -2, 2, -5],\n [4, 3, -1, 1, 1],\n [-5, -3, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -1, 6, 4, -2],\n [0, 3, 5, 6, 5],\n [1, 1, -4, 5, -2],\n [-2, 3, -6, -2, 4],\n [-1, 0, 4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -1, -5, -1, -1],\n [6, -1, 1, 4, 3],\n [-2, 0, -3, 6, 4],\n [-3, -3, 5, 6, 5],\n [-4, 1, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 6, 1, 3, -4],\n [3, 6, -3, 6, -5],\n [-1, 4, 2, -6, 1],\n [6, 6, -3, -5, -4],\n [-5, 6, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -2, 6, -6, -4],\n [1, -2, -2, 2, 3],\n [-4, -4, -4, -1, 0],\n [2, -5, -3, 5, -5],\n [-6, 1, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 4, 5, -3, -3],\n [-2, -6, 6, -4, 3],\n [-4, 5, -3, 2, 1],\n [6, 1, -2, 3, 0],\n [5, 5, -6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 1, 5, -2, 1],\n [-3, 2, 5, -6, 3],\n [-6, 0, 5, 5, 1],\n [2, 5, 4, -3, 2],\n [-6, 4, -3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 5, -4, 3, 0],\n [2, 0, -4, -3, -3],\n [-3, 5, 0, -3, -6],\n [-5, 3, -5, 1, -1],\n [0, 5, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -3, 3, -3, -3],\n [3, 2, 0, -1, -1],\n [-4, 4, -2, -4, -6],\n [3, 6, 1, -2, -4],\n [1, 5, -4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -2, -1, 3, 3],\n [-1, -4, 4, 6, -1],\n [-3, 3, 3, 2, 2],\n [-3, 6, 6, 6, 5],\n [6, -2, -6, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -5, -1, -6, -3],\n [-2, -1, -1, 4, -3],\n [3, 6, 3, 6, -1],\n [0, -5, -6, 2, 3],\n [-5, -1, -6, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -2, -1, 5, -3],\n [-5, 0, 0, 6, -5],\n [6, -3, -3, 5, 4],\n [2, 2, -4, 6, 4],\n [6, -5, 6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -2, -6, -4, 1],\n [6, -1, 2, 0, -3],\n [-6, 2, -6, -3, 4],\n [1, -3, 2, 6, -5],\n [5, -5, -3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -6, 5, 0, -1],\n [1, 2, 0, 5, 6],\n [2, -6, 3, -4, -5],\n [-6, 5, 4, -6, -4],\n [-5, -5, 6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, 6, 4, -1],\n [5, -4, -1, 3, 1],\n [-3, 2, 2, 0, 0],\n [-4, 6, 2, 6, -6],\n [2, 5, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 5, -1, 3, 4],\n [6, 0, 4, -5, -6],\n [1, -1, -5, -3, 3],\n [-5, -5, 1, -2, -5],\n [6, 4, 3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 1, -2, -2, -4],\n [-3, 2, 4, -4, -3],\n [3, -3, -1, 6, 0],\n [-4, 5, 1, -3, -6],\n [-1, 6, 0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -4, 5, 0, 4],\n [-1, 4, 2, 6, -6],\n [3, -1, -5, 6, 6],\n [-2, -1, -6, 3, -6],\n [3, -6, 0, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -6, 4, -3, 1],\n [-1, -1, 4, -6, 4],\n [-2, 2, -3, 6, -5],\n [2, 3, 6, 3, 0],\n [-3, -1, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -3, 6, -6, 5],\n [-5, 1, -3, 0, -6],\n [6, 5, 4, 4, 4],\n [1, 6, 0, 4, -6],\n [-6, -4, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 0, 3, -6, -2],\n [6, 2, 3, 5, 5],\n [-6, -2, 0, 3, -6],\n [0, 0, 5, -3, 4],\n [-1, 5, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 1, -5, -3, 5],\n [-6, -4, -4, -5, 2],\n [3, 5, -3, 2, -3],\n [-4, -1, 1, -4, 0],\n [-1, 5, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 5, -5, 2, 5],\n [-5, 3, -4, -3, 1],\n [-3, 5, 3, -1, 5],\n [-6, -4, 1, 5, 5],\n [0, -2, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -6, 2, 3, -4],\n [-5, -5, -2, -2, -5],\n [-2, 0, 0, -4, 3],\n [-6, -6, -2, -1, 5],\n [0, -4, 5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -1, 6, 3, -1],\n [-4, 5, -4, 5, -1],\n [-4, -3, -2, -4, 0],\n [6, -2, 3, -5, -4],\n [-1, -2, -1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, 0, 3, -1],\n [6, -3, 3, 6, -2],\n [-4, 6, 5, 5, 1],\n [0, 3, 0, -5, 1],\n [-1, -4, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 1, 2, -6, 0],\n [-6, 4, 6, 2, -4],\n [-6, 0, -3, 5, -2],\n [2, 3, -6, 4, -1],\n [5, -5, -4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 0, -6, -3, 6],\n [-4, -4, 4, -1, -2],\n [1, 4, -5, 3, 6],\n [5, -6, 4, -3, 2],\n [-4, 3, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 5, 0, 6, -2],\n [3, 3, 4, -6, 3],\n [2, 1, 0, -1, 4],\n [-2, -4, -6, -6, -2],\n [-4, 3, 2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -5, 5, -2, -3],\n [-1, -3, 5, -6, -2],\n [4, 3, 0, -5, 3],\n [5, 4, 1, -1, -5],\n [-1, -5, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, 1, -4, -2],\n [0, 1, 5, 3, -1],\n [4, 0, -6, 1, -4],\n [3, -6, -2, 4, 4],\n [4, -4, 0, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 4, 3, -4, 2],\n [-1, 3, -5, 0, -4],\n [1, -2, -4, 3, 5],\n [5, -1, 1, 4, -3],\n [5, -6, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -6, 5, 0, -5],\n [-6, -1, -4, -1, -6],\n [1, -4, -1, 1, -6],\n [-2, -5, -2, 2, -6],\n [3, 5, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 0, -1, -3, 4],\n [5, -2, -1, 0, 2],\n [-5, 5, 4, 6, -6],\n [2, -3, -5, 3, 6],\n [1, -2, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 2, 6, -4, 6],\n [-5, 2, 5, -2, 6],\n [6, 6, -1, 1, 1],\n [-5, 5, 4, 3, -6],\n [3, 1, 6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 6, -5, -6],\n [1, -1, -1, -6, 2],\n [3, 3, -5, -6, 2],\n [1, 4, -6, 2, 1],\n [3, -2, -1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -4, 2, 2, 0],\n [1, 3, 0, 1, -4],\n [-2, -3, 2, 0, -1],\n [2, -4, 2, 6, -1],\n [3, -1, -3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, 5, 4, -5],\n [3, -5, -6, -1, 2],\n [-2, -2, 0, 0, -5],\n [1, 3, -6, 1, -6],\n [0, -6, 6, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -3, 1, 4, -4],\n [6, 6, 4, 6, 4],\n [-4, -5, 6, 5, -1],\n [3, 4, 6, -1, 1],\n [2, 1, -1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 1, 1, 5, 6],\n [6, 5, -5, 3, 2],\n [2, 2, -5, -1, 4],\n [1, 0, -4, 3, 3],\n [0, 3, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 4, 6, -3, 0],\n [0, -5, 6, -5, 5],\n [2, 5, -5, 4, -1],\n [-3, -1, 5, 1, 3],\n [-5, -5, -1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -4, 3, 1, 0],\n [4, -2, -4, 4, -1],\n [2, 6, 5, -6, 3],\n [2, 1, -2, 4, -1],\n [3, 4, 3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -1, -2, 4, 4],\n [0, 0, -2, 5, -3],\n [-2, -1, 6, -5, 6],\n [-4, 2, 2, -1, 5],\n [6, 0, 3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -5, -3, -5, -6],\n [0, -2, 6, 4, 6],\n [1, -6, -4, 6, 0],\n [-1, 1, 5, -2, -5],\n [-3, -5, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, 6, -6, 2],\n [2, 5, 3, 0, 4],\n [4, 4, -5, 4, 2],\n [-5, -2, -4, 5, 0],\n [-5, 2, 6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -5, -1, 2, 1],\n [-2, 5, 2, -4, -1],\n [6, 1, 2, 1, 3],\n [0, -5, -6, -5, 4],\n [-6, -4, 1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 1, 1, -6, -1],\n [-4, -1, 6, 3, -5],\n [-3, 4, 2, -1, 5],\n [6, 0, -6, -5, 2],\n [-3, 1, -6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 2, 6, -2, 6],\n [2, -2, 2, 1, 2],\n [-5, -4, 4, 5, 4],\n [-2, 0, -1, 0, 5],\n [2, 2, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -2, 3, -1, -3],\n [1, 3, 2, -3, 3],\n [-1, 2, -6, 6, -3],\n [6, -3, 6, -3, -1],\n [0, -5, -1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -4, 5, 0, -4],\n [2, -5, 3, 0, 4],\n [-1, -5, -2, -4, -3],\n [0, -3, 3, -1, -1],\n [0, 4, 4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 1, -2, 0, 0],\n [-6, -6, -1, 4, -1],\n [1, 6, 3, -5, -3],\n [2, -1, -4, -3, -4],\n [-3, -3, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 6, 0, -6, 1],\n [-4, -5, 0, -4, -3],\n [-4, -2, 3, 5, 1],\n [3, -1, -3, 4, 0],\n [-1, -3, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -6, 6, 5, 5],\n [-3, -1, -2, 5, 3],\n [5, -2, -2, -5, 0],\n [0, 6, 5, 0, 3],\n [1, 6, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 2, 2, -4, 5],\n [-1, 5, -1, 2, -1],\n [-5, -1, 2, 3, 6],\n [5, -1, 6, -1, 1],\n [4, 0, 5, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -1, 6, 5, 0],\n [5, -5, 0, 6, -6],\n [-1, 3, -2, 4, 4],\n [1, -4, -6, 3, 0],\n [-1, 3, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -3, 6, 3, 6],\n [4, 3, -4, -4, 5],\n [-1, -2, 3, -3, 3],\n [-1, -4, 3, 0, 0],\n [4, -2, -1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 2, -1, 3, -6],\n [-5, -1, 3, 1, -1],\n [-2, 1, -3, 0, 5],\n [-4, -6, -4, -6, 6],\n [4, -3, 6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 1, 4, 4, -2],\n [1, -6, 1, -1, 5],\n [5, 6, -5, -4, -3],\n [4, -4, 4, 5, -5],\n [6, 6, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 2, 6, 2, -6],\n [3, -5, 6, 5, 2],\n [3, 3, -4, -5, -4],\n [1, 6, 1, -2, -4],\n [4, -2, -2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 2, 2, 5, -6],\n [-5, -2, 3, -1, -3],\n [2, -4, -1, -3, -5],\n [4, -1, -4, 6, 1],\n [-5, -3, 4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -5, 2, -6, 4],\n [-1, -3, -2, 1, 5],\n [1, -5, -4, 1, 3],\n [0, 4, 5, -3, 6],\n [-5, 6, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -3, 0, -5, 6],\n [2, 4, -6, 3, -3],\n [-6, 0, -5, -5, 1],\n [-4, 2, -1, -3, 2],\n [-1, -3, 2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 2, 4, 5, 3],\n [-1, 5, 4, -6, -2],\n [2, -3, -1, 0, 0],\n [-5, -1, -1, -5, 2],\n [1, -1, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -2, 0, 3, -3],\n [-3, 4, 6, -1, 3],\n [2, -3, -2, 0, -3],\n [-4, 1, -4, 1, 4],\n [0, 3, 0, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 3, 4, 4, 3],\n [-6, -4, 1, -4, 2],\n [-5, 3, -1, -5, 3],\n [6, 6, 5, -6, 3],\n [-5, 0, 2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -4, 4, -2, -2],\n [3, 0, 1, 5, -1],\n [2, 4, 1, 0, 3],\n [2, -1, 2, 6, -6],\n [1, -1, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -5, 6, 0, -4],\n [-1, -1, 5, 5, -6],\n [-3, 1, -1, -1, 3],\n [4, 5, 5, -6, 3],\n [-1, 0, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -6, 4, 3, 5],\n [-6, 4, -3, -4, 4],\n [5, 6, -3, 1, -4],\n [2, 5, 1, 2, -5],\n [-5, 4, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 6, 1, -5, 1],\n [-3, -4, -5, -2, 2],\n [-5, -2, 4, 6, -5],\n [-1, -6, 5, -2, 2],\n [2, 2, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 0, 0, 4, 1],\n [3, -5, -1, 6, -3],\n [1, 6, -5, 5, -3],\n [3, 4, -2, -1, 1],\n [5, -4, -3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -1, 4, -6, 6],\n [0, -1, -1, 6, 1],\n [1, 6, 4, -5, 6],\n [6, 0, 3, 5, 5],\n [3, -2, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -4, 0, 5, -1],\n [5, 4, 2, -6, 3],\n [-3, -5, -3, -6, 5],\n [-5, -5, -5, -5, 0],\n [0, -3, 1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -1, 2, 1, -4],\n [-3, 5, -6, -4, 2],\n [5, -1, -4, 4, -6],\n [-2, 3, -4, -1, -5],\n [-5, -1, 6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -2, -1, 3, -1],\n [-4, 1, -1, 3, -3],\n [0, -5, 5, 0, 3],\n [6, -4, -1, -5, 0],\n [5, 4, -4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 2, -2, 6, 6],\n [6, -5, -1, -3, 3],\n [-2, -2, 6, 4, -3],\n [4, 2, -1, -4, 0],\n [-4, -4, 4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -2, -2, -3, 3],\n [2, 2, -6, 4, -5],\n [-3, 4, -4, -2, 5],\n [-6, 1, 4, 0, -4],\n [-3, 0, 5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 2, 6, -6, -6],\n [1, -2, 5, -1, -5],\n [0, 0, -4, -1, 6],\n [-6, 1, -4, 5, 1],\n [5, -6, -2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 3, 4, 1, 3],\n [1, -6, 0, -2, -6],\n [4, 4, 4, -6, -3],\n [-5, 4, -5, -6, -3],\n [-3, 5, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -4, 5, -1, 1],\n [5, -6, 0, -2, -2],\n [0, -6, -6, 2, -1],\n [6, 5, -6, -3, -3],\n [-3, -4, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, -5, -2, -5],\n [-6, 3, -2, 5, -6],\n [-4, 6, 1, 6, -3],\n [2, 4, -6, -4, -6],\n [6, -5, 1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 6, -5, 6, 2],\n [-5, 4, 2, -1, 1],\n [-2, 1, -1, 0, -4],\n [-3, -5, 0, 2, 2],\n [0, 3, -4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -3, -5, -1, -2],\n [-5, 2, 6, -1, -3],\n [6, -4, 3, -2, -4],\n [6, -2, 4, 5, 3],\n [-4, -4, 6, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -6, 6, -6, -3],\n [-4, 5, -4, -3, 6],\n [2, 0, -3, 4, 1],\n [-2, 0, -3, 0, -4],\n [6, -3, -2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -6, 3, 4, 2],\n [-5, -1, -2, -5, -2],\n [1, -6, 3, -2, 4],\n [-6, -3, 1, -2, -2],\n [1, -1, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 4, -2, -1, 0],\n [-1, 0, 4, 3, 0],\n [-2, -5, -4, -6, -4],\n [6, -6, -5, -1, -6],\n [4, 4, 4, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 0, -3, 2, -2],\n [-3, -2, 1, -6, 2],\n [4, 1, -4, -4, 5],\n [5, 0, 5, 6, -3],\n [-6, 5, 6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -4, 3, -4, 4],\n [0, -2, 6, 1, 4],\n [0, 5, 6, -6, -3],\n [2, 5, -4, -5, 6],\n [0, -5, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 3, 2, -6, -3],\n [-4, -6, -6, -1, -2],\n [-3, 1, 6, 5, 3],\n [-6, -4, -5, 3, -4],\n [6, 6, -6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 6, 4, 4, -1],\n [5, 4, -3, -5, -5],\n [4, -6, -2, 2, -2],\n [3, -1, 3, 2, -3],\n [6, -6, -4, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -3, 5, -3, -2],\n [-3, -2, -3, -5, -2],\n [-3, -1, -4, 1, -2],\n [-6, -5, 3, -3, 4],\n [-3, 1, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -1, 0, -1, -6],\n [-3, 0, 0, -3, -1],\n [-3, 6, -1, 5, -4],\n [0, -1, -6, 4, -4],\n [4, -6, -3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 1, -4, -1, -1],\n [-5, -5, -3, 0, 6],\n [1, -4, 1, -1, -1],\n [-3, 0, 0, 5, 1],\n [-6, 4, 5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, 5, -3, 4],\n [-6, -4, 4, -5, -2],\n [-5, -1, -4, 4, 5],\n [4, 3, 2, 3, -1],\n [-4, 6, -5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 5, -6, 6, 3],\n [2, 0, -6, 0, 3],\n [0, 2, -5, 6, -3],\n [0, -2, 5, 0, -1],\n [-3, -2, 4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -6, 2, 3, 2],\n [-6, -3, -4, 5, -3],\n [-4, 2, -6, -6, -6],\n [1, -4, -6, -2, -2],\n [5, -4, 1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -1, 3, 3, 1],\n [0, 5, -2, -5, 2],\n [-3, 3, 0, 4, -2],\n [-5, 1, 1, 0, -6],\n [-4, -4, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -1, 1, 5, 1],\n [1, 3, -2, 3, -5],\n [4, 2, -1, -6, 5],\n [-2, -6, 6, 3, 2],\n [-6, -1, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -3, -3, -2, -3],\n [6, -3, 2, 4, -2],\n [3, -4, -6, 1, 3],\n [-6, 3, -2, 1, -1],\n [2, 3, 5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 5, 1, -4, -3],\n [0, -3, -3, 5, 0],\n [-5, 6, -5, -3, -4],\n [3, 6, 1, 0, -1],\n [5, -3, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -6, 5, -1, -1],\n [-1, 3, 3, -6, -2],\n [4, 0, 1, -2, 5],\n [-2, 2, 0, 2, 1],\n [5, 4, -4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 4, 6, 3, 1],\n [-2, 2, -5, 4, -4],\n [-4, -1, -6, -4, 2],\n [3, -4, 0, -6, 4],\n [1, 1, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -4, -5, 4, -3],\n [4, 3, -1, 2, -1],\n [5, -6, 0, 1, -6],\n [5, -1, 4, -4, -3],\n [3, 3, -5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -1, 4, 2, -4],\n [3, -1, 5, 5, -5],\n [5, -6, 5, 0, 3],\n [-6, -1, 6, 4, 1],\n [-5, -6, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 5, 1, 2, -2],\n [6, -1, -5, 3, 4],\n [-6, 1, 2, 4, -6],\n [0, 0, -4, -3, -1],\n [6, 2, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -6, 2, 1, -5],\n [-1, -4, -1, 3, 2],\n [-2, 0, -4, 1, -2],\n [-5, -2, 0, 0, -2],\n [-4, 0, -6, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -6, 6, -4, -6],\n [4, 0, -3, -6, 6],\n [-1, 3, 1, -5, 5],\n [-3, 1, 2, 0, 6],\n [-4, -2, -3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 2, -2, -3, 4],\n [2, 1, 6, -5, 2],\n [3, 0, 3, 4, -3],\n [4, -1, -3, 5, 6],\n [5, -3, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -1, 0, 1, 6],\n [-5, 2, 4, 5, 3],\n [-3, -1, 1, -3, 2],\n [1, -4, 0, 3, 3],\n [-1, -5, -3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, 4, 6, -1],\n [-3, 6, -6, -1, 5],\n [-2, -5, -3, 6, 3],\n [2, 6, 3, -5, -5],\n [0, -3, -6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, 6, -5, -3],\n [-4, 0, -5, -3, 2],\n [-2, -1, -6, -4, -2],\n [0, -4, -3, 6, -1],\n [3, 4, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 4, 3, 4, -2],\n [5, 1, -3, -2, -6],\n [-1, 6, -1, 0, -1],\n [1, 3, -6, -2, -5],\n [2, 6, 6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 2, 1, 3, -3],\n [-1, -6, 3, -2, -4],\n [-4, -6, 4, -3, 4],\n [-4, 5, 6, 2, 4],\n [1, 6, 3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 3, 2, 1, -6],\n [-5, 0, 5, -6, -2],\n [-1, 6, -1, -1, 4],\n [4, 1, 6, -1, 6],\n [-6, -1, 6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -4, 3, 3, -2],\n [-4, -1, -3, 3, -2],\n [-6, -6, -1, 6, -1],\n [-2, -3, 6, 2, 2],\n [-2, 4, -1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -2, 5, -6, 2],\n [-6, -2, 6, 0, 4],\n [-6, -3, 1, -2, 4],\n [2, -4, 5, 6, 3],\n [-4, 6, 3, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, -2, -5, 5],\n [5, 0, -2, 1, -5],\n [-4, -4, -2, -2, -3],\n [5, -3, 5, 3, -2],\n [4, -4, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 0, -3, 1, 4],\n [3, 6, -2, 4, 1],\n [0, -2, -2, -4, 5],\n [-3, 2, -6, 0, 3],\n [-6, 1, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, 2, 2, 1],\n [2, 4, 2, -3, -1],\n [0, 1, 0, -5, -1],\n [-3, 0, 1, -5, -5],\n [-4, -5, 6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -3, 5, 3, -3],\n [-6, -4, -1, -4, -3],\n [0, 3, 4, -5, 2],\n [-5, 4, 0, -1, -5],\n [4, -4, -3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 3, -2, -3, 5],\n [-3, 6, 1, -6, 3],\n [4, 2, 6, 5, -5],\n [4, -1, -4, -4, -6],\n [-4, -2, 0, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 5, -1, 2, -1],\n [-4, 4, 3, -1, -5],\n [-4, 3, -4, -5, -4],\n [2, 3, 3, 4, -2],\n [-3, -5, -6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -2, 6, 1, 2],\n [-2, 1, -6, -4, 3],\n [-1, -1, 6, 1, -1],\n [-6, 2, 0, 4, -2],\n [-2, 2, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 1, 6, -2, -1],\n [-1, 4, 5, 5, 0],\n [1, 2, 2, 3, 3],\n [3, 6, 2, -2, -3],\n [-6, 4, -1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 5, 1, -5, 2],\n [0, 0, -3, -3, 6],\n [-4, -3, -3, -6, -3],\n [4, -1, -1, -4, 3],\n [3, -1, -5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 0, -6, -3, 2],\n [-1, 6, 0, -2, 4],\n [5, 5, -3, -5, -4],\n [-3, -6, -6, 3, 4],\n [-2, 0, 2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -1, 0, -1, -6],\n [0, -2, -4, -4, 5],\n [-4, 0, 3, 0, 6],\n [-3, -1, 1, -5, 6],\n [2, 2, -6, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 5, 4, 0, 6],\n [0, -4, 4, -5, 5],\n [3, 2, 6, -5, 2],\n [0, -1, -4, -3, -2],\n [-1, 4, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 5, -3, -2, 4],\n [2, 1, -4, -3, 1],\n [1, -1, 4, -6, -1],\n [3, -4, 3, -2, -2],\n [4, 3, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -2, 3, -2, -5],\n [-2, 4, -5, 5, -3],\n [-6, 1, -6, 3, 0],\n [-5, -6, 6, -1, -1],\n [-2, -1, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 4, -1, 1, -6],\n [5, 6, 2, -6, -4],\n [1, 0, -4, 3, -1],\n [-4, 5, -6, 0, -2],\n [-1, 4, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -5, 5, -6, -1],\n [-4, 5, 4, -1, -4],\n [4, 2, -4, 6, 1],\n [1, -1, -4, 3, -1],\n [3, 0, 1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 1, -6, 0, 4],\n [0, -5, -3, 2, 3],\n [-1, 4, 5, 4, 5],\n [-5, 0, 0, 0, 0],\n [-3, 4, 2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 1, 6, -6, 2],\n [0, -3, -4, -2, 1],\n [1, 5, -1, 0, -4],\n [-2, -4, -2, -2, 3],\n [-4, 6, 1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -3, 5, -5, -5],\n [-1, -5, -3, 6, 6],\n [-2, -3, 0, -5, 5],\n [-5, -5, 0, -1, 3],\n [3, 0, -6, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, 1, 1, -6],\n [5, 3, 0, -1, -2],\n [6, 4, -2, 1, -5],\n [-6, 2, -3, 3, -1],\n [2, -4, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -1, 5, -1, -6],\n [-1, -3, -1, 6, 0],\n [6, 5, -3, 3, 2],\n [-6, 2, 0, -6, -3],\n [3, -1, 5, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 6, 4, 2, 2],\n [-4, 6, -2, 6, -4],\n [-5, 5, -4, -3, 2],\n [-2, -6, -6, 0, 5],\n [5, 0, 0, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -6, 0, -6, -1],\n [5, -4, 0, -6, -2],\n [5, 4, -1, -1, -1],\n [0, 1, -1, 4, 3],\n [5, -1, 3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -2, -2, 1, -5],\n [-3, -5, 3, -6, -3],\n [-4, 6, -1, 6, 3],\n [5, -3, -6, -6, 1],\n [3, -4, -1, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -3, 2, 4, -4],\n [-2, -4, 5, 3, 6],\n [0, -3, -6, -4, 0],\n [2, 3, 2, 5, -2],\n [2, 2, 5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -4, 3, -2, -6],\n [0, -1, 6, 4, 2],\n [-1, 2, 6, -2, 3],\n [-2, 2, -4, 1, -6],\n [-6, 2, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -2, 3, 5, 2],\n [0, 1, -5, -2, -3],\n [4, -3, -6, -1, 4],\n [4, -3, 5, -4, 4],\n [0, -1, -3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -5, -5, 5, -2],\n [2, 0, 0, 2, 2],\n [-6, 0, -6, -4, 0],\n [0, -2, 2, -6, 5],\n [-2, -2, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, -2, -2, 4],\n [6, -2, -3, 2, -6],\n [6, 2, 5, 3, 2],\n [-3, 3, -3, -2, 6],\n [-2, -1, -1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -1, 0, 1, 6],\n [2, -3, -2, 4, 1],\n [2, 2, -6, 4, -5],\n [-2, 5, 6, -1, -4],\n [6, 0, 2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -6, -1, -1, -6],\n [2, -5, 5, -4, 1],\n [-4, 3, 5, -6, 6],\n [1, -3, 4, 1, -6],\n [-5, 4, 0, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -3, 0, 6, 4],\n [-1, -6, -4, 5, 3],\n [5, -1, 4, -1, -4],\n [-4, 6, 5, -4, -3],\n [4, 4, 0, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 3, 5, 0, -6],\n [5, 5, 2, -1, 3],\n [3, 3, 3, -4, 3],\n [-6, 3, -1, 4, -4],\n [1, 4, 5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -6, 1, 0, 0],\n [-2, 3, 2, 3, 5],\n [5, -3, -5, 0, 6],\n [0, -1, -5, 4, -6],\n [-3, 6, -4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 1, -1, -3, -3],\n [-1, 2, 4, 1, -4],\n [-4, 2, -5, -6, -4],\n [-4, -3, -4, 0, 0],\n [2, 4, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 0, -6, -2, 3],\n [4, 1, 4, -2, 3],\n [-2, 2, 4, 2, 4],\n [0, 5, 5, 4, -6],\n [-1, 6, -3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -4, -3, -1, 3],\n [-5, -6, 3, 1, -2],\n [-1, 0, 5, 3, -3],\n [4, 4, 4, -1, 1],\n [4, -2, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -4, 4, -5, 0],\n [5, -5, -4, -5, 4],\n [-1, -4, 1, -6, 6],\n [0, 5, 5, 5, 2],\n [-2, 1, -4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 6, 1, -6, 3],\n [3, -2, 1, 6, 6],\n [-5, 4, -5, -2, -2],\n [3, 5, -1, 6, -4],\n [1, 2, -3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 6, 2, -3, 3],\n [-6, 2, 5, 4, 2],\n [-4, 4, 1, -5, 1],\n [1, 4, -3, -6, -5],\n [5, 4, 4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -1, 3, 0, -1],\n [0, 4, -2, -5, -5],\n [-6, 3, 2, -4, -3],\n [-6, 0, 4, -2, -4],\n [3, -4, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 0, 1, -5, -6],\n [1, 5, -2, -6, 2],\n [-4, -6, 0, -5, -4],\n [5, 5, 3, -3, -4],\n [6, 3, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -4, -2, 2, -5],\n [-1, 2, 4, -4, 2],\n [-5, -6, 0, 2, 1],\n [-6, 6, -4, 3, 4],\n [-5, -3, 1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -5, -6, 3, 4],\n [3, 2, -5, 2, 0],\n [1, 5, -6, -3, -3],\n [-4, 1, -3, -1, -6],\n [3, 1, -1, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 1, -4, 0, -4],\n [-4, 0, 3, 3, -3],\n [-1, 5, 3, 4, -3],\n [2, -6, 0, 1, 6],\n [6, 2, 4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 1, -3, -1, 2],\n [-5, -6, 1, -1, -4],\n [-4, -3, 5, -2, 6],\n [3, -6, 3, -3, 2],\n [-1, -4, 4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, 4, 4, -6],\n [5, 3, 2, -2, 5],\n [-6, -4, 2, 6, -2],\n [-1, -6, -1, -5, 4],\n [6, 4, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -1, -4, 2, 2],\n [-1, -4, -2, -5, 1],\n [4, 5, -2, 0, -2],\n [6, -3, 5, -6, 3],\n [3, -3, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 2, -5, -4, -5],\n [5, 3, 1, -1, 1],\n [-4, -2, -1, 3, -3],\n [-5, -3, 6, 3, 5],\n [4, 1, 4, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 0, -4, -6, 4],\n [-1, -6, -4, 5, 0],\n [1, -2, -1, 4, -4],\n [-1, 4, 2, -3, -2],\n [-6, 4, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -5, -2, -1, 0],\n [-5, 3, 6, 4, -6],\n [-1, -1, -6, 3, -1],\n [2, 5, -4, -5, -2],\n [-6, -3, -6, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -6, -4, 4, 6],\n [-3, 0, 2, -2, -3],\n [0, 4, -2, -1, 5],\n [5, -3, 3, 6, -6],\n [-2, -5, -6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, 4, 5, 2],\n [0, -5, 5, -5, 2],\n [-4, -5, -2, 1, -5],\n [4, -6, 2, 4, -2],\n [-4, 6, -4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, 3, 5, 6],\n [5, 0, -5, -5, -4],\n [-1, 3, -4, 0, -6],\n [-5, 1, 5, 0, -2],\n [1, -6, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -6, -3, 1, 6],\n [1, -6, -3, -3, -4],\n [2, 0, 1, -6, -4],\n [2, 6, -3, -5, 6],\n [-3, 6, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 4, -1, 1, -3],\n [-6, 6, 1, 5, -1],\n [-4, -2, -2, 6, -1],\n [1, -1, -1, 4, 2],\n [-5, 4, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -2, -6, -3, -2],\n [1, 3, 0, -6, -1],\n [-4, -6, 2, -5, 6],\n [4, 3, -2, -3, -3],\n [0, -5, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -5, -2, -4, -2],\n [-1, 0, 4, 4, -2],\n [0, -4, 1, -5, 1],\n [0, 2, 0, 2, 2],\n [3, -4, 2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -2, 1, -6, 5],\n [4, -5, 2, 0, 1],\n [-2, 1, 3, 2, -1],\n [-1, -1, 3, 1, 1],\n [-1, -3, -5, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 2, -5, -1, 1],\n [-1, 5, 2, -2, -6],\n [1, 4, 0, -1, -5],\n [-6, -5, 6, -1, 2],\n [0, -6, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 5, 4, -1, -3],\n [6, -5, 4, 2, -1],\n [2, 2, 5, 1, -1],\n [3, -1, -5, 1, -2],\n [0, -1, -3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 6, -3, -1, 2],\n [5, -2, 6, -5, -2],\n [-1, -5, -2, 6, -2],\n [1, -4, 3, -4, 6],\n [2, 6, -1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 3, -5, -1, 4],\n [-5, 6, 0, -5, -1],\n [-3, 4, -3, -1, 2],\n [-4, -2, -4, 5, -6],\n [-2, 3, 3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 0, 6, 4, 4],\n [-2, 2, 1, 1, 5],\n [6, 5, 6, 5, 0],\n [1, 5, 0, -5, 0],\n [1, -3, 6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -6, 4, 6, 0],\n [5, -4, -6, -6, 3],\n [0, 4, -3, -1, -4],\n [1, -3, -3, 0, -1],\n [-3, -4, 6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 4, -1, 1, -4],\n [1, -5, -3, 6, -4],\n [-3, -4, 2, -4, 6],\n [3, 0, 0, 1, 5],\n [2, -2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, 2, -1, -6],\n [-5, 4, 5, -4, -2],\n [4, 5, 0, -2, 4],\n [5, 2, -6, -2, -1],\n [3, -4, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, 4, -5, 3],\n [4, -3, -5, -4, 3],\n [-4, 1, 0, -3, 5],\n [6, -4, 6, 6, -2],\n [-4, -6, -3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, 6, -2, -1],\n [5, 5, 2, -3, -6],\n [-2, 6, 3, 5, 1],\n [1, -6, -6, -3, 4],\n [1, -1, 2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 3, 3, 4, 5],\n [0, 6, 0, -4, -2],\n [-1, 5, -6, 6, 4],\n [2, -1, -6, 4, -3],\n [-2, 6, 3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 1, -1, 1, -4],\n [3, -4, 4, 5, -2],\n [6, -1, -5, -1, -4],\n [2, 3, 1, 3, 1],\n [-4, -1, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 4, -3, 3, -4],\n [-4, 2, 4, 1, 0],\n [1, -3, 6, -3, -1],\n [-1, -3, 2, -6, 1],\n [6, 1, 6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -3, -5, -2, -6],\n [4, 4, 5, 3, 1],\n [2, 4, -6, 3, -3],\n [1, 3, -4, 6, 0],\n [4, 5, 5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 3, -3, 5, 6],\n [2, 2, 6, -6, -3],\n [4, 3, -2, 6, 6],\n [0, -2, 1, -2, 5],\n [2, -4, 4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 0, 1, 4, 2],\n [-1, 0, -5, -4, -3],\n [5, -1, 1, -5, -4],\n [3, 4, 2, -5, 4],\n [-6, -2, -6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -4, 2, -3, -5],\n [5, -2, 3, 6, -5],\n [-1, -3, 1, -4, -2],\n [0, 3, 0, -4, 3],\n [-5, 6, 5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 2, -5, 3, -3],\n [-2, 0, 1, -2, -5],\n [-4, 1, 3, 3, -2],\n [4, 6, 3, 2, -4],\n [-3, 4, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, 4, 0, 2],\n [1, 5, -2, 4, 6],\n [-3, -1, 3, -5, -5],\n [-6, -3, 4, 5, -6],\n [-1, 1, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 0, -3, -4, -6],\n [4, 5, 6, 5, 1],\n [0, 3, -5, 2, -4],\n [-6, -2, -4, -4, -2],\n [1, 0, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 1, -1, -3, -5],\n [-6, 0, 0, -5, 0],\n [5, -5, -5, -1, 6],\n [4, -4, 4, -2, -2],\n [5, 5, -4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -4, 6, -2, -6],\n [-3, 5, -6, -3, -4],\n [-3, 1, -2, 0, 0],\n [1, 6, -1, -4, -2],\n [4, 0, -4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 4, 3, 4, -6],\n [-4, 5, 1, -6, -2],\n [6, 2, 1, -4, 2],\n [3, 6, 5, 3, -4],\n [-6, -3, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 5, 5, 1, -5],\n [5, 1, -4, -6, -1],\n [-6, -5, -5, -4, 3],\n [0, -1, -6, 2, 5],\n [-4, -5, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 4, -3, 5, -1],\n [-2, 4, 1, 5, -6],\n [6, -2, -1, 6, -5],\n [-2, 2, 0, 2, 0],\n [-3, 1, 6, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 5, 0, -4, 3],\n [2, -5, 1, -6, 0],\n [-4, 0, -1, -2, 6],\n [2, -1, 0, -3, -2],\n [-2, 1, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -1, 3, 2, 4],\n [-1, -6, -3, 1, 2],\n [-6, 5, 4, -5, -1],\n [2, 3, 4, -5, -4],\n [6, -4, -4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -4, -5, 6, -2],\n [3, 4, 6, -6, -5],\n [4, 0, 5, 4, -6],\n [-4, 0, 4, 5, -3],\n [-5, -1, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, 0, -4, -3],\n [-6, -2, -2, -2, -2],\n [0, 2, -4, 0, 5],\n [2, -3, -2, -4, -6],\n [3, -5, -6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 2, 4, 0, 2],\n [5, 6, 3, 0, -1],\n [-6, -3, -1, -6, -3],\n [4, 3, 2, 0, -3],\n [-5, 2, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -3, 1, -1, 3],\n [-6, 4, 5, 6, -4],\n [-5, 2, -3, -1, 5],\n [-5, 2, -6, -4, 5],\n [4, -6, 4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 2, 5, 5, 3],\n [-5, -4, 6, 3, 0],\n [-2, 3, -2, 0, 3],\n [-2, 0, 0, -6, 0],\n [6, 3, -2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 1, 1, 5, -1],\n [-4, 2, -5, 5, -3],\n [0, 0, 2, -2, -3],\n [5, 6, -2, 1, 1],\n [-2, -5, -5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -3, -5, 3, 0],\n [1, 5, -3, -4, -6],\n [-1, 5, 1, 5, -1],\n [4, 6, -4, -1, 3],\n [0, 6, 1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 3, 5, 2, -3],\n [3, 3, 0, 0, 5],\n [6, -2, 0, 1, 5],\n [-1, 1, 6, 1, -6],\n [0, -3, -5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 5, 4, -2, -2],\n [4, -6, -1, 3, -5],\n [-6, 0, 6, 2, -2],\n [1, 1, -1, -2, -3],\n [-6, -3, -6, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -3, -2, 0, 0],\n [1, 3, -1, 0, 3],\n [2, 1, 6, -2, 6],\n [-2, -1, 6, -3, -6],\n [-6, 0, -5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -1, 5, 1, -5],\n [-6, 0, -3, -3, 6],\n [2, 3, -1, -1, -4],\n [2, 2, 4, -2, 0],\n [0, 2, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -5, 3, 1, 6],\n [4, 0, 5, -1, 0],\n [-1, 4, -3, 1, 6],\n [-5, -6, 4, -5, 0],\n [3, 6, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -6, -2, 1, 5],\n [-5, -6, -6, -4, 4],\n [-6, -6, 4, 3, 1],\n [4, 4, 1, 4, 3],\n [1, -2, 4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -2, -2, 4, 2],\n [-3, -5, 4, 4, 1],\n [-4, 4, 2, 1, 3],\n [-4, 5, 2, 1, -5],\n [-2, 1, 3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -1, -6, -1, 5],\n [-6, -3, 5, -4, 2],\n [-2, 4, -2, -3, -1],\n [-5, 2, 2, -1, -1],\n [2, 2, -5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -5, -3, -6, 5],\n [3, -2, 1, -4, 6],\n [-3, 5, 0, -3, 0],\n [6, 0, 3, -2, -4],\n [-3, 4, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -4, 3, -6, -2],\n [3, -2, 4, 2, 3],\n [-1, 0, 1, 4, -1],\n [6, 5, 0, 0, 2],\n [-5, 3, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -4, -2, -4, -6],\n [4, 1, 6, -4, -3],\n [0, -1, -3, -6, 6],\n [-6, -5, -6, 2, 0],\n [-5, 1, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -4, -5, -4, -6],\n [-5, 4, -4, 2, -3],\n [1, -6, 1, -1, -2],\n [1, 1, 0, -2, 6],\n [-3, 1, 3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, -3, -3, -3],\n [2, 1, -4, 5, -2],\n [-2, 0, -4, 0, 1],\n [5, 6, 2, -6, 3],\n [-2, 3, 1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -3, -2, 2, -1],\n [-4, 0, -6, -3, -6],\n [2, 4, -2, 0, 5],\n [5, -4, -6, 4, -1],\n [6, 5, 6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 5, 6, -1, -1],\n [0, -5, -6, -5, -1],\n [-1, -5, 0, 5, 4],\n [-6, 5, 1, 1, 4],\n [-6, 1, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 1, -2, -4, -1],\n [0, -4, 3, 0, -3],\n [-2, 0, 3, -5, -2],\n [-1, 6, 2, 2, 4],\n [4, 4, -4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 4, -1, 3, 1],\n [0, 5, 5, -3, 5],\n [2, -2, 6, 4, -1],\n [3, -4, -2, 4, 3],\n [4, -3, 4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -3, -4, 4, -4],\n [-3, -1, 4, 2, -6],\n [-4, 6, -5, 5, -3],\n [-4, -5, 3, -4, 6],\n [-3, 6, -4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -1, 3, -3, -4],\n [0, -3, 4, 5, 4],\n [-3, -6, 4, 0, -2],\n [0, 2, 5, 1, -5],\n [4, 5, -4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -5, 2, 3, 4],\n [-2, -4, -1, 2, 6],\n [-5, 6, -3, 5, -1],\n [4, -1, 1, -4, 0],\n [-4, -5, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 0, 5, 0, 6],\n [-6, -4, 0, 0, 3],\n [-1, 3, 1, -1, 0],\n [-4, 4, -5, 4, -6],\n [5, -6, 2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 3, 3, 3, 3],\n [-3, 6, 1, -1, -3],\n [6, -1, 0, -2, -3],\n [3, -5, 3, 4, -3],\n [-3, -3, 4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -2, -2, -1, 6],\n [-3, 3, 5, 0, 2],\n [-1, 2, -3, 2, 6],\n [-1, -6, 6, 5, 5],\n [0, 1, 1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -1, -2, 3, 5],\n [4, -2, 4, 6, -3],\n [-1, -6, -2, 6, -1],\n [3, -6, 2, -5, 0],\n [-3, 6, -3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 3, -1, 1, -2],\n [-1, 3, 5, 6, -2],\n [5, -3, -2, -2, -5],\n [1, -5, 6, -4, -1],\n [-1, 5, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 0, 6, 0, -6],\n [-1, 4, 1, -3, -3],\n [1, -6, 1, 3, -4],\n [4, -3, -2, -5, 0],\n [-5, -1, -4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -2, 1, 2, -5],\n [2, -3, 4, -6, 2],\n [-6, -2, 6, 6, -5],\n [0, 2, -2, 5, -5],\n [-1, -6, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -5, -5, 5, -3],\n [-1, 0, -6, -6, 1],\n [3, 0, 2, 6, -6],\n [4, 6, -5, -2, 4],\n [-6, -3, 2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -6, 5, -3, -2],\n [-3, 1, -5, -5, 1],\n [5, -4, 3, 1, 3],\n [-6, -2, 3, 3, -4],\n [3, -6, 6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -1, 5, -5, -4],\n [-2, 2, -4, -3, -3],\n [3, 2, -2, 0, 1],\n [-3, 1, 1, -5, -4],\n [3, 1, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 2, -2, 5, 6],\n [5, 1, -4, 3, -5],\n [5, 2, 5, -6, -6],\n [0, -5, -4, -6, 2],\n [1, -4, 5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -1, 4, -5, -1],\n [-3, 0, 5, -5, -2],\n [5, -4, -5, 2, 5],\n [-1, -5, -5, 4, 1],\n [1, 4, 4, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 2, 1, 6, -4],\n [6, 3, -2, -2, -6],\n [2, 2, 4, 0, 6],\n [-6, 3, 0, 1, 4],\n [0, -6, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -6, -1, 6, 0],\n [5, -5, 6, 3, -5],\n [-6, 1, -1, -3, 2],\n [-1, -1, -6, 0, -5],\n [6, 5, -1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 0, -4, 6, 0],\n [-3, 2, 0, 0, -2],\n [3, -3, 5, -1, 5],\n [6, 3, 3, -1, -1],\n [0, 0, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 5, -2, -2, -1],\n [-1, -2, 2, -6, 1],\n [0, 1, 3, -2, 5],\n [4, -5, -1, 4, -6],\n [6, 6, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, 5, 4, -5],\n [2, 4, 6, -3, 2],\n [6, 6, -1, 6, 5],\n [6, 6, 3, 4, 0],\n [-1, -6, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -5, 5, 3, 3],\n [-4, 3, 5, -1, -3],\n [4, -1, -1, -5, -6],\n [6, 2, 1, -4, 0],\n [-5, -4, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -2, -1, -3, -6],\n [-1, 1, 3, 0, -1],\n [2, 4, -1, 3, -4],\n [-5, 4, 6, 2, 5],\n [-4, 4, 1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 5, -5, 5, -1],\n [-5, -1, 2, 3, 1],\n [0, 0, 5, -6, -2],\n [-5, 5, 5, -6, -5],\n [6, 6, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -4, 1, -2, 6],\n [3, -2, -1, -5, 6],\n [4, 0, 5, 0, -4],\n [4, 4, -2, -6, -5],\n [5, -3, 2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -3, -2, 1, 2],\n [4, 6, 1, -6, -3],\n [-6, 2, -2, -4, 0],\n [2, -2, 1, -3, -4],\n [-3, -1, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 4, 6, -2, 4],\n [1, -2, -6, -5, -4],\n [3, -3, 0, 0, 1],\n [-1, -5, -4, -5, 3],\n [-3, 4, -4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 2, -3, -2, 6],\n [-2, 3, 2, 0, -6],\n [-3, 1, 0, 0, 2],\n [-4, 2, 6, -3, 2],\n [-6, 6, 3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -4, -6, -6, 4],\n [4, -5, 2, 4, -2],\n [3, 3, 3, 3, -6],\n [-5, -3, -5, 6, 6],\n [-6, -2, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 4, -6, 5, -1],\n [-4, 4, -4, 0, 2],\n [-4, 3, -4, 5, 4],\n [6, 0, 0, 6, -2],\n [-3, -6, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 0, 2, 5, 0],\n [2, -4, 6, -4, 3],\n [-1, -3, -2, -3, -2],\n [-2, -1, 0, 1, -3],\n [-1, -3, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -1, -6, 3, 5],\n [1, -2, 6, 5, 6],\n [3, -6, -3, 5, 2],\n [-3, 6, 5, 5, -3],\n [5, -1, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 0, 2, 3, 2],\n [1, -2, 4, -5, -3],\n [1, -1, 4, -5, 4],\n [-5, -3, 3, 0, 5],\n [1, -2, -4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 4, 3, 2, 3],\n [4, 0, 5, 2, 6],\n [-1, 3, 6, 3, 2],\n [4, 0, -5, 5, -5],\n [4, -1, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -5, 6, 4, 1],\n [5, 0, -5, 3, -2],\n [4, 5, -4, 1, -6],\n [-6, -2, -3, 4, 1],\n [-5, 2, -5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 0, -5, -4, 4],\n [-3, -2, 4, 1, -1],\n [4, -5, 3, -6, -2],\n [1, 3, -2, 6, -3],\n [-3, 0, 5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 2, -2, 4, -3],\n [0, -2, 0, 3, -3],\n [0, 2, -3, 2, -5],\n [-5, 4, -1, 5, 2],\n [-6, -3, -6, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 3, 1, -5, 1],\n [-6, 5, 3, 6, 4],\n [1, -5, 0, 5, -6],\n [-2, -4, 4, 0, -6],\n [2, 6, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -1, 3, -3, 0],\n [4, 4, 0, -1, -1],\n [-3, 4, 4, -3, -1],\n [1, 2, 2, 4, -5],\n [5, 2, 1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -1, 0, -1, 3],\n [0, 3, -1, -1, -1],\n [1, -4, 6, 0, -6],\n [-3, 2, -5, -5, 6],\n [-5, -6, 6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -2, -6, 5, 2],\n [-5, -4, 1, 6, -5],\n [-5, -3, -4, 6, 2],\n [4, 0, 6, 2, 6],\n [2, 5, 3, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 3, -4, -5, 6],\n [6, -6, 1, 3, 4],\n [3, 2, -2, 2, -2],\n [-6, 5, 5, -5, -5],\n [-4, -4, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 0, -2, 5, 1],\n [-1, -5, 0, 1, 0],\n [-4, -6, -2, -6, 3],\n [-5, -2, 2, 5, 5],\n [6, -5, -3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -4, -6, 1, -2],\n [3, -2, 2, -5, -4],\n [-6, 6, 5, 2, -6],\n [0, 4, -3, 5, -4],\n [6, -5, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -5, -6, 6, -4],\n [-2, -6, 6, 5, 6],\n [5, 2, 2, -1, -3],\n [-4, 2, 5, 4, 1],\n [3, -5, -2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -1, 5, 1, -5],\n [-6, 4, -2, -3, 2],\n [-2, 6, 2, 4, -2],\n [-2, 3, -4, -6, 3],\n [6, 5, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 5, -1, -4, 4],\n [6, -2, 4, 2, -2],\n [-5, 2, -5, 1, 6],\n [-2, 2, 5, 2, -2],\n [-2, 5, -5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -5, 6, 1, -1],\n [4, 5, 3, -6, -6],\n [-2, 4, 1, -6, -5],\n [-6, 0, 4, -2, 6],\n [4, 2, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, 1, -2, 0],\n [-3, 4, 1, -6, -5],\n [-5, 4, 5, -6, -2],\n [-2, -1, -5, 3, -6],\n [-2, 1, 5, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 3, 2, -1, -6],\n [3, 3, 6, -3, 2],\n [3, 1, -4, 0, -4],\n [1, -3, -4, -6, 6],\n [5, 6, -6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -4, 6, 4, 0],\n [-1, 0, -1, 1, 1],\n [-5, 3, 4, 2, -3],\n [-1, -5, 4, -4, -3],\n [-6, -1, -3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 4, -5, 1, -2],\n [6, -5, 2, 5, -4],\n [0, 2, 2, -2, 2],\n [4, -2, -6, 4, 0],\n [6, 0, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -1, 2, -2, -1],\n [3, -2, 2, -5, 3],\n [3, 1, -1, 5, -4],\n [5, 6, 2, -6, 2],\n [-2, 0, 1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -5, -2, -6, -1],\n [-5, -5, 0, 3, 2],\n [-5, 0, 0, 1, 2],\n [2, -2, -5, -3, 1],\n [-6, 5, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -6, -6, 1, 2],\n [-4, 6, -6, -4, -6],\n [4, 5, 0, -4, -4],\n [-5, -2, 6, 2, -4],\n [-5, 1, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 6, 5, 6, 5],\n [3, 0, -2, 3, -6],\n [-5, -5, -2, -6, 6],\n [1, 3, -3, 2, -5],\n [-2, -6, -5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -2, -3, -6, 2],\n [4, -4, 4, -2, -1],\n [-5, -2, 0, 1, -3],\n [4, 6, -3, 6, 1],\n [-4, 5, -4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 4, -6, 0, 3],\n [-6, 0, 2, 4, 6],\n [4, -3, -6, 3, 2],\n [-1, -4, -2, -1, 2],\n [-3, -3, -5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, 5, -6, 2],\n [-5, -1, -3, -2, 1],\n [2, -4, -2, 4, -2],\n [-4, 4, -1, 2, 3],\n [-4, 2, 1, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 3, -3, 3, -2],\n [4, 0, 0, -6, 1],\n [-3, 6, 2, -1, -1],\n [0, 4, 6, 5, -3],\n [6, 2, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -3, -4, -3, -1],\n [0, 3, 3, -4, -2],\n [-6, 2, 1, 5, 4],\n [-6, -1, 0, 5, 4],\n [-6, -3, 3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -1, -1, -2, 3],\n [-3, 6, 1, -6, 2],\n [-6, -2, 3, -1, -2],\n [-5, 6, -3, -4, 1],\n [-4, 3, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -6, 1, 5, 5],\n [2, 3, 5, 4, -5],\n [-1, 0, -1, -4, 0],\n [6, -3, -4, -2, 6],\n [4, -3, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -6, 0, -2, 3],\n [-4, -2, -4, -4, 3],\n [2, 3, -3, 6, -5],\n [5, -1, -3, -5, 5],\n [4, 2, -3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 3, 4, 2, 1],\n [-3, -1, 2, 0, 1],\n [-3, -3, 0, -3, -4],\n [-5, 0, -4, 6, 2],\n [-1, -2, -4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -2, -5, 2, 5],\n [6, 4, 5, -5, -4],\n [-4, -4, 2, -6, -2],\n [5, 1, 2, -3, 6],\n [-5, 3, 5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -1, 3, -5, 4],\n [6, 5, 6, 2, 2],\n [1, 4, -1, -5, 4],\n [3, -3, -4, 5, -6],\n [-3, 0, 6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 0, 2, 3, -3],\n [-4, 2, -6, -6, 2],\n [2, -1, -4, 1, -1],\n [-2, 5, 1, 4, 2],\n [2, 2, 4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 3, 5, 2, -6],\n [-1, 3, -6, -3, 5],\n [-1, 6, 0, 2, -1],\n [6, 3, 2, -3, -4],\n [4, -3, -3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 1, 6, -3, 2],\n [3, -3, -1, -6, -2],\n [1, -4, 4, -2, -2],\n [-2, 5, 2, -6, -3],\n [0, -6, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 1, -6, 2, 6],\n [0, 2, -5, -1, -6],\n [2, -6, -5, -3, -5],\n [-6, 1, -6, 2, 2],\n [-3, 6, -3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -3, 2, 3, 4],\n [0, -4, -5, 5, -4],\n [-2, -2, 2, -6, 3],\n [6, -2, -2, 0, 3],\n [1, 2, -1, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 3, 5, 3, -3],\n [0, -6, -3, 5, -2],\n [-3, 4, -6, -2, 5],\n [-3, -5, 3, 2, -6],\n [-4, 6, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, 1, -5, 6],\n [1, -1, 3, 3, -3],\n [2, -1, -3, -5, -3],\n [-1, 5, 5, 5, -1],\n [-3, 4, -1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 4, -4, 2, 5],\n [-6, 2, 3, -6, -4],\n [2, 6, -2, -6, -2],\n [4, 3, 5, -5, -4],\n [-4, -6, -5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -4, -3, -3, -6],\n [-4, -2, -4, -1, 4],\n [2, -1, -4, 5, 1],\n [-5, -3, -2, 1, 2],\n [3, 6, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -5, -1, 5, 2],\n [3, 0, -3, -5, -3],\n [3, -1, 5, -4, 5],\n [5, -2, 6, 1, 0],\n [-6, -2, 1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 0, -3, -5, 3],\n [-3, -5, 4, -4, -3],\n [-6, 2, 5, -4, 2],\n [5, -3, -4, 4, -1],\n [5, 3, -6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 5, -4, -6, 0],\n [-5, 6, -4, 5, 2],\n [0, -6, -5, 4, 0],\n [3, -5, 6, 3, -1],\n [-4, -2, -4, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -2, 2, -5, -1],\n [5, -5, -2, 4, -2],\n [2, -3, -4, 1, 4],\n [5, -3, 4, 1, 0],\n [2, 2, 3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -2, 0, 2, -5],\n [-3, 4, -2, -6, -4],\n [-4, -6, -6, -2, -4],\n [1, 4, 6, 6, 4],\n [-4, 1, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -5, 0, 4, -1],\n [-6, -4, -1, 1, -4],\n [-2, -4, -3, 2, -5],\n [4, 4, 5, 3, -5],\n [-4, 3, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 3, 3, -5, 4],\n [5, 4, 2, -2, -5],\n [6, 2, 4, -6, 5],\n [-3, -6, -2, -4, 4],\n [5, 6, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -3, 2, -6, -2],\n [-3, -6, -3, -2, -1],\n [-1, 6, 2, -5, 4],\n [5, -5, -4, -5, -6],\n [-4, -4, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 6, 0, -3, 3],\n [-2, -2, 5, -2, 1],\n [-5, 2, -6, 6, 6],\n [2, -5, -3, 4, -1],\n [-6, 1, -3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -4, -6, 2, -3],\n [0, -2, 5, 5, 1],\n [-3, -6, 3, 2, -6],\n [0, 1, 6, -2, 3],\n [-2, 3, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -4, -2, 6, 0],\n [-5, -2, 3, 3, 3],\n [0, -1, -6, -3, -1],\n [4, -1, -5, -5, 2],\n [6, 2, -1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 0, -1, -3, 0],\n [5, 5, 5, 1, -5],\n [-5, -5, 5, -1, -6],\n [1, 6, 0, 5, 3],\n [-3, 1, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 3, 3, 3, 0],\n [-3, 3, -3, 6, 5],\n [-3, -1, 3, -2, 6],\n [2, 5, -1, 0, 4],\n [0, 4, -2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -2, -2, 2, -5],\n [-4, -2, 1, 5, 0],\n [3, -6, -3, 5, 5],\n [-1, -6, -4, 0, -4],\n [-2, 6, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -5, -3, 6, -3],\n [2, -3, -5, -4, 4],\n [5, -4, 1, 3, 4],\n [-6, -3, -1, 1, -5],\n [3, -2, 2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 4, 3, -3, -5],\n [-3, 3, 3, -5, -6],\n [-3, -2, 1, -4, 4],\n [5, -2, -4, -3, 5],\n [-5, 3, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 5, 2, 0, 4],\n [-4, 6, -3, 3, -6],\n [-2, -6, -4, -4, 4],\n [0, 2, -1, -5, -5],\n [3, 5, -3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 0, 4, -3, -4],\n [0, 2, 6, 1, 5],\n [6, -4, 5, -4, -1],\n [1, -6, -4, 2, 4],\n [2, 3, -6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -4, -2, -2, -2],\n [-5, -4, -3, -4, 5],\n [-3, 1, -1, 1, 5],\n [1, 1, -5, -2, 5],\n [-1, -5, -2, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 5, 3, 0, 6],\n [-6, -3, -6, 3, -6],\n [3, 4, 0, -2, -4],\n [4, 1, -6, 0, 6],\n [-1, -5, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, 4, -4, 2],\n [-1, 5, 0, 1, -2],\n [6, -3, 2, 5, 0],\n [5, -2, 6, 3, -3],\n [-1, 5, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -5, -3, -6, 1],\n [2, 4, 1, -5, -1],\n [6, -5, -1, 5, 5],\n [5, -6, -4, 2, 1],\n [5, 6, 3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -6, -3, 1, -1],\n [0, -5, -2, 5, 3],\n [-2, -5, 6, -4, -1],\n [3, 1, -5, 6, -1],\n [5, -3, -5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 5, 6, -2, -3],\n [-2, 6, -5, 4, -2],\n [-4, -2, -5, 5, -6],\n [-1, 6, 4, -3, 5],\n [0, -5, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -2, 6, -1, -3],\n [-6, 0, 3, 5, -6],\n [-2, -4, 0, 3, 0],\n [6, -4, -4, -1, -1],\n [-1, -6, 3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, -3, -6, -6],\n [0, -4, 0, -2, -4],\n [5, -6, 6, -5, -6],\n [-2, -6, -5, -3, 4],\n [-1, -5, 2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 5, -3, -1, -6],\n [2, -6, 6, 0, 5],\n [1, 1, 6, -6, 0],\n [-2, 4, -5, -5, 6],\n [0, 5, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, 4, -4, 6],\n [2, -6, -4, -1, 0],\n [3, 1, 2, 1, -5],\n [1, 4, 0, -3, 3],\n [2, 6, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 4, -1, -2, -4],\n [3, 5, 2, -4, 0],\n [2, 2, 0, 3, 1],\n [-6, 6, 5, -1, 4],\n [6, 2, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 0, 0, 6, 5],\n [-6, -2, -3, 3, 3],\n [-5, 3, -1, 3, -4],\n [-3, 4, -1, 2, -1],\n [5, -4, -3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 6, 5, -2, 1],\n [-1, 1, -5, 0, -1],\n [-2, -4, 1, -5, -4],\n [-1, 5, -3, 4, 0],\n [-5, -2, 6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -4, -1, -3, -3],\n [4, 5, -4, -3, 5],\n [-6, -4, -6, -5, 1],\n [-2, -5, -6, -5, 4],\n [0, 4, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 3, -5, -5, -5],\n [-2, -2, 4, 4, -4],\n [0, -1, 1, -2, 5],\n [0, -6, 3, 2, 2],\n [-5, 4, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, 1, 0, 4],\n [1, 0, -6, 6, -5],\n [-6, 6, -5, 4, -4],\n [3, -3, 6, -3, -5],\n [0, 3, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 5, 2, 5, -1],\n [-1, -1, 3, 5, 0],\n [2, 0, 4, 4, -1],\n [3, 0, 2, 3, 3],\n [-1, -1, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 3, -1, 4, 3],\n [-1, 6, 1, -3, -6],\n [-6, -4, -6, 4, 6],\n [-3, 5, 0, 5, -1],\n [-1, 3, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -6, -4, -3, 6],\n [-6, 5, 3, -1, -1],\n [-1, 1, 1, -6, 2],\n [-6, 5, 4, -6, 3],\n [3, 3, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, -2, -5, -1],\n [-2, -5, 3, 4, 4],\n [-4, -6, 2, -3, 4],\n [-5, -2, 3, 1, -4],\n [6, 6, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -6, 2, -4, -4],\n [0, -3, 4, -2, -4],\n [-5, 4, 3, -6, 1],\n [0, 6, -5, 2, -1],\n [3, -2, 2, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -3, 6, -6, -2],\n [3, -3, 4, -6, 4],\n [-5, -4, 3, 0, 6],\n [1, -2, 6, 6, -2],\n [6, 6, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 0, 3, 3, -3],\n [3, 4, -2, 2, -2],\n [-3, 4, 4, -4, -1],\n [-4, 2, 0, -2, 3],\n [-4, 4, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -5, 4, 3, 1],\n [4, 2, -6, -6, 5],\n [2, -1, 0, -1, 0],\n [-5, 4, 3, -5, 4],\n [4, 2, -3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -1, -6, -5, 2],\n [1, 2, 2, -5, 3],\n [5, -4, 3, -4, -5],\n [-4, -2, 3, 3, -5],\n [-6, 1, 6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 2, -1, -3, 0],\n [-2, 0, 3, -3, 1],\n [-2, 0, 6, 6, 2],\n [-5, -2, -3, -2, 0],\n [-6, 0, -1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -2, 4, 2, 3],\n [0, -5, -2, -5, 2],\n [4, 5, 3, -6, 5],\n [6, -6, -5, -3, 3],\n [6, 6, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -1, 2, 6, 3],\n [0, 5, -1, -5, 5],\n [-4, 0, -6, -3, 1],\n [-1, -6, 2, 5, 3],\n [3, -6, -1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -4, 1, -2, -1],\n [-4, 2, 6, 0, 6],\n [-2, -3, 0, -4, -5],\n [0, -1, 2, -1, 1],\n [3, 5, -2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -5, 3, 4, -4],\n [-1, -4, 3, 1, -3],\n [4, 1, 6, -4, -1],\n [-1, -6, -3, -5, 1],\n [3, 3, 2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -5, -6, 0, 2],\n [3, -2, 5, 6, -5],\n [1, 0, 3, 2, -6],\n [-4, 3, -5, -4, -1],\n [-2, 0, -5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 3, 5, 4, 5],\n [0, -1, 5, -2, 5],\n [0, 4, -5, -6, 6],\n [-5, 4, -4, 6, 5],\n [1, -2, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 1, 5, 1, 3],\n [-2, 2, -4, 5, 3],\n [5, 2, 4, -6, -1],\n [1, 6, -5, 2, 6],\n [5, 4, -3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -5, -1, 2, 5],\n [-6, -5, 1, 5, -6],\n [2, -4, -3, -5, -4],\n [1, 6, 2, 0, -1],\n [-4, -1, 3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 1, -6, 2, -3],\n [1, -2, -6, -1, -5],\n [0, -6, 0, 1, 6],\n [-1, -4, -1, 1, -3],\n [-4, -1, -5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -2, -6, -4, 6],\n [6, -2, 2, 0, -5],\n [-6, -2, -3, -3, 4],\n [1, 4, -5, -3, -6],\n [1, 0, 3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -4, 5, -1, 6],\n [-2, 5, 2, -4, -2],\n [6, 2, -5, -4, -3],\n [4, -1, -6, -1, -3],\n [2, 2, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 2, 0, 6, 1],\n [2, -5, -2, -2, 2],\n [6, -1, 2, -6, -2],\n [0, 2, -3, 4, 0],\n [-2, 6, 4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 5, 6, 4, -3],\n [5, -2, -2, 3, -4],\n [3, -2, 0, -3, 6],\n [2, -5, -3, 1, 6],\n [2, -4, -5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -4, -4, 3, -4],\n [-4, 2, -6, 1, 6],\n [-2, -2, 4, -5, 6],\n [-5, 4, 0, 5, 4],\n [5, 4, -3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, -6, 1, 6],\n [5, -6, 6, 5, -6],\n [0, 3, -6, -1, -1],\n [-3, 3, 1, 3, -3],\n [0, -2, -1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 5, -4, 0, 4],\n [-1, 2, 4, 5, -1],\n [0, -5, -3, 6, 5],\n [-2, 1, -4, -1, -6],\n [-2, -4, 2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -1, 1, 6, -3],\n [5, -4, -2, 4, 0],\n [1, 6, -6, -5, 3],\n [-1, 3, 1, 0, 2],\n [1, 3, 1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -3, -5, -3, -2],\n [-6, 4, -4, -5, 6],\n [4, 0, 1, -2, 6],\n [-6, 6, 0, 3, 4],\n [-6, 0, 2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 6, -4, -6, 2],\n [-2, 2, -3, 0, -6],\n [-2, -6, -5, 2, 3],\n [4, -4, -3, 6, -6],\n [2, -6, 0, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 3, 4, -2, -6],\n [-3, 3, 6, 2, -4],\n [0, -5, 2, 3, -3],\n [1, -3, -2, 3, -6],\n [6, 5, 1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 3, 0, 4, 3],\n [0, 4, -5, 5, 0],\n [4, -1, -4, 6, -5],\n [-1, -2, -2, 2, -3],\n [-2, 6, 1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -1, -1, -4, 0],\n [1, 3, -1, 0, 4],\n [-2, 0, 5, 4, 6],\n [-1, 3, -3, 0, -6],\n [1, 0, -5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -1, -4, -1, 0],\n [-6, -5, 3, 0, 4],\n [6, 5, 4, -1, -2],\n [-5, 0, -2, 4, -4],\n [3, 6, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -6, 3, 5, -2],\n [6, 1, -3, -4, -3],\n [6, 4, -1, 0, 0],\n [5, -6, -5, 4, -4],\n [-5, 4, -2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 3, 6, -1, 5],\n [-4, 2, -4, -5, -5],\n [-5, -3, -4, 4, -4],\n [-2, -1, 6, 0, 5],\n [1, -4, -6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 4, 3, 4, -5],\n [-6, 0, -5, -4, -5],\n [0, -2, 5, 5, -4],\n [-6, 5, -6, 6, 1],\n [-2, -1, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 4, 2, -5, -6],\n [-5, 1, -5, 2, 0],\n [4, -6, 5, -3, -4],\n [0, -3, 6, -2, -4],\n [2, -2, 2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -3, 0, 4, 1],\n [-5, -6, -5, -2, 6],\n [-5, 6, 2, 2, -1],\n [0, 2, 5, 4, -1],\n [1, 5, -1, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -2, 2, 3, 4],\n [1, -4, -1, -5, -3],\n [-3, 2, 4, -5, -1],\n [-5, -3, 1, 1, 6],\n [0, 0, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -5, -4, 4, 2],\n [2, 0, 3, 1, -1],\n [-1, 6, 0, -6, -3],\n [1, 2, 1, 3, -3],\n [1, -6, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -2, 3, -1, 6],\n [1, -5, -1, 1, -4],\n [2, 4, 0, -6, 1],\n [2, 4, -1, 4, -1],\n [4, -3, 4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -2, -6, 6, -5],\n [4, -5, 3, -5, -6],\n [-4, 0, 5, -2, -3],\n [-4, 5, 2, -2, 3],\n [0, -5, 3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 4, -5, -5, 5],\n [2, 3, 6, 3, -2],\n [-6, 6, -1, -1, -2],\n [2, 5, -5, -5, 2],\n [-2, 2, 0, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 0, 0, 2, 4],\n [-3, 4, -5, -1, 5],\n [-5, 5, 1, 2, 2],\n [5, -3, -2, 1, 1],\n [4, -4, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -4, -4, 5, -6],\n [1, -4, 4, -1, 2],\n [1, 3, 4, -5, 5],\n [-6, -3, 6, -5, 3],\n [1, 3, 2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 4, 1, 5, -1],\n [5, 6, 0, 5, -5],\n [6, 0, -3, 5, 0],\n [-1, -6, -1, 2, 4],\n [4, -2, 0, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -3, 4, 1, 0],\n [0, -1, -1, 6, -2],\n [4, -6, -3, 1, -3],\n [1, 2, 4, -3, 1],\n [-5, 1, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -5, -2, -2, 0],\n [-5, 3, -4, 0, 3],\n [5, 3, -1, 3, 6],\n [5, -6, -1, 3, 3],\n [2, 4, 4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 2, 4, 6, 2],\n [5, 6, 5, 1, -3],\n [-6, 2, 4, -3, -5],\n [4, -2, 5, 1, -6],\n [-2, -2, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 0, 3, 0, 0],\n [3, -1, 5, 0, 0],\n [-1, -2, -3, 6, 4],\n [-5, 0, 5, -3, -6],\n [-3, -3, -4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -3, 4, 5, -4],\n [3, 4, -4, 1, -5],\n [-6, -3, 1, -4, 5],\n [0, 1, -3, -4, -3],\n [-1, -4, 3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 6, 6, 3, -6],\n [-5, 0, 3, -1, 5],\n [-6, 5, -1, 5, -2],\n [0, 0, -6, 4, 3],\n [3, 4, -6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 2, -5, 2, 3],\n [-2, 1, 1, 5, 4],\n [0, -1, 0, 5, -3],\n [0, 6, -2, -5, -2],\n [-3, 4, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -3, 6, -1, 0],\n [-1, -4, 3, 0, 6],\n [5, 0, 2, 2, -6],\n [-3, 3, -5, 3, 3],\n [-5, -1, -2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, -1, 4, 1, -5],\n [-1, -4, -1, 1, 6],\n [-3, -5, 4, 4, -4],\n [-6, 0, 5, -6, 3],\n [3, 6, -3, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 4, -6, -2, -6],\n [1, 3, 5, 0, -1],\n [0, -5, 0, 3, 2],\n [3, -5, 1, -3, 6],\n [6, 1, 2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 1, 0, 3, 5],\n [-5, 5, -6, 1, 0],\n [0, 1, 5, -3, 4],\n [5, -5, 3, 4, 1],\n [4, -1, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -4, 0, -2, 1],\n [-1, 6, -1, 4, -3],\n [-2, -6, -3, -5, 4],\n [5, 0, -5, 6, 4],\n [0, 4, 5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -6, -4, 0, 6],\n [-2, -5, -5, 4, 1],\n [1, 2, 6, -6, 6],\n [-5, 1, -3, 6, -1],\n [5, -4, 1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, 0, -3, 3],\n [-3, 6, 5, 6, 6],\n [-2, 4, 4, 0, 1],\n [-6, -5, 4, 4, 4],\n [-5, -2, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 4, -1, 0, 5],\n [-1, -2, -2, 6, 3],\n [-1, -2, 4, -4, 6],\n [-5, -1, 6, 1, 3],\n [-6, -3, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 5, 1, -2, -3],\n [1, 4, 0, 3, 6],\n [2, -3, 0, 6, -1],\n [-3, -2, 5, 5, 6],\n [-2, 2, -6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -1, -4, -5, 6],\n [0, 0, 2, -6, 2],\n [-1, 5, -6, 6, -5],\n [4, -2, -4, -1, 3],\n [-3, 4, 3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -1, -3, -2, 3],\n [4, -3, 4, 5, 0],\n [-5, 4, -3, 5, -2],\n [3, 3, -1, 1, 2],\n [2, 3, -2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -2, 1, 6, 1],\n [-3, -1, -3, -2, 1],\n [-2, 0, 0, -1, 4],\n [-3, 5, 4, -3, -6],\n [-2, 6, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, 1, -3, 1],\n [-5, -5, 0, 4, 2],\n [5, -6, -6, -3, 1],\n [0, -4, 6, -4, -4],\n [6, -5, -2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, -6, -6, 4],\n [0, -4, 1, 5, -1],\n [2, -5, 4, -2, 0],\n [-4, -6, 4, 1, 5],\n [3, 3, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 2, 6, 1, 5],\n [-2, -3, -1, -5, -5],\n [6, 4, 5, -3, 5],\n [-4, 0, -4, 3, -3],\n [-5, -6, -2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 0, -6, -1, -2],\n [1, 1, -1, 3, 6],\n [1, 6, -2, -5, 2],\n [0, 1, 2, 3, -6],\n [-1, 0, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 2, 6, -4, -2],\n [-1, 6, 2, -2, 4],\n [0, 2, -2, 5, 4],\n [1, -1, 4, -5, -1],\n [6, -2, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -3, -6, -5, -3],\n [-3, 5, -1, 1, 2],\n [-2, -1, -5, 1, 4],\n [1, 1, -2, 3, -6],\n [6, 5, 6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 3, -1, -6, 6],\n [-6, 5, 6, -6, 6],\n [5, 3, 6, -4, -6],\n [3, 3, 6, 1, 2],\n [5, 6, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -3, 1, 6, 3],\n [-5, -5, 3, -5, 0],\n [-1, 5, 6, 0, 0],\n [5, 2, -3, 1, 4],\n [-5, 4, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 4, 1, 4, -4],\n [3, -3, 4, 4, -3],\n [3, 2, 4, -3, -2],\n [0, -5, -3, 0, 4],\n [-6, 0, -5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -5, -2, -5, -2],\n [-6, -5, -5, -1, -3],\n [1, 2, 2, -6, 1],\n [3, -5, 2, 1, -5],\n [5, -3, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 4, 1, -1, 6],\n [0, -6, -5, 0, 5],\n [-5, -3, -6, -5, 2],\n [-3, -1, -4, -4, 5],\n [6, -4, -2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -6, 1, 5, -3],\n [1, 2, -6, 2, 3],\n [1, 4, 2, 3, -1],\n [6, 1, 6, 0, -2],\n [-3, -4, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 5, 3, 0, 3],\n [6, -1, -5, 1, -4],\n [4, -1, -3, -5, -5],\n [4, 2, 5, -4, 1],\n [-2, -2, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, -6, -6, 6],\n [-5, -3, 5, 5, -6],\n [4, -1, 4, -6, 1],\n [-3, -6, 4, -5, 0],\n [-1, 5, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 4, -1, 4, -2],\n [5, -1, 0, -5, -6],\n [4, -2, -3, 6, 1],\n [3, 0, -1, 2, -3],\n [2, 6, 5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 2, -3, 0, 4],\n [1, 4, -5, -5, -2],\n [-1, -1, -3, 6, 5],\n [4, -6, 6, -2, 4],\n [4, -6, -3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -2, 3, -1, -3],\n [2, 0, 5, -3, 1],\n [4, 6, -5, 1, -5],\n [-4, -5, 1, 1, 3],\n [-4, -1, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -1, -1, -1, -2],\n [-5, 2, 4, 5, 4],\n [2, 4, -4, -4, -3],\n [-2, 3, -3, -2, -1],\n [-1, -5, 3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -2, -2, -2, -5],\n [0, -6, -3, -6, 0],\n [-6, -2, -5, -5, 4],\n [-2, -2, 2, 5, -3],\n [-3, 6, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -5, 0, 3, 1],\n [5, 2, 1, -2, 3],\n [3, 4, -5, 6, 5],\n [-1, -2, 1, 5, -6],\n [3, 1, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 2, 2, 1, -5],\n [-6, 4, 1, 6, 1],\n [4, 4, 1, -1, 2],\n [-6, -5, -6, -2, -5],\n [5, -6, 6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 3, 2, 1, 5],\n [5, -5, 0, 1, 1],\n [0, 6, -6, -4, -1],\n [4, 3, 0, -6, -1],\n [5, 6, 0, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 5, 3, 2, 4],\n [6, -1, 5, 1, 6],\n [-2, 4, 3, -5, 1],\n [2, 3, -5, -4, 0],\n [-2, 4, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -4, -3, 1, -6],\n [-4, -5, -4, 3, -4],\n [0, 5, -5, -3, -2],\n [5, 3, 3, 1, 5],\n [-3, 5, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 3, 3, 6, -1],\n [-5, 0, -1, 3, 2],\n [-5, -6, -6, 5, 2],\n [6, 4, 6, 5, 0],\n [-4, 5, -4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -5, -4, -5, 3],\n [1, 0, -4, 6, 3],\n [6, -1, 3, 4, -2],\n [3, -2, -6, 5, -1],\n [4, -2, 2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 2, 3, 4, 4],\n [-6, -2, -5, -6, -2],\n [1, -5, 4, -5, -5],\n [-5, -6, 2, 5, 6],\n [-6, 1, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -3, -6, 6, 2],\n [4, -5, -5, -4, 2],\n [-2, -6, 1, -3, 5],\n [-1, -1, 6, -2, 0],\n [2, -6, 5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -3, -3, -1, 6],\n [6, 2, 0, 6, -5],\n [0, 0, -3, 1, -2],\n [-5, 3, -1, -2, 3],\n [-1, -4, -6, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, -4, -2, 0],\n [5, 0, 5, 3, -1],\n [0, -6, 2, -1, -1],\n [6, 6, 0, -1, 3],\n [-5, 6, 5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -4, 5, -3, 0],\n [-5, -4, -5, -5, 2],\n [1, 0, 3, -5, 4],\n [1, 1, 0, 4, -1],\n [-6, -6, 3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 1, 4, 2, 1],\n [6, 4, 3, -4, 1],\n [-6, 5, -6, 5, 2],\n [-3, -5, -1, 6, 6],\n [-1, 1, -4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -1, 1, -4, -2],\n [4, -5, 3, 4, 3],\n [-3, 1, -5, 1, 0],\n [-1, -4, 1, -5, -4],\n [4, -1, 2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 1, -1, 5, 1],\n [-6, 6, 1, 5, 1],\n [5, 6, 2, 1, -5],\n [2, 5, -3, -6, 2],\n [5, 1, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 4, -2, 4, 0],\n [4, 4, 4, 2, -1],\n [3, -3, -5, -1, 3],\n [-3, -2, 3, 2, 5],\n [4, -2, 5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -2, 1, -4, 0],\n [1, 0, 0, 2, 3],\n [2, -3, 1, -4, 6],\n [-1, 4, 1, -2, 5],\n [2, -4, 4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 2, 6, -1, -3],\n [2, -3, -1, -6, 4],\n [-2, -6, 4, -3, -2],\n [-6, -2, 6, -6, 0],\n [5, -6, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 3, -2, 5, 2],\n [2, 0, -5, -5, -6],\n [1, 0, -5, -1, -3],\n [-4, 0, -3, 6, 2],\n [1, 2, 5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 2, 6, -2, 3],\n [-1, -5, -5, -5, -5],\n [5, -6, -3, 6, 6],\n [6, -6, 5, 4, 0],\n [2, 0, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -6, 6, -6, -5],\n [-3, -2, 2, -2, 0],\n [3, -2, -4, 3, 2],\n [6, 1, -1, 2, 3],\n [-5, 2, 6, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -6, 4, 5, 3],\n [0, 4, 1, -3, -5],\n [-5, 5, 2, 5, 2],\n [4, 4, -6, 2, 6],\n [5, -5, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 5, 1, 5, 2],\n [4, -2, 0, 3, 3],\n [-3, -1, 4, -5, 5],\n [-2, 2, 4, -5, -3],\n [-3, -1, 4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, -5, 4, 0],\n [5, 0, -1, 3, -4],\n [-3, -3, 3, 5, -3],\n [5, 4, -2, -6, -2],\n [3, -4, 6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -5, 4, -2, 6],\n [-2, 0, -2, -3, -6],\n [-6, 5, 1, -3, 2],\n [-4, 2, 1, 1, 4],\n [0, 5, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -2, -4, 2, -2],\n [-2, 4, 5, -5, 6],\n [6, 4, 0, -3, -5],\n [0, -1, 0, 2, 3],\n [6, 5, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -4, -4, 1, 2],\n [-5, 4, 6, -5, 4],\n [3, -6, -3, 2, -6],\n [2, 1, 0, 4, 3],\n [4, 4, -6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 0, -4, -2, -3],\n [0, 3, -1, -4, 6],\n [0, 2, -2, -2, -3],\n [-5, 6, 4, 3, 6],\n [-6, -1, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -4, -2, -5, 2],\n [3, 0, 4, 5, -1],\n [6, 4, 5, 5, -1],\n [-6, 1, -6, -3, -1],\n [3, 0, 4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 3, -4, 6, 4],\n [4, 5, 2, -6, 1],\n [-4, 1, 2, -5, 6],\n [5, -4, -5, -6, 3],\n [5, -3, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 4, -1, 6, -5],\n [-3, 2, 2, -2, -4],\n [-5, 5, 5, 1, 4],\n [-2, -4, -4, -5, 0],\n [6, 4, 1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 3, 6, 2, -6],\n [-3, -1, 0, 5, 0],\n [-1, -2, 3, -6, 4],\n [-6, 2, -6, -4, 5],\n [4, 2, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 4, 2, 5, 3],\n [-1, -5, -1, 4, -5],\n [-5, 4, -1, -4, 1],\n [3, 5, 4, 4, 1],\n [1, 1, 6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 6, 4, -2, -3],\n [-5, 2, -1, 3, -1],\n [4, 6, 5, -3, -3],\n [6, 1, 2, -4, -2],\n [4, -3, -4, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -6, 1, 1, -5],\n [-2, 3, 2, -4, 3],\n [0, 6, 2, 0, 3],\n [-3, -3, -3, -3, -3],\n [-6, -3, -4, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 0, 5, -6, 0],\n [-2, -1, 3, -1, 4],\n [5, 5, 0, -5, 1],\n [2, 5, -2, 5, 4],\n [1, -1, 0, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -1, 6, -6, 6],\n [4, -6, -5, -6, -4],\n [-4, -6, -6, 1, -4],\n [2, -5, 1, 4, -2],\n [-4, -2, 3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 1, 2, -5, 6],\n [5, 4, -1, 5, 5],\n [-5, -2, 3, 4, 6],\n [5, 3, 4, 1, -5],\n [4, 5, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -5, 3, 4, 3],\n [4, 5, -1, -4, -2],\n [2, 1, -1, -2, 5],\n [1, 4, 0, 2, -6],\n [-4, 3, 5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 2, -4, -5, -6],\n [-6, 4, 5, -5, 4],\n [-5, -1, 3, 2, 4],\n [-6, -2, -6, -6, 2],\n [0, -1, -5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -2, 6, 2, -1],\n [0, 5, -5, 4, 6],\n [5, 1, -1, 1, -5],\n [4, -5, 1, 2, -4],\n [-6, -1, 2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 3, 3, 2, 0],\n [4, -1, -5, 5, 5],\n [-4, 2, -3, 4, 4],\n [6, -5, -5, 5, 1],\n [2, -2, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -6, 2, -1, -5],\n [-4, -6, -2, 1, -4],\n [4, -3, 5, -6, 4],\n [1, -3, 5, -5, 6],\n [-6, -1, 1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -2, -5, -1, 3],\n [1, 1, 0, 4, -1],\n [-6, 3, -1, 4, 1],\n [-5, -4, 4, -2, 5],\n [-3, 5, 6, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 1, 1, -5, -1],\n [1, 6, 1, 3, -3],\n [-1, -1, 4, -3, 4],\n [-1, -3, -4, -6, 3],\n [-5, 3, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 3, 5, -3, 3],\n [2, 1, 6, -6, 6],\n [-3, -6, -6, -2, 3],\n [3, 3, 2, 0, 3],\n [-1, 6, 5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 2, -4, -6, 5],\n [-1, 6, -2, 5, -1],\n [2, -4, -3, 2, 0],\n [4, -4, 2, 1, -1],\n [5, -3, -6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -5, -5, 1, -5],\n [-5, -5, -1, -5, 5],\n [2, 5, 3, 1, -4],\n [-6, 0, 1, -3, -4],\n [3, -3, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 6, -5, -6, 5],\n [-1, 5, 1, -4, 3],\n [2, 3, -2, 6, 2],\n [3, -4, 0, 6, -2],\n [6, -1, 3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 5, 1, 4, 4],\n [5, -3, 0, 4, -6],\n [5, 5, 4, -1, 6],\n [-5, -2, 1, 1, -2],\n [-3, 5, -6, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 0, 4, 3, 2],\n [0, 4, -5, -2, -2],\n [1, -2, 1, -5, -4],\n [5, -3, -6, 5, 3],\n [3, -3, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -3, 1, 1, -3],\n [6, 4, 0, 1, 3],\n [0, 3, -1, 3, -4],\n [-3, -1, -5, 0, -6],\n [-2, -4, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -1, -2, -4, 3],\n [-5, 4, 0, -3, -3],\n [-4, 0, 3, 2, 5],\n [-3, 4, -3, -6, -5],\n [5, -5, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -1, -5, 5, 2],\n [5, 5, 2, 6, -3],\n [6, -4, -2, -1, 2],\n [4, 6, 3, -5, 2],\n [-3, -6, 5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -4, 4, -4, 2],\n [6, 4, -5, -2, 0],\n [6, 3, -1, 3, -5],\n [5, 1, -5, 6, 5],\n [3, -6, 3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, -3, -4, -3],\n [5, 0, 5, -2, -5],\n [-2, -1, -3, 1, -2],\n [4, 1, 2, -2, 6],\n [4, -4, 1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -3, 1, 2, 2],\n [-3, 4, -4, 5, -5],\n [-4, -2, 6, -5, 6],\n [-6, -3, 3, 1, -4],\n [1, 1, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 4, -5, 5, -1],\n [-2, 6, 5, -1, -6],\n [-1, 4, 1, 6, 1],\n [-2, 3, -1, 3, 6],\n [6, 1, 2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 5, -1, 6, 6],\n [-4, 5, -2, 6, 3],\n [-3, -3, -5, 1, -3],\n [3, -6, -5, -5, 5],\n [6, -3, 6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 2, -6, 5, 2],\n [3, 4, -5, -1, -5],\n [6, 4, 0, -5, 6],\n [-2, -5, 3, 4, -5],\n [-2, -3, 6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 3, -5, 0, 2],\n [-1, -1, -2, -1, 0],\n [0, -1, -4, 2, 4],\n [-1, -5, -3, -3, -4],\n [5, -4, 0, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 5, 3, -4, -1],\n [-5, -5, -3, -2, -1],\n [0, -2, -2, -6, -2],\n [6, -6, 1, -3, 4],\n [-1, 5, -4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 6, 6, -1, -4],\n [4, 3, 4, -4, 5],\n [3, 0, -4, 2, -4],\n [2, 3, 4, -5, 3],\n [5, 3, 1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -6, 0, 1, -5],\n [2, 6, 0, 3, -6],\n [-3, -4, -3, 3, -1],\n [6, -1, 1, -6, -1],\n [1, 3, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, -5, 5, 1],\n [3, -5, 0, 6, 3],\n [-4, -5, -4, -1, 2],\n [-3, -6, 6, 3, -6],\n [6, 1, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 3, 5, 3, 6],\n [5, 1, 2, 3, -6],\n [-6, 1, 6, 5, 2],\n [-3, -6, -5, -5, -4],\n [6, -5, -5, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 6, 1, 0, 4],\n [6, -1, 4, -6, -2],\n [0, 0, -2, -2, 4],\n [-5, -3, 6, -1, 1],\n [-3, 2, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -4, -1, -4, -4],\n [-3, 1, 3, -1, -4],\n [-4, 4, 1, 2, -4],\n [-4, -1, -2, -4, 3],\n [-6, 5, -5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 4, -3, 4, 3],\n [1, -5, 3, -4, 5],\n [0, -4, 2, 4, -2],\n [0, -2, 2, 5, 0],\n [-4, 1, 5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -6, -2, -4, -3],\n [-3, 0, 3, -1, -1],\n [-5, 5, -1, -6, -5],\n [6, 6, 6, 3, 0],\n [5, -2, -4, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -1, -2, -1, 3],\n [4, 1, 6, -3, -6],\n [3, 5, 4, -1, 4],\n [-3, 4, 1, 0, -2],\n [-5, 2, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -3, 2, 5, -2],\n [-3, 4, 5, 0, 5],\n [5, 4, 2, -6, -4],\n [3, 5, -5, -2, 2],\n [-5, -1, -1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 1, 2, 2, 0],\n [2, 0, -2, 4, -4],\n [3, -2, -3, 4, 0],\n [3, 6, 1, 3, -3],\n [2, 2, -2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -6, 1, 1, 2],\n [-5, -1, 0, 2, -3],\n [5, -5, 6, 4, -5],\n [4, -5, 2, -2, -2],\n [-3, 0, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -4, 0, -1, 1],\n [-4, -3, -5, -4, -2],\n [-1, 1, 6, -4, -2],\n [1, -5, 1, -6, -3],\n [-1, 0, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -2, 1, 1, 3],\n [1, 3, 5, -5, 0],\n [4, 2, 4, 2, -3],\n [3, -3, 1, -5, 5],\n [-5, 2, 3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 3, 4, 4, -3],\n [2, 2, 2, 6, -6],\n [-1, -2, -3, 1, -4],\n [2, 0, 5, 1, -4],\n [-4, -5, 1, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 5, -1, 3, 0],\n [6, -3, -5, 4, 1],\n [-1, 2, -4, 4, -3],\n [6, -6, 6, 6, 6],\n [0, 5, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -2, -1, 5, -4],\n [-1, 1, -2, -6, 6],\n [4, 6, 0, 4, -5],\n [3, 6, -2, 0, 0],\n [4, 3, -1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 3, 6, 2, 4],\n [-6, -5, -1, -6, 0],\n [6, 0, 6, -6, -2],\n [-4, 3, 4, -6, -5],\n [5, 4, -2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 2, 4, 5, 1],\n [0, -5, -1, -4, 4],\n [-5, 5, -2, -5, 2],\n [5, -1, 4, 4, -3],\n [1, 3, -6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, -3, -6, -6],\n [-5, 6, 1, 6, 4],\n [-6, -2, -4, 4, -2],\n [-2, -6, 3, -3, 3],\n [-5, -2, -5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, 3, 4, 4],\n [5, -5, -2, 4, 2],\n [-5, -4, 5, -6, -1],\n [3, -3, 4, 0, 4],\n [-5, -1, 0, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 6, -1, -1, 3],\n [-4, -3, -4, 2, -3],\n [6, 4, 3, -4, 5],\n [-1, 0, 0, 2, 3],\n [3, -1, 3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -6, 3, 1, 5],\n [-1, -6, 1, 5, 2],\n [1, 5, 3, 2, 1],\n [4, -5, 1, -3, 6],\n [-2, -2, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -2, 0, -6, 2],\n [-5, 3, 6, 2, -6],\n [5, 0, -4, 6, 2],\n [3, 6, 5, 4, -5],\n [-2, -4, -4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -1, -2, -3, -2],\n [-3, 5, 1, -1, -5],\n [-2, -2, -6, 3, -6],\n [-2, 4, -1, 5, 4],\n [6, -2, -5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -3, 2, -5, -5],\n [-5, 1, 1, 6, -3],\n [-6, 6, -3, -4, 2],\n [-4, 1, -4, -2, -5],\n [-6, 5, -3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -3, 5, 6, -2],\n [6, -1, 3, -2, -4],\n [2, 4, -6, -5, 1],\n [1, 1, 4, 0, 0],\n [-5, -2, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -1, 5, 1, -1],\n [3, 3, 6, 2, 6],\n [-2, -5, 0, 0, 1],\n [3, 0, 1, 4, 5],\n [2, 4, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 1, -6, -1, 5],\n [-4, -1, -5, 6, -3],\n [-1, -6, 0, 6, 0],\n [-5, 3, -3, 2, 5],\n [2, 5, 3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 3, 1, 6, -1],\n [-1, 2, 1, -4, 4],\n [-4, 6, -6, 2, 5],\n [-6, 4, 2, 4, 4],\n [-4, -3, 5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -1, 1, -6, -4],\n [4, 6, -5, 5, 1],\n [2, 3, -1, 2, -6],\n [-3, -6, 5, -2, -5],\n [-5, 1, 4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 0, 1, -5, 4],\n [2, 1, 2, -2, -6],\n [-6, 1, 2, -2, 6],\n [4, 0, 1, 2, -6],\n [-4, -1, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -6, 0, 3, -3],\n [-4, -5, 4, -5, 4],\n [0, 2, 0, -6, 2],\n [-1, 2, 3, -5, 2],\n [2, 2, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -5, 0, -2, 6],\n [6, 1, 0, -6, -5],\n [-1, -4, -1, -1, -1],\n [2, 6, -6, 4, -1],\n [5, -1, 6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 1, -4, -4, 0],\n [1, 4, -2, 1, -2],\n [-1, -4, -2, 1, -6],\n [-3, -6, -4, -4, 6],\n [-1, 1, -5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -3, -6, -1, -2],\n [2, 0, 6, 3, -1],\n [3, -3, -5, 5, -6],\n [1, 2, -4, -1, 3],\n [4, 6, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -3, -3, -3, 5],\n [-6, -2, -2, -4, 0],\n [-6, -6, 6, 4, -3],\n [-2, 0, -4, -6, 1],\n [0, -6, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -3, 5, 6, -1],\n [2, -1, 4, 3, 3],\n [-1, 1, -3, 0, -6],\n [6, -3, -1, 1, 0],\n [6, 1, -5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -1, 5, 4, 1],\n [-3, -2, -5, 1, -4],\n [-6, -2, -5, 0, -6],\n [-1, -1, -5, 5, 1],\n [-2, 5, 5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 4, 3, -4, -6],\n [6, 5, 6, 3, -1],\n [5, -3, -1, 5, 0],\n [-3, 1, 5, -3, -4],\n [-4, 4, -6, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 2, -5, -1, 5],\n [-6, -3, 6, -6, -2],\n [1, 5, 5, -2, -4],\n [6, -3, -2, 5, 6],\n [1, 3, -5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -3, -2, 3, -6],\n [6, 0, 0, 4, -2],\n [1, 5, -1, 3, 1],\n [-4, -2, 5, -5, -1],\n [-6, -5, 6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 6, 3, -4, 6],\n [-2, -5, -2, -4, -1],\n [6, 4, 0, 0, -6],\n [0, 0, 6, -4, -4],\n [-4, -1, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 3, -4, 3, 6],\n [-4, -2, 1, 4, 1],\n [-3, -3, 5, 0, -5],\n [3, 5, 1, -4, 2],\n [-2, 1, -4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 5, 4, -4, -5],\n [-4, 2, -4, 6, -5],\n [0, 6, -4, -1, -6],\n [5, -1, 6, -1, -3],\n [5, -2, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -2, 1, 3, -2],\n [4, 0, 1, 1, 0],\n [-6, -3, 1, -3, -5],\n [-2, 2, 2, -6, -2],\n [-2, 3, 5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 4, 0, -3, -1],\n [-5, 1, -6, -2, 0],\n [-5, -4, -6, -3, -4],\n [6, 6, -1, -6, -3],\n [4, 2, 3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 1, -1, -4, -5],\n [-1, 0, -3, 4, 0],\n [-3, -1, 4, -6, 5],\n [0, 0, 5, 1, -1],\n [-5, 2, -1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 0, -5, -6, 0],\n [-4, -6, -6, 6, 2],\n [-1, 6, -4, 3, 1],\n [3, -4, -6, 3, 1],\n [-2, 0, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -6, 2, -6, -6],\n [5, -2, 0, 1, 1],\n [4, 5, -3, -5, 0],\n [-6, -1, -3, -5, -5],\n [5, -1, 1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, 5, -1, -2],\n [-1, 3, -6, 0, -5],\n [-3, 5, 2, -2, -2],\n [1, 6, 5, -1, -1],\n [4, -1, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 0, 4, -1, 5],\n [5, -2, 4, 3, 6],\n [4, 3, -3, 5, -1],\n [-4, -2, -1, 1, 3],\n [4, -6, 4, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 0, -4, 4, -3],\n [1, -2, 2, 6, -1],\n [-2, -4, 4, -2, 3],\n [3, 6, 3, 3, 1],\n [2, 3, -4, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -3, 3, 4, -2],\n [5, 0, 1, -6, 0],\n [-2, -4, -5, 2, 0],\n [2, 2, -4, 1, 5],\n [-4, 2, 1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, -2, -3, 2],\n [-2, -5, -5, -3, 2],\n [-2, -4, 1, 0, 2],\n [0, 5, -1, -1, 6],\n [2, 3, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, 0, 5, 4],\n [0, -1, 2, -5, 5],\n [6, -2, -6, 2, 1],\n [-1, -3, -6, 0, 6],\n [2, -5, 3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 2, -1, 3, -1],\n [1, -3, -3, -3, -5],\n [-3, -4, -5, 2, 5],\n [-5, -2, -1, -6, 2],\n [0, 0, 1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -1, 3, -3, -3],\n [2, -2, -1, -3, -2],\n [-5, 4, -3, 1, 4],\n [5, 3, 6, -5, -1],\n [-2, 0, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 3, 6, 2, 5],\n [4, -1, -2, 6, 3],\n [3, 2, -3, -3, 2],\n [2, 6, 4, -2, 6],\n [-4, -5, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, 4, -2, -1],\n [-4, 6, 4, -4, 5],\n [-4, -6, -2, -3, 6],\n [1, -5, 6, 1, -4],\n [2, 2, -2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 4, 4, -1, -1],\n [1, 3, -4, 1, -2],\n [4, -6, -2, 3, -1],\n [1, 4, 2, 5, 1],\n [3, 0, -6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 1, 4, -5, -6],\n [-6, -4, 5, 2, 0],\n [-2, 1, -5, 4, 1],\n [1, 6, 6, -5, 1],\n [-2, 0, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 4, -5, 6, 6],\n [1, 4, 2, -2, 5],\n [-1, 3, 4, 0, -1],\n [-5, -2, -2, -2, 2],\n [-6, 6, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 1, 3, 2, 5],\n [3, 6, -3, -6, -1],\n [6, -3, -3, -5, 2],\n [-6, 5, -1, -5, -1],\n [-6, 3, 5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 0, -5, 4, -2],\n [-4, 1, 2, 2, 1],\n [0, 2, 5, -2, 3],\n [4, -3, 6, 3, -5],\n [1, 6, 5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -3, -4, 6, -4],\n [2, -1, 0, 4, 6],\n [-1, -3, 3, 4, 6],\n [3, -5, -1, -5, -6],\n [6, 1, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 4, 3, 3, 1],\n [4, 6, 4, -5, 6],\n [5, -4, -1, -2, 3],\n [1, -2, -3, 4, -1],\n [-1, 6, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 4, 4, 2, -1],\n [0, -3, 5, 2, -4],\n [0, 3, 6, -4, -4],\n [0, -1, -5, 4, -5],\n [0, 3, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 6, 6, -5, 1],\n [-3, 2, 1, -5, 0],\n [-5, -3, -5, 0, -6],\n [-2, 2, 5, 2, -4],\n [-6, -5, 5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 1, -4, -4, 5],\n [-4, -5, -6, 5, 0],\n [1, 6, -6, -1, -4],\n [-6, -2, 1, -2, -2],\n [4, 0, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, -6, 0, 0],\n [-2, 6, -5, 2, 5],\n [3, -1, -1, -1, 3],\n [-6, -5, 0, -3, 4],\n [3, -1, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -4, 2, 1, -3],\n [4, 3, 6, -3, 6],\n [-4, 2, 5, 4, 5],\n [3, -3, -6, -3, 1],\n [1, 0, 3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 2, -6, 6, 6],\n [3, -3, 5, 3, -2],\n [-5, 5, -1, 6, -2],\n [3, -2, 0, 4, 3],\n [-3, -1, 6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 5, -4, -1, 2],\n [-4, 5, -4, 0, 0],\n [2, -1, -3, -6, -3],\n [2, -5, -5, -2, 6],\n [-2, 4, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -2, 0, -3, -1],\n [2, 2, 3, -4, 1],\n [0, -3, 6, -2, 4],\n [5, -6, -2, 3, -6],\n [0, -5, 6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 3, -2, 0, 3],\n [-6, 5, -5, 0, 1],\n [-1, 3, 5, 0, 5],\n [1, -5, 5, -4, -2],\n [-2, -5, 5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -3, 2, -3, -6],\n [-6, 5, -1, -1, -2],\n [0, -6, 2, -3, 2],\n [1, -5, -5, -2, 0],\n [2, 4, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -1, 6, -6, -2],\n [0, -2, 0, -2, 2],\n [6, 5, 4, -1, 4],\n [-6, -5, 4, 6, 2],\n [1, 5, 0, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 3, -5, -5, -5],\n [0, 4, -6, 4, -2],\n [-2, 0, -3, 1, -6],\n [-3, -5, -3, 3, -2],\n [4, -5, 4, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, -2, -2, -4],\n [6, 5, 2, 3, 2],\n [0, 3, 5, 6, 3],\n [2, 5, 3, 2, 2],\n [4, 2, -4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 0, 0, -6, 0],\n [6, 1, -2, 1, 5],\n [0, -2, -3, 2, 6],\n [-6, 2, 4, 5, -6],\n [-5, 1, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 3, -3, -3, 0],\n [1, 1, 2, 4, 2],\n [-2, -6, -6, -2, 4],\n [-3, 6, 6, -1, -5],\n [5, -3, -1, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -1, -3, 5, 5],\n [-1, 4, -6, -4, -5],\n [4, -5, 4, -6, 5],\n [1, -1, 5, 2, 1],\n [-3, -3, -3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 4, 5, -5, -4],\n [-1, -3, -5, -4, 1],\n [1, 4, -4, -5, -1],\n [3, 1, 4, 0, 4],\n [-6, -3, -3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 2, 2, -3, 4],\n [6, 3, -6, -3, 4],\n [3, 2, -4, 2, -5],\n [-6, 6, 6, -5, 0],\n [4, -6, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -4, 1, -3, 4],\n [-1, -4, -6, 3, 0],\n [1, 4, -4, -3, -3],\n [-5, -6, 5, 4, 2],\n [-3, -1, -1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 6, -2, -6, 1],\n [-5, -2, -3, -1, 6],\n [2, -5, -6, -1, 6],\n [3, -1, 5, -2, 0],\n [3, 3, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -4, -3, 0, -4],\n [-2, -1, -5, -1, 1],\n [-3, -5, 3, -4, 0],\n [0, 4, 3, 0, -2],\n [0, 2, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -3, -4, -5, -6],\n [5, -6, 0, 6, 0],\n [-1, -1, 2, -4, 2],\n [-4, -2, 0, -6, -4],\n [-2, 0, -1, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 6, 6, 1, 2],\n [-1, -4, -6, -2, 5],\n [6, -2, -2, 2, 6],\n [-3, -6, -6, 5, 2],\n [-1, 4, 2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -6, -5, 2, 3],\n [6, 5, -3, -2, -4],\n [-6, -6, -5, -6, 0],\n [-1, -3, 3, 4, 2],\n [-3, -4, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -1, 6, 1, 0],\n [1, 4, -1, -4, 3],\n [-2, -3, 1, 4, 5],\n [5, -6, -5, 0, 1],\n [1, 3, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 6, 1, -4, -5],\n [-5, 3, -4, 3, -4],\n [5, -4, 5, 2, -2],\n [2, -5, 2, -1, -3],\n [6, -2, 1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, 1, -6, 1],\n [0, 5, -5, -2, 5],\n [6, -2, 5, 0, -1],\n [1, -3, 1, -1, -4],\n [-1, -3, 0, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -3, -5, 6, -1],\n [-3, 3, 3, -3, 6],\n [-5, -4, 3, 2, 3],\n [4, -6, 5, -4, 5],\n [6, 6, 4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 1, 4, -4, 3],\n [5, -1, 0, 1, -4],\n [-1, 2, -5, -4, 5],\n [-1, 1, 2, -4, -2],\n [-6, 5, 0, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 4, 5, 3, -3],\n [4, -5, 3, -4, 5],\n [3, 3, -2, 1, 4],\n [-5, -4, -2, -2, 4],\n [-2, 1, -6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 1, -2, -4, 5],\n [2, 6, -4, 6, 3],\n [4, -6, 1, 3, 2],\n [-5, 3, -5, 4, -1],\n [-6, 5, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 2, -6, 5, 0],\n [1, -5, 6, 3, -2],\n [-3, -3, 6, -6, -3],\n [4, 1, 3, 6, 2],\n [5, -2, 5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 1, 0, -4, -5],\n [-5, -4, -3, 6, -3],\n [0, 2, 4, 2, -6],\n [-1, 4, -2, -6, 0],\n [-4, -1, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -6, 5, 3, 4],\n [0, -3, -6, 2, -5],\n [3, 2, 4, 0, -4],\n [6, -4, 0, 0, -5],\n [-2, -4, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 1, -1, -3, -6],\n [2, 6, 5, 1, -6],\n [4, 3, -6, 1, -3],\n [3, -5, 0, 3, 3],\n [-3, -6, -4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, -1, 0, -6],\n [6, 1, -2, -6, 5],\n [2, -1, -5, 4, 6],\n [1, -3, -2, 3, -1],\n [-6, 4, 4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 0, -6, 1, 5],\n [-6, -3, 3, 6, 6],\n [1, -6, -5, 0, 2],\n [-6, -6, -5, 6, -4],\n [6, 6, 1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 6, -2, -3, 4],\n [-6, 2, 6, 5, 2],\n [2, -5, 4, 1, 1],\n [5, 3, 0, -5, -2],\n [4, -1, 0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -3, -2, 3, 6],\n [0, 1, 0, 0, -1],\n [-3, 4, 3, -3, 6],\n [4, 0, -5, -5, 3],\n [2, 0, -6, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, 3, -3, 2],\n [5, -6, 3, 0, 2],\n [-4, 0, 4, 0, -5],\n [-5, -1, -4, -2, 4],\n [-3, -5, 1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 0, -1, 1, -3],\n [-2, -4, -1, -1, -4],\n [-4, 5, -5, 6, 3],\n [-5, -6, 1, -1, -6],\n [-2, -4, -2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -6, 3, 0, -4],\n [-4, -5, 3, 2, 2],\n [-6, 5, -4, 1, 6],\n [5, 5, -2, 2, -2],\n [-5, -6, 5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, 4, -6, 0],\n [0, -6, -4, 1, -2],\n [-3, -5, -3, -5, 6],\n [5, 1, 2, 2, -5],\n [-5, 6, 3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 2, 6, 5, -3],\n [6, -3, 1, -2, 5],\n [4, 4, -6, -6, 5],\n [-1, 2, -6, -4, 3],\n [0, 3, 3, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 1, 4, -2, 0],\n [2, 4, 6, 1, 2],\n [-4, -1, -4, -1, 4],\n [1, 6, -1, -1, 3],\n [-4, 2, -6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -6, 6, 3, -3],\n [0, 5, 6, 0, -1],\n [-6, 1, 0, 4, -3],\n [-5, -5, 6, -3, -1],\n [-6, 5, -3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -2, -6, -5, -5],\n [5, -4, -5, -6, 5],\n [-2, 3, -6, -1, -5],\n [-2, 5, -5, -3, -3],\n [1, 5, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 3, 3, -2, -5],\n [1, 5, -1, -2, 3],\n [-3, -3, -5, 4, 3],\n [5, 5, 5, 5, 1],\n [-6, -3, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -4, -4, -4, 2],\n [5, 1, -1, -6, -2],\n [-3, -5, 3, -2, -1],\n [6, 2, 4, -6, -5],\n [-2, 4, 1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 5, 3, 4, 4],\n [4, 4, 1, -1, 1],\n [-6, 2, 5, -2, 6],\n [-3, -4, 4, -5, -6],\n [3, -5, -4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 0, 0, 2, 6],\n [-6, 6, -4, 0, 5],\n [1, -2, -2, 6, 1],\n [1, 5, 5, -3, -6],\n [-2, 2, 3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 0, -4, 5, 3],\n [-1, 6, -4, 5, 6],\n [2, -1, -6, -4, 5],\n [4, 6, -6, 0, 1],\n [1, -5, -5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 0, -3, -5, 2],\n [-3, 5, 3, 0, 1],\n [6, -2, -1, 3, -5],\n [0, 4, 4, 4, -3],\n [-1, 6, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, 2, 2, -5],\n [6, 4, -5, 1, -3],\n [4, 5, -6, 2, -6],\n [-3, 5, -5, -5, -1],\n [5, -6, 5, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 5, -5, 4, -2],\n [1, 0, 2, 5, -2],\n [4, -3, 0, 6, 4],\n [-2, -3, -6, 4, 0],\n [-1, -3, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 3, 6, -5, 6],\n [2, 3, 6, 1, -2],\n [3, -2, 5, -4, -5],\n [-6, 0, 1, -3, -1],\n [2, -3, -3, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -2, 0, 3, -2],\n [0, 2, 2, 0, 3],\n [3, 2, -6, -5, 6],\n [-5, 3, -6, 1, -6],\n [5, 2, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -5, -5, 4, 6],\n [5, -4, 3, -4, 1],\n [3, -1, 4, -5, 5],\n [1, -1, -4, 3, 2],\n [5, 5, 4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 5, -4, 3, 1],\n [0, -5, 4, -2, 3],\n [-5, 6, -2, -1, -6],\n [-1, -2, 2, -6, -1],\n [2, 6, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -3, 0, -1, -2],\n [1, -2, 5, -1, 6],\n [0, -5, -3, -3, -1],\n [-5, -2, 2, -1, 1],\n [-1, -5, -5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 4, 2, -4, -4],\n [3, -4, -6, -2, 2],\n [-6, -6, -3, 0, -5],\n [-2, -3, -3, -5, -2],\n [5, -1, -2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 3, 3, -4, -6],\n [-4, 6, 1, -2, 1],\n [6, -3, 1, 3, -2],\n [1, -1, 3, 5, -5],\n [0, 0, 2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 5, -6, -2, 1],\n [0, -6, 4, 2, 2],\n [-2, -2, 4, -6, 2],\n [-2, 3, 5, -6, -5],\n [-1, 2, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 2, 0, 3, -2],\n [3, 1, 0, 2, 1],\n [2, -4, 2, -2, -2],\n [-3, -4, 3, -4, 5],\n [-4, 1, -1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -6, -4, -6, 4],\n [-6, -5, 4, 3, 6],\n [-6, 3, -4, -3, 1],\n [-4, -2, -2, -6, 0],\n [-3, 5, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 2, 6, 5, -4],\n [3, -6, -2, -6, 4],\n [2, 3, -3, 6, 6],\n [-1, 3, -1, -4, -6],\n [4, -5, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, -5, -2, -6],\n [4, 2, 5, 3, 2],\n [5, 2, 0, -4, 2],\n [6, -5, 2, 3, 6],\n [-5, -2, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 0, 1, 0, -5],\n [5, 5, -6, 6, 4],\n [1, -6, -4, 3, 1],\n [-3, 0, -6, -4, -1],\n [-3, -5, -5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -1, -4, 6, 1],\n [1, -4, -5, -4, 2],\n [2, 5, 4, -3, 6],\n [3, 6, -3, -6, 1],\n [2, -1, 1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 2, -4, 6, 4],\n [-1, -3, 1, 6, 6],\n [2, 3, 2, 5, 3],\n [-2, -6, 1, 3, -2],\n [-6, -4, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 6, -1, 0, -6],\n [1, 6, 2, -2, 4],\n [-1, -6, -5, -1, -1],\n [5, -2, 3, -6, 2],\n [-4, -1, -5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -5, -1, 3, 2],\n [-6, -6, 5, -6, 2],\n [-2, 3, -4, -4, 6],\n [3, 6, 0, -4, 3],\n [2, 5, 1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 5, -5, 5, 4],\n [-2, 5, -2, 2, 2],\n [0, 2, 6, -5, 3],\n [1, 4, 2, -1, -3],\n [5, -6, -3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -2, 0, -6, 2],\n [-4, -6, -2, 5, 0],\n [-4, -5, -2, -2, 4],\n [-4, -6, 2, -5, 5],\n [-6, -3, -3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -5, 3, -2, -3],\n [3, -4, 0, 2, 6],\n [0, -4, 2, 5, 4],\n [-5, 4, 3, -6, 5],\n [-1, -4, -2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 4, 5, -3, 0],\n [-4, 6, -6, 2, -1],\n [-3, -5, -2, -1, 2],\n [-3, 0, -2, 5, -3],\n [-4, 3, 2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 2, -1, -6, -3],\n [-6, -6, -2, 2, 5],\n [-3, 6, -5, 3, 1],\n [2, 6, 2, -4, 6],\n [1, 3, 5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 4, -6, -6, -1],\n [4, -6, 1, -3, -4],\n [2, 3, 2, 2, 4],\n [0, -1, 6, 1, 0],\n [2, -3, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 6, 4, -6, 3],\n [4, -6, 4, 4, 1],\n [3, 4, 2, -6, -1],\n [-3, -1, 1, 0, 4],\n [-4, -1, 1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 5, -1, 1, 2],\n [-4, -4, 0, 1, -3],\n [0, 0, 0, -5, 1],\n [1, 5, 4, -2, -2],\n [-1, -4, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -2, -1, 3, 6],\n [2, -4, -3, -6, 4],\n [5, 3, 0, 0, 2],\n [-6, 1, -2, 3, 2],\n [0, 6, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 6, -4, 3, -6],\n [-5, -1, 3, 1, -4],\n [1, -6, 0, 2, 3],\n [4, 2, 5, -3, 0],\n [2, 4, -6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -5, -2, 4, -1],\n [5, 5, -1, 5, 3],\n [6, -2, 0, 6, -1],\n [2, -2, 4, 3, 4],\n [1, 6, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 3, 1, 1, -1],\n [1, -2, 4, 5, -4],\n [6, 4, -4, -6, -5],\n [4, 2, 4, -4, 3],\n [-6, 3, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -6, -2, 4, 2],\n [-2, 1, 6, -3, 1],\n [5, -1, 4, 3, 0],\n [-4, 4, -5, -4, -3],\n [-2, -3, -4, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 0, 1, -6, 0],\n [-6, -5, -6, 3, 3],\n [-3, 3, 5, 1, -5],\n [-2, -1, -3, -5, -2],\n [5, -6, 3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 5, 2, -1, 5],\n [-3, 1, 6, -2, 4],\n [3, 5, 4, 1, -2],\n [0, -3, -1, -4, -4],\n [0, 6, -1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -2, 6, 4, 5],\n [0, 6, 5, 1, -5],\n [-1, -6, -5, -2, 0],\n [5, 2, -2, 3, 5],\n [4, 0, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 5, -3, 6, 1],\n [-2, 1, 5, 5, 5],\n [-2, 5, -4, 4, 5],\n [-3, -2, -2, 3, 1],\n [-5, -2, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -2, 0, 0, 5],\n [6, -4, -3, 5, -6],\n [-2, 3, 5, -3, -6],\n [-3, -6, -2, 1, -6],\n [-1, 0, -1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -2, 1, -3, 1],\n [-6, -4, -1, -3, -5],\n [-6, 5, -5, 5, 1],\n [-3, -5, 6, 2, -4],\n [0, 4, 1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -3, 4, 3, -5],\n [2, 6, 2, -1, -4],\n [4, 5, 2, 1, 6],\n [6, 3, -4, -6, 3],\n [6, 4, -6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 6, -3, 0, -3],\n [-6, -1, -4, 6, 1],\n [-4, -2, 4, 4, 2],\n [-2, -3, -1, -4, 1],\n [3, 0, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, 1, 2, -6],\n [4, 6, 1, 0, 1],\n [-2, -5, -1, 2, 2],\n [5, 0, -1, 6, 0],\n [2, -1, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, 6, 2, 6],\n [-5, 0, 1, -3, -4],\n [2, 5, 4, 1, 2],\n [1, 2, 4, 5, 2],\n [-3, -1, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 1, 1, -4, -5],\n [3, -5, 1, 5, 0],\n [-5, 6, -3, 4, -4],\n [2, -5, -1, 5, -2],\n [2, 5, -1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -3, 5, -3, -6],\n [3, -6, -5, -2, 0],\n [2, -1, -6, 3, 4],\n [2, -3, 0, -2, 1],\n [-5, -5, 1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -5, -4, 2, 2],\n [5, -2, -2, -5, 1],\n [0, -2, -5, -6, 2],\n [-1, -2, 5, 3, 1],\n [1, 2, 0, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 3, 4, -5, -5],\n [4, 5, 2, 1, -2],\n [-2, -4, -4, -1, 2],\n [6, 5, 6, 4, 3],\n [-2, 6, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 2, 3, 6, 0],\n [-1, 1, 1, -6, -6],\n [1, -3, -2, 0, 4],\n [-5, 2, -5, -1, 3],\n [-1, -3, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 1, 1, 2, -2],\n [-6, 2, -5, -4, -3],\n [5, 6, 3, 1, -2],\n [2, 4, 1, 5, 2],\n [0, -4, -1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -4, 3, 3, -3],\n [6, -2, 3, -3, 2],\n [1, -4, -2, -1, 4],\n [-3, -2, -2, -2, 6],\n [1, -1, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, -3, -3, 1],\n [-5, 6, 4, 2, -5],\n [-3, 1, -2, -2, 0],\n [2, -5, 6, -3, -3],\n [-4, 6, -3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -4, 6, 0, 4],\n [2, -3, 0, 6, 4],\n [4, 2, -5, -6, -1],\n [-5, -6, -1, 0, -6],\n [-4, 6, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -2, -5, -1, -4],\n [-4, 0, 3, 1, 4],\n [-3, -4, 4, 1, 5],\n [-5, 3, 2, 0, -2],\n [0, -1, 5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 4, -1, 5, 2],\n [2, 1, -3, -1, 6],\n [2, 0, -6, 0, 0],\n [0, -6, 3, -6, 4],\n [-5, -6, 0, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 3, -5, -4, -1],\n [-1, -6, -1, 1, 1],\n [6, 1, -4, 4, -1],\n [-4, -5, -2, -6, 1],\n [-3, 0, 0, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 1, -5, 0, 3],\n [-2, -4, -5, -1, -4],\n [4, -6, 0, 0, -1],\n [-6, -3, -5, -2, -2],\n [6, -2, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 5, 0, -6, 3],\n [0, -5, 3, 4, -5],\n [6, 6, -3, -2, -5],\n [2, 6, 2, 1, 4],\n [2, -1, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -2, 2, -5, 1],\n [4, 1, -3, 1, 2],\n [5, -6, 4, 4, 0],\n [4, 0, 5, 1, -4],\n [4, -3, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 5, 6, -5, 0],\n [-2, -4, 3, -3, 5],\n [-3, 5, 6, 2, -4],\n [-6, 3, -2, -6, 6],\n [3, 2, -1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, -5, 0, 0],\n [-4, 5, 3, 3, -5],\n [-2, -6, 5, 0, 3],\n [-2, -4, 3, -2, 1],\n [4, 2, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 2, -4, -1, 5],\n [-3, 0, 6, 6, 1],\n [4, 3, -4, 0, -4],\n [-4, 6, -3, -2, 4],\n [1, 6, 1, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -6, 6, 1, -6],\n [1, 1, -4, 5, -2],\n [4, -5, 5, 5, 0],\n [6, -4, 0, 6, 3],\n [-1, 1, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, 1, -5, -6],\n [4, -4, 6, -4, 4],\n [3, -1, -6, -1, 6],\n [5, -2, -3, 0, 3],\n [-3, 1, 5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 6, 5, -3, 4],\n [-3, 1, 2, 3, 5],\n [0, 1, 3, -1, -4],\n [-2, -4, 5, 6, 4],\n [-4, 3, 5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 1, -3, 6, 3],\n [-2, 6, 1, 1, 3],\n [1, 6, 6, 3, -1],\n [-2, -6, -3, -5, 3],\n [1, -3, 6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 4, -6, 5, 0],\n [5, 4, 0, -6, -3],\n [-3, -2, 2, -6, -1],\n [3, 5, 6, 2, -4],\n [-6, -2, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 6, 6, -1, 4],\n [-3, -6, 6, 3, 6],\n [-2, -5, 2, 6, 1],\n [-1, -2, -5, 5, 3],\n [0, -2, -6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -5, -6, -5, -2],\n [-1, -2, -6, 2, 0],\n [6, -2, -6, -3, -2],\n [-4, -2, 5, 6, -5],\n [3, 6, -6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 1, 4, -6, 3],\n [5, 5, 3, 2, -3],\n [-4, -6, -6, 5, -3],\n [5, 3, -5, 3, 5],\n [2, 1, -5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -2, 3, 4, -5],\n [2, -4, -2, 3, -3],\n [-5, -6, 5, 2, -4],\n [6, -3, -2, 6, 4],\n [5, -1, -1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 5, 3, 5, -4],\n [5, -1, -2, -5, 4],\n [3, 6, -5, -3, -2],\n [5, 5, 6, -3, 6],\n [-5, -2, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, 2, 1, -2],\n [5, -3, 6, 1, 6],\n [2, -4, 5, -2, -1],\n [-4, 5, -1, 1, -4],\n [1, 1, -3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, -4, 5, -6],\n [-5, 5, -2, 0, -1],\n [6, -2, 5, -3, -2],\n [0, 5, 1, 6, -4],\n [1, 2, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 4, -6, 6, 0],\n [3, 2, 5, 1, -6],\n [4, 5, 0, 0, 1],\n [-6, 4, 3, 1, -5],\n [-6, -1, 3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 4, 0, 2, -1],\n [-1, 6, 3, 3, -5],\n [6, 3, 1, -5, 2],\n [3, 1, 1, 3, -5],\n [-6, 6, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -3, -5, 1, -3],\n [-3, 3, 6, 0, 0],\n [5, 1, -5, 2, 0],\n [-2, 6, 2, -3, 6],\n [3, -1, -3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 4, 2, -3, -1],\n [5, 1, 3, 3, 3],\n [2, 5, -2, 0, -2],\n [0, 4, -5, -1, -2],\n [-5, 2, 2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 6, 5, 5, -2],\n [-3, 1, -1, 3, -2],\n [1, 3, -4, 6, -5],\n [5, 2, -2, -5, 1],\n [-2, -2, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, -5, 3, 6],\n [-1, 2, 4, -4, -6],\n [-4, 1, 0, -6, 1],\n [-5, -6, -2, -6, 1],\n [6, 5, 0, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 3, 1, -2, -4],\n [-5, 0, -4, 4, -5],\n [-5, -2, -1, -5, 5],\n [2, -5, -5, -5, 2],\n [-4, -6, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -3, -5, 4, 1],\n [4, 6, -4, -5, 1],\n [-1, -2, 4, 0, -2],\n [-5, 3, 2, -6, -5],\n [-1, -3, -6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -1, -3, 5, 5],\n [3, -3, 0, 5, 5],\n [-4, -2, -3, -4, 6],\n [1, 2, -6, 0, 3],\n [-4, 5, -4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, 6, 1, 5],\n [-1, -5, 0, -2, 4],\n [-3, -3, -2, -2, -5],\n [1, 6, 1, -4, -6],\n [2, -2, -2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 3, 6, -6, -5],\n [5, -1, 0, -5, 4],\n [4, 0, 1, 6, -3],\n [-6, -5, 5, -1, 0],\n [0, 4, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 0, 6, 4, 5],\n [3, -1, -1, -5, 0],\n [-4, 4, -6, 1, 1],\n [-3, -2, -5, -1, -3],\n [-5, 2, 5, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -4, 1, -5, -6],\n [-2, 6, 3, -4, -3],\n [1, 0, 3, 4, -4],\n [-2, -4, -2, -3, 3],\n [3, 2, -5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 0, 2, 5, 5],\n [3, 5, 6, 1, 0],\n [-4, -3, -4, -2, -4],\n [6, -6, 6, 4, -1],\n [1, -5, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -3, 3, 3, -5],\n [6, 1, -1, 6, 4],\n [6, 4, 3, 4, -2],\n [-3, -3, 2, 4, 3],\n [-3, -1, -5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 6, -5, -5, -1],\n [-1, -1, -6, -4, 3],\n [-4, 4, 1, -5, -2],\n [3, -1, 0, -1, -6],\n [2, 1, 4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -3, -4, -6, 5],\n [-4, -6, -3, 0, 3],\n [0, 1, -1, 6, 3],\n [2, 2, 0, 5, 6],\n [2, -2, -3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, -3, 1, -1],\n [3, -6, -6, -2, 1],\n [5, 5, 0, 5, -5],\n [-6, 3, -3, 6, -1],\n [1, -4, 6, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -5, -5, 1, 4],\n [1, -3, 5, 5, 3],\n [1, -1, 4, -1, 0],\n [2, 5, -3, 6, -5],\n [2, -2, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 6, -1, 3, -1],\n [2, -4, -3, -1, -1],\n [4, 5, 2, 5, -4],\n [6, 1, -3, 5, -4],\n [5, 4, -3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -3, -6, 5, 6],\n [6, -3, -1, -2, 4],\n [6, 6, -2, 1, 0],\n [3, 1, -5, 1, 5],\n [5, 2, 1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 3, 1, 6, -6],\n [-1, -4, -5, -6, -2],\n [4, -3, 1, -4, 0],\n [-1, 0, 6, -5, 4],\n [-4, 4, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 2, 0, -5, -1],\n [-2, 5, 1, 1, -4],\n [0, 3, 1, 0, 6],\n [1, 4, 2, 4, -4],\n [3, -1, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, -4, 6, 1],\n [5, 2, -5, 5, 6],\n [6, -4, 4, 6, -4],\n [-4, -6, -2, -1, -4],\n [-6, -2, -3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -3, -2, 5, 6],\n [6, -2, -5, 1, 6],\n [-6, 3, 2, 3, -3],\n [0, 3, 5, 0, 1],\n [-6, 0, -5, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, 2, 3, 0],\n [4, 5, 2, 0, 1],\n [5, -6, -4, 0, 1],\n [5, 4, 1, 5, -4],\n [0, 5, 0, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 4, 0, -6, 2],\n [-4, -3, -4, 1, 4],\n [0, 4, 5, -6, -3],\n [0, 5, 0, 0, -5],\n [-6, 5, -1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, -2, 0, 0],\n [-3, 2, 6, 0, -1],\n [-5, 5, -5, -5, -6],\n [5, 5, -3, 1, 1],\n [-1, -1, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 5, -6, 1, -1],\n [-2, -6, 3, -3, 3],\n [0, -3, -6, -5, -3],\n [1, -1, 1, -2, -1],\n [4, -4, 3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, 5, 0, -3],\n [-1, -4, -1, -6, -5],\n [-3, -3, 0, 0, 3],\n [-1, -4, -3, -5, 5],\n [-5, -6, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 1, -6, -3, 4],\n [6, -1, 4, 3, -5],\n [-2, 5, -4, 3, 1],\n [6, 1, 2, -5, -5],\n [-4, -2, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -2, -6, 0, 3],\n [-6, -5, -1, 0, -2],\n [1, 6, -1, -2, 0],\n [-6, 1, -1, 1, -4],\n [0, -2, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -1, 3, -2, -2],\n [-4, -5, 0, -6, 3],\n [-3, 4, 0, 1, 3],\n [0, 1, -3, 6, -4],\n [-2, 4, 3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -2, 1, -6, -2],\n [0, 1, 1, -1, -1],\n [-6, -1, -2, 1, -4],\n [-1, -2, 2, -5, 4],\n [-4, 6, 0, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 0, -1, -3, 4],\n [3, 0, 0, 5, 0],\n [-3, -1, -2, 2, -5],\n [-5, -2, -2, -1, 1],\n [-2, -6, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -4, 6, -3, 6],\n [4, 1, 3, -6, 6],\n [5, 3, 5, 6, 3],\n [0, 3, 1, 2, 0],\n [6, -4, -5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -5, 5, 3, 0],\n [4, -5, 4, -4, 6],\n [-2, 6, -4, 3, 3],\n [0, 1, 0, 5, 0],\n [4, -2, 1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, 4, -1, -2],\n [-5, -3, -2, 0, 6],\n [2, 3, 6, 3, -1],\n [-1, 5, 4, 3, -1],\n [0, -5, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -3, -5, 2, 0],\n [6, -4, -3, -3, -1],\n [0, 3, 3, 5, -3],\n [4, -5, 5, 3, -5],\n [3, 0, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -6, -3, -2, 6],\n [0, 5, 1, -1, 6],\n [-6, 2, 5, 1, -4],\n [5, 0, 0, 6, -3],\n [5, 5, 6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -5, 1, 3, -4],\n [-1, -6, 5, 4, -2],\n [2, 2, 5, 5, 5],\n [-3, -5, 6, -4, 1],\n [-6, -2, 6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -3, -1, 5, 1],\n [3, -6, -2, 5, 1],\n [-5, 5, -6, -2, -1],\n [6, 3, -6, -4, 1],\n [-2, 1, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 6, -5, -5, 5],\n [2, 5, 5, -5, 3],\n [6, -3, 6, 1, -4],\n [-4, 0, 5, 3, -1],\n [3, -3, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 6, -1, 1, -4],\n [-1, 2, -5, 6, -4],\n [1, 0, 1, 5, 3],\n [3, 2, 1, -2, 6],\n [-2, 6, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 0, -4, 6, -1],\n [4, 0, 5, -5, -5],\n [-3, 5, -5, 3, -6],\n [-5, -2, 3, 0, 6],\n [3, -5, 5, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 6, 5, 0, 0],\n [-2, 3, 1, 5, 2],\n [-1, 0, 4, 0, 2],\n [1, -1, -4, -5, -6],\n [5, -5, -5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -6, -6, -2, -6],\n [1, -3, -6, 1, -5],\n [1, 4, 1, 3, 6],\n [-5, -1, 3, -3, 6],\n [4, -1, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 2, 0, -3, -4],\n [-3, -2, 3, 0, 6],\n [-4, -2, -6, -2, 3],\n [-2, -5, 2, 5, -4],\n [-4, -2, -1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -2, -1, -1, -5],\n [-2, -5, -4, 6, -3],\n [3, 4, 5, -3, -3],\n [-1, -3, 5, 4, -3],\n [-5, -3, -1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 0, -5, -6, -5],\n [-3, 2, -2, 0, 1],\n [-2, 0, -3, -2, 2],\n [3, -2, -5, 5, -1],\n [4, 3, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -1, 6, 6, 5],\n [5, -2, -1, 2, -3],\n [-2, -4, 1, 2, 2],\n [-3, -1, 0, -5, -2],\n [-4, -6, 1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -3, 6, -5, -5],\n [-3, 0, 1, -3, -5],\n [-5, 2, 5, -4, -5],\n [-4, 1, 3, -5, -3],\n [5, -3, 2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 4, -6, 1, -4],\n [-4, 2, -6, -6, 5],\n [6, 5, -4, -3, 3],\n [-2, -3, 0, -6, 5],\n [-2, 1, 5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 3, -4, 6, -4],\n [-6, -2, -1, -3, -3],\n [-4, 3, 4, 1, 0],\n [-4, 1, 4, -1, 4],\n [-5, 4, 6, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 1, 0, 1, 4],\n [1, 5, -4, 1, -5],\n [-5, -1, 3, -2, -6],\n [-2, 4, 2, -6, 3],\n [-1, -3, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -3, -2, 3, -2],\n [-6, 1, 4, 3, 1],\n [-5, 6, -2, 5, -6],\n [2, 3, -5, -4, -6],\n [2, 2, -5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 1, -5, -3, 1],\n [0, -3, -1, -3, -5],\n [-2, -3, -2, 5, 0],\n [3, 2, -5, -6, 6],\n [2, -2, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, -4, 2, -6],\n [2, -4, 2, 2, -1],\n [3, 1, 5, -6, 4],\n [-5, -1, 5, -5, 3],\n [5, 0, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 6, 0, -1, -6],\n [-1, -3, -4, -2, 3],\n [2, 4, -5, 3, 5],\n [-5, -3, -6, -5, -4],\n [-6, 1, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 0, 2, 2, 6],\n [2, 3, -3, 3, -6],\n [0, -6, -5, -3, -5],\n [4, 6, 0, 5, 3],\n [6, 0, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 5, -5, -3, -6],\n [3, 4, -3, 6, -4],\n [3, -1, -5, 2, 1],\n [1, -2, 0, -2, -1],\n [5, -6, -1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -1, 4, 6, -2],\n [3, -1, 5, -2, 4],\n [-4, 0, 6, 3, -4],\n [-2, -3, -4, -6, 4],\n [-2, -4, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -6, -4, -6, -4],\n [4, -5, 2, -4, -5],\n [-5, -4, -6, -2, -5],\n [5, -3, 2, 2, -1],\n [4, 5, -3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 5, -4, 2, 0],\n [3, -6, -3, -3, -6],\n [4, 3, -6, 3, 0],\n [0, -1, -3, 2, 5],\n [-4, -6, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -5, 1, 2, 4],\n [-3, -6, -4, 4, -6],\n [4, -4, 3, 6, -3],\n [6, -5, 4, -1, 1],\n [4, -1, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -6, 6, 4, 5],\n [-4, 2, 1, 3, -6],\n [3, 1, -1, 0, 2],\n [-1, 5, 2, -2, 1],\n [0, 5, 0, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 6, 2, 1, -3],\n [2, -5, 6, -2, 2],\n [5, 0, 0, -1, 3],\n [6, -2, 5, 6, 2],\n [-1, -3, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, -2, 3, 3],\n [2, 6, -2, 1, 3],\n [0, 5, 0, 2, 3],\n [6, 4, -3, -1, 0],\n [-6, -6, 4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 1, -3, 0, -3],\n [-1, 1, -3, -2, -4],\n [-4, 2, 1, -6, 2],\n [3, -3, 0, 2, 1],\n [5, 2, 2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -2, -5, 3, -3],\n [4, 4, 5, -4, -3],\n [-4, 2, -4, -2, -1],\n [-3, 6, -4, -6, 3],\n [4, -4, -5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -1, -2, 5, 6],\n [5, -6, -6, -2, 0],\n [0, -4, 2, 2, -1],\n [-5, -6, 4, 4, -3],\n [3, -6, -6, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 1, 1, -1, -4],\n [-6, 1, 4, 5, 1],\n [3, 1, -2, 6, -6],\n [1, 2, -2, 1, 1],\n [5, 3, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, 5, 1, 5],\n [5, 6, 2, -2, 0],\n [3, 4, 2, 6, 0],\n [1, 2, -1, -2, -4],\n [-3, 4, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -4, 5, 1, 0],\n [-4, -3, -6, 6, 5],\n [0, -2, 2, -2, 4],\n [-3, 1, -2, -1, 1],\n [-4, 3, 2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 2, 3, -4, 6],\n [-4, -3, 4, -2, 5],\n [6, 2, -1, 6, 1],\n [-1, -4, -6, -6, 4],\n [0, 6, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, 6, -1, -4],\n [-3, 0, 3, 6, 1],\n [-2, 0, -6, 3, 3],\n [-1, 4, 4, -3, -5],\n [3, -4, -6, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, 5, -3, 2],\n [2, 2, 0, 3, -6],\n [6, 5, -5, 4, -4],\n [6, -2, -2, -1, 3],\n [1, -5, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 4, 0, 5, 5],\n [-2, -3, -4, 1, 0],\n [-6, -4, 0, 3, -1],\n [3, 0, 1, 0, -2],\n [-2, -6, 4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -2, 1, 4, 2],\n [4, -4, -6, -3, -3],\n [-1, -6, 6, 6, 6],\n [3, -3, -3, -2, -4],\n [-2, -5, -2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 1, 1, -4, -5],\n [-5, -4, -2, -2, 0],\n [1, 1, -6, 6, -2],\n [5, 1, 1, -3, 3],\n [-1, 2, -2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 5, -3, 2, 4],\n [-1, 4, 0, -6, 1],\n [-4, -3, 1, 6, -6],\n [-1, 5, 4, 0, 1],\n [1, -3, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 0, -2, 4, -6],\n [5, 0, -2, 1, -4],\n [0, -1, -3, 5, 0],\n [-3, 5, 5, 2, -5],\n [-2, 6, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 6, -2, 4, -5],\n [2, 2, -5, 6, 4],\n [-6, 1, -5, 2, -5],\n [6, 4, -3, 4, 0],\n [-5, 2, -4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 4, -1, 1, 1],\n [-5, -3, -1, -2, -1],\n [-1, -4, 5, 4, -5],\n [5, -3, -1, -3, -1],\n [-3, -3, 3, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 0, 4, 6, -4],\n [5, -4, -2, -2, 3],\n [1, -5, 1, 5, -6],\n [-2, 2, -5, 3, -1],\n [6, 0, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -5, 4, -3, -2],\n [1, 1, -4, 5, -5],\n [0, -1, -5, -5, 2],\n [3, 5, -1, 0, -3],\n [2, -6, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 6, -1, -3, 2],\n [-1, 6, 1, 5, 1],\n [2, 6, 1, 6, -1],\n [4, -4, -1, -4, 4],\n [1, -3, -1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -2, 5, -3, 3],\n [1, -4, -6, 5, 2],\n [-5, -3, -6, -2, -1],\n [0, -4, 2, 0, -6],\n [4, 2, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -5, 0, -3, -1],\n [-3, -5, -2, -3, 0],\n [3, 3, -1, 0, 3],\n [1, 1, -4, -1, -3],\n [2, 0, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 3, 3, -4, -2],\n [-1, 6, 3, 6, 4],\n [0, 0, 2, -4, 5],\n [5, -3, 5, -2, 1],\n [1, -1, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -3, -3, 2, -1],\n [2, 0, -1, 1, -4],\n [6, 3, -2, -4, -6],\n [-4, 5, -3, -3, 1],\n [1, 5, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 3, 3, 3, -6],\n [-1, -6, -3, -2, -3],\n [-6, -5, 6, 0, 4],\n [-1, -3, 5, -4, -3],\n [2, 3, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 6, -4, -3, -3],\n [6, 0, 2, 2, 2],\n [1, -6, 2, 3, 5],\n [3, -6, 2, -2, -4],\n [-5, 5, -6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 6, 6, 4, -1],\n [-2, -4, 2, -3, 3],\n [-2, -3, 3, 4, -2],\n [4, -6, 3, -2, -4],\n [5, 4, -6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 0, -6, -1, 2],\n [2, -5, -5, 4, -1],\n [1, 3, 0, 3, -2],\n [2, 2, -3, -2, -2],\n [-5, 5, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -3, 5, -1, 0],\n [0, 1, 0, -3, 2],\n [5, 6, -4, 4, 3],\n [4, 3, -1, 5, 1],\n [-2, 4, 6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -1, 4, 1, 1],\n [-4, 5, -3, 3, -5],\n [4, 4, -2, -5, 6],\n [-1, -6, 5, -3, -2],\n [-2, -6, 0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 2, -4, -1, 2],\n [-5, 2, -5, -6, -6],\n [4, 6, -6, -4, 6],\n [-2, 1, 4, 1, -6],\n [-2, 3, 6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -4, -3, 1, 0],\n [-6, -6, 6, 4, 0],\n [-2, -3, -3, 1, -5],\n [5, 6, -2, -2, 2],\n [-6, -3, -1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 6, -6, 5, 6],\n [1, 6, -4, 2, 2],\n [-4, -4, -1, 5, 2],\n [0, -6, 6, 6, -1],\n [-4, -5, 5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 5, 5, 6, -6],\n [3, 6, -2, 1, 5],\n [3, -4, 6, 2, 2],\n [6, 0, 6, 2, 5],\n [0, 5, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -5, -5, -1, 0],\n [-1, -2, 2, -3, -4],\n [0, 0, -5, -5, 6],\n [-1, 0, -4, -4, -6],\n [-1, -3, 0, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, -3, 3, -4],\n [-2, 5, -2, -6, 6],\n [5, -2, -2, -4, 4],\n [-2, 0, -5, -1, -3],\n [-4, 0, 1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, 0, 2, 4],\n [-1, 5, 0, 2, 1],\n [0, 0, 4, 2, -1],\n [2, 1, 0, 1, 3],\n [-3, 5, -4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 1, 4, 4, 3],\n [-6, 4, -6, -2, -1],\n [0, 3, 0, 0, 3],\n [6, 3, -2, -6, -1],\n [-3, 3, -5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 2, 5, 3, 2],\n [-1, -1, 2, 3, 6],\n [2, 5, 1, 2, 6],\n [-1, -1, 0, -2, -4],\n [1, -1, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 3, 1, -2, -1],\n [-6, -1, -6, -1, -2],\n [5, -5, -3, -2, 2],\n [0, -2, 6, 4, 4],\n [-1, 0, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 4, -2, 0, 1],\n [-1, -4, 3, 2, 3],\n [-1, 0, -6, 2, 1],\n [-4, 6, -6, 0, -4],\n [-5, 5, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 5, -6, 5, -3],\n [-6, 2, 1, 5, 5],\n [-1, -2, 5, 2, -2],\n [6, -2, 2, 1, 4],\n [3, -6, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -2, -4, -4, 3],\n [5, -4, -5, -5, 5],\n [-2, -5, 4, -3, 5],\n [-5, 1, 1, -2, -2],\n [-2, -4, 6, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -1, -3, 6, 2],\n [4, 3, -4, 5, 0],\n [-1, -1, -4, -3, -5],\n [-2, 4, -6, -6, -2],\n [1, 4, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -6, 1, -4, 4],\n [-2, -3, -1, -2, 0],\n [6, 5, 6, 4, 2],\n [2, -5, -6, 6, 1],\n [-6, 2, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, -5, 1, -2],\n [-2, -2, 5, 2, -4],\n [1, 4, -2, 6, 2],\n [-6, 4, -6, -3, 0],\n [-6, -5, 2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -1, 5, 4, 2],\n [-5, -2, -1, -4, 5],\n [-2, 0, 3, 4, 0],\n [4, 4, 1, 1, 0],\n [4, 2, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -6, -4, -6, -2],\n [-1, -3, -6, -1, 0],\n [-6, 4, -1, -5, 6],\n [5, -4, -3, 2, 0],\n [4, 6, 5, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 1, -3, -4, 0],\n [-4, 4, 1, 0, -2],\n [-3, -6, 2, 0, 1],\n [-6, -3, 4, 3, -1],\n [-2, -2, 4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -4, 0, 4, 1],\n [6, -3, 5, 1, 2],\n [-1, -2, -5, -5, -2],\n [-1, -2, 3, 1, 0],\n [-3, -3, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -3, 4, 1, -1],\n [1, 2, 6, 2, 4],\n [-5, 6, -2, 4, -5],\n [5, -5, 1, 2, 4],\n [-1, 5, 1, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 4, 1, -2, -4],\n [-1, -4, -6, 6, 3],\n [-2, 0, -2, 5, 4],\n [-3, 5, -6, -4, 0],\n [-5, -1, 5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 3, 4, -2, -5],\n [1, 3, 4, -5, 2],\n [2, -4, 3, 1, 1],\n [1, 5, -1, 4, 6],\n [0, 5, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 2, 0, 2, 5],\n [2, 1, -2, -3, -3],\n [-5, -5, 6, 5, 3],\n [-3, -2, 2, -6, 0],\n [4, -4, 5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, -1, -2, -2],\n [6, -6, 4, -4, 0],\n [1, 4, 0, 0, 4],\n [-6, -5, 6, -1, -2],\n [0, 1, 1, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 3, 6, -4, 6],\n [3, -2, 5, -6, 0],\n [5, -5, -3, 0, 5],\n [-4, 4, 0, 1, 2],\n [4, 2, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 3, 0, -6, -6],\n [0, 4, -4, -5, 2],\n [-5, 1, -6, -3, 0],\n [-3, -6, -2, -5, -1],\n [4, 5, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 0, -3, 6, 0],\n [1, -5, -2, 1, 6],\n [-6, 5, -1, -3, 3],\n [3, 6, -2, -1, 3],\n [6, 4, 6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 0, -4, 4, -2],\n [2, -1, 6, -4, -4],\n [-1, -4, 6, -3, -6],\n [3, 1, 1, -3, 5],\n [4, 5, -1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 5, -5, 4, 2],\n [2, 4, 3, -6, -5],\n [-3, 4, 2, 2, -6],\n [1, 5, 2, 6, -6],\n [0, -2, 2, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 5, -3, 5, -3],\n [4, -4, -5, 0, 0],\n [1, -2, -5, 5, -4],\n [2, -3, 2, 4, -2],\n [5, 3, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 5, -1, -3, 2],\n [-4, 0, 1, 2, 2],\n [2, -3, 1, -1, 0],\n [6, -3, 3, 5, 4],\n [4, 2, 6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 4, 0, 1, 1],\n [6, 0, -1, -3, 0],\n [5, -5, -4, -1, 1],\n [-3, 0, -5, 2, -1],\n [-5, 0, 2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -4, 2, -1, -6],\n [-1, 6, 6, -1, -6],\n [-6, 1, 0, 4, 6],\n [5, -6, -3, -2, -6],\n [2, -4, 4, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 6, -6, -2, 3],\n [5, 1, 0, 3, -1],\n [-4, 2, 2, -1, 3],\n [-2, -2, 4, 2, -6],\n [-1, -6, -1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -5, 5, 2, -2],\n [3, 5, 6, 1, -3],\n [5, 5, -3, -3, 1],\n [-6, 4, -4, 4, -3],\n [-6, 1, -2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 4, -5, -2, -1],\n [2, -1, -5, -5, 0],\n [-3, -3, -3, 6, -6],\n [-3, 5, 0, 6, -5],\n [2, 0, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 1, -1, -4, -6],\n [4, 3, -1, 0, 3],\n [-2, 3, -6, 4, 5],\n [-3, 3, 5, -2, 5],\n [-3, -4, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -2, 2, -3, 2],\n [2, 5, 5, 2, -5],\n [1, -4, 4, -3, 2],\n [-4, 2, 4, 2, 0],\n [5, 2, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -6, 3, -4, -3],\n [1, 0, 2, 6, 6],\n [-6, -5, 5, 3, 4],\n [6, -3, 1, 4, -3],\n [2, 1, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -6, 2, 0, -5],\n [0, 6, -6, 2, 4],\n [-6, 0, -5, 4, -6],\n [-3, 5, 5, -6, 6],\n [-5, 5, 6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 0, 1, 2, -4],\n [-2, 0, 0, 1, -5],\n [6, -1, -2, -4, -5],\n [4, 6, -2, 0, 0],\n [2, -3, 5, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 1, 4, 2, -1],\n [-2, 0, -5, -6, 3],\n [-5, -2, 4, 5, 5],\n [1, -6, 1, 0, -1],\n [-5, 5, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 4, -4, 6, 5],\n [-5, 3, -1, 5, -2],\n [5, -4, -6, 2, -5],\n [-3, 3, 6, -5, 5],\n [-6, 1, 1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -5, -3, -3, 0],\n [5, -5, 6, 3, 3],\n [-6, 4, -2, -4, -5],\n [-5, -2, 6, 3, -2],\n [6, -2, 2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 3, -1, 1, 2],\n [-2, 4, 3, 6, -4],\n [2, -3, 6, 6, -2],\n [-1, 5, 4, -6, 0],\n [-1, 5, 2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 0, 3, 1, 5],\n [1, -4, -6, -2, 3],\n [2, 5, -6, -2, -3],\n [-6, -1, 5, 1, -5],\n [-1, -5, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 3, -2, 5, 2],\n [-6, -1, -1, 3, 4],\n [4, 3, -5, 0, 4],\n [1, 6, -6, 6, 5],\n [2, 1, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, -1, -5, -2],\n [-6, 2, -3, -3, 4],\n [4, 3, 6, -4, -4],\n [-1, -3, 6, -5, -4],\n [-2, 3, -5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -5, -6, 1, 3],\n [-6, 0, 2, -5, -3],\n [-3, 4, 2, -4, -1],\n [3, -6, 0, 3, 5],\n [2, -5, -1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 4, -2, -3, -5],\n [-2, 0, 3, 6, 0],\n [0, 3, 3, 1, 4],\n [-3, 0, -4, 5, 5],\n [5, -4, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -4, 2, 3, -5],\n [1, -2, 4, 6, -1],\n [2, 0, 2, -6, 6],\n [-4, -5, -6, -6, -3],\n [-6, 3, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 5, 2, 5, -5],\n [5, -4, 0, -5, 6],\n [-1, -4, -5, -6, -6],\n [2, 4, 4, 6, -5],\n [5, 5, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 0, -5, 6, -6],\n [6, -3, -6, 5, 0],\n [-6, -1, -2, -5, 3],\n [5, 2, 2, 4, 6],\n [0, -2, 1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, -3, 1, -4],\n [1, 0, 0, 1, -6],\n [4, 3, -3, -6, -5],\n [5, 5, -6, -4, -6],\n [-2, 5, 4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 6, -6, 2, -6],\n [3, 6, 4, 5, -6],\n [2, -3, -1, -2, -4],\n [-2, 6, 0, 0, -5],\n [-3, 5, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 3, -2, 1, 1],\n [5, 5, -4, -6, -1],\n [4, -6, -4, -6, 4],\n [0, 1, -4, 3, -3],\n [6, -6, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 2, -5, 3, 3],\n [0, -6, 3, 1, -1],\n [1, 3, 3, 3, -3],\n [0, 5, -4, 6, -6],\n [6, -4, 5, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -6, -3, -1, -6],\n [1, 5, -5, -4, 3],\n [-5, -3, -3, -2, 1],\n [-3, -6, 3, 1, -6],\n [1, 2, 6, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 5, 5, -5, -2],\n [-6, -1, 2, 2, -5],\n [-5, -3, 0, 4, 1],\n [0, -5, -4, -2, -4],\n [0, 5, -3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 1, 4, -3, -4],\n [-3, -3, 5, 6, 0],\n [5, 1, -4, 5, -3],\n [-4, -1, 2, 4, 1],\n [6, 3, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, -4, -3, -2],\n [6, -2, 0, -4, -6],\n [-1, -2, 0, 5, -1],\n [2, 3, 1, -6, -1],\n [0, -4, 5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -2, -6, 1, 3],\n [6, -3, -6, 6, 1],\n [-3, 4, -3, 6, -3],\n [6, 2, 3, 5, 3],\n [2, -4, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 2, 6, 3, 2],\n [5, -3, 3, 1, 3],\n [5, 3, 1, 3, -2],\n [5, 3, -4, -5, -5],\n [-1, 4, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 4, -4, -5, 6],\n [-4, -4, 5, -5, -5],\n [3, -2, 5, 0, 0],\n [5, 2, -1, -3, 0],\n [5, -4, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -5, 5, -3, -4],\n [0, -6, 4, 0, -2],\n [4, 2, 3, -1, 1],\n [-3, 4, 1, -2, -3],\n [-1, 2, -4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 0, -4, -6, 5],\n [2, -1, 6, 2, -5],\n [2, -5, -6, -4, -3],\n [-5, -1, 1, 5, -1],\n [-2, -2, 1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, -4, -4, -1],\n [-3, 2, 2, 2, -3],\n [2, -4, -6, -1, -1],\n [0, -6, 5, 6, -2],\n [3, 2, -1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 1, -6, -1, 2],\n [5, -5, 4, 4, -1],\n [0, 1, -4, -2, 4],\n [-1, 2, -3, -2, -1],\n [4, -1, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 4, 3, 6, -6],\n [5, 4, 3, 1, 0],\n [5, 0, 2, -5, 3],\n [4, -2, -6, -3, -5],\n [-4, 2, -6, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -3, -2, 3, -5],\n [1, -3, 2, -3, 5],\n [-4, 5, 1, -3, 2],\n [-3, 6, -4, 4, 4],\n [1, 4, 6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 0, -4, 3, 5],\n [3, 2, 2, 0, 1],\n [3, -6, -3, 2, 6],\n [4, -5, 0, 4, -6],\n [-3, -2, -1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 5, -3, 4, 0],\n [2, 3, -2, 6, -6],\n [1, -4, 0, -5, 2],\n [0, -2, 3, 0, 1],\n [1, 3, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, -3, 0, 0],\n [-2, 5, 0, -2, 0],\n [3, 2, -5, 0, 3],\n [0, 6, 4, -3, 6],\n [2, -1, -4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -3, 2, 4, -2],\n [5, 0, -4, 5, 2],\n [5, 3, 2, 3, -1],\n [2, 1, -5, -6, 2],\n [-3, 4, -3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -4, 6, -5, 1],\n [-1, 3, 1, 4, 6],\n [1, 5, -1, 6, -5],\n [-4, 4, 2, -1, -2],\n [3, -6, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 0, 3, -6, -4],\n [5, 5, 3, 2, -6],\n [2, 2, 6, 0, -5],\n [1, -5, 5, -5, 6],\n [2, -1, -6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -6, 0, 3, 0],\n [-3, 0, 5, 6, 5],\n [-5, -5, 1, 6, 1],\n [-3, -5, -4, -2, 2],\n [3, 3, 1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -3, 3, -2, 0],\n [5, 5, -5, 1, 6],\n [2, 3, 6, 0, -3],\n [4, 6, 2, 4, 0],\n [-6, -1, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -5, 5, 5, 1],\n [-1, -4, -6, -4, 4],\n [4, 6, 0, -2, 5],\n [-5, 0, 0, -5, 2],\n [2, -1, 1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, 5, 5, -2],\n [3, -5, 0, -6, 1],\n [5, -5, -2, 2, -6],\n [-6, -4, 1, 0, 5],\n [-3, -1, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 1, 0, 3, -2],\n [-4, -4, -6, 0, -1],\n [-4, -1, 2, -5, -2],\n [2, 6, 2, -4, -5],\n [-4, 3, 0, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 4, 5, 5, -5],\n [3, -6, -2, 5, -3],\n [-2, 3, 2, -5, 1],\n [-2, -2, -4, -4, -5],\n [-2, -3, -6, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 1, 0, 0, 0],\n [1, -2, 4, -5, -6],\n [3, 6, -2, -1, -6],\n [5, -3, -4, -6, 6],\n [-2, 5, 2, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -2, 4, 6, -6],\n [5, -2, -1, 2, 3],\n [5, 3, -3, -2, 5],\n [0, -2, 5, -5, 0],\n [-5, 3, -3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 1, 0, -4, 5],\n [-6, -3, 0, 3, -4],\n [1, 0, -2, -1, 1],\n [3, -3, -1, 4, -1],\n [5, -5, -5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 4, -1, -2, 6],\n [-6, -1, -5, 0, -6],\n [4, -2, -1, -6, -2],\n [-1, -3, -2, -1, -6],\n [0, -6, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 6, 2, 6, -3],\n [0, 2, 6, -3, 0],\n [2, 1, 4, 1, 4],\n [-2, 1, -6, 2, 1],\n [0, 4, -5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 2, -4, -6, -6],\n [5, -2, 2, -3, -4],\n [-6, 2, -3, 2, -4],\n [1, 6, -3, -1, -4],\n [-4, -4, 5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -4, 0, 3, -3],\n [-6, -6, 1, -1, 3],\n [4, -3, 3, -5, 2],\n [-1, -3, -3, -1, 0],\n [-4, 2, 3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -2, 6, 0, 2],\n [3, -6, 5, 1, 4],\n [1, -4, 4, -6, -2],\n [0, -2, -2, 1, 2],\n [2, -6, -3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -1, -1, 3, 4],\n [2, 0, 4, -1, -2],\n [-1, 0, 1, 4, -2],\n [-1, 2, 0, 5, 3],\n [3, 5, 6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 4, -1, 1, -4],\n [-1, 2, 0, -5, 4],\n [1, 2, -2, -6, 1],\n [0, -4, -3, 2, 2],\n [0, 4, -2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 5, -5, 4, 6],\n [-4, -1, 6, 1, 0],\n [-5, 0, 0, -1, -1],\n [3, -3, 3, -1, 3],\n [-3, 4, -5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 5, 2, 4, 0],\n [-4, -4, 0, 5, 4],\n [0, 4, -3, 3, 4],\n [-3, -2, 2, 4, 1],\n [-5, 4, -2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 5, 3, 6, 0],\n [4, 6, -6, -6, -4],\n [-1, 5, 2, 4, 2],\n [1, -3, 6, 2, -1],\n [-2, -1, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 2, -3, 4, -2],\n [2, -5, 0, -6, 4],\n [6, 3, -2, 1, 6],\n [2, -2, 4, -4, -5],\n [-1, -3, 4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 1, 5, -6, 3],\n [1, -5, -4, -6, 0],\n [4, 4, 5, -4, 2],\n [2, -6, -5, 6, -4],\n [3, 6, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 4, -3, -6, 5],\n [-3, -3, -5, -6, 0],\n [3, -3, -5, 2, -3],\n [3, 5, -6, 4, 1],\n [-2, 2, -5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 6, 5, 3, 4],\n [5, 2, -1, 4, 2],\n [-1, -6, 1, -6, 1],\n [2, 1, 1, -6, -5],\n [-6, 6, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -5, 3, 1, 5],\n [-5, 2, 6, 1, -2],\n [4, -3, 0, -1, 2],\n [-3, -1, 0, 6, 0],\n [-6, 3, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 1, 1, -5, 0],\n [3, 6, 2, -2, 6],\n [1, -1, 1, 4, -1],\n [2, 0, 6, 6, 5],\n [-1, 5, -6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 3, 1, 5, 5],\n [1, 2, -6, 3, -4],\n [1, -6, -3, 3, 6],\n [0, 3, 1, 5, -4],\n [6, 2, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 6, 2, 3, -1],\n [-3, 2, -4, -1, 6],\n [5, -6, -3, -3, -6],\n [-5, 1, 5, -6, -1],\n [1, 1, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 4, 3, -1, 4],\n [6, 4, -4, 6, -5],\n [-2, -5, 3, 4, 5],\n [0, -5, -1, 2, 6],\n [-4, 4, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 3, 5, 2, -3],\n [1, -6, -5, 6, -4],\n [-1, 1, 1, 5, -4],\n [2, -1, 3, 0, 6],\n [-6, 5, 5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 2, -6, 0, 3],\n [-4, -6, -6, 6, 2],\n [3, 4, 0, 0, 2],\n [-4, 4, -4, -1, 3],\n [-6, -2, -2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, 2, 2, -6],\n [6, -4, -3, -5, 5],\n [4, 6, -4, 1, -5],\n [3, -6, 3, 5, 2],\n [-6, 6, -3, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -2, -2, -5, -5],\n [-6, 4, 5, 3, -3],\n [2, 5, -5, 3, 4],\n [-3, -6, 0, 5, -6],\n [2, 5, 4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 6, 5, 4, -5],\n [-1, -6, -4, -2, -4],\n [1, 2, 5, 4, -4],\n [1, -5, -1, 6, 4],\n [-2, 2, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, -4, 1, -2],\n [3, -4, -5, -6, 4],\n [-5, 5, 3, -1, 5],\n [-5, -6, -6, -4, -5],\n [3, -1, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -2, -1, -3, -5],\n [0, -2, -1, -6, 4],\n [2, -4, -3, 1, -1],\n [0, 0, 1, -5, -5],\n [2, -3, -5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 5, 6, 0, -4],\n [4, -4, 6, -6, 5],\n [2, 2, 0, -4, -2],\n [-4, -4, -3, 5, -5],\n [6, -1, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 3, -5, 0, -2],\n [2, 2, 1, -3, 2],\n [-3, 1, -4, 5, -5],\n [4, 2, -3, -5, -1],\n [6, -1, 4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 0, 5, 5, -1],\n [0, -3, -4, 2, 2],\n [4, -3, -2, 0, 2],\n [4, -6, 6, -1, -2],\n [6, 2, 3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -3, 4, 1, -3],\n [-4, -3, -6, 0, -6],\n [2, -3, 2, 1, 4],\n [-2, -2, -5, -1, 0],\n [2, 5, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -4, -4, 1, -6],\n [-6, -4, 5, -6, 2],\n [4, 3, 4, -3, 0],\n [-5, 4, -1, 5, 6],\n [3, 1, 2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -5, 5, 2, 2],\n [3, 5, 1, 5, -6],\n [-1, 2, 4, -6, -5],\n [-3, 0, 5, 6, -5],\n [0, -6, -5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -2, 5, -6, -5],\n [-5, -3, -2, 6, -1],\n [-5, 2, 6, -6, 3],\n [3, -5, -2, -6, 1],\n [5, 0, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, 4, 3, 6],\n [-6, 6, 6, 5, 6],\n [6, -6, 3, 1, -5],\n [-5, -4, 5, 2, 3],\n [-1, 6, 0, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -5, -4, -4, 4],\n [-3, 0, -2, 3, -5],\n [-4, 4, -3, 0, -5],\n [-2, 1, 2, 3, 5],\n [-4, 6, -5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 6, 2, 6, -6],\n [1, 0, -1, -5, -4],\n [3, 3, 2, -3, -4],\n [1, -1, 5, -3, -6],\n [-1, 5, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -5, -5, -4, 6],\n [-6, -5, 3, 4, -6],\n [-2, 3, 3, -6, 2],\n [-6, 3, -5, 1, 3],\n [1, -4, 1, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -1, 1, -2],\n [-2, 3, 1, 2, -2],\n [-2, -6, 6, -6, 3],\n [6, 3, 6, -5, -1],\n [0, -1, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 1, 0, 1, 3],\n [-6, 1, -1, -4, -3],\n [-3, 5, 5, -4, 5],\n [2, 4, -2, 5, -5],\n [0, 4, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, 6, -5, 3],\n [-2, 1, 4, 5, 3],\n [-3, -2, -1, 2, -4],\n [-1, -1, -1, -5, 0],\n [-6, 2, -5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -1, 4, 4, -5],\n [6, 3, -5, -3, -5],\n [-6, -2, -4, 4, 0],\n [2, 6, -1, 3, -6],\n [1, 3, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 6, 1, 3, 1],\n [2, 4, -5, 2, 4],\n [0, -2, -6, 4, 1],\n [-3, 0, 6, -6, 4],\n [-1, 6, -6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 3, -3, 6, 4],\n [6, -5, 6, 1, 2],\n [0, 4, 5, -4, -2],\n [-5, 2, 2, 5, 2],\n [1, -2, -5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 4, 1, -1, -5],\n [0, 6, -5, -3, -4],\n [-6, -6, 4, -5, -3],\n [5, 3, 5, -5, -5],\n [-4, -6, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 1, 6, 5, 2],\n [6, 5, 5, 3, 6],\n [6, -4, 5, 4, 0],\n [-5, -6, -2, 3, 1],\n [-2, -1, -4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -1, 0, -2, -4],\n [0, 6, -6, 0, 6],\n [-5, -2, 1, -2, 2],\n [-5, 0, -4, 5, 2],\n [-4, -1, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -1, -4, 1, 1],\n [2, -6, 5, -4, -2],\n [-1, -3, 6, -1, 2],\n [6, -1, -3, -2, 3],\n [-3, -3, -4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -2, -6, 2, -5],\n [4, 0, 3, -3, 0],\n [6, -1, -5, -4, 4],\n [4, 3, -1, 2, 3],\n [-1, -2, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -3, 1, -4, 4],\n [3, 3, -5, 5, 3],\n [0, 3, 0, 2, -5],\n [-2, 6, -3, 3, -3],\n [2, 2, -1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -1, -2, 1, -1],\n [5, -4, 0, 5, 5],\n [-4, -2, 3, -6, -3],\n [-4, 5, 6, 1, -4],\n [1, -3, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -4, -1, 2, 6],\n [-4, 6, 6, -2, -5],\n [4, -1, -5, -2, -5],\n [-4, -2, -5, 6, -5],\n [1, 4, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -1, -6, -2, 6],\n [2, 3, 5, 6, 2],\n [-3, -5, 6, 5, 4],\n [3, 4, -5, -6, 0],\n [3, 6, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -2, 2, 6, 3],\n [6, -3, -2, -3, -3],\n [-4, 6, 5, -4, -3],\n [-3, 3, -5, 4, 3],\n [-2, 0, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -4, 2, -1, -5],\n [-5, -6, 0, -5, -4],\n [2, 2, 1, 4, 1],\n [-2, -1, 4, 1, -2],\n [-2, 1, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, 3, 4, -1],\n [2, -1, 1, -5, 4],\n [-1, -5, -2, -3, -4],\n [3, -3, -6, -4, -2],\n [-6, 3, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 2, 2, 2, 0],\n [2, -3, -1, -3, 4],\n [-4, -4, 4, 3, -1],\n [1, 4, 3, -6, 2],\n [-3, 6, -3, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -1, 4, -2, -6],\n [2, 5, 4, -4, -1],\n [-4, 3, 1, 1, 6],\n [0, -4, 4, 2, 1],\n [0, -4, 2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, 5, 4, 4],\n [1, -5, 4, -5, -5],\n [5, 5, 1, -2, -1],\n [-3, -2, 0, -6, -6],\n [-1, 1, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, 6, -6, 1],\n [1, -5, -6, -2, 4],\n [-5, 3, -1, -5, 1],\n [1, -4, 6, 6, 6],\n [5, -6, 3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 2, 5, 5, -5],\n [3, -1, 5, 2, 5],\n [-3, 3, -1, -5, -1],\n [-2, 1, -4, 1, -4],\n [6, 5, -1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -1, -4, -4, -4],\n [-3, 6, 3, -1, -3],\n [-3, -2, -2, 3, 4],\n [5, 6, -3, 2, -2],\n [1, -2, 3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, -4, 3, -4],\n [4, -1, 6, -2, -6],\n [-2, 1, -2, -3, 2],\n [-4, -5, 5, -1, 2],\n [-4, -6, -6, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 6, -2, -1, 6],\n [-4, 4, 6, 6, 4],\n [0, -5, 4, 0, -3],\n [-4, 0, -3, 2, -6],\n [-2, 4, -1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -6, 1, 5, 5],\n [-5, 1, 0, 0, 4],\n [-3, 0, 1, 2, -1],\n [4, 1, 5, 4, -2],\n [-5, 5, 5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 5, -2, -5, -6],\n [2, 5, 5, 6, -5],\n [-3, 0, -4, -6, -6],\n [0, 1, -1, -3, 6],\n [-2, -3, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 1, 5, -1, 0],\n [-2, 5, 6, -4, 4],\n [0, 0, 2, -5, -1],\n [2, 1, -1, 0, -5],\n [-2, -4, -5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 0, 6, 5, 3],\n [5, -6, 2, 5, -2],\n [1, 0, 2, -5, -2],\n [4, -1, 0, 6, 4],\n [-4, 3, -4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -5, 0, -5, 3],\n [3, -1, -3, 6, 2],\n [0, 3, 0, 6, 2],\n [-6, 6, 5, 0, 0],\n [5, 3, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 5, 5, -1, -2],\n [6, 5, -6, -5, -3],\n [5, 0, -4, 2, 6],\n [-2, 0, 2, -3, 6],\n [-1, -3, -4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 2, -4, -6, 0],\n [-6, -1, -4, -6, 0],\n [-2, -1, -6, 2, 0],\n [-6, 3, -1, 2, 5],\n [-6, 3, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 1, -2, -4, -1],\n [3, -4, 1, 4, -4],\n [1, 0, 1, -1, 3],\n [6, -5, -1, -6, 1],\n [-5, 3, 4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 0, 6, 0, 4],\n [-2, -5, 1, 4, 1],\n [0, -2, 3, -6, 5],\n [5, 4, 0, -1, -2],\n [0, 1, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -2, -4, 1, 3],\n [6, 3, -6, -3, -1],\n [4, -1, -6, -4, 3],\n [-1, 3, 6, 5, 1],\n [-2, -6, 4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -1, 6, 6, 6],\n [-1, -5, 1, 2, -2],\n [-5, 1, -2, -3, -6],\n [6, 0, -6, 5, 3],\n [-3, -6, 5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 3, -5, 6, -2],\n [-2, -5, -4, -2, -6],\n [0, 3, -3, -2, 3],\n [-6, -1, -6, -3, 4],\n [-1, 6, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -5, 1, -5, 1],\n [-2, 3, -6, -1, -6],\n [-4, -4, -6, -5, 1],\n [6, -6, 3, -6, 0],\n [-1, -5, 5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -1, -6, -5, -1],\n [3, -5, 4, 3, 3],\n [-5, -5, 4, 2, -3],\n [5, 1, 5, 2, 3],\n [-5, -5, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -6, -6, 3, -3],\n [5, -5, 1, -3, 2],\n [-6, 0, -4, -4, 6],\n [-2, 5, -4, -5, -3],\n [6, -3, 5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -4, 3, 4, 4],\n [4, -2, 0, -2, 3],\n [4, -1, 1, 5, 0],\n [2, 4, -6, 4, -1],\n [-6, 6, 5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 3, -1, 0, 2],\n [1, -4, -2, 5, -3],\n [2, 1, 2, 3, 5],\n [1, 4, 0, -6, -2],\n [4, -2, 5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 6, 4, 6, -5],\n [-2, -2, 0, 3, 3],\n [-3, 6, -3, 5, 0],\n [4, 2, 5, 4, 0],\n [-2, -1, -2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, -1, 6, -4],\n [-5, 2, 5, 4, -1],\n [-1, 3, -2, 3, 0],\n [2, 4, -1, -4, 1],\n [6, -4, -3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, 1, -6, 1],\n [-2, -4, 6, -5, -1],\n [3, -3, -5, 5, -1],\n [1, -2, 6, -6, 4],\n [-6, 5, -5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 4, 4, -6, -6],\n [1, 1, -1, 4, -6],\n [-4, -3, -6, -5, 5],\n [-1, 2, -5, -5, 4],\n [-4, -2, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, 5, -2, 4],\n [-2, -3, 6, -4, 5],\n [-6, 2, -1, -6, 3],\n [6, -1, -4, 6, 4],\n [-6, 6, 6, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 6, 1, 3, 4],\n [1, -6, 0, 3, 6],\n [6, 3, -5, 2, -1],\n [-1, -3, -3, 5, -1],\n [3, 1, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 1, -1, -2, 6],\n [1, -2, 2, 6, -1],\n [2, -1, -6, 3, -6],\n [3, 3, -6, -2, -6],\n [4, 5, 2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 1, -1, 1, -6],\n [4, 6, -1, 3, -2],\n [-6, 5, 3, 3, -5],\n [-5, -1, 3, 2, 5],\n [-3, -6, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -5, -2, 0, 0],\n [-1, 1, 4, -1, 0],\n [-5, 5, -4, 0, 1],\n [1, -4, -6, 3, 3],\n [-6, 2, 4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 3, -1, -1, -5],\n [-3, 1, -3, -5, 2],\n [1, -6, -6, 6, -2],\n [-2, -2, 5, 1, 0],\n [-5, 6, 3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 0, 5, 6, -6],\n [-3, 2, 5, 5, 6],\n [-3, 4, -1, 2, 4],\n [4, 3, -4, -4, 3],\n [2, 5, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, -1, 0, -3],\n [2, -3, 2, 1, 1],\n [5, 5, 0, 0, -1],\n [-3, -2, -1, 4, 4],\n [-4, 1, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -1, -4, 1, -1],\n [0, -6, 5, 5, -3],\n [-3, 5, 6, 1, -1],\n [1, -1, -2, 6, -6],\n [-2, -2, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -3, -5, -5, 1],\n [3, 2, -5, 6, 1],\n [6, 5, 0, 2, -6],\n [0, 0, -4, -5, -1],\n [0, 1, -5, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -6, 0, -5, -2],\n [-2, -1, -3, -3, -3],\n [3, -1, 2, 4, 5],\n [-3, 1, 4, -6, 6],\n [-3, -3, -3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 1, -4, 0, -6],\n [-4, -5, -1, 2, -4],\n [5, -3, -5, -5, -5],\n [-6, -2, -3, 0, 6],\n [4, -1, 1, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 2, -6, -1, 2],\n [-1, 5, -5, -1, 2],\n [3, -3, -1, 0, 5],\n [-4, -6, -4, 4, -4],\n [1, 0, -1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 1, -6, 1, -1],\n [5, 0, 6, -3, -6],\n [-2, 5, -1, 4, 3],\n [4, 1, 2, 0, 2],\n [1, 4, 5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -2, -2, 0, -5],\n [5, 5, 4, -1, 0],\n [-4, 1, 5, -2, -6],\n [-5, -6, -6, -4, 2],\n [-5, 4, 5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 1, -4, -6, -1],\n [1, -6, -5, 3, -5],\n [4, 1, -5, 0, -4],\n [-1, -5, 5, 4, 6],\n [-4, -2, 3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, -6, 2, 5],\n [4, 0, 2, -1, -4],\n [-6, 2, 5, 0, 0],\n [3, 5, -3, -3, -1],\n [-4, 2, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 4, 3, 5, 4],\n [3, 5, -2, 1, 3],\n [-1, -6, 4, -4, 0],\n [5, -4, 4, 0, -3],\n [-1, 3, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, 2, 3, 2],\n [5, -3, 3, -4, 3],\n [-5, 5, -2, -1, -2],\n [1, 1, 3, 1, 2],\n [0, -2, 4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -3, 5, 1, -6],\n [1, -5, -6, -2, 2],\n [-2, -2, 5, -5, 0],\n [-1, 3, -3, -3, -3],\n [-3, -2, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -2, 3, 5, 0],\n [4, -4, -3, 6, 4],\n [4, -6, 5, -6, 3],\n [2, -4, 3, -3, -1],\n [-5, 1, 4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -4, -4, -4, 1],\n [0, -3, 3, -5, 3],\n [-2, 4, 1, 4, 0],\n [-6, 3, -3, 1, -5],\n [-3, 1, 5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 4, 0, 0, 1],\n [6, 3, 3, -1, -1],\n [5, 1, 2, -6, 3],\n [1, -1, 0, 2, 1],\n [-2, -6, 6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -4, 0, -1, 5],\n [-1, -6, 4, 4, -2],\n [1, 1, -6, 2, 3],\n [-2, -3, 1, 0, 0],\n [-6, -5, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -4, 3, -1, 5],\n [1, -5, 1, -3, 2],\n [1, 2, -2, -6, -5],\n [-6, 6, -1, 5, 2],\n [2, -1, 0, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -1, -3, -4, -3],\n [3, -6, -6, 1, 2],\n [6, -6, 0, -6, 6],\n [5, -4, 3, 3, 0],\n [4, 5, 4, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, -3, 1, 2],\n [-5, 6, 1, -4, -4],\n [-1, -1, 3, 0, 0],\n [-5, 0, -6, 3, 0],\n [3, 2, -2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 1, 4, -1, 0],\n [1, 1, 3, 3, -3],\n [-5, 5, 4, 1, 1],\n [0, -6, -1, 1, -6],\n [-5, -5, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -2, -5, -6, 3],\n [-1, -5, -4, -6, 6],\n [-4, -5, 2, 2, -3],\n [-4, 2, 6, 5, 1],\n [5, 1, -4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 2, 1, 1, 0],\n [-3, -6, -6, -5, 1],\n [2, -1, 5, -1, -3],\n [5, 2, 3, 1, 2],\n [-1, 4, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -5, -5, 1, -2],\n [-6, 5, -4, 5, -1],\n [-1, 4, -5, -4, 3],\n [-3, -4, 4, -3, -1],\n [6, -3, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 2, -3, -3, 2],\n [-6, -5, 1, -4, 0],\n [-5, -4, -4, 5, 2],\n [5, -6, -1, 6, -1],\n [3, 1, -6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 2, 0, 1, 5],\n [-3, 4, 5, -1, 3],\n [-5, -6, 3, -4, -4],\n [2, 1, 3, 6, -4],\n [6, 1, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -4, 0, -3, 1],\n [2, 1, 0, -3, 4],\n [6, -2, 2, -2, -4],\n [1, 4, -6, -1, 6],\n [4, 2, -1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -3, -5, 3, -4],\n [1, 0, 6, 0, 2],\n [0, 4, 0, 1, 5],\n [-6, -1, 2, 1, -5],\n [0, -5, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 6, 6, 4, 4],\n [2, 0, 2, -5, 6],\n [1, -4, -6, -1, -5],\n [-1, 1, 3, 4, 4],\n [-4, -2, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, 3, -1, -1],\n [0, -5, -2, 0, 4],\n [-4, 5, -6, -4, 0],\n [-2, 1, 2, 6, -3],\n [5, -3, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 3, -1, 2, -2],\n [3, 0, -4, -4, 5],\n [0, -2, 6, -4, 6],\n [-5, -4, -5, -4, -4],\n [-2, 1, 1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -4, -4, -5, -1],\n [-6, -1, 0, -6, -5],\n [5, 3, -1, 0, -3],\n [-2, -5, 2, -2, -5],\n [-5, 2, -3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 3, 4, -5, 1],\n [-2, 6, 5, 5, 2],\n [1, 1, 5, -2, -1],\n [0, -2, 2, -2, -3],\n [-1, -6, 3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, 2, 3, -3],\n [-4, 3, -2, 4, 6],\n [-5, 6, -5, -3, -4],\n [0, 2, -3, 5, 3],\n [3, -6, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -5, -6, 6, -1],\n [-4, -3, -4, -5, -2],\n [5, 2, 3, 4, 4],\n [0, -2, -2, -3, -6],\n [2, 2, -4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 5, -3, 1, 3],\n [0, -6, 3, 1, 6],\n [-2, -4, -3, 2, -3],\n [-1, -1, 0, 3, -1],\n [-6, 5, -6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -2, 0, 4, -6],\n [4, 4, 4, 0, -1],\n [-5, -3, -3, 5, 4],\n [-6, 5, 5, 2, -4],\n [6, -6, 2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -6, 5, -3, -5],\n [-4, 3, 0, -5, 3],\n [2, -2, 5, 0, 2],\n [5, -6, -2, 6, -4],\n [-1, 0, 1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -3, 5, -4, -3],\n [-1, 1, -5, 4, 6],\n [-3, -6, 5, 0, -6],\n [4, -5, -3, 6, -5],\n [3, 6, 6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 4, 6, 5, -6],\n [4, -2, -5, -6, -1],\n [1, 2, -6, -5, -5],\n [-2, -1, -2, -3, -6],\n [4, 6, 1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -2, 6, 1, 3],\n [2, 0, -4, -4, 0],\n [6, -6, -1, 3, -6],\n [-6, 3, -6, 0, -2],\n [3, 6, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 3, -4, -4, 6],\n [1, 4, -1, 0, -2],\n [-3, 1, -5, 0, -1],\n [5, 4, 6, 6, -4],\n [-3, 4, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 6, 6, 3, 6],\n [-1, 6, -6, -3, 2],\n [1, -5, 2, -3, 6],\n [-6, 1, 4, 2, -5],\n [-3, -4, -5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 4, -5, -4, 2],\n [-1, -1, 1, 0, 5],\n [0, -2, -3, 3, 4],\n [6, -5, -3, 1, 1],\n [6, -4, 6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -4, 1, -5, 1],\n [6, -6, -5, -6, -2],\n [1, 3, 3, 1, -6],\n [4, 5, -4, 2, -5],\n [-2, 6, 1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 5, 3, 0, -6],\n [2, 6, 1, -5, -1],\n [-4, 0, -5, 0, 5],\n [1, -4, 0, -6, -1],\n [5, 3, -4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 5, 5, -5, 6],\n [4, -2, -4, -5, -4],\n [-1, 5, 5, 0, -2],\n [4, 3, -3, -5, -2],\n [-2, -1, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -6, -6, -1, -2],\n [-5, 6, -2, 5, -6],\n [-4, 6, -5, 4, 4],\n [-1, 2, -3, -1, 2],\n [3, -1, 3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 5, 2, 3, 1],\n [-6, -6, -1, 1, 5],\n [0, -4, 6, 5, 3],\n [1, 4, -3, -1, -6],\n [-5, -1, 5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 3, 3, -2, 3],\n [6, -5, -4, 0, -4],\n [-1, 4, -5, 0, 3],\n [5, 4, 5, -4, -4],\n [-6, 4, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -3, 5, -6, 5],\n [-2, -3, 4, 5, -6],\n [5, -6, 3, 4, 5],\n [-1, -2, 5, -3, 2],\n [5, -2, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 6, 4, -5, -5],\n [2, 5, 4, 6, 4],\n [-6, -5, 0, 6, 1],\n [-6, 6, 5, -3, 4],\n [2, 6, -4, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, -5, 6, -5],\n [0, -6, 1, 0, 6],\n [-2, -1, -3, 2, 2],\n [3, 2, -2, 6, 5],\n [-4, 3, 6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 2, 4, 1, 3],\n [-2, 3, -2, -3, -5],\n [0, -5, -3, -6, 3],\n [4, 2, 1, -6, 4],\n [4, -1, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 4, -6, 2, -2],\n [-6, -5, -3, 3, -3],\n [-5, -1, 1, 2, 2],\n [-3, 5, -1, 4, 3],\n [-5, -5, 5, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -3, -6, 1, 5],\n [6, -5, -6, -1, -5],\n [4, 3, 2, -2, -3],\n [-3, -1, 6, -5, 4],\n [0, 0, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 2, -2, -3, -3],\n [-3, -6, 5, 3, -3],\n [2, -4, -3, 2, -5],\n [6, 0, -5, 4, 3],\n [-3, -6, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 0, 6, -4, 4],\n [-3, 3, 2, 4, 6],\n [3, 0, 3, 0, -6],\n [-4, 2, 5, 4, 0],\n [-2, -6, 5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 4, -6, 3, -1],\n [2, -4, -1, -6, -5],\n [-3, -1, -4, -4, 5],\n [-5, 4, 6, 1, 2],\n [0, 3, 2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 3, 6, 0, -3],\n [-6, 4, 3, 1, 5],\n [6, 5, 5, 0, 0],\n [-2, 0, -4, 4, -2],\n [6, -4, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -1, 4, -2, 1],\n [-2, 0, 2, -3, 6],\n [-1, -4, -3, -6, 4],\n [4, 5, 0, -3, 2],\n [-6, 3, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 2, -1, 5, 6],\n [-4, -1, -4, 6, -6],\n [1, -1, 0, 5, 4],\n [3, 1, 3, 5, -1],\n [-3, -5, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 3, 2, 3, -3],\n [-1, -1, 3, 5, 1],\n [3, -2, -1, -2, -6],\n [4, 3, 3, 3, 3],\n [4, -4, -3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -1, -6, 1, 5],\n [-1, -3, 3, 1, 2],\n [5, 5, 0, 5, 1],\n [1, -4, -1, -5, -3],\n [5, -2, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -5, -2, 4, -1],\n [-1, 1, -1, 2, 2],\n [5, -1, -1, 3, -5],\n [6, -6, -3, 0, 6],\n [-6, 3, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 4, 5, 6, -1],\n [-5, 5, 0, -2, -4],\n [4, -1, -3, 2, -6],\n [1, -3, -6, 4, 4],\n [3, -5, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 2, -5, -4, -2],\n [-6, 6, 0, -1, -3],\n [-1, 1, -4, -2, 6],\n [1, 2, 4, 0, 5],\n [-4, 6, -5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -4, -2, 1, -4],\n [6, -5, -6, -2, -3],\n [-2, -4, -2, 2, 0],\n [1, -2, 0, 4, -4],\n [6, 0, -4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 0, -3, -3, 5],\n [-2, -5, -3, -1, -6],\n [2, -5, 4, -6, 0],\n [-2, -4, 3, -5, -5],\n [-6, 3, 4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -1, -6, -6, -4],\n [-3, 2, 6, -6, -5],\n [-3, -6, 5, 4, -4],\n [2, -6, 6, 2, -6],\n [-6, 3, 5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 2, -3, 1, -3],\n [-5, 5, -6, -3, 3],\n [1, -3, 0, 0, 5],\n [-2, 6, 0, -3, 1],\n [3, -2, -6, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 2, 1, -2, 0],\n [-5, 1, -2, -5, -5],\n [-3, -6, -3, 5, 3],\n [-4, -6, 0, 3, 1],\n [3, -2, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -4, -1, -6, -2],\n [-5, -5, -1, 4, -5],\n [0, -3, -5, 3, 4],\n [-1, -4, 2, 1, -3],\n [0, -4, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -2, 0, -4, 5],\n [0, -2, -6, 4, 1],\n [4, 3, 2, 6, 1],\n [-5, 6, 0, -5, 1],\n [-1, -4, 2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, 1, -6, -4],\n [-1, 1, -3, -3, 5],\n [-6, -2, -2, 3, 0],\n [2, 2, 3, 1, -3],\n [3, 4, -2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -2, -4, 4, 4],\n [1, 1, -4, 6, -3],\n [-6, 2, -4, 0, 5],\n [-2, -4, 2, 4, 5],\n [0, -5, 3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 3, 1, -4, 1],\n [3, 4, -2, -6, 1],\n [1, 2, 0, 5, -2],\n [3, -5, 4, 4, 4],\n [6, -6, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -6, 1, -6, 5],\n [2, -4, -2, 4, 6],\n [-2, 2, 2, -2, 6],\n [-3, -5, 0, 6, -3],\n [-4, 6, -1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, 2, 4, 2],\n [-3, -4, 6, 1, -2],\n [2, 2, 6, -5, 3],\n [-5, -2, -3, 5, -3],\n [2, -1, -4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -1, -4, -5, -1],\n [1, 3, 3, -6, -4],\n [-5, 0, 1, -6, -6],\n [-5, 6, 4, -1, 2],\n [1, 2, -5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 4, 0, -2, 0],\n [6, 4, 6, -2, -4],\n [5, 1, 2, -2, 3],\n [-4, 3, -6, 3, -1],\n [6, 1, 6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -5, 5, 2, -4],\n [-6, -5, -6, -2, -1],\n [2, 4, 5, 5, 2],\n [1, 1, 3, 6, 0],\n [1, -1, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -1, -1, -4, -5],\n [-3, -2, 1, 6, 4],\n [4, -2, -6, 3, 3],\n [-3, 0, 0, -2, 5],\n [3, 2, 1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -4, -4, -1, -1],\n [1, -4, -3, -4, -5],\n [3, -6, -4, 3, 5],\n [-4, -2, 3, -1, 3],\n [0, 4, 1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 6, -6, -2, 1],\n [-5, -2, 6, -1, 4],\n [4, -4, -5, 1, -3],\n [0, -3, 4, -3, -6],\n [1, -6, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -4, 4, 4, -5],\n [-6, 1, -3, 5, -1],\n [1, 5, 4, 2, -4],\n [-5, -3, -1, 5, -3],\n [-3, 4, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 0, 3, 0, 4],\n [-4, 5, 1, -2, -5],\n [1, -2, 2, 2, -6],\n [-6, 4, -3, 0, 6],\n [6, -4, 3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 6, 6, -1, -4],\n [-2, 6, 1, -2, 4],\n [-6, -2, 0, -1, 3],\n [-3, 0, -5, 0, -3],\n [-1, -5, -6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 4, 1, 1, 0],\n [-3, 6, -5, 1, -3],\n [-3, 1, 4, 5, -6],\n [3, 1, 3, 0, 1],\n [-2, -3, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 6, -4, 5, -1],\n [0, -5, -6, 1, -3],\n [-5, 5, -2, 0, -5],\n [-4, 4, -1, -1, -6],\n [-3, -6, -1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 1, 2, 1, 5],\n [-6, 0, -4, 2, 6],\n [-6, 2, 3, 4, -2],\n [5, -5, 0, 5, -5],\n [0, 2, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -6, 5, -4, 5],\n [4, -2, -5, 6, 2],\n [-5, 6, -1, 2, -3],\n [-2, -3, 2, 6, 5],\n [-4, 6, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -3, -1, -3, -4],\n [-2, 5, 6, -2, 3],\n [-4, 1, 5, -5, 0],\n [-5, -5, 2, -4, 1],\n [-5, 2, 4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 0, -5, 3, -3],\n [-5, -2, 3, 3, -4],\n [-4, 4, 6, 6, 4],\n [1, 3, 1, 5, 4],\n [3, -6, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -6, 4, -2, 1],\n [-4, 5, -3, -5, 6],\n [-4, -3, 5, -6, -2],\n [-1, -3, 6, 6, -2],\n [-5, -4, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -2, 5, 6, 4],\n [-2, 3, -4, -5, -5],\n [-1, -1, -3, -5, -5],\n [0, 6, 0, 6, 3],\n [-6, -6, -6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 3, 5, -3, 3],\n [-2, -4, -1, -4, 1],\n [-1, -2, 1, -3, -6],\n [1, 6, -3, 3, -6],\n [-3, -1, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -3, -1, -1, -5],\n [-2, -5, -5, -5, 1],\n [-4, 5, -5, -3, 0],\n [3, 3, 3, 1, 4],\n [1, 6, -2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -2, -1, -6, -5],\n [-6, 5, 2, 4, 0],\n [-4, 0, 2, -3, -6],\n [5, -6, -6, 5, -5],\n [2, -1, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 4, -6, 0, -3],\n [-4, 3, 1, -1, 1],\n [5, 2, -6, -2, 2],\n [6, -6, -2, 4, 5],\n [6, -5, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 2, 0, 3, -2],\n [4, -1, 0, 2, 4],\n [1, -1, 3, 6, 1],\n [0, 5, 2, -2, 1],\n [1, 0, -3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -1, 5, 0, 6],\n [5, -1, 5, -6, 4],\n [6, 5, -1, -3, -5],\n [3, 4, 5, 3, 4],\n [1, 6, -2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -3, 4, 1, 2],\n [1, -5, -2, 0, 4],\n [1, 4, 0, -3, -4],\n [1, 6, 3, -4, 3],\n [2, 0, 3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -4, -6, -1, -1],\n [-2, -4, 1, 2, 2],\n [-4, 6, 3, -5, -6],\n [5, -4, -5, 2, -6],\n [3, 6, 0, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -2, 1, 6, -5],\n [6, 1, 0, 2, 5],\n [-1, 4, 2, 4, 6],\n [5, -3, -3, -6, 0],\n [3, 4, 0, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, -1, 5, 4],\n [1, 4, 1, 2, 4],\n [-5, 3, 5, -1, 6],\n [3, 0, 5, 2, 5],\n [1, 0, 0, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 4, 4, -2, -6],\n [-1, -4, 0, 1, -2],\n [-1, 1, -1, -2, -5],\n [-3, -1, -5, 0, -6],\n [4, 3, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 6, -5, -6, -4],\n [1, -3, -5, 4, -2],\n [2, -1, -4, 4, 1],\n [-3, -5, -3, 6, 3],\n [-1, 0, -1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -4, -6, -2, -2],\n [-4, -4, -3, 0, -2],\n [-2, -3, 3, -3, 3],\n [5, -6, -5, 4, 6],\n [-3, 1, 0, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -5, 4, 5, -3],\n [-5, 3, 4, -3, -4],\n [-2, -1, 4, 5, 6],\n [-6, -6, -2, -1, 1],\n [2, 0, 5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -3, 0, -3, 0],\n [0, -6, 2, -6, -5],\n [4, -3, -1, -4, -2],\n [-6, -1, 0, 3, -4],\n [5, -5, -6, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 1, 6, -2, 1],\n [3, -2, -2, 1, 2],\n [-4, -5, -3, 2, 3],\n [0, 4, 3, -6, -4],\n [2, -2, 1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -4, -1, 3, -2],\n [-1, -6, -5, -2, -6],\n [3, 1, 0, -4, 3],\n [-3, 5, 4, 3, 3],\n [5, 0, 3, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -2, 0, -4, -4],\n [4, 4, 2, 0, 4],\n [4, 5, 2, 3, 1],\n [2, 1, -3, 4, 3],\n [-5, -6, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 4, -6, 5, -2],\n [1, -6, 6, -5, 3],\n [1, 4, -2, -3, 6],\n [-2, 4, -3, 1, 0],\n [-1, -3, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -4, 3, 6, 0],\n [0, 4, 6, 0, -4],\n [-6, -5, 5, 1, 5],\n [1, 1, 5, -2, 0],\n [1, 3, -6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, 4, -4, -5],\n [0, -5, 3, -4, 3],\n [0, 4, -2, -1, -4],\n [-3, 5, 4, 0, 0],\n [3, 5, 4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -3, -5, 3, -6],\n [5, -1, -1, -5, 3],\n [5, -6, 6, -4, -6],\n [0, -5, -2, 0, -2],\n [-2, 1, 1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -4, 4, -3, 1],\n [-6, -2, -3, 3, -4],\n [2, 1, 5, 1, -4],\n [6, -1, -2, 3, 4],\n [6, 4, 6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -6, -3, -4, -1],\n [-3, -5, -4, 5, 4],\n [5, 3, 5, -5, 2],\n [6, 6, 6, 6, 6],\n [-5, 5, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -1, -2, -1, -3],\n [-5, -3, 3, -1, 0],\n [-4, -2, 0, 4, 2],\n [2, -6, -4, 2, 6],\n [-4, 2, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, 4, 6, -2],\n [3, -4, -2, 4, 6],\n [5, 2, -2, 1, 0],\n [-5, -1, -6, 4, -5],\n [3, -4, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 6, 0, -6, 0],\n [3, 3, -2, 6, -1],\n [3, 6, -6, 6, 4],\n [-6, 6, 6, 6, -2],\n [2, -6, -3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 5, 0, 4, -1],\n [-1, 0, 5, -3, 1],\n [-6, 0, -2, 4, 1],\n [-3, 6, -4, -3, -2],\n [4, -1, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -3, 1, -4, 3],\n [2, 5, 6, 1, 0],\n [2, 1, -2, -3, -6],\n [5, -1, -4, 1, -6],\n [4, 5, 3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 2, -3, 0, -2],\n [-5, 1, 1, -4, 3],\n [0, -3, 0, -1, 0],\n [2, -1, 2, 3, -1],\n [4, 3, -3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 1, -4, -5, -4],\n [-6, -2, -3, -4, 4],\n [-2, -5, -3, 0, -6],\n [2, 3, 6, -1, 0],\n [-5, 0, -4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -6, 0, -2, -3],\n [-3, -5, 6, -4, -3],\n [-2, -5, 3, 1, 2],\n [3, 1, 0, 1, 3],\n [0, -4, 4, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -1, -6, -4, 6],\n [3, 1, -5, -4, 5],\n [-4, 2, 3, -5, -2],\n [5, -3, -2, 3, 3],\n [2, 5, 6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 5, -5, 6, 0],\n [5, 1, -2, 5, -5],\n [0, -6, -1, -3, -4],\n [3, -4, -2, 3, 6],\n [-2, -6, 6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -5, 0, -3, 1],\n [4, -2, 4, -2, 0],\n [0, -4, 4, 4, -6],\n [-6, 2, 3, -3, -2],\n [0, 0, -3, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -2, -2, 1, -1],\n [-5, 5, -2, -4, 5],\n [-2, 0, 3, -6, 3],\n [5, 3, -4, 0, 5],\n [3, 3, -6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -6, -2, 0, -3],\n [5, 5, -1, 1, -1],\n [2, -3, -2, -1, -2],\n [-2, -6, -2, 5, 3],\n [-3, 2, 2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -5, -6, -5, 6],\n [1, -3, -1, -3, 2],\n [6, -6, 5, -5, -2],\n [-5, 3, -1, -3, -6],\n [3, -4, -3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -6, -6, -3, 0],\n [6, 5, 2, -2, -2],\n [3, -2, -1, 3, 6],\n [-3, -2, -1, 3, 0],\n [-2, -1, -1, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -5, 4, -2, -2],\n [-5, -2, -1, -4, -2],\n [-3, -3, -2, -4, -3],\n [6, 0, 0, 6, 3],\n [-5, -2, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -6, 2, -1, 5],\n [-3, -3, 0, 1, -1],\n [0, 4, 0, -6, -4],\n [-2, 5, 0, 3, 1],\n [-3, -5, 4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 1, -5, 1, -1],\n [-4, -3, -2, -4, 5],\n [1, 4, 6, 6, -1],\n [6, 1, 4, -2, -3],\n [4, 1, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 6, 1, 3, 0],\n [-1, -5, 2, -5, 2],\n [1, -3, -4, 4, 6],\n [3, 2, 0, 5, 5],\n [-6, -4, 4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 5, 1, -6, -6],\n [5, 0, 4, 6, 3],\n [5, 6, 4, 4, 2],\n [0, 3, 6, -6, -1],\n [-2, 0, 1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 2, 5, 1, 3],\n [-3, -4, 3, -2, 3],\n [2, -2, 0, -3, 3],\n [-4, 4, 4, -1, 4],\n [6, 4, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 6, 0, -6, 6],\n [3, 6, 1, -3, 2],\n [6, -3, 0, -5, -1],\n [3, 5, 3, 3, 0],\n [-5, 4, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 5, -2, 3, 4],\n [-2, 3, -3, 4, 5],\n [0, -6, -5, 5, -1],\n [-2, 2, -3, 1, -1],\n [3, -1, -1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 3, -3, 6, 5],\n [-3, -4, -1, -6, 2],\n [-6, -1, -5, 4, -6],\n [-1, -5, 5, -3, 4],\n [-4, 6, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, -3, 2, -6],\n [-1, 3, 4, 3, 6],\n [-5, -6, 3, 6, -6],\n [6, -4, -4, 3, 3],\n [-3, -1, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 1, -5, -1, -6],\n [1, 4, -4, -6, -2],\n [6, 0, -4, -4, -4],\n [2, 4, -3, 5, 4],\n [-5, 0, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 3, -5, 5, -2],\n [1, -5, 4, 2, 0],\n [-4, -5, -2, 5, -2],\n [5, -5, -3, -2, 0],\n [-5, -1, -6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 4, -4, -3, 5],\n [-4, -1, -4, 1, -1],\n [-5, -6, 1, 2, 1],\n [3, -2, -6, 3, -1],\n [4, -4, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -2, 0, 4, -1],\n [3, -2, -5, -4, -4],\n [-6, 3, -3, -6, 3],\n [-1, 0, 0, -3, -5],\n [-4, -4, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -2, 0, 0, -6],\n [-6, 4, 5, 6, 6],\n [-2, -1, 3, 6, -6],\n [1, -2, -5, -1, 3],\n [3, -5, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 3, -2, -6, -5],\n [2, 6, 4, 6, 5],\n [3, 6, -3, -5, 1],\n [0, 1, 4, -3, 5],\n [-1, -1, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -2, 3, 1, 0],\n [6, 2, 3, 2, 4],\n [-1, -1, -1, 0, 0],\n [-2, -3, -5, 4, -2],\n [-5, -1, 1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -2, 5, 3, 1],\n [3, 3, -4, -1, 1],\n [6, -6, 6, 3, -4],\n [3, 3, 1, -3, 0],\n [3, -6, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 6, -1, 5, -3],\n [0, -3, -6, -6, 0],\n [-4, 1, 6, 3, 0],\n [-2, -3, 3, -5, 1],\n [3, 3, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -4, 0, -3, -1],\n [-6, -3, 0, -1, 3],\n [6, -1, 2, -3, 6],\n [-4, 3, -5, -1, 0],\n [3, 2, -1, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 2, -2, 3, 6],\n [3, 3, -4, -3, 6],\n [1, -2, 5, 4, 1],\n [-1, 0, 3, -5, 4],\n [-1, -5, -6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 4, 0, -2, 4],\n [-3, 6, -5, 3, -6],\n [-3, -3, 2, 3, -5],\n [-3, -4, -2, -1, -1],\n [-1, -6, 0, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -5, 2, -4, -5],\n [-3, -1, -6, -6, 5],\n [-1, -3, -1, 0, -3],\n [6, -2, 5, -3, 6],\n [-2, 5, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 3, -5, 3, -6],\n [-4, -2, 5, -2, 0],\n [-4, -2, 6, 4, -4],\n [3, -2, 5, -5, 4],\n [2, 1, 5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -3, -5, -6, 6],\n [4, 4, -3, 2, -1],\n [-3, 2, -5, -3, 2],\n [1, 0, -5, 1, 2],\n [-6, -4, 1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -6, -5, 0, -3],\n [5, -6, -5, 4, -6],\n [0, 6, 6, -5, -6],\n [4, -2, 5, -5, -2],\n [1, -6, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 0, -1, -3, -2],\n [1, 3, 1, 6, 4],\n [1, -2, -3, 4, 2],\n [6, 4, -2, 2, 1],\n [5, 6, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -1, -2, 3, 6],\n [-1, -2, -2, 2, 3],\n [-1, -3, -3, -4, -3],\n [6, 5, 1, 6, 6],\n [-5, 6, -5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, 2, -6, -2],\n [-6, -6, 4, 3, -3],\n [3, 6, 3, -3, 2],\n [-5, 3, 6, -5, -1],\n [4, -2, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, 2, -5, 6],\n [6, -1, 2, 3, -5],\n [-2, 6, 0, 3, -5],\n [3, 1, -6, -3, -5],\n [-3, 4, -5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 5, 0, 2, 1],\n [6, -6, -6, -6, 5],\n [-1, -6, -6, 4, 3],\n [0, 1, 2, 1, -3],\n [1, -1, 2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 6, 2, 0, 4],\n [2, -4, 4, 2, 0],\n [-2, -2, 0, -5, 2],\n [-4, -4, 3, 2, -1],\n [3, -1, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 2, -1, -5, 5],\n [-2, 1, 2, -5, 3],\n [-1, -1, -4, -1, -3],\n [-2, 4, -4, 0, 4],\n [5, 1, 4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 3, -4, 1, -6],\n [-6, 3, -3, 4, 4],\n [2, 3, -5, -2, -3],\n [-5, -6, 0, -3, -6],\n [-6, 1, 1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 1, -2, 4, -3],\n [6, -1, -6, 2, 0],\n [-6, 4, 3, -6, 6],\n [-1, 6, -1, -6, -5],\n [-6, -2, -2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 6, -5, 6, -2],\n [3, 6, 6, 6, -3],\n [6, 3, -3, -2, -3],\n [6, -2, -1, -3, 3],\n [-3, 5, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 0, 2, 1, 0],\n [-4, -1, -4, 6, -2],\n [-2, -3, 2, -4, -6],\n [-4, 2, -4, 6, -6],\n [5, 6, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 0, 4, 3, -6],\n [1, -2, 6, -5, -5],\n [-3, 6, 5, -2, -1],\n [5, -1, -2, -4, 6],\n [4, 2, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, -4, 4, 6],\n [4, 1, 0, -5, 4],\n [4, -3, -3, -3, 4],\n [1, -3, -5, -2, 5],\n [5, 1, 5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -6, -3, 3, 0],\n [3, -1, 2, -4, -5],\n [-6, -3, 3, -3, 4],\n [-3, 3, -2, 5, 5],\n [2, 3, -2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 6, -2, -2, 3],\n [2, -2, -2, 2, 3],\n [-6, -6, -3, -2, 6],\n [-4, -5, -6, -1, -5],\n [-4, -4, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 0, 0, -2, -2],\n [4, -2, -2, 0, 0],\n [-6, 3, -6, -1, -3],\n [-3, 3, -6, 0, -2],\n [6, 4, 4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 0, -1, 1, 5],\n [-3, 1, -1, -5, 6],\n [-6, 2, -6, 6, 2],\n [2, 3, -2, -5, -1],\n [0, -1, -6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -2, -6, 0, -2],\n [6, -4, -5, 4, 2],\n [0, 3, -1, 6, 4],\n [4, 3, 0, -2, -3],\n [3, -2, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 0, 5, -6, 0],\n [5, -3, 3, -1, -1],\n [2, 6, -1, -6, 0],\n [-1, 0, 4, 1, 3],\n [-3, 3, 1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 0, 4, -1, 4],\n [6, -1, 1, -2, -6],\n [0, 1, -5, 1, 1],\n [-5, -2, -6, -3, 6],\n [2, -4, 3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 6, -3, -4, -1],\n [-1, 5, 0, 4, 1],\n [3, 1, 1, -6, 3],\n [3, 2, -1, -4, -2],\n [-4, 6, -6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -2, 6, 2, 2],\n [-6, 3, 5, 5, 3],\n [-4, -2, -3, -5, -5],\n [4, 6, -2, -4, -2],\n [-3, -1, -2, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -3, 4, 5, 4],\n [1, 2, -2, -3, -2],\n [5, 6, -3, 1, 6],\n [-5, 2, 6, 3, 4],\n [-3, -2, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, 3, -5, -6],\n [-5, 1, -5, -5, -2],\n [-4, 6, -2, 3, 3],\n [5, -5, -2, -2, -5],\n [-2, -5, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 4, 5, -5, -1],\n [4, -3, 0, 5, -5],\n [6, 6, -2, 1, -6],\n [1, -6, 6, 5, -4],\n [6, 6, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 0, -5, -3, -5],\n [6, 3, -4, 0, 2],\n [6, -4, -3, 2, 5],\n [-1, -4, -4, 5, -3],\n [-4, -5, -4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -4, 6, -1, -2],\n [-1, -2, 3, -6, -2],\n [0, -4, 2, -3, 0],\n [6, -2, -1, 0, 0],\n [1, 5, -1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -1, 0, 2, -3],\n [6, 6, -3, -5, -5],\n [1, 5, -4, -6, 2],\n [0, 2, -3, 0, -4],\n [-2, -5, 6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 0, 2, -1, 4],\n [-4, 0, -2, 6, 0],\n [-4, 5, -3, -4, 4],\n [0, 6, 1, -6, 1],\n [3, -5, -3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, 3, 1, 2],\n [0, 4, 4, 5, 6],\n [-3, 2, -2, 4, -5],\n [-3, 2, -2, 2, -6],\n [-2, -1, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, 0, -3, 5],\n [-5, -6, -5, -5, -4],\n [-4, 0, -2, 3, -4],\n [3, 6, 6, 3, 3],\n [-5, 1, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 6, 6, 4, 2],\n [-5, 5, 3, 1, -3],\n [-3, -6, -2, -5, -4],\n [-5, -6, 1, -1, 3],\n [5, -4, 2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -2, 3, -3, -6],\n [-4, -5, 3, 1, 1],\n [-1, 1, 2, -5, 0],\n [0, -1, -3, -1, 4],\n [-4, 2, 3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -4, -4, 6, 3],\n [5, 2, -5, -5, 0],\n [-2, 5, 5, 5, 6],\n [4, 1, -4, 0, -4],\n [-3, -3, 6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -4, 1, 6, -2],\n [6, -5, -4, -4, -2],\n [-1, -5, -2, 6, 5],\n [0, -6, -4, 5, -4],\n [4, -4, -2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 4, -3, -4, -6],\n [3, 0, 4, 3, 4],\n [-6, -4, 3, -4, -6],\n [-2, 4, -2, 2, 4],\n [5, 1, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 5, 4, -3, 5],\n [5, -5, 5, 1, 6],\n [5, 5, 4, 6, 2],\n [4, -6, 5, 0, 0],\n [0, 6, -5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 0, 2, -1, 0],\n [2, -2, -3, -3, 2],\n [-6, 0, 3, -5, 4],\n [2, 5, -2, -3, 4],\n [-1, -3, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -2, 2, 0, -6],\n [-3, -3, 2, 1, 2],\n [5, -4, 6, 6, -6],\n [0, 3, 2, -4, -1],\n [0, -1, 0, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -4, -5, 4, 1],\n [-4, -2, 0, -1, 4],\n [3, -1, 5, -6, 4],\n [4, 5, -6, 4, 5],\n [-2, 0, 5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -6, 1, 1, -1],\n [4, -3, -3, -4, 6],\n [6, -2, 0, 3, -3],\n [-3, 1, 6, 3, 5],\n [2, -6, 4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 4, -2, 1, -1],\n [-6, 6, 1, 1, 4],\n [-5, -1, -1, 5, -3],\n [-6, 1, 1, -3, 1],\n [6, -5, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -5, -6, -2, -5],\n [3, 5, 4, -2, 3],\n [3, 0, 6, -6, -3],\n [1, 0, -3, -1, 5],\n [5, 0, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 6, 3, 5, -4],\n [2, 6, -1, 3, 5],\n [-4, 5, 0, 2, -4],\n [4, 4, -1, -1, -2],\n [-3, 2, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 6, 4, 2, 0],\n [-2, 6, 6, -5, -2],\n [6, 0, -3, 1, -5],\n [-6, 6, -3, -1, 3],\n [6, -3, 5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 5, 6, 2, -2],\n [-6, 5, 5, 6, -4],\n [-5, 0, -2, 0, -5],\n [-5, -6, -3, -3, 4],\n [-4, 4, -4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 5, 6, 2, -2],\n [0, 1, 6, 6, -6],\n [-1, -6, 1, -2, 1],\n [4, 2, -2, -5, -6],\n [1, -1, 3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -6, 4, -1, 4],\n [2, 6, 1, -2, 6],\n [-5, 2, -6, -2, 0],\n [5, 5, 6, 3, -3],\n [2, -3, 6, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -4, 5, -5, -3],\n [-6, 3, -6, 6, 3],\n [6, -4, 2, -3, 3],\n [-3, 5, -6, 4, 2],\n [5, -3, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -5, 6, -1, -1],\n [4, 1, -4, -2, 4],\n [-6, -6, -1, 0, -6],\n [-4, 5, -6, -6, -6],\n [2, 6, -2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 6, -6, -4, -4],\n [3, 3, 6, -4, -5],\n [0, -6, -5, 3, 2],\n [-4, 1, -4, -5, 3],\n [1, 0, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -6, -4, 2, 2],\n [-6, 0, -1, -4, 3],\n [-3, 0, -4, 4, -4],\n [0, 6, -4, 1, 3],\n [-4, 6, -5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -2, -6, -5, -5],\n [-6, 4, -2, 0, 1],\n [0, 2, -6, -2, -6],\n [-4, -4, 1, 1, -6],\n [5, -1, 6, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 5, -3, 5, -4],\n [-6, -5, 3, 6, 0],\n [3, 5, 6, 0, -4],\n [-2, 0, -2, 3, 4],\n [-1, 1, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -5, -3, -3, -2],\n [0, -6, 5, 2, -4],\n [0, 4, 2, 0, -1],\n [2, 6, 4, 0, 2],\n [0, 3, 6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 2, 2, -2, -3],\n [-4, -4, -1, -2, 1],\n [5, 3, 6, 0, -4],\n [-1, 2, -1, -2, 2],\n [-6, -5, 5, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 1, -4, -3, -3],\n [-5, -6, -6, -6, 6],\n [-6, 6, -6, 2, -4],\n [0, 5, -4, 3, -2],\n [6, 1, 2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 5, 5, 1, 5],\n [-5, 0, 2, 0, 2],\n [-1, 5, 0, 0, 4],\n [3, -3, -5, -6, 2],\n [-4, -6, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 3, 1, 3, 5],\n [-6, -2, 1, -3, 6],\n [-4, -5, 4, -5, 5],\n [2, 0, -2, 4, 4],\n [5, -2, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -2, -2, 1, -3],\n [-5, -6, -1, 6, 2],\n [3, 1, -4, -2, -3],\n [-4, -6, -1, -3, 0],\n [1, 3, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -6, -4, 1, 1],\n [-5, -6, -6, 5, -3],\n [5, 2, -3, -1, 2],\n [6, 3, -2, 5, 6],\n [3, -6, 5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -6, 4, -5, 5],\n [-1, 0, -1, 3, 2],\n [2, 5, -6, 0, 1],\n [2, -6, -6, -3, -4],\n [2, 3, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 4, 5, -2, -5],\n [4, 1, 6, 0, 0],\n [3, 1, -3, -6, 1],\n [-5, -3, 3, 1, 5],\n [-6, 3, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 0, -4, 1, 0],\n [5, -2, -4, -3, 4],\n [-3, 0, -6, -2, 6],\n [1, 4, 1, -3, -2],\n [-4, -5, -6, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 1, 4, 0, -2],\n [2, -5, -4, 3, -2],\n [3, -3, 3, -6, -3],\n [5, -5, -5, -3, 1],\n [6, 6, 5, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 6, -3, -5, -5],\n [-5, 5, 0, 6, -6],\n [-5, 6, -4, 1, 1],\n [-5, 5, 5, -6, -2],\n [-1, 5, 6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, -2, -5, 6],\n [6, 0, 5, -4, 4],\n [6, 2, 2, -2, 1],\n [6, 1, 4, -4, 4],\n [1, 5, -5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 6, 0, -4, -3],\n [1, -6, 0, 0, -1],\n [-6, 0, -6, 4, -3],\n [-6, 6, 6, -5, -1],\n [-4, 4, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 2, 0, 6, 4],\n [-3, -1, -4, 4, 6],\n [5, -2, -1, -6, 5],\n [-3, 4, -2, 4, 0],\n [-2, 0, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -4, -2, 0, -2],\n [-5, -2, -6, -6, -6],\n [-3, -5, 4, -1, -2],\n [6, 5, 1, 0, -2],\n [3, 6, 2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, 1, 5, 5],\n [5, 2, -6, 5, 5],\n [1, -4, -2, 2, -3],\n [-2, 2, 4, -3, -1],\n [0, -6, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -5, 2, 0, -3],\n [-1, -1, 1, -4, 3],\n [-1, 3, 1, 2, -5],\n [2, -4, -3, 2, -1],\n [0, 2, 5, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -4, -5, 1, -3],\n [-5, 2, 5, 5, 4],\n [-5, -5, 1, -5, 2],\n [-1, -6, 4, -3, -1],\n [3, -4, 1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 3, 4, 5, -5],\n [4, 2, -5, -2, -5],\n [-2, -4, 5, -3, 0],\n [4, 5, -1, -5, 4],\n [4, -3, -1, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 5, 0, -4, 1],\n [-3, -4, -4, -1, -2],\n [-3, 6, 2, 5, -5],\n [-4, 4, -5, 2, -2],\n [1, 5, 1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -6, -6, 0, 4],\n [6, 2, 6, 6, 4],\n [4, 4, -3, -4, -5],\n [5, -3, -2, -2, 3],\n [5, -2, -6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 3, 0, 6, -2],\n [0, -1, 4, 2, -1],\n [-6, 4, 0, -2, -2],\n [0, 5, 1, 6, 0],\n [3, -4, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 4, -3, 0, -5],\n [-4, 0, -4, 1, -3],\n [-2, 0, 5, 5, -2],\n [-2, -2, 4, 3, 1],\n [2, 5, -5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -6, 6, 1, 5],\n [-5, 6, -4, -4, 3],\n [-3, 2, 2, 5, 5],\n [-3, 4, 2, -2, 0],\n [4, -2, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -3, 1, 0, 6],\n [4, 5, 0, 0, 4],\n [-5, 1, -4, 0, -1],\n [1, -5, -2, 6, 5],\n [-3, 4, -5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 2, 1, 5, -6],\n [-6, -2, 5, -6, -4],\n [-4, -4, 5, -1, -2],\n [4, -6, -4, 5, -1],\n [-6, -3, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 4, 0, -1, -1],\n [-1, -2, -5, 1, 2],\n [-6, 6, 1, 1, -3],\n [2, -4, 0, 3, -1],\n [-2, -1, -3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -3, 1, -5, 3],\n [5, 3, 0, -2, -5],\n [5, 4, -3, 2, 6],\n [-1, -1, 5, 4, -6],\n [1, -3, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -4, 1, 6, 5],\n [-1, 3, -5, -4, -4],\n [4, -3, 5, 0, 3],\n [1, 4, -4, 3, 3],\n [1, 5, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 5, -4, 5, 3],\n [4, -2, 0, 0, 3],\n [-2, 0, -1, -5, -1],\n [-2, 3, 1, 0, -5],\n [-4, 2, 0, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 3, 1, -6, 3],\n [4, 4, 2, 0, -5],\n [5, 5, 1, 4, 1],\n [5, 6, 0, 1, -6],\n [2, -5, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 4, 6, -3, 1],\n [-6, -3, 2, 0, 2],\n [5, -6, -5, -3, -2],\n [6, 5, -6, 2, 5],\n [5, 4, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 1, 4, -5, -6],\n [-4, -6, -5, 3, -3],\n [5, -4, 4, -4, 3],\n [-1, -5, -5, 1, 4],\n [-1, 6, -1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 3, -1, -5, 2],\n [3, 1, -6, 4, 6],\n [6, 4, 5, -2, -4],\n [5, -2, -3, 6, -3],\n [4, 0, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, 6, 4, -6],\n [4, -6, -3, -2, -4],\n [6, -4, 2, -1, 3],\n [-1, 6, -4, 6, -2],\n [-5, -5, 3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -6, -6, -5, -3],\n [-2, 3, 0, 0, 0],\n [-2, -3, 5, -4, 6],\n [3, 4, 3, -6, 5],\n [-4, 3, 1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -6, -1, 2, -5],\n [4, -3, 0, 5, 0],\n [-3, 0, -4, 6, -4],\n [1, 1, 0, 5, 4],\n [1, 3, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 5, 5, -4, 3],\n [0, 6, -6, -5, 5],\n [6, 3, -3, -2, 3],\n [1, 0, 1, -4, 6],\n [6, 0, 4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, -2, 4, 2],\n [-5, 0, 2, 0, -2],\n [-4, 3, 2, 6, 3],\n [1, -5, -6, 5, 4],\n [3, -5, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -5, 6, -1, -5],\n [-6, 2, -1, -3, 6],\n [5, -2, -6, 3, 3],\n [6, -5, -4, -2, 4],\n [5, 5, 6, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 2, 1, -6, 0],\n [-2, -3, 5, 1, 6],\n [-4, 0, -6, -4, 6],\n [-4, -3, -2, 0, -2],\n [5, 0, 4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, -6, -5, 1],\n [-3, -5, -5, -4, -6],\n [-1, 1, 3, 3, 4],\n [-6, 0, 5, -3, 0],\n [3, -4, -6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 2, 2, 0, -5],\n [-3, 5, 6, -6, -4],\n [-1, 2, -1, -5, 1],\n [-6, -1, -3, -3, -5],\n [-3, 6, 5, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 0, 4, -5, 4],\n [5, -1, -2, -5, 2],\n [3, -6, 3, -3, 0],\n [-1, 5, 5, -4, 0],\n [-5, -3, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -3, 4, -6, 5],\n [5, 3, -6, -3, 3],\n [-1, 6, 5, 4, 1],\n [1, 0, -6, 2, 6],\n [-2, -1, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -4, -3, -6, 6],\n [0, 2, 5, 6, -3],\n [-4, 0, 3, -3, -4],\n [-5, 2, 5, -5, -3],\n [-6, -1, 6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -6, -4, -5, 0],\n [-3, -6, 2, -3, 5],\n [-3, 1, 1, -4, 1],\n [-2, 0, -5, -4, -6],\n [-3, 5, 1, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -4, 4, -1, -2],\n [-1, 4, 4, 1, -5],\n [1, 4, 4, -6, 2],\n [-2, -1, 3, 5, 1],\n [-4, -1, -3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -1, 5, -3, -1],\n [-1, -1, 3, -1, 0],\n [6, -6, 2, -1, 2],\n [-6, -1, 2, -6, -5],\n [-5, -4, -3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -2, -5, 5, -5],\n [5, 5, 5, 0, 1],\n [2, -1, -1, 4, 1],\n [5, -5, -6, 3, -6],\n [1, 0, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, -5, 4, 6, 4],\n [2, -2, -5, -4, 5],\n [-5, 2, 5, -3, -6],\n [0, -4, -1, 1, -2],\n [6, 1, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 2, -2, 3, -5],\n [4, 1, 0, 0, -2],\n [-5, -1, -1, 0, -6],\n [4, -5, -1, 0, 4],\n [-1, 4, -6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -2, -4, 5, -1],\n [-2, 4, -3, 4, -1],\n [-3, -5, 2, -4, 1],\n [1, -1, -5, 5, 1],\n [-6, -1, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 5, 0, -3, -2],\n [1, -1, -2, -5, -1],\n [-4, 1, 1, -6, 3],\n [-5, 3, -5, 6, 3],\n [-5, 2, 2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 6, 5, -4, -2],\n [-4, -3, -3, 3, 3],\n [3, 2, -6, 6, -5],\n [-3, -3, 5, -2, 6],\n [2, -4, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -5, 2, -6, -6],\n [1, 2, -2, 5, 2],\n [-4, 2, 0, 0, 3],\n [-2, 2, -4, 0, 5],\n [1, 3, 5, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -1, 0, 1, 4],\n [2, 3, 5, 5, 0],\n [2, -5, 6, 0, 3],\n [-2, 6, -1, -5, 4],\n [5, -1, 6, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 1, -4, 0, -5],\n [-4, 1, 2, 3, 6],\n [5, 0, -4, 2, 0],\n [0, 5, -4, 3, 4],\n [3, 5, 2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 6, -4, 2, -4],\n [4, 6, 6, -4, 1],\n [-1, 3, 3, -1, 5],\n [-2, 1, 3, 4, 2],\n [-6, -3, 0, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -5, -4, 0, -5],\n [-5, -3, 4, 4, -6],\n [4, 2, 2, 0, 4],\n [-3, 3, -6, -5, 0],\n [-2, 5, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -4, 5, -2, -3],\n [-5, -4, -6, 3, 6],\n [-6, 1, -3, 4, -3],\n [3, -3, -4, -6, 2],\n [1, -2, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 3, -5, -4, -2],\n [-6, -2, -4, 5, 1],\n [0, -4, 5, -1, 6],\n [0, -1, -6, -6, 2],\n [5, 3, -2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 6, -3, 6, 5],\n [-1, -3, -5, -2, 2],\n [1, -6, -2, 0, 3],\n [-1, -1, 4, 2, 5],\n [-4, -4, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -3, -1, -3, 0],\n [-6, 0, 1, -2, 3],\n [6, 4, 5, 6, -6],\n [-5, 4, 3, 6, -2],\n [-6, -1, 6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -3, 2, -4, -2],\n [-6, -6, 0, 1, 3],\n [-4, 0, 2, -3, -4],\n [-2, 6, -4, -6, 2],\n [5, 3, -6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -6, -2, -1, 1],\n [0, 0, -5, -6, 3],\n [0, -1, -4, -2, 6],\n [-3, -1, -4, 6, -6],\n [3, -3, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -2, -4, 0, -5],\n [0, 6, -1, -6, -5],\n [-4, 6, 3, 4, 6],\n [-5, 1, -4, -3, 4],\n [2, -4, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 4, 1, 6, -4],\n [4, -1, -4, -3, 6],\n [-2, 5, 2, 1, 1],\n [-5, -2, -2, 6, 5],\n [-4, 5, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 2, 0, -5, 2],\n [-5, 4, -3, 0, 6],\n [0, 1, -1, -3, 3],\n [-4, -1, 2, 2, -1],\n [1, 1, 1, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -2, 2, 5, 6],\n [-5, -5, -3, -4, 4],\n [3, 1, 0, 3, 4],\n [6, 0, -1, -5, 1],\n [-4, 5, 6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 2, -2, -6, 4],\n [6, -1, -1, 2, -6],\n [2, 1, -5, -1, 5],\n [3, 1, -3, -6, 2],\n [5, -4, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 0, -4, -4, -5],\n [1, -1, 0, -5, -3],\n [3, 3, -5, 5, -1],\n [-6, 6, -3, 4, 5],\n [-2, 4, -3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 1, -5, 2, 6],\n [5, -1, 4, 0, 3],\n [4, 3, -2, 5, -3],\n [0, -5, 0, -1, -6],\n [-1, -6, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 4, -5, 0, 2],\n [3, -3, 2, -1, 6],\n [4, -3, -3, 0, -3],\n [0, 0, 4, -6, 1],\n [2, 5, -4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -6, -6, 4, 5],\n [0, -4, 2, -3, 5],\n [2, -2, 3, 1, 3],\n [3, 2, 0, 4, 2],\n [-4, 0, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 1, -5, 5, 1],\n [-5, 0, 4, 0, 3],\n [1, -3, -3, -6, 5],\n [5, 3, -2, 2, -1],\n [1, 0, 3, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 6, 2, 4, -5],\n [-6, 3, 0, -6, -5],\n [5, -6, -6, -5, 0],\n [3, -4, -6, 4, 4],\n [-2, -3, 5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 3, -4, -4, 1],\n [4, 2, 3, -5, 1],\n [-2, 5, 2, 4, 1],\n [5, -2, 0, -5, -5],\n [-1, 6, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 3, 6, -1, -1],\n [-2, -3, -1, -6, -4],\n [-1, 1, 5, 2, -1],\n [-2, 4, -5, -1, 5],\n [-5, 5, 2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 4, 4, 4, 1],\n [1, 3, 1, -3, -6],\n [5, 4, 4, 2, 6],\n [-1, 0, 6, -4, -6],\n [2, -4, 3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 5, 1, 4, 6],\n [-4, 3, 1, -5, -4],\n [-1, -1, 3, -4, -5],\n [-1, 3, -1, 0, 1],\n [-4, -2, 1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -2, -1, -1, -1],\n [2, -1, 6, 1, 1],\n [-2, -6, -6, 4, -2],\n [4, -6, -1, 2, -5],\n [-1, 5, -2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 4, 6, 4, 0],\n [6, 6, -6, 0, -1],\n [2, -2, 4, -1, 2],\n [-3, -1, 5, -5, -4],\n [-6, -4, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -1, 0, -1, 1],\n [-1, 5, 0, 5, 2],\n [-1, 4, 6, 6, -1],\n [6, -1, 4, 4, 4],\n [6, -4, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 4, -3, 4, 5],\n [-5, 6, 2, 3, -6],\n [5, -2, -6, 0, -5],\n [-3, 4, 4, 3, -3],\n [0, -1, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -2, -1, -6, -1],\n [1, 0, 5, 2, 1],\n [-2, -6, 1, -3, -3],\n [6, 0, -3, -4, 5],\n [4, 0, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -3, -1, 5, 1],\n [-4, -6, 1, -3, 2],\n [0, -3, 0, -5, 1],\n [-6, -2, -2, -2, 3],\n [-1, -5, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 6, 3, -6, 6],\n [-6, 0, 5, 0, 1],\n [6, -6, 5, -6, 0],\n [6, -1, 3, 4, 2],\n [-4, 3, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -4, 6, 0, -1],\n [3, 4, -6, -3, -1],\n [2, 5, 5, 5, -2],\n [1, -3, 0, -5, 1],\n [6, -4, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 1, 1, 0, 5],\n [2, 4, 6, -5, -6],\n [-6, 2, 4, -1, -4],\n [6, -5, -1, 1, 2],\n [1, 2, 2, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 1, 6, 3, 3],\n [6, 2, 1, 5, -1],\n [6, -5, -1, -2, 2],\n [1, 5, -2, -5, -6],\n [2, -1, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 5, 2, -2, -4],\n [0, 2, 6, -3, -4],\n [3, -2, 0, -4, 3],\n [-4, -2, -1, 5, 1],\n [5, 1, -5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -5, -6, -3, 4],\n [4, -4, -4, -5, -4],\n [-1, -5, 2, 4, 5],\n [-5, 1, 2, -3, -6],\n [4, -1, -6, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 4, -4, -5, -3],\n [1, 4, 4, -2, -3],\n [-2, 2, 4, 5, 4],\n [3, 6, 6, -4, 0],\n [-5, -6, -4, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 1, -2, -3, -3],\n [-2, 3, 2, -6, 2],\n [1, 3, 0, -4, 4],\n [-5, 0, 0, 4, -6],\n [6, -4, 2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 0, -4, 2, 1],\n [2, -6, -5, -3, -6],\n [1, -5, -5, 4, 0],\n [4, 0, -5, 5, -2],\n [1, 1, 0, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 4, 3, 6, 6],\n [4, -6, 1, 1, -3],\n [-6, -3, -4, 6, -3],\n [4, -3, -4, 3, 0],\n [-6, -6, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 0, -2, -3, 5],\n [0, 5, -5, -4, -3],\n [-4, 5, 5, -1, 6],\n [-4, 4, 5, -6, -5],\n [1, 4, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 3, -3, 1, 2],\n [3, -5, 4, 2, 2],\n [-2, 2, -5, -3, -2],\n [-3, 5, -2, 1, -6],\n [5, -1, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, 3, 6, -2],\n [-6, -4, 0, 3, 1],\n [1, 6, -2, -5, 5],\n [4, 5, -6, -3, 2],\n [6, 6, -2, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -6, -4, -1, -3],\n [0, 5, 6, -1, -3],\n [-2, 4, 3, -6, -5],\n [-1, -1, -5, -2, -2],\n [-6, 3, 6, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -5, 5, -2, 1],\n [0, 6, 3, 1, 3],\n [1, 0, 1, 2, 6],\n [-4, 5, 1, 1, -3],\n [-3, 0, -2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, -5, -4, 4],\n [-3, -2, 0, -6, 5],\n [5, -4, -6, 5, -5],\n [5, -1, -5, -2, -6],\n [1, -1, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 0, 3, -3, -4],\n [5, 2, 0, 6, -2],\n [6, -4, -4, 2, 1],\n [6, 6, 5, -5, 3],\n [-2, 1, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, -4, -4, -3],\n [0, 2, -6, -3, 2],\n [-4, -1, 0, 6, 2],\n [-2, 2, 2, 6, 6],\n [-2, 2, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -1, 6, 3, -2],\n [2, 3, 5, -4, -2],\n [1, -2, -6, -5, 4],\n [6, -3, -1, -6, 3],\n [-4, -1, 2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 0, 0, 3, 4],\n [3, 2, 3, -2, 4],\n [3, 3, -3, 3, -5],\n [-3, 5, 6, 3, 6],\n [0, -6, 5, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -2, -6, 3, 6],\n [0, 4, 6, -3, 2],\n [0, 4, 0, -3, 5],\n [-5, 5, -3, 0, -5],\n [4, 5, -4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -1, 1, -3, -2],\n [3, -4, 0, -1, -3],\n [3, 2, -2, -5, -4],\n [5, -2, -6, -3, 6],\n [4, 1, 3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -3, 5, -3, 1],\n [-4, 4, 2, -4, 0],\n [-5, -4, 2, -4, -2],\n [-6, -4, -4, 6, -3],\n [3, -4, -5, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -4, 3, -4, 0],\n [-4, 2, -5, 4, -1],\n [-4, 4, -5, -3, 4],\n [-2, -4, 6, -5, -5],\n [-6, 4, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 6, 3, -2, 0],\n [-6, -1, 6, -1, -6],\n [6, -4, 0, -4, -6],\n [3, 0, 6, -1, 6],\n [-3, 4, -3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -4, 6, -1, 0],\n [2, 4, 2, 4, 3],\n [3, 4, 4, -1, 4],\n [-3, -3, 0, 2, -6],\n [1, 5, 3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, -2, -1, -3],\n [-6, 1, -5, -5, 6],\n [4, -2, -2, -6, 4],\n [4, -6, -2, -2, 4],\n [-5, 4, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 1, 2, 6, -2],\n [2, -1, 4, -2, -2],\n [-2, -6, -2, -1, 5],\n [-2, 5, -2, 5, -3],\n [2, 6, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 2, 3, 0, -2],\n [-3, -2, -4, -5, -6],\n [-6, 6, -6, 1, -4],\n [-5, 1, -3, 0, 2],\n [2, -6, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -1, 2, 6, -4],\n [6, -3, -5, 1, 1],\n [2, 1, 4, 6, -5],\n [4, 0, -6, 3, -3],\n [-2, 6, 5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -1, 3, 2, 5],\n [5, 4, 1, 1, 5],\n [-1, -5, -3, 3, -3],\n [1, -6, 6, -5, -3],\n [-1, -3, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -5, 5, -6, 6],\n [-5, -6, 6, 5, -5],\n [-2, 3, -4, -4, -4],\n [-1, 1, 3, 0, 5],\n [-3, 2, -3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -4, -6, 1, 3],\n [4, -6, -1, 2, 4],\n [4, -2, 4, -3, 3],\n [-3, 3, 6, -4, -6],\n [-3, -6, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 5, 2, -2, -4],\n [0, -4, -4, -4, 1],\n [2, -4, 6, 3, -4],\n [6, 0, 6, -2, 4],\n [-4, 0, -2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 4, 3, -6, -5],\n [-1, 5, -2, 4, 0],\n [5, 4, -3, 2, -5],\n [5, 3, 2, 4, -4],\n [-3, -1, 5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -3, 6, -4, 3],\n [-2, 5, -5, 4, 3],\n [-1, 6, -6, -6, 6],\n [1, 1, 3, -6, -1],\n [-6, 5, 1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[4, 5, -5, -2, -4],\n [-3, 1, -3, -6, -3],\n [4, 1, 5, -4, -4],\n [2, 3, 1, 0, -3],\n [-4, 2, 4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -6, 2, 0, -6],\n [4, 4, 2, 3, 1],\n [2, -3, 6, 1, 4],\n [2, 2, -3, 6, -3],\n [-1, 3, 5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, -6, 6, 2],\n [1, -5, 3, 6, -6],\n [-5, -3, 4, 5, -5],\n [3, -4, 1, -3, 6],\n [-3, -2, 5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -3, 2, 5, 1],\n [-1, -1, 5, -6, 5],\n [-5, -2, -4, -3, -2],\n [-1, -1, -4, -3, 1],\n [3, 4, -5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 6, 1, 2, 6],\n [2, -1, 1, -3, -6],\n [4, 1, 3, 6, -6],\n [-4, -1, 0, 1, 0],\n [-4, -6, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -1, -3, 6, 6],\n [3, -4, -2, 0, -4],\n [4, -6, 3, 6, 1],\n [-3, -2, 0, 1, -1],\n [-2, -3, 4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 0, 3, 5, 6],\n [1, -6, 4, 3, 2],\n [-3, 6, 4, 6, 0],\n [5, -1, -3, 4, 0],\n [-5, 6, -4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 5, -5, -6, -2],\n [-3, 0, -5, 6, 2],\n [2, -4, -6, 5, 4],\n [-5, -3, 0, 0, -6],\n [1, -6, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 6, 0, 4, 2],\n [1, -1, 1, 0, -6],\n [0, -1, 5, 3, 1],\n [4, -2, 2, -4, 3],\n [-1, 3, 4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -1, -3, -2, -2],\n [5, 2, 4, 4, 6],\n [1, -4, -5, -6, 3],\n [0, 5, 6, -4, -6],\n [-6, 2, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -5, -3, -1, -5],\n [-3, 0, 4, -5, 2],\n [-4, -1, 1, 3, 3],\n [-6, 2, 4, -5, -4],\n [2, 1, -3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -1, 5, 2, 2],\n [0, -5, -6, -5, 2],\n [0, -4, -5, -4, -5],\n [4, -1, 5, 1, -5],\n [-2, 0, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 3, -4, -2, -4],\n [-3, -5, 6, 4, 6],\n [-1, 4, -5, -5, 4],\n [-2, 2, -3, -6, 1],\n [-5, -2, 4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 2, -4, 3, 3],\n [6, -6, -3, 3, 5],\n [-5, 5, -4, -5, -4],\n [-4, -4, -2, 2, -1],\n [0, -1, 6, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 4, -4, 6, -1],\n [4, -6, 3, -3, 5],\n [5, 1, 5, -1, -1],\n [5, -5, -1, -5, -2],\n [6, 0, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 6, -3, -6, -5],\n [-5, 5, -5, 4, 1],\n [1, 5, -2, -2, -4],\n [-6, -4, -5, -2, -4],\n [-1, -3, -5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -2, 2, 0, 4],\n [4, 0, -5, -6, 6],\n [1, -1, -5, 0, -5],\n [1, 0, 0, 4, -1],\n [0, -4, 6, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -5, 2, -3, -5],\n [4, -3, -6, 0, 1],\n [6, -5, 2, 6, -5],\n [2, 4, 3, -1, 2],\n [2, -3, -6, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -3, 2, -2, 0],\n [-6, -2, -6, 2, -6],\n [-6, 5, 0, 5, -5],\n [6, -2, 4, -4, -1],\n [-1, -5, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -4, 1, -4, -4],\n [4, 1, -3, 0, 5],\n [-1, -2, 4, -4, 5],\n [-6, -6, 1, 6, -5],\n [-4, 5, 2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 1, 4, -4, -6],\n [-6, 6, -4, -3, 0],\n [0, 4, 3, -4, -5],\n [-3, 4, 3, 4, 2],\n [-3, -6, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 3, -4, 0, -3],\n [5, 5, 5, -3, -6],\n [-4, 6, -5, 6, 2],\n [-2, 1, -6, -4, 6],\n [-2, 4, 3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -5, -5, -5, 5],\n [1, 5, -1, -5, -4],\n [-3, -4, 1, 5, 2],\n [1, 3, 5, 6, 4],\n [-6, -6, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, -5, 4, 2],\n [0, -4, 3, -4, -4],\n [-1, -5, -1, 0, -3],\n [6, -3, -5, 1, -4],\n [3, -3, 0, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 3, -2, -1, 0],\n [-2, 6, -3, 2, -1],\n [-5, 1, 5, 5, -1],\n [-1, 4, -5, -3, -6],\n [-4, 0, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, -5, 3, 5],\n [0, -2, 0, -6, 4],\n [3, -3, 5, 5, -1],\n [4, -1, 4, 3, 1],\n [6, 2, 3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -5, 3, 1, 0],\n [2, 5, 0, -3, 6],\n [0, -5, -2, 6, -6],\n [3, 2, 2, 2, -1],\n [0, -5, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, -6, 3, 4],\n [-2, -4, 3, 6, 2],\n [-1, -6, -6, -3, 6],\n [-5, -1, -3, 5, -2],\n [5, -4, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 5, -1, -4, 2],\n [3, -5, 5, -4, 6],\n [6, -3, -4, 5, 1],\n [-6, -4, -3, 1, -6],\n [-5, 4, -5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 0, 6, -6, 4],\n [-2, 0, 3, 6, 5],\n [-5, -5, 3, -4, -1],\n [1, 3, -6, 5, 4],\n [4, -1, 0, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -3, -6, 1, -1],\n [-1, -6, 1, -5, 3],\n [6, -3, 6, 5, 5],\n [-5, -6, 2, -3, 2],\n [2, 0, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -6, -4, 0, 4],\n [-1, 3, 4, -2, 2],\n [-4, 3, 1, -2, -2],\n [-5, 0, 3, 6, -1],\n [-5, -3, 4, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 1, -4, -1, 3],\n [6, -2, 6, -3, 0],\n [-4, -6, 0, -2, -6],\n [-1, -3, 6, 2, 4],\n [1, 6, 2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 0, 6, 3, 5],\n [0, -2, -3, 1, 4],\n [-1, -1, 2, 1, 2],\n [-2, -4, 5, 3, -2],\n [-5, 2, 2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, 6, 1, -2],\n [-2, 6, -3, -4, 0],\n [4, 2, 2, 1, 6],\n [1, -2, -1, -6, 0],\n [6, 5, -4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -3, 4, 6, -3],\n [-3, -1, 2, 3, 1],\n [1, 0, -5, -5, -3],\n [-1, -4, -4, 4, 0],\n [1, 3, 3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 3, -2, 5, 5],\n [-2, 1, 3, 5, -4],\n [0, 0, 1, 4, 1],\n [0, 4, 2, -6, 3],\n [0, 5, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -5, 2, -3, 2],\n [-1, -4, -4, -2, 5],\n [3, 1, -1, -3, -1],\n [-6, 3, -4, 2, -6],\n [0, 4, -1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 6, 3, -2, -2],\n [-4, 0, 5, -1, -3],\n [1, -5, 0, 4, 0],\n [3, 1, 0, -5, 2],\n [0, 3, 5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 6, -6, -4, -1],\n [-4, 6, -4, -4, 0],\n [0, -5, 4, -1, 2],\n [2, -3, -4, -1, -4],\n [3, 4, 5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 3, -2, 3, 2],\n [-5, -3, -4, -1, -5],\n [-6, -3, 1, -6, -4],\n [3, -1, 1, -5, -6],\n [5, 4, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 6, 4, 0, 2],\n [-1, 0, 3, 5, -3],\n [-5, -5, 1, 6, 5],\n [0, 6, -5, 5, 4],\n [0, 5, 6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -1, -5, 1, -6],\n [0, 3, 0, 4, -2],\n [5, -3, 0, 4, -4],\n [-2, -6, -2, 3, -1],\n [3, 0, 1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -3, 0, -3, 3],\n [5, 2, 6, -6, -6],\n [-3, 4, 4, -6, 3],\n [-5, -1, 2, -1, -3],\n [4, -5, -3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, 0, 5, -5],\n [0, 5, -4, 1, 2],\n [1, -1, -1, 2, 4],\n [2, -2, -3, 5, -2],\n [-4, 0, -3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -6, 0, -6, -2],\n [-1, 0, -6, -2, -4],\n [-1, -5, 1, -6, 4],\n [1, 0, 4, 3, 0],\n [4, -1, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -6, 6, -3, -6],\n [-1, -4, 4, -6, -3],\n [2, 3, -6, 3, -4],\n [4, -1, -3, 0, -3],\n [-6, 1, -3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 0, -1, 4, 2],\n [3, 0, 4, -4, 2],\n [-3, 5, -5, -4, 0],\n [6, -1, -4, -1, -1],\n [-6, 0, -5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, 5, -5, -4],\n [6, -6, -6, -2, -3],\n [-2, -2, 3, 5, 4],\n [-6, 5, 1, 3, 6],\n [-6, -3, 2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 4, 1, 3, 6],\n [0, 1, 2, -1, 3],\n [-4, 6, -1, 1, -1],\n [3, 2, -1, -6, 5],\n [1, 0, 5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -2, 5, -1, 0],\n [0, 4, -6, 6, -3],\n [6, 2, 3, -6, -2],\n [-4, -4, 4, 5, 5],\n [6, -2, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -4, 0, 2, 1],\n [0, -2, -2, 0, 0],\n [5, -4, -5, -6, -3],\n [6, 0, 4, 0, 3],\n [3, 5, -5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -3, 0, -3, 2],\n [-3, -2, 1, 0, -2],\n [5, -3, -5, -5, -5],\n [4, 6, 3, 2, -1],\n [0, -2, 5, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 3, -3, -5, 5],\n [-6, -3, 0, -5, -6],\n [1, -5, 6, 2, 5],\n [-5, -6, 1, 1, 3],\n [-6, 4, 5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 5, 5, 2, -5],\n [-2, -6, 1, -2, 2],\n [3, 6, -3, 3, 6],\n [-3, 0, 3, 4, -2],\n [3, 5, -3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 6, -1, 2, 6],\n [5, -2, 1, 5, 0],\n [0, 2, -5, 3, 5],\n [4, 1, -3, 1, -2],\n [-5, 0, -5, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 5, 0, -2, 3],\n [-1, -1, -2, -4, 5],\n [3, 1, -2, 3, 6],\n [0, 2, 1, 2, 2],\n [-3, 6, -4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -5, 1, 6, -1],\n [1, -6, 3, -3, 0],\n [4, -1, -4, -1, 3],\n [1, 0, -4, -2, 2],\n [-3, 1, 0, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 1, -5, 3, 4],\n [4, 1, 4, 3, 5],\n [5, -2, 6, -2, -1],\n [1, 5, -4, 3, 6],\n [0, 5, 4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, 4, 3, 2],\n [-3, -5, -2, 3, 2],\n [0, 4, 3, -2, 3],\n [4, 2, -6, -6, 2],\n [-1, -4, -4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 6, -2, 5, 5],\n [2, 4, 1, 2, -6],\n [1, 5, -5, -1, -3],\n [6, 3, -2, 6, 4],\n [-5, 2, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 3, 3, -3, 6],\n [4, 0, 6, -1, 5],\n [4, -4, 6, -1, 5],\n [3, -1, 4, -1, -1],\n [-5, 5, 2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 4, 6, 0, -5],\n [-6, 2, -2, -1, 1],\n [-2, 1, -6, 2, -2],\n [-4, 2, -6, 4, 0],\n [-6, -2, 3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 3, 3, -6, -4],\n [3, -1, -1, -4, 1],\n [-1, 5, -5, 6, 2],\n [3, 0, -6, -5, -1],\n [-2, 0, -5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 5, -4, -5, 0],\n [0, 2, 4, 4, 1],\n [2, -2, 5, 3, -5],\n [3, 2, 4, -1, 1],\n [1, -1, 6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 4, 1, 1, -5],\n [6, 0, 2, -5, 1],\n [5, 1, -2, -3, 4],\n [3, 2, -5, 3, -2],\n [0, 0, -1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, -6, -6, 6],\n [-6, 6, -5, -2, 6],\n [-2, -3, -5, 1, -4],\n [-6, 4, 4, 0, 6],\n [1, -2, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -3, -5, -4, -5],\n [-2, 3, 4, 3, -5],\n [-4, 6, 2, 2, -5],\n [3, -3, -5, -2, -3],\n [6, -2, 1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -2, -3, -4, 5],\n [-5, -5, 0, 3, 3],\n [-6, -5, -5, 1, 3],\n [1, -1, -2, 4, 2],\n [1, -5, -5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 3, -1, -2, -4],\n [-6, -1, -4, 4, 3],\n [-1, 5, 3, 6, 2],\n [-4, -3, 0, 4, 3],\n [-1, -1, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -4, -2, 2, 5],\n [-3, 3, -6, 3, 6],\n [-3, 4, 0, -5, 4],\n [4, -4, -1, -5, 6],\n [3, -2, 4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -2, -4, -3, -3],\n [3, 3, -2, -4, 3],\n [2, -3, 4, -5, 1],\n [5, 4, -5, 3, 5],\n [-6, -1, 3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -1, 3, -3, 6],\n [-3, -5, 5, 6, 3],\n [-5, -3, 1, -1, 2],\n [4, 0, 1, 5, 2],\n [3, 1, 1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 0, -5, 3, 6],\n [-3, -5, -5, 0, -6],\n [0, 6, 5, -5, -4],\n [4, 2, -4, 1, -5],\n [4, 2, 6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -4, 5, 4, 4],\n [4, -5, 3, 0, -1],\n [0, 5, 1, 4, -2],\n [5, -1, -4, 6, 1],\n [-6, 1, 6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -6, 1, 5, -5],\n [6, -6, -1, 6, -2],\n [-2, -4, -2, -3, 0],\n [5, 4, -3, 0, 1],\n [0, -4, 6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 4, -1, 5, -4],\n [5, -6, 4, -1, 6],\n [-5, 5, 0, 3, 5],\n [-4, -2, 2, 3, -2],\n [1, 1, 6, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 4, 5, -5, 4],\n [5, 1, 3, 4, -4],\n [-5, 2, -6, -5, 1],\n [6, -6, -2, 3, 4],\n [-3, -1, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 4, -4, 2, 6],\n [-6, 0, -1, 1, -6],\n [-1, -2, -1, 2, 3],\n [-3, 1, 2, -6, -1],\n [1, -2, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 2, 2, 3, 3],\n [5, -4, 2, 0, -5],\n [0, 3, 3, 1, 2],\n [-6, 2, -3, 6, -6],\n [-5, -1, -4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -6, -2, 1, -1],\n [1, 3, -1, -3, -2],\n [5, 5, -5, -2, 4],\n [3, -5, 6, -6, -4],\n [1, -3, 3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 4, -5, -1, 0],\n [2, 6, -4, -6, 5],\n [-6, 1, 6, 0, -1],\n [3, -6, 2, 2, 5],\n [4, 4, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 2, 5, 4, 2],\n [-1, 6, -5, -4, -6],\n [2, -1, 5, -1, -5],\n [-2, -5, -5, 5, -6],\n [6, -2, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -3, -1, 4, -2],\n [-4, 1, 1, 3, 0],\n [-5, -4, -3, 0, -4],\n [-5, 5, -2, 1, -5],\n [-4, -4, -1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -4, -3, 6, 5],\n [3, -6, -3, 1, -3],\n [0, 5, -2, -5, -1],\n [-1, 5, -1, -5, 5],\n [-5, -1, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 6, 3, 2, -3],\n [3, 6, -5, 4, -6],\n [-6, -3, 3, 1, 1],\n [2, -4, 6, 3, -5],\n [-5, 2, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -5, -5, 2, -2],\n [5, 2, 5, 1, 2],\n [-4, 1, -5, 2, -3],\n [-1, 0, 4, 5, -5],\n [-6, -1, -5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -6, 4, -1, -6],\n [-6, 6, 2, 4, -5],\n [5, 2, 4, -1, 2],\n [3, 4, 6, 3, -1],\n [1, 1, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -5, -2, -6, 2],\n [6, 4, 1, 5, -3],\n [2, 1, -6, 3, -6],\n [-6, 2, -4, -3, 2],\n [-4, -1, -1, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 4, -2, -6, 2],\n [0, 3, -3, -5, 1],\n [-1, 0, 5, 3, 4],\n [-6, -4, 4, -5, -5],\n [-2, 3, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -6, 5, 1, 2],\n [3, 5, 1, -3, -3],\n [-2, 6, 2, 0, 3],\n [1, 0, 3, 2, 5],\n [-6, -3, 6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -6, -2, 3, -6],\n [4, 3, -3, -6, 5],\n [-1, -6, -5, 3, 0],\n [-6, 5, 5, -6, -4],\n [-5, 1, -5, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 0, 1, 3, 1],\n [-4, 3, 4, 3, 1],\n [-2, -5, 5, 5, 3],\n [2, 1, 4, -5, -4],\n [6, 2, -6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 4, 2, 2, 4],\n [5, 0, 6, 1, -3],\n [-4, -2, 1, -2, 5],\n [0, -3, 2, -4, 1],\n [-3, 4, 4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, -5, 3, 0],\n [1, 1, 6, -5, 4],\n [1, -3, 3, -1, -2],\n [-3, -6, -4, 5, 5],\n [-3, 3, -1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 6, 1, 4, -1],\n [4, -6, 5, 0, 5],\n [3, -6, -1, -2, -3],\n [5, 3, -4, -1, -1],\n [3, -4, -6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 6, 2, 1, 0],\n [-4, 2, -3, -4, -5],\n [-5, 5, 5, 0, -4],\n [-3, 3, -6, -4, 0],\n [-3, 0, 0, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 3, 4, -4, -6],\n [3, 1, 5, 4, -3],\n [1, -2, -2, -3, -2],\n [2, -3, 1, 5, 5],\n [1, -3, 0, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -6, 6, 2, 2],\n [1, 0, -2, -2, 6],\n [-6, -5, 5, -1, 2],\n [-3, 6, 1, -3, 1],\n [0, -2, 4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 5, 6, 3, 3],\n [-5, -4, 4, -2, -6],\n [2, -2, -4, 2, -4],\n [3, -6, 6, -4, 1],\n [5, -3, 1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 0, -3, -1, 2],\n [-5, -2, 1, 3, 2],\n [1, 2, -6, -2, -3],\n [-6, 5, 2, -4, -3],\n [-3, -5, -4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -2, -5, -1, 5],\n [-6, 0, -3, 1, -2],\n [6, 6, -4, -4, 1],\n [1, 0, 1, 3, -4],\n [-1, -4, 3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 3, 0, 3, 4],\n [5, 3, 6, 6, -6],\n [-6, 4, 0, -1, 5],\n [0, 5, -5, 6, 3],\n [-5, -1, -1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -5, 2, -5, 5],\n [-2, 0, -5, -4, 3],\n [0, -2, 5, 5, -6],\n [2, 2, -2, 0, -6],\n [-3, 1, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -3, -5, -2, 6],\n [-1, -4, -4, 0, 4],\n [2, -2, -4, -1, -1],\n [2, -6, 5, 1, 1],\n [-6, 4, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 4, -6, -5, -5],\n [-5, -4, -6, 3, 6],\n [4, -5, 6, -2, 3],\n [3, -6, 4, -6, 1],\n [-1, -3, -2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -4, 6, 3, 1],\n [-6, -2, -3, -2, 2],\n [2, 4, 6, -4, -6],\n [-5, -1, -3, -2, 4],\n [-5, -5, -1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -6, 5, 2, -4],\n [-4, 5, -6, -2, -2],\n [1, 1, -4, 4, -5],\n [-5, -1, -6, -2, -3],\n [3, -1, -2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 4, -2, -1, -4],\n [3, 2, -4, 0, 1],\n [2, 5, -6, -5, -5],\n [4, 3, -1, -5, 0],\n [5, 2, -1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 5, -4, 4, -5],\n [-6, -4, -1, -2, -6],\n [1, 1, 0, -5, 0],\n [-2, 2, -1, -4, 4],\n [-3, 0, -6, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -3, -1, 0, -3],\n [-3, -6, -3, 1, -4],\n [-4, -3, 3, 2, 6],\n [0, -1, 1, 6, 1],\n [-2, -1, -2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -3, 4, 4, 2],\n [-1, 3, -3, 4, 2],\n [4, -3, -2, 0, -3],\n [-2, 1, 1, -5, -2],\n [-1, 2, -6, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -3, -1, 6, 2],\n [2, 1, -1, 6, -2],\n [-3, -3, 4, -4, -1],\n [2, 1, 5, 4, -5],\n [-3, 2, -2, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 3, 2, 1, 2],\n [-5, 4, -3, -3, 5],\n [-4, 1, -3, 6, 2],\n [3, -5, -6, 4, -2],\n [-5, -6, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -4, 6, 5, -3],\n [0, -6, -4, -4, 0],\n [1, 3, 2, -5, -4],\n [-6, 1, -4, -3, 6],\n [0, 6, 1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 5, 0, 2, -3],\n [6, -5, 5, -6, -2],\n [1, -3, 4, -4, -4],\n [4, 1, 0, 3, -2],\n [5, -5, -4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 0, 3, -1, 6],\n [-4, 2, 0, -5, 4],\n [4, 3, -1, -1, 0],\n [-3, 0, 6, 2, 3],\n [5, 2, -6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -6, 3, -4, 0],\n [1, 3, -5, -5, 2],\n [1, 3, 2, -4, 4],\n [1, 4, 4, 2, -3],\n [-6, -6, -6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -6, -1, -1, -2],\n [5, -6, 2, 6, 0],\n [-5, -2, -5, 5, 1],\n [2, 6, -4, -1, 3],\n [-5, 3, 1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 0, 4, 0, 1],\n [6, -5, 0, 4, -1],\n [1, -3, 2, 2, -4],\n [-5, 1, -5, 0, 4],\n [-3, 0, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 5, 1, -2, 1],\n [-5, 3, -1, 4, -6],\n [-5, -5, 2, 5, -2],\n [-3, 5, -1, -6, 0],\n [2, -6, -1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 2, 2, 2, 4],\n [1, 4, 2, -1, 5],\n [-4, 0, -1, 6, 5],\n [-6, -2, 0, 1, -4],\n [-5, 6, 3, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 5, -1, 3, 2],\n [-1, 4, 1, 0, -2],\n [-4, -3, -5, -2, 4],\n [1, -5, -3, 5, -3],\n [2, 0, -3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -5, 4, 0, 1],\n [6, 5, -6, -6, 3],\n [6, 5, 1, -1, 0],\n [-2, 1, 1, 4, -2],\n [2, 4, -2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -5, 6, 0, -4],\n [2, 4, 3, 1, 5],\n [0, 3, -1, 2, 1],\n [4, 3, -3, -3, -3],\n [-4, -3, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, 4, 2, 4],\n [2, -5, 4, 2, 2],\n [-1, 6, 1, 4, -5],\n [5, 2, 2, -6, 6],\n [-4, 5, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -3, 4, 1, -2],\n [-3, 1, -2, 0, -6],\n [-1, 1, -5, -5, 4],\n [-2, -4, 0, 0, -5],\n [-3, 2, 0, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, -3, -1, -3, -3],\n [-6, -3, -6, 4, 0],\n [3, -1, -4, -4, -1],\n [3, -2, -2, -1, -6],\n [-3, 5, 3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 2, 4, 3, 0],\n [-1, -6, -1, -4, -4],\n [5, 1, 5, 3, 3],\n [-3, 1, 2, -2, 0],\n [-6, 4, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, -5, 2, 1],\n [0, 2, 0, 2, -1],\n [4, -1, -1, 0, 2],\n [1, -4, -1, -1, 4],\n [-4, -1, -3, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 2, -4, -5, 6],\n [4, 1, -6, 5, -5],\n [-4, 6, -4, 1, 1],\n [-6, 5, -6, -2, 2],\n [-4, -1, 0, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 1, 4, -2, 6],\n [5, -1, 3, -5, -1],\n [5, 2, -4, 2, -5],\n [6, -1, 6, 6, 1],\n [2, -1, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -3, 3, -5, 3],\n [6, 4, 2, 6, 6],\n [5, -1, 4, 3, 2],\n [-1, -3, 2, 2, 3],\n [2, 0, -1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 0, 5, -2, -2],\n [1, 3, 5, 5, 0],\n [-2, 0, -3, -2, 3],\n [-2, 2, 3, -2, -1],\n [-6, 3, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 4, 2, -4, 0],\n [-6, 5, -1, 6, 2],\n [4, -4, -2, 3, 3],\n [0, 5, 1, 5, 5],\n [5, -1, -4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -4, -5, 0, 6],\n [-1, -4, 6, 0, 1],\n [-3, 0, 4, 5, -6],\n [-1, 2, 2, 1, 4],\n [-3, -5, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 1, -1, 3, 1],\n [3, -5, -5, 1, 6],\n [2, 3, 0, 6, -6],\n [0, 4, 4, -3, 6],\n [-4, 3, 3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 3, -6, -4, 0],\n [4, -6, 1, 0, -4],\n [-1, 4, 3, -6, 5],\n [-5, 0, 1, 2, 3],\n [4, -6, -3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 4, 5, 3, 0],\n [-6, -1, 1, -4, -4],\n [4, -6, -2, -3, 5],\n [3, 2, -2, -5, 6],\n [4, 4, -1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 2, -3, 4, 6],\n [-4, 0, 1, 6, 0],\n [6, -4, -1, 1, 5],\n [-1, -4, 1, -6, 5],\n [1, 0, -1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 6, -4, 3, 2],\n [4, -4, -5, -3, -4],\n [5, -3, 6, -3, -6],\n [4, -5, 4, -3, -1],\n [3, 5, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 0, 6, -3, 0],\n [2, -6, -6, -2, -5],\n [3, -6, -4, 2, -1],\n [2, -3, -2, 0, 4],\n [-6, -4, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 0, 5, -2, 4],\n [-1, -1, 0, 3, 0],\n [-5, 4, 4, 4, -6],\n [-3, 4, 2, -3, 3],\n [-2, 0, 2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -4, -1, -5, -5],\n [1, 1, 6, 5, 0],\n [3, 3, 3, 3, -4],\n [3, 2, -1, 2, 1],\n [3, -1, -3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -4, -6, -5, 1],\n [1, 6, -4, 6, 2],\n [-2, -4, 1, 1, 3],\n [-4, 3, 4, -2, 5],\n [-6, -5, 5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 4, 5, 3, 4],\n [-1, 1, 4, 2, -5],\n [2, 5, 5, 2, 0],\n [4, -5, 1, -3, -1],\n [-2, -4, 5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -6, -1, -2, -2],\n [-3, -3, 4, 0, -1],\n [6, -3, 5, -4, 2],\n [-4, 1, -4, -5, -4],\n [3, -2, -5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -6, 1, -5, 5],\n [-2, -4, -3, 1, 6],\n [1, 0, 4, 4, -3],\n [4, -3, -3, 5, 3],\n [5, 5, -3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -5, 2, -5, 6],\n [-6, -3, -6, 6, -2],\n [5, 2, -1, -4, -2],\n [-5, 3, 2, 3, 4],\n [3, 5, 6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, 6, -4, -5],\n [1, -2, -2, -4, -4],\n [1, 6, 3, -3, 1],\n [-2, 0, 6, 1, 4],\n [-6, 2, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 3, -2, 4, -5],\n [-3, 1, 6, -6, -6],\n [-1, 5, 6, -3, -1],\n [2, 6, -4, -6, -5],\n [-3, 6, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 2, 5, -2, 1],\n [4, 1, 1, 6, 0],\n [-3, -1, 5, -4, 3],\n [6, -1, -6, 0, 2],\n [-4, 4, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 6, -4, -4, 5],\n [-5, 2, -2, 0, 2],\n [-4, 5, 2, -5, -1],\n [-1, 4, -1, 6, -2],\n [3, -3, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 0, -3, 5, -1],\n [2, 5, -2, -5, 1],\n [3, -4, 2, -3, -2],\n [0, 4, -5, -5, 6],\n [4, 2, 5, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 1, 4, -1, -4],\n [4, -6, -4, -6, 1],\n [1, -2, 0, 4, -4],\n [-6, -5, 3, 0, 5],\n [4, -6, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 3, -4, 3, 3],\n [-3, 6, 6, 2, 3],\n [-5, 3, -5, 2, -3],\n [3, 6, 2, -4, -4],\n [5, 6, -5, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -2, -3, -2, -3],\n [4, -2, 2, -5, -3],\n [-6, 4, 3, -4, 4],\n [-5, -6, 6, -1, 5],\n [-6, 5, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -3, 3, 4, -4],\n [3, 6, 3, -6, -5],\n [4, -6, 1, 2, -5],\n [-2, 3, 5, -4, -5],\n [6, -1, -3, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -5, -5, -4, -3],\n [5, 3, 0, -6, 3],\n [-5, 6, 4, 6, 5],\n [-4, 0, 1, 5, -2],\n [3, 4, -1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 6, 1, 6, 1],\n [0, -3, -5, -3, -2],\n [-6, -1, 1, -4, -1],\n [-4, 4, -1, 4, 3],\n [-1, -1, -3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 5, -4, -1, 4],\n [0, -4, -4, -5, -6],\n [5, 1, -6, 1, -6],\n [5, -4, -6, 1, -4],\n [4, 3, 1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 1, -1, 0, 2],\n [-2, 2, -3, -2, 6],\n [-4, 3, 5, 5, 2],\n [-1, 1, -3, 2, 2],\n [4, -4, 4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 6, 3, -1, 3],\n [5, -2, -5, -5, -2],\n [4, 2, 6, 2, -3],\n [6, 1, -1, 1, -5],\n [6, 5, 6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -6, 2, -1, 2],\n [4, -1, 6, 4, 3],\n [2, -1, 4, -4, -3],\n [3, 6, 1, 6, 0],\n [0, 6, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 2, 4, -5, -1],\n [6, 5, 1, 2, -1],\n [-3, -6, -1, 3, 2],\n [2, 3, 4, -6, -4],\n [2, -2, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 1, -4, -3, -6],\n [4, -5, -2, 0, 6],\n [3, -4, 2, 5, -1],\n [-4, -2, -3, -6, 6],\n [0, -1, -5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -1, 3, 3, 4],\n [4, 1, -5, -6, 1],\n [5, 3, -4, 2, 3],\n [3, 5, -5, -4, 6],\n [0, -2, -2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -4, -4, 4, -4],\n [6, 1, 1, 2, 4],\n [-3, 0, 0, -4, -2],\n [-6, -2, 1, 1, -2],\n [-2, 1, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, -5, 0, -2, -1],\n [-2, 4, 3, 6, 2],\n [-3, 4, -2, -3, -5],\n [-6, 1, -1, -3, 1],\n [-6, 3, 4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 0, -5, -6, -1],\n [5, -2, -5, 5, -1],\n [3, 3, -5, 1, 3],\n [5, 1, -2, -5, -4],\n [-1, 4, -5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -5, -4, 2, -6],\n [4, 0, 5, -5, -6],\n [2, 5, -2, 2, 5],\n [-3, 3, -2, 1, 3],\n [1, 4, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, 4, 0, -6],\n [-1, 3, 0, -6, 5],\n [-1, 2, 4, -2, 1],\n [-3, 2, -1, -2, 3],\n [2, 1, 0, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 1, -6, -3, -5],\n [2, -3, -3, 1, 2],\n [-4, -5, -4, -3, -3],\n [-2, 0, 1, -3, 0],\n [-4, 6, -5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 2, -5, 5, 6],\n [-5, 0, 3, 5, -2],\n [-3, -1, 0, -5, 2],\n [-5, 3, 2, 0, 6],\n [2, -3, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, -3, -5, -2],\n [1, -5, 5, -5, -1],\n [-5, -2, 0, 0, 5],\n [-2, -5, 6, -1, -2],\n [-6, 1, -3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -1, 2, -1, 2],\n [0, 4, -1, -5, 2],\n [-1, 1, -4, -3, -3],\n [6, 3, -5, 4, -3],\n [-3, -3, 1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 5, 5, 3, 6],\n [-3, -5, -5, 3, 1],\n [5, -6, -6, -3, 0],\n [6, 6, -1, 0, 0],\n [6, -4, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -2, 5, 1, 2],\n [0, -6, -3, 4, 0],\n [5, 3, -3, 6, -2],\n [-4, 5, -5, 4, 5],\n [-1, 0, 4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 4, 4, 4, -6],\n [1, 1, -2, 3, -6],\n [-4, 5, 3, -2, -3],\n [-4, -1, 3, 4, -6],\n [-6, -2, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 1, 2, 5, 2],\n [-1, 5, -3, -6, -1],\n [-1, 4, 6, 3, -2],\n [6, -4, -5, -1, 3],\n [-5, 2, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 5, 0, 3, -5],\n [-4, 3, -3, 1, -3],\n [2, 3, -2, 4, 2],\n [-5, 2, -5, 2, -2],\n [-1, 6, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 1, 3, -6, -3],\n [-6, 3, 0, 3, -1],\n [0, 1, -1, 2, -1],\n [-3, 0, -4, 2, 5],\n [-2, 4, 2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 1, 5, 1, -4],\n [-4, 3, -6, 5, -6],\n [5, -4, 0, 3, -4],\n [-2, -6, 3, 0, -6],\n [2, 0, -1, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -4, 6, 4, -1],\n [-5, 0, 0, 6, -4],\n [-1, -4, 0, -2, -2],\n [5, -6, -2, -1, 3],\n [1, -4, 0, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, 1, 2, -6],\n [2, -5, 4, -2, 0],\n [3, -4, 6, -6, 2],\n [-4, -1, 0, 4, 6],\n [-3, -3, 5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, -3, 2, -3],\n [1, 5, 0, 5, 1],\n [-4, 3, -4, -2, -2],\n [6, -5, -6, 2, -3],\n [-3, 0, -2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -6, -1, 4, 1],\n [-2, 3, -1, -2, -2],\n [6, -6, 0, 0, 6],\n [-6, -4, -1, 5, -1],\n [3, 1, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -3, 0, 2, -4],\n [-2, -3, -1, -2, 1],\n [-2, 1, 2, 4, 1],\n [3, 4, 5, 6, 6],\n [-4, -5, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -2, -4, -6, 1],\n [-4, 4, -4, -3, 6],\n [-4, 1, 2, -5, 2],\n [6, 1, 4, -4, 6],\n [-5, -1, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -5, -5, 1, 3],\n [1, -5, 3, 0, 6],\n [-3, -2, 3, 4, 3],\n [-2, 6, -2, 3, -5],\n [4, -4, 3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 2, 6, -4, 2],\n [6, -1, -1, 6, 4],\n [1, -5, -1, 2, 4],\n [1, -3, -3, -5, -3],\n [-1, 6, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -1, -3, 0, 0],\n [4, 1, -2, -4, -2],\n [2, -3, -2, 5, -6],\n [5, 6, 2, -6, 5],\n [2, -5, -6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -3, -5, -2, -1],\n [5, 5, 1, 6, -2],\n [-2, 4, 5, -2, 4],\n [-2, 5, -3, -4, 2],\n [-6, -2, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 0, -5, 4, -4],\n [-3, 3, 5, 5, -5],\n [6, 2, -3, 0, -1],\n [-6, -2, 6, -6, -2],\n [0, -5, 1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -3, -1, 4, -5],\n [-1, 0, 4, -5, -5],\n [1, 6, 2, -4, 1],\n [0, -3, 2, 2, 5],\n [5, 3, 5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -3, -4, 0, 0],\n [5, 4, -3, -2, -3],\n [-2, -3, 4, -2, -5],\n [4, 2, 4, -4, 6],\n [-1, 0, 2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -4, -2, 6, 1],\n [-2, -1, -2, -6, 6],\n [3, 5, -1, -4, 6],\n [-2, 1, -1, 3, 0],\n [-1, 0, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 5, 5, -2, 5],\n [-1, -5, 2, 2, 0],\n [3, -6, 2, 1, 1],\n [1, -6, 6, 0, -3],\n [-5, 2, -6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -6, -1, -1, 6],\n [6, 1, 1, -1, -1],\n [1, 0, -3, 0, 0],\n [0, -1, 4, -5, 2],\n [-5, -5, -5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -5, 2, 4, 1],\n [-4, 2, -6, -5, 2],\n [-6, 0, -3, -3, -3],\n [-4, 1, 2, 5, -3],\n [-3, 1, -4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 2, 3, -6, 1],\n [6, 2, 1, 3, 2],\n [4, 2, 2, -4, -2],\n [6, -4, 4, 0, -3],\n [-5, 6, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 5, -1, 3, 1],\n [2, -2, 2, -6, 3],\n [-2, -2, 6, 5, 3],\n [0, 3, 5, -6, -4],\n [-6, 1, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -5, -1, -1, -4],\n [0, -1, -3, -5, 4],\n [-1, -6, 5, 3, 2],\n [-2, 4, -5, -6, 3],\n [-3, -2, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 6, -2, -6, 5],\n [-2, -5, -1, 1, -1],\n [-6, 5, -2, 6, -1],\n [3, 2, -4, -4, 5],\n [-3, 1, -4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 6, 1, -2, 0],\n [-4, 5, 2, -3, 6],\n [-4, 3, -2, 2, -6],\n [-6, 5, -5, -5, -6],\n [-5, 1, 0, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -1, -4, 1, -6],\n [5, 2, 1, 4, 5],\n [3, -5, -1, -2, -3],\n [-3, -6, -1, -2, 3],\n [3, 1, 4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, 6, -1, -6],\n [4, 0, 2, 6, -5],\n [0, -5, 6, 0, 0],\n [6, 3, 5, 6, -4],\n [3, 2, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 6, -1, -2, 6],\n [-3, -1, 0, 4, 5],\n [6, 2, -1, -2, 1],\n [-4, 1, -3, -1, 3],\n [6, -3, -4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -3, -4, -1, 1],\n [5, 5, -3, 0, -6],\n [-5, 5, -6, 0, 1],\n [2, -4, 3, -5, 6],\n [-3, 6, 4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -3, 5, 4, -5],\n [4, -3, -1, -4, -5],\n [-5, -2, 6, -1, 2],\n [4, 3, -5, -3, -5],\n [-5, 3, -6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -6, 5, 6, -5],\n [-5, -1, 5, 5, 6],\n [1, -5, 5, 5, 5],\n [1, 0, 1, -4, -5],\n [-4, -3, 6, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 4, -5, -3, 6],\n [1, -4, 4, -2, 6],\n [0, -3, 5, 0, 0],\n [-2, 5, -1, 2, 4],\n [4, 5, -5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -4, -4, 0, 6],\n [-6, -2, 3, 5, 0],\n [-1, 0, 1, 0, -3],\n [6, 5, 1, -3, 1],\n [-6, -2, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -6, 1, 2, 6],\n [-2, -3, 6, 6, 6],\n [-5, -2, -6, -2, -2],\n [-4, 1, 5, -3, -1],\n [0, 6, -3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -6, -1, 5, -3],\n [6, -2, 1, 3, -1],\n [-1, -3, 1, 2, -4],\n [6, 5, 3, -1, 2],\n [2, 1, 2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 0, -2, -1, -2],\n [-3, -2, 3, -2, -4],\n [-3, 6, 2, -5, 5],\n [-3, -4, -4, 1, 3],\n [2, 5, -6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, 4, -6, -6],\n [4, 6, -2, -2, 5],\n [-1, 3, 4, 2, 4],\n [5, -4, 0, -5, -2],\n [-6, 2, 6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -2, 4, 1, 0],\n [-3, -5, -3, -1, 1],\n [-6, 3, 6, 3, 1],\n [-1, -2, -5, -1, 4],\n [1, 2, 5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 6, 1, -6, 2],\n [1, 6, -6, 2, -5],\n [-2, 5, -5, 1, -5],\n [-3, 6, -3, 6, -5],\n [2, -1, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -1, -5, -4, -2],\n [-4, 3, 6, 5, -6],\n [-6, -4, -3, 0, 6],\n [5, 6, -4, -5, -3],\n [3, 2, 4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -2, 6, -3, -1],\n [4, 2, -2, 0, 4],\n [5, 6, -3, -1, 1],\n [6, -3, -2, 0, -3],\n [2, 0, -5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -1, 2, 0, -6],\n [-4, 1, 4, -1, -4],\n [5, 4, -2, -2, 3],\n [-6, 6, -4, 3, -3],\n [-3, -1, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -5, 5, -6, -6],\n [-1, 1, -3, -1, 2],\n [1, 3, -4, -2, 6],\n [2, -1, -6, -3, 3],\n [1, -2, 0, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 2, -3, -3, -3],\n [-6, -2, 4, -3, -2],\n [6, -2, -1, -2, 0],\n [0, -2, 2, -1, -6],\n [-5, 6, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -5, -4, 6, 0],\n [4, 4, 3, -4, 2],\n [-5, -2, -4, 5, -5],\n [-3, -5, -4, -4, -2],\n [-1, -3, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 4, -1, -5, 5],\n [-4, 5, 4, -1, 4],\n [5, -4, -5, -1, -2],\n [-5, 6, 6, 1, 4],\n [-5, -6, -4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -4, 4, -6, 4],\n [3, 6, 0, -3, -3],\n [-1, -6, 5, -4, 4],\n [-6, -1, -1, -6, 3],\n [-6, -6, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -4, 6, 2, 3],\n [-6, -4, -4, 6, -3],\n [1, -1, -6, 6, 6],\n [-6, -4, -2, -3, -4],\n [6, -4, 0, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -3, 3, 2, 1],\n [-2, 4, 4, -5, -6],\n [0, 4, -5, -6, 5],\n [2, -4, 2, 2, 5],\n [6, 6, 1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, -6, 0, 3],\n [2, 0, 3, -5, -6],\n [6, -1, 2, 3, -4],\n [3, -6, 4, 6, -3],\n [-3, 3, -6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 3, 1, -6, -2],\n [0, -3, 3, 0, -2],\n [1, 4, -6, 6, 5],\n [-5, 1, 0, 0, 3],\n [-1, -1, -6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 6, -3, 6, -6],\n [6, 4, 6, -6, 3],\n [-5, 1, -6, 0, 0],\n [4, -4, 5, 4, 4],\n [-1, -2, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, -4, 1, -5],\n [-4, 4, 4, 4, -5],\n [2, -6, 2, -1, 0],\n [5, 3, 5, 3, 3],\n [5, -2, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -3, -4, 3, 0],\n [1, -6, 1, -2, -5],\n [-6, -3, 4, -3, -2],\n [-2, 5, -4, -1, -2],\n [2, 1, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 2, -4, 3, 2],\n [0, -6, -4, -2, -4],\n [0, -1, -5, 1, 1],\n [-5, 6, -1, -3, 6],\n [0, -4, -4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -4, -5, 6, 4],\n [-6, 0, -3, 5, -1],\n [-3, -6, -2, 6, -6],\n [3, 5, -5, -6, -6],\n [-4, 6, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 3, 5, -1, 1],\n [3, 2, -5, 3, 3],\n [-2, 1, 0, -2, -6],\n [1, 3, -3, -5, 5],\n [-1, -6, 3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 0, -4, -1, -3],\n [-5, 2, 4, 6, 2],\n [-1, -5, -3, -2, 5],\n [-5, 3, 6, -3, 5],\n [-4, 3, -3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -5, 1, -3, 4],\n [-1, 6, 3, -5, -6],\n [4, 5, -3, 3, -1],\n [0, -6, 6, 0, -5],\n [-5, -6, -6, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, 4, 0, 1],\n [5, -3, -1, -2, 5],\n [-3, -3, 2, 5, 3],\n [1, -3, 3, 5, 2],\n [4, -3, -2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, -1, -2, 0],\n [4, -5, -5, -6, -2],\n [-5, 6, -1, -6, -3],\n [4, 1, 6, 4, 0],\n [3, -2, -5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 5, -2, 6, -3],\n [6, -1, -1, -6, 2],\n [6, 6, -6, 5, -3],\n [4, 4, -6, -1, 5],\n [6, 0, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 1, -2, -4, 5],\n [-6, 3, 1, 4, -4],\n [2, -5, 1, 5, 4],\n [-2, 1, 4, -6, 3],\n [3, 4, -6, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 5, 1, 3, 6],\n [6, 5, -4, -6, -4],\n [4, 3, 3, 0, 0],\n [5, 5, 5, 6, -2],\n [3, 1, -1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 6, 2, 5, -6],\n [-6, 4, 6, 6, 3],\n [-3, -6, 1, 5, 5],\n [-4, 1, 1, -6, -6],\n [1, 3, 5, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -5, 0, 6, 6],\n [6, -6, 5, 4, -1],\n [-5, -3, 0, -3, 3],\n [5, 0, -3, 3, 1],\n [0, 0, 1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 1, 1, 1, 6],\n [-1, -1, 3, 0, 1],\n [-1, -1, -3, -1, 0],\n [6, -1, 2, 2, 4],\n [-2, -6, 4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -6, 6, -3, 3],\n [-2, -1, 4, 0, -5],\n [-5, 2, 2, 0, -1],\n [6, 3, 5, -1, -5],\n [-1, -5, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 2, -6, -1, -3],\n [-2, 4, 3, 4, 6],\n [-3, -4, 2, 6, -3],\n [-6, -6, -4, -3, -3],\n [6, 6, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -5, -3, -2, -1],\n [-6, 0, -5, 3, -1],\n [-2, 4, 0, -1, 0],\n [-6, 1, 5, 0, 2],\n [-1, -2, -2, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -2, 4, 6, 5],\n [-1, 2, -3, -6, 6],\n [0, 3, 0, -2, 1],\n [0, -2, 3, 3, -1],\n [-4, -2, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -2, -2, 2, 4],\n [2, 2, 2, -6, -5],\n [-5, 5, 3, 0, -5],\n [-2, -6, 3, -1, 4],\n [5, -1, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 5, -3, -3, 3],\n [3, -1, 5, -6, -6],\n [-4, 2, 3, -1, -2],\n [6, -1, -2, 0, 4],\n [2, 3, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 3, 5, 2, -4],\n [-4, -2, 3, 5, 6],\n [-4, -4, 2, -3, 2],\n [2, -4, 3, -5, -1],\n [-6, -4, 5, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -1, 6, 2, -3],\n [-3, 5, -6, -1, 0],\n [5, 3, 3, -2, 3],\n [0, 6, 2, -3, 5],\n [4, 0, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 4, 4, -4, 5],\n [-1, -2, 0, -5, -4],\n [2, 4, 6, -4, 5],\n [5, -2, -6, 3, 2],\n [5, 2, -6, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -6, -6, -6, 4],\n [1, 2, 4, -1, 3],\n [-5, -4, -3, 4, -2],\n [-3, -1, 5, -4, 5],\n [3, 2, -4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 0, 1, -6, 4],\n [-2, -4, 3, 0, 6],\n [5, -6, -6, 4, -5],\n [6, 3, -4, 0, 4],\n [-4, 1, 5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -6, -2, 6, 6],\n [-1, 2, -2, 0, -1],\n [5, 4, 4, -2, -6],\n [5, 6, 2, 1, -4],\n [0, -2, -5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, 1, 4, 4],\n [1, 6, 1, -5, 4],\n [-2, 0, -5, -5, 0],\n [4, -6, 5, 0, -1],\n [3, 2, -6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -3, 0, 1, 2],\n [6, -2, 6, 3, -2],\n [-2, -1, 2, -6, 2],\n [3, 1, -6, -4, 3],\n [2, -5, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -6, -2, 3, -1],\n [3, 0, -4, 0, 4],\n [-4, -2, 4, -2, -3],\n [-2, -6, -2, 0, -6],\n [-5, -5, -5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -2, -6, -2, -4],\n [0, 3, -5, 4, -3],\n [0, 0, -2, 3, 6],\n [5, -4, 6, 6, 1],\n [2, -4, 4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 4, 2, -6, -3],\n [-2, 1, -1, -6, -3],\n [0, 4, 3, 0, 6],\n [-1, 6, -2, 6, -3],\n [-3, 6, 5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 5, 6, -4, -5],\n [4, 1, 0, 3, -4],\n [1, 3, 5, -6, 6],\n [0, 5, 4, 0, 0],\n [4, -3, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 6, 6, -3, 1],\n [-2, 5, 2, 5, 2],\n [-5, 3, 0, 2, -1],\n [3, -2, -4, -5, -6],\n [0, 2, 4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -5, 4, 3, -6],\n [6, -3, 2, -2, -1],\n [-5, 6, -5, 0, -1],\n [2, 2, 6, -5, 0],\n [-5, -6, -5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 1, -2, -5, -2],\n [0, 1, -2, -5, 2],\n [-5, -4, 2, -6, -4],\n [-2, 4, -1, 1, -4],\n [-5, 0, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 1, -5, 1, 3],\n [1, 1, 6, 3, -6],\n [3, -4, 6, 2, 4],\n [-1, 6, 0, 1, 2],\n [-5, 6, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 0, -1, 6, -3],\n [-3, 4, 6, -4, -1],\n [-3, -2, -6, -3, -3],\n [-1, 4, -1, 6, 5],\n [6, 5, 1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -5, 6, 3, -2],\n [-4, 3, 6, -1, -3],\n [-4, -1, 2, -1, -6],\n [5, 2, 1, -4, 6],\n [-6, 2, -1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 2, 6, -6, 3],\n [-3, 0, 2, 4, -3],\n [2, -6, -2, 4, -5],\n [-6, 3, -2, -4, 5],\n [6, 3, 5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -5, -2, 1, -4],\n [-1, -6, 3, -5, 3],\n [-4, -3, -6, -1, -2],\n [-5, 5, -4, 6, 5],\n [-5, 0, 6, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -3, -1, -5, 1],\n [4, -5, 2, -5, 4],\n [-3, -6, -1, -6, -6],\n [-5, 1, -4, -1, 6],\n [5, 0, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -1, -4, -4, -3],\n [-3, 5, 4, -4, 3],\n [-2, -3, -5, 1, -5],\n [3, 5, 1, 1, 2],\n [0, -1, -3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 2, 3, -3, 6],\n [-1, 4, 5, -6, 1],\n [3, 1, -2, 4, 1],\n [5, -2, 2, -3, 5],\n [-5, 6, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, 6, 1, 1],\n [6, -4, -5, 3, -5],\n [-3, -4, 0, -4, 2],\n [-3, 5, -1, -2, 4],\n [-5, -2, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -5, 1, 3, -4],\n [0, 4, -1, -2, -5],\n [6, -6, 4, 1, -4],\n [5, -2, -1, 0, -5],\n [4, 2, 0, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -1, 1, 4, -5],\n [5, -5, 6, 5, 5],\n [-2, 0, 1, -6, 4],\n [-5, -1, 2, 4, 0],\n [-4, -4, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -2, -5, -4, -1],\n [-6, 0, -3, 1, -6],\n [-1, 3, 6, -4, 1],\n [1, 5, -2, 1, 5],\n [-4, 2, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -6, -5, -5, -6],\n [6, -5, -1, 4, 1],\n [0, -1, 4, 6, 3],\n [0, 2, -5, 5, 3],\n [-5, -6, 4, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, 6, -6, -3, 2],\n [1, -1, 6, 5, 0],\n [2, -2, 1, -6, 3],\n [-2, -6, -1, -6, -3],\n [-4, -2, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 5, 4, 0, -6],\n [-3, -6, -2, 5, 2],\n [1, 1, 3, 3, 0],\n [-1, 1, -3, -4, -2],\n [-2, 0, 6, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, 0, -3, 1],\n [6, 6, 2, -1, -2],\n [-2, -6, 4, 3, -1],\n [-3, -1, 6, 4, -4],\n [3, -2, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -3, 0, 1, -5],\n [-2, 1, -1, 5, -3],\n [-4, 6, -5, -6, -4],\n [6, -1, 3, 6, 3],\n [-4, -3, 6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 6, -4, -3, 2],\n [-5, 3, 5, 2, 2],\n [-1, 4, 1, 1, -6],\n [-6, -3, -6, 3, 4],\n [2, -2, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -1, 6, 0, -5],\n [1, 6, 5, 1, 2],\n [-2, -2, -4, -2, 0],\n [-1, 4, 2, -3, -5],\n [0, -5, 0, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 0, 0, -4, -1],\n [-6, -2, 5, 3, 2],\n [-4, 6, 2, -3, 5],\n [-6, 3, 6, -3, -4],\n [-2, 4, -3, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -4, -6, -5, 6],\n [0, 3, -5, 5, 2],\n [-3, -6, 3, 0, 6],\n [-4, -2, 4, -6, -5],\n [-2, 3, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 6, 4, -1, -1],\n [4, 0, 5, 2, 3],\n [5, 2, -2, -2, -3],\n [2, 2, -2, -4, 3],\n [-6, 1, 4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 3, -5, -4, -6],\n [1, 6, 4, -3, 1],\n [2, -6, 0, 2, -6],\n [0, 2, 6, 6, 1],\n [-1, 3, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 5, -3, -2, 4],\n [2, -2, -5, 5, 1],\n [3, -1, -5, -4, 3],\n [-3, 2, 3, 2, 1],\n [-4, 2, -6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 5, 6, -4, -5],\n [-6, 3, 2, -2, -5],\n [-5, 0, -1, 5, -1],\n [6, -5, -6, -2, 0],\n [0, -2, -1, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -5, -6, 0, 5],\n [-4, 4, 2, 0, -2],\n [4, 4, -5, 5, -5],\n [-5, -2, 5, 3, 0],\n [-2, -5, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 1, 5, -4, 4],\n [1, 6, 5, -1, 1],\n [-4, -3, -6, 1, 2],\n [-4, -4, 2, 0, -5],\n [-2, 3, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 4, 5, 4, 5],\n [0, 5, -1, -2, 3],\n [-5, 2, -6, -4, -2],\n [-3, -5, -4, 5, 5],\n [-1, -2, 2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 2, 0, 2, -4],\n [3, -3, 0, -6, 0],\n [4, 2, -6, 4, -3],\n [0, 6, 1, -2, -2],\n [5, -3, -1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -3, 5, 4, 1],\n [-5, 0, 3, -2, 1],\n [4, -5, -1, -4, 5],\n [-2, -2, 4, 0, 0],\n [-5, -6, -3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -2, 6, 1, 5],\n [-6, 5, -4, -2, 4],\n [-4, 0, 3, -2, 0],\n [-6, -6, -5, 3, -6],\n [-6, 1, -5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, 6, 4, 1],\n [-5, -2, 3, -1, 0],\n [0, -1, 3, -5, -1],\n [-2, 0, -4, -1, 4],\n [-1, -3, -1, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -6, -1, 0, 2],\n [3, 4, 0, 6, 4],\n [3, 6, -4, 4, 1],\n [-5, 0, -5, 0, -2],\n [4, 0, -2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 0, 3, -4, 1],\n [6, -6, -1, -4, -1],\n [-5, 4, 6, -1, 5],\n [-3, -5, -1, 0, 0],\n [-1, 1, -4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -2, 4, 1, 6],\n [-4, -1, 1, 6, -5],\n [-6, -2, 0, 6, 1],\n [6, -5, 4, 3, 1],\n [-1, -6, 0, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 2, -2, -4, -6],\n [-3, -1, 3, 4, -3],\n [-2, 0, 5, -6, -6],\n [-6, -3, -3, -1, -1],\n [6, -4, -6, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -6, 2, 4, 1],\n [-4, -3, 1, 1, 3],\n [-2, 3, -6, 3, 5],\n [-5, 1, -6, 0, -3],\n [-6, 6, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 4, 5, 5, 3],\n [-3, -6, -1, 6, 3],\n [0, -3, 1, 5, 6],\n [-4, 2, 4, -5, 6],\n [5, -2, 3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -5, -1, -4, -1],\n [-3, 5, 3, -6, -4],\n [-6, -3, -4, -3, 1],\n [-6, 5, -6, -4, 6],\n [-3, 2, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -4, 2, 3, 2],\n [-1, 5, -1, 0, 6],\n [2, 6, 3, 3, -4],\n [-1, 3, -5, -3, 5],\n [-3, 3, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, 3, 1, 1],\n [2, -2, 6, 5, -6],\n [0, -6, -5, 5, 0],\n [0, -1, 3, 4, 0],\n [-1, 2, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -2, -1, -5, -4],\n [4, 5, 1, 1, 1],\n [-3, -6, 5, -6, 1],\n [-6, -1, 6, -2, -2],\n [-5, -5, 1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 6, -2, 0, 5],\n [-2, 3, 5, 1, 3],\n [-2, 1, 0, 1, -2],\n [1, -6, -4, -5, -6],\n [-3, 0, 4, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 2, -2, 0, -4],\n [6, 3, -2, 4, -6],\n [1, 2, -2, 2, 2],\n [5, 0, 2, 1, -6],\n [-3, 4, -2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 0, 4, -6, 0],\n [-1, 4, 2, 4, 3],\n [-4, 6, 5, 2, 4],\n [-5, 0, -2, -2, 6],\n [-6, 4, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 0, -3, -4, -1],\n [6, 2, -1, 3, -1],\n [0, -4, 3, -1, -3],\n [3, -6, 4, 5, 4],\n [6, 6, 6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 1, -2, 6, 2],\n [-2, 1, -3, -1, -2],\n [5, -3, -3, 6, -2],\n [1, -3, -2, 4, 2],\n [-4, 6, -2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 5, 1, -6, 0],\n [2, -4, -2, -5, -6],\n [1, -2, 5, 4, 3],\n [-2, 4, -4, 2, -2],\n [-3, 2, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -5, 5, -5, 1],\n [0, 5, 6, 1, 3],\n [-3, 3, -6, -1, 4],\n [3, -6, -3, -5, -4],\n [-6, 1, 1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -2, -5, -3, 5],\n [-5, 4, 3, -1, 1],\n [1, 0, 1, -6, -6],\n [-5, 1, -3, 5, 5],\n [-2, 1, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 6, 0, 2, 5],\n [-5, -3, 5, -1, 5],\n [-3, -6, 2, -6, 3],\n [-1, -5, 4, -4, -2],\n [4, 0, 2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -6, 1, -4, -2],\n [2, -5, 6, -3, 5],\n [3, -4, -5, -5, 5],\n [2, 4, 2, -3, -4],\n [1, -5, 5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -6, 2, 1, 3],\n [1, -4, 6, 3, -5],\n [-2, -4, -1, 1, 3],\n [-1, -5, -2, 6, -3],\n [2, 6, -4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, 3, -4, -5],\n [-2, -4, 0, 2, 4],\n [-4, 1, 3, 5, -2],\n [-2, -5, 0, 5, -3],\n [1, 6, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -6, 1, 6, 0],\n [2, -1, -4, 1, 6],\n [4, 6, -2, 4, 1],\n [2, 4, 5, 4, 0],\n [-5, -1, -2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 2, 5, 3, -1],\n [5, -3, -6, -2, 4],\n [0, 0, 5, 1, 0],\n [-3, -1, -4, -6, 0],\n [-4, -1, 0, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -3, -2, -6, -2],\n [0, 4, 4, 2, 3],\n [-3, -1, -1, -1, -2],\n [-6, -1, 6, 3, -1],\n [3, -5, 2, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 5, 3, -4, 1],\n [-3, -1, 6, -2, 6],\n [2, 0, 2, 5, -1],\n [0, 6, -3, 6, 5],\n [3, -5, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 6, -2, -1, -5],\n [5, -1, 1, -5, 1],\n [3, 1, -3, -5, 4],\n [4, 3, 1, -6, -3],\n [0, 1, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -6, -5, -6, 1],\n [4, 6, -4, -6, 4],\n [5, 3, 5, 0, -1],\n [5, -1, 1, -6, -4],\n [-6, -2, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -6, -6, 6, -2],\n [-6, -5, 3, 4, -3],\n [-5, 1, 3, -5, 4],\n [5, 5, -4, 4, -3],\n [5, 3, 5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -1, -2, 2, -4],\n [-2, 0, -5, 2, -3],\n [-4, -4, 3, -2, 2],\n [-4, -5, -4, 0, 0],\n [2, 1, 6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -6, -5, 6, -3],\n [4, 2, -1, 1, 6],\n [0, 3, -5, 3, 5],\n [-2, 1, 3, 2, 6],\n [3, 0, 2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -5, -4, -5, 6],\n [5, -5, -4, -1, -4],\n [0, -5, 2, 3, 2],\n [6, 6, -4, 3, 0],\n [-2, 2, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -2, 1, 1, -3],\n [0, -6, 0, 4, 6],\n [-4, 1, 6, 4, -1],\n [-6, -5, -2, -4, -6],\n [-2, 2, 4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 0, 6, -3, -1],\n [3, -6, 2, 4, -3],\n [-2, 4, 2, 2, -6],\n [3, 0, 4, -5, -2],\n [-6, -6, 0, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -6, 0, 0, 3],\n [-1, 2, 4, 3, 4],\n [3, -5, -3, -3, 3],\n [-2, 3, 6, 0, 0],\n [-3, 1, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 4, -4, 1, 5],\n [4, -1, -4, -2, -4],\n [5, 2, 6, 6, 6],\n [-4, 6, 1, 1, 0],\n [4, 0, 3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 5, -1, 2, 1],\n [-5, 3, 3, 5, 2],\n [-2, 0, -3, -5, -1],\n [5, -6, 5, 0, 0],\n [-2, -1, -3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 0, 4, -1, -4],\n [6, -4, 6, 5, -2],\n [5, 3, -3, -6, -4],\n [0, 4, -5, -2, 3],\n [2, 2, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -6, 5, -5, -6],\n [-1, -3, 1, -3, 2],\n [-2, 3, 5, 0, -2],\n [-5, -1, 4, 6, 1],\n [-4, -4, -5, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 0, -3, -3, -5],\n [2, 1, 2, 6, 0],\n [-2, 1, 1, 2, -4],\n [-3, -6, 6, 3, 1],\n [2, -3, 3, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -1, -5, -2, -3],\n [6, 1, 4, 4, 4],\n [0, -3, -5, 5, 4],\n [-6, 5, 1, 4, -2],\n [-4, -3, 1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 6, 1, -4, 3],\n [0, 5, -1, 1, -5],\n [4, -6, -4, -6, -1],\n [-1, 2, 3, 0, -5],\n [-4, -3, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 2, -3, -4, 5],\n [-2, -3, -3, 2, 0],\n [-1, -1, -4, -6, 3],\n [1, 2, 6, 6, 0],\n [5, 5, 5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 6, -5, -3, 3],\n [1, 4, 2, 0, 4],\n [0, 6, 6, 0, -6],\n [5, -3, -3, -6, 5],\n [-1, -2, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 6, 5, -1, -4],\n [-4, 3, -4, -3, 4],\n [4, -5, -3, 3, -4],\n [-5, 1, 4, -3, 0],\n [-2, 3, -1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -5, 1, -4, 1],\n [-6, 4, -2, -3, 3],\n [-3, -3, 6, 0, 0],\n [-3, -2, 6, 5, 6],\n [-4, -4, 1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -3, 2, 0, 6],\n [5, 1, -3, 6, -6],\n [-4, -2, -2, -2, 3],\n [1, 4, 2, -6, 3],\n [3, -2, 1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 3, 0, -2, 4],\n [1, 0, -2, 1, 1],\n [-4, -1, -1, 6, 5],\n [-3, 2, 5, 2, -6],\n [6, -1, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 3, 1, -2, 1],\n [-4, -6, -6, 5, -4],\n [3, 2, 6, 6, -1],\n [3, -6, 6, -4, -1],\n [-1, -4, 5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 2, -4, -4, 6],\n [1, -2, -3, -3, 0],\n [0, -6, -4, 3, 0],\n [4, 2, -5, 2, -3],\n [2, -2, -3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -5, 0, 6, 4],\n [2, 3, -6, -4, 6],\n [2, -1, -1, -1, 1],\n [2, -4, -2, -1, -4],\n [-2, -3, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -2, 1, -5, -2],\n [6, -4, 5, -4, 5],\n [-2, 5, -6, 0, 0],\n [-6, -5, -3, 1, 2],\n [-4, 3, -3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -5, 3, -4, 0],\n [2, -6, 0, -1, 1],\n [6, 1, -5, -2, 5],\n [2, 1, 2, 1, 6],\n [-2, -3, 6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -1, 6, -1, 2],\n [3, 2, 2, -1, 6],\n [-1, 3, 2, 2, 1],\n [4, -3, -1, 6, -3],\n [2, 2, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 4, -5, -1, -1],\n [-2, 1, 1, -4, 1],\n [6, -2, -1, 4, 5],\n [3, -2, -4, 5, 4],\n [-4, -5, 6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -1, -2, -1, -1],\n [2, 4, 2, 3, -6],\n [4, -3, -4, 1, -4],\n [-6, -1, 1, 6, -3],\n [6, 1, -1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, -2, -2, 0],\n [-4, -5, 4, -4, -4],\n [1, -2, 2, -3, 0],\n [-3, 3, 0, -5, -6],\n [-2, 2, 2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -5, 2, -3, 5],\n [5, 4, -1, 5, 6],\n [1, 2, 2, 2, 6],\n [-5, -1, -5, -1, 5],\n [3, 6, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 0, 6, -6, 2],\n [2, -6, 5, -5, -6],\n [-1, 0, -1, -1, 2],\n [-2, -4, 4, 6, -2],\n [4, 0, -5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -4, 0, 0, 4],\n [4, 6, 1, 3, -5],\n [2, -1, -3, -1, -6],\n [5, -2, -5, 6, 3],\n [-2, -4, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 3, -6, -1, 0],\n [5, -5, 0, 5, 4],\n [0, -2, -3, 2, -2],\n [-3, 0, -4, -1, -2],\n [0, 2, 1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -2, -6, 4, -2],\n [-5, 3, -6, 6, -2],\n [4, 5, -4, 3, -3],\n [-4, -6, 2, 5, 6],\n [6, 1, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 6, 3, 6, -3],\n [2, 0, 1, -5, 1],\n [-5, -3, 4, 1, -5],\n [-6, -4, 1, 2, -5],\n [-2, 6, -4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -1, -6, 5, -2],\n [0, 3, 5, -1, 6],\n [-2, -1, -3, -5, -2],\n [1, 5, -5, 1, 3],\n [4, 1, 5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 4, 6, -3, -2],\n [4, 5, 2, -1, -2],\n [3, 6, 5, -2, 3],\n [-4, 2, 6, 0, 0],\n [-2, 0, 1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 3, 3, -6, 0],\n [-5, 0, 5, -5, -2],\n [-1, 1, 1, 4, 2],\n [0, -4, -5, 4, -3],\n [3, 3, -6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -4, 6, 5, -3],\n [3, -6, -1, -5, 0],\n [2, -4, 0, -6, 1],\n [-1, 1, 5, -4, -6],\n [1, -5, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -6, 5, -1, 0],\n [-6, 6, -6, 4, 3],\n [5, -6, 2, -3, 1],\n [-2, 4, -1, -4, 3],\n [2, -3, 0, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -6, 3, 3, 4],\n [2, 6, -4, 3, -4],\n [5, 5, -3, 4, 6],\n [1, -5, 6, 6, -3],\n [-6, 0, 6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 2, -3, 3, 2],\n [-5, -6, -3, 0, -4],\n [-5, -1, -6, 5, 1],\n [-3, -1, -2, 3, -1],\n [-4, 1, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 0, -5, -5, -2],\n [1, 0, 0, 2, -3],\n [1, 5, 4, -2, 1],\n [1, -5, -6, 2, 2],\n [-2, 2, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -5, 0, 1, 2],\n [-6, -5, -1, 4, -2],\n [-3, -1, -2, -3, 3],\n [-4, 3, -4, 0, 3],\n [6, -2, -5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 6, 1, 4, -2],\n [5, 5, 6, 6, 6],\n [-4, -2, -5, 0, 2],\n [6, -4, -3, -3, 1],\n [6, 0, -4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 6, -5, 5, -3],\n [-4, 6, -5, 6, 2],\n [5, -1, 2, 0, 1],\n [-3, 3, -3, 2, -4],\n [-3, -1, -4, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 0, -4, -5, 4],\n [1, 6, -2, 6, -3],\n [1, 3, -6, -6, 2],\n [1, 5, -1, 0, -2],\n [-1, 2, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 1, -3, -4, 6],\n [4, 5, -1, -3, -6],\n [2, 2, 0, -1, 4],\n [-4, 3, -6, 1, 0],\n [6, 3, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -1, 3, -5, 3],\n [2, -3, -5, 2, -1],\n [-5, -4, -2, -6, -1],\n [2, -4, 4, 1, 4],\n [-5, 3, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, 5, 0, -2],\n [3, -3, -1, -4, 3],\n [-5, 2, -2, 1, -5],\n [-3, -4, -5, 5, 4],\n [3, 2, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -3, 0, -3, -5],\n [-3, -4, 1, -1, -4],\n [-2, 5, 4, -3, -5],\n [-2, 1, -5, 2, 0],\n [-4, -1, 2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 3, -5, -1, 4],\n [2, -3, -5, -5, -4],\n [4, 5, -5, 5, -6],\n [-3, 4, 2, 4, 2],\n [-3, 1, -1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 1, 2, 4, 1],\n [-2, -2, 1, 4, 1],\n [-1, 1, -5, 3, 0],\n [-6, -6, -5, -3, -2],\n [5, 2, -6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 4, -2, 1, 6],\n [0, -4, 2, 2, 2],\n [4, 3, -3, 1, 0],\n [6, 6, -2, 2, -3],\n [5, -3, -5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, -3, 1, -6, -1],\n [-3, -2, -6, -6, -2],\n [4, -5, -2, -6, 2],\n [0, -5, -4, 1, -2],\n [2, -1, -5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 3, 2, -6, 3],\n [2, -2, -3, 6, 6],\n [-1, 1, 0, 6, 2],\n [-6, 2, 1, -5, -2],\n [-4, 3, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 0, 3, -3, -1],\n [-2, -2, -5, 2, -2],\n [5, 3, 0, -3, -4],\n [5, 2, 0, -2, -4],\n [-5, 5, 6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 1, -6, -6, -4],\n [5, 4, 1, -2, 6],\n [1, 4, 2, -3, 1],\n [5, 6, 5, 0, 2],\n [0, -2, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 0, 4, -4, -2],\n [-3, -3, 3, -2, 6],\n [0, -4, -4, -2, -5],\n [3, -2, 6, 4, 3],\n [5, -2, -1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 4, -1, -6, 3],\n [-1, -6, -2, 5, 5],\n [1, 6, 5, 6, 5],\n [5, 0, 5, -6, 4],\n [6, -3, 4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 0, -2, 3],\n [5, 2, -4, 0, -6],\n [5, -2, -3, 6, 2],\n [-1, -5, 2, -2, -4],\n [4, 0, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -4, -3, -4, -1],\n [-4, -4, 5, 0, 2],\n [0, -4, 3, 5, -5],\n [4, 0, -5, -6, -6],\n [0, 5, -6, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -2, -3, 4, 6],\n [4, 1, -3, -4, -1],\n [1, -3, 4, -4, 1],\n [0, 6, -1, 5, 6],\n [1, 0, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -6, -4, -5, -6],\n [4, 2, 2, -3, -1],\n [3, 5, 1, -2, -1],\n [6, -3, -3, -5, -2],\n [6, 0, -5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 4, -5, 2, -6],\n [-4, 0, 2, 3, -4],\n [-2, 4, 1, 4, 3],\n [-4, 5, -5, -6, -2],\n [-1, -5, 5, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, 0, -1, 5],\n [-4, -1, 6, 4, 3],\n [0, -5, -6, 3, 6],\n [-1, 4, 6, 1, -1],\n [3, 3, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 0, -3, -5, 1],\n [-5, 2, 6, -3, -6],\n [-4, 4, 2, -6, -5],\n [4, 2, 4, 1, 1],\n [-2, -6, -5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 5, -5, 1, -4],\n [2, -6, 4, 1, -4],\n [0, 5, -2, -4, 0],\n [6, 0, 5, 2, 5],\n [1, -5, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, 3, 1, -4],\n [2, 3, -3, 5, -3],\n [6, 2, -2, -6, -5],\n [0, 2, -3, 5, 4],\n [4, 1, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 1, -6, -4, -4],\n [2, -2, -5, 0, 3],\n [-6, 2, 2, -4, 5],\n [3, 0, 4, -1, -6],\n [0, 4, -5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -4, 1, -4, -3],\n [6, 1, 3, -2, 4],\n [5, -2, -1, -6, 5],\n [0, 2, -3, -4, -3],\n [-2, 2, -6, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 4, -3, 3, 5],\n [-2, 6, 0, 2, 1],\n [-6, -1, -2, -1, 4],\n [-3, -2, -1, 2, 3],\n [-5, -4, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 0, 3, -5, 5],\n [-4, -6, 6, 4, 6],\n [-4, 2, -6, 5, -6],\n [-4, 2, 5, 3, -6],\n [-1, 2, -4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -3, -2, -2, -5],\n [-6, 3, -4, -5, -6],\n [-5, -2, -6, 1, 2],\n [6, 3, 0, -2, -4],\n [3, -3, -4, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 0, -5, 6, -5],\n [2, 0, 0, 6, 3],\n [0, -4, -1, -6, 0],\n [3, 5, 1, -6, 1],\n [-5, -2, -6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 6, 4, -6, -3],\n [6, 6, 5, 6, 1],\n [-1, -6, 6, 5, -3],\n [-1, 1, 3, -4, 2],\n [6, -3, 0, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 4, -6, 2, 4],\n [3, 5, -4, -3, -5],\n [6, 1, 5, -1, 1],\n [3, -1, 1, -1, 0],\n [5, 5, 2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -1, 0, -2, 1],\n [-4, 2, -5, -4, 2],\n [4, 6, -2, -2, 1],\n [0, 6, 4, -4, 6],\n [-5, 5, 3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 5, -5, -4, -5],\n [-2, 5, -2, 3, 6],\n [2, 2, 5, -3, -1],\n [-1, 5, 4, -2, 3],\n [3, -2, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -5, -2, 1, -5],\n [-3, -5, -1, 6, -5],\n [-3, -4, -6, -3, 0],\n [-4, -3, 0, -1, -6],\n [1, 3, -1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 1, -6, 6, 2],\n [-6, -6, 4, 3, 2],\n [-3, -4, 6, 6, -3],\n [6, -1, 6, 0, 2],\n [-5, -4, -6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 0, -6, 5, -3],\n [5, -2, 3, -3, -3],\n [-1, -4, 5, 4, -2],\n [5, -3, 3, -2, 3],\n [-3, 4, 3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -1, -6, -6, 1],\n [6, 5, -5, 6, 0],\n [1, 3, 2, 6, 2],\n [2, 4, 6, -3, -1],\n [3, -6, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -1, 3, 1, 6],\n [6, 6, 3, -3, -5],\n [-5, -6, -6, 4, 2],\n [6, -5, 0, -5, -6],\n [4, 3, -4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 3, -1, 5, 5],\n [-2, 6, -4, 1, -2],\n [-2, -6, 5, -1, 2],\n [3, -5, 2, 0, -6],\n [2, -4, -3, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, 3, 1, -2],\n [-5, -4, 2, -2, 5],\n [-1, 1, -5, 3, 4],\n [6, -5, 5, 1, -6],\n [0, -4, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -1, 4, -2, -4],\n [5, 3, 1, -5, -2],\n [5, 4, 6, -6, -1],\n [6, 1, -6, -2, 3],\n [3, 5, -6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 4, 2, -6, 3],\n [-3, -6, 0, 3, 5],\n [-6, -6, -3, 5, -1],\n [-6, 5, 4, 1, 4],\n [4, -2, 5, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -6, -4, 4, -6],\n [5, -2, 5, -1, 0],\n [2, -1, 5, 5, 5],\n [4, 6, -6, 1, -4],\n [-2, -3, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 5, -3, 3, 0],\n [-2, 3, -5, -3, -4],\n [3, 1, -5, 2, 4],\n [-3, 4, 5, 2, -3],\n [0, 1, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 0, -6, -1, -3],\n [-4, 1, 3, 2, 3],\n [4, 2, 2, -4, 2],\n [6, -2, -4, 1, -6],\n [5, -4, 3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 5, -5, -6, -3],\n [2, -5, -4, 1, 6],\n [-5, -6, -3, -1, -1],\n [-6, -5, -6, -3, 0],\n [-4, 5, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 5, 3, 2, 5],\n [-5, -1, -3, -3, 2],\n [-1, 0, 6, 4, -3],\n [4, 1, 4, -2, 1],\n [5, 6, 2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 3, -1, 1, 2],\n [3, -3, -6, 5, 4],\n [-5, -3, 1, -6, -3],\n [-4, -5, -3, -1, 2],\n [5, -2, -3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 3, -4, 5, 5],\n [5, -6, 3, -1, 4],\n [2, 1, 0, 6, 3],\n [0, -2, 0, -4, 0],\n [4, 4, -5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 5, -5, 6, 5],\n [4, -6, -3, -6, -4],\n [0, 2, 4, 2, 3],\n [-5, 6, 5, 0, 6],\n [-1, 1, 4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 3, 2, 3, 6],\n [4, 0, -2, -1, -3],\n [6, -5, 3, -5, 1],\n [-6, 4, -1, -5, 1],\n [4, 3, -5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -6, -4, 0, 4],\n [-3, -4, 5, -4, -4],\n [-2, 3, 1, -4, 3],\n [-5, 2, -3, -3, 4],\n [-3, 0, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 2, 4, -5, 0],\n [-1, 2, 5, 2, 6],\n [-2, 0, 0, -6, -4],\n [1, -3, -1, -2, 1],\n [0, 4, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -6, 4, -3, -6],\n [-4, 1, -2, -1, 6],\n [1, 2, 6, -1, -2],\n [-5, -2, -3, 3, 3],\n [1, 3, 5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 5, -6, -2, 3],\n [6, -4, -6, 3, -1],\n [4, 5, -2, 4, -3],\n [3, -6, -3, 1, -4],\n [-1, 0, -6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, 5, 1, -3, 4],\n [-5, -1, 6, 4, -2],\n [4, -2, -2, 6, -3],\n [0, 6, 2, -5, -2],\n [-1, 1, -3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -4, 0, -3, 6],\n [5, 3, -6, -2, 1],\n [4, -6, -5, 1, 0],\n [0, 2, 4, 5, -5],\n [1, -5, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 1, 0, -2, 1],\n [3, -6, -1, 6, 4],\n [-1, 3, 3, 4, -5],\n [-4, -1, -2, 3, 6],\n [-1, -2, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 0, -3, 5, -6],\n [1, 1, -2, 3, -3],\n [-4, 6, -4, 5, 4],\n [3, 5, 0, -6, 5],\n [-6, 1, 0, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 2, 6, -1, 5],\n [6, 3, 0, 4, -5],\n [6, 4, -5, -1, -1],\n [4, -3, -5, -5, -4],\n [4, 0, -4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 1, 3, 0, -6],\n [-5, 2, 5, -3, -2],\n [-6, 2, -4, -5, -4],\n [6, -4, 5, 5, -6],\n [5, -5, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -5, 3, -4, -2],\n [-1, 1, 5, 1, -2],\n [-4, -4, 4, 0, 4],\n [1, 6, -2, 5, 1],\n [3, 1, -6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 6, 2, -4, 3],\n [5, -2, 3, 0, -4],\n [6, 1, 6, 5, -1],\n [0, 0, -1, 5, -1],\n [3, 0, -6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 2, -3, 6, -1],\n [-2, -4, 5, 5, 6],\n [2, 3, -1, -4, 6],\n [3, 6, -2, 2, 6],\n [0, -6, -6, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -4, 2, -1, 5],\n [-4, -3, 5, -2, 1],\n [4, 3, 2, 0, 3],\n [0, -6, 0, 2, 3],\n [2, 2, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 4, -6, 6, 5],\n [1, 5, -6, -2, -2],\n [-1, -5, 0, -3, -2],\n [-4, 4, 5, 1, -5],\n [3, -6, -3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -2, -3, -4, -2],\n [1, -1, 5, 4, 1],\n [-3, 0, -4, 1, -3],\n [-1, 2, 1, -3, -4],\n [-1, -4, -3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -1, 2, 4, -6],\n [1, 5, -5, -4, 0],\n [-6, 3, 2, 0, 1],\n [5, 1, -3, 5, 3],\n [6, 2, 3, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, 0, 2, -2],\n [0, 0, 4, 2, 5],\n [-6, 0, 5, 0, -5],\n [5, -1, -1, 4, -6],\n [1, -4, 2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 3, 5, -3, 5],\n [-3, 6, -2, -2, -6],\n [5, 5, 6, -1, -2],\n [5, 5, -1, 5, 4],\n [-4, 1, 6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 4, 0, 6, -1],\n [-4, -5, -5, -1, -6],\n [1, -1, -1, 4, 1],\n [4, -4, 4, 2, 1],\n [3, -6, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -2, -2, 2, 3],\n [-6, 4, -1, -3, 6],\n [2, 1, -3, -2, -6],\n [2, -6, -2, 3, 4],\n [3, -5, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, 6, -4, 1, 5],\n [3, 0, 3, 1, -3],\n [1, 1, 6, -5, 4],\n [5, -6, 6, -4, 4],\n [-5, -1, -3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, -5, -3, -6],\n [5, 2, -3, 3, -3],\n [3, 2, 4, -1, 5],\n [5, 5, 1, -3, -1],\n [-6, -1, 0, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 6, 0, 4, -3],\n [0, 6, 4, -1, 3],\n [4, 1, -1, -3, -2],\n [4, -1, 5, 3, 4],\n [-3, -2, -2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -4, -3, 1, 4],\n [5, -2, -2, 0, 2],\n [-2, 2, -5, -1, 1],\n [5, -6, 6, 2, -2],\n [-3, -5, -5, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 5, -3, -4, -6],\n [-6, 3, -2, 5, 0],\n [-1, 3, 6, -1, 2],\n [1, -6, -4, -3, 6],\n [5, 4, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 4, -2, 2, 6],\n [-5, 6, 0, -2, 6],\n [-2, 4, -6, -6, 1],\n [6, -2, -1, -6, -3],\n [-2, 5, 2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -6, 5, -1, 0],\n [0, -4, 5, 3, -5],\n [1, -2, 3, -6, 3],\n [-6, 1, -6, 4, 3],\n [-1, -5, -5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 1, -1, 4, 3],\n [-3, -4, 6, 1, -1],\n [-2, 3, 2, 2, -6],\n [-1, 4, -2, 5, 5],\n [-3, -3, -5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, 4, 6, -2],\n [4, 6, 4, 6, 0],\n [2, 3, -5, 0, 2],\n [5, 4, -5, -3, -4],\n [-4, 4, 6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -3, 2, 0, 1],\n [1, -1, 2, -1, -6],\n [5, 0, 4, 3, 0],\n [5, 4, -3, 1, 2],\n [-1, 2, -1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 4, 2, 3, 0],\n [0, 3, 5, -3, 1],\n [-4, 5, 0, -3, -6],\n [4, -3, 1, 3, -6],\n [-3, -3, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -6, 4, -4, 5],\n [6, -1, -6, -5, -6],\n [-3, -1, 2, 1, -4],\n [6, 1, -4, 1, -1],\n [5, -5, -3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 4, 4, 5, -6],\n [2, 4, 5, -6, 5],\n [0, 5, 0, -6, -5],\n [-2, -6, 4, -4, 5],\n [-1, -6, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -5, -1, -6, -5],\n [-5, 6, 5, 4, -3],\n [1, 1, -3, -1, 3],\n [1, 2, 0, -5, 4],\n [-6, 4, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -5, 0, 2, 1],\n [3, 0, -6, 4, 3],\n [-3, 2, 6, 0, 0],\n [-1, -3, 5, 6, 5],\n [-6, -4, 4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 5, 1, 0, -1],\n [6, 2, -4, -5, 0],\n [5, 4, 3, -3, 1],\n [-2, -3, 0, -2, -1],\n [6, 6, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -1, 4, 1, -3],\n [-6, 0, 3, -4, 2],\n [-4, -5, -3, 5, -1],\n [2, -5, 0, 6, 1],\n [-3, 3, 6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 2, -5, -4, 3],\n [6, 1, 6, -4, -2],\n [4, 4, 6, 5, 2],\n [-6, -5, -4, -3, -5],\n [4, -4, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, -6, 1, 6],\n [0, 4, -6, -6, -1],\n [-5, -5, 2, -4, -5],\n [-3, 6, -3, -6, 6],\n [1, -2, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -1, 6, 6, -4],\n [0, 2, -6, 4, -3],\n [-5, -2, -5, 6, 3],\n [-5, -6, -4, 6, 6],\n [0, 2, 6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, -1, 6, 2],\n [-4, 0, 6, 2, -4],\n [3, 1, -1, 1, 1],\n [6, -2, 1, 6, 0],\n [3, 6, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -6, 3, 2, -1],\n [-3, -3, -2, -3, 5],\n [2, -3, -4, -2, -6],\n [2, 3, 5, -4, -6],\n [4, -3, 5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -3, -1, -2, 2],\n [2, 2, -4, -1, -5],\n [3, 3, 2, -5, 1],\n [3, 2, 3, -4, 0],\n [-5, -4, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 2, 0, -6, 3],\n [6, -4, -2, 4, 2],\n [1, 1, 3, 0, -4],\n [0, -1, -6, -4, -2],\n [4, 1, 3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 2, -4, 3, 5],\n [-5, -2, 5, -2, -6],\n [3, 2, 6, -3, 2],\n [0, 0, 4, -4, -1],\n [5, 1, -3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 1, 3, 4, -1],\n [-2, -3, 5, 2, 3],\n [-3, 6, -1, 0, 4],\n [-3, 5, 4, 6, -3],\n [3, -3, -4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -1, 1, -2, -6],\n [-5, -4, -6, -6, 3],\n [2, -4, 4, 1, -3],\n [0, 1, 5, -5, -6],\n [-1, 0, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 6, 4, -3, -6],\n [-3, 0, -2, 3, -3],\n [-5, -3, 4, 6, -6],\n [-3, 3, 5, -1, -6],\n [1, 6, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 5, 5, 1, 0],\n [2, 6, -2, -4, 0],\n [-4, 2, -4, 0, -3],\n [-2, -2, 2, -3, -1],\n [-2, 2, -1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -4, -2, 1, 6],\n [2, 5, 6, 1, 0],\n [-5, -2, -3, 2, 1],\n [-5, 5, 5, -6, 2],\n [0, -4, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -3, 2, -2, 2],\n [1, 5, -1, -6, 2],\n [3, 4, -2, -2, 2],\n [-6, 2, 2, 4, 0],\n [-3, 3, 5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -6, -1, -3, -3],\n [-5, -2, -5, -4, 5],\n [6, -5, 5, 0, 1],\n [3, -3, 2, -4, 0],\n [0, 3, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 1, -4, -4, -2],\n [-6, 5, -3, 5, -1],\n [3, 3, -4, 1, 0],\n [6, 3, 4, -2, 2],\n [-5, -6, 2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, -6, 5, 4],\n [5, 4, -3, -1, -4],\n [5, -1, 2, 4, -6],\n [6, 4, 6, -6, 1],\n [4, -6, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, -4, 3, 4],\n [3, 0, -2, -3, -5],\n [4, 2, -3, -2, 0],\n [3, -4, 2, 5, -4],\n [3, 5, -2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[0, 3, 1, -2, 6],\n [4, 0, -4, 1, -1],\n [3, -2, 0, 2, 4],\n [-5, 1, -3, 1, -2],\n [-4, 4, 5, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -2, -1, -5, 3],\n [-2, 2, 6, 3, -2],\n [-4, 1, -5, 3, 2],\n [2, 2, -4, -1, -1],\n [6, 2, -2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 1, 6, 1, -5],\n [-2, 5, -4, -2, -5],\n [6, 5, -5, -3, 4],\n [3, -1, 5, -4, -4],\n [-6, 3, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 5, 1, 0, -6],\n [4, 4, -2, -3, 0],\n [-5, -1, -6, 5, -5],\n [-1, 4, -1, 3, -5],\n [2, -6, 1, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 3, -2, 1, 2],\n [4, 3, -1, -5, -6],\n [3, -4, 2, 2, 3],\n [0, -1, 4, 0, -3],\n [6, -2, -2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, 0, -1, 4],\n [0, -5, 5, 3, -2],\n [-1, 0, -5, 5, -1],\n [-1, -4, -3, -1, 3],\n [3, 6, 4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 2, -1, 6, -4],\n [1, -4, -3, 1, 0],\n [-3, -1, 0, 2, -2],\n [-4, -1, 2, 0, -2],\n [-6, -4, -3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 5, -6, -3, -4],\n [-3, -6, -1, -2, 2],\n [-6, -5, 3, 2, -6],\n [5, -1, 1, 5, -2],\n [4, -2, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, 2, -4, -2],\n [2, 1, -6, 1, 4],\n [1, 5, 2, -1, 5],\n [5, -5, 5, 1, 4],\n [-5, -6, -6, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 0, 4, 1, -2],\n [2, -4, -1, 1, 2],\n [-1, -6, 4, -5, -1],\n [-4, -3, 2, 2, 0],\n [3, 3, 5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 0, -1, 2, -1],\n [6, 5, -4, 0, 1],\n [-2, -2, -1, -3, 2],\n [5, -2, 2, -2, 3],\n [-1, -6, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -2, -3, -3, 6],\n [0, -4, -3, -3, 4],\n [-6, 2, 3, -2, 0],\n [-1, -4, -4, -2, 2],\n [1, 0, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -2, 6, -5, 6],\n [-2, -5, 2, -2, -2],\n [-6, -3, 0, -1, -2],\n [-6, 5, 1, -5, 5],\n [-5, 4, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 0, -4, 5, 3],\n [-3, 6, 6, 5, 0],\n [0, -3, 0, -6, 1],\n [-6, -1, 6, -4, -4],\n [-2, -4, 4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 0, 6, -3, 0],\n [1, 4, -6, 5, 2],\n [-3, 3, -1, -4, 1],\n [-1, 4, -6, 5, 6],\n [6, -5, -3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -4, 4, 3, -2],\n [3, 3, -3, 4, 3],\n [-4, 6, 4, -3, 3],\n [3, -3, 2, 1, 6],\n [2, -5, 0, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, 6, 3, 1],\n [-4, -3, 4, 4, 6],\n [4, -2, 6, 6, -5],\n [3, -2, 3, 4, 5],\n [5, -4, -2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 0, -1, -1, -6],\n [-2, 4, -4, -1, -2],\n [-1, 3, -2, 3, -1],\n [3, 0, 4, 2, 6],\n [-2, -5, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -4, -2, -1, -6],\n [5, 0, 0, 1, 0],\n [6, -6, -2, 1, 6],\n [-5, 1, 6, 6, 0],\n [3, 3, 4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 2, 0, 0, -3],\n [3, -1, 4, -2, 4],\n [6, 6, 1, -1, 2],\n [5, -1, 0, 4, -1],\n [3, 5, -5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 1, -6, 3, 5],\n [-1, -5, -3, -4, 4],\n [1, -3, -6, -2, 1],\n [0, 4, -5, 2, -3],\n [5, -2, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, -4, 2, -3, -2],\n [0, 3, -3, 0, 4],\n [-6, -3, 4, 5, 1],\n [-2, 4, 5, -5, 3],\n [2, 0, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 4, -4, -5, -4],\n [-5, 2, 6, -4, -4],\n [-1, -4, -5, -2, 0],\n [6, 0, 0, 1, -3],\n [-2, -3, 3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 0, -1, 6, 2],\n [0, 6, -5, 5, -6],\n [-3, -2, -6, -1, -2],\n [6, -1, -1, -5, -4],\n [4, -5, -5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -1, 0, 6, 3],\n [-3, -4, 6, -1, 5],\n [1, -3, 4, -4, -1],\n [-3, 5, 5, -3, 0],\n [6, 6, -4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -2, -6, -3, -2],\n [6, -3, -2, 0, 6],\n [5, -6, 5, 3, 4],\n [-5, 5, -4, -4, 3],\n [6, 4, 4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -3, 4, 5, -1],\n [0, -6, -6, 5, 5],\n [1, 0, 6, 0, -6],\n [5, -1, 5, -4, -1],\n [4, 1, -1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 2, -1, 3, -2],\n [-5, 0, -5, 4, 5],\n [-2, -5, 1, -5, -6],\n [2, 0, 5, 3, -6],\n [-2, -5, 4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -4, 3, 0, 1],\n [2, -6, 5, -2, 5],\n [3, 2, 5, -2, 5],\n [4, 4, -1, -5, 6],\n [-6, -2, -2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 1, -4, -4, 4],\n [-1, -4, 6, 1, 2],\n [2, 5, -4, -4, 4],\n [5, -3, 3, -6, 3],\n [-2, 2, 3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -6, -3, -3, -1],\n [-3, 0, -6, 1, 6],\n [-3, 1, -3, -6, 3],\n [-2, 2, 0, 1, -1],\n [2, 5, -1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -6, 6, 5, 6],\n [0, 1, 2, 1, 3],\n [-2, -6, 2, 0, 4],\n [-4, 3, 5, -4, -3],\n [-1, 0, 1, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 3, -2, 4, -1],\n [-2, 2, 4, 3, 6],\n [5, 5, -4, -2, 1],\n [-4, -1, 5, -3, -3],\n [2, 6, 4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 6, -5, 6, 3],\n [-1, 0, 0, 6, -1],\n [-6, 2, 2, 0, -5],\n [4, 6, 3, -6, -1],\n [-4, 4, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -3, 3, -2, -3],\n [6, -1, -2, -1, 3],\n [5, 5, 2, 1, 2],\n [5, 3, 1, -2, -3],\n [-3, 2, 2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -5, 0, -3, -2],\n [-6, -5, 0, 4, -1],\n [4, 2, -1, 5, -5],\n [4, -2, -6, -3, 0],\n [4, -2, 0, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 2, 2, 3, -4],\n [4, 5, -4, 5, -2],\n [6, 1, 4, -1, 2],\n [-4, -6, -6, -1, -6],\n [-4, 5, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 5, -4, -2, -6],\n [-6, 3, -6, 6, 1],\n [-4, 6, -4, 6, 6],\n [2, -1, 4, -2, 6],\n [5, -5, 6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -1, -2, -6, -1],\n [2, -1, -4, -5, -3],\n [-1, 4, -1, 5, 6],\n [-5, 1, -4, 4, 2],\n [-4, 3, 1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -6, 6, 1, 1],\n [-4, 0, -5, 3, -2],\n [-3, -5, -3, 5, 0],\n [6, 1, 4, 0, -1],\n [-1, -5, -5, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 2, -3, 4, 0],\n [-6, 4, -2, 1, 0],\n [-2, -3, -4, -6, 6],\n [-1, 1, -3, 1, 3],\n [0, -5, 1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 1, -6, -1, 3],\n [-4, 2, -1, 5, 2],\n [2, 5, 0, 4, 3],\n [4, -1, -5, -3, -2],\n [-3, 4, -6, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 1, -6, -6, -1],\n [-3, -6, -3, -4, 6],\n [-2, -4, 0, -4, 6],\n [-5, 0, -5, 5, -2],\n [-6, -1, 5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 2, -1, 3, 0],\n [-6, -6, 4, 5, -3],\n [-3, 5, -4, 5, -4],\n [6, 6, -5, -2, -6],\n [3, 4, -3, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -3, -4, -6, 6],\n [2, -4, -2, 2, -4],\n [2, -5, -4, 6, -5],\n [-5, 1, 3, 0, 0],\n [1, 6, -6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -3, -5, 0, -5],\n [1, 6, 2, 5, 2],\n [-6, 5, -6, 4, 5],\n [-5, -3, -2, -3, -3],\n [6, 1, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -1, 4, -6, -5],\n [1, -5, 6, -6, 5],\n [-1, 5, 4, 4, 5],\n [-6, 2, 4, -6, 4],\n [-5, -5, -3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -5, 4, 3, 0],\n [0, -2, -5, 2, -6],\n [-2, 6, -2, 2, 4],\n [-3, 6, -6, -1, -5],\n [3, -5, 3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -3, -6, -4, 3],\n [-4, 4, 6, -6, -6],\n [5, -2, -2, -6, 4],\n [2, 4, -4, -3, 5],\n [3, 6, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 6, 4, -5, 2],\n [6, -1, -2, 2, -5],\n [-1, -5, 1, 5, 4],\n [5, 3, -4, 3, -3],\n [-1, -6, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 1, 6, 6, 1],\n [4, -2, -2, -2, 3],\n [-1, 5, -2, 5, 4],\n [4, 2, 0, 4, 1],\n [0, 2, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 6, 0, 0, -4],\n [-1, 5, -2, -1, -3],\n [-4, 6, 3, -6, 5],\n [-4, -5, -3, -4, -4],\n [-1, 4, -1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 6, 3, 0, 5],\n [1, -2, 1, -4, 2],\n [-2, 0, 5, -3, -4],\n [-4, -6, -3, -1, -4],\n [-1, 2, -4, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -6, 5, 1, -3],\n [-4, -1, 2, 5, -3],\n [-6, 6, -4, -6, -3],\n [-2, -6, 3, 5, 3],\n [2, 1, -1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -1, -4, 1, 4],\n [6, 0, -3, -6, 6],\n [4, 2, 4, -4, 1],\n [5, -6, -5, -3, -5],\n [1, -6, 1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 2, 5, 4, 3],\n [-6, -5, -5, 4, 2],\n [1, 5, -6, -3, 6],\n [5, 2, -3, -6, -2],\n [0, -2, 5, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -5, -2, 2, 4],\n [-6, 5, -3, 1, -3],\n [2, -1, -3, -5, 5],\n [1, -6, 4, 3, 6],\n [2, 5, -5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 2, -3, -5, -4],\n [-4, -1, -4, -6, -4],\n [-5, 3, 4, -5, 6],\n [4, -4, 2, -3, -4],\n [-3, 2, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -4, 5, -5, 4],\n [-1, -3, -2, -1, 2],\n [-6, -6, 3, -5, 4],\n [0, -3, 4, -4, -6],\n [6, -2, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 5, -6, -1, 0],\n [-2, -6, 6, 0, 3],\n [0, -6, 3, -5, -2],\n [0, -6, -6, -6, -6],\n [-6, 6, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 3, 3, 5, 5],\n [-6, -6, -3, 1, -6],\n [-1, -4, -4, -2, 6],\n [5, 5, 6, -3, 4],\n [-6, 1, 2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -4, 5, 6, -2],\n [-5, 2, -6, -2, -3],\n [3, -5, -3, -4, -1],\n [1, -2, -5, -4, 1],\n [5, 4, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -1, -6, 1, 5],\n [-2, -6, -6, 5, 3],\n [2, -1, 2, 0, 4],\n [2, -5, -2, -5, -5],\n [-5, -1, -6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -3, 5, 3, -2],\n [0, -6, -4, -6, -2],\n [1, -2, -3, 0, -4],\n [2, 0, -3, 0, 6],\n [-5, 6, 4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -4, 1, 5, -6],\n [4, 3, 3, 3, -4],\n [-1, 5, -5, 6, -3],\n [-5, 1, -1, 6, -4],\n [4, -5, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 5, -4, 5, -2],\n [1, 2, -3, -5, -4],\n [1, -5, 6, 6, -1],\n [1, -3, 4, 5, 3],\n [1, -5, 2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -4, 6, -4, -4],\n [-4, 4, 4, 1, -6],\n [4, -5, 3, -4, 6],\n [4, -1, 2, 2, -3],\n [-5, 4, 5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, -2, -1, 2],\n [4, -1, 6, -5, 1],\n [-5, -1, 4, -5, -3],\n [4, -5, -1, -2, 4],\n [2, -5, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -5, 3, -6, -2],\n [-6, 4, -2, -2, -6],\n [1, 0, -6, 1, -4],\n [-5, 2, 6, 3, 6],\n [-2, 6, -3, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -5, -3, -1, -1],\n [2, 5, 1, -5, -5],\n [6, 6, 0, 1, -6],\n [-1, 0, -4, 3, 4],\n [1, -4, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -4, -1, 5, 4],\n [1, 0, 1, 2, 3],\n [-3, -5, -2, -6, -4],\n [5, 0, 5, -4, 5],\n [4, 3, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 6, -6, 1, 3],\n [3, 0, 5, 2, 0],\n [6, 3, 1, -6, 5],\n [2, 6, 5, -2, 4],\n [2, -5, 2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, 2, 3, 6],\n [2, -4, 6, -6, 3],\n [-2, -4, -5, -1, 2],\n [-2, -3, 5, -4, 3],\n [-2, 5, 6, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 5, -3, 4, -4],\n [3, 1, -3, 5, 1],\n [4, 0, 6, 5, -4],\n [3, 1, 4, 4, 1],\n [-4, -2, -4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -5, 3, 4, -1],\n [-6, -4, -1, -5, 6],\n [2, 5, -4, 1, 1],\n [-6, 3, 0, -3, 3],\n [0, 6, 0, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 1, -5, 6, 1],\n [1, -4, -3, 0, -6],\n [-4, -3, 2, -3, 1],\n [4, 0, -4, 0, 1],\n [-5, 1, -1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 1, 4, -2, 0],\n [-2, -4, 5, 0, 6],\n [-4, -5, -5, 2, -2],\n [-4, 1, 3, -3, 3],\n [-4, -5, 6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 2, -5, -1, -6],\n [6, -1, -3, 5, -2],\n [-2, 2, 4, -2, -3],\n [-1, 4, 4, 4, -1],\n [-6, 4, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -2, -1, -2, -1],\n [0, -5, 4, 2, -2],\n [-5, -3, 3, -2, 0],\n [-3, -5, -2, -4, -2],\n [1, 1, 3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -1, -5, -1, 0],\n [-5, 1, 1, -4, 0],\n [1, 0, -6, -5, 3],\n [-3, 6, -5, 4, 3],\n [5, 0, -3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 3, 4, 4, -3],\n [-6, -2, 5, -1, 4],\n [0, 1, 1, -1, -6],\n [-4, 1, -5, -3, -6],\n [1, 0, -5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 2, 6, 3, -6],\n [0, -4, -2, -2, 6],\n [5, -3, -6, -1, -2],\n [-2, 2, 3, 2, 5],\n [-3, -4, 2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 6, -2, -2, 2],\n [-5, 2, -5, -3, 6],\n [4, -4, -3, 0, -4],\n [6, 1, -2, 3, 2],\n [-1, 3, 2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 3, 3, 1, -3],\n [0, -6, 4, 5, -3],\n [5, 3, 3, 2, -3],\n [-1, 3, -6, -2, 3],\n [-6, 0, 4, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 0, -3, -2, -4],\n [-2, 2, 2, -2, 1],\n [-3, -6, -6, -6, 2],\n [5, 2, 2, -2, -5],\n [4, -5, 2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -2, 4, -1, -2],\n [-3, -3, -5, 1, -6],\n [5, 6, -4, -3, -3],\n [-4, 0, -4, -2, 3],\n [2, 3, 3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 4, 0, -6, 1],\n [-2, -1, -4, 1, 4],\n [-1, 2, -3, 2, 2],\n [1, -4, -5, -4, 0],\n [-5, 3, 4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -5, -2, -6, 5],\n [1, 6, -5, -4, -5],\n [-4, -4, -2, -1, -5],\n [-6, 6, 4, 6, -2],\n [-3, -1, 1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 5, 5, -4, -5],\n [3, 4, -5, 3, 0],\n [-4, 1, -1, -5, -2],\n [3, -6, 4, 2, 5],\n [1, -4, 6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -3, 2, -2, 3],\n [2, 2, 3, -4, 0],\n [-1, 0, -1, -4, 4],\n [-3, 4, 4, 2, -2],\n [0, -2, 1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 0, 4, -2, -6],\n [3, -4, 3, 3, 5],\n [2, -5, -3, 2, 1],\n [-5, -4, 6, -2, 6],\n [-4, 6, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 5, 2, 4, -2],\n [6, -1, 2, 0, 6],\n [-4, -2, -3, 4, 5],\n [6, -4, -2, 0, -2],\n [1, -3, -6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -6, 2, 5, 5],\n [-6, -2, -4, -4, -1],\n [1, -1, -4, 0, 1],\n [3, 4, -5, -2, -2],\n [1, -2, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -4, 3, 6, -1],\n [2, -3, 3, 0, 2],\n [1, 4, -3, -2, 4],\n [4, -3, -1, 2, 5],\n [-6, -3, 5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 5, -5, -5, 0],\n [-2, -1, 6, -2, -5],\n [2, 1, -1, -5, 1],\n [-4, -5, 2, 4, -5],\n [-4, -2, 2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -1, -6, -1, 0],\n [3, -4, 5, 2, -2],\n [-1, 2, -2, 6, -4],\n [-4, 3, 2, 2, 5],\n [-1, 4, 4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 6, -1, -5, 5],\n [5, 1, -6, 5, -5],\n [-2, 1, -3, -6, 0],\n [-5, -3, 0, 2, -2],\n [-6, 5, 1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 6, 2, 2, 2],\n [-5, -1, -1, 2, 6],\n [-6, 1, 1, 6, 2],\n [2, -3, -3, -6, -4],\n [1, 1, 2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -6, 3, 2, -1],\n [-5, 1, 1, 6, -6],\n [-6, 1, 2, -2, -1],\n [2, -5, 1, 6, -4],\n [-1, 0, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, -2, 0, -6, -5],\n [6, 6, -4, -1, 6],\n [-1, -4, 6, 5, 6],\n [2, -6, -5, -4, -1],\n [1, -2, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 2, -2, -2, -4],\n [6, -1, 0, -5, 0],\n [4, -1, 2, 6, 0],\n [-6, 4, 3, -3, -1],\n [-4, -5, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -6, 6, 5, -2],\n [3, -4, 4, -2, 3],\n [6, 4, 3, 3, -1],\n [-3, 0, 5, 6, 6],\n [4, -5, -4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 3, -3, 3, -6],\n [3, 4, 6, -5, -3],\n [2, 4, 6, -6, -1],\n [5, -1, 3, -1, 4],\n [-5, 3, 3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 4, -4, -2, 6],\n [-1, 4, 3, -4, 1],\n [2, 6, -5, 1, -3],\n [-5, -5, -1, 4, 6],\n [-1, -4, 4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -3, -2, -3, 1],\n [4, 0, 4, 6, -2],\n [6, -4, 1, 2, -3],\n [-3, 1, -1, 0, 3],\n [-2, 6, -6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, 3, -4, -1, -2],\n [-3, 6, 4, -6, 4],\n [2, 6, 6, 6, -2],\n [2, 0, 4, 2, 1],\n [1, 4, 4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 1, 3, -1, -4],\n [-1, 3, 0, -4, 6],\n [2, 4, 6, 3, -3],\n [4, 4, -6, 1, -3],\n [2, 5, 1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -6, -3, 0, 6],\n [4, 4, 3, -3, -1],\n [-6, 2, 2, -2, 1],\n [-3, -5, -1, -1, -6],\n [5, -5, 5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 2, 4, -1, -6],\n [5, 2, 6, 3, -4],\n [5, -1, 4, 4, -4],\n [6, 4, 0, -2, -3],\n [2, -3, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 1, 3, 4, -1],\n [-6, 0, -6, 1, -6],\n [-5, -5, 1, -5, -5],\n [0, -4, 0, 1, 5],\n [5, 0, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 4, 0, -6, -3],\n [-5, -6, -1, -5, -3],\n [4, 2, -3, 2, 3],\n [2, -2, 2, -1, 3],\n [5, 5, -2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -1, -5, -2, -2],\n [1, -6, -1, -2, 2],\n [6, 2, 4, 2, 0],\n [2, 5, 6, 2, -1],\n [3, 2, 3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -3, -6, 1, -1],\n [-6, -5, -2, -1, -1],\n [-1, 0, -3, -3, -6],\n [-4, -5, -2, -2, 5],\n [4, 5, -5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -1, -6, -2, 5],\n [-2, 0, -4, 4, 3],\n [6, 0, -1, 0, 6],\n [2, 2, 2, -3, -4],\n [-2, 2, -5, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 6, -3, -5, 5],\n [5, -1, 2, 4, -3],\n [3, -6, 3, -1, -4],\n [0, 0, 1, -4, -3],\n [0, -5, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 3, 5, -2, 6],\n [2, 4, 2, -1, 2],\n [-5, 3, 2, 5, 5],\n [-2, 5, -6, 5, -4],\n [4, -5, 3, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 3, 5, -2, 0],\n [1, -5, 4, 3, -2],\n [4, 1, 4, -4, -5],\n [1, -4, 6, 1, 5],\n [5, -2, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 3, -3, 2, 5],\n [-5, 6, -1, 0, 3],\n [4, -4, 6, 3, -1],\n [0, -4, 0, -3, 4],\n [6, 2, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -5, 3, 2, 6],\n [0, 4, -6, 1, -3],\n [-1, 3, -3, 6, -3],\n [-2, 4, 3, 2, 3],\n [6, -4, -4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 1, 4, -1, 2],\n [5, -6, 3, -6, -3],\n [2, -2, -2, 2, -2],\n [-3, 2, 2, 6, 3],\n [5, -2, 0, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 6, 4, 1, -3],\n [-3, 2, 3, 6, -4],\n [0, 5, -6, 2, 5],\n [-5, -5, -6, -3, 0],\n [-1, -6, 1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -5, -3, -5, 4],\n [-2, 2, 3, 3, -1],\n [2, -1, -6, 1, 0],\n [2, -6, -3, -4, 5],\n [6, 6, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -5, 2, -4, 0],\n [5, -4, -5, 5, -1],\n [-6, -1, 4, -2, 1],\n [-6, 2, -4, -2, -1],\n [5, -5, 2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 5, -2, 6, 1],\n [-4, -2, 3, -3, -1],\n [6, -4, -3, -4, 1],\n [2, -6, 3, 3, 3],\n [-6, 2, 6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -2, 2, 4, 6],\n [-2, 3, 3, 3, 2],\n [4, 4, -2, 4, -6],\n [3, -3, -4, 4, 5],\n [-5, -2, -1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -4, 5, 2, 3],\n [2, -1, -2, 6, -4],\n [6, -1, -2, -1, 0],\n [6, -3, 6, 4, 3],\n [4, 6, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 6, 6, -5, 5],\n [-6, 2, -6, 0, 0],\n [3, -1, 1, -1, 2],\n [-4, 1, -1, -2, -4],\n [5, -6, 2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 3, 0, 3, -3],\n [4, 5, -6, -3, 6],\n [2, -6, -1, -4, 1],\n [5, -2, -6, 5, 6],\n [1, 2, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -2, -2, 1, 5],\n [4, -4, -6, -1, -2],\n [-5, 3, -4, -5, -1],\n [3, -3, -6, 4, 4],\n [-4, -5, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 3, 4, 1, -5],\n [2, 0, 0, 6, 0],\n [-2, 4, -5, -5, -5],\n [-6, -6, 2, 4, -3],\n [0, -6, -1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 1, 1, 6, -6],\n [-1, 5, 3, 5, 5],\n [1, -6, -1, -2, 2],\n [3, 2, 5, -1, -6],\n [5, -2, -1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 1, 6, 0, 0],\n [2, 4, -5, -6, -4],\n [-2, 2, -4, -2, 4],\n [-5, 6, -1, -2, 1],\n [0, 5, 0, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 3, -3, 2, -6],\n [2, 1, -5, 2, 2],\n [6, 1, -1, 5, 6],\n [4, 1, -3, -1, 0],\n [-5, -1, 1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -2, 0, -6, -1],\n [0, -6, 0, -3, -3],\n [4, 4, 1, 3, 0],\n [-1, -5, -6, 6, -2],\n [1, 2, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 6, 1, -3, -3],\n [2, 6, -2, -5, -6],\n [1, -5, 6, -3, 1],\n [-4, -4, 4, -4, 0],\n [4, -5, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -3, 2, -5, -4],\n [6, -6, -5, 3, -3],\n [5, 4, 0, -3, -5],\n [-3, 3, 6, 0, -2],\n [5, 5, -3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -3, -3, 4, 2],\n [1, -2, -3, 0, 2],\n [5, 0, 2, 3, -5],\n [2, 5, -6, -6, -4],\n [5, 3, 1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, -2, -6, 5, -4],\n [-2, 2, -3, 0, 0],\n [-6, -2, -5, -5, -2],\n [3, -5, -2, -5, -4],\n [-3, 4, 5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 6, -1, -6, 2],\n [4, -1, 1, 6, -6],\n [-3, 5, -5, -4, -6],\n [-1, 3, 1, -5, -6],\n [-5, 5, -1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 2, -1, 2, 4],\n [0, 1, 4, 3, -1],\n [-3, 2, 5, 6, 4],\n [4, -1, -4, 3, 1],\n [3, -4, -3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 1, 2, 4, 2],\n [6, 3, -4, -5, -4],\n [0, 2, 0, -4, -5],\n [-4, 1, 1, 2, 5],\n [-2, -1, 4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -5, 1, 3, 4],\n [6, 4, 1, 5, -1],\n [0, 4, 1, -1, -1],\n [-4, 1, -3, -2, 2],\n [2, 6, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -3, -6, -6, -5],\n [5, 6, -3, -2, -1],\n [-3, -5, 3, -5, -1],\n [-5, -1, 0, -2, 5],\n [-3, 4, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 5, 0, -6, 1],\n [2, -6, 5, 1, -6],\n [5, -5, 5, -4, 6],\n [-3, 0, 6, 0, -3],\n [3, -3, 5, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 3, 1, -3, -1],\n [4, -4, 1, -1, -5],\n [6, 3, -3, 5, 6],\n [-3, -4, 5, -5, 4],\n [-1, -3, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 5, 2, -3, -1],\n [4, 5, -5, -3, -5],\n [-5, 6, -2, -3, -1],\n [3, 3, 6, 2, -6],\n [-4, -3, -5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 5, -3, 5, -6],\n [-6, 5, 4, 3, 1],\n [1, -4, -2, 5, 0],\n [-3, -6, 4, 4, 5],\n [-3, -5, 6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 6, 2, -1, -6],\n [1, -5, -3, 3, 5],\n [-2, 4, 5, -2, -1],\n [1, -5, -3, -5, 0],\n [-4, 0, 5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -1, -5, -5, -1],\n [5, -1, 2, -1, 6],\n [-1, 0, 3, 4, 6],\n [-2, 5, 6, 1, -5],\n [2, -2, -5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 4, -4, 5, 6],\n [-3, 0, -4, 6, -5],\n [-6, 6, 6, 2, -1],\n [3, -1, -5, 3, 1],\n [-5, -2, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -5, 5, -4, -4],\n [1, -5, -3, 1, 3],\n [-4, -4, 2, -1, -1],\n [-4, -5, 3, 1, -2],\n [-6, 1, -6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 0, -5, 6, 5],\n [5, -5, -2, 5, -6],\n [-1, -2, 2, 6, 4],\n [4, 6, -6, 3, -4],\n [5, 2, 1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -2, -1, -6, 1],\n [-2, -5, 1, 4, -2],\n [-2, 3, 0, 4, -3],\n [4, 0, 3, -6, -6],\n [0, -6, -4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 4, 2, -3, -5],\n [5, -1, 5, -6, 5],\n [-5, -1, -6, 4, 1],\n [-3, 4, -6, -6, -5],\n [5, 2, -5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 0, -3, 4, 1],\n [0, -5, 6, -6, -2],\n [0, 2, -1, 3, -3],\n [-6, -3, 2, 5, 2],\n [0, -3, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 2, 2, 1, 0],\n [0, 4, -1, -6, -3],\n [-4, 1, -1, 6, 4],\n [4, -1, -3, -3, -6],\n [6, -4, -3, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -1, -1, 0, -1],\n [5, -4, -6, -2, -1],\n [-4, -5, 5, -3, 3],\n [2, 3, 6, -1, -1],\n [0, 5, -1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 3, -1, 1, -1],\n [6, 1, -4, -3, 3],\n [0, 3, -4, -2, -1],\n [5, 5, -1, 3, -4],\n [-1, -2, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 1, -2, -5, 5],\n [3, -1, -1, -6, 5],\n [4, -6, 3, -4, 0],\n [5, 4, -2, 4, 1],\n [6, 1, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 2, 2, 2, 0],\n [-5, 3, -4, 3, 0],\n [-2, -5, 5, -6, 0],\n [5, -4, 2, 1, -3],\n [-6, 4, 6, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, -5, 0, 2, 6],\n [2, 0, 0, 6, 6],\n [5, 4, 4, 4, 4],\n [-5, -3, -2, 3, 3],\n [-2, 5, -1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 1, 5, 5, 6],\n [5, -6, 2, -3, 1],\n [0, 0, -4, -6, 4],\n [-3, 6, 3, -6, 3],\n [1, 3, -4, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -1, -4, 3, 6],\n [-3, 0, -2, -3, -5],\n [-6, 4, -4, -3, -4],\n [5, -2, 2, 5, -5],\n [-1, 1, -6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -2, 4, 6, 1],\n [-5, 4, 4, 0, -6],\n [4, -3, 1, 1, -6],\n [-4, 5, -1, -2, -2],\n [-1, -3, 1, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -4, -2, 0, 2],\n [1, 4, 1, -6, -4],\n [-6, 5, -3, 3, -2],\n [0, -6, -1, -2, -1],\n [-4, 6, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 3, -5, 2, -5],\n [5, 1, -1, -2, 3],\n [6, 4, -1, 1, -4],\n [1, -3, -3, -6, 5],\n [-4, -3, 0, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -1, 3, -3, -3],\n [-4, 2, 1, 6, -5],\n [-5, -5, 0, 6, 4],\n [2, -4, -6, -3, 5],\n [4, -2, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 2, 1, 5, 1],\n [4, 1, 6, 3, 0],\n [0, 0, 4, 1, -4],\n [-6, -4, -4, -3, -1],\n [-4, 3, -4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 6, -4, 0, -4],\n [-4, 4, -5, 2, -5],\n [1, 4, 3, -1, 0],\n [4, -2, 5, -1, -2],\n [2, -3, 2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 1, 2, -6, -3],\n [1, -6, 1, 6, -2],\n [1, -6, -3, -2, 1],\n [0, 2, -4, 0, 5],\n [0, -3, -3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 1, 3, -5, -3],\n [1, 3, -6, -2, -2],\n [6, -3, 6, -3, -5],\n [2, 0, -5, 2, 5],\n [1, -3, -1, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 6, 2, 0, -6],\n [1, -6, 2, -1, 2],\n [-1, -2, -1, 0, 5],\n [0, 1, -4, 5, 6],\n [2, -6, -1, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 2, 1, 4, -3],\n [-4, 6, -2, -2, 0],\n [6, 0, -6, -1, 3],\n [-1, -3, 4, 4, -2],\n [5, 0, -5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, 1, 5, -1],\n [-6, 5, 3, -4, -4],\n [-4, 2, -6, 3, -2],\n [-5, -5, 2, 5, -6],\n [0, 0, 4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -5, -2, 5, -5],\n [-6, -2, -1, -5, -5],\n [3, 2, 2, -5, -3],\n [5, -1, 3, 5, 1],\n [1, 0, -1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -5, 1, 2, -6],\n [-2, -6, -2, -2, 6],\n [6, -4, 4, 2, 0],\n [-5, -2, 5, 4, 2],\n [6, -6, 0, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -6, 6, -6, -5],\n [0, 0, -1, 0, -5],\n [0, 4, 5, 3, -2],\n [-6, -5, 6, 6, -6],\n [-5, 4, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -4, -4, -6, 4],\n [3, -1, -4, -3, 1],\n [-6, 0, -5, -5, 6],\n [1, 4, -5, -6, -4],\n [6, 6, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 3, 5, -1, -2],\n [-2, 6, -2, 5, -6],\n [1, -1, 5, -4, -5],\n [6, 1, 2, 6, 6],\n [6, -4, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -4, 4, -5, 3],\n [-6, 5, 2, 3, -3],\n [-2, -3, -4, -4, -1],\n [-1, -2, -6, 3, 2],\n [6, -4, -6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 0, -6, -3, -2],\n [0, -6, -1, 2, 3],\n [1, -2, 3, -4, 0],\n [-1, -2, -3, 1, 6],\n [0, -2, 1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -4, -2, 0, 1],\n [-1, -2, -4, -2, -4],\n [3, 1, 3, 3, -1],\n [2, 3, -4, -5, -3],\n [2, -1, 4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -2, -6, 4, 0],\n [3, 4, 1, 0, -5],\n [-3, -1, 3, 5, 2],\n [-5, 5, 1, -6, 1],\n [-3, 5, 0, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 5, 2, 2, -6],\n [-2, -5, -5, -6, -3],\n [6, 6, -4, 5, 2],\n [5, -5, -6, 5, 4],\n [2, -4, 0, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -5, -1, 1, 6],\n [-5, -2, -5, -3, 5],\n [1, 6, 5, 6, 3],\n [3, -4, 4, -3, -3],\n [0, -1, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, -4, 5, 3, -6],\n [6, -4, -5, 3, 4],\n [5, 6, 4, 2, -6],\n [-4, -2, 3, -5, 2],\n [6, -5, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, 3, 5, 0],\n [-4, 5, 5, 4, 1],\n [1, 4, 4, 1, -4],\n [-6, 4, 5, -6, 4],\n [-1, -2, -2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 1, 1, 4, 0],\n [-2, 6, -2, -4, 6],\n [-5, 3, 2, 0, -6],\n [-5, -2, 2, 0, -1],\n [-3, -2, -6, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 2, -2, 0, -3],\n [-1, -4, 4, 5, -1],\n [-6, 2, 5, -1, -1],\n [4, -5, 5, -1, 1],\n [3, -1, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 2, -2, -2, -4],\n [2, 0, -3, -4, 4],\n [-6, -1, 1, 3, 1],\n [2, -2, -1, -6, 6],\n [0, -4, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -2, 1, -1, 1],\n [4, 6, 6, 6, -4],\n [4, 2, 0, 6, -2],\n [-5, -3, 4, -3, 2],\n [2, 1, 1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 4, -3, -6, -5],\n [-6, 6, -1, -5, 0],\n [6, -4, -3, 0, 1],\n [-2, 5, -1, 1, -1],\n [-5, 0, -5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -3, 1, -3, -6],\n [3, 5, -3, -6, 2],\n [0, -1, 2, -6, 3],\n [6, -1, 2, 0, -4],\n [2, 4, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 3, -6, -6, 5],\n [5, 6, -1, 6, 3],\n [4, -5, 5, 1, 5],\n [4, -3, -4, -5, 1],\n [4, 1, -1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 4, 6, 4, 2],\n [-3, -6, -1, 2, 5],\n [-2, -5, -1, -2, -1],\n [4, 2, 5, 0, -1],\n [6, -6, 3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -6, -5, -5, 5],\n [-4, 3, 2, -5, 6],\n [0, 3, 0, 1, -4],\n [5, 2, -4, 0, -6],\n [2, 3, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 5, 0, -6, -3],\n [3, 6, -6, 1, -5],\n [-1, 0, 2, 1, 4],\n [-2, -4, -4, 3, -6],\n [5, 0, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 0, -4, -4, -6],\n [2, -5, 0, -3, -4],\n [4, 0, 2, -1, -5],\n [1, -4, -5, 6, -2],\n [1, 4, 3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -5, 4, 1, 1],\n [3, 4, -3, 4, 2],\n [-6, -3, -1, 2, 2],\n [5, -6, -5, -1, 0],\n [2, 5, -6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -3, 3, 1, -2],\n [6, 4, -1, 3, 0],\n [-2, 2, 6, -4, -2],\n [-2, 4, 1, 3, -6],\n [-5, 6, 3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 3, -1, -6, 5],\n [-2, 3, 4, -2, 1],\n [5, -4, 3, 4, -2],\n [1, -6, 6, 5, -3],\n [-3, 3, 4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 1, -4, 5, -3],\n [-2, 5, -6, 5, 2],\n [2, -4, 0, 6, -1],\n [1, 2, 0, 4, 2],\n [2, -5, 5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 4, -2, 5, -1],\n [4, -1, 0, -3, 2],\n [5, 2, 2, -6, 1],\n [-6, 6, -6, -1, -1],\n [-6, -4, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -6, -4, 1, 0],\n [-6, -4, 3, -1, -5],\n [2, -6, 5, -4, 4],\n [-1, 2, 0, 3, 0],\n [-1, -2, 3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 4, 3, -2, 5],\n [-6, -3, -4, -6, -4],\n [-3, -6, 5, 4, 3],\n [2, 0, 6, 3, -3],\n [-2, -2, 3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 6, 4, 3, 4],\n [-3, 4, -5, 4, -6],\n [-2, -1, 1, 5, -6],\n [-5, 1, -5, 3, 0],\n [5, 3, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -5, 1, -1, -6],\n [1, -4, 5, 3, -2],\n [6, 0, 0, -1, 4],\n [-4, -2, -1, 2, -2],\n [-4, 0, -4, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, -2, 5, 6, -5],\n [4, 2, -6, 0, 6],\n [-5, -6, 4, 1, -3],\n [5, -4, 2, -3, 0],\n [0, 2, 2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -5, 5, 1, 2],\n [1, 5, 3, -5, -2],\n [0, -4, 6, 6, 3],\n [-4, 6, -4, -1, 5],\n [5, 0, -5, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 5, 5, 3, 4],\n [2, 4, -3, 1, 2],\n [5, 1, -1, 1, -4],\n [4, 2, 5, 5, -2],\n [-4, -3, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 3, 4, -3, -1],\n [3, -2, -2, 3, 1],\n [1, -2, 4, 2, 3],\n [6, 6, -4, 3, -6],\n [2, 4, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -2, 3, -4, -2],\n [-4, -1, -6, -1, 1],\n [-3, -6, 2, 2, 1],\n [0, 0, 4, 4, -4],\n [-3, -4, -1, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 6, -5, 3, -1],\n [-3, 5, 3, -4, -6],\n [4, -2, 0, 3, -1],\n [-2, 4, 2, -3, 3],\n [-6, -2, -2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -3, -5, -5, 3],\n [0, -6, 3, 1, -6],\n [-5, 1, 1, 2, -2],\n [5, 4, 6, -1, -5],\n [5, -6, 5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -5, 2, 3, 5],\n [2, 6, 5, 4, -2],\n [2, 2, 0, -1, 2],\n [-6, 4, -5, -6, -2],\n [-3, -5, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 3, -5, -1, -5],\n [4, 4, 6, 5, 0],\n [-4, 4, 0, -3, 6],\n [2, 3, 3, 6, 5],\n [-3, -2, -6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -5, 4, 2, -2],\n [5, -5, -6, -3, 1],\n [5, 0, 6, -6, -5],\n [-2, -3, -1, -4, 2],\n [0, 1, 2, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -5, -2, -2, -3],\n [-1, 5, -5, -1, -3],\n [2, -6, 2, -3, 5],\n [-3, 1, 3, 6, 0],\n [5, 5, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -1, -4, -6, 5],\n [0, 0, -5, 3, -3],\n [-6, -5, -1, 2, 6],\n [1, 4, -6, -4, 2],\n [-2, -6, -2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -6, -5, -5, 0],\n [-5, 4, -5, -3, -1],\n [4, 6, 4, -2, 3],\n [-5, -4, 4, 3, 4],\n [6, -6, 6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, -5, 6, -3, 3],\n [-5, 4, 0, 3, -1],\n [5, -2, -5, -5, 6],\n [-2, 0, 2, -3, -1],\n [-6, 0, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 2, -6, 0, -3],\n [4, 3, -4, 0, -4],\n [-4, -1, 4, 0, 6],\n [2, -5, -2, 5, 1],\n [-2, 3, 4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, 2, -2, 3, 6],\n [-3, 5, 0, 6, -4],\n [2, -1, 6, -3, 2],\n [-3, 1, 6, 5, -5],\n [3, 6, -3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 4, 4, -4, -5],\n [-2, -4, 6, -4, 3],\n [-4, 0, -3, -2, -1],\n [1, -1, 3, 0, -1],\n [2, -4, 3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 4, -4, 2, -3],\n [3, -6, -6, -3, -4],\n [4, 6, -1, 6, -1],\n [3, 4, 5, 2, 0],\n [-5, 2, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, 3, 1, -5],\n [-3, -4, -4, -6, -1],\n [-3, -1, 6, -4, 2],\n [3, 6, -3, -1, -4],\n [-3, -1, -1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -3, 4, -5, -2],\n [1, -4, 6, 5, -6],\n [1, 4, 4, 6, 2],\n [6, 5, -3, 0, 2],\n [4, -5, 6, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 4, 3, -1, 6],\n [-4, -1, 4, 2, 3],\n [6, 2, 0, -6, -5],\n [-3, 6, 0, 5, -2],\n [6, 4, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -1, 0, 2, 2],\n [-1, -6, 4, 4, 6],\n [-6, -3, 0, 6, -5],\n [-1, 4, -5, 0, 5],\n [5, 5, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 6, -5, 1, -1],\n [-4, 5, -3, 3, -4],\n [1, -4, -4, -3, -3],\n [-3, -3, 3, -4, -6],\n [-1, 6, 3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 2, -2, 4, 4],\n [-3, 1, -1, 0, 0],\n [2, -4, 6, -3, 3],\n [-1, -2, 6, 6, 1],\n [-6, 2, -4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, 5, 3, -1, -4],\n [-4, 4, 3, -3, -3],\n [3, -5, -6, -5, 1],\n [0, -6, -3, 3, 1],\n [-4, 0, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 5, -1, -2, -4],\n [0, -6, -1, -3, -1],\n [-4, -6, -4, 5, 4],\n [6, 1, 0, -2, 1],\n [-6, 2, 0, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 5, 2, -5, 4],\n [-5, -3, 4, -5, -2],\n [-1, 5, 5, 6, -6],\n [-3, -5, -6, 5, -3],\n [-3, 2, 1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 6, 4, 3, -6],\n [-3, 6, 5, 2, 5],\n [3, -6, 3, 0, 5],\n [-4, -6, -1, -2, -5],\n [5, 0, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -1, 0, -1, 4],\n [5, 0, -1, -4, 3],\n [-6, 0, 5, 0, -2],\n [5, -5, -5, -6, 4],\n [-3, 5, 3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, -5, 2, -1],\n [-3, 3, -3, -3, -4],\n [-2, -3, -1, 6, -3],\n [5, 6, -2, 3, -1],\n [5, 2, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -5, -5, 6, 3],\n [4, 0, 6, 0, -6],\n [5, 5, -6, 0, 3],\n [5, 1, -2, 0, -5],\n [-1, 4, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 4, -2, -3, -1],\n [0, -4, 4, 0, 2],\n [-2, 4, 0, -5, -5],\n [-2, 4, 0, 1, 0],\n [-2, 1, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, -3, 6, -6, -5],\n [-6, -3, 5, 2, -4],\n [4, 3, -1, 5, -1],\n [4, -5, -6, -3, 5],\n [5, 1, -4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -4, -5, 5, 3],\n [-4, 5, 2, -4, 2],\n [-5, -6, 0, 2, -2],\n [3, 1, -1, 2, -5],\n [-4, 2, 0, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, -3, -2, 5],\n [-2, 6, -6, 5, 1],\n [0, -1, 4, 3, -1],\n [-3, 4, 1, -3, 1],\n [-1, 5, 2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 2, 4, -4, 5],\n [-2, -1, 3, 3, 3],\n [2, 1, 4, -1, -6],\n [-1, 1, -1, 2, -3],\n [-4, 5, -1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 6, 2, 5, 0],\n [3, -3, -3, 4, 3],\n [6, -1, -4, 5, -2],\n [4, -6, -3, 4, -3],\n [-4, 6, -3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 6, -5, -4, -4],\n [-2, 2, -3, -1, 5],\n [-6, 4, 2, 0, 1],\n [4, -2, -4, 1, 4],\n [4, 4, -3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -3, 3, -6, -4],\n [5, -6, -2, -6, -3],\n [5, -3, 6, 1, 2],\n [0, 0, 5, 3, 3],\n [-5, -1, 6, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -5, 2, -6, -2],\n [-6, -5, 1, -1, 0],\n [-1, 6, 0, -5, 2],\n [-1, 0, 2, 1, 5],\n [-2, 4, -3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 6, 1, 6, -4],\n [4, 1, -4, -6, -1],\n [-3, 3, -1, -1, 2],\n [-3, 1, 0, 0, -1],\n [-4, 6, -6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -6, 5, 5, -4],\n [1, 4, -6, -1, 6],\n [-1, 0, 6, 6, -5],\n [3, 5, -5, -3, -4],\n [-3, 5, 0, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -1, 3, -6, 0],\n [-3, -2, 6, -6, -5],\n [6, 4, 0, 0, 2],\n [-1, -6, -6, -2, -3],\n [4, 2, 5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, -3, -4, -5, 2],\n [6, 0, -2, 4, 2],\n [-2, 2, 2, 0, -4],\n [-5, -2, 4, -6, 0],\n [6, -1, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 6, 4, -3, 6],\n [-5, -1, 4, 3, -5],\n [-3, -6, -1, -2, 2],\n [4, 2, -1, 0, -5],\n [-3, 1, 6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 0, -3, 3, 5],\n [5, 5, 1, -5, -6],\n [-1, -3, -1, -2, 2],\n [1, -3, -5, 6, -5],\n [3, -4, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 3, -4, -5, -4],\n [1, -1, -5, 6, -2],\n [0, 1, 4, -2, 5],\n [-1, 6, 4, -4, 2],\n [-1, -2, 1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -6, 5, -5, -6],\n [2, -3, -2, 1, 5],\n [3, 6, -3, -5, 4],\n [5, -5, 6, -2, 6],\n [3, -1, -4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, -2, 0, 1, 1],\n [-3, 1, 6, -3, -4],\n [3, -5, 5, 6, 0],\n [0, 2, -5, 3, -5],\n [5, 1, 5, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 4, 3, -3, -6],\n [4, 5, 2, -3, 0],\n [-5, -5, 2, 6, 3],\n [4, 0, 2, -3, 0],\n [-6, 0, 1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -1, 0, 3, 5],\n [5, -3, 5, 3, 2],\n [-3, -5, 5, -4, 6],\n [-1, 3, 1, -4, 6],\n [-6, -2, 5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 4, 4, 2, -1],\n [-1, -6, -3, -4, 4],\n [-4, 5, 5, 2, -3],\n [-3, -3, -5, -6, -3],\n [4, -5, -2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -5, 4, -2, 0],\n [-6, 6, 2, 6, -2],\n [-3, -4, -6, 4, 4],\n [-1, 6, -3, 5, -1],\n [-6, 1, 3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 5, -1, 5, -3],\n [-5, 1, 6, 3, 6],\n [6, 3, -1, 4, -1],\n [-3, -1, -6, -3, -6],\n [-5, -6, 5, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, -2, 0, 4],\n [-2, -5, 2, 2, -4],\n [-2, 1, 3, -4, -4],\n [-3, 1, -1, 5, 0],\n [4, -3, -5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 1, -3, -2, -4],\n [-2, 4, -1, -3, -5],\n [-4, -5, -1, -1, 4],\n [-6, -4, -3, 1, -6],\n [-3, 0, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -1, -3, 4, 3],\n [-1, 5, -6, 4, 0],\n [-1, 1, -4, -1, 4],\n [0, 1, -1, -3, 4],\n [-5, -2, 3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, -1, -2, 2],\n [3, -5, 5, -3, 0],\n [-5, 5, 1, -3, 6],\n [5, -4, -1, -1, -5],\n [-3, 5, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -4, 3, 1, -5],\n [2, 4, -1, 5, -4],\n [-4, -1, 5, -2, -2],\n [5, -6, 1, -1, 3],\n [4, 5, -4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -1, 5, -5, 1],\n [6, -1, 0, -4, 6],\n [-1, -5, 4, -4, 5],\n [-4, -6, 2, -5, -4],\n [-4, 3, -4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -3, 2, 1, 4],\n [-5, 4, 4, -6, -1],\n [-2, -6, 4, 6, 2],\n [1, 5, 0, 2, 2],\n [-5, 5, -6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -1, -5, -4, -3],\n [1, 3, -3, 0, -3],\n [-5, 6, 6, -5, 3],\n [5, -6, -1, 3, 5],\n [5, 1, -4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -6, 4, -1, 2],\n [-3, -4, 6, 6, 2],\n [-5, 3, 6, -3, -4],\n [0, 5, -5, 1, -6],\n [-4, 6, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -1, 3, 5, -6],\n [-5, -6, 4, 3, -1],\n [3, 3, 4, 5, 6],\n [6, -5, 4, 2, 2],\n [2, -1, 5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -1, 5, 5, 4],\n [-4, -3, 0, -5, 0],\n [-4, -2, 4, 6, -5],\n [-1, 0, 0, -6, 6],\n [5, -4, -5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 1, -4, 3, -5],\n [-6, -2, 6, -6, -4],\n [4, -1, 3, -6, 4],\n [-2, -6, -6, 0, 0],\n [-4, -4, -5, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 2, 2, -6, -1],\n [-5, -5, -4, 1, -5],\n [4, -6, 3, -1, 2],\n [1, 3, -3, -3, 6],\n [-1, -4, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, -1, -5, 6, -5],\n [-6, -4, 1, 3, 1],\n [-1, 6, -5, 0, -6],\n [0, -3, -2, 2, -2],\n [5, 3, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 3, -5, 4, 2],\n [4, -2, -5, -1, 5],\n [2, 1, -1, -1, 0],\n [5, 2, -2, 6, -2],\n [-3, -1, 5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -1, 5, 0, -1],\n [-1, 0, 4, -4, 4],\n [6, -4, -3, -4, -1],\n [-4, -2, 5, 5, -2],\n [-3, 4, 1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 2, 1, 3, -3],\n [6, -1, -1, 6, 4],\n [4, -4, 1, -6, -1],\n [5, -5, -2, 1, 3],\n [-2, 3, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 1, 6, -2, 5],\n [1, 1, 5, 4, 6],\n [-6, -1, -2, 2, -3],\n [2, 6, 6, -2, -5],\n [-4, -6, 4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -6, 0, 1, -4],\n [6, -6, -1, 0, 5],\n [6, 0, 1, 4, -5],\n [-1, 3, 1, -6, -4],\n [-3, -1, 6, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -1, -6, 0, 3],\n [-1, -3, 4, 4, 4],\n [-2, -1, -4, -4, -2],\n [-6, -6, 1, 2, 6],\n [6, -5, -6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 2, -3, -4, 5],\n [4, 6, 6, 3, -2],\n [-3, -1, 6, 5, 6],\n [0, -3, -3, 1, -5],\n [-3, 3, 4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 1, -6, -1, 6],\n [1, 5, -2, 5, -1],\n [-4, 0, 2, 6, -5],\n [-2, -2, 3, -1, 5],\n [3, 3, 1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -4, -2, 1, 0],\n [-1, 3, 2, -2, 2],\n [1, 1, 2, 3, 1],\n [5, -5, 2, -3, 2],\n [4, 1, -5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -6, 2, 6, -4],\n [1, 2, 1, -5, 6],\n [-4, 6, -5, 1, 0],\n [-5, 2, 4, 0, -4],\n [1, 3, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 6, -1, 4, -6],\n [4, -6, 2, -6, -2],\n [0, 2, 1, 6, 4],\n [3, 2, -5, 4, 3],\n [-1, -1, 6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -2, 2, -6, -5],\n [2, 1, 6, 1, 6],\n [0, -2, 3, 4, 0],\n [-2, -1, -1, 6, -6],\n [6, -2, -5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 3, -1, 4, 4],\n [2, 4, -4, 2, -6],\n [0, -4, 5, -3, 6],\n [-1, -5, -1, 1, 1],\n [1, 2, -1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -5, -6, 3, 0],\n [-4, 6, -4, -4, 2],\n [6, 0, -4, 3, -3],\n [-6, 6, -1, -1, 0],\n [4, 0, -1, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -1, -1, -1, -5],\n [1, -6, -2, -6, -4],\n [3, -1, -5, 2, -3],\n [0, -6, 5, -5, 1],\n [2, -2, -5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -4, 0, 4, 1],\n [2, 6, 1, -4, -2],\n [2, -3, 4, 1, 5],\n [-6, -6, 4, -2, -2],\n [5, 6, 5, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 6, -4, 3, 3],\n [-2, -2, -4, -6, -3],\n [4, 6, -2, -6, 3],\n [-2, 6, 5, 4, 0],\n [-3, 6, 5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -1, 5, -4, -3],\n [-5, 6, 1, 1, 3],\n [-1, 6, -5, 5, -5],\n [0, 1, 0, 0, 6],\n [-2, 6, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -1, 4, -1, -3],\n [-5, 2, 6, 4, 2],\n [5, 2, 3, 1, 4],\n [1, -6, -4, -2, 4],\n [3, -5, -6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 4, 0, 3, 0],\n [-5, 3, 5, -4, -5],\n [-1, 0, 6, 2, -3],\n [1, -3, -4, 0, 5],\n [4, -5, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 3, 1, 1, 6],\n [6, 0, 4, -2, 6],\n [3, 1, 0, -6, -5],\n [-3, 3, -3, 4, 0],\n [6, 5, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -1, 4, 6, 1],\n [6, 4, 4, 5, -3],\n [-5, -3, 2, -1, 5],\n [5, -2, -1, 2, 6],\n [1, 6, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 6, 0, -4, 3],\n [5, -3, 1, 1, 0],\n [-6, -5, -6, -4, 1],\n [-5, 6, 3, 4, 0],\n [-1, -5, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 5, -2, 2, 3],\n [6, 6, 1, -4, -3],\n [-5, 4, 2, -1, 1],\n [4, -5, 2, -6, -2],\n [5, -4, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 2, 3, -2, -6],\n [3, -4, 5, 3, 0],\n [4, -2, -1, 5, -3],\n [4, -6, -2, 3, 5],\n [-4, -6, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 6, 3, 3, 1],\n [0, 4, -1, -5, 0],\n [-6, 3, 4, -1, -1],\n [0, 1, -5, 5, 0],\n [-6, -1, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, 2, -5, 2],\n [-4, -6, 2, 3, -1],\n [-2, -1, 3, 6, -5],\n [4, -6, -1, 4, 1],\n [4, 2, -6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 6, 3, 4, -4],\n [2, 5, -6, 5, 2],\n [-6, 0, 0, -4, -2],\n [-2, 0, 1, -3, 6],\n [-5, -4, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, 3, 2, 0],\n [1, 1, 2, 4, -2],\n [-2, -1, 0, -5, 2],\n [3, 6, 1, -6, -1],\n [0, 2, 2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 4, -1, 4, -1],\n [5, 6, 4, 6, -5],\n [-6, 5, 6, 5, 1],\n [4, 2, -1, -1, -6],\n [4, 1, -6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 5, -3, 3, 1],\n [-5, -4, -5, 0, -2],\n [5, -3, -4, 6, -3],\n [0, 3, 4, -5, 4],\n [-5, 3, 3, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 3, 2, 2, -6],\n [-2, 1, -6, -1, -4],\n [4, 5, 0, -3, -5],\n [-2, 2, -2, 2, 2],\n [-6, 2, -5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -4, -4, 3, -5],\n [5, 5, 0, 2, 0],\n [6, -2, -6, -4, 1],\n [5, 6, -5, -2, -6],\n [5, -1, 6, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -1, -5, -3, 6],\n [-1, -1, 6, -2, -1],\n [-1, 4, -4, 3, -2],\n [5, -2, 3, 2, 2],\n [-1, 6, 0, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -4, -1, -6, 2],\n [3, 4, 1, -3, -3],\n [-3, 4, -6, 5, 0],\n [-3, 6, -6, -3, -2],\n [1, 1, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 1, 5, 1, -2],\n [-2, 4, -1, 2, 3],\n [-4, 5, 1, 1, 1],\n [4, 5, 1, 6, -2],\n [-3, 5, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -4, 0, -4, 4],\n [-5, 4, 0, 6, -3],\n [2, -5, 4, 3, -3],\n [-2, -1, 5, -4, -6],\n [-6, -6, -5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 5, 3, -6, 6],\n [3, 2, 4, 6, -3],\n [3, 5, 5, 3, 3],\n [-1, 2, -5, 6, -4],\n [-4, -1, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 5, 3, -4, -1],\n [2, 4, 1, -1, 5],\n [5, -3, -2, -6, 6],\n [5, 4, -2, 0, 3],\n [5, -3, -1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 6, -3, 3, 6],\n [6, -4, 5, -4, 0],\n [-1, -6, 3, -5, 1],\n [-1, -2, 6, -3, -2],\n [-1, -6, 1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 3, 4, 0, 5],\n [2, -1, 3, -6, -2],\n [0, 2, -5, -2, -5],\n [-2, -5, -6, -2, 1],\n [-3, 1, 3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 4, -2, -5, -3],\n [-3, -1, 4, -1, 2],\n [5, -1, 6, -5, 0],\n [2, 1, -6, 5, 4],\n [6, -3, -4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 5, 4, -2, -3],\n [1, 2, 4, 5, 1],\n [5, 3, -4, 1, 0],\n [1, 4, -1, 6, -6],\n [-3, 1, 3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 4, -2, -6, -1],\n [-3, 4, -2, 1, -6],\n [4, -2, 4, -1, -4],\n [-5, -2, -1, -6, -2],\n [2, -1, 1, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -2, 1, 3, -6],\n [-5, -5, 4, 0, 3],\n [-3, 4, 4, 2, 5],\n [3, 3, 5, 2, -6],\n [5, -2, 1, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 0, 1, -1, 5],\n [-1, -1, -4, -4, -3],\n [5, 4, -3, 3, 3],\n [5, 5, -5, 4, 6],\n [0, -4, -2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -4, 0, -3, 0],\n [-2, -5, 3, 3, -6],\n [-3, 1, -4, 2, -3],\n [3, 3, 3, -2, 4],\n [1, -3, -4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -3, -5, 1, 4],\n [2, -4, -4, 6, 1],\n [0, 6, -2, -6, -1],\n [3, -5, -5, -1, 3],\n [6, 1, -6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, -2, -3, 5, -5],\n [6, -1, 4, -6, 6],\n [5, -1, -1, -5, -5],\n [-1, -3, -1, 5, -6],\n [0, -1, 1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 6, 6, 5, 6],\n [3, 3, 0, 1, -4],\n [2, 2, 2, 2, 6],\n [-3, -4, 5, -5, 0],\n [-4, 0, -3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -6, -6, 0, 2],\n [4, -2, -1, -2, 3],\n [2, 2, -1, -1, 1],\n [-5, -4, -3, 0, 0],\n [3, -2, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 6, 1, 6, 5],\n [-6, -6, -6, 4, -3],\n [-1, 0, 2, 1, -3],\n [2, -2, -1, 0, -1],\n [-4, 0, -5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, 6, -1, 1],\n [1, 6, -1, 2, 3],\n [-3, 6, -2, -5, 6],\n [3, -2, -1, -5, 1],\n [6, -2, 6, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 5, 3, -5, -3],\n [-6, 4, 2, 6, -3],\n [-2, 3, -2, -1, 1],\n [2, -3, 3, 0, -4],\n [1, -1, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 2, -6, -4, -5],\n [0, 5, 2, 0, 4],\n [-6, -4, -5, -4, 0],\n [3, 4, -4, 0, -6],\n [-6, 6, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 2, 0, -2, -4],\n [-4, 6, -1, 5, -3],\n [-2, 6, -5, 0, 3],\n [3, -5, -6, 4, -6],\n [5, 1, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -3, -2, -6, 4],\n [5, 2, -6, 3, -4],\n [-4, -1, -4, 1, 3],\n [3, 1, 6, -4, -6],\n [-4, 5, -2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -2, 5, 6, -1],\n [3, -2, -5, -4, -1],\n [2, 0, -5, -6, -5],\n [-3, -5, -5, 6, 2],\n [-5, 4, -1, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, -3, 0, -6],\n [5, -5, 4, -3, 6],\n [-5, 0, -3, -5, -2],\n [3, -6, 6, 1, 1],\n [-5, -6, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 3, -2, 1, -3],\n [-3, -2, 1, -6, 2],\n [6, 0, -1, 1, -6],\n [2, 2, 3, -5, -4],\n [-6, -5, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, 0, -3, -5],\n [-6, 1, -6, 6, 0],\n [1, -4, 0, 0, 1],\n [0, -3, 4, -4, 0],\n [-5, -1, -4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 5, 6, 6, 2],\n [-2, 6, 3, 6, 5],\n [-2, 0, 4, -1, -1],\n [2, 1, -6, 3, 2],\n [4, -6, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -1, -2, -1, 0],\n [-3, 6, -1, 5, -6],\n [-6, -6, -3, 4, -2],\n [6, -2, 1, 1, -6],\n [3, 4, -6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 3, -2, 3, -3],\n [5, 5, -5, 4, 1],\n [0, 0, -3, -4, -4],\n [-5, 5, 3, -1, 0],\n [5, 2, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 6, 1, -2, 1],\n [4, 2, -3, 0, -6],\n [-5, 4, -4, -6, -1],\n [-2, 1, 3, 1, 6],\n [6, -5, -5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -5, -4, 2, -2],\n [6, 3, 2, -3, -3],\n [3, 0, 3, 3, -4],\n [-4, 6, -1, 0, -3],\n [-3, -6, -3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -3, -2, -2, 6],\n [-2, 0, 6, 1, 2],\n [3, 2, -1, 4, -2],\n [1, 4, -4, -3, 6],\n [4, 6, 0, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -1, 2, 3, 0],\n [3, -6, -2, 0, 5],\n [4, -4, -6, -3, 2],\n [3, -2, 5, 6, -6],\n [3, -2, 1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 4, 4, -1, -3],\n [0, -4, 4, -1, -5],\n [1, -5, -4, -5, 5],\n [5, -1, 3, 4, -6],\n [-2, -5, -1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 6, -3, -5, 6],\n [4, 6, 1, -1, 6],\n [1, -6, -5, -6, 0],\n [-6, -2, -1, 5, -4],\n [5, 1, 2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -5, -6, 0, 5],\n [5, -6, -2, 3, -2],\n [4, 3, 3, -3, 2],\n [-1, 6, 1, -5, -4],\n [1, 1, -6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 6, 1, -3, 5],\n [-4, 3, 5, -2, -1],\n [-5, 5, 6, 6, -2],\n [3, -5, -1, -6, 5],\n [-3, 6, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, 5, -5, 3, 2],\n [5, 6, 1, -5, -6],\n [2, 3, 5, 1, 1],\n [3, 4, 5, -5, 1],\n [1, -3, -6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -1, 3, 5, 1],\n [3, 4, 1, -1, -2],\n [2, 1, 6, -1, 2],\n [3, -3, -3, -2, 6],\n [5, 2, -3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 5, -4, 5, 1],\n [3, -2, -5, 0, 4],\n [-4, -2, -3, -3, 1],\n [-4, -2, 1, 1, -4],\n [5, 5, 4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -2, -6, 0, 4],\n [-5, -4, -4, -3, 1],\n [-6, -5, 6, 3, -2],\n [2, 5, -6, 4, -4],\n [3, 6, 4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 6, 1, 2, -5],\n [-2, 5, 5, 4, 0],\n [5, -3, -3, -6, -2],\n [-4, -4, 5, 2, 5],\n [1, 5, -4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[5, 4, 6, -2, 4],\n [-5, -6, 4, -1, 2],\n [-5, -4, -6, 2, 0],\n [0, -4, -5, 4, -2],\n [-5, -2, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, 2, 5, -1],\n [-3, 3, -1, 1, -5],\n [4, -3, 4, 4, -4],\n [6, -2, 5, -6, 2],\n [0, 6, -2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 6, 4, 1, -4],\n [6, 6, 6, 6, -6],\n [6, -6, 3, -1, 3],\n [3, 5, 4, 4, 4],\n [1, -5, 6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 0, -1, -3, 0],\n [4, -6, 3, 6, 4],\n [-3, -2, -2, -6, 6],\n [3, -6, -5, -6, -2],\n [0, 2, 2, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -2, 6, -4, -3],\n [-5, -1, -5, -1, 1],\n [4, 1, -4, 6, 3],\n [-5, -2, -5, -5, -4],\n [-6, -5, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -6, 6, 5, -3],\n [-2, -6, -3, 6, 4],\n [6, -2, 3, 1, -1],\n [4, -2, -2, 6, -1],\n [1, -1, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 5, 3, 1, 0],\n [-1, 4, 2, 0, 3],\n [-4, -5, -6, 5, 5],\n [-3, 0, 6, 1, -5],\n [6, -2, -3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -1, -4, -4, -3],\n [2, 4, 0, 3, 5],\n [-4, 5, -5, 3, -5],\n [-2, -4, 1, -2, -1],\n [1, -3, 0, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -3, -1, 2, -6],\n [1, 3, -3, 5, 0],\n [-1, 6, -6, 1, -5],\n [-1, -5, 0, 6, -2],\n [6, 5, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -6, 1, 3, 3],\n [6, 2, 5, 2, 0],\n [3, 2, 0, -4, -3],\n [0, 2, -2, 0, -5],\n [-2, -3, 5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 6, 6, -1, -5],\n [-2, 4, 5, -4, 4],\n [1, -5, 6, 2, 1],\n [4, 6, 6, 1, -3],\n [0, -1, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -2, 3, -4, -1],\n [4, -2, -6, -1, 5],\n [4, -4, -5, 4, 1],\n [-4, 1, 5, 4, -5],\n [-1, 4, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, -5, 3, -3, -6],\n [-3, 3, -6, -6, 3],\n [6, 3, 4, 4, -6],\n [0, 1, 2, -1, -2],\n [4, 3, 6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 2, -4, -2, 3],\n [6, 1, 5, 1, 5],\n [3, 3, -1, 2, -2],\n [-4, 3, 3, -5, -2],\n [2, 6, 1, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -4, -1, -3, 1],\n [0, -3, 0, 5, -5],\n [-5, 2, 1, 2, 5],\n [-1, 5, -3, -5, 1],\n [2, -2, -3, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 4, 1, 3, -1],\n [3, 2, -6, -3, 0],\n [6, 0, 4, 3, -1],\n [-3, -4, -4, -3, 3],\n [1, -4, 1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 4, 5, -3, -4],\n [-3, -4, -6, -2, -5],\n [-1, -4, 6, 6, -5],\n [1, -3, -3, 6, -3],\n [-3, 6, 2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -6, 1, 1, -6],\n [1, 1, -2, 5, 4],\n [-1, -6, 0, 2, 2],\n [-2, -2, -1, -3, -3],\n [3, -6, -5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 0, 6, 2, 5],\n [-4, -1, -5, 3, -2],\n [-5, 2, -5, 4, 1],\n [-6, -3, -2, 6, 5],\n [3, -2, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 2, -4, 2, 4],\n [0, 6, -4, 0, -6],\n [-6, 6, 0, 2, 6],\n [-1, 1, 6, 0, 0],\n [6, -5, 6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 3, -5, -2, -1],\n [0, -3, 0, 1, 4],\n [1, -2, 2, 5, -2],\n [-5, -3, -3, 6, 6],\n [4, -4, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 0, -5, -6, -4],\n [-1, 5, 4, -1, -4],\n [-3, 5, 3, -2, -1],\n [6, 1, -6, -4, -4],\n [0, -1, 6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -1, 4, 5, 2],\n [6, 0, -1, -2, -3],\n [-2, -6, 6, -3, 0],\n [-4, -3, -2, -6, -6],\n [5, -3, 5, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 0, -1, 2, -3],\n [0, 3, -2, 6, 4],\n [-5, -3, 1, 2, -4],\n [6, 1, 6, 3, 3],\n [1, 5, -1, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -2, 5, 3, -4],\n [2, 4, -4, -6, -3],\n [0, 4, 0, 0, -6],\n [6, 0, -5, 5, -6],\n [-4, -5, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -3, -3, -5, 4],\n [6, 3, 6, 4, 6],\n [-3, -2, 1, 3, 6],\n [-3, 3, 6, 1, 1],\n [-5, -2, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 5, 4, 4, 1],\n [-1, 3, 3, 2, 3],\n [2, -2, -5, 2, 6],\n [5, 2, 1, -5, 0],\n [1, -2, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 3, 0, 1, -6],\n [-1, 4, -6, 2, 0],\n [-3, -1, -3, 6, 5],\n [6, 3, 1, -2, 6],\n [4, -3, -6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 5, -1, 1, 5],\n [-4, -4, -1, -2, 3],\n [2, 4, -1, -4, -4],\n [-4, -2, -3, 2, 6],\n [6, 4, -4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 0, -1, 4, 1],\n [1, 0, -6, 4, 0],\n [6, 6, 6, 2, -3],\n [0, 2, 5, -4, 1],\n [2, 6, 6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -5, 3, 6, 5],\n [3, -3, 6, -4, -5],\n [-4, 6, -3, 5, -1],\n [2, -5, 4, 1, -5],\n [-6, -4, 4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -4, 4, 2, 4],\n [-2, 2, -4, -2, 0],\n [-2, 0, 1, -4, -4],\n [1, 1, 2, -3, -4],\n [-5, 2, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 5, -4, -4, -1],\n [0, 4, 1, 1, -1],\n [3, 0, -3, -5, 0],\n [6, 4, -5, -3, -5],\n [3, 3, -4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -2, 1, 0, 4],\n [-6, 1, 4, -4, -1],\n [-6, 4, 2, 0, 1],\n [4, -3, 6, 5, 0],\n [1, -2, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -2, 1, -6, 0],\n [2, 3, -6, -4, 1],\n [-4, 2, 4, -5, -2],\n [1, -6, -3, -5, -3],\n [2, 1, 0, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 5, -3, 0, -2],\n [-3, 5, -6, -3, -5],\n [-5, 0, 5, -5, -4],\n [2, -2, -6, 1, -4],\n [-3, 6, -1, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 6, 3, 5, 4],\n [-6, -6, -6, -1, 5],\n [1, -6, 0, -6, -3],\n [0, 0, 6, 6, 0],\n [-5, 2, 4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 5, 1, 0, 6],\n [2, 6, 4, -5, 0],\n [-6, 5, -5, 3, 3],\n [5, -6, 1, 2, 0],\n [-3, -5, -5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 0, -5, 2, 3],\n [-5, 4, -2, 4, -4],\n [-2, 4, 5, 2, -5],\n [2, -4, 1, -5, -2],\n [-2, -1, -3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 5, -6, 1, -4],\n [-4, -1, 3, -5, -1],\n [1, -3, -4, -6, 1],\n [-2, -4, 0, 3, -3],\n [5, -1, 3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -5, -4, 4, 5],\n [-1, -2, -6, 0, 6],\n [2, -6, -5, 2, 1],\n [3, 6, 5, 3, 1],\n [0, -4, -1, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, -2, -2, -5, 3],\n [0, 0, -6, 1, -2],\n [0, 4, -5, -4, 3],\n [-6, 6, 5, 6, -6],\n [-5, -1, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 1, 6, -2, -5],\n [-6, -6, -1, 6, 6],\n [-3, -6, 4, -1, 6],\n [-6, -4, -5, 5, 6],\n [2, 0, -6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 2, 0, 0, -1],\n [6, -6, -3, -1, -1],\n [5, -1, 2, 2, -5],\n [6, -5, -2, 5, -2],\n [-1, 2, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, -5, -4, 4],\n [-2, -1, -4, -6, -6],\n [4, -2, -1, -3, -2],\n [5, -2, 3, -3, 1],\n [5, 2, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 4, 0, 4, -1],\n [-4, -1, -4, 1, -6],\n [6, 4, -4, -4, 5],\n [-4, 2, -5, 4, 3],\n [6, 5, -3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -2, 4, 1, 3],\n [0, 0, -1, 1, 0],\n [1, -1, 1, 5, 6],\n [-3, 4, 6, 4, -6],\n [3, -2, 5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -4, -5, -2, -4],\n [1, -1, 5, 1, 0],\n [-5, 0, -4, -6, -1],\n [3, 2, -1, -2, 1],\n [3, -4, -6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 2, -1, -5, -3],\n [-1, 0, 2, 1, -1],\n [3, -3, -3, 6, -4],\n [-3, -6, -4, -2, 4],\n [-6, -2, 3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -4, -3, -2, -5],\n [-2, 4, 1, -3, -1],\n [-3, 5, 2, -4, 0],\n [-2, 3, -6, -1, -5],\n [-1, 0, -1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -3, -5, 2, 0],\n [-4, -5, -5, -5, -4],\n [1, 5, -2, 6, -4],\n [1, 3, 3, 5, 2],\n [1, -6, 0, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 4, -6, 6, -2],\n [2, 6, 4, -6, -3],\n [-1, -6, -6, 3, 6],\n [2, 3, -2, -4, -1],\n [4, 4, 4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -4, 1, -5, 0],\n [2, 4, -3, -1, -3],\n [2, -1, 6, 4, -6],\n [-4, 3, 3, -5, -6],\n [1, 6, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -2, 6, -6, 4],\n [-1, 0, 3, -4, 4],\n [2, -2, 6, -6, 1],\n [-2, 0, -1, 1, 0],\n [-5, -2, -1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -2, 1, -3, -5],\n [2, -1, -2, 4, 2],\n [1, -5, 1, 6, -4],\n [5, -4, -3, 3, 1],\n [5, -2, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 1, 6, 6, -6],\n [-6, -1, 1, -2, 5],\n [5, 6, -3, -5, 4],\n [-3, 3, 3, -2, -2],\n [-1, 4, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -6, -5, 5, 2],\n [-3, 3, -5, -2, 1],\n [-3, 6, -2, 0, 4],\n [0, -5, -4, 1, 6],\n [-1, -1, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -3, 3, -2, -4],\n [-1, -3, -3, 1, -2],\n [1, 6, -1, -4, 4],\n [3, -1, 0, -4, -3],\n [-6, -3, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 3, -6, -4, -2],\n [-5, 2, 4, 0, 3],\n [-6, 1, 0, 1, -4],\n [-5, -3, -1, 4, -2],\n [-6, 3, 5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 6, -3, -2, 0],\n [4, -4, -3, -2, -2],\n [4, 1, 0, -6, 3],\n [-5, 6, -1, 2, 5],\n [6, -4, 6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 6, -4, 4, -1],\n [-4, -5, 1, -5, 3],\n [4, 2, 3, 0, -2],\n [5, 5, 5, 1, 6],\n [5, -3, 5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 2, -3, 0, 0],\n [5, -6, 6, 4, 4],\n [-5, 2, 2, -3, 5],\n [4, -3, 2, 5, -3],\n [6, -5, 4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -5, -2, -1, -2],\n [1, -4, -3, 6, 3],\n [0, 1, -6, -4, 0],\n [6, 4, 5, 2, 6],\n [3, 1, 2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 2, 3, -1, -4],\n [0, -2, 5, -5, -3],\n [0, -6, -3, 3, -1],\n [-6, -5, -5, 5, 2],\n [2, -4, 5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 0, 2, -6, 1],\n [4, -4, -5, 1, 6],\n [-1, 0, 4, -5, 4],\n [-4, -4, 2, 1, 2],\n [-4, -3, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 5, 2, 2, -2],\n [-5, 3, 4, -4, 0],\n [-2, -5, -2, 3, -4],\n [-4, -6, 2, 4, 3],\n [-5, -4, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, -4, -5, 0, 1],\n [1, 2, -1, 3, 2],\n [-3, -5, 5, 5, -3],\n [3, 1, -4, 5, 4],\n [-1, 0, 6, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 2, -3, 3, 6],\n [2, -6, 4, -5, 1],\n [-5, -5, -1, -6, -5],\n [0, -2, 4, 6, 2],\n [-5, 5, 3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -5, 4, -5, 0],\n [-4, 1, 0, -2, 0],\n [6, -3, 1, 6, 3],\n [-2, 3, -1, -1, -1],\n [5, 1, 6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -6, 0, 5, 5],\n [-3, -3, -1, -5, -6],\n [3, -6, 2, 5, 3],\n [-4, -1, 0, -4, -1],\n [5, 6, 1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 5, 0, 2, 2],\n [-4, 0, -1, 0, 2],\n [-2, 2, -1, 3, 4],\n [-5, -2, 0, -2, 3],\n [4, 4, -1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 1, 2, 2, -3],\n [6, -5, 0, -2, 2],\n [4, -5, -1, -6, -5],\n [-4, 1, -3, -2, -2],\n [4, -5, -5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-1, 4, 6, -4, 5],\n [2, -5, -3, -2, -3],\n [-2, -1, 3, 2, -1],\n [6, 5, 1, -3, -1],\n [-2, -4, -4, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -1, -1, -5, -1],\n [-4, -3, 0, 4, 3],\n [-2, 1, -5, 3, 4],\n [0, 0, -3, 6, 3],\n [0, -2, 5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 6, 4, -1, -5],\n [5, -5, 0, 6, 1],\n [-5, 2, 5, 0, 5],\n [-4, 3, 2, 5, 0],\n [3, -6, -3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -2, -6, 6, 4],\n [1, -3, 6, -6, 0],\n [-5, -6, -4, -2, 1],\n [0, -4, 1, 1, -6],\n [0, -1, 3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -6, 6, -5, 0],\n [-4, 0, 1, -2, 4],\n [3, -2, 1, -3, 0],\n [1, -3, 6, -6, 3],\n [6, -2, 3, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 1, -1, 6, 5],\n [3, -2, -1, 4, -3],\n [5, -2, -6, -3, 0],\n [-2, -6, 0, 4, 5],\n [-2, -1, -5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 2, 4, -3, -1],\n [-6, 1, 2, -3, 5],\n [3, -6, 1, -2, 5],\n [0, 3, -5, 4, 6],\n [1, 1, -4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -1, -2, -1, -6],\n [-2, 3, 4, -2, 0],\n [0, -3, 1, 5, -3],\n [-4, 6, -6, -2, 4],\n [-1, -2, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 4, 3, 0, -2],\n [4, 3, 4, -5, 4],\n [5, -4, 4, 1, -2],\n [5, 5, 5, -6, -4],\n [-3, -1, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -3, 6, -3, 0],\n [-1, 2, -6, -6, 1],\n [4, -1, -1, -1, 4],\n [-5, 0, -2, -4, 5],\n [3, -2, -3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -2, 6, -3, -1],\n [1, -2, -1, -1, -4],\n [-5, 0, 3, 5, -4],\n [-6, -2, -6, 4, 0],\n [4, -4, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 0, 2, 0, -4],\n [6, 5, 2, 1, -3],\n [-2, -5, 0, 3, -3],\n [3, -4, 2, 5, 5],\n [1, 1, -5, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 4, 0, -2, -2],\n [-6, 1, -4, 3, -3],\n [0, -5, -6, 5, 4],\n [4, -5, 5, 0, 4],\n [4, -4, 3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 1, 4, 0, -5],\n [2, 6, 4, 4, -2],\n [6, 0, -5, 5, -6],\n [-2, 0, -2, -4, -2],\n [2, 0, -2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 0, 5, 5, -3],\n [4, -1, -5, 3, -5],\n [-5, 1, -2, 2, 2],\n [-5, 3, 5, 1, 6],\n [3, 2, -4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, -1, -6, 1, 5],\n [3, -1, 6, -4, 0],\n [5, -1, 3, 6, 3],\n [-3, 3, -5, 0, -3],\n [-3, 6, 6, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 2, 1, 2, -1],\n [3, 2, -3, -6, -2],\n [-6, -1, 0, 1, 4],\n [-4, 1, -4, -6, -5],\n [5, 2, -5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -3, -6, -2, 3],\n [-1, -1, -6, -4, 2],\n [-5, 0, -5, 6, -2],\n [-1, 1, -3, 6, 6],\n [4, -5, -4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 5, -4, 2, 4],\n [-2, 1, -3, -6, 6],\n [4, -4, 3, 5, 0],\n [3, 6, -1, 3, 0],\n [2, -4, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -4, 5, 3, -5],\n [6, -6, 4, -1, 4],\n [-4, -5, 3, -2, 0],\n [2, 1, -1, -3, -2],\n [0, -5, -3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -5, 1, 0, -5],\n [3, 1, 4, -2, -5],\n [-6, -2, 2, -1, 5],\n [0, -5, -6, 1, -4],\n [-6, 1, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, 6, 3, 0],\n [-1, 4, 6, 6, -3],\n [-3, 5, -6, -3, 6],\n [-2, 6, -4, 1, -2],\n [-5, -2, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 0, -3, -5, 4],\n [-4, -2, -4, -6, -1],\n [-2, 4, -3, -6, -1],\n [2, 3, 2, -1, 1],\n [0, -4, -3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, 5, -3, 0, -5],\n [0, -6, 1, 2, -3],\n [-5, -2, 2, 1, 2],\n [-2, -6, -5, -4, 4],\n [-6, -4, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -1, 5, -5, -1],\n [0, 5, 1, -5, 3],\n [6, 4, 5, -4, 3],\n [-2, -1, 4, 2, 1],\n [-6, 3, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, -3, 2, 2, -5],\n [2, -4, 5, -1, -1],\n [-4, 2, -6, 0, -6],\n [5, 2, 0, 6, 5],\n [0, 4, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 4, 4, 0, 6],\n [5, 0, -3, 0, -2],\n [2, 0, -2, 1, -1],\n [-4, -6, 6, 6, -6],\n [-3, 1, 1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-3, 4, 2, 0, -1],\n [4, -2, 5, 1, 4],\n [2, 1, 3, 0, 2],\n [-2, -4, -2, 3, -6],\n [-3, 3, 5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 4, 5, 5, -1],\n [3, 2, -2, 1, 3],\n [5, 5, -3, -2, -1],\n [-6, -4, -1, -6, 0],\n [3, -6, 6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -5, -3, -6, 0],\n [-5, 2, 5, -6, 4],\n [5, -3, 1, -1, 4],\n [5, -6, -6, 4, 3],\n [2, -4, -1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -2, 6, -4, -4],\n [-5, -3, 5, -5, 5],\n [-5, -1, 4, -5, -4],\n [-2, 4, -6, -1, 6],\n [-3, 2, -1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -3, 0, 2, -5],\n [-1, 1, 2, 0, 0],\n [-3, -3, -4, -4, 1],\n [-1, -6, -1, 6, 5],\n [-2, -2, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -6, -3, -2, 6],\n [-5, 2, -1, 2, -3],\n [0, -1, -6, 2, -1],\n [-2, -6, 5, -3, 3],\n [-3, 1, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -1, 3, -6, -2],\n [-5, 6, -5, 5, 3],\n [4, -3, 5, -1, 5],\n [2, -4, -1, 4, -2],\n [-3, 6, -3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 0, 2, 1, 0],\n [-4, -4, -2, -5, 4],\n [5, 5, -2, 0, 2],\n [0, 6, -1, 0, 3],\n [2, -1, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-4, 6, -5, -6, 4],\n [-6, 1, -5, 6, 6],\n [-5, -4, 4, 1, 6],\n [6, -2, 0, -5, 6],\n [4, -3, 4, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 6, -3, -4, -6],\n [-6, 2, -4, 5, -2],\n [0, 0, -1, -1, 2],\n [-4, -6, -4, -5, 0],\n [-6, -4, 6, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -6, -6, -6, -4],\n [-1, 4, -5, 3, -3],\n [6, -3, -1, 2, -5],\n [-4, -1, -1, -2, 5],\n [0, -5, 4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 4, -5, -2, -1],\n [-4, 3, 2, -2, -4],\n [6, 1, 4, -3, 3],\n [-4, 5, 5, -6, -6],\n [-5, -5, 1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 2, 0, 3, -1],\n [5, 3, 6, -5, 2],\n [1, -6, -6, 2, -1],\n [-6, -5, -5, 1, -3],\n [-1, 0, 5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -3, -6, -1, 6],\n [6, 1, 6, -4, -5],\n [-6, 6, -3, -2, 3],\n [0, 0, -5, 2, -6],\n [-6, -1, 4, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, 2, -3, -3, -1],\n [-5, -5, 4, -6, -2],\n [-2, 0, -5, -5, -5],\n [-4, 5, -6, 3, 6],\n [-2, -4, 4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 0, -5, 5, -2],\n [3, -2, 5, -3, -1],\n [5, -6, -3, -2, -6],\n [-1, 6, -5, 6, 4],\n [-5, -3, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 2, -6, 1, 6],\n [-2, -2, -2, -1, 6],\n [-5, -2, 0, 6, -4],\n [5, -2, -3, -6, 5],\n [5, 5, 4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 2, 5, 1, -5],\n [5, -1, -1, -1, 2],\n [-2, 0, -5, -4, -3],\n [0, -6, -6, 2, -4],\n [-4, -2, 2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 4, -2, -2, 4],\n [-6, -6, -1, -2, 5],\n [0, 4, -6, -1, -3],\n [-6, -6, 4, 3, 1],\n [0, 3, 0, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -6, 6, -2, 4],\n [5, 6, 5, 1, 0],\n [-5, 0, 6, -4, -6],\n [1, 0, -2, 2, 5],\n [-6, -3, -2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 2, -5, 3, 4],\n [0, 2, 3, 2, 4],\n [0, 3, 2, 0, 3],\n [-4, 3, -1, -1, -5],\n [2, -1, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, -6, 3, 0, -6],\n [0, 6, 0, 2, -5],\n [5, 6, -6, 0, 4],\n [4, -2, 0, 2, 0],\n [6, 5, -3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 3, -3, -5, 6],\n [4, 2, 1, 6, 3],\n [-6, 3, -6, -5, 3],\n [0, -5, -3, -4, -1],\n [4, 2, 5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 1, -6, -2, -2],\n [3, -6, -4, 6, -4],\n [6, 3, -5, -3, -6],\n [3, 4, 3, 1, 6],\n [-2, 6, -6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -5, 0, -5, -2],\n [-1, 2, -2, 4, 6],\n [-6, -2, 5, -6, -4],\n [5, -3, 3, -5, -5],\n [3, 3, 1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 4, -4, -3, 4],\n [-5, -5, -3, 1, -3],\n [-5, 0, -3, -1, 0],\n [-5, -3, -4, 3, 5],\n [-3, 5, 2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 5, -4, 3, 5],\n [0, 5, 2, 2, -2],\n [-6, -2, -4, -1, 6],\n [1, -2, 5, -6, -3],\n [-2, -3, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -6, -4, -4, -1],\n [-3, 0, -2, 3, 3],\n [-2, 0, 4, -6, -6],\n [2, 4, 2, 3, -1],\n [1, 0, -6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -5, 0, 0, 5],\n [-1, -4, 5, -1, 0],\n [-4, 4, 2, 2, 4],\n [5, -5, 4, 6, 2],\n [0, 5, -5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -1, 5, 1, 2],\n [-1, 1, 4, -4, 4],\n [-6, -3, 0, 2, -2],\n [5, 6, -4, -2, 3],\n [6, 6, -3, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -1, 3, -3, -4],\n [-2, 1, 2, -5, -6],\n [2, 3, -1, -2, 3],\n [2, -4, 0, 1, 2],\n [5, 3, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 5, -1, 6, 0],\n [2, 5, -3, 1, 1],\n [-6, -4, -2, -6, -6],\n [6, -1, 6, -6, -1],\n [1, -6, 3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 6, -5, -4, -6],\n [-1, -5, -5, 0, 6],\n [-6, -1, -6, -6, 5],\n [4, -6, 3, 1, -3],\n [-5, -1, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 1, 4, -5, 0],\n [3, 3, 0, 3, 4],\n [-5, 0, -5, -1, -2],\n [4, 5, -2, 2, 0],\n [-6, 0, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -4, 0, 4, 5],\n [-6, 3, -2, -5, -4],\n [-6, -1, -6, -4, -4],\n [2, -3, -2, 3, -5],\n [-5, -1, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, 4, -3, -5],\n [0, 2, -4, -3, -2],\n [0, -5, -3, 1, -5],\n [-3, 1, -3, 3, 1],\n [-6, -4, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -6, -3, 0, -1],\n [4, -3, 6, 1, 4],\n [4, 0, -1, 1, -2],\n [-1, -5, 3, -4, -3],\n [4, -2, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 5, 0, -4, 6],\n [-2, 1, 0, 1, -5],\n [1, -5, -1, 4, -3],\n [-6, 4, -4, -5, 6],\n [-5, -5, -3, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 4, 0, 0, -4],\n [4, 1, -5, 5, 1],\n [6, 6, 1, -3, -2],\n [-6, -6, -1, 2, 3],\n [2, -5, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 6, -3, 3, 3],\n [-1, -5, -4, -4, 0],\n [3, 2, 5, -4, -3],\n [-5, -6, 5, 4, 1],\n [2, 4, 5, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 0, -4, -1, -4],\n [-2, -2, 1, -2, 4],\n [-2, 3, 0, 1, -4],\n [6, 2, 2, 2, 1],\n [1, -4, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 0, 2, -5, 3],\n [-2, -5, -2, -2, 1],\n [-4, 6, 2, 6, -5],\n [-2, -2, 3, 4, 6],\n [-4, -2, -3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -4, -1, -4, -4],\n [3, -4, -1, 6, -3],\n [0, -3, -4, -6, 0],\n [-3, -2, 6, 6, -5],\n [0, 1, 0, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 0, 3, 5, 0],\n [-5, 1, -3, 3, -4],\n [1, 1, 4, -1, 4],\n [1, -5, -2, -2, 2],\n [-5, -5, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 3, -4, 2, -6],\n [3, 4, 0, 0, -2],\n [6, 4, -4, -4, -3],\n [5, 3, 4, 6, -3],\n [5, 1, 5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, 4, -5, 3, -6],\n [-3, -5, 4, 0, 4],\n [6, 6, 0, -3, -3],\n [-1, 1, 0, -1, 2],\n [3, -4, 6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 4, -5, -6, 0],\n [5, 6, 0, -4, 6],\n [-3, 6, 6, -6, 4],\n [-2, -6, -1, -6, 2],\n [-1, -6, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 0, -5, 2, 3],\n [-6, -6, 3, -6, -6],\n [-2, 5, -4, 3, 6],\n [1, 0, -3, 1, -3],\n [-2, 5, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, 3, 6, -2, -2],\n [-2, 1, 6, -3, -6],\n [3, -3, -2, 1, 4],\n [-3, 2, 2, 4, -6],\n [-2, 6, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -1, 2, -3, -1],\n [-6, 3, 1, 5, -3],\n [5, 2, -4, -1, -5],\n [1, 5, 3, 3, 0],\n [6, 6, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 1, 3, -3, 0],\n [-3, 2, -2, -6, 0],\n [-1, 5, -4, -1, 3],\n [2, 6, 5, -3, -6],\n [2, 3, -5, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 1, -4, 4, 4],\n [-5, 5, 1, -1, -3],\n [-2, 6, 0, -6, -6],\n [-2, -5, 1, 2, -5],\n [-1, 1, -6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 0, 0, 5, 1],\n [-4, -5, 0, 5, -2],\n [1, 0, 2, 2, 0],\n [3, 6, -6, 0, 1],\n [-2, -4, 4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -6, -1, -6, 2],\n [-3, -4, -2, 1, 5],\n [-4, -6, -5, 0, -1],\n [-5, 1, 3, -1, 2],\n [-6, 2, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -3, -5, -4, -3],\n [-6, -3, 2, 1, -1],\n [6, -1, -2, -5, 0],\n [6, -2, 0, 5, -5],\n [3, 5, 2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -4, -5, -1, 6],\n [-5, -1, 1, 4, 2],\n [-1, 1, 4, -1, 6],\n [3, 2, -1, -3, -4],\n [-4, 3, -2, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 2, -4, -5, 4],\n [-5, 2, 2, -5, -3],\n [-2, -5, -1, 5, -3],\n [2, 0, 1, -3, 5],\n [-2, 3, -5, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 0, 0, 3, 2],\n [0, -1, -1, 3, 4],\n [-3, -3, -1, 0, 5],\n [-4, 4, -5, 0, -4],\n [3, 3, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -4, -4, 0, -6],\n [6, 2, -6, 5, 3],\n [6, -3, -1, -5, -1],\n [1, 3, 0, 6, 4],\n [-5, -3, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 3, -2, 2, -4],\n [5, -6, 5, -4, -6],\n [-1, -3, -6, -6, 1],\n [-4, 4, -6, 4, -2],\n [5, 2, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 0, 4, -6, 3],\n [6, -5, -1, 3, 3],\n [-4, 3, -4, 0, 2],\n [3, 4, 3, -3, -2],\n [-4, -5, 6, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -4, 5, -1, -1],\n [4, -1, 2, -4, 2],\n [-3, 6, 6, 5, 0],\n [4, -6, -6, -6, 1],\n [6, 4, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-1, 2, -3, -5, -4],\n [-5, 4, 0, 0, 4],\n [-2, -3, -3, 0, -5],\n [-5, 2, 3, -2, -2],\n [-3, 1, 3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 1, -2, -5, 2],\n [3, -6, -5, -5, -6],\n [0, -2, -6, -1, 5],\n [-1, -4, -5, 4, -4],\n [3, 1, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, -4, -6, -6, 0],\n [1, -5, 5, 3, 4],\n [-2, 0, 4, 3, -1],\n [5, 2, 2, 0, 6],\n [-6, -1, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -1, -2, 2, 5],\n [5, 0, 0, 2, -3],\n [6, -4, 3, -6, 5],\n [5, -4, 0, -2, 2],\n [6, -3, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -3, -2, 1, 1],\n [4, -3, 6, 1, 4],\n [-2, 5, -5, 6, -1],\n [2, 1, 5, -3, -5],\n [6, -5, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -3, 1, 0, 0],\n [5, 3, -2, -2, -4],\n [0, 6, 3, 2, 1],\n [-5, 2, -4, -4, -2],\n [5, -6, 0, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, 3, -3, 4, 0],\n [-2, 1, -3, 2, -1],\n [4, 0, 3, -4, 2],\n [-2, -6, 5, -2, -3],\n [-4, -5, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -3, 4, -6, 0],\n [-1, -3, -3, -5, -5],\n [4, 6, 1, 2, -5],\n [2, -5, 2, 4, -4],\n [-5, -1, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 2, -3, -3, -4],\n [-5, 6, 1, 2, 0],\n [2, 1, 1, 2, 2],\n [-3, -4, 2, 1, 4],\n [4, -5, 6, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -2, 2, 0, 3],\n [5, -3, 3, -3, -3],\n [4, -3, 6, 3, 1],\n [-3, -4, -2, -3, 6],\n [5, -1, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -5, 5, 1, -3],\n [2, 1, -1, -1, 3],\n [2, 2, -6, -5, 4],\n [6, 1, 6, 1, 1],\n [0, -5, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -2, -3, -1, 2],\n [-5, 0, -2, 5, 4],\n [6, 2, 3, -6, 4],\n [-6, -5, 1, -2, -5],\n [-1, -6, 5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 1, -4, -5, -3],\n [3, -2, -1, -1, -5],\n [-1, 6, 1, 2, 2],\n [-2, 5, -5, 5, -3],\n [-1, -1, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 3, 2, 1, -5],\n [-6, 2, 4, 2, -1],\n [5, -5, -2, 5, 6],\n [4, -2, 1, 4, 0],\n [4, -4, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -6, 1, -5, -3],\n [-4, -5, -6, 1, 0],\n [2, 1, -3, -3, 3],\n [1, -4, -1, -6, -6],\n [0, 0, 1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -5, 5, 0, -6],\n [4, -3, -3, -4, -3],\n [2, -6, -6, -2, 3],\n [2, 1, -5, 3, 0],\n [-5, -4, 0, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -2, -6, -4, -4],\n [3, -5, -6, 1, 0],\n [-4, -5, 0, 3, 2],\n [1, 1, 5, 5, 5],\n [-6, 5, -6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, 4, 2, -1, 4],\n [1, 4, 4, 4, 5],\n [2, 5, -1, 2, -6],\n [5, -6, 2, -5, 6],\n [0, -2, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 5, 3, 6, 4],\n [-1, 6, -3, 1, 2],\n [3, 2, 4, -3, -5],\n [-6, -5, 6, 5, -5],\n [-4, 4, 0, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -2, 3, -2, -1],\n [-2, 0, 6, 2, -1],\n [4, -3, 2, 3, -2],\n [5, -6, 5, 2, -1],\n [0, 1, 5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 3, 5, 0, -1],\n [5, 5, 6, -2, -4],\n [-5, 6, -6, 3, 4],\n [-3, -1, -6, 2, 4],\n [4, -5, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, -3, -3, 5, 4],\n [-3, -1, 3, -3, -1],\n [5, 1, 1, -3, -4],\n [0, -1, 5, 6, -4],\n [-6, -3, -3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -2, -1, -1, 4],\n [-1, 4, -1, -4, -4],\n [1, -3, -2, 4, -6],\n [0, -2, -3, -5, 1],\n [-5, -2, -3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -6, 1, 2, -4],\n [-2, -3, 4, -5, 2],\n [-5, -3, 6, 5, 2],\n [5, 1, -4, 5, -1],\n [-6, -1, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 3, 0, -1, -1],\n [2, 2, 0, -5, 5],\n [0, -4, -2, -4, -2],\n [-6, 3, -5, -2, 3],\n [0, -1, -4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, -3, -4, 6, 2],\n [-4, 1, -1, 1, 4],\n [-4, -5, -4, -5, 6],\n [6, -4, 6, 0, 6],\n [-4, -3, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, 3, -2, 0, -4],\n [-5, 4, -1, 2, -5],\n [-1, -3, 5, 5, -1],\n [-1, -5, 2, -2, -6],\n [-5, 5, -6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -2, 3, -4, -3],\n [4, -3, 4, -3, 6],\n [0, 3, -4, 3, 3],\n [-1, 1, -4, -1, -5],\n [-4, 2, 6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 4, -5, -6, -2],\n [3, -2, 3, 2, -2],\n [-2, -3, -1, -5, -2],\n [-4, -5, -3, 4, 5],\n [-1, -6, -4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 1, -1, -2, -4],\n [5, -4, -1, -4, -4],\n [-2, -3, 5, 2, 0],\n [4, 2, 6, 4, -2],\n [-2, -6, -2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, 1, 2, -6, -2],\n [3, 4, 3, 2, -1],\n [2, 3, 1, 6, -4],\n [-2, 3, -4, -5, -4],\n [-2, 1, -6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 6, 4, -5, 4],\n [5, -6, -2, 2, 6],\n [-4, -3, 2, 6, 1],\n [-4, 4, 4, -2, 4],\n [0, 1, 3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 2, 6, 6, -1],\n [-6, 0, 6, -6, 5],\n [-6, 0, -3, -5, 6],\n [-3, 2, -4, -3, -2],\n [6, 1, -5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -4, 1, -5, 6],\n [-3, 1, 5, 3, -1],\n [0, -4, 1, -1, 0],\n [4, 3, 5, -1, 4],\n [-5, -4, 0, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -5, 4, 3, -5],\n [-4, 2, 3, 6, 6],\n [4, 5, -1, 2, 3],\n [1, -6, -2, -6, 2],\n [0, -1, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 6, 5, -5, -2],\n [-5, -6, -6, -3, 2],\n [-1, -5, 3, 6, -4],\n [5, 4, -2, 2, -3],\n [4, -1, 2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 3, -3, 0, 4],\n [2, 2, 3, 1, 2],\n [-1, -4, 1, 3, 1],\n [2, 5, 0, 4, -6],\n [4, -1, -1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -6, -5, 6, -3],\n [-1, -5, 2, 2, -4],\n [-5, 1, 5, 3, 5],\n [-2, 2, 5, 5, 6],\n [-3, 2, 3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -6, -1, -2, -4],\n [-5, -2, -3, -5, -4],\n [6, -6, 5, -2, 4],\n [-6, 3, 4, 4, -3],\n [4, 6, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 6, 4, 3, -1],\n [0, -5, -1, 5, -2],\n [-1, -2, 5, -4, 2],\n [0, 1, -5, -5, -6],\n [5, -5, -4, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 0, -4, 0, -1],\n [-1, -1, 4, -3, 1],\n [-4, -2, -5, 4, 2],\n [0, -2, -6, -6, 5],\n [-2, 2, 5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -4, 2, 6, -5],\n [-5, 5, 3, -2, 6],\n [2, 5, 4, 5, 6],\n [6, 6, -5, -3, -3],\n [6, -1, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 0, -3, 0, 0],\n [4, -1, 3, 4, -1],\n [1, 0, -1, 0, 2],\n [0, 1, 1, 4, -5],\n [3, 5, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 3, -4, 6, -4],\n [5, 2, -1, 1, 0],\n [-4, -1, 2, -2, 5],\n [4, -2, -2, 4, -6],\n [3, 5, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 3, 6, 5, -4],\n [0, -6, -5, -1, 3],\n [2, 6, 3, -6, -2],\n [-3, 4, -1, 5, 4],\n [-2, -4, -1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 3, -4, -1, 1],\n [0, -5, -1, 4, -1],\n [-2, 5, 1, 3, 0],\n [-3, 4, 1, 0, 2],\n [-6, -1, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -3, 6, 6, -2],\n [1, -1, -3, -5, -2],\n [-1, -5, -3, 6, -4],\n [2, 1, -6, -4, 5],\n [-4, 2, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -6, 6, -6, 5],\n [-4, 4, -4, 4, 3],\n [3, 0, 6, -3, -6],\n [0, 2, -6, 4, -6],\n [1, -4, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, 0, 2, -2],\n [-4, 1, -2, -4, -4],\n [5, -4, -2, -6, 1],\n [-2, -6, 0, 2, -6],\n [-3, 0, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -1, -4, -2, 5],\n [-6, 5, 2, -3, 0],\n [5, 4, 2, -1, 0],\n [-3, -6, 2, -6, 4],\n [3, 4, 2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 2, -4, 1, -6],\n [-3, 2, -6, -2, 0],\n [4, 6, 6, -5, 6],\n [6, -1, -4, -6, -1],\n [-6, 6, -1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 1, -1, 4, -4],\n [-2, 0, 5, 3, 6],\n [6, 4, 6, 1, 6],\n [2, -4, 1, 0, 5],\n [2, 1, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, -5, 3, -6, -5],\n [-6, -2, 0, -2, 6],\n [4, 3, 0, 1, 1],\n [4, -3, 6, 2, -4],\n [-6, 6, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 5, 3, 5, 1],\n [5, -3, 1, -4, -3],\n [3, -5, 3, -3, 0],\n [-5, 0, 5, -5, 0],\n [-4, -1, -4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, 2, 5, 6, -6],\n [1, -5, -5, 4, 3],\n [2, 1, -1, 0, -1],\n [6, -1, 1, 4, 0],\n [-1, -2, -1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[0, -5, -6, 4, -2],\n [1, -1, -6, -5, -2],\n [2, 2, 0, -2, 1],\n [-3, -6, -3, 3, -3],\n [-3, -6, -2, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -2, 4, -5, 6],\n [6, 2, -2, 4, -2],\n [3, 2, 4, -2, -2],\n [5, 4, -1, -2, 1],\n [-6, -2, 3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -3, -3, -4, -4],\n [2, -6, 6, 6, -6],\n [5, -3, 6, 0, -1],\n [5, -2, 3, 3, 4],\n [2, -2, -3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 2, -1, 3, 0],\n [6, 4, -5, -6, -6],\n [-1, -2, -3, -4, 5],\n [5, -5, 4, 6, -4],\n [-4, -5, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 6, 4, -5, 4],\n [4, 3, 3, -1, -2],\n [-3, 3, -4, 1, 5],\n [-3, 4, 5, 6, -3],\n [5, -1, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[5, 0, -1, 3, 2],\n [-3, -1, -4, 6, 3],\n [-5, -3, 6, 6, 6],\n [4, -5, -3, -1, -1],\n [-1, 6, -3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, 0, 5, 1, 4],\n [5, 6, -4, 2, -3],\n [4, -2, -2, -1, 5],\n [6, -4, 4, -1, -6],\n [5, -5, -5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -3, 3, 6, 6],\n [-4, 6, 3, 4, -3],\n [2, 5, -1, 0, 2],\n [-4, 4, 4, 6, -3],\n [5, -6, 2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -1, -2, -2, 3],\n [4, 1, -5, -1, 3],\n [-3, -6, 6, -1, -2],\n [-5, 5, -6, 6, 0],\n [-3, -3, -2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -1, -4, -2, -2],\n [-2, -1, 6, -4, 4],\n [-2, 6, -1, -1, -4],\n [5, 3, 5, -2, -4],\n [1, -2, -1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -2, 4, -3, -5],\n [6, 1, -6, -1, -6],\n [5, -1, 2, 4, -2],\n [2, 1, 0, 3, 2],\n [4, 4, -3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, -1, 2, -4, 4],\n [-6, -2, 3, -1, -2],\n [-1, -5, -2, 2, 3],\n [1, 3, 6, -4, 4],\n [-1, -1, -3, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 3, -5, 0, 2],\n [-1, 6, -5, 0, 6],\n [-3, 6, 1, 3, 1],\n [6, 2, -4, 4, -6],\n [0, -2, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -5, -6, 6, 6],\n [-1, -5, 1, 4, -3],\n [4, -3, -1, 6, -1],\n [6, 5, -3, -2, 2],\n [-5, 1, 5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 3, 6, 5, 4],\n [-6, 6, 2, 2, -3],\n [3, 2, -2, 2, -6],\n [6, -6, 3, 4, -6],\n [6, 0, 0, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 1, 5, -4, -5],\n [2, 2, -4, 0, -3],\n [-6, 6, 0, 2, 4],\n [-5, -4, -1, 1, -1],\n [5, -3, -6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, -3, -1, -3, 6],\n [6, 6, 2, -4, -3],\n [2, 6, 2, 1, 6],\n [1, -5, 4, -5, 4],\n [3, -2, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 0, -5, -6, 3],\n [-2, -2, -4, -2, -5],\n [-5, -3, -4, 3, 6],\n [-3, -5, -1, -4, -1],\n [2, -5, 0, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 0, 1, 1, 0],\n [6, 6, 3, -3, 4],\n [1, 5, -5, 5, -5],\n [0, 3, 2, -5, -2],\n [-6, -6, 3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -5, 0, 6, 5],\n [5, 5, 1, 3, -1],\n [1, 2, -1, 5, 6],\n [5, 3, -2, 4, 6],\n [-5, 6, 1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, 4, -5, -4, 6],\n [-2, -1, 2, 3, -5],\n [-6, -1, -5, 2, -4],\n [-3, -3, -1, 0, -1],\n [-2, -3, 0, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 3, -5, -5, 4],\n [-1, 4, -2, -4, 6],\n [-3, -4, -4, 6, -2],\n [1, -5, -1, 6, 3],\n [2, -4, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-6, 5, -1, -1, -4],\n [1, 2, -3, -5, -2],\n [-1, 2, 1, -5, -4],\n [5, -2, 6, -6, -3],\n [-6, -1, 1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 2, 6, 2, 3],\n [2, -6, -4, -4, 5],\n [-6, 5, 5, -4, -4],\n [-1, 4, -4, 4, 1],\n [-1, -1, -2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, 3, -6, 6, -5],\n [-3, 4, 6, 5, 0],\n [1, -3, 6, -5, 1],\n [0, 0, 0, 2, 4],\n [-2, 0, 3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 1, -2, -4, 1],\n [-4, -4, -2, 2, 1],\n [3, -5, -4, -5, 4],\n [2, 4, -2, 4, 0],\n [-1, -2, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 0, -3, 3, 1],\n [-3, 6, 5, 0, -1],\n [2, -1, 6, 2, 4],\n [-1, 6, -5, 5, 2],\n [4, 2, 1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -2, 2, -1, -5],\n [3, -5, 2, -3, -1],\n [5, 3, 3, 6, -4],\n [4, 6, -1, -1, 3],\n [3, 3, 2, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 6, -1, -2, 4],\n [-1, 6, 3, -6, 5],\n [-5, 5, 5, -1, -6],\n [-4, -1, 2, 2, 0],\n [-2, 5, 6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -4, -5, 0, -5],\n [4, -5, -4, -6, 1],\n [5, 3, 1, -6, 5],\n [4, -1, 1, 5, -5],\n [-3, 4, 0, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, 1, 5, -4],\n [5, 4, 2, -1, 0],\n [6, 6, -3, 4, -4],\n [0, -1, -4, -4, 6],\n [0, 5, -3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -6, 1, 1, 5],\n [0, -3, 4, -5, -4],\n [2, 6, 6, 2, 1],\n [3, 3, 6, -2, 6],\n [-6, 3, -2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 3, 5, 2, 3],\n [-4, -5, -2, 6, 6],\n [-5, 6, 2, 0, 0],\n [0, -1, 5, -2, 2],\n [2, 5, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 0, 4, -4, 0],\n [0, -3, 1, -3, 2],\n [6, -5, -2, 3, 2],\n [3, -5, 4, -5, 1],\n [-6, -6, -5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 1, -6, 1, 2],\n [-6, -1, 5, -1, -3],\n [-6, -2, -2, 6, 2],\n [5, -2, -5, 6, -4],\n [4, -5, -5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -4, 5, -3, 1],\n [-6, 0, -3, 6, -6],\n [-3, -2, -1, -5, -1],\n [5, -6, -1, 2, 2],\n [0, 5, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -4, 5, -4, 1],\n [2, -2, -6, -5, -6],\n [3, -1, -6, 0, -6],\n [1, 0, 6, -2, 0],\n [-2, 3, -3, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 6, -1, 6, 1],\n [-5, -6, -2, -3, -5],\n [-1, 4, 4, 5, -5],\n [-6, 6, -3, -1, -1],\n [-3, -5, -6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 2, 2, -6, 1],\n [-4, -3, 4, 6, 5],\n [5, -2, 5, 1, -1],\n [3, -3, 1, 4, 2],\n [5, 6, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -6, -6, -5, 4],\n [-6, -2, -1, -4, 1],\n [-1, -2, 1, 3, -2],\n [-3, -3, 5, 5, -5],\n [6, -3, -6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 2, 1, 2, 2],\n [-4, 4, 6, -3, 2],\n [-4, -4, -4, 0, -4],\n [-1, -4, 0, 3, 6],\n [-2, -3, 5, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -1, -6, -1, -1],\n [-4, -3, 5, -1, -4],\n [4, 1, -6, 2, 3],\n [5, -4, 0, -6, -6],\n [-6, -2, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 4, 5, -2, 3],\n [-2, 3, 1, 6, 4],\n [-4, -4, 4, 3, -4],\n [6, 2, -1, -6, -2],\n [-4, 5, 6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 6, 3, 2, 3],\n [3, 0, -1, -5, 0],\n [-4, -2, 1, 2, 3],\n [3, -3, 5, -3, -5],\n [-2, 2, -6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 3, 6, -2, -4],\n [3, 2, 1, -6, 1],\n [-4, -3, 0, 4, 0],\n [-4, 0, 5, 5, 3],\n [-5, -6, -2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 0, -5, -3, -1],\n [-3, 3, -1, -5, -3],\n [6, -6, 1, 1, -4],\n [-2, -5, 5, -6, -4],\n [5, -2, -1, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -6, 1, 2, 5],\n [-1, 3, 3, 2, -6],\n [6, -5, 2, -3, 2],\n [-2, -6, -2, 5, -1],\n [2, 0, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 0, -6, 3, -5],\n [2, -2, 0, 3, -3],\n [5, -5, 5, -2, 5],\n [-2, 3, -4, 5, 2],\n [1, 6, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -4, -4, 6, 6],\n [-3, 1, 3, 4, -2],\n [5, 4, -2, -3, 3],\n [1, -4, -2, 5, 2],\n [0, 5, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -6, 3, -4, -4],\n [2, -1, 0, 4, -3],\n [6, 5, -3, 3, 1],\n [-3, 4, -2, -5, -6],\n [2, -5, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -4, 5, -1, -1],\n [4, -5, 5, 0, -6],\n [5, -4, -6, -4, 4],\n [4, 6, -2, 2, -4],\n [1, -2, 0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 0, -6, -1, 5],\n [-4, 2, -1, 6, -2],\n [-5, 5, 2, -5, 6],\n [3, 3, 3, -4, 3],\n [0, 2, 6, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -1, 2, 2, 3],\n [3, -6, 3, 4, 6],\n [-3, 0, 2, 6, -2],\n [-5, 6, 0, 4, 2],\n [2, 5, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 1, -2, -4, -3],\n [-3, 0, 3, 2, 5],\n [6, -3, -2, 5, 2],\n [0, -4, -2, 3, -6],\n [6, -5, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 5, -1, 3, 5],\n [4, 2, -6, 5, 5],\n [-3, 1, -5, 6, -5],\n [-1, 0, -4, 5, -3],\n [-3, 2, 4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, -2, 1, -4],\n [1, -1, 6, 5, 5],\n [5, 2, -1, 4, -1],\n [-5, -6, -4, 2, -6],\n [-3, -1, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 6, 0, -5, 3],\n [-4, -4, 3, 0, 6],\n [6, -4, 5, 6, -2],\n [-4, -2, 5, -5, 0],\n [-2, -3, 6, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, -6, -3, -6, -3],\n [3, -2, -4, 2, 1],\n [3, -2, -4, 5, -2],\n [-4, 4, -3, -4, 1],\n [-2, -3, 6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, -2, -3, -4],\n [-3, 0, 6, -5, 6],\n [-4, -2, 0, 6, 3],\n [6, 2, 0, -6, -3],\n [-2, -2, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, 1, 2, -5, -2],\n [6, -2, -5, 6, 1],\n [-6, -1, -6, -2, 0],\n [-6, -1, 1, 1, 3],\n [2, -1, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 4, -2, 0, -6],\n [3, 3, 2, -6, 3],\n [5, -2, -4, -1, -3],\n [-1, -4, -3, -4, -6],\n [6, -2, 1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 6, -4, -1, -5],\n [1, -4, 0, -2, 3],\n [4, -6, 5, -3, -2],\n [-5, -3, 3, -4, 2],\n [-5, 1, 5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 5, 1, 6, 4],\n [3, -6, -6, 5, 1],\n [4, 4, -6, 4, 6],\n [-3, -2, -4, 5, -3],\n [6, 3, 2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 0, -6, -3, -3],\n [4, -2, -3, 3, 3],\n [-2, 1, -5, 6, 6],\n [-5, -1, 5, 3, 5],\n [0, 6, -1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -4, 6, -5, 4],\n [2, 3, -6, -1, -1],\n [-2, -4, -4, 2, 1],\n [2, 2, 6, 6, -4],\n [6, -2, -1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 1, -4, 0, -3],\n [2, 4, -5, -1, -5],\n [-5, -6, 4, -1, 4],\n [5, -1, -6, -1, 4],\n [-1, 5, -2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 1, -4, 0, -5],\n [-1, -5, -5, 4, -4],\n [-5, -6, -3, 3, 3],\n [3, -6, 5, 3, -5],\n [-4, 5, 6, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -1, -3, 6, -1],\n [5, -3, 2, 6, 0],\n [5, -3, -2, -5, 5],\n [0, 3, -5, -4, -5],\n [2, -1, 3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 3, 1, 3, -6],\n [4, -6, -4, 3, 4],\n [-5, -4, 3, -3, -6],\n [6, 5, 1, 5, 0],\n [-5, 1, 5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[5, 1, 1, -3, 4],\n [-5, -2, -2, 4, 4],\n [-5, 0, 6, -1, 6],\n [4, 6, 6, 3, -6],\n [-5, -5, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -5, -3, -4, -1],\n [0, -1, 3, 3, -4],\n [-6, 6, 2, 1, 1],\n [5, -1, -6, -5, 0],\n [1, -1, -5, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 4, -5, 2, 5],\n [-5, 0, 6, 1, 2],\n [-5, -5, -5, 2, -4],\n [-6, 6, -2, -6, -6],\n [4, 1, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -5, -4, -6, 5],\n [-4, -6, -3, -5, -2],\n [4, -6, 3, -5, -2],\n [3, -4, -6, 5, 4],\n [-1, -1, -3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 4, -6, -1, 1],\n [-4, -4, -4, -4, -4],\n [0, -3, 5, -2, -5],\n [-1, 4, 5, -3, -4],\n [-3, -1, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -2, -2, -1, 6],\n [-1, -5, -3, 4, 4],\n [4, 5, -1, 2, -6],\n [-2, 2, 1, 2, -1],\n [-5, -5, 4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -5, -2, -3, 5],\n [-6, 0, -6, 1, -1],\n [-5, 6, -6, -6, 6],\n [-4, 2, 2, -2, 0],\n [0, -2, -6, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 5, 3, -1, 4],\n [3, 2, 6, -4, 4],\n [6, 5, 5, -2, 4],\n [5, 5, -6, -3, 4],\n [3, -3, -5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, 4, -6, 4, 6],\n [-4, 4, 2, 1, -1],\n [3, 0, -2, -4, 4],\n [6, -5, 0, 6, -1],\n [-3, 0, 4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 4, 4, 3, 2],\n [4, -6, 0, 2, -5],\n [5, -3, 3, 5, 5],\n [-4, -4, 4, -4, -4],\n [-2, -4, -1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 2, 6, -6, 1],\n [5, -1, 6, 1, -4],\n [5, 2, -5, 4, -1],\n [-4, 5, 5, -2, -3],\n [-6, 2, 1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, -1, -4, -6],\n [-2, 4, -5, -4, 1],\n [-5, -6, 4, 0, 5],\n [0, 1, 2, 1, -4],\n [-2, 0, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, 4, -6, -3, -2],\n [0, 3, 2, 5, -6],\n [-3, 1, 3, 4, 5],\n [6, 3, 4, -3, 5],\n [2, -4, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -6, 1, 3, -4],\n [-3, 2, -5, -5, -5],\n [5, -6, -6, 1, 2],\n [0, -3, 1, 5, -1],\n [-3, 6, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 6, -4, -5, 5],\n [3, 3, -5, 2, 4],\n [2, 6, 4, 2, 2],\n [6, 3, -2, -1, -4],\n [6, 3, -6, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 1, 1, 0, -5],\n [3, -6, 2, -3, -3],\n [-2, -6, -1, 4, 2],\n [-2, -4, 3, -2, -5],\n [5, -1, -5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -3, -5, 4, 0],\n [5, 6, 0, -2, -2],\n [5, -3, -6, 1, 2],\n [-5, 2, 6, -3, -1],\n [3, -6, 2, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, 4, 6, -1, -2],\n [-1, 1, -1, -3, -1],\n [-6, -6, 6, 1, -6],\n [0, -4, -4, 0, -5],\n [5, 6, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, -1, 6, -3],\n [-3, 1, 2, 5, -4],\n [6, 1, 4, 1, 6],\n [-3, 0, -6, 1, -1],\n [6, -2, -4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 3, -1, 6, 3],\n [3, -3, -1, -3, 2],\n [-6, 2, 1, -4, -3],\n [-2, 3, 4, 6, 3],\n [-2, -5, 5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 2, 1, -6, -5],\n [0, -1, 0, 2, 3],\n [1, 0, 2, -6, 5],\n [-2, 4, -6, 0, -6],\n [4, 1, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 0, 3, 4, 1],\n [2, -1, -1, 4, -3],\n [4, 3, 1, 4, -5],\n [3, -4, -3, -1, 4],\n [0, 4, 0, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 1, -4, -4, 5],\n [0, 2, -2, 6, -5],\n [2, 3, 0, 3, 3],\n [6, 2, -3, 6, 2],\n [-4, -4, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 5, -2, 4, 3],\n [-2, 5, -6, -3, -2],\n [3, -3, 3, 0, 3],\n [2, 1, -5, 4, -3],\n [-1, -4, 5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, 2, 1, -1, 6],\n [1, -5, 2, 6, 3],\n [-1, -5, 4, 2, 3],\n [6, -1, 4, -5, 0],\n [-2, -1, 3, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 4, -3, 6, 4],\n [-1, -4, -2, -5, 0],\n [-5, 2, 3, -3, 5],\n [6, 5, 6, 6, 4],\n [-4, -4, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 4, 0, -5, -3],\n [1, -2, 5, -2, -4],\n [-6, -6, -4, 1, -5],\n [1, 4, -2, 1, -3],\n [6, -4, 5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 0, 1, 4, 5],\n [-2, 0, 3, 2, 3],\n [4, -4, 3, -4, 1],\n [-1, -5, -6, -2, -6],\n [-6, -3, -2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -3, -3, 6, 3],\n [5, 4, -2, -1, 0],\n [-6, 2, 3, 4, -6],\n [1, 5, -2, -5, -4],\n [6, -5, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 1, 0, 4, -1],\n [5, 6, 4, -5, -6],\n [6, -1, 2, 2, 0],\n [4, 1, 2, -3, -5],\n [-3, -3, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, -5, -1, 0, 0],\n [-1, 4, -1, 5, 3],\n [2, 2, -3, -3, 3],\n [1, 6, -3, 5, -3],\n [-2, -6, -5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 4, -4, 0, 0],\n [5, -6, -4, -6, 4],\n [3, 5, 6, -2, -1],\n [4, -2, -6, -4, 3],\n [-1, 5, 4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 0, -5, 6, 1],\n [-4, -5, 6, 6, 2],\n [6, -1, -2, -2, -4],\n [-4, 3, 1, 1, -3],\n [-5, -6, -6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 3, 6, 0, -5],\n [6, -2, 1, 6, -4],\n [-5, 5, -3, 3, 1],\n [0, 3, 0, -2, 1],\n [-3, -6, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -1, -3, -3, 3],\n [-2, -1, 0, -3, -4],\n [0, -5, -5, -4, 3],\n [-3, -3, 1, 1, 3],\n [-5, 0, -4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 1, -5, 0, -4],\n [6, -4, 3, -4, 0],\n [4, -2, 0, -1, 1],\n [-5, 0, 2, 6, -5],\n [-3, -3, 5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 3, -6, -3, 6],\n [2, -6, 3, 4, 0],\n [-1, 1, 5, 1, 3],\n [-1, -3, -2, -3, 4],\n [-4, -6, -6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 4, 5, 2, -6],\n [5, -1, 3, -2, -1],\n [4, -1, -5, -2, -5],\n [-6, -4, 4, 3, 4],\n [5, 0, 2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, 4, 4, 2, -1],\n [-2, 3, 0, -4, 2],\n [6, -1, -3, -4, 2],\n [-4, -3, -5, 2, 5],\n [-5, 1, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 6, -3, -5, 2],\n [0, 4, -2, -6, -1],\n [-3, -5, -3, -5, 4],\n [-5, 0, -5, 5, 6],\n [0, 6, 6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 5, -5, 5, -6],\n [-1, 5, -4, 1, -5],\n [3, -1, -5, 5, 3],\n [6, 6, 2, 6, 3],\n [-2, 6, 4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -4, -3, 0, 1],\n [-5, 0, -1, 6, -6],\n [5, -3, -5, 3, 0],\n [4, -4, 0, 6, 0],\n [-5, 3, 1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 5, 2, 5, -1],\n [3, 0, 1, 5, 0],\n [3, -2, 6, 2, 6],\n [2, 2, 1, 2, 5],\n [0, -4, 1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 2, -1, 3, 5],\n [1, 6, -6, 6, -3],\n [0, -5, 2, 5, 3],\n [-6, 1, -5, 4, -4],\n [-5, -2, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 2, -2, -3, 6],\n [-1, -3, -5, -1, 1],\n [-1, -1, -1, 0, 1],\n [-3, 3, -5, 5, 3],\n [-4, -3, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 0, -5, 4, -2],\n [-2, -1, 6, -2, -2],\n [4, -3, -5, -2, -2],\n [2, -6, 3, 3, -1],\n [-4, -5, 2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 0, 0, 2, -5],\n [0, -5, -1, 4, 6],\n [-1, -5, -4, 6, 1],\n [5, 2, 1, -3, -4],\n [-5, -1, -6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -4, -1, 0, 4],\n [1, 4, -5, 1, 2],\n [-3, -1, 3, -4, 3],\n [5, -5, -2, 0, 1],\n [0, -3, 3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 3, 1, 6, 2],\n [-4, 5, -4, 5, -2],\n [-5, 5, -4, 1, 0],\n [-3, 0, 3, -6, 2],\n [-3, -4, -4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 3, 2, 0, -6],\n [2, 1, 5, 2, -2],\n [-6, -4, -2, 2, 3],\n [-6, -3, -5, -5, 1],\n [1, 0, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, 6, 3, 6],\n [4, 2, 5, 2, -1],\n [4, -3, -2, 2, 0],\n [-4, -2, 4, -3, -6],\n [-3, 2, -5, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 3, 0, -2, -5],\n [1, 1, -6, -2, 4],\n [-2, 2, -2, 2, -1],\n [-6, 2, 5, 1, -1],\n [-6, 6, 3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 4, 2, -1, 3],\n [2, -2, 2, -5, -2],\n [-3, 6, -6, 1, 0],\n [-2, -3, -3, 2, -5],\n [5, -3, 1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 3, -5, 5, -1],\n [-1, 4, -1, 1, -5],\n [-6, -3, 2, 0, 4],\n [3, 4, -3, 4, -4],\n [5, 2, -5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -5, -5, -1, -5],\n [-3, 5, 0, -3, -1],\n [-5, -2, 1, 3, 1],\n [-3, -6, -6, -6, 3],\n [3, 3, -6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, 4, 4, 1, -1],\n [3, 1, 3, 5, -2],\n [-3, 0, -5, -3, 3],\n [0, -2, 5, 2, 1],\n [1, -1, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 5, 2, 6, -6],\n [4, 0, -3, 6, -2],\n [3, 1, -1, -3, -5],\n [-4, 3, 1, -3, -5],\n [-2, -4, 6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 5, 5, -2, -2],\n [-2, 2, 6, 0, 4],\n [5, -1, 0, 5, -1],\n [0, -2, -2, -4, 5],\n [3, -4, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, -4, -6, 2, 6],\n [0, -2, -6, 4, -4],\n [1, -3, -1, -3, 5],\n [4, 6, 1, -4, -1],\n [4, 4, -5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -6, -2, 3, 5],\n [1, -5, 6, 6, 1],\n [-1, -6, -1, 4, -2],\n [-4, 0, -6, -2, 2],\n [1, 0, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -4, -4, 2, 2],\n [1, 2, -5, -4, -1],\n [4, -3, -5, 6, 1],\n [-1, 2, -6, -1, 5],\n [5, 0, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 3, -3, 6, 5],\n [-5, -1, 5, -2, 0],\n [-2, 5, -5, -3, 2],\n [5, -4, 2, -6, -2],\n [-4, -5, 3, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 3, 5, 2, 3],\n [-3, -1, 3, -2, -4],\n [-3, 3, -6, 0, 4],\n [5, -1, -1, 0, 3],\n [0, 5, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -3, -2, 0, 0],\n [0, 0, -2, 4, -6],\n [0, 2, 2, 2, 6],\n [-5, 2, 6, -4, -1],\n [-1, 0, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, -5, -4, -6, 3],\n [2, -1, -2, -6, -6],\n [-3, -4, 0, 1, 6],\n [5, -6, 5, 2, 6],\n [6, -3, -6, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 1, -5, 1, 4],\n [1, 3, -6, -1, 2],\n [4, -1, -1, 3, 1],\n [-2, 3, -3, -4, -1],\n [-1, 1, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -1, 4, 1, -3],\n [6, 0, 2, 4, -3],\n [4, -6, 6, 2, 1],\n [3, 4, -5, -6, -1],\n [6, 3, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 5, 1, -1, -5],\n [-5, 6, 4, -1, 5],\n [6, 4, 1, -4, 4],\n [4, 1, 4, -3, 4],\n [-2, 0, 6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 6, -5, 1, -4],\n [-1, 6, -3, 4, 6],\n [3, -2, 2, -4, 5],\n [-5, -4, 1, 2, -6],\n [5, -5, -6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[4, 1, -2, 0, 6],\n [0, -3, -5, 1, 4],\n [4, 1, -5, 5, 4],\n [-1, -6, 4, -1, 3],\n [6, 2, -3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 2, 1, 1, -5],\n [0, -5, 1, -4, -4],\n [-2, -5, -3, 5, -1],\n [0, 5, 5, -5, -5],\n [-3, -2, 1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-5, 2, 5, 2, 4],\n [-6, -2, -2, -5, 6],\n [-2, 4, 2, 6, -5],\n [4, 0, 5, -6, -5],\n [1, 3, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, 2, -2, -2],\n [1, 4, -4, -2, 4],\n [2, -5, 5, -4, -3],\n [3, 1, 1, -3, 2],\n [3, 1, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, 2, 5, -4, -3],\n [-1, 2, 3, 5, 1],\n [2, 4, 2, 6, 3],\n [-6, -4, -6, 1, -3],\n [3, 0, 2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 6, 4, -6, 3],\n [-6, 4, -1, 3, -6],\n [3, -6, -3, -5, 6],\n [-2, 2, 3, -6, -5],\n [4, -6, 3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 5, 6, -6, -2],\n [-1, 5, -5, 6, -6],\n [-6, 4, -5, 6, 6],\n [4, 2, 2, 1, -4],\n [3, 5, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 1, -6, 3, 0],\n [-6, 0, -1, 2, -4],\n [-3, -3, -1, 5, -3],\n [-2, 0, -4, 1, 3],\n [6, 5, 1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 6, -6, -1, -5],\n [5, 3, 1, 6, 2],\n [-1, -4, -6, 3, -6],\n [3, 5, -2, -2, 2],\n [5, 4, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -4, -3, -4, -4],\n [6, -6, -3, -1, 5],\n [0, -5, 4, -2, 5],\n [-2, -4, -2, 3, -6],\n [5, -1, 6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 6, -1, -2, 0],\n [-1, -1, 3, 3, 4],\n [-2, 4, -3, 6, 1],\n [-5, 0, 4, -3, -1],\n [3, -5, -2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 3, 3, 1, 5],\n [4, 2, 1, 2, 3],\n [3, -6, -6, -2, 0],\n [-1, -4, -4, -6, -1],\n [0, 3, 1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 3, -4, 5, -4],\n [-1, -6, -5, -6, -2],\n [2, -5, -3, -2, 6],\n [-6, 3, 1, -6, -2],\n [-1, -1, -3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 2, -1, 6, -2],\n [-3, 3, 5, -3, -6],\n [3, 3, 5, 6, -4],\n [-5, -6, 1, 6, -1],\n [6, 5, 0, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -5, -5, 2, 6],\n [1, 1, -1, -6, 4],\n [5, 5, 5, 2, -2],\n [0, -6, 2, -5, 6],\n [-5, -2, -5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 6, 5, -3, -3],\n [2, 6, -4, -5, 1],\n [0, -6, 6, -1, -2],\n [4, 1, -5, 1, 5],\n [6, -4, -2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -5, -2, 3, 0],\n [5, -5, -2, 0, -3],\n [-4, 5, -1, 1, 6],\n [-3, -5, -6, -2, -6],\n [-2, 2, 6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, -3, -3, 5, -5],\n [5, 6, -3, 1, -1],\n [-2, -6, 1, -1, 3],\n [5, -1, -2, 0, 1],\n [-2, 0, -3, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 4, 2, 2, -5],\n [-3, 2, 6, -5, -6],\n [1, 3, 0, 6, 4],\n [4, 4, 1, 1, 4],\n [4, -6, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, 3, -5, 6],\n [-2, 6, 1, -1, -2],\n [-3, 1, 5, -4, 2],\n [3, -5, 6, -6, -6],\n [-5, 2, 0, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 3, 2, 2, 3],\n [-3, 0, -4, -1, -4],\n [1, 2, -3, 2, -6],\n [4, 5, 4, -4, 6],\n [0, 1, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, 4, 6, 2],\n [3, -5, 2, 5, 0],\n [-1, -3, 5, -3, 1],\n [6, -1, 5, 6, 2],\n [6, -4, -2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 6, 3, -2, 0],\n [6, -6, 6, -3, -2],\n [-5, 2, -5, -6, 1],\n [-5, -6, 3, 5, -4],\n [-5, 6, 1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 3, 6, -2, 3],\n [3, -1, -2, -6, -3],\n [0, -3, -3, -5, 0],\n [5, 1, -2, 3, 0],\n [5, 3, 1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 4, -2, -2, 0],\n [-2, -2, 5, -1, 2],\n [-2, -2, 1, 4, 0],\n [5, 6, -4, 4, 1],\n [0, -1, 5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 0, -1, 5, 3],\n [-1, 3, -3, 0, 6],\n [-1, -3, 2, 6, -6],\n [5, 4, -3, 3, -4],\n [-3, -3, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, 5, 3, -5],\n [2, 5, 4, 3, -3],\n [-4, -5, 3, 6, -3],\n [-5, -2, 0, -3, -5],\n [-4, 0, -2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 1, -3, 6, 3],\n [0, -3, -2, -4, -5],\n [4, 2, -3, 0, -2],\n [-5, 0, 1, 4, -5],\n [-5, 2, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, -6, -6, -3, -5],\n [4, -1, -5, 6, -1],\n [-6, 5, 2, -2, -5],\n [-1, 2, -1, 0, 0],\n [-1, 6, -4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -1, -3, -3, -4],\n [-6, 4, 0, -5, -4],\n [6, -5, 6, 0, 5],\n [-2, -6, -4, -2, 4],\n [-3, 2, -4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-4, -4, -2, -6, 1],\n [3, -5, 2, -1, 6],\n [5, -4, 5, -1, 4],\n [-4, -1, 5, -5, 0],\n [-4, 3, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, -6, -3, -4, -6],\n [1, 3, -1, -2, -5],\n [5, 3, -1, 1, 5],\n [-6, 3, 6, 6, -4],\n [1, -3, -5, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -2, -2, -5, 3],\n [-2, 2, -3, 4, -6],\n [-2, 4, 1, 4, 6],\n [4, -5, -4, 1, 1],\n [0, -6, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, 5, 0, 2, -1],\n [-5, -2, -3, -6, 1],\n [-3, -6, -5, -1, -3],\n [-3, -5, 1, 0, -6],\n [2, -1, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, 5, -2, 5, -3],\n [4, -2, 4, 3, -2],\n [-2, 2, 2, -5, -3],\n [6, 3, 0, -3, 5],\n [4, 6, 5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 6, -6, -1, -1],\n [-5, 1, -1, -5, -4],\n [-1, -3, -2, -4, -1],\n [-4, -3, 0, -2, -5],\n [0, 0, -5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 3, 5, -1, -3],\n [1, -2, 3, -3, -3],\n [-3, 1, -6, -2, 5],\n [-5, 1, -1, 5, 1],\n [5, -5, -3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 2, -6, 0, 0],\n [-4, 0, 3, 6, -4],\n [-4, -3, 6, -3, -5],\n [4, -2, 2, -2, 2],\n [0, -3, 6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 1, 6, 1, -4],\n [1, 1, -6, -5, 2],\n [-3, 2, 3, -4, -1],\n [2, -2, -6, -6, 4],\n [-4, -1, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -6, 4, 1, 4],\n [-5, -3, 1, 3, -2],\n [-2, 3, -5, 4, -4],\n [-3, -4, -5, 1, -5],\n [-4, -3, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 2, 0, -6, -2],\n [-1, -5, 4, 2, -6],\n [3, -3, 4, 4, -5],\n [-4, 4, 6, 6, 5],\n [-3, 4, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 2, 1, -6, -3],\n [2, -1, -4, -3, 1],\n [-6, 6, -3, -6, -1],\n [-1, 5, 0, 4, 4],\n [-5, -2, -3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -6, 4, -1, 3],\n [-3, 2, 5, 5, -1],\n [-2, 3, 4, -2, 5],\n [-3, -2, -3, -4, 0],\n [2, 2, 4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -1, -5, 1, -5],\n [-4, -3, 6, -6, 2],\n [1, 0, -6, 6, -1],\n [-1, 2, 1, -6, -5],\n [2, 5, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -3, -6, -4, -1],\n [4, 3, 2, 4, 1],\n [2, -1, -3, -4, 1],\n [2, 6, 6, 2, 1],\n [-2, -3, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, -3, 5, -5, 0],\n [1, 0, 5, -3, 2],\n [5, -1, 5, 3, 3],\n [-4, 3, -3, 6, 3],\n [5, -6, -5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -2, -4, -6, 5],\n [6, -3, -6, 3, 4],\n [4, 2, 6, 3, 6],\n [1, 6, 4, -3, 3],\n [3, 5, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 6, -4, -4, -4],\n [2, 1, 1, -6, -1],\n [-1, -2, 5, 5, -5],\n [4, 2, 1, -1, 1],\n [-5, -4, 4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -1, -2, 4, 1],\n [-5, 6, 0, 2, 1],\n [5, 5, -2, -6, 1],\n [0, 4, -5, 0, 5],\n [-2, -2, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 2, -2, 6, 3],\n [0, -2, -1, 4, -1],\n [-3, -2, 4, -3, -4],\n [-2, -5, 5, 5, 2],\n [-6, 1, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 4, -6, -4, 5],\n [-2, 4, 1, -4, -4],\n [5, 2, 0, 4, -2],\n [-4, 0, 5, -2, 3],\n [3, -1, 0, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 4, -2, -3, -5],\n [-5, 1, 1, 1, 1],\n [-4, 2, 5, 6, -5],\n [2, -5, -1, -5, 5],\n [-3, 6, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -2, 5, 4, -4],\n [-4, 0, 5, 5, 2],\n [-5, -4, 1, 1, -2],\n [3, 6, 5, -6, 0],\n [-3, -6, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}