{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[16, 6, -8, 20, -15, -2, 16, -4, 0, -12],\n [-12, 1, 13, 17, 1, -20, -1, -21, 1, 21],\n [7, 15, -21, -2, 10, -11, -1, 21, 2, 4],\n [19, 5, -7, -8, 21, -20, 14, -16, -2, -14],\n [16, -5, -19, 2, -9, -14, 3, -21, -3, 5],\n [-16, 21, -15, 12, -9, -6, 13, 17, -19, -21],\n [-17, 19, -19, 6, -5, 3, 21, 11, -13, 13],\n [-9, 8, -8, -15, -9, 0, 17, -2, -7, 22],\n [-5, 1, 3, 2, 22, 18, 6, -8, 22, -22],\n [2, -16, -14, 1, -22, 21, -15, 1, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, 12, 12, 10, -18, 19, 16, 18, 5, -16],\n [-14, -15, -11, 11, 10, 0, 1, 14, 12, 21],\n [17, -1, 4, 12, -22, 12, 14, -9, -20, -22],\n [-18, 3, -9, 16, 4, -14, -8, -8, 3, 19],\n [-10, 9, 16, 9, -19, 7, 14, 0, 16, 22],\n [-8, 20, 6, 13, -10, 9, -16, -1, 5, -21],\n [19, 22, -17, 5, 5, 21, 21, -3, 7, -12],\n [5, 2, 16, 10, -22, 4, -10, 18, -20, 16],\n [-17, -15, 4, -14, 14, 10, 19, 21, 1, -8],\n [9, 9, 1, 18, -11, 16, -21, -20, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-21, -21, 5, 0, 14, 9, 10, -22, -4, -21],\n [21, 3, 9, -17, 9, -19, -12, -6, 15, 1],\n [-18, 11, -17, -1, -12, -7, 10, -14, -17, -7],\n [6, -20, -3, 13, -4, 3, -20, -4, -3, 9],\n [-16, 18, 10, 17, 16, -5, 17, -22, -12, 5],\n [2, 0, 8, 7, 19, 12, -16, -7, 3, -21],\n [-22, -11, -18, 14, 9, -14, 18, 12, -4, -7],\n [-20, -3, 1, 10, 1, -12, -15, 13, 15, 17],\n [-3, 12, 2, 12, 2, 6, -5, -5, -21, 12],\n [-7, 18, 13, 10, -19, 10, -9, -2, -3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-16, -20, -6, 10, -11, -1, -1, 7, 15, 15],\n [22, -15, 4, 4, 11, -2, 7, 10, 5, 10],\n [-18, -4, -19, 12, -6, 21, 5, 7, 6, -17],\n [12, 18, 14, 1, 6, 8, 12, 10, -2, 9],\n [0, 10, -20, -5, 2, 19, 8, -20, 17, 1],\n [9, -1, 0, -21, 4, 19, -21, 3, -6, 17],\n [10, -14, 20, 16, 6, 19, 3, 12, 2, 1],\n [-10, -16, 13, 22, -3, -22, -15, -7, -9, -11],\n [0, -8, 5, 11, -21, 9, 0, -1, 2, -1],\n [-1, 19, -17, -8, 20, 14, 10, -15, 21, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-18, 16, -19, -17, 22, 9, 7, 12, 17, -7],\n [-10, 19, 7, -4, -6, -4, 5, 3, 14, 3],\n [0, -14, -11, -22, -22, 11, 9, 2, 17, 22],\n [-22, -7, 16, -18, -1, 6, -20, -11, 3, -7],\n [14, -1, 6, -9, 5, -18, 7, -18, -11, -7],\n [3, 3, -2, 16, 13, 10, 7, 14, 0, -13],\n [-18, 13, 11, 8, -13, -4, 9, -22, -18, 22],\n [-19, -7, 1, -7, -21, 5, 9, 4, -3, 1],\n [-11, 12, 10, 10, 20, 14, -11, -20, -22, 10],\n [17, -13, 20, 21, 6, -10, -11, 8, -21, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "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, -15, 6, 3, -13, 3, 11, 18],\n [-16, -19, 22, -12, 6, 13, 2, -2, 13, -13],\n [14, -14, 1, 12, 12, 13, -5, 16, 9, 1],\n [0, 9, 14, -11, -10, 0, 2, 12, 18, 7],\n [-6, -3, 2, -1, -10, -4, 13, -11, 18, -4],\n [-11, -14, -16, 5, -9, 8, -4, -7, -18, 12],\n [-11, 2, -2, 13, 0, -7, 16, 22, 19, 16],\n [-9, 8, -18, 12, 0, 6, 20, -12, -5, -11],\n [-14, -13, 21, -6, 15, -16, -10, 17, 19, -14],\n [4, -21, -18, 6, 14, 15, -4, -15, 22, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -6, -16, 2, 22, -19, 13, -17, 8, -4],\n [21, 16, 4, -13, 3, -4, 16, -20, 22, -10],\n [5, -3, 5, -15, 18, 16, -22, -20, -10, 5],\n [2, 10, 15, -17, 21, 22, 9, 22, -2, -7],\n [-2, -12, 14, 13, 12, -4, -3, -5, 18, -9],\n [-8, 8, -22, -20, -7, 0, -12, -11, -13, 9],\n [-7, -15, 15, -11, 1, 5, -15, 5, 13, 3],\n [-15, 5, 5, 14, 18, 13, 4, -6, -14, 10],\n [-3, -10, 5, 6, -10, 12, -17, -5, -18, 2],\n [-21, -13, 7, 22, -18, 10, -22, -5, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 3, 2, -1, 4, -10, 10, 11, 18, 12],\n [-22, -2, -17, 5, -6, -18, 8, -18, 15, -20],\n [0, 14, 14, -13, -13, -4, -6, -2, -9, -14],\n [-22, 22, -10, -19, -22, 17, 9, 11, 5, 8],\n [-15, 16, 3, 11, -20, -11, -22, 21, -18, 7],\n [7, -6, 0, -8, 14, -2, -9, -21, -12, 16],\n [15, 11, 15, 11, -5, 7, -8, 4, 11, 15],\n [10, 1, -8, 7, 19, -6, -18, 6, -19, -13],\n [-6, -13, -6, -3, 1, -18, 11, -17, -21, -10],\n [20, 20, -12, 0, -7, 8, -12, -7, -15, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[17, -19, 2, -20, 9, -20, 4, 6, 9, -4],\n [-2, -18, -5, 5, 19, -1, -2, -17, -22, -18],\n [18, -11, 3, 11, -9, 3, 22, 4, -14, 3],\n [-1, 7, 20, -6, 3, 13, -22, -15, 12, -8],\n [-1, -9, 3, 5, 0, -9, 1, -21, 22, 3],\n [-9, -16, -20, 0, 20, 22, -5, 15, 12, -8],\n [2, 14, 5, -13, 16, -6, 16, -1, 3, 21],\n [2, -6, -10, -3, 2, -19, -13, -20, 18, 22],\n [-5, 13, -1, 11, -15, 17, 21, -4, 19, 18],\n [14, -17, 3, 11, 22, -17, 14, 10, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-17, -17, -19, 7, -12, 7, 8, 1, -14, -20],\n [8, 17, 14, 13, 1, 8, -17, -21, -3, 5],\n [-12, -19, -8, -17, 7, 15, -21, -8, -12, -15],\n [3, 22, 21, -18, -17, 3, -19, -4, -3, 10],\n [-3, -11, -22, 3, -9, 15, 14, -12, 13, -10],\n [20, -20, 10, -17, -13, -18, 0, -13, 21, -21],\n [-10, 17, -21, -3, -22, 14, -14, -6, -14, -12],\n [-8, 1, 15, 12, 7, 8, -18, 21, -9, -12],\n [-14, 11, -11, 12, 12, -22, 17, -1, 6, -15],\n [-12, 18, 14, -9, 7, 12, -2, 14, -18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-9, 3, -19, 2, 22, 19, 2, -5, 17, -15],\n [16, 17, -9, 9, 15, 10, 0, -8, 10, 2],\n [-6, 10, -21, -9, 17, 17, 16, -17, -17, -20],\n [-16, -15, 19, -8, 6, 10, 7, 16, 4, 13],\n [6, 15, 10, 14, 4, 10, -19, -1, -21, -13],\n [-18, -13, 10, 15, -10, 8, 13, 22, 1, -8],\n [6, -15, -18, 6, -19, -11, 22, -21, 4, 8],\n [13, 13, 3, 20, 4, -18, -3, -12, -13, 17],\n [15, -17, -15, 0, 3, 20, -11, 3, -10, 17],\n [-5, 2, 10, 17, 20, -11, 21, 13, -19, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, -15, 19, 5, 8, -14, 6, -9, 17, 18],\n [-1, -12, 0, -22, 14, -2, 3, 13, 0, -22],\n [17, -8, -2, -14, -14, -13, 3, 18, 12, 2],\n [3, -12, 15, -21, -16, -5, 4, 11, 4, -6],\n [20, 21, 1, 2, -16, -17, 1, 10, 6, 20],\n [-1, 3, 5, -2, -16, -6, -3, 18, -3, -1],\n [5, 17, -16, -22, 9, -10, 7, 0, -4, 9],\n [7, 6, 22, 6, 7, -7, 17, -4, -5, -22],\n [-9, -21, 5, 7, 15, -19, -22, -15, 6, 16],\n [-20, 9, -13, -13, -4, 11, 10, 0, 5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, 6, -15, -22, -20, 1, 0, -15, 14, -20],\n [10, 5, -15, 11, 12, 9, 1, -9, 9, 20],\n [-7, -19, 14, -2, -9, 8, -5, -16, -13, -16],\n [10, 0, -2, -4, -4, 13, 6, -5, -21, -22],\n [-18, -3, -12, 19, -21, -20, 0, -11, -3, -18],\n [14, 15, 7, -14, 11, 21, 12, -1, 21, 1],\n [-6, -13, 7, 0, 9, -6, -6, -9, -14, 17],\n [-21, 22, 2, 16, -14, -1, 20, -19, 3, 6],\n [22, 11, 0, 14, -12, -17, -5, -2, 19, 13],\n [18, 15, 11, -6, 14, 2, 15, -11, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -2, 4, 8, -17, 4, 17, 11, -11, 22],\n [-16, -13, 22, -6, 3, -2, 5, -21, 20, -22],\n [13, 3, 6, -2, -12, 17, -12, 13, 16, 17],\n [12, 11, 1, -1, -18, 10, 13, -3, -4, 12],\n [20, -6, 22, 20, 11, -14, 3, -21, -14, -14],\n [17, -6, -22, 2, 20, 17, 19, 2, 16, 12],\n [-20, 14, 21, 21, 7, 15, 11, -11, -4, 14],\n [21, -6, -13, -11, -7, 1, -4, -15, 8, -2],\n [-6, 0, 14, -7, -17, -15, 2, -5, 2, -11],\n [-8, 3, 18, 22, 3, 9, -13, -7, -16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "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, -1, -16, -9, -8, -16, -14, -15],\n [0, 6, -5, 8, 7, 16, 12, -5, 19, 16],\n [-6, -9, 8, 1, 12, 21, 22, 11, -20, 14],\n [20, 17, 3, 0, 21, 16, -8, -19, 6, -1],\n [2, -10, -5, 10, -7, 22, 19, 21, -21, 12],\n [19, 11, 7, -10, -10, -5, 9, 9, 12, 16],\n [6, 6, 21, -7, 21, -13, 7, 2, 16, -3],\n [-18, -22, 7, -20, 22, -9, 7, -19, -5, 14],\n [2, -22, -8, -14, -8, 1, -19, -11, 14, 14],\n [20, -17, 16, 1, -12, -10, 11, 2, -16, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-15, -3, 6, 22, -13, 20, 11, 3, 18, -20],\n [-17, -18, -18, 0, -14, 12, -3, 19, 12, -5],\n [-6, 1, -20, 9, 12, 15, -10, 2, -14, -19],\n [-9, 14, 11, -12, 18, -20, 5, 6, -14, -20],\n [2, 11, -11, 19, -14, -8, 17, 2, -18, -12],\n [11, 1, -8, 15, -15, -18, 3, -5, -17, 14],\n [-10, 5, -18, -10, -6, 17, 22, 9, 6, -20],\n [17, 11, 17, 4, -10, 22, 10, -17, 1, -4],\n [-7, 17, 5, 10, 18, -10, 20, 22, 2, 19],\n [13, 4, 15, -16, -18, 20, 22, 8, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-13, 9, 20, 7, 16, 8, -5, 13, -21, -9],\n [-10, 6, -11, 16, -21, 9, -10, 4, 18, -6],\n [17, 8, 11, 1, 22, 12, -17, -4, 7, -16],\n [-13, 18, 9, 11, 5, -8, 7, 14, 6, -1],\n [-19, -3, 9, 13, -19, 4, -6, -11, -1, -6],\n [-13, -22, -1, 3, -5, -9, 6, -11, 13, 12],\n [-11, -16, 6, -12, 10, -17, -8, 9, -12, 0],\n [3, 11, 11, 6, -19, -6, 12, -10, 18, 16],\n [-8, 6, 6, -12, 9, -21, -9, -3, -1, -12],\n [4, -20, -6, 21, 5, 6, -2, -7, 14, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-17, -4, -18, -20, -22, 15, -8, 11, 12, 2],\n [1, -11, -5, -8, 21, -7, 4, -15, 2, -6],\n [6, -15, -8, 4, -16, -20, 6, 21, 1, -20],\n [-3, -8, 2, 7, -9, -16, -6, 21, -3, 13],\n [-14, 15, -1, -21, 1, -15, -12, -10, -6, -15],\n [-2, -5, 7, -5, 8, 15, 9, -12, 22, 2],\n [10, 15, 18, -15, -12, -1, 1, 18, -6, -11],\n [9, -8, -7, -1, 5, -3, 10, -13, 17, 9],\n [10, -21, 10, 10, 18, -10, 7, 10, -10, 3],\n [-1, 16, -21, 15, 16, 3, -8, 11, 19, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[17, -12, -20, -17, -14, -17, -14, 16, 8, 9],\n [18, -11, -15, -15, 5, -3, -16, -12, -3, -7],\n [-19, -17, -1, 3, -20, 18, 19, -9, -12, -5],\n [-11, 0, -11, -10, 2, 22, -4, 13, 22, -15],\n [6, 9, 21, -5, -17, -5, -4, -1, 14, 9],\n [18, -20, 5, -13, 12, 6, -8, 10, -16, -11],\n [7, -2, 8, 1, -3, 14, -19, 5, 21, -3],\n [1, 9, 18, 13, 11, 13, -21, -8, 11, 13],\n [-17, 16, 19, -11, -20, 22, -5, 17, -2, -8],\n [10, 12, 3, -15, 13, 7, 0, 19, 21, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-9, -21, 14, -18, 15, 22, 18, -9, 16, 2],\n [-3, -21, 16, -17, -6, 2, 5, -21, 12, 14],\n [-18, -22, 17, -11, 13, 22, 0, 8, -12, -13],\n [-20, -9, -7, -13, 6, -13, -11, 7, 18, -22],\n [-18, -3, -15, 20, -11, -22, -3, 5, 20, 14],\n [14, -11, 14, 21, 5, -8, -17, 21, -3, -9],\n [-21, -14, 14, -3, 3, 6, -22, 12, -17, 14],\n [-18, 10, -9, -11, 19, -3, 1, 20, 11, 2],\n [6, 16, 8, 20, 0, 21, 15, -3, 0, 22],\n [-7, 19, -15, -2, -22, -15, 6, 9, 15, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 11, -22, 3, 20, -13, 7, -5, -6, 3],\n [-15, 17, -11, 4, -15, 2, -19, 10, -22, -4],\n [8, -7, -9, -18, 18, 3, 5, -21, -17, -14],\n [10, 18, 2, -10, -14, -10, 8, 18, -12, -19],\n [11, 15, -19, 15, -4, -17, 11, -5, -10, 18],\n [0, -4, 22, -12, -22, 1, -16, 2, -2, -8],\n [-22, -11, -16, -8, -2, -4, 6, 2, 10, 9],\n [12, 21, 15, 3, -12, 12, -15, -9, -13, -21],\n [-14, -20, -2, 3, -15, -21, -17, 5, 6, 3],\n [2, -11, -18, 11, 14, -8, 21, 13, -8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -17, 21, 20, 22, -2, 0, 20, -7, -8],\n [2, 13, -12, -8, -19, -2, -10, -1, -4, 11],\n [-9, -19, 4, 6, 5, 12, -15, -7, 19, 13],\n [7, -5, -21, -10, -19, 3, 2, 7, -12, -16],\n [8, 21, -13, 16, -10, 8, -16, 19, 19, 13],\n [-3, -19, -16, -22, 21, 22, 19, -10, -1, -2],\n [-1, 5, -14, 3, -14, -8, -13, 1, 19, -15],\n [1, -7, 3, 4, 14, -19, 1, -4, 13, 16],\n [-13, 2, -5, -4, 13, -13, 10, -18, 12, 21],\n [11, 10, -2, -6, -1, 14, -8, 12, 5, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[9, -12, -13, -14, -9, -10, 2, -21, 12, -16],\n [-2, -5, -20, 19, 16, 18, -12, 16, 1, -4],\n [-19, 3, 15, 19, 9, 16, 22, 13, 17, 14],\n [10, 13, -20, -14, -15, 10, -17, 18, 16, -19],\n [-10, -21, -18, 21, 4, 9, -2, -15, 15, -15],\n [-20, 21, -20, -1, -17, -21, 0, 21, -21, 15],\n [-6, 12, 11, 0, 7, -15, -1, 21, 13, -18],\n [-10, 6, 8, -7, 19, 7, -7, -11, -6, -7],\n [-11, -15, -3, -20, -7, 7, 22, 0, 5, 17],\n [-18, -3, 17, 21, -22, 7, -2, -3, -17, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -15, 16, 9, 10, -7, -11, 15, 11, -9],\n [13, 10, 0, 22, -21, 18, -2, -21, 4, -14],\n [-22, -12, -20, 0, 3, -19, -5, -17, 12, -1],\n [20, -8, -1, 14, 19, -11, 19, 15, -5, 22],\n [12, 7, 1, 19, 7, -9, -17, -20, -7, -16],\n [-9, -14, -8, -2, 12, -21, 4, -21, 12, -5],\n [-9, -3, -5, -13, 2, -21, 2, 10, 13, 8],\n [-9, -22, -7, -20, 12, 18, -17, 2, -10, 11],\n [-15, -2, 11, -19, 2, -8, -19, 22, -11, 9],\n [9, 5, -10, 8, -9, -3, -5, 6, -17, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "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, 20, -21, 0, -4, 8, -18, -4, 11, -13],\n [2, -21, -12, 8, -8, -14, 0, -4, -14, 12],\n [-2, -14, 5, -16, -7, -7, 10, -19, -19, 16],\n [17, -6, 14, 16, 6, 13, 15, 16, 14, 12],\n [-16, 4, 5, -1, -9, -16, 14, -1, -18, -21],\n [4, -2, 15, -8, -2, -13, 0, 16, -18, -22],\n [-10, -2, 3, 22, -2, -5, 14, 22, 9, 13],\n [-6, 12, -12, -2, 3, -19, 11, -5, 17, 12],\n [18, 6, 6, 15, 19, -2, 19, -10, 18, -6],\n [-14, 18, -22, -21, 6, 10, -13, 17, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-12, 11, -15, -1, -15, -8, -6, 0, 1, 22],\n [-4, -18, 9, 21, -22, 0, 14, -15, -10, -15],\n [0, 20, -22, 22, 1, 12, 1, -6, -18, -3],\n [-2, 17, 8, 13, -12, -8, -4, -16, 5, 20],\n [-18, -18, 7, 9, -15, -13, 15, 9, 5, -6],\n [8, -15, 17, 2, -14, -21, -8, -20, 13, -19],\n [-9, 18, 18, 2, -13, -2, 13, -11, 4, 17],\n [-21, -10, 9, 8, -7, 9, 9, 11, -12, -13],\n [-8, -6, 17, -5, -14, 2, 17, -9, 2, -1],\n [7, -3, -2, 21, 9, -2, 12, 9, 7, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-11, 18, -5, -2, -10, -2, -15, 17, -16, 0],\n [21, 9, -12, -1, -1, 20, 2, -1, 5, 6],\n [-10, -5, -21, 6, -2, -8, 4, 8, -8, 0],\n [1, 21, -10, -1, 20, 14, 10, -20, -4, 0],\n [6, 7, 16, 21, 2, 14, -15, 19, -7, -15],\n [-22, 21, -18, -20, -22, -19, 17, 12, 9, 19],\n [11, 20, 2, -13, -2, 16, 4, 4, -21, 18],\n [-10, -14, 13, -1, 19, 3, -11, -6, -9, -9],\n [11, -3, -12, -7, 8, -17, -4, 14, -19, -19],\n [-3, -13, 1, 12, 3, 14, 15, -2, 17, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"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, -13, 15, -19, 22, -3, -6, -16, -19, 6],\n [-9, -20, 1, 14, -7, -19, 1, 11, 7, -5],\n [-4, 8, -4, -4, -1, 1, 22, -11, 7, 15],\n [8, 13, -4, 22, 13, 7, 10, -5, 5, -12],\n [22, 10, -6, -17, -19, -3, 4, -8, -17, -9],\n [-12, 16, -14, 3, -7, -18, -13, -20, -10, 20],\n [7, 22, -17, -6, 22, -4, 19, 12, 3, -18],\n [6, 14, -3, -2, -13, -18, 13, -17, 3, -19],\n [16, 16, 12, -22, 1, 13, -17, 18, 21, 8],\n [-3, 1, 2, 13, -2, 7, 1, 21, 19, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, 5, -16, 12, 5, -9, -13, -7, -7, 8],\n [19, 2, -10, -17, 21, -14, 22, 13, 20, -3],\n [-5, 20, -2, -19, 10, 4, -16, -17, -8, -5],\n [9, -12, -3, 1, -8, -16, -2, 19, 3, 21],\n [-9, 14, -2, -5, -18, -20, 0, 3, 14, 1],\n [-4, 2, -2, -11, 18, 10, -19, 19, -16, -1],\n [10, -6, 1, 11, 5, 20, 18, 16, -1, -6],\n [11, -17, -17, 11, -22, -13, -2, -18, -21, -1],\n [-21, -13, 11, -7, 16, -1, -11, 1, 17, 15],\n [-13, 12, 9, -16, -2, -3, 3, -19, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, -2, -8, -1, 5, -9, 4, 18, 17, 5],\n [3, -21, 2, -20, -15, 21, 10, 19, 12, -17],\n [16, 0, 2, 20, -4, -18, -12, -11, -13, -15],\n [1, 5, 18, 13, 14, -2, -15, -14, -8, 17],\n [-5, 19, -3, -17, -11, -21, -16, -7, -20, 22],\n [-20, 4, 20, 17, 15, 10, 5, -22, -15, 14],\n [9, 20, 14, -19, 7, -17, -4, 9, -14, -11],\n [-12, -7, -22, 22, -2, 7, -10, 11, -19, 5],\n [15, 8, 4, -18, 2, -20, 10, -19, 2, -3],\n [11, 3, -18, 12, 5, 6, -14, 15, -17, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[21, -12, -21, 21, 21, -14, -2, 1, 11, -1],\n [-20, -11, 5, 7, 3, -2, 5, 3, 10, -2],\n [12, 11, 18, -5, -12, 0, -1, -6, -18, 21],\n [-12, 7, -8, 4, 12, 10, -3, -7, 11, -21],\n [12, 17, 5, 16, -17, -14, -3, -22, -15, 0],\n [-20, -19, 2, 15, -8, -2, 12, -9, 13, -11],\n [-6, 16, -14, 12, -10, -8, -5, 10, -17, 4],\n [0, 4, 11, 15, -9, 13, -15, 12, -4, 7],\n [-9, -3, 2, 17, 1, -9, 3, 15, 0, -1],\n [-4, -20, 19, -4, -14, 5, -3, 22, -16, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-14, -4, -9, 15, 13, 17, -6, 7, -14, 10],\n [2, -9, -12, 12, 18, -9, 7, 18, -19, -19],\n [5, -15, -21, 18, -1, 18, -7, 6, 7, -11],\n [12, -12, -2, -2, -18, -3, 14, -20, 21, 10],\n [-14, -14, -19, 12, -6, 11, 1, 9, -22, -15],\n [22, 0, 17, -11, -11, -8, 18, -4, 3, 6],\n [-1, 17, -2, 15, -3, 6, -19, -16, 5, 5],\n [-19, -1, -11, 22, -20, -1, 21, -21, 1, 11],\n [4, 18, -22, -15, 0, 15, -17, -1, 2, -5],\n [-6, -11, -17, 3, 4, -15, -4, 19, -22, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[22, 12, 17, -9, 12, 22, -3, -10, 15, -15],\n [20, -3, 10, 3, 16, -2, 19, 20, 18, -14],\n [1, 14, 18, -6, 1, -2, 16, 18, 16, -10],\n [-12, -4, -12, -10, 22, -22, 17, 21, -4, -11],\n [-15, -15, 22, -11, 10, 22, 3, 16, 5, -18],\n [-15, 2, 4, 0, 7, 22, 0, -3, -5, -5],\n [-21, -19, 7, 10, 13, -5, 14, -4, 5, 17],\n [-3, 10, -11, -8, 18, 16, -21, 6, 18, -13],\n [-21, -12, -10, -13, -9, -5, -14, 16, 5, -20],\n [-3, -17, 4, -21, 6, 15, -20, -7, 7, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-21, -6, 18, -11, 12, 20, -22, 22, -8, 3],\n [14, -2, 8, 2, 0, 1, 15, 5, -2, 20],\n [-5, 13, 12, 22, -14, 15, 7, 21, 11, 9],\n [-20, -20, 5, 21, -8, 18, 0, 17, -12, 9],\n [13, 10, 1, 16, 11, 5, 14, -16, -19, 14],\n [-22, -22, -3, -4, 6, -13, -5, 5, 12, 20],\n [8, 4, -12, 15, -18, -15, 11, -11, 15, -22],\n [8, -19, 22, -18, 7, 1, -20, -12, 22, -19],\n [3, 4, 20, 4, 19, -17, -8, 7, 19, 14],\n [14, 19, 14, 12, 0, -17, -19, -5, -14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-10, -6, 22, 9, -1, -19, -18, 14, 18, -10],\n [11, 22, -1, 0, -20, 19, 11, 9, 22, -2],\n [21, -2, 21, -12, 16, -19, -22, 5, 1, 12],\n [-10, 11, -12, 13, -6, 12, -5, 17, -1, 1],\n [-4, 14, 16, -2, -15, 5, -18, -6, 14, 13],\n [-4, 4, 11, -12, 22, -11, -2, -12, 16, 5],\n [-18, -6, -3, 18, -11, -17, -6, -4, 3, 21],\n [21, 9, -17, 13, 15, -12, 10, 1, 0, -8],\n [4, -12, -6, -9, 4, -5, 5, -19, -16, 22],\n [12, -14, -15, 22, -6, -6, 10, 9, -15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[15, -20, -18, -10, 8, -7, 9, -1, 6, -1],\n [20, -20, -13, 19, -2, -7, -11, -21, 18, 1],\n [12, 7, 7, 12, -4, -15, 3, 17, -16, 7],\n [-16, -20, -22, 13, 2, 14, -22, -8, 14, -10],\n [17, -15, -18, -14, -22, 13, 12, -21, 17, 0],\n [-14, 11, -9, -19, 7, 8, 15, -12, 12, -15],\n [-20, -9, -10, 22, 9, 11, 22, -4, 15, -7],\n [-21, 17, -6, 11, 19, -7, 15, -21, -21, 3],\n [-10, 8, 11, 16, -20, -15, 0, -9, 4, 6],\n [16, 16, -22, -6, 18, 7, -10, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"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, 8, -6, 0, 9, -13, -13, 13, -15],\n [-3, 9, -9, 5, 1, -8, -1, 7, -19, -10],\n [0, -15, -5, -11, 8, -9, 11, -5, 11, -12],\n [18, -11, -8, 8, 6, 3, -5, 9, -1, 15],\n [-6, 0, 1, -15, 18, -17, -18, 21, 6, 5],\n [-12, -22, 20, -4, -14, 4, 11, 21, -19, 13],\n [-5, -8, -10, -4, -17, -11, 14, -6, 0, 3],\n [6, 10, 4, 2, -13, 0, -2, -2, 20, -10],\n [14, 10, 1, 21, -12, -6, -19, 2, 7, -14],\n [-2, -3, -4, -4, -11, 14, 19, -6, 14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 18, 12, -5, -9, 12, 21, 18, -16, 18],\n [-10, -5, 14, -10, 13, 8, -21, -7, -14, -14],\n [15, -12, -1, 10, 13, 22, 0, 22, 22, 11],\n [-14, 1, -15, -16, 13, -5, -20, 5, -17, 21],\n [21, -2, 5, 17, -22, 13, -2, 20, 12, -10],\n [-13, 21, -13, -10, 14, 15, 1, -21, -1, -6],\n [13, -9, -13, 12, 2, -20, 15, -6, -11, 1],\n [6, 20, 2, 13, 3, 15, -22, -3, 5, -7],\n [-6, 17, 5, -11, 4, 19, 7, 18, 11, 14],\n [-17, -16, 9, 9, 2, 10, -16, -11, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[20, 13, -10, -16, 13, -14, 9, -12, -15, 10],\n [0, 2, -15, 22, -1, -19, 17, -20, 6, 18],\n [6, 11, 11, 5, -10, -8, 0, 21, 3, -19],\n [3, 17, -14, -18, 9, -3, -12, -8, 9, 5],\n [-1, 18, -6, 3, 21, -16, 19, 3, 2, -13],\n [22, -4, -12, -10, -15, 17, -19, 8, 5, -12],\n [20, -22, 15, 1, 8, 18, 3, -18, -3, 18],\n [-12, 10, 15, 4, 11, -8, 9, -2, -18, -17],\n [15, -1, -5, -9, -13, -10, 8, 7, -20, 7],\n [-17, 6, -15, 21, 22, 20, 21, 10, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-10, -12, 8, 5, 21, -17, 18, -7, -19, 12],\n [3, -11, -12, 14, 2, -5, -4, 0, 15, -5],\n [3, -17, -19, 21, 6, 11, -6, 20, 20, -7],\n [-21, 11, -15, -10, 19, -15, 7, 9, 13, 7],\n [-22, 20, 16, -6, -3, 1, -1, 6, -1, 21],\n [-14, 14, -13, 13, 14, 5, 5, 19, 20, -2],\n [1, 19, 17, -21, -15, 4, -1, 14, 4, 6],\n [-20, 21, -10, 22, -13, 13, -14, 4, 11, -22],\n [9, 2, 6, -16, -20, -3, -3, 7, 12, 12],\n [16, 4, 3, -9, -6, -5, 22, 6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -19, -22, -22, 3, 22, -3, 0, -13, -12],\n [18, 18, -18, -22, -6, -1, 11, 22, 18, 6],\n [-19, -18, -12, -2, 12, -11, 3, -4, 22, -16],\n [-16, 3, 17, -18, -2, -9, -19, 0, 19, -3],\n [-8, 22, 6, -15, 18, -4, 16, 5, 4, -19],\n [-8, 12, 14, -22, -20, 1, 4, 17, 13, 11],\n [6, 1, 1, 19, -19, -20, 11, 0, 0, 22],\n [-18, 8, 18, -17, 14, -13, 17, -16, 16, 15],\n [-2, -3, -20, -1, -19, 5, -11, 15, 13, 18],\n [-18, -10, 0, 7, 14, 2, 4, -9, 13, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-7, -1, -2, -2, -15, -7, 8, 19, -13, 9],\n [11, -14, -6, -12, 9, -13, -1, -6, -19, 2],\n [-2, 14, 15, -22, 2, 13, -6, 18, 1, -21],\n [17, -8, 9, 16, -17, -22, 0, 16, -6, 11],\n [18, 6, -14, -10, -17, -17, -3, -20, -6, -11],\n [22, -22, -6, -20, 3, -8, 13, 9, 9, -19],\n [-5, -4, 20, 12, 17, -9, 10, -9, 11, -19],\n [1, 6, -4, -17, 10, 17, -4, -22, -18, 4],\n [-7, -17, 17, -10, 12, -4, -11, -7, 20, -13],\n [2, -3, 8, -19, 21, 0, -21, -1, 14, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, -9, -20, -7, -4, -5, -7, -15, 10, -11],\n [-12, -18, 4, -11, -6, -17, 10, -18, 5, -9],\n [-18, 10, 18, -4, -1, -18, -21, 7, 16, -19],\n [10, -10, -3, -16, -8, 0, -9, 0, -4, 6],\n [-3, 6, 1, -5, -13, 18, -15, 3, 6, -13],\n [-6, -21, -17, -18, 5, 18, -18, -5, 3, -3],\n [18, 4, -11, -16, -20, -13, 11, 2, 12, -7],\n [-21, 1, -13, 15, -1, 3, 20, 16, 4, 6],\n [15, -3, 4, 18, -3, 21, -4, -3, 12, -21],\n [7, 11, -1, -20, -17, -8, 4, -13, -14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[9, -17, 18, 13, -21, 6, -19, -22, -4, 3],\n [2, -13, -8, -1, -2, -1, 13, 11, 7, 2],\n [22, 5, -22, 22, -19, -16, -14, 13, -4, -22],\n [-13, 13, -14, 22, 19, 9, 9, -17, 15, -6],\n [-13, 4, 12, -2, 2, 5, -8, -19, 6, -14],\n [4, 3, -4, 5, -6, 20, 18, 19, -3, 22],\n [17, 16, 0, 9, 10, -18, 20, 11, 17, -12],\n [-20, 10, -12, -7, -5, 7, -13, -5, 15, -4],\n [13, -10, -20, -13, 15, -22, 4, -15, 19, -6],\n [-14, -17, 20, 2, 16, 5, 10, 14, -14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -21, 20, 15, 17, 13, 20, 14, -8, 5],\n [-5, 11, -1, -12, -10, -19, -1, -16, 20, 1],\n [-19, 5, -8, -22, -20, -9, 15, -22, 15, 15],\n [-2, 6, -18, -13, 5, -2, -16, -20, 22, -3],\n [-4, 12, -19, -18, -22, -19, -11, 4, 19, 0],\n [2, -2, 1, 2, 22, 9, 9, -18, 13, 19],\n [19, 16, -7, 10, -2, -14, -17, 22, 12, 16],\n [-1, 18, -18, 19, 0, -6, -11, 0, -7, -20],\n [7, -1, -14, 6, 14, 0, -10, 9, 0, 22],\n [-6, 17, -2, -21, 14, -17, 21, -5, 7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, 7, -6, 20, 9, 19, -9, -13, 13, 11],\n [-14, 19, 5, -12, -9, 16, -4, -8, 5, 1],\n [-15, 20, -14, 10, 10, -4, -20, -13, 17, 19],\n [-22, 6, 11, -10, -22, 11, 6, -10, 6, 16],\n [1, 3, -6, -16, -10, -18, 3, -20, -16, 16],\n [-22, -6, 20, 2, -20, -8, 6, 20, 9, 3],\n [-7, 2, 5, -14, -22, 6, -1, -7, 18, 21],\n [18, -16, -9, 6, -4, -4, -21, 18, 22, -8],\n [-20, -12, 7, 17, -5, -21, 9, -15, -1, -17],\n [-11, 17, 13, -8, 5, 22, -5, -21, -10, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-8, -3, 6, 19, 6, -20, -4, -20, -9, 17],\n [-19, -12, 8, 20, 9, 4, 7, 20, -21, -14],\n [5, 8, 11, -8, 2, 13, -15, -14, 14, 22],\n [16, 9, -6, 12, 14, -4, 21, 6, -16, 5],\n [-14, 5, -17, 6, -6, -7, 0, 8, -20, -2],\n [3, 13, 19, 14, -1, 19, -11, 19, -10, -12],\n [-7, -15, 17, 17, 22, -21, 7, 7, -11, -13],\n [21, -12, -8, -7, -6, 3, -21, -11, 3, 0],\n [-5, 9, 15, -20, 15, -20, 7, -22, 7, 22],\n [9, 5, -2, -10, 4, 13, -16, -1, -13, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, -8, -19, 9, 0, -17, 1, -3, 14, -3],\n [-11, 10, 5, -15, -22, 14, -1, -17, -2, 9],\n [12, -8, -18, -17, 2, 17, 6, -16, 17, -10],\n [15, -5, -21, -15, -12, 10, 15, 4, -3, -11],\n [20, 8, 4, 9, -13, -20, 22, 4, 12, 8],\n [-8, -7, -10, 12, -12, -2, -12, 7, 12, -1],\n [15, 8, -9, 1, 9, 13, 9, -8, 20, 12],\n [-20, -7, -18, -2, -13, -4, 2, -19, 6, -4],\n [20, -21, -13, 20, 2, -3, -4, 0, 1, -12],\n [11, 5, -18, -18, -2, -11, -19, 19, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -9, -12, 9, -12, -5, 4, -5, 0, -12],\n [-2, 21, -18, 0, 18, 2, 18, -13, -1, -4],\n [-22, -16, -19, -22, -8, 17, -11, -1, -1, -6],\n [6, -9, -3, 10, 20, -8, -11, 17, -3, 7],\n [15, -20, 5, 3, 7, -10, -10, -21, 14, 15],\n [-21, 13, 3, -12, -15, 21, 17, 20, -1, -3],\n [-15, 6, 17, 3, 7, -6, -3, -7, 20, -16],\n [-7, 22, 4, 0, 1, -14, 12, -3, 14, 19],\n [-6, 8, -15, -8, 8, 7, -3, 16, -11, -6],\n [19, 7, 6, -4, -12, 11, -16, 21, 11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[15, 1, -13, 9, -8, 14, -3, -20, 14, 17],\n [-15, 17, 21, 0, 17, -12, -15, 6, 7, -13],\n [16, 5, 13, -10, 9, 13, 14, 3, -1, -19],\n [8, -5, 15, 1, 0, -1, -21, 8, -12, 5],\n [9, -18, 15, -13, 17, 1, 12, 21, 0, -6],\n [-22, 8, 8, 19, 19, 11, -14, -1, -10, 2],\n [-5, -11, 17, -6, -8, 19, -8, -8, 16, -10],\n [-6, 9, -14, 17, -3, 3, 4, -2, -5, -10],\n [-7, -14, -11, 21, 15, -4, -16, 12, -5, -7],\n [16, -19, 2, 9, 17, -10, 22, -6, 14, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -10, 3, -9, 8, -19, 16, -15, 2, -10],\n [9, 15, 15, 5, 7, -20, 5, -20, 22, 11],\n [-7, -1, 9, 15, -15, -15, -17, -9, 9, 12],\n [-13, -20, -11, 8, 6, -18, 2, 18, 8, -2],\n [-3, 16, -1, -19, -10, 22, 19, -3, -10, -6],\n [13, 10, -22, -8, -10, -6, 1, -15, 4, 22],\n [0, -15, -15, 3, -10, 16, 14, 5, 2, -7],\n [-21, -5, -6, 7, 16, -10, 9, 6, 7, -5],\n [-10, 20, -2, 7, -2, -6, 17, -4, -8, -14],\n [-13, 21, 8, 0, 7, 10, -14, -22, 21, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-12, 11, -7, -14, 9, -8, -11, 10, 22, -9],\n [-15, -15, 4, -11, -22, 20, 17, 19, -12, 16],\n [20, 8, -6, 10, 9, 6, -2, -2, 17, 0],\n [-17, -1, 15, 14, 22, -15, 18, 12, -12, 1],\n [-2, -21, 17, -4, 16, 5, -6, -17, -4, 15],\n [5, -21, 15, 14, -19, -1, 3, 20, 13, -10],\n [9, -6, 18, 13, -4, 12, 17, 5, -22, 19],\n [-5, 17, 10, -11, -15, 1, -7, -19, 15, 21],\n [4, -14, -7, -11, 8, 1, -9, 22, 2, 11],\n [-20, 1, 19, -14, 3, -3, 17, -13, -4, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "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, -18, -20, 4, -7, -8, 12, -11, 18, 21],\n [3, 11, 0, 8, -3, -11, 0, -19, 0, -22],\n [2, -21, 7, -20, -2, 2, -3, -1, -2, 10],\n [15, -8, -8, 2, -2, 1, -18, -17, 20, 21],\n [0, -19, 4, -5, -2, 5, 12, -1, 17, 0],\n [-20, 17, -13, 2, -15, -12, -18, 22, 14, 22],\n [15, 6, -18, -14, -21, -22, 17, 7, -12, 5],\n [21, -11, 16, 3, -10, -15, 5, 7, -14, 16],\n [8, -2, 11, 8, 2, -11, -22, -1, 17, 14],\n [-22, -22, 19, 19, -2, -8, -6, -1, 15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[22, -7, -15, -6, -6, 3, -10, -6, 15, -6],\n [-9, 22, -17, 12, -9, -15, -8, 4, -10, 8],\n [12, -17, -18, -1, 0, 2, 11, 3, -18, 3],\n [-3, -17, -17, -5, -19, -6, -9, -9, -10, -16],\n [21, -8, -4, 20, 21, 12, -6, 12, -4, -3],\n [13, 12, 9, 21, 17, 1, -6, -16, 20, -22],\n [12, 9, 13, -10, -17, -9, 14, -8, -19, 17],\n [-7, 5, -7, -19, 22, 3, 5, 9, 22, -21],\n [8, -20, -15, 1, -8, 20, 8, -14, 16, 22],\n [-21, -15, -16, 21, 16, 19, -7, 12, 7, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[15, -5, -18, 6, 16, 11, 20, 22, 0, -18],\n [7, -17, 21, -19, 6, 0, -17, 9, 19, -5],\n [-8, 17, 9, -14, 14, -13, -3, -17, -20, 19],\n [-12, 20, -6, 9, -19, -19, -6, 18, -4, -18],\n [9, -1, -17, 12, -1, -22, -3, -1, -12, -10],\n [19, -20, -14, -11, 0, -9, 10, -5, 18, -14],\n [0, -13, -4, -18, 0, 7, 2, 5, 11, 22],\n [2, -13, -9, 19, 7, 18, 2, -9, 12, 11],\n [-13, 12, -12, -12, -2, -2, -1, 22, -16, -6],\n [-21, -11, 19, -5, -12, -7, -5, 12, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-17, 21, 20, 19, -11, -10, -19, 16, -21, 3],\n [4, 4, -8, -15, -16, 17, -11, -10, 20, -6],\n [-6, 13, -2, -15, -18, 3, -7, 13, 5, 6],\n [-11, 14, 7, 0, -7, -9, -13, -16, 22, 14],\n [6, -20, -8, 13, -4, -10, 19, -2, 14, 4],\n [6, -3, 2, -17, 13, -21, -1, 9, -7, -5],\n [-18, 13, 7, 22, -4, 0, 11, -10, 20, 6],\n [13, -1, 13, -14, 16, -4, 15, -17, -8, -3],\n [-14, 9, -19, -5, -18, -3, 0, -12, 14, -1],\n [-19, 6, 21, 11, -10, 19, -14, 19, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "339", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-19, -4, 19, 7, 8, 12, -2, 8, -4, 8],\n [9, -21, -13, -21, -21, 1, -6, 9, -7, -7],\n [16, 8, 20, 1, -22, -12, -2, -19, -16, 3],\n [-11, 8, -6, 10, -12, 5, 9, -22, 5, 19],\n [-16, -21, 19, 1, -19, 21, -4, 3, -12, 17],\n [20, -12, 22, -20, -11, -20, 19, 4, -21, -7],\n [-21, 7, -3, 15, 5, 2, 9, -13, 19, 17],\n [10, -10, 18, 19, 14, -7, 22, -1, -3, 20],\n [4, 18, -7, 11, 9, 3, 2, -21, -11, 17],\n [-14, -11, 3, -14, -13, 9, 11, -3, 16, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-22, 13, 1, 4, -21, 8, -9, -21, 6, -8],\n [-11, 14, 5, -3, 16, 1, -2, -13, -9, 14],\n [-5, 1, -9, 11, -11, -1, -17, 13, 22, 13],\n [-1, -9, -7, 13, 2, 9, 10, 22, 13, -3],\n [-5, 15, -20, 0, 9, 22, -7, -18, -19, -2],\n [17, -9, 16, 8, -9, -17, -11, -7, -6, 22],\n [0, -9, -16, 9, -8, 21, -6, 18, 21, 11],\n [-18, 22, 4, 0, 17, -9, -8, 20, 10, 8],\n [12, -6, 5, -4, 0, 9, 17, -10, -3, 12],\n [-18, -14, 6, -17, 2, 8, -1, -21, 22, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 2, -15, -22, -3, 21, 0, 9, -12, 16],\n [1, -12, 6, 3, -7, 12, -3, -20, -22, -22],\n [-6, -21, 6, -3, -17, -15, 6, 10, -20, 12],\n [-18, 4, 21, -11, -3, 22, -3, -14, 16, -19],\n [-4, 15, 4, 22, 20, -10, -10, -1, 5, 22],\n [-1, 20, -4, -15, -15, 19, 3, 3, 0, 20],\n [-10, 5, -14, -3, -4, 16, -11, -8, 8, -9],\n [-12, 3, 19, 4, -12, 15, 11, 20, -4, -17],\n [15, 19, 5, -22, 12, 17, -15, -16, -12, 16],\n [-19, 2, -11, 3, 15, -11, 20, 14, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-10, 2, -19, -12, 9, -16, -12, 5, 18, 0],\n [22, 0, 5, 20, 3, 2, 6, -4, 10, 13],\n [-9, -9, 12, 7, 5, -6, -20, -7, 7, 6],\n [22, -8, 2, 15, 19, 15, 0, 2, 19, -16],\n [-1, -6, -5, 18, -13, -13, -16, 15, 4, 10],\n [-22, 21, 11, -19, -6, -19, 20, 3, -19, -22],\n [-16, 7, -14, 12, -15, 1, -4, 13, 20, 4],\n [9, -9, -5, 5, 6, -7, 12, 8, -19, 14],\n [-6, 16, 3, 16, 18, -19, 7, 7, -1, -12],\n [-21, 21, -11, 7, 13, -5, 3, -16, -22, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "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, 22, -17, -17, 21, -15, 1, -1, -4],\n [14, -5, 8, 14, 7, 19, 10, -13, 14, -11],\n [7, 4, 16, -14, -2, -11, 6, 10, 20, -8],\n [-21, 16, 21, -5, -20, -16, 20, -5, 21, 15],\n [14, 10, 21, 8, -12, -19, -5, -19, 11, 6],\n [1, -1, -21, 21, -17, 19, 2, -2, -7, 8],\n [-9, 16, 5, 9, 5, -14, 22, -1, 9, -18],\n [0, -18, 19, 9, -13, 16, -8, -16, 6, -20],\n [-4, -13, 5, 6, -8, 12, -17, -11, 15, -10],\n [6, -4, -20, -15, -15, -3, -19, -2, -20, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-15, 0, -7, -10, -20, -14, -9, -10, -16, -8],\n [-16, 15, 11, 18, -1, 1, 14, 21, -22, -13],\n [20, -7, -15, 2, -11, 2, -6, 3, -9, 18],\n [13, 0, 20, -17, -18, 20, 2, -5, -10, 20],\n [-9, 5, -5, 5, 4, 9, -14, 17, 9, -3],\n [5, 10, -19, 11, -20, 3, -15, -17, -7, 1],\n [16, 7, 22, -10, -18, 2, -3, -5, -5, -21],\n [-13, 22, -11, -10, -12, -4, 12, 16, 3, -9],\n [22, 21, 1, 18, -22, 20, -1, 0, -4, -5],\n [-11, 5, 5, 10, -4, 5, 14, 3, 12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[12, 17, -7, 15, -10, 0, -1, -7, 5, 12],\n [22, -15, 21, -1, -2, 3, 17, -2, 2, 18],\n [-22, -17, 0, 0, 20, 20, 0, 9, 7, -10],\n [20, -5, 0, -8, 10, -2, 16, 0, 4, 22],\n [21, -5, 1, 17, 19, -16, -3, 4, -17, 4],\n [-14, 22, 8, -2, 3, 17, 22, -10, 0, -3],\n [14, 5, -6, 5, 18, -21, 2, 18, -17, -12],\n [15, -17, 22, -12, -9, -21, 17, -20, 12, 10],\n [1, -4, -5, 1, 22, 12, -22, 13, 2, 22],\n [20, 11, 2, -7, 11, 6, -4, 0, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "342", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-7, -14, -22, 19, -4, 10, 11, -7, 21, 17],\n [-5, 11, 2, 22, -17, -2, -17, 9, 18, 20],\n [16, 8, 19, -13, 7, -5, 1, -14, 8, -8],\n [-19, 17, -14, 22, -14, 3, -19, -6, -7, -8],\n [12, -18, -18, -3, -8, -5, -21, 6, -10, -19],\n [19, 22, -13, 8, 18, -15, -20, -14, 7, -12],\n [12, 14, 19, -10, 13, -10, -11, 14, -13, -14],\n [-16, -21, 0, 16, 17, 16, -2, 0, 6, -9],\n [3, -18, 8, 2, 8, -3, 21, -6, 22, -21],\n [2, -10, 16, 5, 19, -17, -20, 12, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "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, -18, -4, -1, -4, -7, 1, 18, -19, -8],\n [2, 21, 12, -9, -4, 15, 13, -16, 7, -4],\n [2, -7, 17, -15, -5, 5, -7, -4, 19, -6],\n [22, -10, -16, 4, -13, 11, 13, 2, -17, 1],\n [-5, 0, -17, 6, 2, -6, 1, -12, 3, 11],\n [5, -20, -12, 15, -9, 3, -2, 16, 7, -15],\n [-3, 9, -1, -16, -14, 22, -22, 6, -15, -19],\n [12, -20, 22, 17, -16, 4, -22, 4, -7, 15],\n [-16, 21, 0, 18, -12, 19, 10, 13, 14, 18],\n [-6, 12, -18, 9, -20, 12, -9, 8, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"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, -9, -8, -8, -17, 4, -8, 13],\n [-15, -8, -20, -10, 18, 11, 1, 17, 9, 9],\n [7, -10, -22, 11, -8, 21, -9, 6, 11, -5],\n [-16, 6, 8, 2, 15, -9, -15, 4, -21, -6],\n [14, -9, 2, 7, 6, -3, -2, -1, 12, 14],\n [-7, 20, -6, -7, -21, -19, -2, 16, 11, 7],\n [-17, -6, 16, 2, -18, -18, -3, -7, 18, 14],\n [17, -14, -18, 19, -21, -14, 20, 13, -1, -1],\n [-1, 11, 6, 15, 10, -5, -16, -22, 10, -22],\n [1, -19, -19, -5, 4, 20, 9, 10, 5, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[18, 13, -17, -7, 11, 0, 19, 1, -10, -5],\n [-10, 14, 20, 16, 19, -6, -8, -5, 0, 7],\n [11, -19, -20, -16, -5, 19, -16, 17, -17, -1],\n [-22, -19, 20, 6, -2, 3, -9, -14, -11, 19],\n [-17, -3, 1, 4, 15, -15, -22, 1, -16, -4],\n [-1, 12, 7, 6, -1, -12, -3, 6, 18, 19],\n [11, -22, 8, 7, -5, -6, 15, -9, 0, 2],\n [-8, -1, -20, -4, 21, 11, 12, -22, -2, 6],\n [-17, 14, -22, -22, 4, -2, -7, 21, 17, 3],\n [-7, 5, -22, 13, -13, 20, -6, 0, -16, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, 21, -8, 11, 22, -19, -9, -9, -7, -16],\n [9, -4, -21, -13, -6, 14, -11, -17, -1, 9],\n [18, -3, -22, -17, -4, -5, -17, 22, 10, 0],\n [0, 3, -10, -16, -8, 21, 4, 3, 10, -8],\n [13, 22, 4, -18, -21, 10, -7, 0, 15, -7],\n [-9, 6, 3, 12, -8, -20, 0, 6, 11, 10],\n [18, 18, 0, -16, -20, 9, 8, -5, 20, -16],\n [18, -22, -9, 9, -17, 16, -13, -16, 3, 11],\n [7, 13, -2, -6, 10, -13, 19, -11, -7, 18],\n [9, -8, 4, 5, -6, -21, 13, -16, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "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, 3, 10, -12, -13, 2, 14, 20],\n [15, 18, 22, 1, 17, 10, -6, 1, 14, -21],\n [9, 1, -14, -19, -6, -6, 7, 17, -12, -2],\n [-2, -5, 6, 1, -13, 22, -6, -5, 19, -3],\n [14, 22, -5, -6, -14, -9, 6, 8, -19, -5],\n [-3, 20, 21, -14, -10, -8, 4, -8, 5, 14],\n [-4, 3, 3, 2, 3, 3, 5, -5, 9, -20],\n [-21, 10, 19, -4, -6, 21, 10, -11, -20, 20],\n [3, 12, -15, 13, -16, 13, -7, 1, -22, 2],\n [-13, -7, -7, -15, 6, 16, 5, -17, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-7, -16, 18, -9, 20, 3, 3, -9, -16, 10],\n [3, 22, -3, -20, -19, 3, -12, -21, -9, 21],\n [7, -11, 3, 21, 10, -10, -9, 1, 11, 21],\n [3, -2, 5, 13, 17, -21, 19, -14, 0, -8],\n [-10, 0, -6, -21, -3, -3, -20, -11, 17, -21],\n [13, -9, -7, -4, 11, 21, -17, -10, 13, -1],\n [-5, -11, 7, 17, -16, 9, -4, -17, -3, 4],\n [20, 14, -16, -18, -12, -8, -20, -18, 0, 14],\n [-14, -8, -20, 6, -17, -6, 3, -2, -15, -2],\n [-12, 15, -15, 19, 1, 12, -9, -9, -13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[15, 21, 11, 18, -13, -6, -6, -20, 8, -22],\n [-11, 16, -19, 19, -10, 11, 19, -2, -1, -19],\n [-5, -18, -4, -21, -11, -6, -13, 11, -17, -15],\n [-12, -11, -14, -21, -15, -12, 13, -13, -2, -3],\n [-15, 13, 6, 19, -11, -9, -2, -1, -2, 21],\n [7, 16, -3, 1, 0, -16, -14, -22, 3, 15],\n [15, 21, -1, 21, -13, -17, -6, 15, 1, -13],\n [-15, -2, -17, -2, 16, 1, 10, -5, 5, 9],\n [-11, 19, 4, -13, 19, 9, 19, 3, 2, -12],\n [0, 11, 17, 0, 6, 8, -16, 17, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-21, -5, 10, 14, 11, -3, 12, -5, 1, -15],\n [7, 21, -13, 0, -12, -21, 3, 13, 10, -10],\n [17, 2, -19, 19, -4, -5, 14, 7, -4, 0],\n [-7, -22, -11, 1, 11, -15, -5, -18, 3, 7],\n [-10, -4, 6, -20, 3, 17, -11, -21, -12, 21],\n [5, -5, -10, 14, -1, -11, -21, 14, -16, 3],\n [3, 1, -11, -7, 0, 17, -14, 9, -8, 14],\n [-10, -18, -12, -13, -10, 18, -8, 19, -16, 17],\n [5, 9, 12, -8, 13, -2, -17, -22, -19, -12],\n [21, 3, 14, 0, 6, -2, 22, 22, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[17, -10, 0, -7, 7, -19, 17, -7, 8, 19],\n [2, 21, -11, 3, 14, 10, 5, -14, -11, -18],\n [5, 12, -18, 11, 11, -10, 16, 19, 22, -9],\n [-12, 19, 15, -19, 10, -16, 18, -15, 14, -13],\n [20, -8, 15, -8, -18, 6, -4, -13, -11, -19],\n [8, -5, -7, 17, 13, 2, 0, -11, 11, 13],\n [14, -20, -14, -5, 20, 12, 11, 18, -9, -19],\n [6, 18, 22, -8, 5, 19, -7, -11, -18, 11],\n [19, -22, 16, 9, 3, -6, 4, 1, 12, 19],\n [16, 3, 15, 0, -1, -19, -14, -19, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-21, 1, 17, 8, 8, 17, 20, 11, 1, 3],\n [-7, -10, -8, 4, -19, -7, 7, 21, 7, 13],\n [-20, -1, -1, -11, -2, -19, 8, 21, 8, 0],\n [-3, -8, 0, 5, -7, 14, -2, -8, -6, 14],\n [-10, -4, 7, 22, -5, -9, 13, 13, -3, -4],\n [22, 21, -16, 21, -19, 11, -21, -18, -13, 9],\n [19, 18, -10, 16, -18, -13, -13, 15, 4, -2],\n [-15, -22, 5, 16, -9, -2, 7, -2, -14, -6],\n [-18, 8, 17, 15, 20, -4, 13, 10, -10, -9],\n [10, 6, 20, 13, 21, -13, 8, -17, -22, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"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, -7, 0, -3, 15, 2, 5, -18],\n [-2, -5, -17, 6, -4, 10, -22, 22, -20, 19],\n [-2, 12, 18, 17, -20, 2, 22, 15, 22, -3],\n [21, 22, 11, -2, 0, -17, -10, 0, -14, -6],\n [-21, -4, -4, -16, 19, 19, -3, -14, -6, 4],\n [-21, 13, -4, -6, -18, 16, -5, -16, -6, 16],\n [13, 17, 22, -19, 15, 2, -18, 7, -11, -19],\n [1, 6, -14, -19, 1, -9, -18, -5, 19, -4],\n [-11, -5, -6, 7, 1, -12, 12, 0, -6, -22],\n [-8, 9, -14, -8, 5, 1, 12, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[22, -11, -3, -22, -2, 22, -22, -13, 9, 16],\n [-1, -5, 9, 4, 5, -5, 16, 6, -5, 21],\n [-15, 8, 11, -16, 13, -5, 15, -14, -14, -15],\n [12, -5, -18, -9, 5, 7, -19, 16, -3, 2],\n [5, -11, -21, 20, -9, -1, 8, 0, -3, 15],\n [-19, -8, 1, 2, -22, -16, 8, -11, 19, -18],\n [21, 19, 15, -11, 16, -5, -21, -13, -8, 7],\n [21, -6, -19, -16, 18, 8, 16, 11, -17, 15],\n [22, 11, 21, -8, -9, -17, 14, 9, -20, -20],\n [-1, -1, -13, -20, -11, 6, -6, -16, -10, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-19, -13, 16, 1, -6, -17, -4, -18, 9, -13],\n [-14, 4, -10, -4, -2, 1, 15, -19, 1, 12],\n [-20, -19, 14, 17, 12, 8, 21, 2, 17, -10],\n [-19, -9, -10, 4, -17, -6, 13, 17, 12, -6],\n [18, -21, -10, -21, 5, 20, 3, -1, 20, -20],\n [12, -11, 1, -18, -3, 16, 16, -10, 18, 22],\n [-11, -10, -13, 10, 17, -7, 22, 12, -20, -18],\n [3, -12, -16, -13, 19, 11, -20, -15, 8, -12],\n [22, -16, 22, -21, -17, 18, 9, -3, 11, -7],\n [2, -11, -16, 16, -6, 22, -12, -17, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-17, 15, -21, -1, -3, 2, -8, 6, -15, 14],\n [10, -1, -18, 16, -5, 15, 14, 7, 8, -13],\n [-8, 19, 21, -5, 0, 10, -7, 15, 12, 11],\n [5, -21, 7, -10, 18, -7, -18, 5, 16, 22],\n [-3, 1, 4, 7, 22, 4, 3, -16, 19, 15],\n [-18, 0, 5, 11, -8, 9, 3, 8, -4, -14],\n [6, 16, -19, -20, 6, -12, 10, 15, -12, 4],\n [10, -2, 16, 8, 15, -21, 4, 13, -12, -5],\n [-22, 12, 12, 8, 5, 16, -22, 2, 20, 15],\n [-3, -20, -21, -5, 21, -13, -18, -14, -21, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[15, 8, -13, -11, 13, -2, -17, -20, -13, -18],\n [3, -2, 22, 3, 15, 21, 3, -15, -18, -8],\n [-7, -22, -7, 14, -20, 8, -10, -7, 20, -2],\n [-21, 4, 15, 3, 15, 2, -12, -15, -15, 10],\n [-16, 15, -2, -15, -2, -3, -15, 8, 6, -14],\n [-8, 7, 3, -13, 6, -7, 13, -3, 22, 14],\n [-1, -16, 0, 18, 17, 6, -7, 15, 5, 15],\n [8, -9, 10, -14, 4, 1, -10, 3, 6, 20],\n [5, 5, -15, 0, 6, -18, 19, -16, 19, 13],\n [18, 4, -21, 2, -14, 4, -22, 0, -13, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "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, -20, -17, -17, -21, -5, 0, -21, -11, -1],\n [14, -3, 16, 1, -3, -22, -22, -6, -22, 22],\n [7, 18, -20, -12, 1, -1, 21, 22, 3, -10],\n [-22, 1, -13, 12, 1, 5, 13, -7, 17, -7],\n [-6, -8, -7, -8, 11, -12, -22, -8, 3, -19],\n [20, -18, 12, -10, -13, -12, -5, 11, 16, 18],\n [19, 0, -16, 16, -20, -11, -16, 3, 10, 14],\n [-8, -21, 18, -16, 9, -19, -3, 13, 9, 5],\n [-10, -22, 12, 7, 13, 2, -7, -4, -22, -18],\n [-1, 1, 20, 22, 14, 13, 13, -19, 13, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-7, 18, -5, -1, -21, -2, 13, 21, 16, 16],\n [6, 3, -2, -6, -7, 8, -14, 8, -9, 14],\n [-21, -9, 10, 12, 16, -3, -21, 18, -4, 14],\n [-5, -7, -19, -11, 6, -16, -9, -11, 12, -18],\n [-6, 19, 9, -13, 20, -6, -18, 22, 19, -14],\n [10, 13, 13, -5, -14, 6, -9, 2, -8, -17],\n [19, 6, -8, 6, -19, -5, 21, 16, -7, -12],\n [-9, -20, 19, 15, 22, 19, -5, -3, 2, 15],\n [-10, -19, -9, 10, 5, 14, -15, 21, 11, 21],\n [-18, -18, 8, 22, -14, 19, 9, 10, -20, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-11, 6, -20, 3, 7, -14, 3, -21, -20, -19],\n [2, -10, 16, 21, 12, 0, -14, -21, 18, 21],\n [8, 21, -21, 9, -5, -10, -18, 19, 21, -13],\n [20, 2, 11, 14, 7, -16, -17, -20, -10, -20],\n [3, 1, -17, 20, 19, -11, 13, -21, -12, 16],\n [11, 3, -5, -2, 13, 17, 21, -1, 7, 20],\n [7, -15, 11, -14, -3, 17, 2, -4, -18, -12],\n [-8, -15, -4, 0, 4, 17, 9, 3, 4, -4],\n [19, 6, 16, 18, 10, -4, 14, -4, 10, -7],\n [0, -16, 3, 9, -11, -15, -18, 19, 5, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -18, -1, -8, -10, 5, 10, 20, 0, 10],\n [20, -5, 7, 3, -7, -10, 16, 10, 3, -22],\n [15, -21, -17, 15, 19, 1, -5, 4, 18, -15],\n [5, -13, -6, 6, -17, -9, -1, -17, 3, 16],\n [-11, 12, -9, -1, 0, -16, 17, 2, -10, -2],\n [18, -13, -14, -8, -21, 2, -10, 11, 11, 12],\n [15, -20, 19, -17, -4, -20, -5, 16, -14, -11],\n [-18, -20, -12, 7, -19, -18, -22, 4, 5, 6],\n [-5, -11, -10, 18, -21, 14, 22, -7, 1, 12],\n [-1, 13, -12, 6, 12, -8, 8, 19, 18, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-7, -13, 9, -21, 1, 0, -21, 15, 8, 17],\n [3, 6, -20, -9, 2, -22, -20, 3, -5, -14],\n [15, 0, -2, -22, -2, 4, 19, -17, 21, 13],\n [5, 22, -6, 17, -20, -11, 16, -11, -21, -1],\n [0, 7, -18, -14, -2, -12, -18, 12, 4, -21],\n [1, 8, 10, 16, 7, 14, 5, 8, -12, 0],\n [-21, 17, 18, 4, 12, -21, 16, 14, -2, -18],\n [22, -2, 6, -3, 15, -3, 2, -21, 9, 3],\n [-17, 18, -20, 10, -22, -18, -10, -4, -11, 2],\n [12, -11, 7, -18, 11, -1, 16, -10, -20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[8, -18, 1, 17, 10, -15, 1, -3, -7, -11],\n [-10, 22, 19, 16, 2, 9, 1, 21, -14, 17],\n [0, -10, 9, -8, 13, -18, -1, -7, 18, -13],\n [1, -5, -5, -16, -19, 3, -18, -7, 12, 3],\n [-5, 6, 0, -9, -8, 10, 2, -2, -6, 0],\n [20, -6, -9, 6, -3, 7, -4, 16, -10, -5],\n [0, 10, 16, 17, -5, -14, 10, 9, -6, -4],\n [4, -17, 12, 14, 11, -3, 2, -19, -13, -13],\n [1, -2, -12, 4, -7, 3, 7, -7, -16, -7],\n [12, -7, 17, -11, 12, -2, 20, 13, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[18, -17, 1, 4, -3, 2, -21, -14, 5, 15],\n [-20, -3, -17, 16, 10, -22, 14, -17, 22, 11],\n [-8, 22, 3, -9, -16, 8, 1, 8, 6, 19],\n [9, -6, -9, 17, 13, 1, 22, 4, 2, 9],\n [-5, -5, 14, 3, -14, 12, -15, -3, 19, -1],\n [-4, 7, 5, 12, 20, -12, 8, 16, 13, 7],\n [0, -4, -11, -8, 8, 20, 14, 14, -8, 6],\n [20, 3, 21, -21, -3, -8, -19, -1, 15, 0],\n [3, -12, 5, -21, -15, 6, -12, 14, -5, -9],\n [-13, 12, -14, 12, -12, 21, -11, -20, 16, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -12, 16, 2, -2, -13, 20, -8, -4, -1],\n [-2, 21, 9, 0, -10, -18, -19, 5, -9, -15],\n [-14, 12, 14, -2, -5, 10, -15, -6, 20, 8],\n [11, -17, -1, -9, -20, -11, 13, -11, 22, -21],\n [-21, -8, 0, 6, -6, 9, -16, 7, 5, -9],\n [21, 7, -6, 9, -17, 1, -17, 4, -5, 1],\n [14, 1, 15, 11, 17, -8, -12, -1, 1, -22],\n [-5, 21, -11, 20, 5, 17, -16, 0, -2, 11],\n [-12, -1, 19, 12, 6, 19, 5, -5, -9, -5],\n [5, 1, -15, 19, 22, -15, -19, 4, 13, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[10, 11, 7, -15, 16, 3, 14, 11, -16, 17],\n [5, 16, 16, 5, -9, 15, -19, 19, -5, 21],\n [2, -16, 15, 5, -18, -20, 21, 8, 19, -3],\n [-4, -12, 17, -20, 0, -16, 0, -16, 11, 19],\n [-4, -14, -5, 18, 22, 19, 2, -9, 21, 2],\n [-4, 16, -8, -7, 4, 17, -13, -19, -4, 5],\n [-2, -9, 10, -13, -4, 7, -1, -20, 14, 18],\n [-5, -12, -21, -11, -17, 20, 17, 21, 6, 7],\n [-21, -14, -21, 6, 10, -13, 11, 21, -15, 14],\n [10, -17, 21, 17, 22, -4, 9, 4, -22, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, 17, 9, -18, -6, -15, 19, 11, -14, 0],\n [12, -16, -8, -3, 2, -20, 1, 11, -1, -12],\n [-15, 16, 20, 12, 15, -15, 14, 4, 5, 17],\n [11, 9, -8, 21, -6, 10, -7, 6, -14, 10],\n [6, -10, -2, -2, -18, -13, -17, -10, -22, -3],\n [-15, -13, -14, 18, -20, -12, -11, -13, 2, 2],\n [-12, 13, 16, 3, -9, 16, 17, -22, -19, 7],\n [-11, 12, -10, 8, 15, 20, 0, -19, -7, -16],\n [-1, 6, -12, 10, 6, 16, -11, -16, 16, 19],\n [3, 17, -14, 18, 11, 22, -10, 13, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[21, -6, -21, -10, 8, 6, 5, 4, -8, 8],\n [17, -8, 10, -3, 19, -11, 14, -14, 0, -15],\n [9, -9, 4, 2, -10, -2, 22, 8, 14, 20],\n [-18, -10, 5, 20, 2, 12, 16, -16, 15, 9],\n [-20, 22, 16, 14, -1, -15, -6, 4, 10, -6],\n [19, -11, 4, -15, 0, 19, 6, -3, -7, -6],\n [-7, -4, -15, 15, 15, 6, 18, 13, 3, 8],\n [21, -11, -6, -8, -14, 16, 19, -11, 9, 2],\n [16, -5, -8, 9, -17, 21, 20, 12, 11, 15],\n [-18, -5, -7, -15, 2, 9, 3, -1, 8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-13, -11, 5, -17, -3, -18, 0, -14, 6, -7],\n [-1, -15, -3, -9, 16, 14, 11, -12, 17, 10],\n [8, 21, 11, -16, 0, -16, 2, -20, 15, -3],\n [11, 21, 21, 7, -6, -13, 12, -3, -5, 22],\n [21, 4, 13, 0, 9, -13, -12, 15, -17, 18],\n [11, 13, 14, -6, 17, 17, -11, -2, 17, -4],\n [-20, -5, -4, -17, -7, -15, -5, 20, 16, -11],\n [22, -13, -16, -22, 13, -2, 14, 1, 2, -16],\n [19, -6, 6, 7, -16, 10, -16, 1, -12, -14],\n [-11, 12, -19, 13, 5, -10, 0, -4, 19, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[16, 1, -7, 10, -11, 11, -16, -12, 8, 6],\n [-10, 8, -21, 16, -8, -12, 11, 16, -19, -12],\n [6, -21, -7, 16, -10, 14, -6, -2, 21, -4],\n [-16, 15, -15, -10, 14, -21, 18, -12, 1, -17],\n [3, -16, 16, -4, -17, 20, 6, 20, 16, -21],\n [-4, -19, -17, 14, 5, 7, -16, -14, 2, 10],\n [-22, -17, -5, -13, 5, -12, 10, -22, -10, 14],\n [-3, -22, -20, -5, 18, -9, 8, 4, -6, 6],\n [13, 14, 3, -6, -1, 2, -21, -1, -18, -19],\n [13, -17, -2, -10, 14, 2, 3, 16, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 13, -6, -2, -7, -7, -3, 6, 5, -15],\n [1, -20, 2, -4, 10, -21, -8, -1, -13, -5],\n [-1, 4, -10, 10, -18, 3, -10, 4, -9, 1],\n [-20, 7, 12, -9, -11, 5, 21, 6, 20, -6],\n [17, -2, 0, -3, -12, 11, -13, -13, 20, -17],\n [13, 1, -11, 20, 0, 4, 22, 14, -17, -22],\n [-17, -1, 18, 1, 2, -8, 3, -15, 1, 15],\n [-17, 12, 19, -22, 13, -11, 15, -12, -11, 19],\n [16, -16, -12, 13, 8, 10, -10, -5, 18, 1],\n [-14, 8, 18, -13, -21, 15, -8, -20, 20, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "317", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-17, -20, -12, -8, 22, 5, -13, 15, -16, -8],\n [-5, -5, 18, 1, -21, 17, -3, 11, 20, 3],\n [-16, 15, 7, 19, -18, -12, -22, 11, -22, -4],\n [-21, -2, -3, 0, -2, 1, -19, -11, -1, -3],\n [-5, -22, 7, 10, 1, -9, 13, -18, -12, 1],\n [8, -10, -7, 1, -10, 1, 3, -21, -7, 15],\n [-22, -12, 12, 20, 6, 14, -6, 16, 19, 5],\n [6, 20, -20, -13, 19, -9, -11, 19, 7, 9],\n [9, 19, 9, 3, -22, 19, -21, -6, 7, 16],\n [-16, 4, -14, -1, 11, -22, -14, -3, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[17, 22, -19, -14, 18, -1, -5, -11, 19, 20],\n [16, -14, -17, -4, -16, -7, -18, -7, -22, 14],\n [16, -4, 14, -6, 3, -1, -15, 10, -21, 7],\n [-3, -5, 20, -13, 1, -19, 14, -19, -10, 2],\n [-10, -5, 1, -21, 10, -4, -14, 5, 12, 16],\n [-13, -22, 19, -2, -14, -8, 12, -18, 18, -1],\n [18, 0, -16, 0, 21, 2, 4, 18, -17, 11],\n [-14, 10, -17, 14, 8, 11, 18, 6, -9, 13],\n [13, -8, -15, 3, 13, -2, 5, -19, -7, -1],\n [-11, -7, 17, 15, 19, 14, 6, -5, -13, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[16, -5, -22, 16, -2, -22, -8, -19, -3, -13],\n [0, 18, 11, 10, 11, 16, -13, -3, -22, -10],\n [-22, -18, -7, -8, 5, 8, 0, 22, 20, -6],\n [11, -10, -9, -12, 5, 19, 9, 12, 8, -6],\n [-14, -13, -15, -2, -10, -18, -17, 7, 8, -6],\n [-12, -3, -14, -21, 14, -22, -19, 13, 2, -20],\n [-14, -1, 0, -11, -13, 11, 20, -13, 7, -1],\n [-17, -21, 7, -21, 9, 19, -7, -11, -22, -15],\n [-10, -8, 21, -15, -13, -18, -4, 15, -12, 20],\n [-3, -3, -2, -5, -13, 11, 3, 7, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, -19, -17, -9, -19, 3, 16, -6, -4, -17],\n [6, -12, -7, 7, 2, 17, -12, -16, 3, -1],\n [2, -4, 8, 3, 19, 18, 13, 0, -10, 2],\n [-21, -21, -7, -14, 5, -10, 12, 18, -10, 8],\n [-2, 9, 11, -15, 18, -21, 15, 9, 17, 5],\n [14, 18, -22, 18, -13, -19, 12, -13, -12, -9],\n [15, -11, 22, -6, -7, 12, -21, -12, 18, -20],\n [6, -5, -3, -9, 11, 8, 17, 19, -5, 7],\n [2, -4, -15, 5, -15, 8, -20, -20, 21, -1],\n [-6, 13, -6, -9, -14, 7, -2, -11, 14, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-12, -3, 12, -12, -15, -19, 4, 21, 17, 15],\n [7, 21, 4, -2, -3, -19, -12, -10, -14, -19],\n [-11, -14, -10, 3, 15, 19, -10, 16, 5, -4],\n [1, -4, -10, -10, 5, -21, -13, -1, -10, -14],\n [10, -9, -3, -8, 9, 10, -6, 1, 7, -10],\n [-7, -21, -6, 9, 20, -15, -20, -11, -3, -7],\n [-9, -7, 20, 10, 7, -11, -8, -5, 5, 0],\n [-9, 7, 10, 22, -8, -16, -8, 19, 15, 21],\n [-12, 6, 8, 2, 1, -4, -21, -1, -3, 10],\n [-15, 2, -14, 11, 0, -18, 2, -15, -7, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-8, -22, -1, -20, 15, -9, 13, -5, 18, -5],\n [-20, -13, 16, -22, 4, 4, -12, -18, -16, -4],\n [6, -8, 12, 14, -11, 7, -3, 14, -20, -14],\n [18, 16, 3, -21, 0, 0, -2, -7, -14, -10],\n [5, 4, -6, 15, 13, -22, -5, -14, -10, 17],\n [22, -8, 20, 21, -19, 10, 1, 13, 18, -13],\n [13, -3, 18, 22, 21, -12, -11, -5, 7, 21],\n [14, -3, 2, -11, -2, 2, -12, -14, 2, 12],\n [9, -9, -22, -6, 2, -15, -18, -18, 18, 12],\n [-4, 0, -14, 7, -7, 10, -21, -9, -22, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -7, -8, 3, 21, -7, -9, 6, 1, -8],\n [-4, -15, 11, -21, 4, -13, 12, 0, -15, 5],\n [0, -19, -9, 19, 6, -22, -19, 9, 10, 3],\n [-6, 16, 0, 9, -8, -10, -21, -4, 1, 22],\n [1, -12, -1, -8, -13, 18, 4, -14, 5, -22],\n [-6, 8, 21, -13, 14, 6, -5, 15, 16, -17],\n [17, -11, -9, 21, -13, -3, -8, 8, -16, 18],\n [-13, -13, 16, 5, 7, 14, -20, 20, -8, -2],\n [14, -11, -19, -14, 16, 19, 5, 0, 22, 17],\n [21, -1, 1, 3, 7, 10, -7, -1, 20, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-16, 3, -15, -17, 7, 16, 0, 9, -1, 19],\n [20, 22, -14, 8, -16, -14, -10, -20, 12, 10],\n [-2, 8, 11, 9, 12, -8, 9, -17, 22, -2],\n [10, 9, -4, 10, 5, 8, -2, 11, -8, -9],\n [-4, 20, -8, -17, -14, 14, -3, 11, 15, 3],\n [-5, 5, -14, 9, -17, -9, 5, 1, -10, 20],\n [-11, -4, -2, 4, -4, 1, 3, 22, 5, -5],\n [21, 13, 19, 6, -6, -19, 21, 22, 6, -19],\n [-13, 2, 8, -20, -21, 2, -17, 3, -15, 12],\n [4, 2, -5, -22, 16, -20, -19, 18, 14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-15, 15, -4, 3, 16, -13, 15, -9, 18, -4],\n [7, -18, 8, -16, -4, 8, 16, 1, 11, 0],\n [22, 17, -17, 15, 18, 13, 4, -12, -18, -6],\n [-16, 4, -8, -10, -12, 22, 3, -1, 5, 1],\n [6, -14, 19, -19, -5, 20, -7, 10, 6, 16],\n [-13, -14, 8, 5, -20, -9, 2, -8, -21, 1],\n [-9, -16, 13, 1, 4, 14, 15, 7, 4, 16],\n [-8, 3, -22, -19, 6, -22, 20, -1, -12, -13],\n [-6, 13, 3, -2, -10, -14, -12, -12, -17, -22],\n [-17, -10, -1, 8, -1, 14, 4, -9, -18, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[9, 11, -16, 19, -13, -6, 7, -2, -10, -22],\n [-22, 10, 15, 2, 3, -10, 5, 10, 14, 18],\n [7, -15, -22, -11, -18, 1, -17, 2, -22, 2],\n [-22, 9, 19, 19, -20, -4, 20, 6, -21, -14],\n [-6, 13, -6, -11, -3, -20, 20, -19, -6, 14],\n [19, -8, 10, -7, -12, -3, 15, 1, -7, 7],\n [11, -22, 1, 1, -14, -1, -11, -6, 2, 5],\n [-8, 7, 4, -1, -13, 8, 4, -11, 8, 9],\n [9, 18, 22, 12, -2, -13, -7, -16, -19, 4],\n [2, 8, -12, -3, 13, -6, 22, -12, 7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[18, 15, -1, 20, 4, 14, 12, -19, -7, -7],\n [-2, 3, 13, -4, -6, 22, 3, -1, 5, -22],\n [21, 13, 20, 14, -21, -6, 17, 15, -2, -14],\n [-10, -12, -7, -7, -21, 19, 21, -15, 20, 19],\n [-10, -6, 16, 1, -20, 7, -10, -4, -16, -14],\n [-4, 22, 17, -1, -5, 0, -21, -12, 8, 10],\n [-9, -7, -12, 10, -16, 8, -9, 5, 20, -7],\n [-4, -6, 3, -17, 20, -14, -6, 8, -11, 0],\n [-18, 20, 13, 13, -20, 1, -6, 16, 3, -19],\n [22, -11, -22, -2, -4, -2, -5, 20, -20, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, -13, 17, -8, -18, -19, 5, -19, -8, -6],\n [21, -20, -13, 19, 0, -5, -22, 12, 8, 21],\n [-22, -20, -20, 14, -4, 6, 2, 10, 13, 6],\n [3, -19, -9, 4, 10, -1, -20, 0, -2, 18],\n [0, -19, -2, 14, 20, 8, -2, 3, 18, 12],\n [15, 1, -12, 18, 6, -20, -22, -4, -1, -9],\n [-9, 21, -7, 10, -10, 15, -11, 15, 16, 10],\n [10, 6, -18, -17, 8, -7, 8, 2, 10, -10],\n [-13, 1, -13, 18, 8, -10, -20, 11, 5, -4],\n [0, 22, 9, -10, 10, 11, 10, -18, -20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -1, 22, 0, 7, -5, 9, -16, 10, -18],\n [5, -15, -8, -19, 11, -18, 10, -18, 15, 11],\n [3, -22, -19, 16, 3, 10, 10, -15, -3, -7],\n [-2, 22, 3, 0, -5, 8, 19, -11, -22, 19],\n [-14, -20, 3, -14, 19, -7, 1, -9, -20, 11],\n [10, 1, -14, -10, -21, -16, -2, -4, 2, -1],\n [-12, 10, 9, -2, 16, -3, -15, 19, 14, -14],\n [2, 2, 10, -21, -4, -3, 19, 18, 19, 6],\n [-17, -6, 2, 15, -19, 7, -3, -20, 0, -5],\n [3, 13, -15, -6, 8, 14, 22, 10, 4, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-19, -1, 3, 9, 1, 12, 14, 9, -16, 10],\n [8, -11, -12, 1, -15, 9, 15, -1, 11, -4],\n [-3, -9, 10, -13, -7, -19, 4, 5, 20, -7],\n [10, -4, -2, -1, -14, -14, -14, 4, -6, 21],\n [22, -15, -7, -5, 10, -22, -11, -17, 18, -18],\n [-7, -5, -5, -22, -4, -15, -20, 2, -18, 17],\n [-4, -5, 8, 10, -5, 16, -7, -7, 15, 18],\n [-16, -9, 20, 2, 9, 15, -1, -7, 6, -7],\n [-11, -6, 14, 4, 2, -10, -15, -18, -11, 18],\n [-20, 12, 10, -1, 21, -14, 18, -5, 6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 13, 22, -6, 11, -20, -18, -9, -20, 0],\n [16, 7, 22, 0, 4, -13, 2, -10, -7, 18],\n [11, 14, -1, -6, 0, 13, -14, -21, 9, -1],\n [20, -10, -15, -22, -6, -11, -19, -10, 8, 18],\n [-16, 0, 1, -18, -18, -6, 7, -14, -17, 2],\n [-4, -7, -2, -21, -13, -7, 14, -8, -10, -10],\n [9, 22, -15, 20, -5, 13, 3, -13, 8, 10],\n [6, -18, -10, -22, 0, 17, -20, -20, -16, 13],\n [12, -8, 17, -20, 6, 7, 16, -5, -12, 20],\n [15, 17, -22, 6, -13, 5, 8, -4, -20, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[20, -8, 10, 18, 20, 22, 3, -7, 13, 10],\n [-3, -10, 10, -18, 14, -9, 4, 0, -9, 17],\n [-19, 16, -4, -19, 7, -4, 8, 8, -14, -10],\n [-9, -13, 8, 14, 0, 4, -17, 3, -21, 22],\n [-10, -4, -22, 17, 9, -1, 6, -21, 17, 15],\n [-12, -6, 20, -15, -1, -19, -12, -15, -14, 3],\n [-21, -7, 8, -17, -2, 3, -4, 5, -15, -9],\n [1, 21, 14, 3, 8, 9, 18, -21, 2, 21],\n [-21, 19, -22, 13, -11, -14, 13, 18, 5, 15],\n [10, 19, -1, 2, -5, -17, -5, -7, -8, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-10, 20, -16, -6, 9, -1, -10, 0, 6, -1],\n [-22, 6, -18, 12, -13, -4, 14, -16, 12, 22],\n [-10, -13, -21, -17, -15, 13, 2, 21, 17, -16],\n [0, -4, -1, -10, -2, -22, -4, 10, -19, 19],\n [-20, 4, 18, 12, 5, -17, -17, 21, 0, 10],\n [-7, 1, -18, 18, 19, -10, -11, -18, 14, 8],\n [5, 5, 7, -5, 21, 4, 12, 3, 16, -5],\n [10, 2, 8, 14, -21, 10, 16, 20, 20, 9],\n [-5, -6, 11, 16, -16, 19, 12, 7, -11, 12],\n [-12, 21, -19, 2, 9, -3, 8, -19, 15, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-20, 14, -1, -6, -9, 18, 12, -10, 12, 20],\n [-21, -10, -7, -5, -16, 22, 13, 18, 7, 19],\n [18, -16, -8, 17, -4, 20, 14, -21, 19, -10],\n [17, 18, 20, 20, 8, -7, 19, 21, -17, 5],\n [9, 21, -13, -5, -19, -14, -16, -15, 20, -16],\n [18, 17, -20, -6, -21, -8, 6, -1, -19, -17],\n [15, 3, -12, 3, -6, 1, 5, 12, 8, -10],\n [12, -7, -8, 20, -5, 14, 18, 4, 12, 22],\n [12, 5, 16, 15, -14, -11, -8, -2, 12, 19],\n [10, -4, 0, -10, 21, -22, 6, 1, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 5, -7, 20, 15, -12, -20, -8, -22, -16],\n [-22, 9, -14, 6, 3, 0, 22, 20, 6, 15],\n [10, -16, -11, 8, 9, -3, -6, 13, -20, -22],\n [4, 17, 10, -3, -9, 13, -18, 0, 22, -8],\n [-17, 10, -4, -10, 6, -17, -8, -7, 1, 0],\n [-13, 18, 18, -6, 21, 22, 7, 21, -13, -4],\n [6, -21, 13, -4, -16, 3, -8, 15, -20, 15],\n [-7, -21, 8, 5, -16, 7, 20, -16, 13, 6],\n [1, 16, -19, 6, 21, -18, 6, 7, 6, 3],\n [-4, 3, 14, 4, 7, 7, -20, 20, -16, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[18, 19, -10, -8, -18, 6, 12, 4, 4, -15],\n [9, -3, -13, -10, 6, 12, -15, 6, 8, 18],\n [7, -1, -2, -11, -12, -21, 18, -21, 11, -20],\n [-7, -19, 0, -3, 2, 7, -5, 19, -12, 6],\n [-6, 3, 0, -3, 22, -21, 1, 8, 4, -21],\n [-9, -19, -10, 13, 12, 21, -15, -21, -17, 8],\n [-13, 21, -2, 19, -13, 0, -20, 9, -3, -13],\n [6, 18, 11, 14, -3, -15, -16, -17, -12, 21],\n [-5, 19, 6, 2, -2, -20, -5, 1, 15, -13],\n [4, -11, -16, -6, -22, 3, -8, 10, 14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[12, -22, -15, -11, -4, 2, 9, -11, -10, 5],\n [-22, -17, -15, -19, -18, 2, -1, 5, 16, 0],\n [-19, -19, -2, 14, 18, -21, -16, -7, -6, -3],\n [0, 11, -12, 11, 10, 3, -21, 0, 18, -1],\n [11, -8, -13, -8, 19, 6, 0, -6, -14, 13],\n [-14, -7, 13, 10, 8, -17, -13, -7, -19, -1],\n [-10, -7, 6, -17, 3, -12, 1, 6, -20, -13],\n [-22, 20, 3, -11, -9, 2, -15, 20, -19, 5],\n [-16, -13, 13, -21, 3, -9, -7, 20, 19, -6],\n [-1, -19, -4, -21, 16, -14, -4, -7, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"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, -12, 16, 18, -19, 2, 9, 7, 22],\n [3, 13, 11, -14, -11, -21, 15, -18, -18, -1],\n [-18, -19, -14, 6, -1, 4, -13, -7, 19, 19],\n [-13, -17, -18, -17, 2, -19, 17, 9, 12, -13],\n [11, 13, -17, 20, -7, -4, 11, 2, 8, 18],\n [-6, 7, 16, 8, -4, 12, 6, -22, -19, 5],\n [-5, 3, 17, -4, -17, -22, -15, 10, 20, -2],\n [1, 2, 20, -4, 6, -13, -11, 10, -16, -6],\n [-13, 8, -17, -6, 14, -5, 3, -7, -15, 1],\n [-10, 6, 9, 1, -7, -12, 9, -17, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 14, -10, -13, 14, 3, -6, -22, 2, 11],\n [16, -13, -3, -16, -7, 14, 6, -11, -6, -3],\n [3, -4, -11, -2, 19, 11, -16, 22, 12, -8],\n [-22, 3, 12, 2, 19, -8, -1, -17, -8, 1],\n [-2, -16, 6, 9, 9, -18, -19, -1, -5, 12],\n [-6, 1, -21, -10, -8, -18, -20, 14, 14, 14],\n [-20, 12, 0, 5, 7, -5, 13, 10, 3, 17],\n [-6, 17, -16, -15, 8, -11, 8, 21, -4, -13],\n [16, -11, -3, 14, 18, -16, -9, -12, -16, 6],\n [-13, 6, -14, 13, -13, -4, 8, -6, -14, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[10, 11, 22, 1, -14, -16, -7, -4, 16, -17],\n [-12, -11, 19, -10, -11, -2, -13, -3, 13, 5],\n [1, -18, 14, -11, 12, 17, -21, 18, 22, 16],\n [19, -14, -1, -18, -11, -22, 21, -1, 15, -4],\n [-7, 8, -20, 0, 19, -5, 3, -10, -5, -20],\n [0, -20, 2, 4, 21, 4, 16, 2, 1, -15],\n [-14, 14, 7, -4, -7, 1, 21, -2, 13, 17],\n [16, -17, -18, -9, 22, 19, -19, -15, 1, -12],\n [-6, -2, 3, 20, 21, 22, 4, -7, 3, 10],\n [8, -17, 21, -15, -16, 11, 21, -9, -7, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-14, -13, -6, -11, -17, -4, 20, 18, 6, -17],\n [2, 1, 2, -7, -7, -17, 14, -2, -19, 11],\n [5, 15, 18, 5, -6, -9, -16, -1, -22, 6],\n [8, 7, -8, -5, 12, 7, 11, 19, -12, 4],\n [1, 12, 16, -15, -5, -10, 22, 1, 0, -11],\n [7, 8, 5, -1, 21, 5, -10, 2, 21, -16],\n [22, -17, 1, -4, -4, 13, -14, 13, 15, 17],\n [6, 1, -18, 19, 22, 3, -9, 16, 6, -17],\n [-16, 14, -5, 0, 21, 15, -22, -19, 21, 12],\n [0, 4, 3, -15, 20, -7, 18, -20, 9, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -9, 9, 3, -17, 13, 17, -18, -10, 9],\n [-7, -22, -10, -12, -15, 2, 17, 9, 1, 5],\n [-9, 22, -20, 13, 4, -3, -8, 4, 22, 18],\n [5, 2, 19, 21, 10, -9, -15, -9, -22, -7],\n [-5, -16, -8, 1, -10, -14, -8, 12, 1, 10],\n [-7, -15, 6, 0, 22, 8, 17, -9, 7, 16],\n [4, -7, -17, 10, 21, -5, -7, -11, -3, 22],\n [17, 6, 7, 3, -1, 10, 16, 6, -1, 22],\n [-10, -14, 1, -8, 13, -10, 4, 21, 14, -16],\n [-15, 14, 18, -9, -11, 13, 17, -6, 17, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "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, -22, 11, -19, 1, -2, 10, -16, -22, 18],\n [-20, 21, -8, 8, -7, -13, 6, -17, 6, -6],\n [-1, 1, -6, -2, -12, -16, 19, 16, -18, 21],\n [-2, -5, 12, -3, -8, -18, -10, -11, -2, 14],\n [-17, -16, 3, 19, -15, -14, 4, -19, -2, 8],\n [-2, 17, 2, 16, -8, 12, 20, 18, 14, 19],\n [5, -9, -19, -3, 11, -11, 10, 1, -3, -18],\n [15, 7, 1, 20, 17, -16, 13, 15, -7, -8],\n [0, -11, 6, 21, -8, 6, 22, 20, -2, -8],\n [-9, 19, 21, -7, -8, 19, -19, 4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[18, -14, 20, 20, -16, 19, -19, -18, -18, -12],\n [18, 5, -7, 18, 7, -19, -21, -20, -2, -17],\n [20, -5, 21, -18, -14, -3, 5, 3, -5, -4],\n [-20, -14, 13, 8, -6, 0, 11, 18, 18, -18],\n [-8, -20, -4, 5, -20, 15, -19, 1, 8, 22],\n [22, -12, 14, -22, -14, -6, -22, -20, 3, 8],\n [3, 0, 7, -13, -15, 21, 2, -1, -8, 18],\n [-13, -3, 18, 0, -22, -21, -4, -9, -15, 15],\n [-11, 3, 4, 6, -8, -22, 20, 5, -20, -5],\n [11, 9, 6, 2, 3, 16, -15, -4, 19, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 10, 15, 22, 12, 20, -20, -4, -13, 4],\n [-8, -12, 3, 1, -10, 9, 14, -19, -10, -14],\n [11, 14, -16, -22, -11, -2, -12, 21, 21, 21],\n [-9, 11, 11, 2, -19, 3, -7, -13, 22, -21],\n [12, -4, -17, -4, -15, -9, -13, -20, 15, 6],\n [-8, 0, 0, -5, -4, 5, 3, -13, -19, -21],\n [-20, -16, -7, 8, -13, -4, 5, -6, 5, -4],\n [14, 0, -3, -10, -10, 20, -12, -8, -6, 5],\n [-4, -19, -1, -1, 14, 16, 11, 10, 21, 19],\n [17, 10, -11, -21, 5, -13, -1, -6, 3, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-16, 21, -15, -3, -11, 12, -6, 5, 18, -13],\n [-1, 15, 10, -1, 21, 14, -10, 4, -8, -1],\n [7, 20, 17, 14, 11, 21, 11, 12, 19, -4],\n [-15, 16, 10, 21, 5, 14, 2, 13, -6, 1],\n [-2, -21, 8, 21, 10, 7, -11, 21, -11, 1],\n [1, -12, -10, 4, -15, -13, -15, -3, -15, -14],\n [-16, -9, 5, -21, 20, -15, -10, -2, 5, 12],\n [0, -8, -21, -11, 13, -20, -18, -20, -4, -21],\n [21, 14, -6, -9, 5, 4, -13, -20, 13, 15],\n [2, -1, 16, 7, -2, 7, 5, 8, 3, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -2, -22, 14, -10, -2, -14, -6, -2, 8],\n [16, -1, -11, -17, -7, 3, -18, -14, 17, -9],\n [21, 19, 7, 3, 22, 6, -4, -15, 0, 19],\n [12, 8, 12, 9, -18, -7, -6, 9, 15, 9],\n [-3, -21, -3, -5, -22, 6, 6, -4, 21, 17],\n [-17, 21, 16, -15, 1, -3, -9, -18, 18, 17],\n [11, -7, 22, -16, -7, -16, 4, -9, -9, 21],\n [10, 10, 21, -3, 13, -16, 9, -20, 16, 6],\n [1, -1, -17, 1, 17, 0, 15, -13, -7, -12],\n [9, 22, -17, 1, 10, -11, 4, 15, -5, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[16, -10, 17, 7, 18, -10, 11, 13, 7, 2],\n [-21, 13, -5, -18, -4, 19, -5, 9, -2, -13],\n [14, -1, -10, -6, -14, 1, 21, -9, -15, 14],\n [-4, 5, 18, 7, -16, 3, 17, -12, -9, -2],\n [-15, -20, 5, 6, 0, -5, 12, -10, -11, -18],\n [16, -12, -12, 19, 8, 8, -10, -9, 22, 19],\n [2, 10, 10, -8, -7, 21, 15, -17, 21, 2],\n [-8, -19, -19, 7, 11, 4, 8, 9, 21, 16],\n [-14, 18, -15, -9, 10, 0, -2, -11, -21, -10],\n [-19, -3, -9, 7, 6, -15, -11, 18, 15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, 17, -9, -17, 19, 17, 8, -6, 2, 9],\n [-11, -10, -4, 21, 2, 8, 14, 2, -7, 15],\n [20, 0, -9, -17, 2, 0, 20, -11, -10, 13],\n [16, 11, -17, 15, 17, -15, -15, 17, 10, 11],\n [21, -8, 13, 12, -1, 0, 17, 22, -1, -18],\n [8, -10, 5, -3, 10, -7, 6, 0, 1, 11],\n [-16, 15, 14, -19, 11, 19, -1, -18, 19, 0],\n [-8, 8, -14, 20, 2, 2, -2, -14, 15, -1],\n [20, 0, -19, 6, -8, -22, 7, 6, -3, 10],\n [18, 21, 13, -1, -10, -16, -15, 5, 22, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-14, 2, -7, -13, -12, 8, -11, 8, -9, 21],\n [9, -6, 12, -22, 6, -19, 0, 5, -7, -11],\n [-2, 22, -6, 17, -10, 9, 14, -8, -11, -8],\n [11, -17, -6, -3, -14, -18, 0, 10, 15, -9],\n [-6, -4, 10, -22, -10, 4, -17, -17, 10, 7],\n [12, 0, -13, -4, 5, 0, -19, -3, -4, 19],\n [4, 11, -19, 15, -16, -16, 3, 3, -4, -14],\n [-3, 19, 22, -7, -6, -1, -10, -11, -13, -22],\n [9, 7, -15, -2, -1, -5, -21, 21, -14, -20],\n [3, -2, 7, 5, 13, 3, 11, -15, -13, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-9, 17, -8, -6, -5, 9, 15, 0, 0, 12],\n [16, -8, 1, 5, -7, -7, 17, 16, -17, -21],\n [-10, 21, -14, 11, -6, 4, 6, 14, 20, -1],\n [1, -16, 11, -11, 0, -8, 10, -10, 0, 15],\n [9, 22, 12, -22, 22, -18, -10, -18, 9, -2],\n [1, -5, -2, -13, 1, 17, -2, 2, 0, -1],\n [-19, 11, -17, 5, 8, 12, 16, 19, 0, -17],\n [-7, -21, 1, -6, 22, -22, -17, -18, 22, 6],\n [-11, 16, -20, -22, 4, 1, 21, -4, -15, 21],\n [-21, 7, 7, 16, 22, 9, -22, 15, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-13, 3, -3, -6, -6, -19, -18, 0, -13, 5],\n [10, 20, 3, 6, 4, -5, 17, -13, 19, -18],\n [-13, -2, 1, 15, -20, 17, 8, 18, 14, -21],\n [-21, 16, 19, 21, 11, 19, -3, 10, -19, 22],\n [21, -12, 19, -18, 2, 14, 11, -14, -17, -5],\n [-9, -4, -9, 17, -6, 12, 6, 19, -6, 20],\n [-15, -22, 22, 13, -16, -18, 1, 5, 20, -6],\n [14, -3, -20, 14, 3, -8, -15, -10, -20, -22],\n [-14, 8, 18, 3, -6, 11, -14, -10, -18, 18],\n [-10, -22, 2, -19, 13, -13, 5, -17, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "387", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-20, 10, -13, 8, -8, -16, 13, -9, -9, -20],\n [-20, -1, -4, 12, -11, -18, -13, 18, 10, -10],\n [12, 9, -12, 15, 1, 12, -4, -17, 17, 22],\n [21, 19, 12, -19, 10, -10, 13, 20, -4, 20],\n [-11, -12, -17, -11, 4, 18, 2, 19, -20, -20],\n [-3, 5, 0, -20, 19, 1, 20, 17, -17, -3],\n [-12, 9, 4, -2, 21, -10, -1, 12, -1, 5],\n [-2, -5, 8, 14, -2, -9, 2, 4, 17, 0],\n [8, 6, 7, 3, -3, 15, -4, 4, 2, 17],\n [15, 0, 6, -8, -20, -13, -8, -7, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-12, -18, -18, -9, 3, -15, -18, -16, -7, -9],\n [14, 18, -19, 13, -6, 13, -17, -7, 6, 13],\n [15, 14, -13, 18, 13, 6, -9, -19, 21, 19],\n [13, 22, -10, -5, 10, -2, -7, -8, -18, -17],\n [15, -20, -11, 13, 10, 13, 10, 8, -2, 4],\n [4, -15, 14, 9, 3, -21, -11, -1, -6, -16],\n [20, -19, 14, 15, 9, -12, -22, 2, 19, 1],\n [20, -6, -15, 22, 4, -5, 4, -1, -7, -21],\n [-18, -5, -20, 4, -6, -7, -17, -16, -9, 15],\n [17, -8, 10, 20, 4, 6, 14, -18, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-17, -21, -17, 20, -19, 6, 2, -14, -20, 3],\n [20, 4, 13, 9, -22, -7, -12, 3, 17, -22],\n [3, 5, -14, 21, -1, -15, 19, 4, 16, -4],\n [2, 15, -2, 1, 1, -4, -21, -9, 9, 19],\n [9, 5, 16, 17, 19, 17, -10, -11, -15, -8],\n [3, -11, 20, 4, -5, 22, 13, 4, -14, 16],\n [-22, -16, 3, -16, -16, -15, -7, -20, 22, -13],\n [-16, -2, 14, 8, 0, 4, -1, 16, 4, -19],\n [1, 0, -4, 19, -20, 4, -20, 5, -6, 8],\n [-13, -1, 7, -2, 13, 0, 15, -11, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[19, -16, 6, 6, -10, -20, -21, -7, 7, 15],\n [-17, 22, -16, -18, -16, 11, 9, -10, 7, 2],\n [-2, -2, 5, -3, 11, -18, -5, 16, 20, -12],\n [-6, 22, -1, 14, -3, -17, 11, -9, 0, -3],\n [-10, 21, 18, 9, 3, -9, 13, -15, 17, -1],\n [-1, -7, 4, -13, 2, 8, -2, 4, -6, 10],\n [8, 19, 3, -2, 13, -22, -19, -19, 3, -19],\n [-14, 7, 22, -19, -18, 22, 0, -7, -1, 14],\n [-15, 10, 15, 20, -7, -18, -7, -16, -22, -14],\n [-5, 22, -20, 1, 5, -13, -14, -10, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -16, -7, 17, 13, -3, 1, -18, 22, -17],\n [5, -18, 16, 15, -21, 20, 16, -2, 17, 14],\n [-5, -11, -6, 14, 15, -8, -16, -9, -22, 15],\n [-20, 14, 21, 8, 20, -10, -5, -6, -6, -12],\n [-3, -13, 6, 11, -6, 19, -10, 21, 16, 4],\n [3, 5, -10, -11, 21, 5, -21, 14, 11, 0],\n [22, 6, 12, -12, 10, -12, -14, -9, -14, 16],\n [-20, 6, -4, 13, 9, -16, 5, 21, -5, -18],\n [0, -1, 3, 19, -11, 17, -4, -22, -20, 4],\n [-5, 7, -21, -18, 6, 10, 19, -3, 7, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-18, -2, -8, -3, -15, 8, -11, -2, 7, 4],\n [21, 3, 10, 3, 3, 13, 17, -22, -8, -22],\n [-12, -21, -22, 8, 21, -7, -1, 19, -5, -6],\n [7, -13, 12, -2, -7, -17, -20, 18, 20, -2],\n [-10, -5, 1, 4, -19, -1, 1, 17, 22, -13],\n [-21, 17, -17, -5, -6, 15, 22, 0, 7, -2],\n [-13, 20, -10, -11, -14, -19, 16, 1, 11, 16],\n [18, -18, -8, -19, 16, -15, 22, 1, 5, 20],\n [4, -22, 11, -6, 14, 15, 3, 1, 16, -2],\n [7, -10, 14, -20, 9, 12, -4, -9, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-19, 22, 17, -4, 14, -21, -8, -21, -12, 22],\n [0, -13, -20, -18, -20, 15, -10, 19, -4, 17],\n [12, 1, 1, -6, 17, -13, -21, 21, 0, -17],\n [-21, -2, 12, 6, -16, 6, 14, 0, 10, -15],\n [-11, -13, -8, 1, 3, 19, 16, -20, -21, -17],\n [-2, -14, -13, 13, -20, 18, 1, -1, -9, 19],\n [22, 21, 4, 10, -1, 6, -4, -4, -17, 22],\n [-4, -10, 3, -1, -2, 13, -21, 21, 7, 4],\n [-16, -3, 8, 0, -10, -6, -19, -9, -3, -10],\n [-20, 3, 3, -5, 9, -9, -20, -22, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[12, -9, -20, -10, -9, -2, 3, -20, 17, -19],\n [13, 20, -22, 17, 10, -16, -12, 4, -9, -1],\n [-7, -11, -13, 1, -5, -1, -14, -6, 15, 17],\n [-10, 14, -17, -2, 13, -16, 13, 2, -12, 21],\n [-9, 22, 6, -13, -18, -15, -18, 1, 17, 3],\n [-17, -7, 13, -11, -12, -20, 21, 14, -17, -4],\n [-5, -7, 0, 20, 14, -14, -20, -15, 15, -19],\n [-11, 21, 8, 2, -7, 19, -9, -10, 18, -16],\n [-11, 14, -19, -21, 12, 21, -20, -19, 15, -11],\n [-4, -13, -22, -6, -7, -14, -14, -14, -11, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "388", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-8, -21, -12, -12, -15, 9, -17, -3, 16, 12],\n [-15, 20, 11, -4, -16, 8, -5, 17, -9, 16],\n [13, -6, 14, 21, -14, -3, 22, 5, -3, 18],\n [13, 4, -15, 9, -22, -6, -14, -3, 22, 9],\n [-21, 9, 22, -14, 7, -3, 15, -22, -18, 12],\n [13, -22, -9, -14, 7, 1, -19, -9, 2, -19],\n [2, -13, 12, -16, 19, -10, -19, 20, 13, -9],\n [-5, -15, 9, 4, 19, 14, 0, -16, -11, 2],\n [-20, 3, -19, 19, 13, -8, 9, 6, -13, -2],\n [-7, -4, 6, -5, 21, -7, -22, -21, -8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "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, -22, -18, 19, -1, 13, -10, -22, -7, 18],\n [-1, 9, -7, -8, 19, -11, -22, -6, 18, 5],\n [-16, -14, -1, 3, -11, -16, -8, 15, -2, -9],\n [-21, -15, 22, -17, 14, 14, 10, 18, -17, 3],\n [16, 18, 14, -9, 14, -15, 16, -10, -10, 17],\n [20, 5, -5, -4, 15, 9, -1, -21, -10, 0],\n [2, 5, -12, 10, 1, -21, 7, -6, 17, 11],\n [15, -1, -18, 17, -7, -10, 3, 8, 16, 0],\n [-11, -9, -5, 4, 5, -5, -7, -7, -10, 6],\n [-14, 3, 5, 18, -10, 13, -14, -9, -11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[15, -20, -7, -3, 9, 0, -6, -7, 15, -15],\n [-4, 7, 11, -9, -1, 21, -6, -8, 9, -10],\n [-2, 17, 10, 4, 12, -7, 5, 11, -22, 18],\n [8, 13, 21, 10, 10, 16, -5, 0, 0, -8],\n [3, 7, 2, 22, -7, 16, 22, -9, -6, -11],\n [6, 9, 1, -10, -3, -8, -19, 11, 5, -21],\n [7, 3, 3, -3, 19, 5, -3, -12, -13, 0],\n [14, 18, -4, 22, -5, 4, -17, -13, -21, 1],\n [15, 5, 5, 22, 16, -21, -18, -12, -13, 20],\n [-21, -8, 16, 18, 14, -16, -3, 11, 12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "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, 8, 0, -4, -19, 1, -3, 16, 5, 16],\n [-6, -4, 12, 9, 16, 12, 7, -6, 19, 6],\n [-17, -6, -6, -9, 1, 14, 17, 16, 9, 13],\n [14, -9, 4, -4, 8, -14, 15, -6, -4, 21],\n [-19, -12, -1, -19, -6, -15, 11, -12, 8, -12],\n [15, -2, 7, -13, 3, 4, -15, 16, -15, -15],\n [11, -7, 18, -10, 0, -11, 4, -1, 9, 4],\n [-21, 22, 10, 3, 5, -4, 20, -18, 10, -3],\n [7, 22, -15, 15, -6, 21, -22, -20, 3, 8],\n [-15, 20, -15, 12, 16, 5, -19, -7, -10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-18, 14, -3, 1, 13, 11, 22, 11, -4, -6],\n [-18, 2, -5, -15, 4, -8, 22, -10, -7, -1],\n [-3, -10, -3, -21, 12, -4, 22, 14, -17, -9],\n [-19, -1, 16, 13, 11, 4, -16, -20, 10, -21],\n [19, -7, 2, -8, 1, -8, 8, -9, -9, -17],\n [-9, -6, -5, -3, -6, -7, 17, 16, 9, 21],\n [-14, 4, 10, -13, -6, 13, -6, -5, 0, 11],\n [-15, -10, 0, -3, -1, 0, 18, 12, -20, 11],\n [10, -6, 22, -4, 7, 0, -8, -9, -21, 16],\n [-5, -17, 9, -2, 17, 5, 4, -21, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[16, -1, 20, -10, -21, -9, 15, 18, 5, -16],\n [-5, 18, 13, 18, 13, 21, -19, 7, 1, -3],\n [8, 1, -16, 3, -10, -15, -18, 21, -10, 6],\n [-3, -9, 9, 4, 2, -19, -2, -5, 16, -8],\n [15, 1, -15, 5, -2, -7, -7, 12, -6, -14],\n [12, 6, 16, -5, -11, -4, -1, -8, -22, -21],\n [-15, -1, 2, -21, -14, -14, -10, -17, 7, -8],\n [-8, -16, -12, 17, 15, 17, -21, 16, -13, 21],\n [-6, -16, 17, 16, -19, 12, 13, 8, 2, 18],\n [-10, -5, -2, -22, 13, -15, -2, 20, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 0, 20, 12, 17, 19, -18, 18, -15, -12],\n [-7, 16, 1, -2, 0, 15, -15, -16, -21, 7],\n [-10, 0, 6, 15, 14, -3, 10, 6, -8, 0],\n [19, -20, 14, 6, 22, -15, -1, 6, -21, 18],\n [22, -22, 21, -3, -2, 14, -15, 4, 12, -17],\n [22, 21, -4, -5, -22, 2, 4, -16, 21, 19],\n [6, 8, 21, 20, 13, -4, -17, 2, 8, -14],\n [-3, -13, 14, 4, -10, 18, -21, -2, 10, 1],\n [21, 19, 11, -14, -21, 7, -1, -12, 20, -6],\n [13, -10, -16, -7, 10, 22, -22, -12, -17, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[12, 21, 14, 18, 3, -11, 7, 5, 4, 19],\n [-4, -18, -18, 18, 4, 5, 3, 4, 19, -2],\n [-22, 5, -8, -6, 3, -3, 2, -10, 10, 2],\n [-15, -18, -17, 0, 7, -9, 0, -12, 8, -17],\n [-12, -10, -11, -21, 12, 13, -6, 5, 5, -1],\n [15, -16, -8, 9, -12, 1, -20, 7, -17, -21],\n [-9, 18, -5, 21, 8, -10, 3, 21, -11, -5],\n [-14, -2, 17, 20, 1, 11, -15, 21, 10, 0],\n [-10, -9, -9, -7, 15, 16, 3, 3, -22, 9],\n [-8, -2, -5, 7, -10, 1, 7, -21, -4, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -9, -17, -11, -3, 0, 7, 7, 15, 7],\n [18, 7, 13, 11, -7, 1, -9, 3, -15, -9],\n [8, -21, -19, -22, -3, -9, 17, 2, 2, -20],\n [-18, 15, 3, 17, 15, 15, -19, -16, 7, 7],\n [-4, 16, 12, 17, 10, 10, -9, 15, -13, 5],\n [-9, 13, 15, -7, -2, 5, 10, -17, 18, -8],\n [21, -20, 20, 12, -9, -21, 6, -19, 3, -11],\n [-21, -6, 12, -13, -1, 18, 20, -2, -8, 12],\n [-2, -2, -2, 21, 9, -18, 16, -14, -5, -2],\n [-15, 21, 11, -13, 18, 1, 17, 1, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[15, 21, 11, -12, 8, -5, 0, -1, 20, -5],\n [17, 18, 16, -3, -10, 22, -22, -19, 1, 13],\n [13, 22, -21, 5, 3, 0, -8, 13, 4, -17],\n [12, 16, 15, 12, 13, -13, 7, 18, 15, 6],\n [20, 16, -19, -18, -19, 13, 22, -7, 2, -9],\n [-12, 6, 11, -1, -9, 1, 16, 3, 20, 13],\n [16, -7, 15, 9, -17, 11, -15, 7, 4, -16],\n [4, 2, 18, -8, 2, -1, -5, -11, 0, 22],\n [16, 2, -13, 7, -13, 11, -10, 6, 15, 18],\n [22, -14, -10, 14, -9, 14, -14, -15, 16, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-20, 17, 10, 9, -16, -4, 11, -9, -4, 3],\n [-6, 5, -4, 4, -4, 10, -16, 6, 20, -18],\n [7, 20, -15, 19, -11, 19, -10, 3, -5, 19],\n [-3, -7, 14, -20, 4, -8, 11, 22, -1, 17],\n [0, -19, 18, 0, -14, 1, -2, 18, -7, 2],\n [3, 22, -14, -8, 16, 10, -22, -18, -14, 21],\n [-17, 5, 22, 3, 5, 17, -8, -17, 4, 15],\n [-19, -12, -2, 7, -5, 12, -20, -11, 4, 7],\n [-2, 15, -2, 15, 17, -8, -5, 6, 15, -2],\n [-6, 18, -5, 14, 15, -11, -12, -3, -14, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-20, -2, 0, -14, -4, 22, -4, 0, 4, 4],\n [16, 13, -11, 4, 11, 10, 5, 8, 9, -3],\n [17, 12, 8, 8, 15, -1, 22, 18, -14, -14],\n [-8, -10, -1, -7, 9, -21, 3, -9, 15, 11],\n [-15, 13, -2, 20, 5, 21, -17, -3, 8, 10],\n [21, -16, -15, -14, -21, -6, 22, 14, 19, 21],\n [-6, 15, 12, 16, 7, -17, -19, 14, 12, -14],\n [-17, -10, -1, 5, 7, 13, -21, 13, -15, 22],\n [19, -14, -22, -10, -8, 9, 11, 20, 8, -9],\n [-9, 6, -4, 4, -14, 14, 14, 20, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"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, 13, -5, 2, 12, -19, -9, 16, 3, -15],\n [1, -7, -3, -8, -16, -6, -1, -1, -11, -5],\n [-8, 14, -7, -18, -21, 5, 18, 4, 8, 18],\n [13, 20, -22, 6, -22, -15, -7, 5, -1, -5],\n [-1, 18, -11, -4, 2, -18, 11, 16, -13, -16],\n [14, -8, 19, 1, 3, 3, 3, -13, -6, -9],\n [-21, -10, 4, -14, -16, -13, -14, -1, 0, -16],\n [-14, 4, 1, 6, -6, -3, -16, 20, 17, -16],\n [5, -4, -3, 21, 16, 17, -16, -17, 2, 18],\n [-10, 16, 17, -1, -6, -1, 11, -15, 22, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 19, -21, -21, 4, -9, 16, -11, 9, 5],\n [5, 2, -19, 3, 13, -20, -22, -6, -16, -18],\n [-4, 16, 11, 12, -7, 17, 16, 4, 18, 15],\n [2, 3, -9, -9, -9, 2, 13, -19, -8, 9],\n [-5, -9, -22, 19, -3, -13, -13, 1, 11, 5],\n [4, 17, -22, 10, -19, -16, -14, -7, -18, 11],\n [0, 20, 2, -10, 1, -12, -6, 14, -10, 4],\n [-3, 10, 19, 9, -15, 6, 17, -4, -17, 21],\n [16, 18, -2, -1, 19, -13, -13, 6, -7, -22],\n [-6, 7, 3, -4, -2, -6, 17, -2, 18, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[22, -4, -16, -6, -22, 14, -17, 3, -21, 9],\n [-18, 14, 8, -11, 12, 7, -17, -8, -8, -7],\n [-3, -10, 21, 19, 8, 11, 6, -20, -14, -12],\n [-12, 2, -1, 19, -14, -3, -2, -13, -1, 6],\n [-14, -18, 17, -12, -22, 19, -22, 16, -18, -1],\n [3, -17, 9, -12, -13, 16, 11, 8, -11, 21],\n [-7, 15, -20, -21, -18, -12, 2, 12, 12, -1],\n [14, -1, -12, 9, 12, 8, 22, -15, -3, 19],\n [11, -19, -5, -19, -3, -14, -7, 3, 15, 2],\n [-19, 18, 22, 18, 15, -4, -9, -2, -8, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[14, -7, -9, -14, -16, -9, -17, -2, -8, -15],\n [11, 17, -22, 9, -18, 7, -1, -3, -7, -16],\n [-16, -21, -9, 8, 18, -9, -18, -12, 17, -18],\n [6, -12, -18, 9, 13, -8, -4, -1, 11, -6],\n [-11, 2, -6, -13, 5, -5, -5, 22, 9, -9],\n [-7, -5, -7, -6, -16, -11, 11, -13, -18, -2],\n [-20, -4, 22, 21, 12, -17, -9, -19, 22, -5],\n [6, 12, 15, -7, -3, 1, 12, 21, -4, -19],\n [10, -21, -10, 22, 7, 11, 7, 1, 21, 10],\n [18, -13, -5, -4, -16, -4, 1, -8, 18, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -19, 15, -19, -18, 18, 21, 0, 17, 14],\n [-12, -12, -10, -9, -15, 2, -5, 21, 21, -5],\n [-13, -16, 21, -9, -8, -7, -21, 7, 7, -5],\n [8, 21, -10, -3, 12, 0, 19, 10, 15, 12],\n [13, -3, -20, -15, 17, 9, 6, -16, -21, -2],\n [-17, 5, 19, 13, 9, 22, 19, -14, -12, 0],\n [-12, -21, -20, -12, 12, -8, 20, -12, 8, 5],\n [5, 9, 2, -3, 5, 2, -12, -4, 5, -22],\n [-18, -13, 19, 11, 13, -21, -5, -10, -18, -3],\n [-21, -12, 7, 9, 9, 15, 5, -13, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 20, -4, -6, 1, 13, 9, 13, 5, -9],\n [13, -17, -14, -2, -11, 7, 8, 17, -19, 8],\n [4, 2, -18, -17, -18, 4, -15, -14, -8, 13],\n [18, -16, 9, -15, -8, 14, -4, 16, -17, -4],\n [5, -6, 19, -4, 8, -12, -8, -13, 20, 0],\n [-20, -20, -5, 2, 20, -3, 6, -1, -8, 16],\n [-13, -2, 6, 9, -13, -10, 0, 0, 8, -19],\n [-20, -2, -21, -19, -22, -8, 10, -17, -16, -4],\n [21, -22, 16, -4, 22, 3, 21, -11, -1, -10],\n [5, -9, -1, 7, 21, -3, 21, 4, 15, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[18, 11, 16, 18, 21, 14, -22, -8, 9, -15],\n [10, -5, 22, 6, 9, 10, -18, -5, -13, 13],\n [10, 0, 17, -18, 11, 1, -6, 8, -16, -6],\n [5, 15, -1, -8, 14, -8, 2, -2, 15, -21],\n [4, 9, -2, -19, 21, -4, -21, 3, 11, -9],\n [-8, -3, 11, 13, -4, -14, -16, 7, -10, 4],\n [21, 12, -10, -8, -14, 22, 0, 13, 17, -20],\n [11, -4, 5, 0, 17, 22, -16, 18, -11, -9],\n [-8, -20, -8, 1, -15, -18, -19, -9, -7, -3],\n [1, -17, 8, -17, 12, -8, 6, -20, -12, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -13, 10, -7, -13, 10, 13, -20, -18, -11],\n [21, -10, 1, 21, 9, -7, 9, 22, 14, 13],\n [-2, -11, -2, -2, 20, -17, -14, -22, -11, -9],\n [-17, -22, -1, 11, -12, -20, 19, -17, -17, -3],\n [-2, -21, 3, 8, 3, 9, -13, 0, -17, 0],\n [5, 7, -9, 14, 9, 11, 18, 21, -1, 8],\n [-16, 18, -2, -7, -3, 20, 21, -4, 9, -8],\n [-18, -12, -8, 6, 22, -19, 13, 0, -8, 21],\n [-20, 9, -13, 17, 15, -1, -9, -6, -2, -8],\n [-8, -22, 1, -11, -13, 19, 19, 8, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -9, -4, 8, -14, 13, 16, 3, -15, 1],\n [-15, -4, 7, -1, -14, 21, -19, 14, -15, -22],\n [5, -17, 13, -12, -18, 1, -5, -3, 5, -10],\n [-18, 7, -22, -1, -5, -18, 8, -17, 4, 2],\n [6, 5, -7, -11, -3, -5, 11, 0, 22, 4],\n [-6, -2, 17, 8, -20, -6, 3, 0, -17, 5],\n [-15, 22, -15, -4, 15, 6, 0, 9, -13, 4],\n [-22, 16, 6, 22, -20, 14, 8, -12, -1, -5],\n [12, -17, -20, -18, -14, 5, -4, 5, 4, -10],\n [15, 20, -2, 4, -17, 15, -12, 18, -6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-16, 7, -2, -22, 2, 9, -15, -18, 7, -15],\n [-4, 21, 7, -8, 13, 21, 4, -10, -9, 14],\n [7, 16, -10, -7, 21, -16, 4, 22, 12, -8],\n [5, 12, -16, -3, 9, 15, 17, 9, 3, 16],\n [-3, -5, -8, -1, -1, -2, -21, 17, 20, -5],\n [0, -10, 18, -14, -16, 18, -22, -21, -19, -9],\n [9, 13, -21, 17, -9, -3, 2, 19, -15, 5],\n [-2, 0, 9, -15, 8, 14, -7, 17, 19, 4],\n [17, 18, -5, 12, -8, 4, -6, 17, -21, 8],\n [14, 18, 18, 11, 11, -20, -6, -9, -9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[12, -22, 6, -19, 10, -6, 5, 3, -15, 11],\n [-5, 8, 4, -7, -13, 17, -11, -1, -7, -11],\n [-12, -3, -22, 4, -20, -11, 7, -14, 14, -22],\n [19, -19, -8, 4, -15, 0, -8, 4, 8, 16],\n [-15, 7, 19, -5, -19, 20, -1, -20, -8, 12],\n [15, 10, -9, -22, 3, -15, -7, 15, -13, 19],\n [14, 3, 5, -11, -3, -9, 12, 6, -11, -5],\n [21, -21, -21, -6, -13, -5, -1, -4, -22, 1],\n [13, 2, 13, 8, 8, -21, -4, -11, -13, 8],\n [22, -1, 0, 0, -8, 3, -20, 0, -3, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[17, 16, -15, -5, 18, -17, 4, 13, -8, 14],\n [-18, 16, -14, -16, 18, -3, -13, 3, -19, 15],\n [1, -9, 18, -22, -6, 22, 1, 4, -16, -14],\n [20, 12, -11, -2, -20, -8, -2, -13, 10, -17],\n [-21, 6, 17, 10, -19, -19, 6, 14, -3, 18],\n [0, 22, -5, 2, -22, -8, 11, -3, 14, 4],\n [-1, -18, 11, 16, -20, -6, 1, 1, -20, 22],\n [-16, 2, -20, -8, 6, 6, -13, 9, 0, 16],\n [-14, 14, 17, -9, -19, -3, 5, -9, 21, 11],\n [-10, 8, 10, 16, 5, 2, 9, -14, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 0, -10, -13, -7, -17, -12, -20, 5, 18],\n [-8, -10, 19, 22, -6, -16, 5, 15, -10, -6],\n [-8, 13, 5, -8, -12, 8, -19, 12, 11, 4],\n [-13, 7, 22, -3, 6, 6, 0, -2, 20, -13],\n [18, -11, 7, 10, -5, -9, -1, -2, -22, 20],\n [-8, 13, -1, 9, 10, 18, 16, 0, 20, -21],\n [-21, 15, 6, -20, 16, -16, 13, 6, 14, 13],\n [0, 22, -7, 8, 11, -22, -5, 17, 20, -8],\n [-6, 21, -13, -3, -17, -15, 22, 11, 9, 19],\n [-19, 21, 16, -3, 1, 1, 3, 2, 13, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-13, -11, -22, 2, -7, -18, -4, -19, -17, 3],\n [16, 16, -14, 22, -9, -14, -8, 14, -3, -15],\n [9, -2, 18, -4, 6, 8, -17, -19, 20, 6],\n [19, -20, -22, 21, -8, -2, 8, -16, -6, -4],\n [16, -20, 7, 12, 6, -9, 12, 5, 7, 3],\n [-16, 16, 8, -18, 12, -9, 13, 4, 1, 17],\n [6, 22, -1, -15, -8, -18, -19, -12, -5, 19],\n [7, -8, -17, -7, 17, -14, 20, 11, 4, -10],\n [13, 4, -14, -18, -1, 8, -20, 7, -2, 12],\n [-17, 5, 9, 19, 14, 2, 9, 12, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[16, 7, 9, 8, 0, 17, 10, 2, 13, 1],\n [8, 16, -10, -13, 0, -5, 9, 10, 13, 5],\n [-7, -7, -5, -15, 19, -7, -12, -17, -22, -11],\n [15, 5, 22, -6, -22, 9, -15, 17, 20, 1],\n [-13, 16, 16, -13, 13, 2, -13, -4, 22, -8],\n [-7, -21, 6, -19, 6, 8, -6, -13, 4, 18],\n [-8, 21, 8, -2, 18, 22, 3, 15, 13, -6],\n [-20, -9, -10, 18, 4, -22, -6, 11, -9, -6],\n [-20, 11, 17, 2, -21, 11, 3, 8, -14, 7],\n [-3, -2, 6, 2, 15, 21, 2, -14, 16, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, 14, -7, 14, -11, 1, 3, -3, -14, 0],\n [16, 6, 8, -4, -3, 0, 20, 4, 7, -2],\n [21, 12, -16, -1, -13, 0, -8, 7, 11, -10],\n [-19, -5, 0, 10, 11, 11, 13, 12, -6, 5],\n [-9, 11, -12, -10, 10, -21, 11, 6, 14, -19],\n [-11, 3, 5, -20, -3, -13, -5, 4, 8, 4],\n [19, -22, -17, -12, 11, 16, -3, -2, -2, -5],\n [-2, -4, -19, -10, -5, 6, 2, -10, 4, -4],\n [-22, 15, -4, -22, 17, -6, -2, -1, -8, 16],\n [16, 9, -19, 21, 22, 9, -19, -22, 10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-14, -22, -7, -5, -17, -21, -14, -19, 22, 0],\n [20, 22, 20, -15, 16, 2, -7, 12, -6, -5],\n [4, -8, -6, 20, -18, -7, -8, 19, 11, -4],\n [-15, -13, -18, 3, -1, 21, 0, -10, -14, -3],\n [5, 21, 14, 1, 21, 10, -3, 7, 21, -14],\n [22, -6, 13, -9, -4, -16, -20, 10, 21, 9],\n [-12, 19, -21, 3, -19, -6, -6, 5, 7, 17],\n [0, 1, 6, -19, 15, 6, -4, 4, 6, 13],\n [12, -17, 0, 16, 21, -15, -21, -10, 17, -2],\n [8, 13, 15, 4, 13, 0, -2, -10, 14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[17, -16, 16, -1, 16, 0, 7, -5, 19, -5],\n [-13, 16, 7, 3, -16, -16, -18, -22, -5, -10],\n [2, 17, -15, -13, 9, -6, 15, -8, -8, 17],\n [-3, -8, 12, -17, 7, -15, 8, 9, 22, -8],\n [-5, -10, 1, 17, -9, 5, -12, -17, 2, -22],\n [2, -21, 9, -10, 10, 9, 1, 4, -19, 1],\n [0, 6, 11, -2, 7, 3, -3, -7, -20, 14],\n [17, 21, 2, 0, 21, -22, 10, -8, -6, 11],\n [-6, 18, 21, -19, -10, -19, -16, -14, 0, 10],\n [10, -3, -19, -22, 19, 11, 4, -2, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[12, 2, -14, -6, -2, -10, -20, -19, -19, 20],\n [5, -16, 3, -12, 1, 20, -13, 14, -10, 21],\n [19, 16, -4, -4, -11, -1, 14, 7, -11, 6],\n [-2, -12, 14, -5, 21, 4, 14, -11, 0, 11],\n [15, 0, 2, -19, 7, 7, -10, 19, -9, -15],\n [1, -5, 12, 2, -6, 9, 1, -16, -10, 4],\n [-18, 13, 3, 19, 22, 8, -13, 3, -1, -11],\n [9, 4, 10, -3, 16, 18, 17, -10, -9, 21],\n [17, -1, -5, 6, 20, -7, 12, 11, -20, -19],\n [-18, -13, 6, 9, 8, -21, -11, 4, -18, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"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, 10, -19, -2, 1, 21, 8, 21, 1],\n [-13, -21, 8, 2, -19, -12, -6, 21, -21, -17],\n [-14, -18, -3, 6, -2, -14, 5, -15, 8, -3],\n [4, -15, -2, 5, 0, -17, -20, -18, -14, -16],\n [-19, 16, -18, -12, -8, 11, -10, -16, 17, -17],\n [16, 7, -1, 2, 5, -3, 16, -20, -18, -22],\n [-8, 3, -20, 17, 18, 19, 11, -18, 8, -10],\n [20, -22, -1, -8, 3, -5, -14, -22, 20, -14],\n [0, 20, 22, -21, -9, 15, 17, -5, -7, 6],\n [21, -12, -17, -20, -9, -21, 9, 8, -12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-20, 8, 10, 1, -22, 21, -8, 14, 4, 15],\n [4, 21, -11, -20, 7, 9, 0, -21, -16, 11],\n [9, 16, 9, 20, 20, -9, -20, 9, 20, 13],\n [-6, -20, -13, 17, -5, -20, 16, -13, -14, -12],\n [10, 13, 3, 4, 15, -1, 3, -1, -18, 12],\n [-21, 12, -14, -5, 20, -11, -20, -5, 15, -16],\n [10, -17, -5, 22, -1, 16, -14, 12, 0, -11],\n [1, 17, -14, -10, 17, 19, -6, -16, -6, 1],\n [-21, 12, 5, -4, 10, -2, -13, 22, -14, 15],\n [-17, 19, 12, -5, -4, -18, 2, -12, -13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[13, 3, 8, 9, -2, -5, -5, -22, -9, -15],\n [-21, -8, 11, 13, -22, -2, 19, -22, 9, -3],\n [13, 16, 7, -16, -1, 22, -13, -15, 4, -13],\n [-9, -12, -17, -2, 10, -4, 16, 1, -5, 12],\n [20, 14, -4, 1, 11, -1, -19, -13, -21, -15],\n [10, 15, 20, 5, -13, 22, -22, 11, -20, -14],\n [-18, 19, -13, -11, -5, -2, -2, -22, -20, -18],\n [2, -15, -6, -14, 9, -17, 17, -2, -16, -16],\n [16, 4, -15, -14, 5, -8, -21, -16, -5, -1],\n [-13, 10, -16, -20, -9, 21, 13, -10, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-18, 2, 15, 15, 15, 16, 18, 3, -10, 21],\n [3, -22, -15, -19, -2, -1, 14, -20, -4, -22],\n [6, 0, 10, 18, 0, -18, -16, -17, -1, -10],\n [-11, -19, -15, 14, 8, 14, 22, 3, 20, -15],\n [17, 10, 22, 6, -18, 5, 17, -6, 0, 22],\n [-14, -21, 9, 8, -16, 7, -20, -14, -13, 3],\n [-22, 7, 15, -8, 2, -17, -5, -22, -20, -6],\n [-15, 17, -6, 2, 18, -11, 6, 2, 13, 2],\n [6, -12, -19, -9, 15, -6, -21, -15, 13, -13],\n [-16, 13, -7, -9, -7, 2, 18, -19, 6, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-22, 16, -22, 17, -20, -22, -22, 16, -2, 22],\n [7, 9, 10, -1, 7, -19, 0, 21, 2, -11],\n [-6, -8, -13, 12, 6, -11, -22, -22, -13, -5],\n [-21, -15, -1, -1, 3, 3, -14, -2, 8, 20],\n [-17, -9, 10, -16, 1, -14, -12, 0, -21, -8],\n [12, 13, 5, 16, 21, -19, -13, -17, 7, 12],\n [20, -13, 9, 19, 19, -20, 3, -8, -6, 4],\n [-5, -4, -11, 1, -18, 1, 4, 7, -8, 15],\n [21, 11, 4, -3, 18, 9, -19, -18, -15, -1],\n [19, -16, -1, 7, 14, -7, -8, -18, -20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-13, -18, 0, -8, -5, 2, -15, 8, -2, -21],\n [-1, -15, 0, 9, -15, -19, 7, -4, 0, -5],\n [6, 0, 10, -5, 21, 10, -16, 5, -22, 16],\n [11, 16, -4, 8, -10, 1, -18, 0, -4, -22],\n [10, 10, 9, 5, 14, 18, -11, -14, -12, 10],\n [-4, 19, 11, -16, 8, -21, -4, 15, 9, -13],\n [18, -15, 3, 7, -12, 18, -3, -3, -14, -15],\n [-8, 11, 1, 10, 18, 18, 22, 17, 4, -2],\n [-18, 12, -2, -19, -7, 8, 3, 12, -17, 10],\n [-2, -7, 16, 11, 19, -8, -17, -21, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-22, -22, 5, 13, -3, -15, -22, 3, 20, 2],\n [-13, -11, 18, -16, -11, 17, -6, -18, -9, 11],\n [-6, 12, -22, 13, -8, -4, 19, -18, -4, 20],\n [16, -18, -11, -4, -11, 13, -11, -5, 20, 11],\n [10, -5, 6, 22, -18, 2, 1, 6, 15, 10],\n [-13, 14, 10, 0, -12, 1, 1, -16, -2, -3],\n [-13, 2, 13, -8, 21, 17, 17, -17, 14, -21],\n [-11, -19, 0, -10, -6, 8, -7, 18, 3, 5],\n [-22, -11, 14, -3, -21, 13, -8, 15, -1, 21],\n [9, -3, 13, 10, -8, -20, 6, 4, -18, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, 12, -16, -17, 3, -22, -4, -16, 13, -11],\n [-3, 0, 2, 7, 6, 8, -5, 18, -4, -19],\n [-22, 18, -8, -15, -8, -8, 16, -1, -5, -7],\n [-21, 13, -3, -7, -20, 7, -21, 12, 3, -18],\n [-21, -3, 11, 11, -3, 2, -3, 2, -9, 21],\n [20, 20, 16, -11, -18, -21, -7, 7, 20, 15],\n [22, 19, 1, 7, 14, 16, -12, -9, 0, -7],\n [-2, -19, 10, -9, -4, -18, 13, 8, 22, -5],\n [21, 8, 7, -2, 7, 18, -19, -18, 18, 22],\n [-13, 4, -7, 7, -10, 13, -2, 22, 17, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-8, -3, -3, 22, -18, 9, -17, 7, 3, 14],\n [-10, 6, -18, 2, -10, 1, 8, -3, -15, -14],\n [-2, -3, -8, 3, 19, -12, 14, 18, -12, 4],\n [7, -4, 11, 15, 0, -22, -20, -20, 5, -9],\n [7, -18, -8, 15, -9, -9, -15, -15, -4, 9],\n [8, 6, 18, -12, 22, -10, 4, -4, 3, 14],\n [-14, 5, 9, -20, 9, -18, -15, -9, -20, 1],\n [-10, 20, 6, -15, 19, 8, 3, -5, -5, -16],\n [15, -7, 10, -20, 15, -19, 13, -19, 19, -14],\n [17, -6, -6, 10, -3, -9, -1, 4, 20, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, 7, -15, -1, 2, -13, 6, 17, -22, -2],\n [16, 1, -14, 21, 3, -14, -3, 12, 13, 19],\n [13, -14, -1, -22, -18, -14, 14, 15, -4, -15],\n [19, 20, 9, -10, -3, 13, 20, 21, 14, 7],\n [-13, 8, 2, 6, 1, 16, -2, 18, -14, 19],\n [19, -21, -19, -15, 9, -9, -10, -2, 1, -5],\n [22, 17, 3, 9, 21, 10, 8, -5, 12, -11],\n [2, 22, 8, -13, 11, -20, 16, -15, 9, 20],\n [6, -1, -3, -17, 20, 6, 19, -6, 8, 11],\n [15, 14, -19, -21, -11, 12, -17, -15, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "377", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-8, -16, -8, 22, -17, -6, -19, -1, 9, -1],\n [4, -8, 21, -1, 5, 19, 15, -14, 11, 13],\n [-14, -8, 22, -3, -15, 5, -4, -7, -12, 19],\n [-15, 10, -13, -5, 12, 20, -20, 17, 4, 5],\n [-17, -9, -16, -13, -8, 8, 6, 19, -6, 6],\n [21, -8, 3, -11, 2, 18, -18, -19, 21, 18],\n [8, -20, -20, 3, -6, -13, -21, 1, -12, 1],\n [12, 0, 9, 0, 11, 18, -4, -21, -21, -8],\n [-2, 12, -18, 20, 4, 1, -16, -17, 10, -6],\n [19, 7, -15, 17, -16, -17, -19, -22, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 10, 12, -18, -18, 13, -6, -9, 6, -15],\n [11, 17, -22, 6, 13, 14, 6, -18, 9, 1],\n [-4, -11, -22, -16, -6, 11, 20, -16, -6, -20],\n [6, -1, 15, 20, 6, 19, -18, 7, 0, -2],\n [3, -2, -3, 0, -19, -2, -2, -22, -8, -6],\n [-9, -4, 11, -17, 22, -17, -18, -16, 10, -10],\n [-22, -10, 20, 4, -16, -20, 2, 10, 17, -6],\n [22, -9, 14, 0, 1, 6, 15, 4, 15, 17],\n [22, 0, 8, 13, -6, 14, -20, 13, -18, -8],\n [-17, -13, 9, 0, -6, -3, 21, 18, -8, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -17, -19, 0, 21, 22, -4, 22, 8, 21],\n [-20, 5, -20, -9, -5, 4, -13, -8, -4, -14],\n [-19, -8, -15, -22, -16, 8, -5, -11, 7, 10],\n [-16, 5, -20, 20, -17, 8, 15, -8, -16, 20],\n [7, 4, -6, -5, -1, 3, 4, 17, 1, -15],\n [-2, 6, 20, -2, -20, 8, 4, 4, -14, 10],\n [10, 3, 5, 21, 20, 8, -22, -3, -11, -6],\n [-8, 11, -7, -19, -15, 11, 2, -8, 5, -14],\n [-21, -6, -13, -14, 8, -21, 1, -4, -6, 20],\n [-13, 5, 15, 5, -22, -20, -8, -13, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-8, 0, -9, -8, -13, -14, 21, 16, -18, 2],\n [19, 3, -15, -1, 2, -11, -14, -13, -13, -14],\n [3, 12, 4, 8, -4, 20, 15, -17, -8, 6],\n [22, -18, -9, -21, 0, 21, -4, 1, -3, 4],\n [1, -6, 2, 8, 5, 5, -1, -18, 21, 19],\n [-15, 15, 5, -11, 2, 15, 21, -8, 21, 18],\n [11, 22, -10, -15, -10, 13, -17, 15, 9, -2],\n [21, 21, -16, 3, -8, 19, 0, 15, 18, -8],\n [17, -7, 9, 14, -5, -3, -21, 0, 7, -20],\n [16, -22, 18, -1, 6, -9, 5, -2, 22, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-17, -22, -2, -19, -20, 7, 8, 11, -4, -3],\n [0, 17, 2, -8, 15, 0, -21, -8, 21, 12],\n [-13, -9, 4, -9, 12, 10, -22, 11, -4, 1],\n [19, -19, 13, -10, 9, -14, 16, -7, -20, -3],\n [-13, -1, -20, -12, 2, 19, -15, -14, -8, 9],\n [-20, -19, 7, -10, 21, -2, 18, -4, 16, -1],\n [-3, 14, 8, -13, -5, 20, 16, -3, -5, -12],\n [-1, 21, -5, 11, 0, -22, -13, -22, 15, 16],\n [-14, 8, -16, -6, 12, 14, -5, 10, -19, 0],\n [-12, -14, 7, -15, 17, -18, -11, -22, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "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, 15, 19, 3, 17, -20, -1, 3, -4, 21],\n [21, 16, 13, -2, 18, 3, -10, 13, 1, 18],\n [3, -2, -5, -8, -8, -17, 20, 8, 5, -15],\n [6, -2, -6, 1, 13, 8, 11, -21, 19, -20],\n [7, -15, -16, -11, -4, 3, 5, -8, -9, -9],\n [-20, 6, -17, 0, 5, -9, -9, -3, -10, 4],\n [12, 22, -21, 18, 22, 17, 1, 6, -20, 22],\n [-19, -21, -3, -8, 9, 19, -22, 15, 12, -16],\n [22, -10, -22, -9, 6, -20, 1, -22, -13, -10],\n [13, -14, -9, 13, -13, 17, 0, 12, -16, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[12, -21, -8, -14, -6, 16, -5, -8, -5, 1],\n [0, -11, 0, -2, 3, -15, 7, 11, -21, -18],\n [8, 10, -19, -17, 0, 22, -4, 20, 22, -15],\n [16, -10, -22, -17, -16, 4, -8, 11, 0, 1],\n [-8, 12, -19, 21, 14, -6, 8, 15, -13, 4],\n [19, -17, -17, -8, -19, 17, -16, 22, 3, 8],\n [-21, 5, 19, -10, -5, 7, -12, -10, 1, 6],\n [-18, 12, -4, -10, -18, 21, -9, 15, -1, -14],\n [17, 3, 22, -18, 6, -1, -20, 5, 15, -9],\n [-9, 20, -12, -14, 15, 21, -17, -22, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-8, 11, -6, -20, -20, 14, -6, 15, -22, -16],\n [3, 16, -4, 7, 20, -9, -10, -3, 3, 4],\n [2, -14, 18, -11, -13, -17, 11, 18, -4, -17],\n [-21, -8, -6, -7, 5, -2, -15, -13, -13, -13],\n [-14, 5, 1, -4, 10, -19, -20, 19, -11, -5],\n [0, -3, -17, 11, 19, -21, 7, -14, 4, 19],\n [11, 17, 1, -6, 6, 13, -11, 8, -14, -4],\n [-6, -21, 17, -18, 16, -7, -6, 4, -16, -15],\n [-15, 0, 9, 20, -5, 15, -11, -8, 5, 15],\n [8, -14, -15, -4, -15, 11, -19, 8, 15, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[12, -4, 20, 6, -13, -11, 7, 7, -5, 1],\n [9, -14, 1, 3, -20, 0, -12, -13, 13, -10],\n [6, 15, -10, 3, -3, -18, -3, -9, 22, -9],\n [-15, -10, 1, -8, -22, -1, 11, 17, -20, 3],\n [-9, 18, -15, -7, 19, -2, -13, 2, 15, -1],\n [-19, -19, 7, -21, 6, 20, 13, -2, -2, -2],\n [-19, -22, 3, -21, -14, 22, -5, 19, 18, -12],\n [2, 3, 13, 19, 12, 15, -20, 18, 12, 17],\n [-1, -15, -8, 22, -16, -4, 17, 19, -6, -22],\n [22, 6, -10, 6, 18, 19, -17, -18, 11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-14, 15, 17, 18, -14, -15, 21, 17, -20, -10],\n [-4, 11, 9, -7, 13, -5, -9, 7, -21, -10],\n [4, -6, 8, -8, -3, -18, -16, -5, -12, 9],\n [4, 3, 14, 22, 5, -21, -3, -19, -10, 1],\n [15, 17, 22, 6, 13, -21, 18, -5, -15, -8],\n [18, -6, 0, -21, -17, 6, 4, 14, 11, -5],\n [19, -13, 15, 21, -6, -10, 19, 4, -21, 11],\n [8, 0, -16, 15, 10, -11, 22, -11, -4, -14],\n [-13, -6, 17, 16, 18, -13, -11, -8, 8, -8],\n [5, -19, 13, -22, 21, 11, -6, 16, 15, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[10, -2, 3, 13, -18, 10, -22, -17, 14, -21],\n [-18, 3, 18, -10, -11, -18, -21, -19, 4, -13],\n [-10, 21, -21, 3, -8, -13, -1, 17, 2, -8],\n [-10, -15, -2, -2, -1, 10, 22, 4, 17, -1],\n [7, -14, 22, 12, -5, 19, -18, 4, -17, 9],\n [-15, 16, -2, -5, -9, -8, 19, 3, 21, 9],\n [16, 5, 16, 20, 9, -10, -8, -5, 16, -17],\n [-12, 9, 17, -3, 10, 17, -15, 12, -18, 12],\n [-9, -2, 1, -6, -5, 11, -11, -7, -19, 2],\n [11, 5, -12, -10, 8, 2, 16, -13, 1, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, 5, 13, -5, -17, -21, -20, -15, 8, -4],\n [-17, -9, -20, -22, 21, 7, -4, -4, -14, -16],\n [14, 18, -16, -14, -19, 2, -11, -17, -5, 17],\n [-2, -8, -20, -21, 18, 17, -19, 9, -21, 6],\n [-21, 11, 4, 16, 21, 15, -5, 13, -4, 4],\n [22, -3, -2, 0, 7, 2, 8, 4, 11, -15],\n [-4, 18, 3, 5, -19, 8, -7, -13, 15, -13],\n [22, -14, 16, 13, 13, -4, -4, -11, -10, 2],\n [13, 2, 5, 19, 16, 7, -18, -6, -5, 20],\n [-2, -1, 16, -17, -7, -21, -22, 7, 20, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, -22, -4, -20, -21, 14, -6, 5, -5, 10],\n [-8, -1, 18, 4, 14, 9, 22, -4, 5, 5],\n [-13, -3, 2, -2, -9, -1, 3, 21, -12, -16],\n [-6, -5, -16, -3, 15, -12, 21, -7, 4, -12],\n [-7, 0, -11, 17, -20, -21, 15, 1, 6, 11],\n [-3, -5, -9, -5, -21, -22, -3, 11, 18, 18],\n [-12, 4, 0, 15, 21, -20, -11, 7, 8, 0],\n [-22, 18, -3, -17, -12, 12, -19, 6, -13, 6],\n [15, -22, 17, -15, 15, -6, -4, 10, -8, 22],\n [8, -2, -20, -21, 12, 18, -7, 22, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -11, 10, -3, 17, -2, 16, 18, 19, 13],\n [-1, 3, -16, -16, -15, 3, 1, 1, 17, -11],\n [-15, -14, -20, -2, 8, 1, -19, -3, -7, -13],\n [20, 3, 6, -18, -12, 6, 22, -8, -17, -8],\n [20, -3, 11, -21, 21, -7, -4, 11, -9, 1],\n [5, 9, 14, -13, 22, -14, 1, 13, 6, 6],\n [0, 4, 8, 20, -16, 22, -19, -9, 19, 19],\n [-13, 21, 11, 3, 0, -14, 14, -15, -9, -16],\n [-16, -14, -20, -9, -6, 21, -1, 3, 5, 22],\n [-9, -14, 3, -21, -12, -6, 11, -4, 16, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-10, -18, 0, 1, 6, -15, 3, -8, -22, 5],\n [-9, 19, 11, 8, -17, -18, 8, 14, -8, -8],\n [20, -18, 5, 10, -12, 20, -17, 0, 17, -21],\n [-8, 0, -1, -14, 17, 7, -7, 7, 22, -14],\n [-22, 15, -15, -5, 4, -5, 9, 9, 22, 13],\n [13, -2, 9, 8, 14, -7, -9, 1, 2, 12],\n [-6, 19, 22, -19, -12, -8, 7, 1, -21, 20],\n [11, 0, 8, 14, -10, 10, -16, 9, -16, 19],\n [15, 21, -10, 1, 5, 9, 20, -5, 11, 11],\n [15, -22, 20, 19, 8, -22, -7, 16, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 18, 11, -6, 2, 19, -17, 8, -18, 17],\n [17, 7, -18, -11, -16, 22, -10, -19, 19, -20],\n [-11, -22, 4, 20, -10, -6, -15, 9, -3, -6],\n [11, 12, 12, 15, 19, 1, -5, 16, 10, 0],\n [2, 14, 4, -22, -2, -13, 8, 21, 2, -3],\n [-21, -8, 5, -10, -9, -21, 11, 12, 14, 2],\n [-8, -11, -14, 8, -9, 6, 20, 15, 19, -15],\n [-20, -21, -7, -4, 7, 18, -7, 8, 5, -19],\n [-13, 22, -5, 9, 7, 13, -14, 13, 6, -7],\n [5, -2, -21, 12, 5, 13, 8, 10, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"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, -22, 19, 0, 4, 2, 9, -4, 1, -20],\n [-11, 12, -8, -6, 9, -16, -4, -16, -18, 17],\n [-2, -16, 14, 0, -12, -13, -2, 18, 10, -3],\n [10, 17, 12, 11, 13, 4, -4, 20, -18, 6],\n [-13, 17, -10, 6, -18, -11, -10, -1, 17, -8],\n [-10, -22, 15, 20, 22, -22, -12, 20, 17, -1],\n [12, 21, -17, 5, 8, -15, -18, 19, 21, -6],\n [15, -14, -13, -3, -9, -9, 3, 6, 4, 2],\n [-7, 13, 11, -7, 10, -20, 0, -12, -5, 18],\n [21, 6, -18, 1, 6, 6, 3, 17, -20, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -4, 17, -21, -4, -22, 4, 22, 12, 18],\n [-18, 15, -19, -6, -2, 8, -1, -12, 11, -8],\n [-13, 15, 9, 8, 14, 21, 5, 8, -17, -9],\n [0, -7, 2, 16, -21, 15, 18, 16, 11, 17],\n [20, 2, 13, -7, -5, -10, 14, 4, 11, -12],\n [-22, -10, 7, -18, -5, -9, -10, 9, -16, -15],\n [-16, -7, 20, 8, 4, 10, 6, -15, 10, 18],\n [-4, -2, 18, -2, 2, 19, 0, -12, 10, -3],\n [2, 3, 17, -11, 9, 10, -13, -19, -8, -17],\n [4, -18, -18, -5, 5, 12, -1, 11, -19, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[18, 3, 19, -1, 10, 20, -9, 8, -13, 1],\n [-2, -15, 9, 8, 11, 0, 2, -16, -4, -16],\n [-15, -9, -22, -10, -20, 5, 15, -8, 13, -20],\n [-19, -18, 3, 2, -13, -15, -11, -20, 4, 0],\n [17, 10, -9, 0, 8, -10, -11, 12, -5, -2],\n [22, 19, -22, 15, 18, 19, -14, 0, -9, -12],\n [-16, 8, 1, 3, 7, 11, 15, -18, -18, -4],\n [15, 5, 3, 19, 0, 7, -20, 5, 10, 19],\n [-20, -18, -4, 19, -22, 15, -14, -18, 19, 11],\n [14, 10, 2, 19, 6, 2, -14, -20, -8, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[22, 15, -3, 0, 14, -15, 14, 22, 10, 10],\n [-16, -1, -18, -8, -2, 2, -6, -16, -4, -16],\n [17, 22, 1, -12, 18, -22, 9, 17, 21, -21],\n [-8, -2, 1, -6, -14, 12, -3, -4, -5, -3],\n [7, 17, -22, 1, 1, -4, 7, 3, 19, 21],\n [15, 6, -10, -19, 22, -6, 10, -18, 5, 1],\n [-6, 16, 17, 21, -12, -11, -10, -15, -22, -14],\n [5, -21, -9, -10, -21, -19, -11, -13, -20, -19],\n [-17, 0, -18, -20, -13, 20, -4, -9, -2, 20],\n [5, -2, 13, 1, 15, -6, -1, -4, 22, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-12, 15, -21, 10, 20, 8, 12, 14, 13, 0],\n [13, 17, 16, 3, 2, -6, -8, 14, 22, -19],\n [-1, -6, -1, -6, -9, -9, -6, -15, 11, 3],\n [22, 7, -1, -7, 7, -7, 15, 1, 13, 12],\n [-17, -19, -5, -17, 3, 14, 4, 18, -12, 15],\n [-7, -4, 20, -8, 3, 18, 8, -4, 1, -14],\n [0, -19, -13, -14, -4, -8, 11, 19, -4, -2],\n [11, -6, -5, -6, -21, -22, 20, -13, 14, -18],\n [-11, 13, 8, 15, -14, 21, 3, -8, -7, -10],\n [2, 7, -16, -19, 20, 17, 15, 7, -13, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[16, -16, 13, 12, 1, 16, 13, 22, -3, 9],\n [16, 3, 3, 13, 20, 12, 20, 12, -11, 10],\n [13, -9, 10, 22, 22, 1, -8, 8, -6, -11],\n [-1, 0, 3, -9, -11, -19, -10, -5, 20, 5],\n [15, 18, 21, -4, 20, 15, -20, -4, -3, 2],\n [-12, -6, 12, -9, 16, -4, -20, 11, 18, -1],\n [15, 4, -2, 18, 8, 4, 14, -21, -14, -4],\n [19, 13, -13, 17, 22, 16, -16, -19, -8, -11],\n [-17, -14, 12, -15, -16, -19, -10, -4, -16, -13],\n [2, 21, 12, 2, 6, -11, 17, -11, -17, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-21, 22, 2, -16, 17, 0, -12, 13, 0, 20],\n [-16, 4, -10, -6, 9, 3, -1, -10, -11, -16],\n [-22, 10, -9, 20, 18, -6, -19, 16, -22, 18],\n [22, 1, 11, 11, 1, -8, -6, -10, -16, -14],\n [21, 12, 0, 16, 0, 3, -22, -9, 9, -13],\n [-22, -18, -20, 4, -1, -5, -7, -21, -10, 22],\n [-7, -15, 20, -15, -13, 10, 8, -11, -14, 14],\n [-14, -5, 7, 9, 17, 0, -12, -3, -4, 13],\n [3, -13, 1, -10, 11, 6, 13, -16, 7, -6],\n [-10, 1, 8, 4, -2, 21, -22, -8, -20, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, 15, 10, 15, -15, 3, -8, -9, -3, -4],\n [10, 13, 1, -13, 11, 13, 13, -7, -8, -5],\n [-16, -1, 9, 20, -4, 17, -22, 12, -18, -11],\n [-11, -2, -4, -14, 20, 13, 19, 9, 12, 8],\n [9, 14, 9, 20, 14, 16, 15, 7, 9, 22],\n [-21, -12, -3, 14, -14, 15, -4, 17, -16, -18],\n [19, 1, 18, -16, -12, -14, 7, 18, -20, -1],\n [17, -3, 9, -16, -16, -3, 2, 22, 12, 21],\n [1, 17, -10, 16, -19, -11, -6, -22, -6, -21],\n [-17, 21, -12, 20, -5, 17, 2, 16, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-11, 18, 6, 0, -2, -7, 18, 22, 3, 14],\n [-1, -13, -16, -14, 2, -8, -10, 19, 3, -2],\n [0, 21, 5, 15, -11, 1, -10, 17, -21, 16],\n [-11, 16, -9, 7, 18, 20, -4, 8, 20, 20],\n [2, -19, -10, 13, 19, 14, -20, -7, 3, 17],\n [16, -4, -8, 9, -2, -22, -17, 4, 0, 8],\n [-11, -2, -21, -18, -14, -3, -5, -1, -15, 11],\n [-14, -16, 7, -5, 4, -7, -2, -18, 6, 14],\n [20, -1, -9, -4, 12, 1, 19, -17, -20, 11],\n [22, -21, -8, 14, -8, 9, -2, -6, 11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"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, 12, 14, 20, 18, 14, 10, 2, 14, 17],\n [-2, 15, 17, 11, -4, 4, -14, -18, -18, 2],\n [3, -4, 7, 13, -7, -16, -5, -2, 8, -22],\n [-20, 8, 2, -15, -22, -16, -16, -15, -4, -6],\n [-12, 18, -12, 15, 18, -21, -19, 5, 10, -12],\n [-20, 17, -18, -2, -1, 14, -12, 21, -1, 18],\n [-10, -20, -10, 5, -12, -12, -2, -2, -16, -6],\n [-9, 10, -12, -10, -22, 11, -14, -10, 14, 7],\n [18, 22, 14, -16, -9, -17, 11, -7, 14, 13],\n [-17, -15, 1, -20, -19, 9, -22, 11, 22, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-11, -13, -13, 21, 0, -17, 1, 1, -2, 19],\n [8, 18, 7, 11, -5, -11, 12, -16, 18, 17],\n [2, -17, -22, -7, -19, 6, 15, 5, -1, -15],\n [9, 10, -10, 4, -5, -5, -10, -1, -9, -12],\n [16, -1, 13, -6, 9, -9, 19, 6, -17, -19],\n [-12, 22, 17, -13, 5, -12, 12, -8, -15, -3],\n [-2, -22, 6, 1, 7, 17, 12, 10, -3, -7],\n [-14, 8, -6, 8, 0, -17, 7, -16, 17, 19],\n [-12, 11, -11, 22, 4, -11, -10, -15, -7, 6],\n [12, 6, 8, -10, -11, -21, 10, -15, 18, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[18, 9, 15, 5, -8, 0, 1, -10, -2, -11],\n [-10, 16, 0, 20, 5, -9, -6, 1, 11, -1],\n [-13, -15, -2, 14, -16, 3, -10, -7, 7, 8],\n [-18, 9, -7, -14, -1, 21, 17, 22, 14, -9],\n [-7, 20, -3, 21, -8, 21, 3, -14, -22, 12],\n [21, -3, 22, -17, 19, -13, 10, -7, 13, -17],\n [-4, 8, -21, -5, 19, 5, -19, -22, 19, -7],\n [22, -21, 13, -22, 16, 0, 3, -12, 19, -22],\n [-12, 1, -13, -9, -9, -16, 0, 20, -1, 13],\n [4, -21, 16, -4, -16, -11, -20, -18, -15, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[13, -16, -16, 9, -15, -11, -13, -9, -14, 15],\n [7, -18, -22, -22, -3, -12, 3, 21, -20, -17],\n [20, 22, -12, -15, 6, -13, 11, 1, -6, 9],\n [-12, 11, 1, -18, 6, 11, -7, 2, 14, -15],\n [6, 2, 19, 0, 11, -20, 7, 11, 9, 6],\n [-14, -21, 16, -16, -18, -15, 9, -5, 15, -5],\n [18, 22, -7, -2, -13, 19, -19, 21, -15, -4],\n [17, 17, -14, 7, -6, 17, 21, -8, -19, -17],\n [-7, 3, 14, 0, -10, -6, 4, -1, 14, -4],\n [16, 12, -10, -9, 8, 22, -21, 16, 14, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-14, -13, -16, 5, 2, 5, -21, -6, -19, -10],\n [-5, -20, 14, 10, 18, 1, -15, 12, -21, 10],\n [-11, -1, -10, -13, -6, 20, -18, -14, -10, 0],\n [7, 20, -19, -2, 20, -14, -16, -7, 0, 0],\n [8, -18, -17, -22, 5, -5, 1, -10, 10, -13],\n [-16, 14, 9, 22, -1, -7, 1, -9, -12, -4],\n [0, 11, 17, -10, 16, 21, 5, 17, -7, 5],\n [-19, 5, -11, -7, 13, -3, 3, 3, -1, -14],\n [-18, -6, 11, -21, -16, 13, -10, -3, 7, 7],\n [-12, 8, -20, -21, -20, -8, -6, -16, -18, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[10, 22, -7, 14, -20, 20, -2, 18, -15, -1],\n [-18, -6, 14, -9, 16, 18, 5, 8, -6, 12],\n [17, -1, 22, 6, -13, -5, 12, 21, -7, -16],\n [7, -4, 0, -15, -6, -2, 3, 5, 16, 10],\n [17, -4, 6, -3, -3, -13, -11, 10, 2, 2],\n [-19, -19, -14, -8, 3, -8, 3, 5, -16, 9],\n [-11, 12, 9, -14, -9, -10, 21, 10, 9, -4],\n [7, -7, -11, -13, -21, -5, -10, 6, 1, 15],\n [-11, 6, -1, 13, -22, 20, 17, 11, 11, 10],\n [-19, 15, 7, -3, 3, -8, -16, -16, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[11, -3, -8, 10, -6, -3, -10, 21, 1, 14],\n [-16, -15, 0, -9, -19, -2, -13, -1, 7, 7],\n [-7, -12, -1, 6, 2, -9, -9, -21, -10, -20],\n [7, -5, 13, -2, -4, -7, 5, -19, -8, -22],\n [-7, -3, 10, -6, -18, -18, 16, -10, 21, 13],\n [7, -19, 0, -2, -2, -17, 1, 8, -4, 15],\n [-11, -9, -11, -8, -4, 5, 17, 18, -18, -18],\n [-17, 0, -20, 14, 10, 20, -2, -3, -22, 16],\n [-6, 6, -15, 3, 5, 11, 3, -10, 21, 14],\n [-10, 15, 2, 0, -1, -2, 7, -12, -19, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-11, -14, 9, -12, 14, 1, -16, -15, 10, 2],\n [-22, -20, 17, 5, 20, 10, -22, 15, 4, 15],\n [12, -13, -11, -13, 11, 1, 5, -1, 22, -7],\n [-10, 13, 13, 20, 0, -9, 9, -20, 4, -4],\n [-1, -22, -18, 10, -4, 13, -17, -8, 13, 10],\n [1, 4, -12, 0, 10, 18, 6, 8, -22, 11],\n [-5, -5, -17, 17, -22, 19, 7, -19, 9, -13],\n [20, -18, -14, -18, -12, 12, 4, -19, -13, 16],\n [10, 15, -15, 1, 16, 10, 18, 20, -4, -21],\n [-12, 12, -6, 19, -20, -1, 12, -2, 2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-21, -22, -16, -3, 20, -17, 13, -2, 12, 13],\n [-15, -19, 20, -7, -20, -16, -21, -22, -22, 15],\n [-16, 1, -18, -2, 5, -5, 1, 9, 22, 10],\n [-13, -14, 10, 10, -16, -19, 5, 0, 9, 21],\n [-7, -13, -9, 16, 13, 11, 1, -5, -7, 18],\n [14, 18, 2, -15, 1, -3, 7, -3, -5, -19],\n [13, -17, -20, -5, 17, -5, 0, 12, -17, 3],\n [-2, 1, -8, 4, 9, -11, -18, -16, -1, 4],\n [-8, 16, 22, 12, 3, 0, -10, 3, -20, 6],\n [-21, 5, 0, 13, -17, -12, 15, 11, -6, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[21, 11, -1, 6, 6, -18, -13, -13, -14, -2],\n [-10, -13, 15, -12, -19, 8, 11, 19, 12, 16],\n [16, 10, -15, 9, 10, -15, -9, 11, -15, 19],\n [-16, -10, -2, 9, -12, -9, -12, -21, 11, 21],\n [-6, -9, 2, 4, -15, -6, -18, -11, 15, -5],\n [3, 8, 14, -17, 18, -8, 19, 3, -11, 18],\n [-9, -22, -6, 10, 6, 22, 8, -15, 7, -10],\n [-7, -21, 22, -5, 12, 22, -4, -10, -19, -4],\n [2, 15, 8, 13, -19, 16, -16, -7, -18, 0],\n [13, 9, 1, 2, 22, 5, -4, -16, 21, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "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, -21, -7, 16, -5, 16, -22, -20, -2, 7],\n [-12, -1, 2, -20, 7, 1, 22, 13, 0, -15],\n [-19, 16, 20, 8, 6, 13, -10, 18, -14, -2],\n [-20, 2, 2, -11, 6, -12, -12, 3, -9, -7],\n [-13, 8, 8, 13, -13, 3, -3, 21, -14, -8],\n [-14, -16, 3, 1, -11, -3, -9, -1, -7, 6],\n [9, -4, 12, 20, 9, -3, 17, -3, -15, 12],\n [19, -10, 18, -17, -7, -18, 22, 11, -17, 10],\n [-8, -8, -9, 16, -18, 3, -6, 20, -7, 12],\n [15, 0, -10, 10, 6, 11, 11, 4, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "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, -20, 13, -18, -3, -3, -18, -13, -7, 2],\n [21, 2, 7, -9, -1, 20, 5, 7, -4, 15],\n [19, -3, 12, -1, -8, -12, 11, 1, -17, -6],\n [5, 8, 13, -14, -13, -2, 11, 8, 6, 20],\n [20, -12, 10, -22, -2, 0, -14, -22, -2, -1],\n [-19, -22, -13, -8, 13, 6, -18, 6, 4, 2],\n [-7, -7, 13, 2, 18, -22, -18, 18, -3, -18],\n [13, 6, 11, -5, -21, -7, 6, 10, -7, 12],\n [20, 19, -6, -19, -19, 2, 10, -9, 1, -12],\n [2, 5, -16, 13, -13, 13, 8, -4, -5, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -16, 15, -11, 18, 11, 2, -6, 10, 0],\n [-14, -17, -21, 15, -14, -20, -7, 2, 1, 6],\n [21, 17, 3, 15, 12, 0, -19, 19, -9, 16],\n [-16, -15, 19, -4, -21, -22, 19, 15, -10, 19],\n [21, 1, 9, 7, -17, 15, 10, 21, 0, -13],\n [-8, 0, 13, -22, -15, -20, -9, -6, 11, -17],\n [-18, 18, 17, 6, 12, -5, 17, 7, -8, -8],\n [-7, 10, -13, -4, 14, -20, 13, -19, -12, 18],\n [10, 5, 9, -7, -14, -12, -17, 4, -11, -1],\n [17, 14, -2, 10, -6, 6, 17, -13, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -13, 9, 18, 22, -20, -1, 4, -20, 10],\n [-21, -12, -13, 16, 10, -16, -8, 3, -12, 15],\n [4, 16, -16, -22, -13, -2, -8, 7, 7, -15],\n [1, -4, -20, -8, 13, -17, 19, -5, 15, -4],\n [7, -10, 16, -11, 11, -11, 21, 1, -19, 13],\n [-9, -6, -20, 15, 0, -10, -14, -2, 18, -15],\n [-6, -7, -7, 5, -7, -9, 21, 15, -3, 22],\n [18, 11, 6, -20, -13, -3, -21, 4, 9, -13],\n [17, -6, 10, -17, 16, -5, -14, -15, 2, 8],\n [19, -19, -3, 5, 17, -22, 17, 21, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-7, 3, 8, -22, -6, -7, 14, -13, 15, 21],\n [8, -13, 11, -17, 5, 5, -10, 18, -11, 17],\n [-21, -15, 19, -14, -15, -20, -14, -10, -14, 8],\n [2, 21, 22, -15, 8, 22, 22, 8, -6, -4],\n [-20, 7, -13, 6, 17, -5, -11, 0, -12, -14],\n [1, 2, 2, -14, -11, -12, 15, 5, -15, -13],\n [2, 13, 20, -14, 18, -15, -20, -5, 12, -6],\n [13, 5, -8, -4, -1, -17, -16, 21, -14, -3],\n [14, -12, -21, -1, 13, -18, -16, -17, -1, -13],\n [17, -3, 5, 0, 12, -22, 6, -14, -14, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, -7, 17, -17, -10, 10, -4, -8, 10, -13],\n [-22, -11, 20, 6, -6, -19, 6, -16, 21, -10],\n [-18, -17, 11, -16, 5, -13, -19, -20, 2, 0],\n [4, -9, 15, 9, 0, 17, 14, -20, 12, -10],\n [11, 1, -22, -11, -15, -4, -14, 5, -9, 4],\n [-5, 19, 18, -17, 10, 14, 19, 2, -10, 0],\n [13, 10, -2, 11, 13, -6, -13, 0, 21, -21],\n [12, -9, 22, 18, -21, -4, -7, 20, 21, 2],\n [-22, -21, 4, -21, 7, -13, -4, 19, -7, -10],\n [-15, 8, 22, 2, 16, -2, 15, 18, 6, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "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, 21, 12, 4, -18, -16, -13, -13, 5, 13],\n [-13, 12, 12, 14, -3, -10, -12, 22, -4, 5],\n [15, 22, -19, 14, -4, 14, -9, 8, 5, 13],\n [21, 15, -4, 19, -22, 0, 5, -19, 18, -5],\n [16, 2, -5, -17, -4, -11, 2, 12, -22, -18],\n [-22, -15, 16, 20, -5, -14, -18, -19, 21, 6],\n [-22, 7, 22, -22, -20, -1, -15, -5, 2, -3],\n [8, 7, -7, -21, -6, -13, -16, 19, -14, -6],\n [-14, -14, 14, 1, 16, -12, -15, 2, -21, -13],\n [1, -7, -4, 8, -12, -17, -17, 9, 16, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-20, 18, 12, 15, -6, -20, 11, -11, 1, -17],\n [19, -12, 4, 1, -5, 4, 18, -2, 11, 10],\n [-5, -20, 1, -22, -17, -4, -1, 20, -15, -18],\n [-14, -2, 5, -19, 1, -15, -6, 11, -3, -7],\n [-13, 11, 20, -13, 7, 7, 2, 20, 18, -16],\n [-3, -6, -20, 17, 13, 3, -13, 11, -9, -15],\n [4, -13, -8, 14, -1, 22, 8, -21, 22, 8],\n [-9, -13, 7, 13, 17, -8, -9, 8, 6, 4],\n [-2, -14, -3, 12, -8, 1, -7, 13, -12, -15],\n [-20, -4, 18, -20, 13, 2, 13, -12, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, 1, -6, -3, -1, -17, -16, -9, -12, -11],\n [-18, -18, -3, -8, 3, 10, 7, 1, 0, -14],\n [-20, 13, -16, -1, -9, 6, -7, 11, -13, -16],\n [2, 4, -8, 9, 5, -14, -16, -7, 3, 12],\n [-6, 0, -15, -21, 8, 9, 6, -20, -15, -21],\n [8, 14, -3, 6, -6, -13, 18, -1, -17, 20],\n [11, 8, -11, -11, -7, 2, -1, 4, 1, -11],\n [-5, 22, -7, -19, -11, 10, -1, -5, 10, 4],\n [19, -4, -9, 2, 11, 1, 15, 0, -18, 21],\n [13, 1, 13, -18, 16, -17, 22, 13, 22, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-13, -22, -2, 17, 16, 14, -20, 8, 4, -6],\n [0, -10, 4, -3, -10, 21, 1, 18, -20, 20],\n [-13, -22, -10, -9, 10, -21, -21, 16, 18, 8],\n [-19, 11, -4, 14, -14, 1, -10, 21, 7, -4],\n [18, -13, 19, 21, -9, 17, -3, -19, 15, 21],\n [16, -18, 19, 9, -17, -9, -17, -9, -11, 4],\n [3, -11, -15, -13, -7, 3, -15, 18, 22, 6],\n [-3, -6, -4, -6, 16, -22, 6, -9, -6, -10],\n [6, 11, 4, 10, 6, 14, 16, -4, 1, -9],\n [14, -18, 1, 11, 8, 7, -14, 4, 5, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "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, 13, -15, -5, -3, 9, 6, -5, -16],\n [-22, 5, 10, -19, -3, 13, 8, 15, 5, -20],\n [-17, 22, 0, -16, 13, -22, -17, 1, 14, 22],\n [13, 1, 15, 22, 6, 14, 22, 9, 2, -13],\n [12, 2, 4, 22, 9, -11, -19, 19, 3, -20],\n [-6, -14, 6, -22, -5, 18, -3, 18, 11, 5],\n [12, -7, -2, -10, 12, 19, 9, 15, -17, 15],\n [15, -10, 16, -10, -11, 10, 5, -20, -5, 3],\n [17, -21, -19, 5, 5, 2, 3, 22, -21, 19],\n [11, 7, -2, 21, 14, 21, 0, 10, -21, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "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, 11, -7, -3, 3, -7, -17, 22, 21, 0],\n [19, 14, -15, -17, 14, -1, -17, 9, -6, 15],\n [-6, 14, 0, -10, 9, -1, -16, -1, -2, -17],\n [-9, -7, -20, -14, -2, 7, 7, 19, 19, 9],\n [0, -20, -22, -20, 14, -16, -20, 13, -20, -19],\n [8, -21, -9, 14, 8, -21, 8, 20, -1, -13],\n [7, 10, -4, 2, -22, 9, 2, 18, -6, -9],\n [22, -10, 15, 16, -21, 9, 9, 17, -17, 2],\n [-20, -5, 15, 20, -20, -18, 1, 11, 16, 1],\n [13, 5, 11, -7, 13, -16, -5, -17, 5, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[11, 18, 6, -19, -9, -18, 2, 16, -15, -8],\n [-4, -12, -3, 13, -5, -9, 15, 2, -7, -5],\n [-22, 17, -22, -22, -2, 2, 4, -13, -11, 5],\n [9, 10, -15, 19, 3, 19, 18, -21, 12, 11],\n [-17, 8, 0, -11, 5, -8, -4, -11, -21, -12],\n [21, 14, 15, 2, 20, -2, 19, 13, -14, -11],\n [-13, -18, 10, -18, -7, 14, 14, 6, -5, 6],\n [-17, -5, 9, 19, 8, -12, 3, 5, 4, -4],\n [22, 4, -3, -20, -7, 16, 21, 6, -8, 7],\n [17, -22, 6, 7, 17, 9, -13, 4, -15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[19, 12, 13, 13, 2, -3, 22, -6, 0, 2],\n [8, -17, 12, -19, 17, -3, 18, -22, 22, 3],\n [11, -13, 0, 1, -10, 6, 4, 8, 20, -13],\n [8, 16, -13, 1, 10, -9, 12, 22, 11, -6],\n [-2, 9, -20, -8, -15, 9, 15, 3, 7, -14],\n [9, -12, -1, 11, 18, -5, -4, -5, 14, -5],\n [-11, -19, 20, 4, -18, -17, -10, 0, 19, 2],\n [-19, 9, 21, -8, 3, 19, -12, -14, -12, -21],\n [22, 4, 3, -15, -2, -2, -15, -22, 15, -10],\n [-14, 5, -17, 0, 13, -6, -14, -11, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-17, 21, -14, 14, -20, 11, -15, -13, 18, 19],\n [20, -14, -9, 14, 4, 18, 9, -19, -21, 10],\n [-2, -22, 21, -12, -22, -12, -16, -21, -8, -15],\n [3, 17, 19, 12, 18, 18, -2, 15, -15, 20],\n [9, -15, 21, -13, 0, -19, 15, 7, 18, 0],\n [-18, -2, -17, -6, 2, 1, -1, -10, -6, -9],\n [11, 3, -4, 3, -20, -21, 5, -21, -1, -16],\n [-19, 15, 16, -3, -17, -14, 8, 3, 13, 3],\n [5, -18, -13, -5, -8, 10, -18, 14, 17, -1],\n [-1, -1, -8, -6, 22, 5, -1, -2, 19, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-18, -5, -6, -19, -16, 2, 14, 17, 17, 20],\n [-14, -4, -14, 0, 8, 9, 8, -6, 16, -1],\n [12, 7, 17, 14, 3, -17, 11, 9, 2, -10],\n [15, 15, -21, -18, -12, -12, 1, -9, 22, 7],\n [17, 21, 12, -2, -18, 15, -21, 17, 14, 11],\n [-12, 13, -12, -14, -17, 11, 14, 9, -11, 22],\n [9, -6, -19, 19, 10, 20, 20, -14, 11, 16],\n [7, -3, 16, 0, 18, 21, 12, 0, 16, 0],\n [14, 0, 16, 5, -4, 7, -2, 1, -2, 3],\n [13, 3, 10, 13, -19, -14, -15, -21, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-17, 20, 13, -2, -1, -14, 11, 3, -22, 13],\n [21, -18, 18, -1, -19, -21, -7, -7, -1, 20],\n [-22, -8, 1, -19, -5, -6, -16, 22, -13, -22],\n [-21, -1, 9, 6, 12, -6, -11, 1, 7, 21],\n [7, -3, 19, -16, 19, 15, -16, 7, -11, 8],\n [-5, 20, -21, 10, -12, 11, -7, 12, 10, -2],\n [-3, -15, 3, 10, 3, 14, 7, 8, 10, -12],\n [18, -18, -21, -10, -5, 3, 2, 21, -9, -18],\n [19, -21, -19, -11, -12, -19, 20, -14, -13, 4],\n [-17, -8, 19, 8, -1, -17, 10, 6, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "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, 13, -1, -3, -1, 17, -12, 8, 17, -10],\n [-5, -1, -6, 15, 2, 9, -8, -10, 3, -12],\n [-10, 10, 14, 15, -22, 16, 4, 13, 9, 18],\n [-8, 8, -17, 2, -5, -1, 8, 13, -14, -20],\n [10, 4, 20, -22, 21, -14, -18, -8, -14, 22],\n [5, -10, 1, 22, -13, 19, -1, 16, -1, 14],\n [16, -3, -13, -13, 3, 2, 5, -10, -8, -17],\n [-11, -4, 9, -12, 15, 10, -21, -8, 13, -18],\n [-8, 20, -13, -6, 11, 1, -13, 7, -20, 14],\n [-20, 17, -18, 5, 21, -9, 16, -12, -15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-15, -11, -8, -4, 5, -16, 17, -16, 7, -5],\n [1, -17, -19, -20, -17, 3, 21, 15, -12, 6],\n [-3, -13, 3, 4, -9, 13, -11, 0, -2, -15],\n [16, -14, 1, 8, 2, -6, 19, 6, -20, -2],\n [-15, -9, 16, -7, -5, 8, -12, 15, -3, 22],\n [-19, -3, 8, -3, -12, -22, 21, -5, 16, 21],\n [10, 13, -5, 8, 12, 16, 15, -8, -17, -15],\n [17, -1, -22, -10, 1, -2, 22, 20, -19, -16],\n [-11, -10, 21, -7, -17, -9, 8, 13, 14, 18],\n [12, -13, -6, 19, 7, 21, -16, -5, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[16, 21, -1, 16, 19, 7, -3, 9, 19, 2],\n [0, -18, 18, 7, 16, 4, 19, 14, -16, -18],\n [-8, 19, -15, -14, -12, -1, 11, 12, -10, -12],\n [9, 19, -8, 15, -22, 1, 20, 17, -1, -20],\n [-9, -21, 9, 15, 10, 19, -17, 18, 16, 2],\n [11, -12, 14, 18, -16, -1, 16, -13, -2, -17],\n [-22, 11, -9, 13, 4, -14, -17, 8, -6, 20],\n [13, -2, 4, 18, 5, -7, 12, 13, 12, 22],\n [-4, -2, 10, 0, -17, 9, -1, -20, 12, -7],\n [19, 2, -6, 16, -10, 5, -12, -13, 16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[15, 1, 10, -6, 21, 13, 12, -17, -7, 22],\n [5, 18, 9, 3, -12, 2, 8, -2, 22, -20],\n [-11, 17, 18, 2, -6, 15, 13, 13, -4, 21],\n [-21, -6, 7, -13, 12, 13, 10, -22, -5, -19],\n [4, 2, 5, -1, 19, 2, -6, 21, -11, -7],\n [14, -7, -6, 8, -8, -10, 17, 4, -2, -21],\n [-15, 19, -16, -13, -19, 20, 18, 13, 12, 20],\n [-20, -5, 20, 1, 9, 11, -21, -21, -13, 0],\n [-8, -11, 20, -6, -5, -9, -6, -8, -11, -7],\n [9, 0, 15, 11, 11, -7, 11, 17, -16, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-19, 20, -16, -5, -19, -12, 20, -3, -12, -8],\n [-6, 11, -11, 19, 5, 12, -15, 4, -1, 1],\n [-21, 8, -1, -22, -9, 2, 13, 13, 18, -20],\n [-18, -22, -4, 10, 19, 7, -11, -13, 11, -7],\n [17, 6, -8, -12, 21, 11, 13, 7, 12, -14],\n [-5, -4, 16, -19, -17, 10, 9, -7, -12, -1],\n [13, 0, 3, 8, 6, -18, 15, 2, 11, -11],\n [-1, -14, -3, 6, 21, 6, 22, 4, -6, -18],\n [22, -10, 19, -8, -8, -5, -21, 0, 20, -10],\n [20, -19, 2, -12, 19, -11, -10, -14, 22, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-17, 20, 20, -13, 0, -8, 22, 0, 17, 14],\n [11, -7, 22, 18, 9, 15, 17, -18, -6, -1],\n [16, 18, -5, 5, -10, 19, -22, -4, 11, -19],\n [20, -20, 18, -13, 5, 11, 16, -4, 19, 13],\n [20, -20, 0, -6, -16, 3, 20, -5, -17, 8],\n [6, -14, 12, -6, -11, 13, 1, -13, 7, 6],\n [16, -13, 16, 5, -5, 18, -6, -12, -22, -6],\n [13, 13, -14, 22, 5, 10, -20, -15, -17, -17],\n [6, 14, -11, -14, 18, -4, -6, 21, 9, 12],\n [-9, -7, -2, -11, 1, 11, -15, 21, -2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -7, -13, -8, -19, 3, -8, 13, 9, 20],\n [15, -19, 18, -14, 12, 5, 14, -14, -21, -20],\n [21, -18, -13, 5, -8, -9, 0, -10, -7, 7],\n [17, -15, -6, 7, -6, 12, -22, 1, 2, -21],\n [2, -9, 16, 10, -6, 8, -13, -17, 16, 2],\n [15, 14, 7, 11, -5, 1, 4, 4, 16, -2],\n [-4, 16, 0, 16, 21, -8, 20, -21, 12, -3],\n [5, -8, -7, 10, -11, 16, 16, 20, -3, 6],\n [20, -20, -18, -21, 0, 3, 3, -16, -13, -18],\n [-11, 9, 19, 8, -1, -6, -3, -3, 20, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[11, 0, 15, 5, -10, 6, -15, -12, 22, -5],\n [2, -1, 22, 12, 6, -2, -16, -11, 13, 1],\n [9, 4, 9, 9, 9, 3, -12, -5, 16, -18],\n [-7, -12, 12, -12, 19, 0, 11, -6, -13, -5],\n [21, -15, 3, -20, 1, -20, 15, -21, 12, -6],\n [-14, 13, -1, 8, 11, 1, -14, 20, -21, -2],\n [11, 4, 14, -16, -1, -19, -9, 11, 0, 21],\n [19, 2, -22, -8, 9, -9, 18, -2, -16, 13],\n [-2, 17, -11, -8, -8, -6, 11, 21, 12, 16],\n [15, -9, -18, 7, -19, -8, 16, 12, 22, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-21, 21, 1, 5, -1, 21, 9, 8, -4, -2],\n [-20, -17, 9, -21, 1, 22, 4, -14, -10, -9],\n [-12, -9, -7, -13, -3, -7, 11, -7, -9, 5],\n [-5, 3, 15, -16, 22, 11, 22, -16, 10, 12],\n [16, -2, 5, 9, 21, -7, -13, 0, -8, 20],\n [-17, 10, 16, -11, 13, 8, -13, 11, 18, -13],\n [-12, -9, -20, 10, -16, -19, 16, -13, -8, -7],\n [15, -19, -19, 13, 4, -1, -1, -6, 22, 11],\n [9, -17, 10, -15, 13, -18, -18, -13, 17, -16],\n [-11, 7, 2, 5, 20, -10, -1, -5, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-17, -12, 6, 18, -18, -16, -1, -19, 9, -4],\n [22, 10, -22, 18, 21, 18, -15, 9, 7, 5],\n [18, 9, 2, 11, 10, -10, 2, 19, 17, 16],\n [21, 21, -13, 8, 21, -12, 2, 22, 11, -3],\n [-16, 10, 12, 6, -11, -18, -11, 6, 12, -3],\n [14, -22, -7, 7, -14, 19, -13, -10, -3, 6],\n [-19, 5, 14, -10, -20, 14, -4, 5, -4, -6],\n [-5, -5, 0, 17, -14, 6, 19, 6, -21, -6],\n [22, 8, 5, 20, 16, 7, 12, -3, -7, 11],\n [-9, 3, -3, 19, 1, 20, -5, 20, -14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 19, 7, 3, 8, 12, -20, 17, 6, -17],\n [-22, 1, 15, 11, -16, -12, -12, 13, -3, -7],\n [-18, 1, 7, 7, 16, 14, 10, -3, -1, 18],\n [-2, 14, 4, 15, 12, 15, 17, -17, 9, -7],\n [5, -7, 4, -20, -2, 15, 15, 7, -1, -4],\n [8, -3, -4, -21, 17, 16, 4, -15, 22, 4],\n [-8, -11, -9, -16, -6, 3, 14, -3, -13, -4],\n [-5, 7, 7, 2, 1, -13, -21, 15, 9, 12],\n [14, -16, -16, 4, -13, 10, 20, -16, -17, -17],\n [-10, -10, -21, -4, -4, 15, -21, 3, -17, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -8, -17, 5, 12, -12, -15, 1, -2, 13],\n [-16, -18, 6, -7, -17, -9, -21, 2, 8, -10],\n [-5, -6, 22, 5, -11, 12, -1, 16, -22, 14],\n [-2, -22, -19, 9, -22, -10, -6, -11, -16, -20],\n [3, 8, 13, 3, -20, 21, 5, 21, -6, 15],\n [7, -21, -15, -9, 14, 12, 19, 16, -12, -8],\n [-21, 14, 20, 9, 17, -10, 20, -6, -8, 10],\n [-7, -10, -1, 0, 13, 20, -13, -6, 7, -10],\n [7, 7, -16, -13, 12, -21, 7, -4, 16, 14],\n [-20, 2, 11, -1, 15, -9, 16, -21, 9, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "356", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-20, 18, -15, 3, 9, -12, -22, -8, -19, -19],\n [5, -13, -12, 0, -20, 16, 16, -6, -1, 4],\n [-7, -7, 17, -20, 10, 19, -21, 16, 4, -8],\n [-16, 22, 19, -14, 18, -17, -11, 7, -3, -3],\n [4, -3, -16, 17, 17, 7, -15, -21, -9, -13],\n [-5, -5, -7, -18, 8, 14, -3, 0, 9, 19],\n [-6, -10, -10, -6, -8, 3, 21, 5, 19, 22],\n [7, 20, 12, -1, -13, -12, 15, 10, -17, 14],\n [-16, 21, -11, -16, -21, -22, 0, 2, -5, 21],\n [-16, -20, 6, -13, 20, -18, 11, -15, -9, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-17, -22, 10, 17, -12, 1, -13, 21, 0, -7],\n [14, -7, 21, 8, -17, 7, 14, -22, 19, 2],\n [-2, 12, 15, -18, -11, -18, -14, 21, -14, 12],\n [-22, -13, 16, 13, 14, 12, -6, -10, -17, 14],\n [9, -12, -6, -18, -17, -13, 10, 7, -2, 19],\n [-6, 4, -20, 6, -21, 6, 13, 11, 14, 19],\n [-22, 3, -22, -19, 16, -9, -5, 11, -22, -1],\n [-7, -1, -7, 5, 5, -1, -17, 2, 19, -21],\n [-16, -6, 12, -3, 21, -21, -16, 9, -4, -11],\n [-14, 4, -9, -21, -2, -19, -2, -1, -21, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 17, 1, -3, 15, -11, 2, 0, 11, 9],\n [1, 19, 2, -20, 2, 5, -11, 3, 21, -15],\n [-18, -12, 19, 12, 4, 18, 21, 15, -4, 9],\n [5, 13, -5, -13, 9, -5, -11, -15, 10, 15],\n [-9, -21, -14, 21, -18, 11, -4, -16, 16, 19],\n [-6, 3, 4, 20, 5, -3, -17, -15, 9, -4],\n [9, -4, 1, 1, -6, -5, -11, 18, 0, -5],\n [-7, -7, 13, 0, -1, 16, 10, 1, -3, 10],\n [8, 17, -15, -13, -22, -2, 2, 9, -13, -14],\n [-3, -3, 17, -16, -12, -2, 15, -4, -8, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "309", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-13, -7, 22, -12, 12, -15, 5, -20, -21, -9],\n [6, -20, -22, -8, -3, -1, 11, 10, -14, -20],\n [-21, -19, -7, 10, -14, 17, 15, -5, -7, -15],\n [0, 13, -20, -8, 15, 10, -5, 0, 20, -20],\n [7, 22, -6, 9, -16, 16, -9, -8, 21, -11],\n [-15, -7, 18, 11, 1, 6, -7, -18, -18, 7],\n [-18, 20, -10, 12, 2, -9, 21, 3, -5, -3],\n [11, -16, -13, -8, -6, -12, 11, 4, -2, 8],\n [-19, 18, -6, -3, 2, 17, 0, -8, 10, -4],\n [-8, 18, -18, -7, 22, 9, -1, 20, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[15, 3, -6, -18, 10, 4, -18, 14, -16, -5],\n [8, -17, -21, -10, 19, -12, 3, -2, -21, 17],\n [-3, -6, -7, 19, -18, -9, 1, -19, 1, -14],\n [-20, -14, -5, 13, -4, 1, -19, -14, 10, -22],\n [12, -13, -11, -5, -9, -13, -13, -5, 1, -22],\n [7, -8, -15, 12, -5, 18, -7, -2, -8, -18],\n [22, -16, -16, 4, 2, -1, -10, -6, 18, 21],\n [-10, 3, -14, -18, 16, 10, -19, 5, 3, -19],\n [-7, 14, -1, 13, 15, 12, 2, -15, -6, -5],\n [-11, 10, 0, -11, -12, -10, 12, 4, 2, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-20, 2, 22, -13, -6, -20, 22, -1, 15, -9],\n [4, 19, -3, -5, -10, 19, -17, -13, 14, 6],\n [-17, 16, -12, 2, 21, 21, 7, -3, 14, -7],\n [8, 6, -17, 6, 9, -14, 14, 0, -7, -5],\n [-4, 21, -21, -13, -11, -5, -4, 15, 14, 4],\n [-9, 22, 11, -21, 21, 10, -4, 4, 7, -16],\n [4, -2, -16, 2, 15, -5, 10, 10, 9, 2],\n [-9, 15, 15, -19, 21, -5, -13, 12, 12, 17],\n [0, 2, -22, -5, -8, 2, 9, -3, -6, -12],\n [-10, 2, -3, 2, 19, 22, 8, -22, -7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"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, 7, -20, 11, -17, 20, 6, -20, 10, -12],\n [22, -18, 9, -5, -3, 16, 17, 5, -10, 3],\n [-7, 2, -13, 6, 15, -3, 3, 9, 16, 15],\n [1, 8, 17, -11, 13, -13, -17, -16, 8, 4],\n [-15, -20, 17, -2, -22, 22, -8, -16, -8, 2],\n [-20, 7, -9, -19, 13, -20, -18, 2, 8, -12],\n [-15, 3, -21, 5, -13, 16, 14, 16, -2, 5],\n [15, 10, -12, 22, 21, -22, 10, -20, 3, -8],\n [18, -9, 0, -15, 13, -3, -17, 10, 5, 15],\n [7, 20, -6, -14, 5, -16, 5, -6, 17, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[21, -18, -18, -9, -17, -16, -6, -14, 8, -1],\n [22, -14, -7, 13, 11, 22, -10, -4, -11, 13],\n [-13, -7, 5, -4, 17, -17, -19, 7, 16, 8],\n [4, 22, -2, 14, -14, 12, 19, -2, -6, 1],\n [8, -17, 12, 14, -10, 2, 9, -22, 12, -4],\n [-11, 17, 17, 20, -3, 10, 6, -7, -9, -16],\n [-17, -2, 13, -1, 17, -4, 2, -20, 13, 22],\n [11, -12, 19, 4, 19, -21, -17, -21, 19, -6],\n [17, -9, -13, 22, 10, 19, -11, 9, 1, -9],\n [-18, -18, 9, 22, 10, -19, 7, 18, -6, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-10, 21, 13, -5, 0, 12, 10, 13, -6, 16],\n [11, -11, -18, 17, 4, 17, -10, 3, -9, 9],\n [-12, 15, -7, -1, -7, -10, -11, -5, 6, -5],\n [-21, -21, -20, 6, -15, -12, -11, 9, -19, -14],\n [1, -7, -6, -1, -16, -13, 6, 13, 1, -9],\n [-9, 2, -1, 0, 9, 3, 4, 22, -11, -4],\n [-4, 11, 9, 6, -2, 12, 19, -18, -11, -16],\n [18, -21, 2, -13, 15, 21, -17, 4, 12, -13],\n [-14, -3, 14, 12, 14, 17, -15, 8, 20, -7],\n [5, -17, 9, 5, -12, 19, 0, 7, -14, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "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, -8, 16, 10, 11, -1, 6, 11],\n [19, -13, 22, 7, -12, 11, -2, -10, 2, -2],\n [-22, -18, -1, -16, -10, 22, 0, -2, -17, -3],\n [-11, 17, -14, 5, -12, 9, -12, 1, -8, 18],\n [12, -6, 2, 12, -4, 18, 8, -6, 0, -22],\n [-13, -15, 19, 3, 11, -4, -9, -15, -22, 2],\n [1, -3, 7, -18, -20, 9, -6, 19, -18, -12],\n [15, -19, 16, -4, 16, 0, -6, -10, 4, -22],\n [-21, -5, 13, 22, 10, 13, -21, -19, -7, -19],\n [-14, -2, 0, -21, -20, 0, 3, -16, 13, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[10, 13, -19, 0, 2, 18, 3, 5, 5, -2],\n [-13, 4, -8, -6, 16, 12, -18, -7, 0, 16],\n [-14, 10, 12, 17, 1, 1, 1, -4, 16, 2],\n [8, 15, 2, 4, 9, -12, -18, 21, 10, -4],\n [20, -7, 12, -12, -12, -13, 11, -18, 0, 2],\n [6, 17, -10, 9, 11, -11, 1, 17, -2, 6],\n [0, 10, -15, 19, -10, -18, 18, -13, -9, 1],\n [-12, -20, 6, 7, 14, -16, -6, -3, -12, 21],\n [2, 1, -21, 4, -4, 6, 14, -12, -4, 5],\n [16, -2, 3, -1, -17, -12, -9, 13, 17, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, 20, -3, -1, 16, -19, 6, 1, -22, 1],\n [7, -11, -4, 14, 17, 20, -19, -8, -3, 21],\n [-3, -2, -13, 7, 1, 17, 17, 15, -20, 6],\n [-15, 6, -13, -18, -12, -19, 12, 17, -11, -2],\n [-7, -9, -2, 4, 13, -22, -22, -1, -8, -3],\n [-20, -9, -14, -4, 17, 11, -19, 10, 20, 14],\n [-21, 4, 22, -6, 8, 18, -17, 8, -20, 17],\n [-20, 10, -10, -2, 14, -7, -2, 21, -10, -19],\n [8, -14, 10, 14, 14, 1, 2, 18, 6, 17],\n [13, -8, 22, -5, -3, -18, -5, 17, -22, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 3, 6, 11, -4, -5, -21, 4, -17, 16],\n [-17, -17, 8, 18, 17, 7, -2, 18, 21, -5],\n [0, 15, 0, 5, 13, 2, -16, -5, -3, -18],\n [-5, 19, 17, 10, -8, 12, -22, -2, -15, -16],\n [18, 21, 17, 17, 7, 15, 12, -21, -15, 15],\n [-19, 14, -2, -10, -14, 22, 6, 18, 1, -7],\n [-11, -21, -4, 7, -7, 1, -10, -18, 0, 15],\n [8, -6, -20, 3, -10, 21, 15, -1, -2, 6],\n [22, 16, -18, -9, -5, -19, 10, 16, -3, -10],\n [13, 22, -19, 12, -15, 17, 13, -17, -1, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, 13, -14, -7, 16, 15, 10, -5, -11, 4],\n [-22, -8, 4, -7, -2, -22, 6, -20, -11, 5],\n [16, 14, 8, 8, 10, 10, 17, -12, 6, 2],\n [-10, 21, -4, 13, 5, -19, -20, 15, 14, 20],\n [2, 18, 12, 6, 18, 6, -11, 12, -3, -6],\n [-11, 13, -13, -5, 7, -15, 18, -10, 8, -17],\n [-16, -2, 15, 20, 5, 21, -2, -2, 1, 4],\n [4, -10, 6, 16, 5, 14, 6, -1, 13, 7],\n [5, 0, 10, -19, -20, 9, -19, -22, -11, -10],\n [11, 6, -14, 8, -16, -10, -21, 10, -16, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-15, -11, 20, 7, -14, 5, -19, 16, -6, -12],\n [-21, 0, -1, 3, -11, 9, -14, 20, -18, 3],\n [-16, 6, 10, 1, 2, 8, 6, -18, 15, 22],\n [-12, 9, -15, -3, 11, 19, -15, -21, -2, -8],\n [-17, -18, -20, 20, 20, -7, 12, -14, 12, -4],\n [20, 11, 16, -13, -13, -3, -22, -17, -21, 15],\n [10, -20, 13, -10, 12, -8, 22, -1, 20, -19],\n [-6, -18, -2, 1, 8, 17, 7, 19, -16, -16],\n [4, 1, -4, 18, 11, -1, 4, -17, -13, 22],\n [8, 2, -21, -13, -13, 3, -18, -1, -19, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-16, -6, -12, -15, 5, 21, 10, 2, -2, -11],\n [3, 6, 15, 12, 14, 21, 22, 22, 6, 1],\n [-8, -17, 9, 21, 11, 13, -3, -11, 12, 15],\n [-6, 4, -6, -12, 16, -21, -21, 6, 22, 1],\n [1, -7, 8, 20, -14, 4, 18, -9, 22, 2],\n [20, 21, -1, 12, 10, 4, 17, 3, -4, 22],\n [16, 22, 3, -17, -20, -17, 5, -20, -10, -10],\n [-10, -22, 17, 14, 8, -6, -14, 22, -10, 14],\n [-9, -12, 2, 8, -9, -16, 1, 13, 19, 19],\n [21, 18, -20, 21, 3, 3, -22, -8, -12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-16, -11, 15, -20, 19, 3, 7, 9, 13, 22],\n [14, -5, -22, -2, 5, -7, 5, -1, -4, -22],\n [8, 19, 11, 17, -17, 5, -20, 8, -7, -6],\n [21, 4, 1, -3, 9, 12, -10, 20, -3, -21],\n [-19, 4, 2, -19, 9, -6, -22, 10, 7, -18],\n [-11, 15, 9, 15, -6, 22, 17, 9, 1, -11],\n [8, -4, 6, -2, 3, 5, -6, -14, -2, 11],\n [-12, -3, 16, -7, 6, -22, -5, -1, -15, -16],\n [2, 7, 11, 21, 18, -12, -8, 12, 0, 22],\n [-2, 5, -10, 11, 15, -17, 21, -19, -18, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-17, -2, 5, -20, 0, -15, -4, -12, -13, 5],\n [-3, 21, 5, 6, -15, -4, -2, -5, -14, -19],\n [18, 2, 11, -14, -14, -5, -12, -10, 15, -14],\n [-7, -19, 11, -16, -8, 15, -12, 9, 4, 7],\n [-6, 13, -4, -16, 20, 22, -2, 5, -20, -9],\n [-21, 6, -5, 14, 22, 22, 1, -11, 22, 9],\n [-5, -10, -19, 0, -13, -18, 17, -9, 11, 5],\n [-15, -7, 8, -16, -20, 6, 13, 16, -19, -14],\n [-6, -3, -9, 6, -10, 13, 22, -6, 20, -19],\n [-3, -12, 19, -1, 22, -15, 5, 22, 18, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[10, 10, 13, 4, -3, 10, 2, 21, 20, -4],\n [-2, 19, 10, -20, -9, -8, 10, 19, -1, -22],\n [8, 12, -3, 9, -11, -7, -15, -9, -5, 7],\n [10, 11, 21, 11, -16, -17, -17, -1, -15, 14],\n [-8, 3, 16, -20, -13, -20, 7, -1, -20, -22],\n [10, -4, 13, 11, 8, 20, 1, -11, -10, -7],\n [-7, -3, 18, 4, 16, -10, -19, 9, 22, 17],\n [11, 16, 20, -6, 1, 6, 5, 22, -1, 5],\n [2, 18, -20, -10, 8, -10, 18, -5, 14, 20],\n [11, -6, -2, 13, 17, -4, -11, 5, -12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"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, 12, 21, -8, -7, 22, -16, -20, 8, -11],\n [-15, 2, 21, 12, -11, -2, 3, -21, -9, -19],\n [-6, -18, 1, -16, 0, -6, -11, -12, -12, 11],\n [14, 6, 13, 4, 19, -1, -21, 13, 7, -16],\n [-11, -20, -6, 18, 9, -15, 0, 15, 7, -8],\n [-13, 15, -8, 7, 3, 22, -9, -20, 13, 3],\n [-9, 8, -9, 17, -13, -14, 17, 20, 19, -5],\n [13, 13, -11, 17, -20, -5, -16, 8, -22, 8],\n [-10, 6, -20, 6, 12, -8, -2, -4, 5, -19],\n [22, -10, -8, 16, 9, -20, 7, -3, -21, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-12, -22, -13, -6, 7, 12, -4, 11, 9, -11],\n [20, -6, -17, -10, 16, -1, -12, -16, 22, 22],\n [-2, -22, 7, -4, 6, 12, -3, 13, 16, -22],\n [0, 8, 12, 22, -1, -16, 10, 22, 13, 21],\n [-16, 4, -21, -6, -22, 7, -1, 5, 10, 3],\n [12, -12, -16, 5, 2, 18, 8, -20, 10, 11],\n [-2, 14, -4, 14, -2, -9, -13, -16, 6, 17],\n [-15, 16, -10, -4, -12, -21, -17, 6, 18, -18],\n [18, 7, 16, 13, 4, -5, 13, -7, -18, -14],\n [11, 11, 13, 8, -3, -6, -3, 5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-20, 7, -18, 19, -17, -20, 19, 1, 21, -22],\n [13, -8, 18, 15, 21, -5, 0, 6, 18, -1],\n [1, 22, -10, 10, -1, 12, -6, -1, -18, 2],\n [-17, -6, 8, -6, 10, 16, 14, -19, 20, -9],\n [-10, 4, 1, 4, -15, 16, -2, 18, -12, 8],\n [4, 19, 4, -15, 10, -11, 12, 11, -7, 13],\n [-21, -11, 4, -6, -3, -2, 7, 19, -3, -15],\n [-5, -5, -5, -21, -11, 9, 19, -15, -13, -12],\n [-9, 3, 7, 19, -19, 16, -12, 1, -1, -20],\n [14, -21, -11, -2, -18, -16, -19, 20, 18, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "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, -14, 3, -11, -22, -15, 10, -19, -9],\n [6, -9, -14, -14, 3, 19, -6, 18, -19, -20],\n [6, 2, -2, -11, -22, -22, 22, -16, -13, -8],\n [17, -12, 22, 0, -10, 4, 18, -6, -10, -11],\n [6, -2, -3, -3, 8, -15, 1, -12, 16, 10],\n [19, -8, -19, -22, 9, -12, 7, 14, -4, 13],\n [11, -16, 22, -3, -11, 9, -21, -1, 18, 17],\n [1, 8, -19, 1, 20, -6, 17, -4, 17, 15],\n [11, 10, -17, 13, -10, -14, 12, 11, -7, -5],\n [-5, 15, 20, 9, -16, 0, 0, -5, -16, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[17, 1, -9, -18, -1, -1, -13, 3, -8, 15],\n [18, 19, -22, -9, 13, 8, 5, 11, 12, 16],\n [0, 21, -4, -5, -8, -22, 2, 3, 12, -8],\n [-19, -8, 19, 15, 22, 16, -22, -1, -12, 15],\n [14, 3, 4, -10, -16, -15, 0, 3, 21, 4],\n [-14, 15, -10, -16, -12, -13, 10, 16, -20, 18],\n [6, 14, 22, -7, -7, 21, 20, -16, -8, 15],\n [-17, -5, -4, -21, -20, 2, 13, 5, 15, 5],\n [9, 18, 13, 16, 13, 20, 0, -21, -13, -17],\n [-15, -8, 22, 6, 5, -1, 11, -3, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-16, 1, 3, -13, -8, 14, 1, -12, 17, -2],\n [17, 15, -8, -8, 14, 22, -9, 20, -2, 21],\n [-3, 10, -20, 17, 0, 21, 0, 4, 12, 2],\n [9, -1, -15, 15, -5, 5, 5, -12, -11, -21],\n [14, -19, 18, 22, 22, 11, 0, -10, -16, 9],\n [0, -15, 14, 11, 6, 14, 0, 15, 6, 21],\n [-18, 17, -12, -9, 19, -21, 12, 22, 12, 19],\n [5, -15, 9, -19, 22, -16, 16, 4, 14, -6],\n [-13, -19, 0, -9, -18, -21, 1, -5, 4, 1],\n [6, -12, -5, -19, 10, -9, 21, 19, 9, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -2, -20, 2, -19, -12, -7, 13, -17, 8],\n [17, -10, 0, -19, 14, 19, 14, 21, 10, 19],\n [6, 14, -4, -3, 9, 21, -7, -18, -11, 22],\n [-2, -9, 14, -1, 7, 0, -18, 6, 7, -5],\n [-22, 16, -6, -20, 19, -16, 4, 5, 21, 8],\n [-8, -15, -17, 5, -19, 7, 20, -6, 11, -17],\n [13, 12, 16, 16, -7, -21, -15, -8, 4, -7],\n [-22, -13, -16, -13, -11, -6, 22, -11, -8, 9],\n [9, 3, -9, 3, -18, 15, -19, 5, -22, -10],\n [20, -20, 2, 19, -7, -2, -10, 21, 13, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[21, -4, -7, -11, -3, -5, -11, 2, -12, -1],\n [11, -10, 15, -11, 16, 13, 5, 4, 16, -10],\n [20, 17, 4, 8, -21, -5, 3, 19, 8, 15],\n [-1, 13, -4, -9, -9, 6, -6, 14, -14, -22],\n [-19, -16, -12, -9, 19, -4, 17, -20, -15, 6],\n [14, 20, -14, -4, -11, 4, 14, 2, 22, 15],\n [-6, 21, 10, 16, -9, 5, -5, 10, 19, -8],\n [-12, 13, -8, 7, -8, 0, 20, -8, 6, -12],\n [22, -5, 17, 8, -14, -1, -12, -6, 10, -12],\n [16, -15, -19, 13, -4, 1, 18, -5, 10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-13, -9, -16, -11, -1, 4, 14, -12, 13, -10],\n [9, -15, -16, 20, 20, -6, -1, 11, -3, -15],\n [-1, 4, 11, -2, -8, -18, 15, -6, -15, -4],\n [-18, 0, -4, -9, -13, 8, -10, -1, 14, 16],\n [-13, 8, 20, 12, -10, 7, 11, 13, 12, -19],\n [-19, -17, 5, 7, 4, -18, 21, 16, 12, 16],\n [21, -8, -4, 7, 15, 9, 17, 6, -17, 3],\n [4, 12, 5, -18, 18, -7, 18, -5, -10, 20],\n [2, -13, 6, -13, -17, -7, 2, 21, -19, 14],\n [11, -4, 10, -19, 21, 11, -11, 8, -7, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-21, 13, -17, 0, 16, 21, 14, -7, 20, 21],\n [-4, 1, 4, -16, 7, 18, -9, 21, -8, -11],\n [6, 0, -10, -14, 1, 16, 7, -22, -13, 15],\n [-8, -14, -10, 0, 10, -14, -20, 7, -14, 2],\n [1, 9, -16, 13, 2, -3, -6, 13, 3, -4],\n [14, -20, 20, 5, -1, -4, -7, -17, 14, 8],\n [11, 8, -12, 13, -17, 4, -16, 9, -15, 10],\n [21, -8, 4, 7, -1, 6, 18, 7, -21, -8],\n [4, -16, 4, -2, -10, -6, -12, -13, 10, -9],\n [14, -15, 10, -16, 11, -16, -16, 18, 13, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -5, 22, 20, 18, -9, 17, -9, -2, 4],\n [3, 4, 1, -18, 19, 15, 5, 19, 20, 9],\n [1, -17, -13, -20, -16, 6, 11, -16, -6, -10],\n [-2, 8, -14, 22, -10, -6, -15, -14, -14, 17],\n [7, -16, -6, 16, 15, -18, -6, 17, -22, -7],\n [-6, 7, 8, 12, 22, -15, 7, 16, -2, -8],\n [11, 4, -21, -13, -18, 4, -19, -10, -6, -2],\n [0, 10, -8, -9, -14, 21, 14, 7, 6, 0],\n [11, -16, -14, -19, -21, 4, 10, 9, 21, 22],\n [14, 4, 5, -20, 13, 20, -15, 21, 18, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[22, 15, -1, -9, -8, -19, -5, -22, -11, 18],\n [19, -6, -4, 13, -16, -14, -15, 2, -16, 19],\n [-15, 1, -6, -11, 8, -11, -21, -11, 4, -16],\n [-10, 13, -22, 12, 7, 8, -6, -15, -20, -13],\n [11, -1, -19, 9, 6, -12, -10, -19, -21, 11],\n [20, -1, -18, -14, -3, -2, -6, -11, 5, -5],\n [-20, -18, -9, 3, -4, 18, -6, 16, 19, -19],\n [19, 12, 1, 18, -10, 10, -8, -8, 8, 20],\n [5, -13, -16, 10, -16, -18, 3, -7, -15, -1],\n [11, 17, 5, 13, -16, 17, 20, 5, -21, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-17, -22, -20, -13, 14, 21, 0, 10, -14, -10],\n [5, -16, 3, -7, 17, 3, 16, 9, 13, 19],\n [-22, -2, -10, 3, 22, -14, 14, 0, -22, -21],\n [20, 5, 13, 8, 18, -18, 14, 2, -15, 11],\n [16, 9, -12, 2, -20, 22, 9, 12, 9, 11],\n [14, -18, 22, 5, 5, -15, 4, -7, -5, 2],\n [-22, -15, -2, 11, 1, 14, 3, -9, 6, 7],\n [-20, -16, 13, -12, 9, -11, -8, 15, 1, -22],\n [-5, -16, 19, 18, -21, 17, 8, 10, 7, 8],\n [11, -16, 2, -7, -1, 13, 4, -6, -19, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[18, -1, 12, 21, -8, 17, 21, -2, -10, -12],\n [4, 8, 21, 9, 7, -5, -7, 12, -14, 16],\n [14, -13, -11, -15, -20, -4, -12, -15, 3, 22],\n [0, -13, -5, -11, 16, 3, -12, -13, -20, -16],\n [-19, 17, -15, 15, -10, -11, 12, 15, 20, 13],\n [-21, -8, 11, 16, 3, -18, 2, 11, -19, 11],\n [4, 19, 6, -18, -5, -19, -22, -3, -17, -3],\n [-3, 4, 3, 9, -13, -5, 18, -11, -13, 1],\n [1, 15, 2, -15, -9, 20, 8, 1, -7, -3],\n [15, -8, -9, -11, 11, -15, -4, -18, 4, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-10, 9, 8, 18, 14, -21, -16, -12, -12, 0],\n [8, 21, 22, -15, 9, -2, 8, -22, -10, -12],\n [6, -19, 13, -8, -20, 6, -2, -21, -17, 8],\n [1, 17, -6, -18, -21, -11, -18, 19, 18, -3],\n [-15, -22, -17, -12, -20, 8, 5, 20, -18, 3],\n [-7, 8, 5, -16, 15, -14, 16, 12, 20, 4],\n [-11, 2, 20, 6, 8, 11, 10, 4, -21, -9],\n [-10, 1, -18, 11, 0, -4, 7, 20, -7, 17],\n [11, -12, -9, -8, 12, -16, 6, 21, -1, 0],\n [1, 12, -13, -15, -11, 6, 6, 0, 3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, 15, -17, -15, -6, -11, -1, -9, 11, -4],\n [-17, -5, 13, 14, 15, -8, 15, 17, -14, -17],\n [-21, -7, -22, 7, 10, -22, 16, -7, -6, 15],\n [-5, -1, -1, 12, 8, 17, 4, 13, -19, -18],\n [2, 8, -9, 7, -11, 4, 22, 1, 7, -5],\n [-9, -4, -1, 3, -16, 5, 15, -18, 13, -5],\n [-9, 0, -9, 9, -18, -1, 5, 20, -11, -5],\n [13, 8, -10, -3, 22, 13, -16, 0, 11, 9],\n [-2, -17, -7, 12, -3, 19, 18, -12, 9, -9],\n [1, 21, 16, 20, 8, -6, 2, -14, -1, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[12, 14, -6, 5, -22, -14, -10, 9, 5, 8],\n [-15, -15, 11, 0, -13, 14, 2, 10, 22, -19],\n [-16, 10, -21, 9, -18, -6, -11, -11, 12, -2],\n [-2, -21, -2, -8, -12, -13, -5, 0, 8, 3],\n [-21, 16, -16, 1, 16, 9, 3, 0, -9, 6],\n [2, 8, -21, -21, 0, -12, 6, 19, 12, -14],\n [9, 7, -8, -9, -6, -1, 7, -6, -7, -15],\n [16, 8, -11, 10, -11, 2, 15, -5, -4, -20],\n [12, -18, 12, 4, 14, -2, -7, 5, 2, 10],\n [-6, 20, 7, 18, -19, -21, -14, 8, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[13, -18, 1, 1, 6, 22, 8, 14, -4, 0],\n [12, -17, -17, 14, 7, -22, -15, 5, 2, 10],\n [15, -9, -12, -21, 7, 7, -19, -10, -16, 15],\n [-20, -14, -9, -12, 14, -9, -4, -15, -16, -16],\n [-20, -20, -5, 22, 10, 14, 5, 13, -7, -8],\n [6, -5, -4, 6, -17, 22, 4, -16, 4, -4],\n [-6, 18, -12, -18, -21, -11, 19, 19, -12, -13],\n [5, -16, -9, -10, -18, 19, -15, -22, -18, -12],\n [20, -13, -8, 16, 6, 2, -17, -12, -6, -8],\n [-7, -21, 13, -4, 15, -2, -12, 18, -20, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -8, 2, -8, 7, -6, -5, 8, 20, -5],\n [12, -10, -9, 13, -5, -18, -9, 2, 21, 16],\n [-11, 17, 5, 12, -22, -20, 20, -16, -14, 13],\n [0, 1, -13, -11, -4, 9, 1, -1, -20, 17],\n [4, -4, -14, -10, -21, 13, 6, -12, 11, -19],\n [-19, -22, 2, 3, -12, 0, -21, -4, 6, 17],\n [-19, -7, 14, 4, -18, -8, 0, -20, -5, 20],\n [3, -17, 21, -6, 15, 19, 4, -3, -17, 12],\n [-11, -20, -19, 22, -19, -19, 16, -2, 21, -21],\n [-7, -16, -4, 20, 10, -14, 14, -6, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-11, 22, -12, -10, 8, -10, 15, 3, 8, -1],\n [-17, -3, -2, -13, -4, 12, 3, -16, 14, -15],\n [-18, 21, 13, 5, -20, 16, -15, -8, 4, 13],\n [-7, 3, 22, 21, -19, -11, -6, 18, 21, 3],\n [8, -8, 11, 6, -14, -9, 13, -19, 15, 14],\n [1, -6, -10, -3, -6, 4, 10, -2, -6, -1],\n [2, -20, 4, 4, -11, -8, 15, -3, -1, -21],\n [-19, 22, -10, 9, -1, 2, 4, -6, -17, 20],\n [-7, -15, 10, -13, 11, -4, -9, -20, 18, 0],\n [17, -12, -17, 11, -22, 12, 2, 6, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-9, -6, -21, 8, -4, 9, 5, 18, -15, 19],\n [18, 17, 16, -1, 1, 15, -21, 18, 18, -4],\n [18, -21, 5, 9, -4, -7, 7, -1, -9, -22],\n [22, -21, -1, 10, -8, 18, -1, 17, 16, 18],\n [18, -12, -19, -16, -2, -16, -19, -11, 4, -6],\n [-3, 8, 3, 8, 12, -14, -18, -15, -2, -7],\n [-7, -5, 5, -5, -9, 14, 17, -7, -2, -22],\n [-12, -12, -21, 9, -4, -18, -20, 5, 3, 0],\n [7, -15, 13, 6, -10, 2, -1, 10, 14, -16],\n [0, -17, -8, -8, 17, 11, -9, 6, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -13, -19, -11, 19, 11, -19, -3, 5, 5],\n [-17, -9, 12, -22, -4, -22, -10, -15, -5, 12],\n [0, 3, 18, 15, -3, -21, 3, 13, 2, 7],\n [-5, -16, 4, -12, 14, -15, -12, 1, 7, 7],\n [-8, 12, 16, 1, -15, 20, 19, -3, 18, 3],\n [1, -1, -18, -8, 13, 14, 6, -8, 4, -15],\n [6, -4, 8, -14, -13, 14, -13, 10, 2, -19],\n [-18, 0, 16, -18, -15, -6, -22, -11, 12, -9],\n [-5, -13, -8, 19, 10, -4, 11, 22, 2, -7],\n [-15, 12, -2, -4, -12, 21, -12, -12, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -5, 19, 17, 15, 7, 22, 22, 10, -2],\n [-21, -10, -21, 20, 22, 8, -13, 0, -1, 6],\n [10, 8, -9, -13, -5, -12, 16, -20, -21, -15],\n [8, -15, 20, -21, -1, -18, -16, -3, 5, -10],\n [-21, 9, 3, -20, 18, 19, -10, -2, 22, 14],\n [0, -16, -6, 5, 7, -18, 1, -16, 11, 19],\n [10, 4, -9, -4, 15, -11, -20, -16, 12, 2],\n [-8, -4, -4, 0, -12, -2, 11, 16, -16, 19],\n [21, 4, 0, 15, -3, 4, -15, 14, -20, -21],\n [-1, -17, 16, 17, 13, 21, 1, -11, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -14, -11, 9, 8, -6, 0, -13, 7, -4],\n [3, 3, -12, -3, 22, -19, -11, 2, -13, -1],\n [-16, 1, -21, 9, -2, -16, -15, 15, -2, -15],\n [2, 5, 5, 8, 13, 2, 18, 14, 15, -11],\n [14, 14, 8, -5, 3, -17, -14, -12, 8, -21],\n [6, 19, -18, 0, 13, -16, -10, 19, -13, 13],\n [-7, -8, 20, -4, -2, 12, -8, -9, 6, -18],\n [-5, -22, 4, 4, 2, 18, -2, -9, -3, 5],\n [-2, 0, -12, -21, -3, 1, 2, 14, -1, 1],\n [-8, -11, 8, 20, 8, 7, 18, -3, -15, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[7, 12, -2, 17, 5, 16, -6, -11, -5, 5],\n [-20, -8, -7, -1, 8, 8, -22, -12, -17, 0],\n [-14, -7, 15, 21, -4, 22, -10, 9, 13, -14],\n [14, 8, 8, -4, -21, 22, 9, 20, 11, -22],\n [-2, -20, 4, 21, -16, 10, -14, 7, -5, 3],\n [-3, 15, 18, 8, -15, 0, 2, -22, -5, -4],\n [19, -17, -6, 22, -15, 19, -14, 14, 4, 13],\n [-17, -17, 22, -19, -1, 17, 4, 14, -21, -14],\n [-12, -3, 20, 16, -9, 3, 15, 7, 13, 15],\n [12, -17, -20, -22, -5, 0, 9, 6, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-17, -6, -5, 8, -17, 11, 21, 21, 4, 13],\n [19, 2, -13, 16, 16, -11, -12, 20, -20, -1],\n [-19, -15, -9, -3, 1, -9, 5, -7, 9, -11],\n [-7, -4, -18, -11, 6, -18, 19, -6, -15, 17],\n [17, 7, -13, -3, 22, -7, 18, -7, 19, -20],\n [0, -1, 5, 22, 13, -19, 15, 1, -4, -12],\n [17, 17, 16, -5, -11, -9, -5, 21, 19, -11],\n [17, 4, -17, 1, 10, 22, -7, -11, 8, 14],\n [-10, -15, 15, -20, -3, -19, 21, 22, -21, 13],\n [0, 22, -4, 17, -15, -7, 20, -5, 13, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-22, -22, 13, -12, -5, -7, -6, 1, 11, -19],\n [12, -8, -21, 8, -14, -13, 2, -18, -9, 19],\n [15, 17, -21, -5, 6, -3, -15, 14, 3, 14],\n [-19, 10, -1, -17, 10, 5, 1, -19, -21, -10],\n [-12, 12, 16, -13, 20, -13, -15, -18, 0, 11],\n [9, -7, -19, 5, 21, -9, -11, -2, -7, 21],\n [-21, 0, 6, 20, -14, -16, 6, 21, -6, -14],\n [-17, 21, -3, -13, -14, -11, 10, 9, 11, -4],\n [10, -7, 0, 3, 22, 21, 18, 14, -14, 7],\n [-10, 19, -7, -21, 8, 20, -4, -12, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-16, -8, 7, 8, 1, 2, -15, 7, 13, -9],\n [6, 4, 13, 11, -2, 15, -12, 10, -8, -11],\n [1, 14, -12, -4, -22, -6, 17, -7, 3, 20],\n [20, -8, -15, 7, -9, 10, 19, -16, -5, -11],\n [-21, 6, -2, -16, 4, -11, -3, -9, -13, 18],\n [0, 7, 8, -13, -4, -4, 21, 0, 21, 18],\n [9, -3, -19, 10, -22, -10, -20, -11, 6, 8],\n [18, 13, -21, -1, -1, 18, 8, 22, -9, 6],\n [12, -14, 9, 4, -13, 2, 22, 10, -12, 14],\n [-14, -16, -16, 11, -4, -3, 19, 2, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 2, 14, -8, -19, -9, -6, -2, -7, 3],\n [-14, -21, 20, -8, 12, 1, 15, -9, 14, 14],\n [-17, -5, -1, -5, -21, 9, -6, -22, -14, -10],\n [13, 14, 7, 8, 0, 5, -13, 2, 13, 3],\n [3, 22, -10, -6, 17, -19, 0, 12, -12, -11],\n [-14, -8, 22, 14, -18, -4, -12, -14, 12, 4],\n [-10, -11, -14, 19, 5, -10, -3, -10, 4, 3],\n [6, 6, -1, -14, 1, 19, -4, 15, 8, 16],\n [-8, 9, 6, 11, -14, 12, -17, 14, -9, -14],\n [-4, 0, 18, 5, -7, 3, 15, 17, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, -16, 0, 2, -22, -1, -19, 5, -9, 10],\n [-19, 19, -12, 16, 9, -19, -22, 3, 10, -6],\n [4, 19, -18, -16, 2, -15, 11, 18, -19, -11],\n [8, -12, 14, 21, 13, 22, -1, -22, -19, 13],\n [-15, 2, 5, 15, 13, 13, 20, 18, -19, -10],\n [15, 22, 2, -20, 9, 16, -22, -12, -21, -18],\n [-1, -10, 0, 8, 12, 15, 18, 12, 22, -10],\n [-16, -18, 6, -15, -15, -16, -4, 16, 0, 13],\n [19, 9, 22, -19, 7, 19, 16, -18, -20, -1],\n [5, -1, -1, 11, 6, 20, 19, -10, -16, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "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, -19, 9, -1, -3, -3, -17, -14, 5, -10],\n [8, 16, -9, -1, 14, 22, 1, -15, -8, 18],\n [-17, 0, 2, 8, 6, 0, -13, -14, -10, 9],\n [22, 18, -22, -22, 14, 17, -5, 13, 8, -22],\n [13, -14, -1, 5, 3, -13, -20, -21, 14, 8],\n [10, 9, 20, -11, -20, 3, -9, -11, 3, -7],\n [-15, 5, -16, -8, 18, 13, -15, -13, -8, -5],\n [14, 18, 22, 20, 21, 12, -21, -1, -8, 14],\n [16, 13, -18, -8, 4, -7, 13, 15, -5, 12],\n [2, -1, 8, 14, 11, 0, -7, -17, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[15, -10, 1, -10, -22, 13, -5, 10, 15, 20],\n [-17, -6, -19, -9, 7, -3, -15, -21, 14, -19],\n [-13, -3, 12, -13, 5, -8, 13, -22, -1, 4],\n [6, -8, -13, -3, -1, -14, 9, -6, 19, -4],\n [17, 4, 14, 11, -13, 7, -2, -2, 11, -14],\n [11, -11, -2, -3, -17, 22, 13, -11, 18, 8],\n [-21, -7, -22, -19, -22, 12, -10, 22, 19, 8],\n [-3, -16, 17, 10, 5, 21, 21, -3, 9, -14],\n [11, -9, -19, 6, -8, -6, -4, 15, -14, 4],\n [-8, 14, 5, -19, -2, 11, -4, 14, -19, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[9, 22, -11, 18, -7, -9, -22, 9, -2, -19],\n [-14, -1, -11, 7, 7, 9, 13, -16, -6, -22],\n [-9, 21, 21, 15, 3, 4, 22, -7, -16, 9],\n [2, 8, -7, 18, -9, 2, 7, -16, -11, -20],\n [4, -4, 20, 14, 22, 19, -16, -7, 9, -15],\n [-10, -12, -3, -5, 14, -17, -3, 9, 21, 6],\n [-19, -16, 20, -3, 11, 13, -16, 10, -8, 9],\n [-1, 17, 6, 2, -18, -9, 12, -21, 2, -7],\n [-7, -12, 12, 0, -18, 12, 6, -18, -20, -17],\n [0, -21, -5, 7, 15, -18, -12, -22, -13, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[21, 3, 10, 4, -11, -21, -22, -22, 10, -1],\n [-11, 16, 13, -2, -3, 13, 3, 8, -22, 15],\n [-9, 3, 19, -16, -11, 1, -4, -14, 12, -19],\n [22, 19, 9, -17, 5, 5, 17, 6, 19, -18],\n [-18, 14, 18, 5, 18, -14, 6, -9, 15, 17],\n [11, 14, 19, -9, -5, 10, 11, 5, 13, 22],\n [14, 0, 19, -6, -12, 9, 14, -8, -19, 16],\n [7, -13, 0, 1, 13, -18, 14, 20, -4, 14],\n [-15, -16, 17, -10, 14, 4, -5, 1, 18, -21],\n [-7, -9, -6, -17, 12, -6, 22, 15, 17, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[15, -2, 12, 0, -11, 6, 4, -17, -2, -16],\n [20, 18, -7, -18, -8, -2, -19, -18, -16, 12],\n [13, -8, 5, -21, -18, -16, -1, 8, 9, -15],\n [18, 19, -12, -22, 17, -4, 21, 15, 19, 14],\n [-16, 16, 2, -1, 4, 18, 15, 16, -8, -21],\n [-15, 21, 20, -17, -3, 4, 22, 0, 17, -6],\n [-10, -19, -3, 19, 2, -1, -6, 17, -12, 2],\n [-18, -2, 3, -7, 17, -2, 9, -19, 15, -15],\n [-14, 22, -6, 18, -10, -14, -17, 4, 19, 14],\n [16, 20, 1, -14, 19, -12, 12, 6, -15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-16, -11, -8, 6, 22, 1, 14, -9, -12, 12],\n [-6, 4, 21, -20, -21, -19, -5, -3, -2, -9],\n [-15, -21, 3, -4, 19, 5, 6, -18, 20, 5],\n [18, 3, -18, -8, -14, 9, 3, 14, -8, 18],\n [-19, 13, -3, 4, -2, -1, -16, 8, -6, -16],\n [-4, 5, -13, 4, -10, -21, -1, -3, 20, -18],\n [-17, 12, -22, 12, -20, 13, -16, 6, -8, -12],\n [-5, 21, -19, 1, -12, -17, -5, -8, -20, -6],\n [10, 11, 7, -4, -14, 17, 21, 8, 4, 2],\n [-16, -16, -3, 21, 20, 13, -4, -21, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -14, -22, 19, 5, -8, -2, -8, 0, -21],\n [13, -14, -21, -21, -5, -6, 18, -15, 11, 11],\n [-18, 21, 6, 5, -7, -9, -21, 17, -19, 18],\n [8, 3, 4, 11, 8, -12, -15, -11, 12, 22],\n [11, -10, 4, -15, -2, 18, -12, -1, -2, 5],\n [-20, -16, -9, -8, -14, 20, -16, -11, -4, 4],\n [-5, -10, 20, -22, 15, -2, 11, -10, 22, 18],\n [0, -22, 0, 5, 9, -15, 3, -9, 1, 6],\n [-19, -5, -9, 4, 18, -20, 7, 13, 0, -5],\n [17, -13, -11, 18, -15, 9, -6, 18, 22, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[14, -14, 3, 1, 0, 8, 16, 21, -21, -5],\n [-7, 6, -12, -21, -9, -19, 16, 11, 16, -14],\n [17, 18, -16, -6, 0, 22, -12, -1, -5, 5],\n [-7, 19, -19, 13, -1, -12, -2, 17, 18, -7],\n [19, -14, 12, 11, -14, -10, -17, -19, 5, -12],\n [11, 12, -18, 16, -12, -11, 20, -4, -10, -19],\n [-9, 21, -21, -15, -1, -10, -2, -2, 5, 10],\n [6, 14, -1, 3, -12, -12, 22, 11, -4, 14],\n [-9, 6, -4, 14, -2, 1, 3, 18, -11, -4],\n [7, -8, -20, -10, -14, -10, -7, -9, -15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[9, 12, 0, -2, -5, -9, -7, 1, 9, -12],\n [22, -12, -19, 3, -18, 13, 10, -9, 9, -16],\n [-13, -21, -13, 12, -2, 17, 19, -15, -5, -14],\n [18, 7, -19, 12, -9, -9, 14, -3, 6, 0],\n [-2, 8, 9, 18, -16, -10, 0, -15, -11, 13],\n [-7, 3, 6, 6, -17, 14, 10, 8, 18, -5],\n [15, 8, -7, 17, 14, -9, 16, -19, 7, 10],\n [13, 7, -9, 0, 5, -16, 19, -13, -19, 21],\n [15, -10, -2, 10, 17, 5, 0, 9, -18, 3],\n [16, 3, -20, 1, 11, 11, -3, 7, 19, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[18, -5, 15, -3, -17, 19, 2, 18, 18, -20],\n [21, 20, -4, -13, -18, -1, -14, 10, -8, 1],\n [7, 13, 16, -17, -8, 15, 16, -1, -20, 6],\n [6, 8, 22, -21, 12, 22, -14, -1, -4, 14],\n [-13, -2, -6, -20, -16, 18, 14, 13, -20, -10],\n [18, 7, 0, -16, 7, 6, -15, -13, 10, -3],\n [6, 6, -2, -22, 11, 21, 9, 22, -9, 14],\n [12, 1, -22, -17, -19, 15, -22, 18, 8, 13],\n [-14, 18, 22, 0, 8, 6, -2, -20, 3, -17],\n [-3, -10, 18, 0, -8, 8, -19, -12, -21, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[8, 16, 20, 21, -19, 5, -7, 16, 2, -10],\n [-18, 7, -22, -18, -9, -12, 11, 6, -5, -8],\n [2, 7, 22, -21, 17, 4, -8, 9, -3, -9],\n [4, -20, -20, -10, 2, -5, -22, 16, -18, -21],\n [7, -6, 6, 19, -19, -14, -2, 20, -11, -11],\n [-19, 5, -14, 17, 9, -10, 11, -4, -9, -18],\n [4, 5, 3, -13, 1, -6, -7, -6, -22, -2],\n [20, -1, -18, 13, -2, -14, 4, -11, -5, 12],\n [-8, 21, 7, 22, 10, 13, 17, 7, 3, -2],\n [14, 20, 8, -6, -6, 11, 1, 10, -19, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-21, 12, 15, 22, -8, 20, 19, -20, 8, 18],\n [19, 0, -11, -15, -2, -2, 9, -6, 14, 1],\n [-15, -5, -12, -13, 3, -17, -6, 0, 19, 14],\n [5, -7, -11, -2, 1, 5, 14, -2, 10, -21],\n [14, -4, 5, -8, -22, 20, 5, 12, 9, 5],\n [-14, 1, -19, 22, 18, -20, -1, 17, 16, 2],\n [-1, 11, -3, 13, 14, 16, 4, 9, 19, 6],\n [18, 9, 1, -20, 4, -14, 17, 0, -16, -6],\n [14, -16, 7, -10, -5, 8, -1, -9, -5, 12],\n [-6, -4, 8, 16, 13, -8, 6, 17, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "331", "dataset": "MATH"}
{"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, -7, 7, 11, -21, 17, 21, 20, 15, -5],\n [-18, 17, -17, -11, -11, -11, -14, 19, -1, -7],\n [-19, -20, -7, -9, 18, 15, -19, -21, -13, -12],\n [16, 3, 14, 3, -19, 3, 15, 5, -21, -21],\n [-7, 0, 0, -10, -2, 16, 2, 14, -10, -8],\n [5, -20, 0, -19, -20, 16, -15, 20, 2, 18],\n [-11, -18, 10, 2, 2, 12, -8, 19, 3, -13],\n [1, 12, 6, 15, -18, 1, -4, 21, -14, 3],\n [2, 12, 13, -9, -17, 9, 3, -8, 8, 14],\n [15, 14, -4, -9, 13, 14, -12, 4, -21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-21, -3, 21, -6, -19, -9, -16, -8, 7, -7],\n [17, -21, -4, -22, 8, -19, 4, 2, -1, 20],\n [-13, 10, 21, 7, 7, -7, -14, -6, 12, -8],\n [5, -3, 10, 10, 13, -10, -19, 0, -15, -10],\n [1, 17, 7, 7, 2, 10, -14, 3, 1, 10],\n [16, 2, 22, -8, 18, 18, -17, -3, 21, -7],\n [-2, -8, 16, 19, -19, 1, -20, -22, 7, -10],\n [-5, 17, -12, 19, 6, -19, 2, 13, 13, 21],\n [17, 5, 22, -15, -2, 12, 21, -5, 2, 18],\n [-18, -15, 0, -20, 21, 14, 8, 6, 18, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-20, 0, 17, -2, -10, -15, -18, 2, 16, 14],\n [18, -18, -15, 21, -19, 18, -1, -9, -4, -10],\n [12, -19, 10, -1, -22, -12, -7, -19, 6, 16],\n [21, 15, 1, -14, -15, -9, -8, -1, 14, -8],\n [-17, -22, -3, 18, 13, -21, -17, -21, -20, -16],\n [-3, 18, 18, -18, 2, 15, -5, -22, 2, -6],\n [-8, -18, -6, -2, 0, 20, -13, -6, -22, 14],\n [-16, -11, 17, -22, -3, 21, 8, -19, 3, -11],\n [-1, -22, -22, -20, -11, -2, -10, -10, 18, -5],\n [10, -17, 2, 0, 1, 14, 3, -19, 15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-12, 13, 2, -3, -22, 7, -19, 0, 12, 19],\n [-1, 8, -22, -19, -4, 7, -22, -4, -2, -1],\n [-21, -17, -2, 10, -4, 4, 14, 6, 5, 11],\n [-22, 2, -2, 11, 3, 13, 12, 0, -6, 19],\n [-11, 21, -3, 16, 4, 19, 14, -3, -12, 5],\n [-21, 1, -7, -11, -7, 13, -21, 2, 6, 5],\n [-13, 22, 0, 9, 8, -4, -8, 10, -6, 13],\n [-3, -14, 15, -20, -21, -5, 0, -4, -16, 12],\n [-3, -3, -4, 18, -7, 15, -2, 6, 21, 15],\n [22, 1, 14, 6, 8, 22, 16, -11, 7, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[7, -18, -7, 4, -19, -15, -15, -6, 21, -20],\n [4, 11, 22, -2, 20, 1, 21, 18, 6, 16],\n [-17, -9, -9, 14, 1, -10, -22, -11, 19, 1],\n [14, -3, -17, -11, -2, -20, 4, 13, -6, -8],\n [16, -19, -6, 15, -12, -11, 9, 4, 21, 20],\n [4, 17, 21, 6, -14, 20, -20, 16, 6, -2],\n [12, -13, 0, 16, 2, 1, -3, -8, -2, 19],\n [-11, -5, 0, 18, 6, 18, 13, -18, 16, 3],\n [16, -12, 19, -12, -5, -11, -7, 4, 13, -6],\n [-2, 14, 8, 22, 12, 4, 0, 9, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-22, 5, -5, 18, -3, -16, 14, -7, 16, 22],\n [22, 0, 9, -6, -4, 19, 11, -9, -20, 16],\n [2, -12, -8, -4, 20, -8, -8, 15, -8, -14],\n [-18, -4, 1, 6, -18, -1, -10, 6, -7, 13],\n [-6, -3, -9, -17, -1, 17, -14, 9, 1, 10],\n [-10, 12, -17, 17, 7, 15, -7, -22, 19, -5],\n [-1, 3, -9, 14, -9, 3, 13, 0, -21, 16],\n [-16, 16, 22, -1, 5, 15, -3, -5, 1, 10],\n [22, 3, -4, 19, -10, -13, -9, -14, -12, -20],\n [17, -11, 12, 16, 16, 9, 16, -9, 21, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, 14, 20, -22, 22, 6, 1, -6, 12, 8],\n [19, 9, -4, 8, 16, -3, 5, -20, 9, -1],\n [21, 19, 21, -8, 15, -4, 8, 3, -18, -3],\n [-21, -2, 13, 5, -3, 14, 16, 13, -12, -20],\n [14, -3, 9, 2, -2, -7, 19, -22, 0, 20],\n [1, 2, -16, 15, 16, 12, -9, -14, -20, 15],\n [-3, 18, 10, 18, 21, 9, 13, 3, -18, 7],\n [-6, -17, -8, -22, -10, 11, 7, -4, -21, 21],\n [-11, 17, 21, 1, -12, -21, -22, 5, -19, 18],\n [7, -16, -1, 3, 6, 2, -13, -3, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "363", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-18, 22, -17, -1, -6, -8, 16, 17, 5, -21],\n [-5, 4, -2, 0, -16, -4, -14, -11, 7, -16],\n [-21, -6, -12, -11, -20, -2, -9, -8, 19, 18],\n [-13, 13, -13, -6, 21, 2, 4, 10, -12, -10],\n [-22, 8, 10, -2, -7, 16, 0, -13, 10, -1],\n [18, -17, 13, -13, -7, -10, -3, -19, -3, -1],\n [6, -7, 20, 20, 0, 7, 7, 20, -20, 1],\n [14, -10, 19, 9, 14, -11, -15, 1, 21, -7],\n [9, 11, 12, 9, -6, -21, 3, 21, -6, 15],\n [-21, -15, -17, -14, -22, -18, 16, -14, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, 13, 6, -3, -8, 13, -20, 0, -14, 7],\n [-4, 15, -20, -20, 11, -21, 4, 0, 19, 9],\n [12, 17, -5, 4, -12, 16, -4, 2, -16, 8],\n [-21, 15, -18, -9, -5, 13, -19, 1, -10, -2],\n [10, -3, -18, 1, 12, 7, 5, 22, -16, 19],\n [12, 7, 11, 16, -14, -11, 6, -13, 4, -4],\n [-10, 19, 14, 9, -8, -2, -20, -15, -17, 6],\n [-4, -6, -13, 10, -10, 4, 19, -11, -21, -13],\n [-2, 0, -22, 10, 3, -8, -1, 2, -22, 3],\n [-2, 18, 1, 16, -7, 9, -7, -10, 19, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[18, 21, 1, -10, -12, -8, -13, 19, 18, -20],\n [-7, 21, -6, 2, 7, 12, 14, -10, 1, 15],\n [3, -14, -4, 5, -16, 22, -1, 7, 14, -7],\n [13, -18, 6, 0, -17, 13, 10, 18, -7, 11],\n [20, 3, 14, -10, -6, 9, 9, 5, 6, 2],\n [-1, 4, 21, 15, -3, 22, 1, -15, -9, 16],\n [-9, -18, -2, -8, 13, 10, -6, -3, -22, -7],\n [22, -5, -13, 0, -5, -14, 7, -10, 8, 20],\n [-10, 9, -6, -20, -22, -18, 9, 2, 22, -18],\n [14, 0, -11, 11, 0, -7, -18, 21, 5, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "339", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, 20, 7, 3, -6, -14, -7, -5, -10, 6],\n [20, 22, 1, 22, 21, -10, 2, 18, -22, -14],\n [-19, 5, -11, 1, -14, 12, 15, 12, 10, 12],\n [-3, -21, 21, 3, 19, -10, 7, 9, 13, -4],\n [-1, -22, -12, 3, -4, -4, -11, -20, -5, -18],\n [1, -9, 15, -20, -17, -11, -12, 16, 3, -22],\n [-7, -14, -18, -15, -2, 10, 16, 20, -3, 22],\n [-1, -10, 16, -12, -5, 7, 10, 21, -20, -22],\n [13, -17, 14, 6, -12, -10, -12, 15, 2, -8],\n [-10, 19, 10, -10, 15, 1, -3, 21, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 17, 9, 6, -9, 14, -1, 11, 4, 5],\n [-1, 20, -20, -1, -2, -7, -14, -10, -13, -2],\n [19, 17, -16, -1, -5, -2, -9, -13, 10, -14],\n [-5, -10, -6, 0, 2, -7, 1, 8, -12, 0],\n [18, 16, -1, 10, 18, 19, -5, -9, 5, -12],\n [1, 13, -4, -10, 10, -4, 9, -8, -12, 0],\n [-18, -1, 19, -5, -16, 10, -20, 5, -22, 14],\n [-1, 21, -4, -9, -20, -4, 10, -2, -22, 3],\n [-13, 12, -10, -17, 20, -17, 12, -7, 18, -15],\n [-20, -18, -2, 8, -9, 14, -4, 14, -3, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "313", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-16, 10, 19, -17, -16, 21, -5, 20, 6, -4],\n [2, -19, -10, 9, 4, 11, 5, -14, -15, -2],\n [7, 6, -14, -10, -5, 15, -1, 8, 12, 19],\n [19, -13, -14, 8, 21, 17, 1, 18, -15, -3],\n [-6, 5, -17, 19, 10, 5, -22, 18, 12, 1],\n [-17, -16, -14, 14, -7, 11, 12, 12, -3, 0],\n [19, 12, 0, -19, -13, 20, -12, 17, -14, 17],\n [-11, -6, 9, 0, -8, 5, 15, -18, 17, -5],\n [-2, -8, -20, 3, -8, 22, -3, -2, 3, 18],\n [0, 2, -19, -13, -1, -20, -4, 8, -14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[14, -16, 15, 1, -15, 11, 3, 5, 5, -16],\n [-20, -1, 15, 21, -5, -11, 8, 16, -18, 21],\n [18, 6, 20, 13, -9, 21, -5, -16, 0, 10],\n [22, -7, 14, 2, -14, 5, -14, -11, -5, 4],\n [3, 3, -13, -6, 9, 1, 20, -15, 7, 3],\n [1, 4, -8, 5, -12, 16, -21, -14, 22, 0],\n [10, -4, -10, -9, 9, -1, -3, 10, -18, -3],\n [-9, 4, 3, 9, 7, 4, 3, -5, 22, 0],\n [21, 1, -19, 18, -20, 20, 7, -7, -16, 16],\n [-1, 18, 8, -10, 18, 18, 6, 5, 21, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "324", "dataset": "MATH"}
{"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, -15, 2, 15, 15, 12, 3, -20, -21, -18],\n [-3, -11, 15, -7, 14, 15, 13, 6, 12, 14],\n [-2, -2, 5, -17, -3, 13, -10, 17, -12, 1],\n [-4, 0, 8, 14, 14, -20, 11, 6, -20, -8],\n [-16, -20, 20, -7, 22, 11, -3, 21, 16, 10],\n [-9, 19, 12, -12, -3, 7, 5, -8, 15, -10],\n [12, 1, -22, 19, 1, 4, -5, 3, 6, -15],\n [21, 3, -18, 10, 17, -18, 13, -10, -6, -10],\n [2, -21, 1, 13, 2, 11, -11, -4, 19, 7],\n [14, 20, -22, -20, 3, -8, 5, -19, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[17, -17, -7, 9, 7, 12, -15, -18, 14, -11],\n [2, 10, 16, 1, -12, 19, 12, 17, -22, -15],\n [0, -3, 9, -12, -16, 7, 16, -10, 19, -20],\n [-16, 20, -10, 14, 2, 0, 10, -18, 9, 7],\n [8, -10, 19, -18, 0, -22, -13, 4, -15, -20],\n [-4, -21, 8, -13, -7, 14, -3, -20, 12, 11],\n [-2, 13, 9, -5, 11, 15, -20, -20, 4, -21],\n [-20, -6, 16, 15, 17, -4, -4, 21, -18, -18],\n [-9, 4, 13, 17, 12, -2, -18, 1, 16, 1],\n [17, 20, -10, 15, 22, -22, 20, 16, -13, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-7, 14, -7, 0, 3, -7, 4, 18, 7, 10],\n [9, -14, -12, 14, -17, 7, 17, -8, 7, -5],\n [-11, -19, -7, 0, -12, 1, -1, 16, -8, -8],\n [-13, 5, 13, -6, 13, -1, 0, 6, -1, -12],\n [13, 21, 6, 19, 9, -9, -5, 15, 14, 11],\n [22, 0, 9, -20, 20, -1, 0, -19, -10, 9],\n [6, 17, 17, 22, -13, -10, 22, -6, 15, -21],\n [-6, 21, 3, 15, 14, -18, 2, -14, 5, -1],\n [6, 12, -3, -18, 16, 21, 9, 16, -13, 17],\n [-6, 14, -8, -14, 9, 0, -12, -10, -5, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[19, -18, 20, -1, 9, -21, -2, 5, 1, 1],\n [-9, 14, 4, 1, -17, 3, -8, 6, 13, -13],\n [5, -14, -2, -13, -19, -19, -17, 3, 17, -7],\n [-15, 5, -7, 15, -22, -4, -6, 5, 21, -11],\n [-17, -16, -15, -20, -2, -15, 5, 7, 9, -12],\n [-3, -7, 2, 22, -14, 16, 17, 17, -20, -7],\n [-11, -8, -19, 0, 4, 16, 20, 14, -10, 20],\n [14, 17, -2, 6, 6, -12, 5, -13, -18, 2],\n [10, -6, 10, 2, 10, -14, 4, 2, -19, -14],\n [-8, -7, -7, -10, -9, -1, -2, -14, 18, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-13, 12, -14, -7, -5, -13, -2, -8, -8, -12],\n [17, 19, 18, 14, -3, 11, -1, -5, -7, -18],\n [-22, -4, -13, -2, -10, 1, 0, 0, -12, -21],\n [-17, -12, -8, -14, -11, 13, 5, 0, 4, 1],\n [-9, 12, 4, -2, -10, -15, 21, 21, 21, 11],\n [19, 0, -14, -22, 13, -7, 2, -5, 11, 15],\n [-20, -3, -4, -10, -6, -9, 7, -1, 20, 20],\n [6, -21, -15, -9, 11, -10, -13, -15, -16, -10],\n [3, 9, -4, -8, -21, 14, -4, 10, 16, 10],\n [-22, 16, 5, -6, -17, 21, -3, -10, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -21, -5, 5, -19, 19, 20, -17, 15, -14],\n [-3, 22, 7, 14, 15, -19, 15, -10, 12, 7],\n [19, -19, 2, 8, -11, -8, 3, -13, -11, -1],\n [17, -2, 12, -16, -5, 4, 12, -21, 9, -8],\n [22, 1, -3, -13, 1, 1, 1, 17, 11, 18],\n [17, -12, 3, -22, 7, 20, -5, 3, -14, -14],\n [-22, -16, 21, 19, -7, 15, -12, 2, 6, -4],\n [-5, 6, -7, 17, -15, 11, -17, 22, 22, 7],\n [21, 11, -2, -11, -17, 16, -17, -19, -14, -18],\n [-13, -15, 0, -19, 14, -16, -17, 22, 19, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[12, 9, -9, 12, -12, -13, -6, -10, 11, 22],\n [-18, -13, 9, -11, -10, -2, 10, 18, 9, -11],\n [12, 13, 15, 5, -10, -11, -1, 21, -21, 6],\n [-10, 12, -10, 11, -4, -14, 8, 10, 4, 22],\n [-21, -8, -4, 8, -7, 20, -8, -17, -9, 4],\n [15, -4, 14, 20, -19, 3, -14, 18, 17, -8],\n [18, 14, -19, 3, -5, 18, 12, 18, 18, 6],\n [1, -19, -2, 16, -16, 0, 17, -2, -22, 18],\n [2, 8, 21, 15, 22, -18, 8, -22, 7, -5],\n [-15, 3, 17, -8, -4, -13, 1, -7, 20, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[21, -7, -7, 5, -3, 12, -14, 17, -13, 22],\n [-5, 22, 22, -8, 22, 7, 9, 17, 4, 4],\n [-4, -13, 21, -17, 1, -14, 4, -16, -17, 10],\n [-2, 15, 21, -6, 8, 14, -12, 5, -18, -11],\n [-20, 18, 15, -21, 3, -21, -11, 17, -21, 18],\n [-7, 7, 13, -19, -12, 1, -5, 4, 14, -21],\n [-8, -12, 4, 0, 12, 7, 1, -4, 6, -10],\n [0, -11, 18, 6, -17, 0, 8, 22, -2, 1],\n [-15, 21, -14, -1, -19, -10, 11, -20, 14, 5],\n [3, 11, -8, -15, 12, 1, 14, -19, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-8, 7, 22, 14, -11, -4, 11, -16, 5, 5],\n [6, 14, -3, -12, 16, 19, 0, -3, -3, -12],\n [-21, -10, -10, 18, -8, 8, 0, -1, -7, 19],\n [6, -3, 5, 4, 21, 6, -18, 19, 15, 15],\n [21, -21, 22, -3, 20, -10, 3, 12, -15, 5],\n [18, -8, -15, -12, 6, -18, -16, -5, 5, -11],\n [-11, 13, 6, -12, -17, -2, -13, 9, 10, -6],\n [-20, 20, -5, -13, 18, 16, 20, -15, 11, 14],\n [18, 10, -13, 17, -5, 2, 19, 18, 13, -21],\n [-4, -13, -20, -4, 3, 2, -6, -13, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-11, 17, -15, 1, -9, 0, 13, -6, 22, -18],\n [-20, -14, -3, -3, -4, -2, -7, 10, -18, 1],\n [-8, 3, 21, 2, 5, 10, -5, -5, 15, 10],\n [4, -8, 21, -10, 11, -19, 12, -4, 8, 2],\n [17, -11, -11, 19, 2, 10, 14, 5, 20, -14],\n [-9, -20, -18, 3, 18, -5, 15, -2, 16, -7],\n [17, 0, 6, -13, -18, -12, 6, 22, 4, 11],\n [-9, 18, 19, -13, 19, -12, -12, 12, -4, 1],\n [-22, -11, -9, -20, 22, 9, -7, 15, -13, -6],\n [17, -19, -8, 10, 16, -13, -16, 10, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}
{"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, -7, -9, -20, 21, 7, 18, 12, 3, -11],\n [8, -6, 14, -15, -4, 3, -19, -8, -9, 7],\n [19, 1, 20, 11, -4, -20, -19, -12, -10, -5],\n [-4, 21, 10, 15, -20, 12, -22, 12, 13, 15],\n [16, 2, 17, -10, -19, -17, -12, -22, -15, 11],\n [17, -14, 13, 16, 19, 14, 19, 21, -2, -3],\n [15, -22, 12, 5, -16, 20, 21, -14, -22, 13],\n [11, 11, -6, 9, -21, 13, 2, 20, 3, 22],\n [3, -2, -5, 6, 1, 5, -11, -12, 4, 0],\n [10, -7, 5, 5, 22, 15, -17, 19, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-20, -17, 15, -10, 13, -8, -17, 10, 18, -11],\n [20, -10, 10, 5, 13, -18, 2, -6, 14, -4],\n [12, 20, 11, -17, -4, -22, -16, 11, -4, 10],\n [3, 18, 19, 4, 15, 3, 12, -3, 1, -2],\n [3, -3, -17, -20, -13, -11, 10, -1, -7, -6],\n [-13, -11, -4, 17, 0, 17, -13, -13, -13, 16],\n [7, -19, -22, 20, -4, -18, 7, 3, 17, 11],\n [-21, 1, -9, 18, 19, -10, 6, -22, 11, -19],\n [5, -4, -22, 13, 20, -10, 19, -18, 10, -9],\n [-7, 9, 4, 12, -20, -19, -16, -10, 18, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -13, -22, 5, -13, -16, 16, -20, -16, -14],\n [17, 12, 3, -18, -10, 22, 7, 17, 16, -13],\n [19, 0, -12, -11, -10, 17, -7, -14, -13, 6],\n [-14, 10, 1, 12, -12, 16, -10, 0, 2, -7],\n [-2, -13, 18, 17, -4, 12, 5, 18, -21, 7],\n [17, 17, -18, 15, 19, -8, 13, -20, 1, 18],\n [18, -11, -15, -9, -5, 21, -3, 0, -18, -22],\n [22, -21, -7, -18, -1, -22, -11, -4, -1, 19],\n [21, -6, -10, 16, 5, -20, -18, 13, -8, -6],\n [21, 6, -19, 9, 20, 15, -19, -10, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[19, 14, -11, 2, 7, -8, 13, -15, 5, -1],\n [15, -7, -18, 11, 15, -12, -21, 2, 2, -22],\n [8, -18, 17, -19, -18, -18, -7, -5, 20, -6],\n [12, -5, -19, 8, 8, -14, 8, -18, 13, -7],\n [19, 18, -7, -3, 7, 3, 8, -8, 18, 15],\n [15, 20, -3, 12, 0, 21, 16, 2, -1, -15],\n [-14, -8, -3, 12, 14, -20, 11, 11, 13, 12],\n [-14, 7, 3, -11, 1, 18, -4, 21, -7, 3],\n [0, 10, 19, 7, 0, -13, 13, 8, 20, -1],\n [20, 20, 15, -21, 0, 12, 14, 9, 20, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[12, 18, -20, 11, 15, 1, 15, -6, 17, -22],\n [-15, -8, 22, 2, -15, 9, -10, -8, -17, 10],\n [-16, 10, 6, 15, 14, 21, 9, -20, -3, -9],\n [5, 15, -19, -8, -6, 14, 1, 15, 19, 18],\n [13, 18, -15, -20, 7, -1, 10, 2, 7, 14],\n [-20, -19, 6, 9, 0, -4, -8, -7, 0, 17],\n [14, -22, -4, 14, 12, 7, -6, 16, 3, -10],\n [-1, 0, 21, 20, 10, 4, 12, -11, -14, 11],\n [-9, 14, -20, 21, 21, -2, -16, 10, 12, -12],\n [22, 9, -1, 19, -4, 13, 14, -12, 18, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -8, -10, 20, 10, -15, 9, 14, -19, -5],\n [0, 6, -21, -10, -7, -15, -4, 9, -20, 9],\n [18, -2, 2, -6, 2, 10, 8, 13, 0, 21],\n [2, 21, 7, -10, 20, 6, -7, 15, 4, 3],\n [-12, 14, -20, 3, 11, 10, -8, -21, 5, -3],\n [15, 21, -7, -19, -15, 21, -3, 3, 9, -10],\n [-18, 21, 19, -10, 18, -12, 14, 9, 22, 19],\n [-5, 6, -8, -3, 21, 13, -18, 17, 14, 10],\n [-5, -4, 9, 19, -1, 18, -22, 2, -3, 12],\n [22, -17, -17, 14, -20, 14, 8, 12, 22, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -8, -18, -1, -12, 5, -9, 16, -20, 19],\n [-12, 7, 15, -18, -1, -10, 21, -2, 14, 2],\n [-2, 5, 18, -19, 6, 12, 0, -16, -14, 0],\n [-20, -14, -19, 2, -17, -5, 22, -16, 12, 8],\n [15, 9, 12, 5, 21, -18, 7, -1, -6, -13],\n [-16, -19, 19, 4, -16, 0, -12, -15, -15, 14],\n [-18, -16, -1, 13, -21, 1, -21, -11, 19, 3],\n [15, 22, -17, 0, -21, 3, -9, -5, 15, 9],\n [-9, 7, -10, 17, 8, 14, 22, 15, -1, 5],\n [-4, 20, -7, -18, 21, -21, -13, -4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"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, -10, 22, -7, 12, 13, 16, -20, -14],\n [17, 6, -18, -20, -13, 8, -12, -6, 17, 18],\n [-15, -21, -19, -7, 18, 18, -2, -18, 12, -9],\n [-8, -17, -7, 0, 8, 19, -11, 18, -4, -11],\n [22, -10, -21, -3, 8, -14, -2, -15, 16, 14],\n [6, -4, 12, 22, 15, 3, -12, 13, 12, -19],\n [-20, 22, -11, 9, 3, 20, 20, -10, 21, 15],\n [6, -4, 12, 18, 4, 8, -20, 12, 1, -16],\n [12, -2, -22, 21, -17, 16, 11, -5, 2, -8],\n [9, 19, -5, 8, 6, -8, 0, 15, 18, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-8, 0, -20, -4, -22, 1, -12, 7, -12, 16],\n [-22, -11, -19, 2, -15, -8, 20, 7, 17, 9],\n [21, 12, -2, 8, 13, 4, 21, -15, 0, 0],\n [19, 10, -10, 16, 12, -7, -11, 8, -18, 17],\n [21, 2, -2, -20, -13, 0, -6, 19, 12, 2],\n [-21, 4, -14, -19, 3, 9, 6, -1, -10, 0],\n [8, 18, 13, 17, 8, -8, -9, 12, 1, 7],\n [7, 4, 17, -9, 22, -12, 21, 3, -2, -14],\n [-22, 21, -17, -22, -1, -10, 15, 22, 18, 17],\n [8, -8, -21, 8, 3, -21, -12, 10, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[8, 3, 7, 16, -2, -7, -16, -1, -16, -21],\n [14, -9, -15, 6, 21, -16, 15, 22, -1, 21],\n [-6, -7, 10, 16, 12, 15, 9, -20, -20, -15],\n [8, -14, -18, 5, -8, 4, 19, 8, 17, -5],\n [15, -19, -2, 19, 0, 22, -1, -22, 2, 18],\n [5, 14, -12, -1, 2, -2, 13, -3, -7, 5],\n [6, 3, 17, -21, -13, -10, -8, -14, 4, -15],\n [-17, 13, 1, -20, 3, 13, -2, -10, -12, -15],\n [-9, 10, -21, -22, -12, -17, 9, -8, -11, 14],\n [6, 21, -1, -9, -4, -18, 12, 2, 15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, -5, -21, -13, 21, -21, 22, -15, -16, 12],\n [0, -15, -2, 10, -22, -11, -12, 7, -19, 11],\n [0, 9, -20, 5, -19, -11, 1, 10, -20, -19],\n [7, -17, 7, -15, -5, -7, -17, 1, 5, 9],\n [2, 5, -2, -15, 13, -14, 17, -2, -22, -19],\n [-13, 3, 17, -20, 21, -14, 9, -20, -19, -17],\n [-14, 3, -21, -21, -2, -1, -20, 12, 15, 10],\n [-8, -12, -13, 13, -9, -21, 22, 21, 14, 6],\n [12, -3, -2, 11, 20, 10, -4, -15, 8, -12],\n [-15, 2, -3, 15, -16, -10, 16, 20, -13, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[19, 20, -3, -6, -12, -7, 14, 19, 9, 3],\n [14, -14, 12, -20, 8, 19, -16, -21, 2, 17],\n [-11, 7, 7, 6, 18, -12, 0, -6, -10, 10],\n [-22, 17, -10, 15, -20, -7, 19, -16, -20, -9],\n [-7, -19, 8, -10, 4, -22, 2, 14, 21, -12],\n [-14, -16, -9, 7, 1, -20, 16, 4, -22, 15],\n [3, -17, 19, -11, 15, 12, -13, -14, 0, 7],\n [-1, -14, -4, -15, -19, -18, -4, -5, 6, -4],\n [-17, -18, 20, -18, -15, 4, 14, 20, 22, 15],\n [14, -5, 3, 19, -7, -1, 0, -20, -20, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, -12, 19, 6, -17, -7, 11, 14, -12, -12],\n [2, -4, 9, -15, -11, 18, 12, -17, -2, 3],\n [-22, -6, 12, 4, -21, 13, -22, -13, 8, 14],\n [-18, 18, -10, 22, 1, 4, -22, -3, -15, -20],\n [9, 21, 2, 2, -9, 20, 4, 9, 4, -19],\n [16, -12, -20, 2, 1, -14, -15, 16, 8, -6],\n [20, 8, -19, -19, 14, -15, 19, -17, -14, 19],\n [-15, 9, -8, -5, 0, -18, 4, 10, -21, 19],\n [15, 5, 1, -2, 8, -12, 5, 17, -19, 20],\n [19, -7, -11, -1, 12, 20, -7, 1, 12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, 6, -2, 2, 16, 8, -8, 19, 12, 15],\n [-1, -18, -10, 9, -20, -8, 4, 4, 7, -17],\n [2, 5, -1, -19, -8, 3, -5, -14, -19, -18],\n [22, -17, -11, 8, -14, -16, 6, -9, -3, 9],\n [-1, 13, 21, -5, 17, 2, 8, 12, 3, -19],\n [19, -3, 11, -11, -7, 19, -18, 21, 12, 21],\n [4, -22, 11, 20, 9, 21, 16, 10, 8, -10],\n [22, -21, 7, -13, 0, 10, 16, 22, 6, 7],\n [11, 16, -6, -1, -18, -12, -1, 9, 1, -12],\n [-12, -6, 9, -4, 4, 9, 2, 5, 17, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 19, 16, -21, -6, -22, 22, 9, -4, -9],\n [8, -5, -9, -9, 1, -18, -7, -18, -10, -7],\n [-8, 8, -18, -2, 7, 0, 15, 6, -10, 9],\n [19, 4, 11, 22, 10, -19, -5, -17, 5, 21],\n [4, 3, -3, -10, 5, 11, 0, -13, 7, -1],\n [-18, 21, -14, 20, -19, 19, -22, 11, 18, 3],\n [-5, -7, 0, 13, 3, -21, 21, -18, 6, -19],\n [12, -1, -15, 21, -2, -15, -18, -2, 4, 15],\n [-18, -2, -15, -1, -5, -19, -19, 14, -8, 15],\n [4, -2, -19, -12, -4, -4, 4, 17, 19, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-18, 2, -20, 3, -13, 1, 6, 22, -16, 21],\n [0, 4, 19, -14, 21, -20, -10, -17, 15, -2],\n [-4, 2, 16, -19, -1, -18, -22, -6, -14, -14],\n [1, -13, -3, -6, -10, 6, 13, 0, 4, -5],\n [-5, -14, -20, -16, -8, 7, -14, 18, 4, 13],\n [-5, 8, -6, -17, 16, 2, 19, 19, 15, 15],\n [8, 6, 17, -14, -22, -7, 15, 0, -15, -11],\n [-13, -7, 20, 1, 16, -15, -12, 18, 3, -16],\n [-8, -8, -20, -7, -8, 2, 10, -9, 1, -12],\n [-20, -14, -17, 8, -7, -12, -6, -20, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[19, -15, 13, 17, -21, 0, 17, 7, 2, -16],\n [5, 18, -6, 9, -22, 4, 21, 13, -16, -20],\n [7, -22, 11, 15, 20, 13, 10, 20, -7, 15],\n [-12, -15, -22, -9, 7, -2, -2, 11, 15, 3],\n [18, -9, 17, 12, 19, -5, -3, -14, 18, 22],\n [10, -19, -19, -7, 3, -17, 14, -1, 19, 16],\n [-16, 19, 7, -13, -8, -17, 1, -21, 17, -8],\n [-2, -5, -18, 2, 13, -13, 0, 1, 22, -13],\n [-17, -10, -2, 9, 20, -8, -21, -8, -6, -3],\n [-17, -8, -6, 3, -1, -14, -11, -1, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, 1, -15, 3, 9, 5, 9, -1, -14, -20],\n [2, 16, -11, 6, -20, 18, 0, 0, -5, -12],\n [13, 3, -15, 5, -5, -10, 13, 19, 17, 21],\n [-11, -1, -21, 17, 5, -10, 10, -20, 11, 0],\n [9, -3, 5, -15, -20, 7, 2, 7, 6, 7],\n [11, 2, -6, 1, 15, 5, 10, 13, -16, 0],\n [3, -9, 19, 5, 1, -16, 13, 16, -8, -20],\n [-21, -16, -7, -2, -14, -11, 6, 1, 10, -9],\n [20, -5, -18, -8, -16, 2, -9, 17, 13, 12],\n [21, 1, -8, -12, 1, -12, 21, -6, -17, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-15, -8, 9, -13, 5, -8, -11, 20, -5, 14],\n [21, 1, 14, 6, -13, -9, -7, 14, -12, 3],\n [17, -4, -5, 7, 9, 0, -11, -10, -2, -2],\n [6, 6, 4, 6, -8, -11, 18, -4, -11, 0],\n [-18, 3, -13, -1, 16, 0, -12, 5, 8, -15],\n [16, 5, -7, 8, 18, -7, -18, 12, 2, -10],\n [6, 4, 17, -6, 14, 15, 6, 11, 7, 8],\n [-1, 2, -19, 12, 18, 21, -14, 3, 4, 4],\n [-5, 7, 22, 8, 19, -20, 6, -16, -5, -7],\n [9, 15, 2, 21, 9, -4, -20, 12, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-17, -4, 14, 22, 4, -18, 3, 12, -4, -6],\n [12, -10, -9, 7, 20, -6, 14, -8, -5, -9],\n [-9, 22, 10, 15, -12, -12, 3, -20, 2, -6],\n [-1, 6, 3, 11, 3, -14, 17, -12, -16, 7],\n [-21, 7, -19, -9, -10, 2, -10, -10, 14, 21],\n [-17, 3, -9, -15, 1, -1, 17, 16, -2, 20],\n [3, -13, -10, 19, -9, -14, -16, 16, 8, -7],\n [-15, -8, 2, 15, 18, -8, 2, -16, 3, -15],\n [-5, -2, -7, -20, -22, -10, 9, -11, 8, 18],\n [-21, 18, -15, 2, -18, 22, -21, 19, 15, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-20, 15, -1, 17, 10, 9, -6, -5, -20, -17],\n [-10, 8, -6, -2, -7, -6, 9, -22, 15, -15],\n [-22, -21, 14, 1, 4, -3, -2, 19, 14, 12],\n [15, -8, 19, 7, -19, 20, 16, -8, 0, 18],\n [-8, 3, -11, -5, -17, -5, 1, 15, 5, -8],\n [-4, -18, -19, -6, -13, -11, -18, -16, 21, 0],\n [-21, 7, 22, 14, -18, -3, 3, 21, 21, 16],\n [-17, 6, -13, -7, 11, 8, 13, 18, -18, 10],\n [20, -4, 9, 0, -20, -22, 13, 18, 5, 16],\n [-18, -10, -12, -1, 0, -11, -2, -4, -18, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[7, -15, -21, 11, 0, -20, 1, -5, 14, 8],\n [-9, -22, -9, 18, -18, 8, 8, 7, 13, -22],\n [-20, -3, 20, 20, -2, 7, 19, 21, 7, -18],\n [-13, 1, 22, 16, -17, -13, 19, 20, -13, 2],\n [-9, 16, -10, -12, 16, -12, -7, 10, 18, 18],\n [9, -13, -8, -7, 20, 4, 22, 9, -17, 13],\n [-15, 2, -16, -6, 7, -21, -6, -19, 3, -9],\n [-15, -18, -18, -18, 4, -18, -20, 15, 7, -22],\n [-15, -10, -3, -17, -15, 7, 17, -8, -13, 10],\n [-14, 10, -14, -9, 9, 14, -17, -18, -19, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-13, 8, 8, -9, -10, -19, 3, 1, -14, 12],\n [19, -8, 1, 8, -4, -21, -21, 18, 13, 14],\n [11, 16, -4, 15, 0, -7, 21, -17, 3, -1],\n [22, 1, 17, -2, 7, -12, -14, -11, 3, 15],\n [-20, 10, -8, -18, 1, -12, 10, 0, -13, 20],\n [5, 16, -6, 21, 3, 2, 13, -11, -20, 6],\n [21, 1, -4, -10, -7, 17, 4, -17, 19, -13],\n [15, -15, -5, 9, -6, 19, -21, 21, -3, -13],\n [-14, 16, 18, 2, 2, 1, -17, 7, -13, 16],\n [8, -5, 20, 10, -4, 0, -18, 3, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-17, 16, -19, 19, 3, -8, -10, 17, -1, -10],\n [16, -6, 13, 16, 2, 11, -2, 2, 2, -1],\n [0, 2, -9, -9, 3, 17, 7, 3, 15, -1],\n [16, 16, 11, 2, 13, -10, 6, 19, -14, -8],\n [8, 21, 4, 8, -13, 14, -16, 9, -12, 22],\n [5, -19, 22, 8, 6, 10, -19, 3, 8, 8],\n [4, 2, 13, 8, 20, 14, 22, 21, 0, 12],\n [-19, 5, 19, 18, 19, -10, -22, -11, 20, 17],\n [3, 0, -1, 5, -6, -17, -9, -6, 15, -18],\n [-10, -14, 21, 19, 3, -10, -4, -6, -7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[9, -9, -8, -11, 14, -12, -18, -12, 11, -4],\n [3, 3, -6, 8, -4, 21, -3, 0, 2, 5],\n [14, -11, -22, -21, -13, 11, 9, 2, -13, -22],\n [9, 14, -11, -5, 7, -10, -20, -2, 19, -9],\n [17, -13, -21, 22, 14, -12, -22, 3, 19, -10],\n [5, 13, -2, -13, -11, 4, -20, 5, -21, 5],\n [8, 20, -2, -16, 8, -9, 16, 16, -14, 0],\n [-11, 6, 15, 16, -1, -19, -16, 17, -15, 12],\n [-14, -10, 16, -3, -2, -4, -21, 21, 17, 7],\n [0, 17, -10, 10, 9, 5, 1, 19, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[18, 6, 11, -1, 2, -9, -13, -13, -15, -9],\n [22, 15, 9, 22, 9, -20, -3, -10, 0, -4],\n [-7, 13, 12, -16, 14, -15, 2, 0, -13, 7],\n [10, -12, 12, 4, -20, -15, -10, 19, -20, -3],\n [22, 12, -10, -3, 1, -14, 7, 2, -7, -15],\n [21, 5, -11, 1, 6, -8, -5, -16, -10, -4],\n [20, -18, 3, -21, 10, 14, 2, 2, 16, 7],\n [18, -19, -4, 4, 16, 1, 14, 2, 6, 8],\n [22, 12, 5, 15, 21, -19, 5, 8, 0, -9],\n [5, -9, -22, 20, 9, 18, -5, -18, 19, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "325", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, -7, 13, 13, 17, 7, 15, 0, -12, 2],\n [22, 20, -21, 12, 1, -10, 19, 14, 7, -12],\n [0, 5, 6, -8, 22, -20, -14, -15, 10, 11],\n [-14, -6, 18, -22, 17, -18, 7, -12, 5, 15],\n [-6, 0, -5, 14, 4, 2, -18, -4, 4, -10],\n [-16, 3, -9, 4, -15, 8, 12, 4, -19, 19],\n [-19, -5, 0, 9, -11, -3, 22, -11, -15, -1],\n [4, 18, 18, -6, 9, 10, 8, -17, 16, -14],\n [19, 9, 13, -7, -11, 18, -20, 4, 4, -14],\n [-6, -18, 3, -2, -22, -22, 12, -14, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[18, -19, -4, 14, -18, 5, 19, 0, 15, 0],\n [-5, 6, 5, -14, 16, -13, -21, -10, 15, 4],\n [18, -3, 17, -13, -7, -8, -10, 15, -3, 1],\n [18, -16, 0, 1, 6, -18, 20, 22, 12, -22],\n [13, -5, -17, 0, -13, -16, 21, -15, -10, 7],\n [-5, -9, -12, 19, 15, -10, 19, 21, 10, -10],\n [2, 1, 6, 13, -17, -5, 5, -18, -5, 14],\n [-16, -14, 12, -11, 17, 21, 16, 1, -14, -11],\n [13, 14, -14, 16, -1, -6, 10, 1, -8, 6],\n [9, 10, 6, -8, 4, 11, -19, -5, -2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-17, -3, -21, 22, -1, -2, -17, 9, -17, -10],\n [-22, -1, 1, 18, 7, -1, 21, -11, 3, -19],\n [-4, -7, -11, 10, -2, 13, -14, 16, 19, 22],\n [-15, -3, -13, 9, 5, -13, -15, 10, -10, 21],\n [12, 6, -18, -20, 14, 18, -17, 19, -7, 12],\n [-5, -12, 0, -12, 6, 19, 4, -14, 12, -14],\n [-5, 21, -2, 13, -22, 4, 22, 17, 15, 6],\n [17, -4, 1, 21, -22, 13, 0, -10, 7, 14],\n [-12, -16, 12, -12, 20, 17, -2, -20, 7, 1],\n [15, -20, 14, 10, -1, 8, -11, 22, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -10, 1, 15, -14, -15, 14, -8, -16, 1],\n [-7, 1, 20, -16, 20, 5, -21, 11, 15, -20],\n [-22, 8, 0, -3, -7, 9, -6, -5, -19, 12],\n [17, 13, 0, -8, -10, -9, -9, 14, -18, -1],\n [5, 22, -19, 15, 6, 14, 12, -3, 12, 12],\n [-3, -21, -5, 7, 19, 6, 16, -1, 6, -13],\n [-3, -7, -17, -6, -17, -1, -5, 9, 5, 19],\n [-13, 18, -1, 5, -8, 20, 6, -16, 11, 9],\n [-21, 3, 22, -12, 2, -4, -3, 10, -6, 7],\n [-5, 9, 17, 22, -19, 9, -4, -20, 15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[15, -17, 17, -6, 19, -18, -4, 20, 19, 12],\n [-1, 1, -13, -21, 5, 18, 14, -6, -17, 20],\n [-18, 16, -16, 9, -19, -2, 19, 9, -5, 10],\n [-9, -17, -12, -3, 6, 12, -7, -16, 17, 13],\n [21, 21, 8, 19, 21, 20, 20, -17, 6, 4],\n [20, -21, -1, -14, -12, -7, 22, -10, -5, 2],\n [10, -13, 7, -22, 10, -8, 6, -21, -12, 11],\n [18, -4, -21, -3, 18, 8, -19, 6, 7, -10],\n [-8, -3, 11, 5, -3, 2, 4, 7, 18, -3],\n [-22, 12, 20, 1, 2, 17, -11, -12, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, 2, -6, -11, -12, -13, -6, 22, -7, -3],\n [-18, 18, 9, 4, -19, 18, -16, -9, 16, 1],\n [-5, 15, 16, 17, -22, -6, 3, -1, 16, -5],\n [15, 5, -2, 15, 10, 7, 19, -15, 7, 16],\n [-14, 10, 20, 6, 8, -20, 15, -12, -18, 8],\n [-3, -19, -15, 19, 12, -10, -18, 17, -4, -5],\n [10, -19, -5, 1, 20, 6, 8, 5, -14, 22],\n [3, -21, -17, 6, 3, 5, -16, 11, 22, -13],\n [18, 17, -1, 4, 16, -1, -4, 13, -14, -4],\n [-21, 5, 16, -1, -17, -16, -17, 10, -9, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"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, -17, 5, -5, 4, -21, 17, -2, 0, -21],\n [-7, -19, 11, -18, 11, -1, -3, 16, -10, 21],\n [11, 21, -17, 6, 10, -22, -16, -1, 9, -9],\n [1, -4, 4, 0, 22, -2, 21, 6, -22, 8],\n [4, 21, 13, 4, -8, 2, -8, 17, -4, -12],\n [18, 10, 18, 0, -11, -21, 20, -2, -9, 11],\n [-8, -2, 0, -2, -9, -2, -11, 19, -18, -21],\n [-1, -17, 21, -21, 6, 13, -16, -7, 10, 10],\n [-9, 20, -11, 20, -17, -11, 8, -11, -13, 17],\n [4, -16, 13, 10, 4, -15, -18, -15, 17, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -16, -4, 8, 13, 4, 6, 0, -3, -17],\n [-11, -11, -20, 19, 16, 12, -4, 22, -19, 8],\n [19, 15, 10, -17, -15, 5, -8, 8, -15, -17],\n [6, 11, -16, 17, -13, -10, -1, -2, -22, 18],\n [19, -21, 6, -12, 14, -16, 12, 7, -7, -8],\n [17, -3, 5, 14, -20, 6, 14, -14, 4, 9],\n [16, 8, 3, 17, -20, -12, 6, 4, -13, 12],\n [0, -17, -12, 20, 4, 8, 7, -20, -10, 17],\n [-2, 20, -12, 22, -20, 15, 8, 1, 19, -11],\n [20, 4, -2, 2, 7, 7, -13, -20, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 22, 1, -9, 16, 21, -19, -7, -13, 14],\n [4, -22, -18, -10, 22, -20, -6, -4, 14, -18],\n [19, 21, 1, 20, 10, -2, -20, -19, 9, 1],\n [12, -5, -20, 16, 3, 1, -22, 11, -11, -6],\n [-2, -2, -20, 21, 5, 2, 21, -17, 19, 7],\n [9, -1, 15, -9, 11, 20, 3, 17, -10, 7],\n [-4, 19, 18, 16, -20, 8, -11, -8, 22, 15],\n [17, -9, 12, -7, 1, -6, -5, 19, -6, -7],\n [-2, 1, 11, 13, 20, 4, 16, -6, 2, 15],\n [19, -2, -19, 2, 7, 10, 16, 3, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "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, -18, 19, 16, -10, 7, -16, -6, 4, 12],\n [-18, 19, -18, 1, -16, -16, -9, -8, -18, 14],\n [-19, 7, -3, 3, -14, 7, 21, -1, 17, 18],\n [21, 7, -3, 5, -16, -19, 5, 12, 10, -16],\n [-14, 11, 16, 19, 11, -10, 6, 12, 22, -13],\n [7, 21, 3, 12, 5, 6, -17, -20, 6, -21],\n [-1, 4, -1, -13, -4, 1, 4, 13, 20, -6],\n [-13, -6, 21, -13, -13, 15, -6, 3, 3, 11],\n [-19, 4, -2, 13, 15, 8, -16, 21, 11, -5],\n [1, -10, -10, 2, -18, 16, 6, 21, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-13, 2, 18, -13, 16, -7, 5, -11, 21, 9],\n [6, 22, 4, 3, -20, 3, 16, -22, 12, 4],\n [-19, -4, -1, -17, -14, -12, -1, -14, 6, 20],\n [-13, 11, 8, -1, -19, -21, -18, -8, -4, 15],\n [-8, -15, -3, -11, -19, 15, 20, 16, 13, -8],\n [-22, 8, -14, 0, 3, 17, 21, 16, -5, 10],\n [18, 16, -9, -22, -10, -8, 14, -18, -9, -9],\n [-18, -12, 9, -18, 13, -8, -16, -18, 7, -8],\n [7, -9, 1, 1, 12, -18, -11, -3, -18, 13],\n [-2, 16, -20, 6, 2, 4, 13, -1, 15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-22, -20, 1, -15, 16, -5, 18, -20, -5, -7],\n [9, -22, 3, -11, 15, -2, 18, -10, -11, -10],\n [-5, -4, -4, -17, -16, -16, 5, 5, -4, -7],\n [-6, -1, -4, 6, -4, 12, 2, -3, 14, -4],\n [19, -10, -11, -8, -19, -8, -6, 4, -12, 0],\n [-8, 8, 3, -16, -10, -10, -3, 11, -13, 14],\n [4, 11, 13, -7, -2, -7, -6, -8, -10, 10],\n [-18, 4, -22, 21, 7, 0, -8, 13, -4, 7],\n [-7, -5, 3, -6, -12, 22, 6, -14, -6, 4],\n [14, -1, -15, -20, 15, 12, 9, -15, 21, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[9, 13, 11, 2, 8, 19, -10, -8, -10, 10],\n [8, 2, 17, 0, 15, -20, -7, -21, 0, 11],\n [7, -13, -22, -1, 10, 2, -1, -7, 7, -5],\n [1, -18, 14, 0, 19, 4, -11, -13, 11, 10],\n [-7, 6, -5, 4, -16, 13, 4, -13, -13, -12],\n [7, -20, 6, -9, -10, -4, 2, -13, -8, 5],\n [17, 15, -16, -9, 7, 17, -11, 5, -9, -22],\n [-19, -5, 13, 9, 5, 5, 15, 9, -15, 2],\n [-3, 10, 7, 14, -7, 2, 15, 19, -13, -18],\n [-15, 10, 14, -22, 8, -16, 0, 1, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-14, -15, -15, -20, 9, -19, 15, -21, -14, -22],\n [-12, 6, 3, 4, 15, 6, 10, 5, 8, -4],\n [3, 6, -12, 18, 9, -2, 15, 11, 17, -1],\n [4, -15, 17, 8, -22, 16, 11, 1, 5, -19],\n [-5, 6, 0, 14, 4, -7, 22, 4, -14, -18],\n [-15, -5, 12, -17, 20, 0, 3, 16, 1, -13],\n [-8, 15, -3, 6, -17, -14, -18, 16, -4, -18],\n [-3, -12, 4, 6, -16, -20, -18, -10, -7, -11],\n [16, 4, 22, 10, -8, -2, 21, -6, 14, -8],\n [-3, -4, -22, -19, -20, -15, 18, 21, -18, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-22, 20, 7, -16, -1, -3, 6, 4, 2, 12],\n [4, -12, -6, 8, -5, -4, 15, 6, -8, -16],\n [14, 14, -16, -1, -11, -15, -5, 5, -5, 8],\n [-6, 0, -12, -8, 7, 8, -17, -11, 0, 16],\n [17, 13, 12, -20, 19, 5, -8, -10, -4, 17],\n [-5, 8, 14, -2, 16, -18, -6, -4, -19, 3],\n [1, 16, 15, -4, 7, 3, -12, 16, -20, -1],\n [-6, -12, 16, 4, 20, 6, -11, -10, -12, 8],\n [-12, 18, 20, 13, -21, 0, 13, -9, 14, 4],\n [-11, 6, -17, 21, 0, -13, 11, 21, -11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -16, 9, 10, -5, 12, -3, 8, -18, 9],\n [19, -4, -22, -16, -1, 11, -13, 19, 3, 9],\n [19, 4, -11, 17, 0, -9, 11, -6, -17, 4],\n [-15, 10, 12, -6, 3, -16, 1, 2, 12, 3],\n [-18, 15, 12, 7, 2, 1, 7, -3, -20, 9],\n [-15, 0, -7, 12, 2, -8, -15, 11, 2, 21],\n [-4, 20, -10, -11, -8, 0, 17, -21, 17, 0],\n [-18, 11, -13, 4, 19, -19, -19, -15, -17, 2],\n [4, 17, -3, 4, -16, 0, -3, 11, 6, 21],\n [-18, 4, -11, -6, 14, 11, 7, 13, -17, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[9, -14, -1, -13, 6, -12, 5, -21, -2, 8],\n [18, -6, 4, 7, 18, -15, 14, -18, 3, -17],\n [-7, -22, -14, -2, -16, 20, -8, 1, -18, 15],\n [6, -12, -19, -13, 11, -19, -13, 10, -5, -11],\n [0, 21, 2, 14, -19, -10, -5, 6, 21, 7],\n [15, 5, -16, 1, 18, -13, 14, 4, -2, 13],\n [20, 6, -16, -10, 22, 0, 2, 18, 22, -10],\n [14, 7, 3, -11, -22, -5, -2, 1, -6, 19],\n [-14, 17, 5, -8, -10, 5, -6, -14, -2, 7],\n [-12, 7, 13, 2, -16, -3, 12, -13, 12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 22, -18, 17, 21, 15, 11, 1, -19, 4],\n [-18, 20, -10, 17, -2, 14, 9, 15, 8, 9],\n [-8, 7, 20, -16, 15, 8, 21, 3, 13, 20],\n [3, 21, -21, 20, 22, 20, -14, -18, 4, -11],\n [12, 6, -7, -4, 20, 4, -5, 18, -10, 7],\n [3, -17, -20, 0, -11, 18, 18, -8, -22, -15],\n [8, -12, -6, 4, 8, 4, -9, 0, -18, 7],\n [11, -4, 8, -7, 22, 4, 3, 16, 6, 16],\n [21, 22, 6, 22, 8, -21, -17, -14, -8, -3],\n [-21, -20, 7, -15, 17, -2, 16, 20, -10, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[18, 14, 9, -9, -22, 4, 1, -1, -9, 22],\n [-15, 4, -20, 10, -2, 9, 17, 18, 22, 21],\n [18, 9, 1, -12, 14, -2, -5, -12, 4, 20],\n [15, -22, 6, -2, 6, -14, -16, 15, 8, 4],\n [19, 9, -18, 10, -8, -18, -3, 15, 14, -6],\n [-19, -2, 11, 17, -18, -19, -1, -9, -19, -15],\n [-20, 6, 3, 7, -11, -8, 18, -21, -22, 5],\n [17, 12, 11, -19, -5, -11, -2, -13, -2, 17],\n [2, -6, -17, -9, 14, 17, 17, -5, 7, -14],\n [-9, -6, 11, -1, 9, -11, -7, -1, 15, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-21, 22, -15, 21, -22, 18, 17, 18, -18, 22],\n [13, -6, 18, 7, -8, -3, 13, -21, 22, -19],\n [1, 19, -21, -21, -22, -10, -17, -1, -6, -1],\n [20, -17, -20, -17, -6, 12, 14, 12, 0, -15],\n [-16, -13, 3, -13, -4, 0, 8, 10, -21, 5],\n [9, 10, -14, 6, -8, -5, -5, -16, -9, 6],\n [-4, -18, 18, 22, -18, -8, 3, 1, -4, -3],\n [20, -14, 5, -7, -12, 11, 2, 17, -2, -18],\n [-12, 20, -14, -12, 14, 18, -22, 3, -13, 17],\n [-4, -7, 22, 14, 18, -19, -9, 7, -16, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "376", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 16, 20, -1, 7, 16, -3, 3, -18, 17],\n [19, -17, 11, -18, -13, 5, -20, -10, -21, 12],\n [5, 14, 0, 20, 0, 12, 18, 16, 9, -21],\n [21, -7, -7, -20, 5, 6, -3, 13, 10, -1],\n [-15, 1, 14, -3, -11, -3, -3, -19, 7, 8],\n [-1, -8, 15, 14, 5, -12, -9, -12, -14, 1],\n [-13, 15, 20, 18, 14, 19, 9, -3, -9, 15],\n [-19, 1, 9, -13, 20, -7, 16, 9, -5, 2],\n [-16, -5, -5, -20, -22, 10, -16, -13, 21, -15],\n [9, 0, -6, -9, -6, 2, -2, -17, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 9, -15, 22, 21, 6, -6, -5, 17, -5],\n [-12, 22, -11, -8, 3, -20, -20, 15, 12, -14],\n [20, 17, -19, -3, -8, 6, -18, 16, 17, -16],\n [-15, 9, 13, 10, 14, 9, 20, 13, 11, 2],\n [21, 9, -21, -14, 15, 6, 15, -5, -1, 12],\n [-8, -16, -10, 19, 13, -7, 18, -2, 5, -13],\n [-4, -6, -22, -10, 13, 19, -3, 18, 17, -17],\n [0, 19, 1, -18, 9, -6, -12, 4, -19, 0],\n [0, 11, -2, -1, -22, 9, 5, -5, -16, 15],\n [-17, -9, 7, 21, -9, 21, 18, -14, 8, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -18, 3, 0, -11, -9, -10, 12, -8, 12],\n [-4, -8, -15, 0, -10, 0, 8, 7, 19, -21],\n [-12, 2, 6, -1, -4, -14, 18, 15, 6, -13],\n [-1, 1, -15, -17, -16, -3, -6, 13, -15, -10],\n [1, 8, 0, -6, 1, 20, -13, 8, 22, -3],\n [-7, -9, -20, 7, -5, -17, -3, 12, -4, 3],\n [12, -11, -15, 14, -13, -2, 18, 22, 19, 6],\n [8, 17, -16, 11, 11, 7, -19, 18, 7, 2],\n [-9, 1, 20, 8, 16, 5, 2, -4, -19, 11],\n [9, 2, -1, 5, -5, -16, -12, 19, -12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[12, 14, 0, 10, -22, -3, -18, 6, 3, 15],\n [-20, -2, -10, 8, -6, 12, 0, -20, 22, -21],\n [-20, -3, 21, -14, -19, 2, -22, 16, -11, 17],\n [17, 1, -14, -3, -18, -3, -2, -21, -2, 19],\n [1, -14, 16, 7, -5, 21, 20, -13, 22, 18],\n [-2, -1, -6, -18, -17, -13, 20, -21, -16, -19],\n [14, -4, 5, -3, 7, 19, 15, -21, -20, 19],\n [16, 2, -21, 16, -8, -20, -18, 17, 13, 17],\n [15, 14, 4, -18, -6, 15, 22, 18, -11, 19],\n [8, 10, 20, 6, 15, -20, 15, 18, 17, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 15, 9, 20, -13, 9, 20, -19, 6, 22],\n [-15, -3, -16, -22, 2, 3, -14, 0, 17, -21],\n [3, -9, 21, 8, 3, -4, 15, -18, -17, 12],\n [-7, 8, -5, -9, 2, -8, 3, 13, -12, 14],\n [18, 14, -16, -5, -3, -21, 3, 0, 9, -10],\n [-10, -6, 2, -1, 4, -6, 3, 15, -9, -9],\n [-11, -18, 14, -19, 6, 2, 22, -19, -7, -21],\n [0, -19, -3, -6, -17, -5, -3, 16, 22, 18],\n [11, 17, 1, -5, 7, -22, 0, 6, 18, 18],\n [9, -21, 13, 22, -6, 20, -21, -19, 21, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-22, 0, -17, -7, -21, -11, 4, -4, 5, 12],\n [20, -19, -16, 14, 2, 18, -6, 18, -9, 14],\n [-21, 1, -8, 10, -11, -4, -18, -22, 20, -14],\n [16, 11, 6, -21, -4, 5, 12, 17, -1, -19],\n [-15, -22, 13, -16, 2, 6, -22, -5, -19, -3],\n [-15, 4, 16, 12, 2, -9, 21, 17, 8, -18],\n [-6, -13, 20, -7, -19, -18, 19, 18, -3, -17],\n [-12, -6, 18, -20, -7, 13, 3, 1, 11, -3],\n [-6, -3, -7, -19, -5, 13, 12, 7, -5, -2],\n [9, -18, 18, 0, 7, 4, -8, 18, -9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[11, 3, 2, 22, 8, -17, -19, 1, 19, 8],\n [-4, -12, 6, -18, -5, -20, 17, -12, -2, 7],\n [-4, 2, 12, -11, 3, -18, -4, 4, 15, 6],\n [-11, -4, -14, -5, 6, -20, 0, 7, 1, 14],\n [14, -19, 5, -7, -10, -15, 2, -21, 7, 17],\n [-20, 0, 6, 18, 7, -12, -2, 4, 1, 8],\n [7, -22, -22, -15, 19, 11, -7, 4, -19, -4],\n [6, 18, -20, -12, -15, 16, 10, -15, 2, 1],\n [3, 3, -6, 4, 6, 20, 16, -14, -9, -18],\n [7, 5, 22, 14, -15, -8, 5, 13, 10, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-11, -16, 22, 5, -16, 18, -22, 1, 22, -4],\n [9, 7, -22, 9, -3, -2, -4, 7, 5, 9],\n [7, 0, 4, 14, 3, -20, 8, -21, -13, 15],\n [-4, 8, 6, 2, 9, -6, 22, 0, -5, -12],\n [-3, -10, 1, 20, -3, 19, 5, 12, -2, -17],\n [-16, 6, 0, -18, -1, -14, 9, -13, 20, 5],\n [-12, -16, 7, 20, 22, 15, 11, 5, 9, -7],\n [16, -22, 11, 18, 0, -3, -5, -5, 19, 17],\n [-2, -15, 11, -12, 20, 20, -13, -15, -15, -4],\n [-22, -20, 21, 9, -7, 7, 5, 5, -7, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, 2, -5, 3, -17, 15, 21, -20, 20, -17],\n [-9, -5, -7, 1, -10, -22, 15, -9, -6, -10],\n [-10, -14, -17, -17, 7, 14, -9, -19, 11, -21],\n [-6, 19, -9, -6, 7, 20, 6, -16, -14, 0],\n [13, -9, -3, -6, 9, 2, 7, 4, 4, 8],\n [22, 3, -9, -2, 5, -8, 7, 2, -12, 21],\n [-12, 5, -18, 5, -15, 3, -17, 9, 9, -11],\n [-17, -10, 16, 17, 21, 11, 0, 18, 22, -6],\n [22, -22, -16, -10, -9, -6, 7, 11, 4, 2],\n [21, 12, -14, -17, 3, 15, 16, 4, 17, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "339", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-20, 1, -8, -17, -12, 7, 12, 15, 20, 17],\n [6, 0, 19, 19, -20, 3, -9, -4, -2, -2],\n [-14, -10, 18, 21, 14, 15, 22, 22, 1, 15],\n [-12, 6, 22, 21, 15, 18, -6, 3, 3, -11],\n [-5, -14, -20, -13, 20, -21, -15, 20, -5, 16],\n [8, -9, 16, 10, 6, 21, 10, 12, -21, 12],\n [9, 13, 0, -18, -7, 17, 1, 17, 5, 2],\n [-16, 15, -16, -1, -1, 4, 10, 22, 9, 16],\n [9, -22, -13, 22, -19, 6, -16, 15, -17, -12],\n [-14, 7, -1, 16, -14, 15, 10, 3, -7, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -8, -4, 19, -7, 2, 12, -10, -16, 11],\n [-9, 0, 0, -6, -10, 4, -21, 14, 7, -19],\n [7, -20, -9, -12, 17, 0, 18, 9, -20, 19],\n [-22, -14, -14, -11, -22, -7, 7, -15, -13, 10],\n [15, 18, -1, -7, -4, -12, -12, -9, 16, 3],\n [21, -3, -3, -18, -22, -12, -13, 5, 22, 11],\n [-10, 21, 2, 0, 13, -11, 22, -21, -3, -7],\n [-9, -21, -7, -19, 20, -10, 15, -22, -14, -2],\n [-5, 20, 9, 11, -3, 20, -21, -19, 22, 15],\n [-16, -1, -3, 12, -19, -3, 12, 10, -2, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, 8, -1, 7, 6, 13, 19, 6, -16, 9],\n [-10, -10, -9, -17, -7, 18, -2, 21, -7, -18],\n [1, 20, -22, -13, 20, 12, 8, -8, -12, -14],\n [-21, 21, 7, -7, -22, -17, -12, 10, -6, 11],\n [17, 2, -1, 3, 4, 15, -14, 14, -18, -5],\n [-1, -11, 21, -1, -17, 13, 4, -8, -6, -20],\n [-13, 2, -2, 17, -14, 1, 9, -20, 10, 20],\n [22, -11, 6, -2, 16, 11, 10, 9, -3, -20],\n [-19, -6, -6, -4, -19, 6, -6, -1, -21, 19],\n [-11, 22, -12, 17, 6, -3, -18, 2, 11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, 11, -17, -4, -11, 2, -10, -6, -11, -20],\n [1, -15, 13, 3, 22, -15, 9, 9, -22, -20],\n [-22, -8, -3, -20, -8, 14, -2, 19, 16, 0],\n [17, 12, -5, -6, 8, 3, -1, 22, 13, 12],\n [-12, 4, 11, -5, 4, -19, -6, -17, 19, -12],\n [-18, -5, 2, -13, 18, -7, -13, -13, 13, -2],\n [-9, -15, -22, -7, 3, 19, -17, 16, -21, -14],\n [-18, 17, -18, -15, -18, -18, -6, -14, 11, 10],\n [-1, -2, 20, -8, -22, -16, 0, -17, -3, 3],\n [19, -11, -10, -10, -21, 9, 8, -12, 14, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[11, -7, 8, 2, 16, -15, -15, 11, -8, -18],\n [-4, -13, -14, 6, 17, 14, -4, -10, 17, -7],\n [7, -18, 10, -4, -4, -6, 1, 5, 19, 14],\n [-1, 16, -7, 12, 4, -11, 5, -22, 16, -5],\n [0, -1, -19, -12, -5, -16, -2, 12, 14, 7],\n [-6, 10, -7, -8, -10, 16, -20, 1, 0, 22],\n [-22, 9, 10, 7, -21, -5, 7, -5, -18, -18],\n [-15, -14, 9, -9, -10, -5, -19, -1, -3, -8],\n [-16, -10, 11, 18, 7, -18, -22, 8, -3, -4],\n [6, 22, 15, -13, 6, 8, -12, 0, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-7, 0, 10, 14, 5, 4, -17, 15, 14, -17],\n [2, -10, 10, 10, 2, -9, 17, 18, 19, 15],\n [-14, -5, -8, -19, 11, 15, -6, -16, 9, 0],\n [-3, -21, -2, -11, 19, 4, -13, -15, -2, -1],\n [-10, 17, -11, -6, -14, 17, -11, -14, 7, -17],\n [2, 5, -13, 18, 5, 6, 13, -12, -2, 15],\n [3, -5, -19, 21, 18, -8, 0, 18, -17, 20],\n [-16, -8, -14, 7, 21, 20, 5, 7, -15, 12],\n [12, 3, 7, 12, 15, -12, -3, 8, 11, -11],\n [5, -20, 19, -18, -10, -11, -22, 20, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[16, 19, 2, -7, -6, 5, 16, 20, -18, -22],\n [-20, 1, 6, -8, -19, 21, -22, -8, 1, 8],\n [-3, -13, -12, -5, 11, 5, 15, -7, 1, 16],\n [-11, 19, -16, 13, -6, -19, 14, 10, -4, 3],\n [-12, 8, -22, 17, 13, 6, 2, -5, -20, -5],\n [-16, 5, -6, 2, -5, 17, 20, -20, 2, -16],\n [-13, 21, 21, -4, -8, -2, -2, 14, 5, 22],\n [9, 18, 4, 0, -13, 17, 18, -17, 1, -5],\n [-13, -8, 22, 20, 11, -15, 12, 4, 2, -20],\n [-2, 16, 9, -2, -14, -22, -19, -19, 3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -8, 22, 9, 18, -16, 21, 21, -9, 0],\n [-22, 9, 18, 3, -14, -7, 8, -21, 9, -13],\n [2, -5, 22, 11, 6, 22, 1, -20, -8, -20],\n [8, -13, 15, -1, -9, -14, -5, -15, 15, -8],\n [-8, -17, -11, 19, -4, 17, -18, 4, -13, 20],\n [-9, 11, -8, 6, 3, 4, -20, -20, 12, 12],\n [-17, -9, 3, -20, 10, 19, -10, 6, -14, 9],\n [-1, -1, 11, -13, 2, -11, -20, -4, 10, 3],\n [-10, -16, 11, -1, -3, 20, 0, -9, 7, 0],\n [-4, 16, 18, 13, -17, 0, -13, 12, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[7, 10, -17, -18, -8, 20, 2, -10, -17, 14],\n [-21, -6, 1, -11, 21, -9, -16, 3, 9, 6],\n [16, -14, -9, -6, 2, 7, 22, 6, 6, -5],\n [8, -4, -6, -17, -11, 15, -20, 12, 10, 6],\n [-20, -18, -9, 13, 5, 18, 9, -5, 19, 17],\n [-10, -21, 2, -3, -16, -12, -18, 6, -5, -15],\n [4, 19, -21, 12, 3, 0, -18, -7, 19, -12],\n [-4, -7, 9, -11, -21, 20, -1, 3, 10, 1],\n [-18, -2, -5, 16, -18, -15, -2, -18, -10, -4],\n [6, -21, 14, 3, 6, -18, 9, 15, -21, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[10, 12, -4, -8, 12, -15, -22, 15, -1, -6],\n [-7, 22, -22, -20, -17, -20, 7, -12, 4, -1],\n [-17, 15, 18, 8, 20, -17, -3, 18, -12, -21],\n [8, 15, 3, 4, 8, 1, -10, 2, 14, 18],\n [2, 6, 8, 20, 16, -21, -11, -18, 4, 11],\n [-9, -16, 14, 13, -13, 6, -7, 15, -2, 15],\n [18, 10, 6, -6, -10, -17, -21, -15, 9, 13],\n [-14, 0, -16, 8, -2, -22, -21, 17, -12, 14],\n [-5, 21, 1, -4, -18, 6, 16, -21, -6, 22],\n [-12, 14, -10, 6, 9, 22, 17, 20, -15, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "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, -12, 5, 10, 16, 3, -15, 15, 3, 9],\n [5, -16, 12, -21, -1, -1, -20, 22, -15, -19],\n [-8, 21, 16, -11, 6, -14, 19, 17, -3, 11],\n [3, -2, 0, -5, 1, 19, 6, 15, 15, -10],\n [9, -4, -6, -21, -5, 16, 4, -9, -8, -15],\n [-14, -2, 20, 12, -9, 4, -15, 12, -5, -9],\n [-15, -15, 14, 21, -21, -6, -10, -9, 18, 18],\n [-14, 4, -3, 15, -11, 19, -1, 14, 16, 8],\n [-10, -22, 15, 17, -14, 16, -13, 6, 17, 7],\n [-21, -5, 5, 9, 1, 15, -9, 2, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 9, 8, 1, 12, 7, 10, 10, 4, 10],\n [10, -19, 7, 21, -8, 6, 5, 9, 13, 7],\n [19, 20, 15, 19, -11, -20, -8, -13, -1, 0],\n [-12, -7, -7, -9, -17, 19, -6, 8, 19, -13],\n [-3, -14, -8, 16, -21, -19, 1, -5, -12, 14],\n [3, -15, -1, -18, -21, -18, 12, 9, 21, -4],\n [16, -19, 0, -4, 3, 3, -16, 9, 10, 21],\n [3, 1, 0, 15, 3, 22, 8, -17, 22, 8],\n [17, 22, 22, -11, -6, 3, -20, -8, 15, 1],\n [7, 21, 13, 21, 4, -1, -21, -16, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[7, 21, -22, 4, -14, -16, -18, 7, 19, 4],\n [-13, 2, -5, -16, 8, 9, 22, -12, -13, -1],\n [8, 18, -9, -20, 1, -9, -7, 5, 12, 17],\n [-21, 11, -5, -16, 15, 19, -16, -19, 20, -7],\n [-17, -3, 8, -4, -1, -2, -5, 9, 11, 4],\n [15, 21, 7, 10, 4, 0, 20, -4, 8, -19],\n [-4, 15, 17, -1, -14, 8, -13, -13, 7, -13],\n [13, -5, 21, 20, -4, 20, 0, -19, -11, 1],\n [-10, -19, 4, 15, 16, -15, 3, 11, -14, -13],\n [-22, -15, -13, 20, 2, 8, 16, -20, 16, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[12, -15, -22, -18, 4, 22, 3, 20, 3, -12],\n [11, 18, -21, -2, 3, -11, -14, 18, 0, 19],\n [-18, -14, -13, -13, -9, 13, -13, 14, 18, 15],\n [-1, 0, -7, -12, 12, -3, 14, 18, -18, 13],\n [-10, -6, 3, 21, -3, 16, 10, 7, -7, -16],\n [7, -21, -11, 20, 17, -22, -20, -15, 3, 17],\n [-12, -2, -18, 17, 3, -2, -14, -6, 14, -21],\n [17, 5, 4, 17, -22, -12, 16, -5, 4, -13],\n [13, -2, 5, -22, -9, -3, -14, 22, 4, -19],\n [14, -5, 8, 16, -13, -14, 5, 5, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-11, -15, 0, -18, -16, -8, -20, -5, 15, 3],\n [15, 10, -2, -6, 20, -21, 2, 18, -4, 15],\n [2, 16, -19, -20, 11, 19, -13, 4, 3, 4],\n [-22, 21, -3, 2, -13, -22, -7, -12, -19, 12],\n [-10, -2, -8, -13, 15, -12, 9, 10, -3, 13],\n [7, -13, -8, 6, -22, -2, -8, -20, 10, 15],\n [-4, -19, -11, 2, 11, -6, -17, -11, -8, -6],\n [-22, -9, -21, -19, -21, 3, 17, 10, 16, -17],\n [7, -1, 4, -4, -13, -17, 3, 19, -20, -20],\n [-17, -13, 15, -10, 15, -11, 4, -15, -18, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "377", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[15, 20, 7, 14, 6, -1, -9, -13, -12, 12],\n [0, -15, -2, 14, 5, 8, 5, 19, 4, 17],\n [-2, -14, 6, -8, 10, 14, 13, 5, -13, 0],\n [5, 11, -18, -5, -17, 19, 0, 5, 18, -10],\n [2, -16, -21, -7, -21, 13, -21, 15, -13, -9],\n [4, -8, -2, -11, 20, 10, 17, -1, 15, 21],\n [-5, 21, -21, 6, -16, 8, 18, -5, -14, -15],\n [10, -18, -9, -10, -12, -3, 0, 22, 4, -8],\n [7, -7, 22, 17, -5, 19, 0, 13, 15, -15],\n [16, 6, -11, -5, -4, 13, 10, -18, 16, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 20, -2, 0, -2, -12, 19, 16, -7, 10],\n [4, -22, 21, -7, -18, -5, 18, 11, 21, 2],\n [19, 11, -8, -19, -19, 2, 18, -10, 19, 2],\n [-20, 12, -14, -9, -1, -14, 1, 0, 14, 22],\n [-8, 13, -9, -3, 16, 13, 4, -6, 3, 18],\n [-19, -20, -4, 18, 17, 16, -16, 13, -4, -11],\n [-3, 15, -11, 6, 7, -3, -19, -21, 7, 0],\n [-17, -5, -1, 14, -19, 20, -12, 18, 12, -12],\n [11, -14, 8, 19, 9, 20, 12, -12, -6, 13],\n [-21, 1, -8, 5, -20, 6, 22, -10, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-16, 3, 8, 15, 15, -19, 12, 10, -20, -4],\n [-14, -4, -4, 3, -10, -1, -15, 1, 3, 18],\n [18, -20, -16, -21, 10, -11, -11, -13, 18, 4],\n [-5, -19, 17, 0, -2, 13, 7, -2, 0, -2],\n [-15, 16, -10, 17, -1, -16, 1, -18, 3, -13],\n [-12, 17, 15, -12, 7, -19, -21, -10, 16, -6],\n [0, 22, -13, -10, 19, 16, 19, 6, -7, -20],\n [13, -19, 13, -7, 18, -17, 19, 5, 13, 0],\n [-11, 19, 8, -11, 9, 2, 6, -4, -1, 1],\n [10, 13, 22, 17, -7, -21, -15, -10, 7, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-11, -16, -9, 19, 12, 5, -11, 17, 1, -22],\n [-6, 15, 5, 10, 1, 22, -17, -2, 22, -19],\n [10, -13, 13, -10, 13, -14, 8, -19, -3, -15],\n [4, 13, -14, 20, 1, 14, 18, 17, 7, 3],\n [-19, -22, -3, 5, 22, 1, 5, 5, -18, 9],\n [7, -2, 19, -7, -15, -11, 9, 2, -20, 3],\n [13, -6, 4, -1, 22, 15, 12, -16, -20, -17],\n [-10, -8, 3, 10, -8, 16, 18, -9, -4, 5],\n [1, 18, 10, -11, -13, -16, -22, -8, -22, 22],\n [-3, -21, -20, 13, -7, 6, 21, 13, 21, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-20, 14, 21, -11, -3, 0, -1, 9, -16, -1],\n [21, -21, -9, -7, 1, -16, -19, 14, 18, -18],\n [-21, -18, -20, 19, -15, 3, -13, 11, 13, -11],\n [-3, 6, -9, -18, 4, -19, 6, -20, 10, 7],\n [13, -14, -22, 0, -20, 9, 1, -17, -10, -8],\n [7, -11, 17, 12, 5, -19, -16, 20, -7, -1],\n [22, 18, 2, -20, -1, 8, 14, -1, 4, -21],\n [-1, -6, -3, 1, 22, 8, 20, -15, -18, -21],\n [-19, 12, 11, -20, -3, -14, -17, -18, 18, 15],\n [12, 8, -10, 3, -1, 9, -8, -12, -7, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-12, -13, -7, -11, -16, 16, 4, 1, -8, -17],\n [-4, -15, 13, -10, 10, 9, 5, 17, -13, 10],\n [-22, -2, -18, -22, -2, 2, -3, 22, -14, -7],\n [5, 17, 13, 16, 1, -7, -9, 11, 1, -12],\n [22, 13, -22, -11, -2, -14, 16, -20, -7, -19],\n [3, -10, -3, -4, 4, -21, -13, 2, -4, -8],\n [16, 1, -7, -6, -7, -5, -19, -21, 8, -21],\n [-21, -8, 20, 6, 11, 17, 9, -2, 7, 1],\n [21, -9, 5, -9, 21, 11, -9, 2, -11, 18],\n [17, -3, 19, -16, -8, -14, -19, 8, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -11, -1, 1, 11, -4, 1, -3, 11, 4],\n [21, 6, -22, 13, 20, 16, 22, -16, 20, -3],\n [-3, 2, 20, -2, -14, 4, 5, 2, 13, 11],\n [-21, -14, -4, -8, -2, -7, -21, 3, 21, 6],\n [10, 11, 4, -16, -8, -6, -14, -10, 9, -21],\n [9, -3, 20, -4, 4, 13, 7, -12, -7, 3],\n [7, -21, 11, 18, -1, 8, -2, 13, 17, 0],\n [3, -5, -8, 11, -1, 5, 20, -16, 17, 19],\n [1, 12, -10, -10, 8, -4, 6, -1, 18, -2],\n [-7, 7, -18, 18, 18, -17, -2, 19, -12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, -8, 16, 17, -4, -6, -20, -20, 16, 5],\n [8, 19, -15, -6, 12, 13, 4, 17, 22, 10],\n [-12, -2, -17, -2, 5, -6, -5, -12, 21, 2],\n [7, 2, -16, 14, 4, 3, -10, 1, -11, -9],\n [-14, 8, -19, -4, -22, 6, 22, -17, -22, 2],\n [4, -1, -6, 6, -20, -6, -21, 9, -1, 16],\n [10, -1, -19, 15, -10, 0, -10, -3, 10, 11],\n [15, 6, 9, -12, -5, 22, -2, -11, 16, -3],\n [-16, 4, -16, -21, 20, 10, -2, 6, 9, 22],\n [-11, -10, 16, 21, 17, -20, 16, -15, -21, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[18, -8, -11, 18, 9, -17, 4, -10, 0, -13],\n [-9, -20, -11, 2, -22, 9, 1, 19, -14, -22],\n [19, 16, -13, 21, 20, 18, 7, -18, -19, 22],\n [-15, -7, -22, -8, 1, -8, -17, -21, -18, 16],\n [18, 11, 16, 9, 6, 6, 1, 8, 1, -8],\n [-11, -3, -19, -10, 18, 21, -13, 18, 0, -16],\n [-11, -8, -16, -15, -16, 20, -19, -16, 22, 18],\n [7, -5, 7, -16, 0, 14, -16, 15, 6, 11],\n [16, 18, 22, -5, 20, 2, 4, 4, -11, 0],\n [-6, 21, -16, 1, -16, 6, 5, 0, -13, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[20, 11, 2, -21, -18, -9, 8, 17, -17, 5],\n [-14, -17, -6, 17, 12, -11, 22, -5, 20, 11],\n [-22, -8, -5, -1, -5, -22, -3, 13, 15, 2],\n [-7, -3, 15, 10, -16, 0, -12, 10, 17, -18],\n [22, 18, -15, -6, -5, 4, 8, -19, -21, -18],\n [-6, 16, 9, 6, -7, -22, -11, -4, -14, -16],\n [7, -8, 21, -19, -17, 15, 12, -21, -18, -15],\n [7, -4, 7, 8, -7, 15, -1, 10, -1, -15],\n [14, -11, -18, 2, 6, -10, 3, -1, 6, -11],\n [20, 5, -14, -13, 19, 3, 13, 17, -12, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-19, 4, 1, -18, -20, -16, 1, -1, -11, 12],\n [-6, -20, -12, -17, 20, 13, -6, -1, -22, 21],\n [-20, -7, 12, -9, -16, 3, 20, 8, 1, -4],\n [14, -22, 2, -13, -5, 19, -22, 6, -10, -19],\n [-11, -4, 3, 21, 15, -7, 21, 2, -13, 14],\n [5, 5, 2, 2, -11, -15, 13, 16, 1, 0],\n [14, -12, -6, 5, -20, -21, 6, 11, -9, 10],\n [-5, 6, -21, -12, 8, -10, 21, 3, 11, -13],\n [-11, -1, 8, -4, 22, 1, 2, 12, -15, -18],\n [-1, 5, -11, 10, -7, 3, -11, 0, 3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, 0, 8, 13, 4, 13, 19, 0, 15, -20],\n [7, 9, -8, 15, -12, -21, 3, 11, -22, -12],\n [-18, 3, -17, 12, -18, -14, 5, -4, -18, 0],\n [21, 21, -7, -16, -9, -1, -14, 0, 20, -19],\n [20, 3, 18, -17, 8, -6, -14, 4, -17, -17],\n [-19, 20, -20, 1, -5, 9, -2, 6, 9, 2],\n [-11, -14, -16, -9, -3, -3, -13, -12, 16, -4],\n [-4, 20, -17, -15, -22, 0, 17, 14, -13, -21],\n [13, -21, -8, -3, 19, -2, 7, 1, -21, 15],\n [-1, 6, -9, -18, 1, 3, -21, 22, 11, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[18, 12, -8, -20, -11, 15, -6, 15, 4, -4],\n [-2, 17, 1, 1, -4, 8, 17, -3, -8, 17],\n [12, 12, 10, 17, 18, 21, -5, -6, -15, -3],\n [-12, 7, 4, 16, -9, 19, -8, -11, -3, -6],\n [17, 3, -9, 2, 3, 2, 2, 4, 20, -11],\n [-3, -7, 2, 4, -5, -13, 7, -22, -19, 0],\n [-16, 7, 3, -22, 6, 2, 17, 3, -6, 8],\n [-15, -18, -22, -8, 13, -16, 21, 4, 12, 4],\n [-3, -5, 17, -21, 7, 15, 7, -16, 16, -10],\n [10, 17, 7, 7, 0, 22, 1, -3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-10, -7, -8, -12, -11, -1, 2, -20, 1, 2],\n [-14, 5, 7, -16, -12, -13, -20, -4, -21, -6],\n [6, -21, -7, -13, -19, 20, 3, 1, -11, -2],\n [19, -7, 13, 12, -14, -17, 21, -22, -9, 1],\n [-13, -5, 22, -14, 4, -4, 13, -20, 15, -14],\n [-13, -14, -6, 19, 15, 20, -3, -16, -19, -13],\n [-2, -9, 2, -6, 5, -9, -10, 11, 18, -20],\n [-19, 21, -8, -3, -15, -18, -21, 5, -1, -14],\n [5, -22, 13, 19, -21, 15, 3, 8, 18, -4],\n [8, -14, -20, 15, -17, 22, 22, -16, 18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -22, -1, -3, -10, 17, -2, 0, 18, 10],\n [-14, 6, 9, -12, 13, 6, 8, -9, 2, 3],\n [-1, -14, 10, 0, 12, -3, 10, 12, 7, 7],\n [-1, 22, -22, -8, 2, -3, -16, -7, 0, -2],\n [-22, -3, -4, -17, 15, 9, -22, 7, -7, 4],\n [-5, -10, 21, 5, -13, -9, 6, -12, 4, 21],\n [-6, -20, 8, -2, 10, -22, -17, -19, -1, -10],\n [21, 7, 17, 3, 16, 16, -16, -9, 3, -5],\n [1, 2, 9, -17, -7, -20, -2, 9, -21, -3],\n [-12, -5, -12, 12, 13, 15, -11, 8, 13, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "325", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[21, -19, -21, 21, -10, 3, 6, 13, 5, -15],\n [-18, 9, 7, -9, 20, -13, -13, -17, -7, 3],\n [-2, 13, 18, 19, 7, -18, -13, 8, -12, 15],\n [-16, -11, 22, 18, -15, 5, -7, -20, 14, 9],\n [-2, 22, -5, -12, -15, -11, -21, 18, -1, -14],\n [-9, -8, -12, -10, 5, 2, 14, -17, 14, 10],\n [2, 0, -15, -6, 8, 3, -12, 7, -12, -20],\n [17, 17, -2, 12, 5, -1, 19, -5, 0, 3],\n [12, 6, -12, 19, -22, -7, 2, 15, -5, -7],\n [-4, -7, -18, 4, 21, -17, 11, -7, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[21, 9, 20, 0, -3, -4, 6, -15, 6, -5],\n [-18, -11, -13, 14, -6, 9, -19, 8, 3, -11],\n [-5, -15, 9, -3, 17, -10, 0, -20, 12, 16],\n [-2, -16, 3, 0, 9, -21, 16, -21, 16, -8],\n [-7, 3, -15, -7, -2, 16, -12, 1, 13, -5],\n [0, -10, 21, 19, 16, 21, 21, 22, -22, -16],\n [-2, -7, -9, 20, 20, -21, 8, 16, -14, 18],\n [-9, -13, 1, 10, 11, -3, 5, -19, 11, -19],\n [-17, -1, -19, -18, -12, 22, 12, -4, -12, -12],\n [4, -21, -15, 11, 17, -3, 0, -8, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-9, -22, 4, 10, 12, -8, -18, 14, -19, -3],\n [16, -1, 1, -12, -17, 4, -13, 16, -13, 3],\n [14, 10, -15, 5, 13, 17, 2, 13, -10, -16],\n [-22, -14, 5, 13, 7, -14, 7, 12, 4, 6],\n [-18, -22, 20, -18, 6, -6, 14, 1, 4, -14],\n [15, -10, 3, -12, 1, 10, -17, 12, -7, -10],\n [21, -12, 0, -21, 7, -4, 17, 22, -8, 19],\n [10, 21, 18, -18, -1, 4, 12, -4, 16, -16],\n [16, 11, 11, 4, 21, -18, -19, -16, -20, -2],\n [11, -14, -3, 17, -11, 16, 5, 10, -13, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-16, -5, -4, -9, -6, 0, -4, 22, -20, 11],\n [2, 18, 8, 16, -9, 14, -3, 9, 10, 8],\n [-16, -18, -19, -12, -4, 15, -3, 4, 6, -5],\n [14, 2, -3, -17, 13, -8, -5, 15, 2, -3],\n [-1, -11, 18, 17, 10, 6, -21, 3, 9, -20],\n [7, -4, -13, 2, -4, 20, -2, -17, -9, -15],\n [-21, -5, -1, 7, 13, 5, 12, -21, 13, -5],\n [20, -14, 5, -15, -15, -18, -10, -16, -2, 6],\n [14, 22, -9, 14, -19, -1, -12, 11, 22, -7],\n [-14, -7, 16, -7, 8, 8, -10, -18, 16, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "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, -21, 17, 7, -13, 19, -12, 6, 17, -7],\n [5, -6, 15, 21, -8, 8, -16, 7, 13, 3],\n [-12, -17, 19, 6, 5, -8, 6, -17, -11, -7],\n [15, -14, -1, 10, 3, 17, -16, 9, 17, 20],\n [1, 18, 16, 15, 14, -4, 20, -18, 7, 2],\n [7, 2, -14, 4, 1, 17, 20, 15, -8, 15],\n [3, 7, -12, 6, -8, 21, -14, 19, 6, -8],\n [-6, -7, -1, 17, 20, -12, 15, 2, 7, -21],\n [-22, 15, 14, -14, -18, 1, 4, 7, -8, -14],\n [14, 7, -8, -3, 2, -14, 22, -1, -10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -9, 7, 16, -18, -11, 12, 18, 19, -22],\n [-22, 19, 20, -3, 11, 11, 1, 5, -12, -15],\n [12, 18, -7, -7, 19, -17, -3, -12, -15, -3],\n [9, 10, -17, 5, -15, -9, -20, -21, -1, 10],\n [20, -2, -17, 17, -16, -17, 21, -15, 1, 4],\n [5, -18, -4, -14, 2, 21, 22, -10, 14, -21],\n [17, -9, 8, -17, 2, 16, 8, 15, -7, 4],\n [7, -19, 16, -7, 13, -16, -2, -21, -15, 19],\n [4, -21, -17, -19, -2, -22, 15, -11, 4, -9],\n [-8, 1, -5, -6, -14, -5, -5, -18, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[21, -22, 18, -14, 9, -3, -10, 17, -12, 20],\n [19, 3, 17, -12, 2, 17, 2, -3, 19, -12],\n [21, -13, -20, 16, 4, 12, 17, 8, -2, -1],\n [-4, -9, 14, 22, 0, 3, 20, 21, 17, -11],\n [-22, 11, 21, -4, 0, -16, -16, -22, -5, -15],\n [2, 19, 6, 0, 6, -22, -8, -8, 5, 13],\n [19, 17, 9, -10, -2, 16, 15, -14, -3, -3],\n [-15, -9, -3, 12, 22, -2, 18, 18, -1, 20],\n [-17, 21, 4, -19, -19, 5, 4, -6, 16, 15],\n [6, 17, -16, -15, 18, 10, 9, 12, -5, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-7, -5, 15, 2, 11, -19, -18, -9, -22, -1],\n [-2, -10, 13, 6, 15, -14, 10, -1, -6, 0],\n [13, -17, 16, 6, 4, -18, -14, 1, -4, 10],\n [7, 17, -19, 9, -22, 11, -2, 8, -9, 3],\n [-1, 11, 10, -10, 9, -15, -1, 18, -3, -2],\n [11, 7, -17, 12, 4, -3, 15, 17, -9, -13],\n [19, -8, 17, 20, -20, -8, 22, 8, -12, 16],\n [-4, -8, 15, -3, -1, -16, -9, -19, -14, 16],\n [2, 12, 14, 4, 5, 1, 10, 10, -7, 0],\n [-12, 17, -4, 11, 0, -13, 14, -22, -21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "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, -2, 17, 6, -9, -15, 7, -1, 0],\n [17, -10, 5, 7, -18, -13, 16, -14, -9, 15],\n [-13, 10, -12, 17, -17, -6, 13, -17, -13, 19],\n [-18, -4, -16, 1, 19, -4, -12, -20, 7, 20],\n [15, -17, 12, -1, -12, -15, 4, 6, -15, 0],\n [6, -7, 12, -15, -15, 22, 10, 19, -18, 14],\n [-6, -1, -9, 15, 9, -9, 21, -3, -1, 7],\n [10, -18, -5, -16, 6, -14, 18, -16, -16, 20],\n [-17, 17, 4, -19, -22, -17, 8, -22, -18, -4],\n [-18, -18, 8, 21, -16, -8, -10, -11, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 15, 10, -17, -10, -10, -10, -3, 13, 14],\n [22, -14, -6, 12, -5, 2, -8, 0, -22, 18],\n [15, -5, -22, 16, -13, 8, 15, -16, 15, -15],\n [11, -14, 2, 4, 18, -16, 9, -14, -6, 12],\n [-7, -21, 20, 8, -7, 10, -2, -6, 12, -16],\n [6, -12, 7, -5, -7, -17, -21, 20, 20, -13],\n [-19, -13, -14, 22, 20, 19, 1, -18, 12, -19],\n [12, 19, -10, 14, 9, 22, -22, -12, 3, -20],\n [-10, 9, 0, 0, 7, -17, -16, 7, 14, 9],\n [-17, 12, 9, -11, -19, 9, 12, -7, -8, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-21, -17, -9, 18, 6, 19, 3, -5, -19, 14],\n [15, 2, 6, 11, -7, 14, 7, 0, 13, 5],\n [-22, -15, 19, -8, 11, -4, 21, 7, -13, 21],\n [4, -3, 2, -14, 17, 11, -2, 1, -16, -19],\n [-15, -10, -2, 12, -18, -15, -21, 1, 19, -7],\n [-19, 7, 7, 12, 19, -10, 14, -12, -4, -5],\n [-6, -12, -8, -15, 21, 6, -6, 3, -18, -19],\n [1, -12, 7, 17, 12, 21, 22, 10, 13, -2],\n [15, -18, -18, -2, 2, -13, -4, 9, -5, 11],\n [-8, 1, -18, 9, -14, -18, -18, 18, 18, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-16, 3, -22, 11, 3, 9, -11, -17, -3, -4],\n [-7, -19, 9, -5, -18, -17, -9, -5, -13, 0],\n [-5, -19, 9, -17, 3, -17, 12, 18, 20, -18],\n [-9, -21, 17, -10, -18, 13, 13, -4, -3, -1],\n [8, 18, 21, -19, -20, 14, 2, 14, -19, 16],\n [-16, -16, 2, -8, -16, -19, 11, 22, 21, 19],\n [-4, 15, 4, -18, -10, -9, 7, -13, 9, -22],\n [1, 6, 20, -16, 8, -6, 7, 2, 5, 13],\n [-16, 12, -3, -9, 7, -22, 15, 18, 2, 11],\n [-15, -3, 7, -19, -2, 4, -13, 0, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[18, -4, -12, -19, 0, -18, -18, -5, -6, -20],\n [20, -15, 17, 0, 0, -21, 16, -2, 1, 15],\n [-3, 16, 4, 21, 16, -16, 10, 6, -13, -13],\n [-11, -20, -20, -10, 22, 8, 4, -17, 4, 12],\n [-14, -17, -17, 17, 3, 20, -4, -7, 18, 0],\n [-12, -7, 6, 15, -3, -2, 5, 10, 17, 3],\n [-13, 11, -14, 13, -12, -13, -16, 15, -7, 3],\n [9, 8, 9, 22, -11, 4, -1, -8, -15, -19],\n [-15, 0, -7, 11, -1, 0, -18, 14, 21, -16],\n [14, 3, 5, -19, 9, 15, -14, 13, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 15, -8, 12, -14, 10, -12, -1, -17, 14],\n [-2, -11, -16, -21, 16, 18, 1, 3, 2, -3],\n [17, 18, 19, 21, -21, 19, 12, 10, -6, -1],\n [-22, 14, 7, -17, 18, -9, 13, 10, 15, 16],\n [-17, 3, 1, 10, -15, 21, 20, 11, 11, 1],\n [-21, -15, 2, 7, 9, 7, -16, 1, -14, -7],\n [-21, 12, 11, -1, -4, -2, -11, -12, -4, -17],\n [19, -9, 10, 15, -10, 3, -9, 22, 1, -22],\n [22, 7, -13, -13, 5, -19, -9, -11, 15, 14],\n [-13, 18, 4, 19, -11, -1, -19, 6, 13, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, -11, 22, -3, 22, 0, -1, 11, -2, -14],\n [-13, -13, 22, 7, 10, -21, 9, 22, -6, 5],\n [22, -6, -9, -13, 11, -9, -6, 14, -1, -5],\n [12, -5, 7, 14, 17, -17, -8, 12, 3, 18],\n [4, 7, -12, 1, -9, 0, -14, 19, -5, 16],\n [-4, -18, -5, 10, 21, 15, -10, -14, 3, -22],\n [-11, 1, -22, -19, -16, 5, 14, -18, 16, 9],\n [8, 21, -8, -20, -8, 20, -5, -2, -13, -2],\n [3, 18, -20, -22, -2, -12, -7, 12, -2, 18],\n [-12, 8, -22, 18, 9, -20, 9, 19, -18, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[14, -11, -9, 21, -14, -16, -7, 5, -16, -9],\n [9, -15, 4, -20, 4, 7, 11, 3, 14, 17],\n [-1, 9, 18, -21, -15, 19, -16, -4, 10, -21],\n [-20, 5, -9, -8, -2, -9, 17, -5, 16, -3],\n [-22, -14, -14, 20, 15, 16, 6, -8, -3, 15],\n [18, 7, 3, -17, 16, -6, -17, 5, -14, 4],\n [12, -17, -19, -7, 0, 0, 6, 18, -19, 17],\n [17, 1, -17, 17, -17, -9, -9, 22, 12, -17],\n [0, -3, -6, -3, -17, 17, 5, -10, 6, 22],\n [-3, -6, 12, 22, 16, 14, 20, 0, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -16, 13, 19, -22, 14, 12, 18, -20, 12],\n [6, -14, 14, 19, 2, -11, 15, -16, -16, -19],\n [22, 8, 16, -13, 0, 3, 0, 6, -15, -4],\n [6, 20, -17, 6, 1, -13, -9, -17, -19, -8],\n [14, 16, 5, -21, -10, -21, 18, 9, -18, -20],\n [-21, -9, 17, 21, 6, 15, -17, 11, -15, -21],\n [3, -6, 1, 8, -7, -2, 15, 3, -6, 19],\n [-19, 20, -19, -4, 15, 2, -15, -5, -5, -16],\n [-6, -20, -1, -8, 8, 13, 3, -9, -6, -14],\n [-16, 4, 5, -11, -6, -14, 21, 21, -15, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[19, -11, 14, -3, -22, -14, 1, 11, 13, -19],\n [6, 0, 12, -7, -15, 4, 16, -11, 21, -19],\n [2, -17, -20, 16, 1, -2, -17, 10, -15, 10],\n [-20, -21, 15, 17, 16, 16, 1, -2, -5, 12],\n [-12, -12, -20, 0, -22, 0, -1, 19, 7, -21],\n [-6, 18, -3, -14, -12, -6, -9, -5, -5, 21],\n [-15, 6, -15, 3, 5, -15, -3, -15, -9, -10],\n [17, -6, 3, -17, -6, -19, 2, -16, -6, -1],\n [5, -17, 7, -13, 16, -9, 19, -1, 18, 3],\n [-13, -21, -20, 19, -12, -13, -11, -9, 7, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, 7, 15, -12, -22, 4, 16, 20, 14, -14],\n [20, 3, 2, -6, -17, -8, -20, 8, 5, -14],\n [21, -5, 17, 9, -4, -18, 21, -17, -11, 19],\n [-6, 16, -16, -12, 11, -21, -9, -5, 20, -14],\n [16, -19, -9, -12, 7, 17, 20, 4, 6, 9],\n [7, 3, 7, -13, -11, 10, 11, -5, 16, -7],\n [22, -19, -13, 5, 18, -5, -14, -1, -13, 17],\n [0, 20, -10, 1, -10, 22, 2, 21, 6, -7],\n [17, -17, -15, 11, -5, 20, 9, -13, 11, 0],\n [-4, -3, 11, 15, -6, 21, -18, -21, 18, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -21, 5, -5, 21, 16, 12, -8, 16, 17],\n [16, -20, -4, 0, -4, -5, 7, 16, -4, -18],\n [-10, 11, 1, -5, -19, 13, -15, 20, -22, 18],\n [15, 13, 15, -10, -1, 6, -14, 4, 21, -19],\n [17, -6, 14, -20, -19, 17, -7, -12, 4, 3],\n [8, 11, -15, 16, -22, -21, 4, 22, 20, -20],\n [11, -7, -22, -16, 12, -1, 9, 3, -17, -12],\n [8, -2, -1, -22, -2, 22, -3, -14, 4, 6],\n [20, 10, 22, -22, -20, 9, -3, -6, 14, 15],\n [-13, 20, 22, 6, 19, 9, -10, 8, -19, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-12, 19, -5, 18, 14, 10, 14, -20, -22, -4],\n [-17, -13, 14, -11, 21, -6, 4, -21, 2, 21],\n [5, 22, 14, 14, -6, -18, -4, -19, 16, 20],\n [15, 22, 21, 7, 9, 14, 4, 9, 19, -12],\n [18, -10, 12, -6, 7, -5, 14, 7, 3, -7],\n [-12, -19, 18, -8, -11, 4, -19, 12, -2, 13],\n [-21, 16, 5, 11, 10, -15, -15, 19, -1, 4],\n [5, -12, 4, -22, 16, 5, 4, -15, 1, 17],\n [13, 1, 19, -1, -13, -19, -15, 16, -8, -15],\n [6, 19, 16, 12, 18, -9, 9, -16, 21, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[12, 4, -22, -17, -21, -16, -15, 22, 6, -7],\n [6, 8, -1, -13, -19, 2, -10, -6, 17, -15],\n [0, -16, 9, 1, -22, 13, 4, -17, 19, 8],\n [-11, 3, 2, -19, -17, -10, 2, 8, -1, 12],\n [-2, -8, -20, 14, 22, 3, -6, 15, 12, 18],\n [-15, -12, 1, 20, -15, 7, -22, 11, -3, 13],\n [11, 11, -10, -17, 13, 2, 4, 8, -20, 5],\n [-19, -6, 15, 11, -3, -10, -18, 1, 15, -6],\n [8, 5, -22, -21, 10, 17, 6, -19, -5, 1],\n [9, -14, -7, -2, 7, -20, 10, 8, 22, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "339", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-17, -18, 6, 14, 13, -2, -11, 0, -9, 20],\n [19, -13, 4, 18, -21, -9, -16, -6, -3, -15],\n [-3, 13, -18, -10, 16, 15, -6, -17, -4, 2],\n [-20, 18, 5, 3, -15, -8, -22, 17, 0, 13],\n [19, -7, -19, -15, 13, -13, 7, 13, -7, 7],\n [21, -13, -12, 11, -7, -4, 21, -19, 21, 8],\n [12, 11, 3, 16, -17, 10, 4, -11, 22, -15],\n [-14, -22, -18, -16, -5, 17, 1, 3, -13, 17],\n [21, -11, -1, 4, -20, -5, -18, -9, 2, 8],\n [-2, 15, -3, -9, -3, 14, 7, 20, 18, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-16, -18, 8, 6, -8, 2, -10, 21, 1, -8],\n [1, 3, -4, 1, -4, 19, -6, -18, -19, -1],\n [-13, -2, 2, -17, 7, 6, -12, -12, 4, -4],\n [-1, 5, -19, 14, -4, -6, 17, 13, 0, 5],\n [-12, -9, -10, 1, -7, 5, 7, 21, 18, 16],\n [19, 4, -6, 3, -16, 12, -8, -7, -2, -6],\n [22, 3, 12, -3, -3, 0, -18, -14, 0, -5],\n [6, -12, 20, -15, 4, -21, 0, -2, -13, 15],\n [-19, -2, 14, 20, -11, -9, -3, -15, 4, 14],\n [18, -2, 12, 21, 16, -8, -11, 11, -15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[7, -20, 7, 6, -22, -7, 19, 8, -13, 7],\n [20, 3, -11, 17, -18, -14, -12, 0, -6, 20],\n [-10, -6, 0, 16, -14, -5, -5, 7, 19, 21],\n [3, -5, -2, 18, 18, 19, 10, 20, -9, -13],\n [5, -9, -4, 3, -13, -6, 11, -9, 3, 11],\n [-4, 1, 8, 17, -17, -3, 16, 22, 11, -1],\n [-16, 10, -17, -7, -15, 22, 0, -5, -9, 13],\n [-8, -18, -8, -12, -21, 0, 1, -5, -19, -8],\n [-11, -20, 9, 13, -2, -17, -21, -14, -11, 21],\n [1, -9, 18, -11, 4, -13, 20, -21, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-7, -22, -1, -22, 8, -1, 11, -11, 0, 5],\n [-11, 4, 0, -22, 20, -21, 21, 8, -21, 2],\n [15, -4, 5, -17, 16, -4, -6, -17, -8, -1],\n [18, 11, -18, 0, -18, 21, -13, -19, -11, -13],\n [7, 1, -18, -10, 13, -14, -5, 12, 8, 1],\n [20, -19, 18, 3, 21, 19, -13, 18, 19, -14],\n [-22, -7, -10, 15, -9, 17, 0, -5, 5, -3],\n [-22, -11, 4, 20, -10, -19, 2, -17, 22, -1],\n [22, 15, 13, -20, -8, -12, 11, 4, 0, -6],\n [0, 11, -2, 10, -18, -6, -22, -16, -20, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-7, -7, 21, 18, -9, 21, 3, 4, -6, 21],\n [-19, -6, 10, 7, -2, -6, -12, 7, -5, -3],\n [11, 18, 5, -14, 21, 8, 22, -7, 8, 6],\n [-10, 0, -9, 16, -21, -11, 5, 9, 1, 14],\n [6, 19, -5, -20, -10, -10, 19, 6, -21, 5],\n [-19, -18, 16, 18, -18, -15, 11, 2, 4, -16],\n [13, 9, -2, -5, -21, 19, -18, 21, 19, 15],\n [5, 8, 21, 1, 10, 16, -11, 16, -14, -8],\n [0, 21, 22, -1, 13, -13, 5, 12, 6, -18],\n [-19, -8, 7, 3, 0, 16, 6, -1, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[12, 10, -16, 11, -13, 1, 2, 21, 4, -17],\n [-15, -2, 18, -4, 11, 16, 20, 0, -10, 19],\n [16, 5, -17, -11, -20, -3, 18, 19, 22, -15],\n [3, 15, 5, 12, 21, 18, 18, 20, 15, -21],\n [-16, 18, 2, 9, -11, -12, -13, 12, 21, -19],\n [19, -21, 21, 5, 20, -9, 21, 6, -21, 11],\n [10, -3, 7, 19, 3, -3, -22, -22, 2, 10],\n [0, -12, 21, -8, -9, -22, 10, -17, 0, 3],\n [-20, -17, 17, 2, -6, 5, 9, 6, 0, 18],\n [-7, 9, 3, 10, -4, 18, -6, 15, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "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, 16, 19, 16, 5, -3, -17, 3, -17, 16],\n [3, -6, 17, -21, -2, -16, 21, -3, -20, 13],\n [20, 21, -4, 7, -12, -10, 10, 15, -21, 0],\n [-3, 7, -8, -21, 7, 2, -19, -22, -15, -9],\n [-12, 1, 1, 9, 2, 5, -7, 19, 16, -7],\n [13, -11, -11, 11, 15, -3, -8, -1, -7, 1],\n [-20, -22, 21, 15, -6, 18, -2, 22, -10, -21],\n [-21, 20, 2, 5, 3, 12, 5, 10, -5, -9],\n [18, -14, 21, 7, -20, 11, 10, 4, -14, -10],\n [7, -7, 19, 3, -18, 4, -8, 5, -20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-22, -22, -17, -12, -7, 10, 1, 9, -13, 2],\n [-13, -10, -22, 12, -9, -2, 15, -22, -3, -18],\n [17, 21, 9, -22, 22, 18, 17, 22, -21, 8],\n [3, -14, 7, -15, -18, 16, -19, 17, 13, -2],\n [10, 3, 17, 16, -12, -2, -1, 14, -16, 19],\n [-10, -3, -8, 15, 11, 13, 2, 6, 5, -9],\n [-19, 15, -16, -10, -6, 6, -6, 13, -4, 3],\n [22, -14, -21, -3, 0, -5, 3, 2, -6, 16],\n [-13, 2, 5, 3, -11, 21, -4, 0, -9, -6],\n [-8, -2, 15, 7, -4, 9, 6, -1, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[15, 13, -22, -4, 20, 3, -16, 11, 13, -17],\n [14, -1, -14, 20, 6, -6, -10, -6, -13, 2],\n [-5, 21, -8, 4, -4, -8, 22, -16, 20, 17],\n [-7, 1, 0, -12, 1, -18, 16, 7, -7, -3],\n [6, -6, -4, 3, -8, 2, -8, -3, 7, -2],\n [12, 21, -17, 14, -12, 0, 21, 16, -14, -5],\n [13, 17, 13, 5, -4, 7, 15, -8, 21, -11],\n [-21, -14, 12, -22, 8, 5, 22, 14, -16, -7],\n [-9, 10, -17, -2, -13, 9, -17, -21, 16, 4],\n [-9, 0, 16, -2, 18, 7, 2, 1, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-19, 14, 13, -10, -14, 5, -7, -17, 4, -13],\n [0, -2, 3, 22, -20, 20, 12, -16, 4, 19],\n [10, -19, 3, -15, -3, -6, -18, -14, -15, -16],\n [14, 13, -20, -15, -18, -18, -6, 4, 17, 16],\n [-11, 5, -19, 5, 2, 13, 19, -20, 8, 14],\n [-11, 14, 14, -19, 7, 15, 19, 15, 4, -1],\n [-22, 20, 15, -3, -5, -17, -11, -6, -1, -5],\n [-13, 1, -3, -11, -19, 19, -18, 3, 13, -7],\n [-18, 3, -4, -17, 1, 8, 8, -16, -13, 16],\n [-1, -9, 5, 19, -1, 9, -12, -9, 8, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-19, 22, -1, 6, 12, -10, -3, -4, -8, 3],\n [-3, 13, -17, -8, -19, -17, -21, 13, -8, -11],\n [17, 21, 18, -16, -1, -15, 19, -12, -21, 7],\n [-19, 2, -2, 2, -14, -15, -18, 5, -21, -2],\n [-15, 11, 0, -8, 4, -21, 5, -12, -2, 19],\n [9, 9, -16, -1, -9, -10, -2, -1, 11, -13],\n [-22, -22, 1, -20, 8, 20, 18, -10, -19, 0],\n [-17, 11, 18, -5, 13, 3, 10, 10, 2, -6],\n [-20, -1, 12, -19, 5, -10, 7, -11, -20, -2],\n [17, -22, -5, -10, -16, -10, -6, 22, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "342", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[22, 7, -12, -9, -13, -15, 8, -17, -4, -4],\n [-11, 16, -5, -20, -14, -17, -22, 19, 17, 6],\n [12, 12, 7, 12, 16, -1, 20, 5, -5, 9],\n [-18, 11, 8, 10, -19, -9, -8, -3, -3, 12],\n [-19, -5, 1, 4, 10, 2, -18, -5, 22, -3],\n [12, -17, 4, 5, -12, -14, 5, -4, 16, -2],\n [8, 19, -16, 14, 2, 5, 13, -6, 3, 5],\n [14, -6, -6, 10, 11, 0, 7, 4, -14, -3],\n [0, -4, 14, 22, -19, -10, 15, -11, -14, -8],\n [-2, -8, -18, -18, 2, 1, 14, 8, 11, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-9, 4, -19, 0, 15, -18, 4, 20, -9, -16],\n [22, -5, 9, -21, 18, 20, -3, 6, 20, 3],\n [15, -22, -18, -9, 2, -14, 7, -4, 17, -15],\n [-7, -15, 0, -14, 9, 14, 11, -5, 22, 21],\n [-8, -8, 6, 0, 0, -22, -1, -16, 22, 9],\n [5, 9, 10, 20, -10, 5, -14, 20, -20, -6],\n [11, 9, -14, 18, -22, 19, -3, -18, 17, 22],\n [-2, -18, -19, -15, 2, -16, 14, 19, 9, -6],\n [5, -17, 19, 19, 13, -21, 8, -22, -20, -10],\n [8, 6, 21, 10, -13, 15, -14, -22, 21, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[9, 10, -21, -21, -18, -13, 15, 14, -21, 18],\n [19, 17, 2, 15, 14, -5, 4, -3, 11, 21],\n [-15, -19, 7, 13, -14, 18, -11, -9, 12, -17],\n [0, -19, -22, -14, -14, 21, -8, 1, -15, 5],\n [19, -6, 12, 8, -19, -9, 2, 17, -16, 8],\n [12, 15, -3, -7, -1, 13, -4, -21, -19, 11],\n [-16, -9, 20, 9, -6, 14, -9, -6, 9, -21],\n [16, -19, 17, 7, 7, 10, 19, -22, 10, 13],\n [8, 14, -9, -17, -16, 17, 1, -19, 2, -20],\n [5, 0, 13, -10, -1, 2, 20, 1, 20, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, -9, 1, -1, 14, 0, -17, -4, -11, 3],\n [6, -9, -6, 7, -16, -2, -22, 15, -19, -15],\n [-5, 22, -15, 8, 8, 5, 14, -20, 22, -8],\n [-19, 12, 11, 13, -17, -19, 7, 16, -5, -1],\n [-13, 6, 0, -19, -4, 3, -16, -10, -20, 17],\n [-12, -7, -3, 0, 0, 9, 18, 19, 15, -20],\n [-15, 15, 17, -9, -15, -12, 19, 19, 20, 10],\n [-8, 14, -9, 3, -15, -19, 13, -5, 4, -4],\n [-20, -14, 16, -21, -14, -17, 15, 5, 11, 6],\n [-20, -7, 21, 12, -12, 20, 0, 7, -18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[20, 20, -13, 5, 13, -13, -9, 15, 14, -18],\n [-17, 7, -4, -9, -12, -18, 22, 8, 21, 9],\n [1, -13, -10, -10, 13, -1, -14, -4, -16, -8],\n [-6, -9, 18, -21, -9, -19, -20, -20, -12, -18],\n [6, 5, 0, 7, 0, 18, -1, 20, -11, 4],\n [17, -8, 0, 21, 18, 21, -4, 21, -12, 15],\n [17, 20, -20, -7, 9, 15, -14, 18, 15, -18],\n [-22, 12, 12, -11, 13, -2, 20, -15, 4, -14],\n [5, 7, -9, 0, 6, 3, -1, -8, -14, 3],\n [-6, -14, -20, -7, -10, 3, -6, 9, 1, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"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, -14, -1, 18, -3, -20, 13, 10, -5, 13],\n [-13, 13, -2, 2, 17, -14, 4, -8, 9, 21],\n [16, -7, 5, -17, -17, 15, -21, 18, 17, -16],\n [4, 5, -7, -14, -8, 11, -3, -9, -12, 7],\n [-20, -21, -9, 6, -18, 21, -17, -15, 16, 16],\n [21, 6, 16, 21, 4, -7, 4, 16, 17, -22],\n [22, 10, 16, 4, -6, -8, -1, -4, 5, 0],\n [13, 16, -3, -14, 0, 22, -16, 8, -12, 17],\n [-6, 13, 3, 13, -5, 8, 12, 18, 5, 3],\n [-17, 11, 5, 21, -14, 6, 11, -11, -7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, 10, -16, -20, -3, -18, -20, 15, -8, 12],\n [0, 10, -21, 13, -2, -9, -9, 19, -12, -19],\n [7, 13, -3, -7, 11, 22, -15, 22, -3, -2],\n [17, 7, 13, -18, -2, 15, 0, -4, -13, 4],\n [12, -10, -14, -6, 8, 19, 21, 22, 1, 19],\n [-4, 7, -18, -15, 14, 13, 2, 22, -18, 10],\n [-1, 19, 2, 20, 6, 22, 7, 7, 21, 8],\n [11, 5, -13, -19, 10, -6, -12, -16, -6, 5],\n [-6, 18, -13, 3, -17, -6, -7, 16, 3, -19],\n [-3, 18, -12, 0, 10, 8, -16, -1, -18, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-22, -17, 22, -19, 7, 7, -6, 1, 8, 5],\n [22, 20, -19, 16, -4, 1, -16, -14, -1, -21],\n [4, -7, -18, -11, 3, -8, -20, -14, 5, 16],\n [13, 2, 18, 5, -2, 6, 2, 7, 16, -12],\n [-4, -12, 2, -22, 9, -2, 22, -10, 11, -6],\n [-4, -13, 19, -14, -12, 15, 8, -21, 1, 19],\n [-18, 7, 16, 12, -6, 8, -21, -7, -2, 7],\n [-22, -9, -7, -14, -15, -14, 11, 22, 10, -1],\n [7, -16, -5, -2, -18, -16, -11, -6, 1, 14],\n [21, -4, 22, -7, 2, 4, 19, 21, -16, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-15, -8, -7, -15, 13, 9, -6, 13, -1, 9],\n [-12, 22, -17, -1, -9, 5, 16, -11, 4, -22],\n [-13, 10, -7, 16, -17, 2, -3, 13, 0, -7],\n [-22, 7, 4, -21, -2, -14, 1, 18, 16, 19],\n [-16, 7, 22, -21, -11, -10, -20, 20, 17, 20],\n [-5, 16, 21, -17, 19, 4, -8, -8, -4, 15],\n [-3, -3, -5, 11, 16, 14, 12, 15, 15, -22],\n [-11, -18, 4, 16, -3, 17, -4, 15, -8, -17],\n [-14, 13, 0, -13, -22, -12, -3, 5, -1, -3],\n [15, -7, -21, 2, 4, -20, 0, 9, -6, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"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, 7, 5, 22, 0, -4, 2, 1, -22, 5],\n [6, 21, 12, -6, -12, 14, -16, 3, 0, -5],\n [6, 16, 11, 15, -15, -2, -2, 13, -6, -7],\n [-8, -8, 17, -6, -22, -10, 15, -13, 10, 3],\n [-11, -4, -8, -18, -21, -9, 6, 18, -22, -10],\n [9, 11, -9, 15, 15, 18, -8, 16, -17, 6],\n [14, -4, -22, -2, 16, -5, 4, 5, -15, 8],\n [-11, 19, -17, 3, -7, 7, -4, -5, 1, 22],\n [-3, -16, -16, -7, 19, -9, -11, 6, -8, -15],\n [16, -14, 5, 4, -16, 21, -9, -12, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-17, 12, -17, 1, -14, -21, 15, -9, 8, 7],\n [4, 13, 8, 19, -17, 20, 22, -5, -9, -3],\n [-12, 14, 17, -19, 21, -17, 0, -15, 7, 13],\n [19, -12, -18, -20, -8, -21, -21, -15, 7, 18],\n [-18, 7, 21, -13, 10, 1, -4, 7, 2, -12],\n [12, -22, -6, 8, -17, -10, 3, 13, -18, -9],\n [-8, -11, 19, -15, 8, 3, 6, -19, 5, 2],\n [17, 9, 13, -12, 14, -13, 15, 13, 4, -6],\n [-16, -14, 12, -14, 13, 7, 8, -4, 18, 0],\n [-3, -17, 20, 1, -1, -17, 1, 19, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-7, 13, -10, 14, 1, -4, -3, 4, -6, -7],\n [-22, -2, 4, -22, 7, -3, 1, -21, -8, 6],\n [12, -10, -4, -22, 22, -7, 20, -20, 17, -17],\n [8, -18, 3, 5, -8, -14, -1, 14, -2, 19],\n [6, 3, -17, -12, 13, -3, 21, -3, 4, -17],\n [10, 7, 11, -18, -7, -11, -11, -12, -2, -16],\n [11, 6, -17, 13, 11, -15, 14, -13, -7, -21],\n [-4, -16, -21, 22, 0, 8, -19, -7, -13, -2],\n [5, -11, -10, 17, -6, -5, -13, 5, -10, 11],\n [-17, -11, 6, -10, 3, -19, -8, -7, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "307", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[9, -17, -17, -18, -21, -21, 14, -20, -17, 8],\n [20, -18, -13, 4, 1, -1, 2, -20, -7, 7],\n [20, -19, 20, 17, -7, 17, 18, -15, 1, -7],\n [4, -21, -3, -3, -3, -4, -5, -10, -6, 10],\n [5, -18, 5, 2, -3, -2, -10, -17, 6, 19],\n [-14, 6, 15, -22, 7, 9, 0, 16, -13, 21],\n [-2, 3, -8, -6, 12, 2, -8, 10, -12, 1],\n [-17, 5, 6, -2, -11, -1, 4, -2, -8, -5],\n [-13, -1, 21, -3, -4, 5, 14, 21, -22, 11],\n [12, 3, 7, -11, -9, 16, -19, -11, 1, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[8, -22, 14, -22, -8, -10, 6, 22, -19, -8],\n [21, 17, -11, 2, 4, -17, 0, -8, 16, -18],\n [0, -8, 2, 7, 21, 20, -19, -10, 17, 16],\n [0, -7, 12, -7, -16, 22, -10, 6, 16, -3],\n [6, -5, -1, 13, 18, 13, -15, -20, 6, -14],\n [-15, 7, -11, 5, 19, 20, -13, -10, -21, -22],\n [-1, 10, -7, 19, 6, -13, 16, -16, -22, 3],\n [22, -18, 12, -10, 4, -11, 7, 9, 8, -18],\n [14, -21, 15, -16, -22, -20, -3, -21, 19, 20],\n [-2, 22, 9, -3, 20, 8, 20, 10, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "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, 9, -18, -21, 3, 2, -1, 16, -1, -12],\n [-12, 22, -19, 10, -5, 8, 21, 5, 19, -1],\n [17, -20, -16, -3, 20, -16, -16, 6, 3, 18],\n [-20, 20, -6, 17, -3, 11, 10, -7, 0, -19],\n [18, 17, 10, -15, -18, 10, 2, -16, -16, 10],\n [18, 10, 6, 21, 16, 18, 9, 14, 21, 6],\n [-1, -21, -14, 6, 10, -13, 5, 16, -11, -1],\n [-17, 22, 17, 0, 11, 19, 15, -7, -13, -2],\n [-13, -12, -2, 2, 11, 8, 4, 2, 19, 9],\n [21, -12, 3, 13, 14, 10, 10, 19, 13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-9, 14, 20, 17, -22, -18, 7, -5, 22, 14],\n [16, -11, 11, 22, -9, 15, -7, 19, -12, 10],\n [-8, 19, -13, -20, -12, -12, -7, 15, 7, 18],\n [-22, 15, 22, 11, -4, 11, 13, -19, -13, -6],\n [-7, -2, 5, -15, 6, -17, 7, -21, 8, 2],\n [0, 20, -2, -7, -19, 20, -15, -17, 4, 13],\n [13, 1, -17, 20, 10, -21, 18, -7, 15, -14],\n [-18, -13, 7, -16, 6, -21, -3, -19, 5, -15],\n [12, -21, 18, 5, -12, 13, -14, 15, -22, 4],\n [-20, 16, -14, 17, 5, -2, 5, 22, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-14, 3, 1, -17, -11, 13, -14, -13, -20, 6],\n [-16, 3, -15, 20, -10, 12, -4, -1, -7, -8],\n [-21, 15, -2, 7, -16, 8, 18, 18, 12, -19],\n [11, -22, -13, 7, 9, -20, -13, -14, -6, -20],\n [4, 12, -19, -19, 9, 15, -12, 21, 16, 22],\n [-17, 12, 9, 0, 19, 14, 3, 11, 15, -12],\n [-2, 20, 1, -8, -20, -21, -16, -18, 22, 17],\n [6, 18, 9, 7, -15, 9, 19, -21, -13, 20],\n [20, 14, -20, 0, 11, -5, 10, 10, -6, -17],\n [-10, -2, 8, -2, 10, 5, -17, -15, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[17, -1, -22, -10, -22, -13, -18, -3, -10, 14],\n [-13, -20, 11, 11, 7, 14, -19, 11, 9, -2],\n [18, 1, -14, 18, 1, 2, 13, -15, 18, 6],\n [2, 12, 15, 5, -4, 9, 14, 5, 12, -15],\n [18, 0, 17, 0, 9, -13, -6, 12, 12, -20],\n [13, 6, 4, 8, 11, -11, 14, 2, -21, 7],\n [21, -14, 0, -14, -3, -22, 16, 0, -5, 19],\n [9, -14, -12, -22, -12, 10, 7, -18, -22, -13],\n [-10, 4, -15, 5, 22, -21, -11, 4, -10, -1],\n [17, -8, 8, -16, 16, 12, -16, -11, -9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[16, -14, 10, -11, 11, 4, -1, -5, 21, -5],\n [14, -16, -19, 22, -7, -1, 13, -3, 8, 10],\n [-10, -3, 18, 19, 15, -1, 16, 0, 10, 18],\n [7, -9, 13, -15, -1, -19, 12, -15, 11, -1],\n [2, 2, 17, 17, -6, -7, 16, -8, -6, 12],\n [10, 17, 16, -5, 7, 0, 14, -16, -13, -7],\n [5, 0, 11, -5, 0, -3, 8, -9, 0, -21],\n [6, -14, 10, 21, -11, -4, 19, -3, 14, 8],\n [12, 18, -2, 20, -10, 16, 4, 2, -21, 12],\n [-15, 10, 2, -2, 13, -10, -14, 12, 13, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-13, -18, 8, 1, 9, -20, -7, 18, -3, 21],\n [1, 11, 0, 15, -21, 18, -18, -5, 6, -13],\n [19, 19, -7, 0, 7, -17, 21, 13, -3, -7],\n [5, 3, -1, -12, -22, -18, 20, 18, 19, 13],\n [-21, -17, 4, 3, 12, -10, -11, -5, 15, 19],\n [-17, 5, 5, 2, -18, -8, 21, -14, 22, -21],\n [-14, 3, 0, 5, -17, -19, 7, -5, 7, 4],\n [21, 8, 21, 16, 7, 14, -11, -6, 11, 5],\n [-19, 11, -9, -10, -20, -2, -7, 15, 3, -17],\n [-5, 18, -17, 18, 2, 1, 7, 0, 22, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-15, -14, -17, 10, 10, 22, -16, 19, -5, -17],\n [22, 14, -2, 3, -8, 21, 7, -12, -15, -18],\n [-15, -18, -13, -8, 15, -20, 18, -13, -16, 1],\n [3, 11, -15, 16, -18, 13, 20, 3, -13, 10],\n [13, 8, 15, 2, 22, -10, -22, 13, 13, 1],\n [4, -5, -8, -6, 6, -18, -12, -7, 11, -6],\n [10, 8, -5, 2, -18, 7, 22, 0, 15, 22],\n [-5, 9, 7, 6, 13, -14, 0, -20, -1, 17],\n [22, 8, -1, -12, 19, 20, -20, -9, -4, 8],\n [13, 9, 3, -22, -21, -17, 22, -9, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 17, -5, 11, -11, 4, 1, 10, -8, 20],\n [9, -6, 12, 22, 12, -10, -14, -13, -22, 11],\n [14, 2, -1, -13, 3, -4, 17, 22, 18, -19],\n [17, -18, 6, 15, -18, -22, 5, -4, 13, -22],\n [6, 13, 9, -9, 9, -14, -4, -12, -19, 18],\n [2, -6, -15, 22, -22, -21, -13, 4, 4, -10],\n [-12, -9, 9, -7, 6, 15, 11, 3, -18, -4],\n [16, 5, 5, -6, 14, 21, -4, 4, -11, -20],\n [-19, -12, 11, -5, 12, -5, -17, 11, 10, -15],\n [19, -3, -3, 20, -5, 4, -18, -16, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[20, -10, 9, 1, -7, -9, 16, -16, 21, -11],\n [-3, 10, -17, 17, 4, -10, -18, 1, -13, 9],\n [-14, 12, 21, -11, -12, 13, -15, -13, -9, 7],\n [-22, -11, -18, -9, 13, -6, -1, 8, 3, -10],\n [-20, 20, -12, -18, 15, -19, 9, -13, -13, 21],\n [-5, 0, -5, 12, -20, -22, -6, 19, -17, -12],\n [-9, 5, 16, 13, -12, 18, 17, -19, -17, 15],\n [-4, 8, -21, 20, 2, 18, -12, 17, 22, 19],\n [21, -2, -20, -21, -12, 1, 1, -2, 2, -19],\n [17, 20, 0, 1, -2, -21, 0, -8, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 3, 22, -21, 12, 9, 7, -3, -10, 4],\n [0, -7, 8, -11, 10, 15, 22, 9, -21, 0],\n [9, -8, 17, 18, 17, -15, 20, -1, 15, 11],\n [-22, -13, 17, -7, 1, 1, -9, 3, 16, -5],\n [-3, 18, 13, 1, 3, 6, -1, -12, 18, -12],\n [-20, -2, -12, -15, 8, -13, -17, -6, 15, -16],\n [9, -10, -17, -20, 4, 22, 19, 3, -19, 14],\n [-2, 5, -5, 9, 16, 10, 3, -6, 6, -3],\n [7, -18, -17, 19, -13, -17, -13, 19, -2, 21],\n [-19, -10, -13, -7, -4, -17, 3, -14, -13, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-20, -4, 12, -17, 6, -4, 21, -8, 15, -2],\n [21, 16, 0, -3, 19, -21, 22, 9, 5, -19],\n [-16, -20, 2, -14, 0, 0, 3, 17, -5, 1],\n [4, 22, -21, -22, -7, 20, 1, 13, -12, 3],\n [-17, 3, 6, 20, -22, -14, 4, -16, -20, -14],\n [-21, -13, -6, 8, -22, -5, -17, 15, 18, 19],\n [-19, 17, -19, 12, -19, -22, 18, 20, 8, -4],\n [-2, 7, -16, -18, -21, -20, -8, 16, 14, -13],\n [-14, 0, -9, 22, 10, -7, -3, -15, 15, 11],\n [8, 22, -15, 2, 18, -10, -5, 18, 11, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, -11, -7, -10, -12, -9, 19, 5, 1, -6],\n [-14, 7, 14, -20, -15, -5, 7, -20, 11, 20],\n [5, 14, 2, 7, -16, 6, -21, 3, 18, 19],\n [-16, -5, -17, 18, 17, 4, 18, 1, 10, 8],\n [11, -1, 1, 13, 5, -3, -5, 19, 9, 10],\n [-13, -14, 2, -10, 22, -18, 8, 8, 11, 3],\n [-16, 18, -3, 20, -1, -18, -11, -2, -14, 6],\n [4, -6, 17, 1, 4, -15, 21, 6, -4, -13],\n [1, 11, 17, 8, -19, 18, 22, 8, -14, 3],\n [-10, 3, -22, 17, -14, 8, 1, 22, -1, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[16, 0, -3, 19, -2, 4, -18, -6, 11, -14],\n [11, -13, 21, -21, 2, -20, 11, -16, 5, -14],\n [-12, 6, -7, 16, 6, -10, 12, -12, 12, -15],\n [-16, -18, -17, 12, 7, -12, 15, 4, -2, -9],\n [12, 6, 1, 13, 18, 22, 9, -17, -13, -3],\n [-3, 3, -2, 22, 0, -11, -10, -13, -16, 14],\n [-11, 2, -21, 17, 3, 17, -18, -15, 19, 22],\n [-14, 16, -3, -12, 17, -1, -7, 19, 15, 19],\n [-13, 2, -4, -19, -4, -20, -6, -9, -13, -17],\n [8, 8, -14, -11, 21, 3, -21, 19, -19, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "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, -17, 7, 5, -10, 13, -13, -13, -18, 6],\n [13, -11, -1, 16, -21, -9, -13, -20, -15, -6],\n [-19, -2, 7, -4, -8, -3, 19, 7, -13, 0],\n [1, -11, -14, -8, 6, -5, -3, -22, -20, -15],\n [16, 8, -15, -8, -1, 9, -18, 21, 21, -14],\n [18, -8, 21, 14, 10, -1, -12, -17, -6, 21],\n [-18, 16, -14, 6, 0, 13, 8, -3, 0, -16],\n [13, -19, 1, -9, 2, -16, -8, 21, -10, -4],\n [-11, 3, 10, -8, 14, -17, 2, -6, 20, 13],\n [-14, 5, 12, -20, -12, -3, 0, 7, 14, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[21, -11, 13, 12, 11, -19, 1, 13, 5, 16],\n [-21, 20, -18, 5, -10, 13, -14, 16, 7, 4],\n [-10, 19, 16, 5, -5, 11, -2, -22, 22, 0],\n [11, 13, -14, -15, 7, 13, 13, -5, -21, -12],\n [13, 8, 8, 1, -2, 9, 7, -15, 10, 16],\n [-22, 10, 19, -10, -1, -18, -11, 6, -20, 13],\n [22, -12, 3, -21, 6, 18, 6, 21, 13, -4],\n [-13, -12, -16, -10, 18, 21, -21, 7, -1, -22],\n [4, -16, -22, 2, -19, 7, -15, -2, -19, -19],\n [-15, 19, 3, 6, -7, -4, -22, 14, 11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 22, 7, -17, 13, 16, -21, 19, -9, -15],\n [-20, 12, 4, 11, 5, 8, -6, -4, 19, 21],\n [-12, -14, 7, 22, -17, -9, 8, -12, -18, 8],\n [-21, 16, -6, 15, 13, -20, 20, 6, 10, -9],\n [15, 6, 0, -6, -12, 5, -16, 22, 17, -15],\n [18, 6, 2, -16, -1, -14, -12, 11, 4, -1],\n [-20, 17, -15, -17, 2, -21, -7, 18, -2, -8],\n [11, 20, -3, 21, 8, -8, 5, -17, -20, 15],\n [0, -20, 22, 21, -15, -21, -16, -6, -16, 10],\n [13, -19, 21, -7, -2, -5, 5, 20, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-17, 7, 22, 5, -6, 13, -11, 17, -11, 13],\n [17, 6, -21, 6, 7, 13, 21, 2, -2, -1],\n [-13, 8, -14, 18, 16, 11, 16, 18, 0, -11],\n [-16, 9, -4, -1, -7, -15, 7, -17, -21, 11],\n [6, 17, 19, 20, -3, -20, 12, -15, -11, 22],\n [20, 9, 6, 22, -2, -20, 15, 4, -20, -22],\n [-3, -16, 18, -22, -13, 22, -11, -19, -16, -13],\n [-1, 2, 6, 16, -8, -4, 16, -5, 19, -20],\n [-17, -1, 18, 8, -2, -15, -22, -20, 6, -17],\n [10, -5, 19, -22, -1, 8, 0, -15, 6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -7, -4, 14, -1, -4, -19, -18, -18, 2],\n [1, -22, 5, -2, -4, 0, -9, -17, 9, 9],\n [-15, 14, -1, -15, 15, -13, -20, -10, 16, 7],\n [-19, 22, -17, -7, -1, 4, -2, 6, -22, 7],\n [1, -10, 7, 3, 11, -3, -17, 20, -14, 14],\n [14, -7, -19, 9, -3, 6, 8, 22, -6, 18],\n [2, 22, -7, -3, 19, -13, 0, 10, 20, -10],\n [2, 14, 13, 1, -17, -8, 11, -19, -9, -19],\n [5, 6, -5, -3, 18, 9, -15, 20, -10, 17],\n [20, -14, 17, 10, -11, 14, 2, 2, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[16, 12, 0, -15, -20, 1, 20, -1, -9, -1],\n [11, 13, 8, -2, -18, -4, 19, -2, -21, -20],\n [7, 11, 2, 12, 6, -11, 0, 5, -6, -7],\n [-14, -20, -1, 8, -9, -20, 15, 0, -2, 1],\n [9, 22, -18, 10, 21, -4, 11, -20, 16, 5],\n [-12, -13, 17, -21, 22, 16, 4, -14, 16, -22],\n [10, 15, 10, -20, 9, -10, -2, -19, -6, 19],\n [-19, -3, -11, 3, 22, 13, -7, -16, 10, -21],\n [10, -9, -3, 14, 4, 19, -2, -21, 20, -7],\n [-4, -19, -13, -1, -11, -21, -21, 18, 21, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, -7, -4, 2, 7, -17, 4, -8, 8, 21],\n [-1, -11, -13, -2, 8, 13, -13, -4, 0, -13],\n [4, 20, -21, -12, -15, -4, -7, -19, -9, -1],\n [-6, 20, 3, 12, 13, 22, 7, -2, -3, 19],\n [3, -11, -15, 12, 6, 19, -16, -13, 16, -3],\n [5, -9, -11, -15, -16, -18, -22, -14, 21, -5],\n [20, 19, -13, -22, -3, 20, 6, -21, 3, -12],\n [2, 11, 18, -22, 8, 15, -1, -21, -22, 1],\n [13, 22, 13, 11, -14, -11, -3, -19, -8, -19],\n [-18, -13, 21, 21, 17, 13, 12, -22, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-17, -17, 19, -4, 9, 19, 7, 3, -20, 10],\n [8, -3, -19, 9, -5, -13, -1, -6, 19, -19],\n [14, -16, -15, -22, -15, -4, -6, 18, -14, -7],\n [22, 14, 4, -21, 13, -11, 12, 8, -4, 3],\n [13, -19, 20, 8, -10, 20, 16, -19, 17, 21],\n [-10, 18, -14, -21, 12, -11, -6, -19, -9, -2],\n [18, -15, 10, 22, 5, -20, -9, -4, -17, 13],\n [-3, -22, -13, -10, -11, -12, 13, -6, 6, -20],\n [6, -13, -4, -19, 15, -11, 8, -21, -22, -6],\n [2, -18, -9, -13, -2, 2, 12, -20, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[16, 10, -6, 17, -17, 11, 3, 19, 8, 5],\n [13, -10, -2, 3, 8, -7, 8, -10, 7, 9],\n [-18, -11, 16, 18, 14, -19, 19, 20, 6, 18],\n [-18, -12, 7, -14, 5, -1, -12, -2, -17, 3],\n [-7, -9, 12, 19, 13, -1, -21, -10, -12, -11],\n [10, -1, -14, 21, -16, -6, -13, 15, 16, 2],\n [4, 7, 7, 20, 11, 10, 9, 19, -11, 18],\n [0, 6, 20, -22, -3, -13, -4, 0, -2, 20],\n [12, 9, -13, -21, 13, -17, 20, -6, -8, 13],\n [1, 17, 6, -9, -21, -1, -17, -14, -11, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[16, -18, 17, 21, -22, -13, -12, 4, 0, -3],\n [-18, -10, -13, 13, 18, -7, -16, 9, 2, 21],\n [3, 13, 5, 21, -11, 3, -19, 21, 0, 17],\n [1, 8, 7, -20, -7, 11, 15, 5, 21, 18],\n [-16, -15, -16, 14, -16, -5, 16, -2, 11, 4],\n [-15, 11, -5, 18, -11, -1, 17, -1, -15, 19],\n [5, 9, -12, -2, 3, -9, -8, -9, -11, 13],\n [-20, 21, -16, 16, -22, 16, 2, 8, -1, -13],\n [-5, -10, -15, -14, -8, -15, 10, 12, -4, 7],\n [-14, -4, 3, -22, -20, 11, 2, 7, -22, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, -14, -16, 7, -10, -6, -10, -10, 19, 15],\n [14, -13, -9, 20, -18, 13, 12, 22, 0, -18],\n [21, 5, 0, 19, 11, 8, -16, -16, -19, 21],\n [9, 5, -19, 16, 22, -15, -9, 7, -20, -21],\n [-13, -17, -16, -7, -17, -7, 4, -11, -1, -8],\n [-1, 12, -8, 0, 15, -21, -21, -4, -18, -19],\n [5, -5, 17, 18, 8, -1, -12, -7, -19, -2],\n [18, 22, 2, -3, -15, 20, -14, -5, 8, 12],\n [7, -5, -4, 18, 1, -1, -9, -4, 6, -1],\n [7, -8, -2, 3, 13, -11, -16, -12, 16, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[12, -19, -21, -3, -3, -11, -6, -5, 17, 1],\n [-15, 14, 18, 7, -3, 0, 14, -13, 10, 1],\n [13, -7, 5, -11, -3, -5, 14, 3, -16, 20],\n [-2, 20, 9, -16, 0, -3, -3, 9, 3, 13],\n [1, -22, 5, 3, 11, 3, 13, -18, -21, 9],\n [11, 7, 1, 5, -20, -13, -17, 11, 8, 20],\n [-10, 16, -3, 9, -13, 3, -4, 6, -10, 11],\n [-3, 21, 17, -5, 11, -15, -7, 17, 0, 9],\n [-10, 3, 15, -22, -21, 16, -10, 4, -19, 18],\n [-3, -20, 0, -21, -7, -13, 5, 21, -5, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 21, -3, 17, 0, -16, 22, -9, 14, -15],\n [-18, 0, 18, -13, 4, 12, -22, -16, -15, -12],\n [11, 5, 11, 20, -3, 5, 19, 14, -20, -14],\n [-1, 2, -21, 0, -6, 2, -11, 4, -3, -14],\n [0, 13, 5, 6, 19, 9, -11, 7, -12, 14],\n [-3, -12, 15, 22, -7, 12, -22, 2, 4, 9],\n [-17, 18, 13, 16, 0, 6, 7, -1, -12, 3],\n [0, -20, -17, -16, 21, 16, -1, 19, 10, 17],\n [-20, 7, 1, -20, -21, 21, 17, -4, 1, -3],\n [8, 18, 8, 14, 20, 6, -19, -13, 13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "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, 20, 18, -22, 19, -11, 1, -21, -3, -7],\n [11, -10, -5, 6, 20, -9, 7, 12, -14, 14],\n [16, -11, -2, -5, -12, 4, 1, 18, 20, 11],\n [-3, -10, -15, 14, -18, -16, 21, -11, 18, -19],\n [17, -4, -22, 20, -10, 19, 22, 2, 21, 22],\n [11, 12, -6, 3, -2, -11, -7, -3, -13, 0],\n [7, -15, -18, -11, 19, -9, -11, 1, 22, -6],\n [-22, 19, 14, -12, 19, -17, -8, 18, 17, 0],\n [0, 15, 15, -11, -16, 14, -7, 15, 17, 12],\n [17, 6, 16, -6, 3, -3, 2, 15, 16, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -2, 9, 5, 16, 18, -11, -8, 5, -2],\n [-7, 0, 3, -8, 14, -11, -19, 12, 8, 4],\n [9, 10, -10, 14, 21, -21, 15, 14, -18, -5],\n [-6, -21, 19, 12, -9, -11, 10, -16, 16, 22],\n [-14, -18, -19, 9, -18, 21, -15, -10, -19, -12],\n [-8, -5, -3, -22, -22, -12, 6, 6, 1, -3],\n [7, 15, -18, 22, -13, -17, -19, -19, -16, 10],\n [-14, 3, 18, -2, -1, 10, 10, -18, -2, 4],\n [18, -22, -7, 12, 13, 21, 9, 6, 16, 0],\n [-8, 3, 14, 2, -21, -11, -4, 9, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "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, 12, 6, 15, 22, -3, 13, -16, -1, -5],\n [-2, -1, 16, -11, -12, -11, 3, 7, -8, -15],\n [20, -5, -13, -15, 15, 12, -3, -11, -20, -3],\n [-11, 1, -7, -13, -4, 18, -9, -9, -1, -19],\n [11, -5, 11, -5, 17, 8, 19, -3, 13, 19],\n [-13, -20, -2, 13, -13, -16, -1, 0, -11, 16],\n [-10, 17, -10, 10, 8, 5, -4, -2, 9, 3],\n [-10, 6, -16, 3, -17, 9, 13, 0, -12, -2],\n [-4, 11, 21, 12, 8, 6, -17, 13, 8, 9],\n [17, -3, -1, -20, -15, 22, -4, 8, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[16, 8, -20, 9, -13, 5, 4, 17, 20, 8],\n [11, -18, -12, -16, -15, -6, 21, 16, 18, -9],\n [1, 7, -8, -19, -10, -18, 8, -11, 7, -13],\n [7, 3, 21, -17, 4, -3, 5, -3, -11, 22],\n [-2, 7, -13, -18, 14, -15, 7, -6, -20, -2],\n [-7, 9, 4, -17, 19, -7, 22, -20, 17, -3],\n [17, -16, -12, 6, -20, -2, 9, 7, 16, -12],\n [-6, 2, 2, -14, 22, 6, -8, -4, -8, 16],\n [12, 17, -10, -7, -20, 8, -22, 12, -7, -22],\n [-9, -16, 0, 12, 6, -1, -7, 6, -17, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 2, 22, -21, 21, 9, 13, 9, 18, -3],\n [14, 19, 15, 10, -18, -17, -1, -2, -4, 20],\n [-8, 11, -16, -6, 21, 21, -18, 16, -21, 4],\n [22, 1, 18, 5, -22, -2, 5, -20, 7, -22],\n [22, 22, -5, 10, -8, 1, 13, 11, 3, 17],\n [-1, -7, 17, 19, -7, -18, -17, 19, 1, 7],\n [14, 9, -4, 22, 5, -15, 20, -22, -19, -1],\n [-1, 7, 4, 4, -10, 16, 4, 16, 15, -15],\n [-11, 1, -5, -8, -7, 10, -13, 1, 22, -4],\n [4, 22, 18, 8, -2, -7, 0, -9, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "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, 13, -11, 14, -12, -18, -2, 9, 6, -16],\n [13, 17, 4, -17, 15, -19, 12, -13, 15, 7],\n [19, -14, -7, -19, 3, 6, 5, -12, 5, 21],\n [9, 1, 19, 16, -16, -5, -20, 21, -3, 11],\n [7, -14, -13, -17, -6, -8, 10, -10, 19, 21],\n [-1, -7, 11, -20, -15, -3, 1, -5, 0, -22],\n [-21, -18, -5, -7, -13, 6, 12, 2, 19, 1],\n [-10, -2, 19, 20, 16, 11, -4, 5, 4, 3],\n [-12, 12, -3, -11, 5, -21, -22, -14, -1, 17],\n [4, -14, -16, 13, 15, -21, 20, -18, -6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, -15, 20, -20, -20, -22, 1, 22, 7, 19],\n [3, 15, 20, 17, 20, 15, 21, -20, -10, 13],\n [18, -11, -3, 16, 21, -15, -21, -12, -2, 14],\n [-17, -4, 7, 16, 21, 13, -3, -13, 1, 10],\n [6, 7, 13, 22, -17, -9, -20, 1, -4, 15],\n [11, -14, 7, 9, -10, -5, 21, -1, -19, 0],\n [-16, 21, -12, 16, 19, 18, 11, -18, 19, 2],\n [5, -9, 4, -7, 4, -21, -4, 0, 18, -9],\n [3, -15, 4, 17, 5, -19, 15, -12, 21, 1],\n [5, 18, -5, -2, 3, -20, -10, 15, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-22, 5, 13, -12, 20, 17, -19, 11, -22, -13],\n [-6, -16, 16, -10, -1, -22, 5, 10, -10, -22],\n [15, 2, 19, -2, 10, 14, 11, -20, 7, -20],\n [-5, 0, -15, -14, -21, -21, 4, 16, 13, -18],\n [-22, -1, -13, 22, 1, -8, 10, 0, -9, -5],\n [2, -1, 21, 21, 14, -16, 3, 1, -10, 18],\n [-17, -2, -16, -5, -8, -15, -7, -20, 22, -14],\n [3, 3, 7, 4, -7, -19, -4, 11, -17, 22],\n [-8, -13, 19, 13, 17, -17, 21, 17, -17, -8],\n [6, 2, -4, -9, -20, 19, -9, 16, 16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-12, -13, -8, 7, 21, -6, 6, -6, 10, 15],\n [-2, -9, -13, 19, 0, 16, 16, -9, -1, 18],\n [5, -14, 0, -16, 1, 20, 14, -14, 15, -16],\n [0, 2, -1, 20, -16, -17, 13, -1, 12, 10],\n [-2, -12, -10, -20, -10, 18, 11, 5, 17, 11],\n [9, 0, 1, -22, 1, -20, -6, -16, -13, -4],\n [1, -14, -8, -1, -6, -4, -14, 15, -4, -15],\n [-17, 15, 22, -2, 6, 11, -11, 16, 9, -17],\n [-6, 9, -15, 15, 6, 8, -4, -14, 5, 16],\n [17, 8, -4, 10, 3, 22, -22, -12, -21, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "339", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-10, 16, 11, 11, 12, 9, 22, -11, 10, -5],\n [-18, -4, 8, 4, 19, 15, -8, -19, -4, -2],\n [17, -22, -3, -1, -10, 18, -22, -8, -8, -9],\n [-18, -17, 18, 8, 3, 2, 16, 17, -8, -17],\n [-22, 18, -16, -19, -22, 18, -21, 11, 12, -10],\n [-6, -13, -20, -19, 2, 14, 20, 15, 6, -22],\n [7, 16, -13, 6, 21, 9, 21, -22, 18, -6],\n [-11, -21, -14, -11, 2, 13, 21, 12, -1, 10],\n [-2, 17, -1, 5, -19, 3, 0, 0, 18, -15],\n [9, 16, 21, -22, 7, 5, -6, 0, 15, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "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, -18, 2, -16, -1, 21, 14, 11, 13, 17],\n [-3, 14, -6, -19, -5, 5, -7, 20, -15, 21],\n [-5, 6, 17, -7, 7, 11, 7, -2, -1, 2],\n [-1, 5, 16, 10, -21, -19, -7, -11, -6, 13],\n [-7, 16, 0, -15, -14, -9, -14, 3, 13, -20],\n [-13, 2, -19, 7, -12, -4, -10, 13, -20, -9],\n [-13, 15, 17, 4, 1, -7, -13, 4, -16, 5],\n [3, -5, -10, -15, 4, -9, 18, 21, -17, -3],\n [5, 0, -11, 1, 21, -1, 3, -1, -16, -8],\n [7, -19, -17, -21, 8, 1, 12, 8, 2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-11, -21, -8, 17, 9, -12, -6, -2, -1, 10],\n [6, -8, -2, -21, 19, 15, -20, 2, -10, 1],\n [8, -8, -17, 18, -13, -14, 18, 18, -18, 22],\n [21, 18, -4, -3, 10, 20, 14, 8, 16, -10],\n [15, 22, -17, -15, 20, -13, 18, -19, -9, -19],\n [1, -2, -13, 2, -17, -7, 21, 5, 13, 10],\n [7, 13, 2, -10, 16, -8, 15, 7, -9, -19],\n [-22, -20, 22, 13, -19, 20, -9, 2, 16, -20],\n [-16, -15, 21, -16, 2, -6, 3, -19, -5, -19],\n [-6, -6, 22, 2, -20, -11, 4, -6, -1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[16, 20, 13, -7, 14, 6, -9, -16, 18, 5],\n [-10, -7, -2, -19, 16, 12, -8, 3, -16, -5],\n [2, 14, -2, -15, -3, -5, -4, -20, 15, -5],\n [4, -8, -2, -1, -15, -12, 20, -11, 16, 4],\n [12, -21, 12, 8, -15, -3, -15, -19, 8, 9],\n [-10, -1, 3, -6, 6, 4, -1, -5, -18, -11],\n [-21, 19, -16, 3, 16, -8, 10, -20, 19, -21],\n [-6, -22, 13, 20, -6, -21, 10, 6, -17, 20],\n [13, 1, -12, -18, 7, -13, 14, 4, 4, 1],\n [-20, 15, 3, 22, 16, -5, -20, 15, 19, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-10, 2, 1, 18, -7, 20, 18, 19, -12, -2],\n [8, -8, 22, 13, 20, -22, 5, 10, -20, -8],\n [10, 9, 0, 3, -6, -14, -18, 6, -17, 18],\n [12, -2, 22, 22, 0, 12, -21, 19, -14, -10],\n [20, 11, -7, -18, -22, 17, -1, 3, 11, -2],\n [-16, 2, -11, 8, 4, -1, 11, -6, -12, 6],\n [11, 14, 3, 22, 22, 22, 9, 14, -18, -3],\n [-16, 20, 0, -22, 16, -20, 22, -20, -17, 8],\n [4, 6, -8, 13, -18, -20, 2, 9, -2, -6],\n [-14, 3, -1, 18, 0, -12, -13, 0, -18, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-19, 20, 4, 15, 11, -20, 9, 3, -5, -16],\n [22, -10, -17, 12, 8, 19, 14, 20, -19, 19],\n [-19, 22, -15, 15, -12, -21, -5, -5, -1, -11],\n [-6, -6, 13, 6, -7, 18, -12, 21, 20, 22],\n [-1, 7, -15, -5, -7, -3, 16, -15, 7, 15],\n [6, -10, -6, 17, 20, -6, -14, -21, 19, 1],\n [-2, -21, -18, -6, 1, -15, 7, -1, 1, 3],\n [-15, -11, -9, 7, 12, 8, 5, 4, 13, -22],\n [18, -9, -13, 19, -16, 17, -9, 13, 4, -12],\n [19, 14, 19, -13, -16, -6, -11, 14, 14, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-16, 1, 11, -22, 6, 3, -13, -22, 22, -6],\n [18, 13, -14, 16, 0, 6, -21, -5, 5, 19],\n [-16, -12, -16, 20, 1, -8, 8, -4, -13, -15],\n [-22, -21, 6, 19, -13, 19, -14, 8, 9, -21],\n [1, 14, 20, -17, -15, 17, 2, 19, 20, 2],\n [-12, 12, -22, 0, -20, 18, -22, 21, -11, 15],\n [17, 8, 6, 12, 5, -2, -12, 3, -12, -18],\n [-16, 8, 16, 19, -15, 4, -2, 7, -9, -22],\n [22, 1, -17, -17, -18, 12, 21, -8, 12, 18],\n [-15, 20, 12, -18, 8, 19, 8, 14, -15, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "397", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -7, 21, -15, -19, 9, -20, -7, 11, -10],\n [10, -1, 8, 1, -20, 10, 7, 3, 11, -1],\n [7, 12, 2, 5, 10, 0, 3, -14, -15, 14],\n [10, -8, -15, -2, -20, -14, -9, 15, 4, -3],\n [-19, 1, 4, -11, 5, 12, 1, 8, -20, 7],\n [4, -6, -17, 20, -5, 12, 4, -6, -12, 15],\n [14, 19, 11, 9, 20, 12, 5, -1, -7, 19],\n [17, -11, -18, 3, 3, -10, 1, 21, -20, 9],\n [0, 14, 15, 22, 15, -10, -8, -21, -12, -7],\n [-5, 11, -13, -10, 9, -15, -16, -6, 18, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "317", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, 6, 14, 4, 14, 1, 22, -7, 3, 8],\n [4, 3, 20, -8, -8, 0, 2, 21, -19, 13],\n [-7, 17, -2, 17, 20, -6, -20, -16, -11, -22],\n [20, 14, -17, 0, 2, 2, -20, -19, 7, 10],\n [6, -19, -9, -2, -16, -2, -16, -22, 11, 0],\n [-20, -5, 20, -11, -9, 18, 5, 19, 22, 1],\n [1, -20, -14, 1, -21, 17, 5, -16, -14, 22],\n [16, 16, 10, 11, -2, 6, 4, -6, 19, 0],\n [22, -2, -15, -14, 10, -19, -5, 9, 7, 2],\n [10, 12, 19, 11, -21, -10, 18, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-21, -21, -18, -9, 0, 12, -22, 18, 17, -8],\n [7, -2, -15, -16, 18, 11, 19, 14, 9, 10],\n [-17, 19, -13, 3, 22, 3, -4, 12, 22, -19],\n [2, -15, -11, 1, 1, -6, 2, 10, 4, -21],\n [-14, 10, -4, -18, -3, 1, 8, 21, -19, 9],\n [12, -9, 13, -17, -6, -5, -15, -11, -6, 8],\n [-22, -12, 19, -7, 14, 5, -14, -15, 2, -13],\n [17, -20, 0, 0, 21, -19, 0, -14, -19, 11],\n [16, -5, 11, 11, 19, -20, -4, 11, 3, 12],\n [18, 20, 8, 20, 4, -20, 14, -11, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-7, -6, -8, 3, 22, -21, -6, -22, 7, 9],\n [7, 19, -19, 19, 21, 9, 12, -22, -4, 10],\n [-4, 13, 4, -10, 4, -9, 1, 12, -4, 2],\n [-12, -14, -17, 13, 14, 6, -14, 10, 0, -8],\n [-12, 0, 3, -22, 7, -6, 18, 0, 13, 18],\n [-18, 12, -14, -19, -16, -22, -7, 2, -17, 15],\n [-9, 14, -12, -22, 19, -22, 13, -15, 9, 10],\n [-15, -9, 1, 18, 6, 2, -17, -22, 0, 18],\n [10, -9, 5, 6, 20, 17, 0, 21, 15, 20],\n [-13, 4, -15, 21, -19, -2, -2, 7, -10, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 13, 17, -18, -1, -21, 2, 17, 1, -18],\n [-7, -8, -10, -12, -7, -5, 2, 15, 17, -19],\n [-2, -12, 11, 7, -19, -9, -12, -19, 3, -20],\n [14, 15, 18, -19, 3, 16, 22, 19, 21, 19],\n [-12, -12, 15, 15, -3, 3, 15, -11, 6, -9],\n [2, 19, 19, 16, 3, -13, -9, -18, -1, -12],\n [6, -16, -5, 8, 20, -3, 12, -16, 7, -19],\n [7, 7, 7, -5, 20, -13, -9, 13, 0, -11],\n [-11, 11, 3, -17, 14, -8, 19, 16, -4, 17],\n [0, 13, -10, 8, 14, 3, 20, -5, 10, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[9, -19, 18, -4, -16, 12, 3, 21, 0, 11],\n [-16, -12, -15, -10, 9, 18, 11, -5, -8, 20],\n [1, -2, -5, -9, -4, -10, -7, -21, 11, 3],\n [-1, -3, 6, -5, 6, 19, 21, 4, 12, 6],\n [-17, 14, 2, -2, 8, 17, -7, -9, -17, -12],\n [4, 15, -18, -8, 15, -7, -5, 10, 12, 1],\n [12, -16, -9, 7, 1, -8, -10, -4, 6, -1],\n [-21, 16, -10, 13, 15, -5, -8, 12, -6, -10],\n [-1, 17, -2, 3, -19, -16, -13, -8, 3, -7],\n [17, 11, -6, 15, -7, 11, 6, -5, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, -21, -5, 15, 10, -14, -8, 5, -15, 13],\n [16, -15, 19, -4, -19, 4, -10, 15, -2, 3],\n [22, 0, 7, 8, 8, -7, 19, 18, -16, -6],\n [1, -3, 16, 4, -21, -22, 11, 4, 14, -17],\n [15, 4, -7, 12, 4, 12, 13, 15, 5, -20],\n [18, 8, -20, 15, 1, 3, 18, 5, -14, 14],\n [4, -20, 18, 5, 9, 12, -16, -16, -2, 9],\n [15, -3, -15, -19, 3, -8, -17, 9, -18, 21],\n [-17, -20, 6, -4, -13, -16, 22, -22, -22, -6],\n [-1, 13, -9, -17, 7, 10, -3, -7, -19, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-22, -10, -15, -1, -19, 11, 22, 14, 0, -3],\n [1, 4, -10, -18, -7, 15, 6, 3, -1, 1],\n [-10, 20, -2, -22, -19, -20, 0, -7, 22, -10],\n [16, 8, 1, -8, -18, -1, -1, -12, 1, 22],\n [-13, 11, -12, 20, 6, -1, 10, -15, 9, 17],\n [22, 0, -18, 8, 6, -17, 2, 2, 8, -9],\n [-6, -7, 5, -14, -21, -19, -3, 18, 13, 14],\n [-17, -22, 22, -20, 14, 22, 19, -20, 20, 10],\n [-8, -19, -8, -16, -19, -20, 0, -9, -17, 10],\n [-14, -11, 12, 8, -20, 13, -10, -10, 11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "390", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[11, 19, 20, 5, 12, -9, -5, -4, -4, 10],\n [12, -3, 6, -15, 2, -6, -22, 15, 7, 5],\n [10, -10, 1, 21, 14, -1, -10, 17, -11, 18],\n [-16, 13, 6, 6, 3, 4, 1, 8, -16, -6],\n [10, 11, -5, 18, -18, -22, -16, 11, -20, 13],\n [12, -11, -8, -19, 10, -7, 6, -17, 14, 0],\n [-10, 21, -22, -11, 4, 2, -1, 11, -5, 18],\n [-7, 6, 7, 7, -3, -1, 19, 11, -19, 8],\n [-9, -15, 14, -18, -15, -12, 6, -2, 16, -10],\n [-4, -20, 11, 15, -4, 9, 13, 16, -9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"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, 9, 8, -1, -18, 8, -8, 21, -6, 14],\n [-4, -13, 21, 11, 2, 14, 5, -8, -3, -10],\n [-3, 20, 8, -5, 18, 5, -19, 1, 21, 22],\n [-14, 9, 9, 16, -2, 21, 19, 16, 4, 13],\n [-15, -4, 6, -4, -18, -1, 12, -13, -8, -21],\n [19, -1, 12, 16, -4, -11, 11, 22, -3, -16],\n [1, -20, -17, 10, 11, 10, 6, 0, -19, -18],\n [11, -7, 17, 20, 19, -20, 20, 19, -9, 10],\n [5, 18, -8, -19, -3, 2, 12, 16, -1, 12],\n [5, -13, -7, 0, -4, -22, -22, 3, 11, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -3, 19, 4, 5, 8, -16, -15, 9, -12],\n [3, 2, -16, -3, 18, 7, -22, -5, -15, 6],\n [17, -1, 9, 17, -9, -21, 12, -16, -20, -8],\n [20, 11, -1, -5, -5, 11, 13, 16, 15, 14],\n [-5, 20, 17, 6, -11, -5, 8, -8, 17, 7],\n [13, 5, -8, 20, 10, -21, -15, 10, 12, -5],\n [3, -2, 5, -3, 22, -3, -19, 13, 11, 22],\n [-10, 8, 16, -16, -6, 19, -11, 7, 11, -1],\n [-2, -14, -11, -6, -7, -18, -4, 5, -6, -1],\n [12, -8, -4, 3, 21, 21, 12, 20, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -12, 3, -22, 13, -2, -15, -3, 22, -6],\n [-8, -2, -22, -20, 8, 8, -2, 0, -6, -1],\n [-1, 13, -15, -15, -9, 15, 1, -1, -8, -3],\n [4, 5, -1, 8, -14, 0, -18, 22, 16, -6],\n [17, -18, -16, -15, -16, -1, 21, 15, -2, -19],\n [9, 6, 7, -20, -18, -4, -15, 14, 8, 4],\n [-10, 19, -17, -22, 7, -12, 18, 8, -7, -8],\n [-18, -8, -22, -8, 13, 16, -15, -1, 4, 11],\n [7, -11, -21, 15, -1, -6, 12, 19, 22, 0],\n [6, 6, -4, -6, -15, -16, -12, -20, -21, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"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, -12, 17, 20, -21, -11, 18, 15],\n [-11, 2, 14, 8, -6, -11, 7, -21, -7, -22],\n [11, 22, -22, 13, -20, 11, -11, 22, 4, 14],\n [2, -11, 10, -14, -22, 0, 5, -20, 15, 13],\n [21, 21, -18, 6, -10, 21, -19, -17, 15, -17],\n [-12, 4, 12, 17, -19, 4, -7, -5, -16, -12],\n [-15, -17, -18, -17, 15, -21, 8, 16, 9, -14],\n [-8, -2, 5, 22, 4, -18, -6, 14, 1, 8],\n [12, 18, 18, -19, -3, 20, -6, -13, 14, -2],\n [-2, -7, 10, -13, 21, -5, 10, 6, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-11, -3, -17, -15, -9, -18, 13, 15, -20, 13],\n [-1, -15, -9, -16, -19, -4, 20, 1, -7, -17],\n [21, -15, 2, 9, 2, -13, 20, 18, -6, -20],\n [-14, -5, 7, -18, 9, 4, -2, 1, 15, -20],\n [-7, -8, 2, -15, 18, -19, 9, 22, 12, 7],\n [16, 7, -6, -4, 8, -6, -21, 14, 6, 7],\n [20, -1, 15, -12, 10, -4, -20, 17, -1, -5],\n [22, 7, -22, -3, -18, -11, -12, 1, -5, -15],\n [6, -1, 22, -21, 0, -7, 21, -15, -19, -9],\n [-14, -12, 15, 21, -7, -10, 13, 21, 13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-9, 6, -6, -22, -3, 10, -21, -6, 0, -1],\n [-22, -11, -10, -9, -13, -11, -1, -5, 16, -4],\n [7, -8, 16, -9, -14, -18, 10, -18, 1, -15],\n [-4, -11, -15, -15, 15, -3, 6, 18, 11, -5],\n [-22, -12, 21, 12, 9, 19, -7, -17, -14, 17],\n [-1, -15, 9, 3, -5, 14, -11, 15, 11, -19],\n [-7, 1, -9, -6, 8, -19, 21, 11, 15, 15],\n [-20, -15, -11, 12, -21, 6, 0, 10, -5, 17],\n [-1, -9, 6, 22, -8, -8, 22, -19, 13, -18],\n [-20, -11, -3, 21, -3, 16, 16, -22, 21, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -3, -14, 8, 5, 12, 17, 15, 21, -21],\n [-20, -9, -6, 12, -19, 7, 16, -9, 4, -10],\n [-3, 1, -13, -16, -6, -1, 21, -12, 19, 0],\n [-1, 17, -5, 22, 3, 7, -10, -19, 20, 4],\n [17, -13, 21, 5, -2, -12, -3, 13, -4, -13],\n [-8, 22, 22, -5, -16, 7, -9, 14, 18, 7],\n [4, 14, 18, -6, 7, -5, -20, 5, 14, 7],\n [-2, -3, -1, 13, 13, -2, 1, -2, -16, -15],\n [-1, -1, 7, 11, 6, -13, -18, 16, 11, 15],\n [-13, -14, 9, -18, 12, -12, 19, -7, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-22, 3, -12, -8, 16, 17, -5, 1, 5, 2],\n [0, -12, 10, -7, 13, 0, -17, 20, 1, 15],\n [19, -17, -13, -1, 0, -18, 5, -14, 16, 21],\n [5, 2, 20, 15, 4, 1, 20, 20, -7, -21],\n [-21, -18, -2, -13, 19, -5, 3, -3, 18, 13],\n [-2, -21, 10, 0, 16, 8, -19, 18, -20, 14],\n [-13, 19, 9, 13, 4, -4, 15, -22, 3, -10],\n [12, -21, -1, 16, 5, 21, -21, -12, 14, 3],\n [5, 3, -6, -20, -9, -7, 13, 5, 5, 2],\n [-14, -12, 14, 20, 22, -2, -21, 11, 19, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-18, -12, 6, 5, 5, -18, -3, 14, 16, -13],\n [9, 6, -21, -22, -3, -22, -19, -8, 7, -17],\n [15, -22, -16, -18, -16, 13, -20, -11, -8, -3],\n [18, -2, 9, -11, 14, 17, -16, 22, 8, -22],\n [-12, 22, 11, -4, -12, 10, 10, -15, 22, -15],\n [11, 17, 4, 6, -9, 11, 22, 14, -22, -14],\n [-13, 7, 20, -5, -6, -17, -12, 1, 13, 10],\n [10, -5, -18, 8, -7, -21, -14, -21, 14, -3],\n [-6, 2, -4, 19, -15, -12, -10, -10, -14, -18],\n [-5, 17, -9, 11, -1, 10, 1, 6, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-22, -16, -19, -13, 17, 12, 16, -7, 4, -3],\n [-13, 22, 10, -16, 19, 21, -1, 20, -6, -14],\n [17, -13, 13, 8, 8, -18, -5, -17, 19, 5],\n [20, 1, -18, 5, -20, -5, -19, 17, 19, 9],\n [9, -4, 6, 10, -21, -12, 10, 18, 17, -22],\n [19, -6, -7, -21, -19, 9, -16, 6, -14, 12],\n [-18, -2, -6, 16, -9, 9, -8, -2, -9, 18],\n [-7, -22, 17, -5, 11, 3, 13, -2, -22, 4],\n [-12, 15, -9, 5, 4, -1, -2, 1, -4, 1],\n [3, 2, 22, 21, 6, -13, -12, 1, 1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, 17, -6, 12, -17, -11, -8, 9, 0, -16],\n [15, 8, 6, 21, 5, -11, 4, -19, -2, -14],\n [11, 14, -2, 0, 1, -13, 15, -17, -2, 14],\n [6, 17, -2, -1, 12, -18, -8, 18, -4, -7],\n [17, 20, 0, -19, -2, 1, 19, 3, 19, -21],\n [17, -15, -14, -21, -9, -3, -21, -19, 12, -9],\n [-2, -8, 16, -3, -17, 5, 20, -21, 5, 11],\n [-9, -14, 0, 21, 12, -1, -18, 18, 6, 12],\n [11, -19, 22, -14, -9, 22, -18, 4, -12, 7],\n [14, 16, 11, 1, -7, 7, 1, -20, 6, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-11, 4, 6, -21, 6, 17, -14, 21, 5, 14],\n [0, -10, -18, 9, 5, -8, 1, 9, -2, -18],\n [14, 13, 5, 9, 0, -7, -13, 6, 4, 12],\n [19, 22, 1, 0, -20, 13, 22, -9, -19, 21],\n [19, 9, -3, -6, 6, 16, 9, -19, 1, 21],\n [19, -21, -9, 17, 19, 15, 11, 20, -21, 13],\n [-17, 13, -1, -18, 15, 18, -1, -12, 20, 8],\n [19, 6, 10, -1, 4, -15, -17, 2, 11, -14],\n [13, 8, -4, -22, 1, 11, -6, 11, 12, 13],\n [-10, 2, -11, -2, 14, 15, -22, -17, 22, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-12, -7, -1, -12, 14, 3, 3, 19, -2, 3],\n [-8, 16, 12, -12, -14, 19, 0, -19, 7, 5],\n [2, -1, 2, 3, 6, 18, 9, 3, 5, -3],\n [-21, 0, 16, -18, -2, -1, -12, 7, 5, 13],\n [-6, -2, 14, 13, 2, 1, 7, 19, 12, -2],\n [-17, -2, -15, -18, 17, -13, 8, 7, -2, 13],\n [4, 15, 12, 9, 3, -19, 4, 13, 14, 4],\n [-17, -5, 3, 21, 1, -16, 21, -9, -10, 3],\n [20, 20, -21, 0, 5, -22, 9, -11, 12, 3],\n [8, -11, 6, -18, 12, -16, -7, 9, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "296", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 17, -8, 0, -15, 2, -12, -2, -13, -14],\n [-22, -1, -17, 7, 11, -10, -1, -17, 18, 1],\n [-2, 16, 0, -18, -16, -20, -10, -11, -17, 11],\n [-8, -5, -20, -1, 12, 5, 18, 19, -11, -22],\n [13, 7, 0, 14, 5, -18, 13, -13, -18, -9],\n [1, 5, -2, 22, 17, -11, -3, 9, 15, 17],\n [19, -2, -6, -22, 21, 5, -21, -6, 16, -9],\n [-9, 21, -5, 17, 11, 20, -22, 19, -5, 11],\n [0, -7, -4, 14, -17, 1, -6, -7, 16, 18],\n [-17, -7, -14, 6, -19, 3, 15, 3, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[20, 1, -15, 17, 2, -19, -8, -7, -12, 5],\n [-16, 15, 1, 8, -19, 14, 12, -17, 10, 9],\n [15, 12, -6, 9, -9, -4, 1, 16, -12, -16],\n [22, 1, 1, -9, 1, -12, -15, 21, -8, 19],\n [-21, 1, 22, -13, 9, -6, -13, -1, -17, 4],\n [-3, -22, -6, -22, 14, -8, -22, -6, 22, 20],\n [21, 15, 20, -21, -5, -11, 6, 0, -14, -15],\n [-7, 0, 6, -13, -11, -11, 7, -13, -9, -19],\n [-3, 18, 16, -16, 7, 18, 1, -13, 22, 15],\n [13, -6, -2, -20, -22, -5, -21, 17, -19, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "356", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -3, 19, -16, -14, -16, 4, -2, 12, 1],\n [9, -11, 0, 13, 6, -20, 20, -15, 11, -9],\n [13, 9, -16, -13, -11, 17, 0, -12, -10, -11],\n [-16, 21, -13, -16, 4, -16, 1, 0, 2, 21],\n [13, 10, 14, 19, 16, -16, 7, 8, 22, 14],\n [-2, 11, -2, 17, -3, 11, -15, 9, 7, 6],\n [-18, 7, -11, 16, 4, -10, -13, 13, 8, -7],\n [16, 22, 13, 3, 21, -3, 11, 14, -15, -19],\n [6, 8, -21, 2, 15, -20, 19, 20, -18, -1],\n [-7, -14, -14, -11, 19, -19, -5, -5, 19, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[10, 19, -20, 15, -6, -11, -12, -6, 12, 18],\n [-17, 12, -17, 9, -12, 20, 16, -10, -10, 16],\n [11, -20, 9, -19, 17, -22, -14, -16, 4, -20],\n [-1, -7, -15, -18, 7, 5, 4, -1, 7, 14],\n [-16, 7, -10, -1, -12, -18, -1, -8, 16, 14],\n [8, 6, 16, -6, 18, -17, 18, -6, 11, 0],\n [7, -10, 7, -3, -17, 8, -4, -17, 11, 5],\n [-10, -13, 18, 22, -16, -5, -1, -9, 13, -15],\n [-11, 17, 10, 1, 19, 16, -9, -18, -4, -20],\n [-22, 17, 18, 14, 10, -6, -14, 8, 12, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-10, 14, 15, -9, -17, 6, -14, 13, 0, -8],\n [-16, 2, 14, 0, -12, -15, 13, 19, 16, -22],\n [21, -10, -7, -10, 14, -9, -10, -11, 5, -1],\n [-3, -4, -12, 7, 3, -8, 7, 6, 9, 7],\n [21, -7, 13, -5, 18, 16, 5, -4, -12, -6],\n [-2, 14, 21, 11, 10, 6, -19, 9, -12, 3],\n [-5, 9, 4, -7, -13, 21, 11, 10, -13, 19],\n [3, 19, 2, -21, 3, -3, -20, 9, -22, 1],\n [20, 21, 10, 15, 12, -6, 20, 21, 10, -12],\n [0, 15, 9, -4, -11, 5, -21, -13, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-15, 20, 0, 22, 7, 5, -10, 14, -11, -13],\n [-6, -22, -1, -8, -7, -3, -13, 19, 3, 0],\n [-6, 11, 18, -1, -19, -16, -18, 8, -4, -19],\n [-1, -20, 0, -19, 1, -9, 18, -20, -2, 3],\n [-22, 7, -19, -9, -5, -11, 15, 19, 13, -7],\n [-22, -20, 16, 12, -8, 15, -7, -6, 11, -13],\n [-12, 5, 4, 15, -5, 7, -10, -7, -21, -3],\n [-11, 6, -15, 15, -3, 12, 16, 8, -7, 0],\n [11, 9, -6, 20, 1, 12, 0, -15, 0, -2],\n [-4, 8, -16, 1, -15, -10, -20, 11, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[12, -2, -22, -21, 19, 20, 3, -20, 1, 3],\n [-15, 14, -15, -5, -5, -11, 13, 17, -21, -3],\n [-20, 17, 21, 11, -17, 17, -13, 1, -5, 10],\n [16, -16, 22, 21, 6, -4, 15, 16, 2, -6],\n [14, -20, 1, -5, 3, -2, -12, 18, -6, 22],\n [15, -2, -19, 9, -5, 21, 5, 13, 14, 21],\n [3, 1, -13, 15, -15, -21, 21, 12, -2, 4],\n [0, 9, 3, -16, 10, -6, -15, 19, -6, 19],\n [-5, 13, 16, 21, 0, -11, 0, 10, 5, 21],\n [0, -16, -21, -22, -19, -15, 6, -5, 14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-17, 21, 1, 18, -8, 17, -11, -9, 4, 14],\n [-10, 15, 15, -20, -7, -11, -9, 11, 8, 16],\n [-18, -11, 3, -6, 21, -12, 10, 18, 17, -19],\n [9, 8, -12, -6, 4, -15, -2, 10, -18, 9],\n [2, -15, 4, 3, 17, 6, -14, -5, -16, 19],\n [-2, -7, -20, 9, -13, 9, -15, 9, -19, 6],\n [-11, 14, 13, -4, 14, 8, 21, 3, 22, -17],\n [6, -6, -3, 19, -13, -17, 9, -21, -13, 14],\n [4, 18, -4, 18, -7, -3, 13, -18, -5, -15],\n [-10, 18, -13, 13, -4, 8, 13, 6, 22, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[9, -12, -21, 9, -18, 8, -10, -1, 12, -4],\n [6, 0, -4, -7, 8, -7, 3, -20, 0, -14],\n [1, 10, -9, 5, 1, 20, -16, 15, 21, 2],\n [-21, 22, -22, 0, 17, -5, -15, 11, 20, -15],\n [6, -10, -22, 6, 14, -22, 21, -18, -21, -1],\n [7, -12, 6, 19, -20, 22, -10, -20, -13, -19],\n [-9, 0, -6, -22, -8, -21, -5, 16, -1, 5],\n [7, -10, -20, -20, 22, 3, -19, -7, 5, -15],\n [17, -7, 8, 0, -21, -14, 4, 22, -1, 21],\n [11, -14, 10, 15, 11, 12, 3, -16, 22, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -11, -6, -2, 20, -1, 3, 16, -10, 19],\n [19, 22, 0, 7, -6, 4, -3, -16, -19, 8],\n [7, 8, -19, -5, -3, 17, 17, 0, 15, -14],\n [-7, -2, -14, 2, 13, 20, -9, -6, 5, 22],\n [18, -15, -9, -8, 16, 2, -12, 6, -20, 16],\n [-1, 14, 18, -3, -4, -10, 4, -4, -7, -21],\n [-22, -20, 1, 21, 15, -21, -7, 6, 14, 21],\n [-19, -9, -6, 21, 22, -6, -3, 6, 18, 3],\n [19, 15, -6, -11, 5, -14, 9, 11, -7, 8],\n [4, 6, -22, 4, 9, -12, 12, -21, -22, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, -21, -21, -18, -10, -4, -4, -22, 12, -5],\n [9, 9, -15, -12, -3, -15, 5, -2, 15, 15],\n [-17, -21, -13, 19, -14, -20, -21, 13, -15, -14],\n [3, 11, 7, 15, -15, -20, -12, 2, -18, -11],\n [7, 4, 20, -18, -3, -2, -20, 18, 21, -19],\n [1, -16, 1, -12, -21, 21, 18, -17, -16, 15],\n [-5, 22, -14, 5, -4, -19, -19, -10, 5, -12],\n [-21, -17, -11, 17, 14, 1, -14, 3, -19, 18],\n [21, -19, 11, -1, -10, -8, 17, 15, 18, 20],\n [21, -21, -21, 20, -15, 15, -5, 6, -12, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-14, -1, 2, 8, -2, 15, -4, -13, 14, -11],\n [-4, -21, -8, 15, -15, 12, 15, 20, 7, -14],\n [7, -4, 6, -21, 5, -15, 2, -13, -1, 12],\n [19, 1, 3, 8, 0, -21, 16, 10, 1, -11],\n [14, -14, 21, 20, 21, -20, 21, 0, 1, 10],\n [7, 15, 20, -21, 17, -1, -12, -11, -4, -3],\n [-14, 20, -5, 18, -5, 17, 13, 4, -10, -15],\n [20, 0, -10, -16, 17, -21, -20, 19, 16, 0],\n [-16, -19, -15, 9, -4, -11, -13, -9, 4, 21],\n [-2, -3, -19, -4, 6, -16, 10, -15, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"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, 10, 13, 3, 13, -12, 7, 10, -13, 6],\n [2, 9, -19, 16, 11, -1, -10, 13, -17, -6],\n [3, 1, -14, -21, -3, 4, -17, 4, 1, -8],\n [10, 19, -13, -2, -17, 7, 0, 13, -20, 3],\n [11, 7, -5, -6, 22, 19, -2, 1, -19, 2],\n [1, 4, 8, 12, -3, -7, 8, -16, -5, -15],\n [4, -9, -5, -22, 8, -3, -17, 22, -22, -4],\n [16, 4, -7, -9, 11, -16, -3, 8, -1, -3],\n [-8, 2, -22, -6, -7, 14, -2, 4, 12, 1],\n [-21, 2, -4, 22, -10, 6, 9, -17, -14, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -13, 12, -17, -3, 15, -11, -20, -5, -2],\n [12, 14, -4, 2, -5, 17, 7, 19, 19, 11],\n [-13, -1, -19, -20, 5, -1, -11, -10, 18, 10],\n [-4, 18, -6, 11, -19, 16, -15, 10, -22, -18],\n [9, 17, -22, 12, -1, 6, -6, 7, 12, -22],\n [-19, -14, 22, 9, -18, -9, 3, 0, -1, 4],\n [2, 13, -19, 9, -14, -21, 19, 16, 2, -13],\n [14, 2, 17, 6, 14, -18, -9, 10, 4, -18],\n [21, -8, -20, -22, 1, -11, 22, -9, 19, -3],\n [-9, -9, 22, 12, -4, -3, 19, 21, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-22, -19, 17, -6, 3, -9, 9, 13, -3, -7],\n [-4, 22, 16, 1, -9, 6, 19, -9, -12, -12],\n [17, 1, -1, -2, -17, -9, -14, 12, 21, 13],\n [2, -8, 22, 5, -9, -10, 18, 8, -18, -4],\n [-15, -10, 18, -6, 9, -18, -14, 20, 11, 22],\n [-22, 17, -8, 9, 11, 12, 5, -6, -12, 0],\n [3, -18, 3, -17, 20, 11, 19, -10, 2, -21],\n [-9, -6, 18, 17, 17, 16, 2, 4, 1, 10],\n [4, 22, 8, 15, -8, 21, 17, -22, -12, -8],\n [10, 9, 2, 16, 10, 6, 11, -15, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-18, -4, -2, -20, 3, 10, 7, -1, -18, -4],\n [-14, 1, 16, -11, 22, 4, 19, -2, 15, 12],\n [9, 13, 10, 20, -6, -18, 21, -3, 0, 16],\n [-19, 3, 7, 6, 11, -13, -3, 1, 11, 14],\n [-10, 0, -13, -1, 22, -9, 2, -5, -3, 5],\n [-15, -18, -2, -3, 21, -7, -3, 2, -16, 2],\n [13, -13, 17, -7, -19, -13, 8, -11, -3, 9],\n [-21, -12, -3, 0, -10, 12, -6, -13, 17, 15],\n [-9, -4, 9, 10, 20, 2, 2, -9, 22, 21],\n [15, 13, 1, 18, 16, 16, -10, -21, 11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-21, 2, -18, 11, 16, -18, 20, -15, -9, 6],\n [7, 14, -19, 12, -16, 3, 9, 20, 10, 1],\n [-22, 6, 22, 15, 15, -2, 0, -18, 7, 17],\n [-5, -17, -18, 19, -5, -10, -3, 15, -2, -19],\n [-10, -5, -10, -10, 16, 14, 12, 15, 17, 4],\n [3, -11, -21, 20, -3, 12, -13, -15, 17, 13],\n [8, -8, 19, -5, -8, -4, 1, 12, -21, -10],\n [22, -14, 12, -21, -7, 13, -21, -7, -15, -22],\n [-5, 18, 3, 21, -18, -2, 12, 17, 5, 3],\n [9, 21, 21, -2, -19, 19, 18, 13, 1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-18, -20, -12, 22, 9, -1, -12, 15, -1, -19],\n [16, -20, -13, 14, -4, -5, 5, 8, -6, 1],\n [-22, -18, 9, -6, -2, 18, 20, -1, 16, 16],\n [11, -9, -7, -18, -5, -19, 21, 5, 22, 4],\n [-17, -12, -2, -6, 8, 11, -10, 0, -22, -19],\n [7, 8, -7, 20, -20, -11, -11, -12, -7, 6],\n [-2, 22, 21, 19, 20, -18, -10, -6, -11, -6],\n [-22, -15, -7, -8, -4, 2, 8, 19, -21, 2],\n [8, -19, -19, -11, -6, -2, 6, -1, 13, 17],\n [-7, -8, 7, -12, -10, 0, 17, 18, 11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-21, -15, -5, -16, 20, 8, -1, 5, 2, -22],\n [9, 2, -7, 6, 19, 1, -6, 19, -17, -9],\n [3, 5, 13, 8, 4, -21, -4, 5, 22, 21],\n [-2, 22, -8, 11, 17, -20, -22, 1, 20, 4],\n [-14, 1, -6, 5, 16, -19, 6, 22, 5, 14],\n [6, 21, 6, -18, -12, -21, -19, -13, 16, 21],\n [-15, 0, 4, 0, 11, 12, -6, -13, -21, -6],\n [8, -7, 1, -16, -4, -7, 10, 13, 22, -13],\n [20, -8, 20, -20, -21, 20, 19, 12, 4, -18],\n [-8, 13, 10, -22, -11, 19, 18, -14, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 0, 6, 19, 12, 4, 4, 7, -20, -11],\n [8, 14, 4, 1, 18, 17, -12, 4, -14, -7],\n [-9, 7, 1, 19, -10, 10, -14, 3, 19, 22],\n [-10, -2, 6, 5, 1, -10, 19, -3, 16, -16],\n [18, -8, 2, 12, -10, 20, -15, -2, -17, -13],\n [18, -2, -9, 22, 10, 2, -4, -14, 14, 13],\n [13, -8, -18, -6, 7, -16, -17, -8, -13, -17],\n [19, 18, -10, -9, -22, 10, -4, -14, 14, -11],\n [-18, -17, -12, 15, -13, -8, 16, 5, -20, -7],\n [22, -6, 13, -4, -19, 2, 4, -11, 4, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -6, 3, -5, -1, -17, -4, 14, 11, -12],\n [1, 22, 14, 0, 17, 20, -19, -5, 7, -8],\n [14, 0, -11, -19, -19, 18, 18, -9, -15, 0],\n [-22, -12, 4, -19, 6, -6, -4, 22, 1, 21],\n [18, 21, 9, 8, -7, 9, 21, 19, 11, 12],\n [14, -7, -2, -10, -5, -21, 10, 18, -5, 5],\n [14, 12, 14, -11, 17, -15, 2, -16, -21, 10],\n [10, 17, 0, -18, -9, -15, -3, -5, 0, 6],\n [-16, 1, 2, -9, 15, -20, -9, -20, 19, -14],\n [-16, 3, -16, -16, 21, 13, -10, -20, -3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 22, 10, 0, 0, 15, 3, 9, 5, 7],\n [17, -6, -5, 2, -19, 3, 8, -11, -5, -13],\n [13, -21, 2, -14, 9, -18, -20, -6, -10, -20],\n [5, -19, -5, 12, -9, -7, -11, -12, -21, 10],\n [-10, 7, 3, -5, -10, -19, 10, -8, -6, -17],\n [-18, 10, -7, 1, -18, -20, 12, 4, -11, 18],\n [2, -6, -3, 5, 12, -8, 10, -20, -16, -13],\n [18, 3, 18, 17, -17, 10, -7, 1, 7, -13],\n [-12, 21, -1, -20, 15, 17, 0, 22, -4, 17],\n [-10, 13, -20, -1, 2, -3, 5, -20, -1, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, 15, -5, -3, -18, 20, -14, 6, -6, -11],\n [3, 10, 10, 13, 6, -1, -5, -6, 21, 1],\n [-1, 21, -18, -22, -4, 7, 16, -8, 12, -18],\n [-17, 2, -12, -1, 11, 21, -9, -14, -3, -7],\n [-6, -6, 11, 19, -12, 12, 11, 13, -15, -4],\n [10, 0, -21, -15, 6, 19, -16, 6, 8, 7],\n [12, 2, -19, 20, 15, -6, -13, -22, -5, -4],\n [9, 8, 10, -1, -22, 18, 12, 21, -6, 11],\n [6, -17, -22, 4, -11, -19, -7, -12, -3, 3],\n [5, 19, -15, -21, 17, 3, 4, 10, -16, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "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, 11, 0, 11, 17, -16, 3, 17, -6, 8],\n [16, 2, 14, -8, -21, -12, 9, 7, -6, 1],\n [22, -19, 9, -4, -20, -19, 2, -14, -2, 0],\n [6, 7, 2, 6, 11, -9, -1, -7, -12, -9],\n [-16, -18, 17, 6, -6, 7, 2, -9, 19, -1],\n [21, -18, 17, 5, -11, 13, -10, -2, 9, -2],\n [14, 15, -14, 14, -21, -20, 20, -13, 12, -14],\n [17, 9, -2, 11, 2, 19, 9, 14, -1, 2],\n [-22, 22, 13, -2, 18, -7, 9, -2, 5, -4],\n [-9, 0, 1, -3, 9, 17, -13, -22, 8, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, 17, 8, 5, -13, -17, -8, 4, -13, -2],\n [-4, -19, -1, 15, -8, -17, -12, 21, 7, 17],\n [1, -1, 7, -19, -17, 15, 3, -4, -21, -19],\n [-18, 12, 6, -7, 22, -11, -2, -14, -12, -15],\n [3, 9, 16, -19, 11, 5, 2, 21, 12, -4],\n [12, 16, 6, -9, -2, 13, 15, -9, 17, -8],\n [7, -11, -18, 4, -8, 3, -14, 17, 17, 12],\n [-10, 22, 21, 10, 11, -19, -10, -13, 22, -22],\n [-12, -14, 15, 0, -10, -18, 2, -13, -18, -1],\n [19, 2, 14, -3, 5, -2, -12, 6, -18, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-18, 10, 22, 13, -15, -17, -8, -8, -14, -18],\n [3, 0, -7, 16, 12, -13, 4, -7, -2, -11],\n [-14, -7, -14, 6, 0, 16, 20, 1, -1, 8],\n [-13, 19, 4, 11, 16, 1, -2, -8, -6, 22],\n [-4, 2, 17, -1, 18, 19, -9, 5, -11, 4],\n [1, -1, 16, 18, 16, 13, 0, -15, 5, 6],\n [-8, 16, -15, 5, 10, -12, 19, 14, 2, 11],\n [-1, -21, -7, -12, -9, 9, -1, -18, 13, 0],\n [-4, 6, 19, 0, -14, -5, 8, 14, -6, -5],\n [4, -2, -22, 9, -9, -9, 10, 13, 16, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[22, 2, -8, -3, 11, -9, 7, 21, -10, -9],\n [6, 3, -20, 2, 4, 22, 17, -7, 15, -12],\n [6, 1, 6, 11, -12, -3, -3, -14, 0, 13],\n [4, 1, 17, 2, 2, 10, 8, -13, 16, -8],\n [-22, -7, -2, -21, -20, -8, 9, 4, 13, 12],\n [16, 1, -15, -16, -19, 7, -13, 2, 19, 9],\n [9, 9, -13, -14, 2, 2, 18, -7, -7, 7],\n [15, -18, -16, -10, -15, 10, -13, -3, 9, 6],\n [-22, 4, -3, -9, -8, -17, -21, 6, 16, 9],\n [-18, -1, 5, 9, 6, 17, -20, 8, -10, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -9, 2, -16, 20, -1, 9, 18, 9, 19],\n [7, -6, 17, 15, -2, 3, 20, -20, 15, -6],\n [16, -17, -2, 22, 17, -10, -14, -18, 20, -16],\n [15, 21, 21, 15, 8, -19, -10, 21, -8, 17],\n [-10, 20, 20, 20, 3, -4, -22, -10, 2, -3],\n [18, 0, 1, 20, 18, 16, 17, 7, 11, -13],\n [18, -22, -11, 6, -12, 18, -6, -3, 15, -17],\n [-3, -13, -13, 8, 3, -6, -9, -18, -20, 20],\n [-3, -8, -20, -20, 0, -14, -12, 21, 18, -10],\n [-15, -1, 15, 4, 3, 0, 16, 8, 6, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "384", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-13, -19, 8, -19, 6, -14, -8, 21, 18, -20],\n [-8, -12, -17, -16, -19, -2, -22, 0, -10, 20],\n [5, 6, -5, 0, 5, -14, 20, -17, -7, 14],\n [-22, -1, 0, -2, 8, 15, 5, 21, 4, 16],\n [19, 19, -10, 9, -16, 10, -10, 9, -16, -11],\n [17, -8, -2, -11, -10, 17, 19, 16, -21, 6],\n [6, 13, 15, -16, 7, 0, 5, 0, 13, 19],\n [6, -19, -3, -18, -12, -21, 18, 21, 1, 10],\n [-1, -17, 1, 6, 9, 7, 18, -20, 2, 5],\n [-8, -6, -21, 4, 13, -9, 20, 9, -11, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-7, 21, -21, -16, -2, 8, 0, 2, 12, 12],\n [22, -16, -18, 9, -18, 2, 8, -3, -1, 15],\n [-10, 16, -21, -1, -14, -21, 22, 9, -15, -7],\n [10, -12, 9, -15, 9, -2, 2, -3, -22, -2],\n [-16, 2, -14, -1, -21, -4, -17, -18, 22, -13],\n [-22, 3, 3, -5, -2, -11, 15, -9, 9, 16],\n [12, -6, -13, 12, -7, -17, -19, -14, 6, -16],\n [-7, -17, 21, -20, 21, -9, -9, -14, 13, 0],\n [-8, -16, -3, -4, -17, 16, -22, -16, 12, 2],\n [15, 0, 2, 15, -12, 11, 8, 15, -11, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-10, -3, -2, -1, -22, 17, 18, -6, 22, -19],\n [-17, 22, -4, 7, 0, 9, 6, -15, -2, -6],\n [-6, -2, -8, 4, 2, 10, -21, 19, -7, 13],\n [-15, -7, -16, -18, 0, -15, -20, 12, 13, 13],\n [-8, 7, -8, 6, -19, 11, 0, 12, 5, 8],\n [19, 10, -5, -18, -14, -3, 15, -14, -5, -8],\n [-8, -9, 12, 17, 20, 13, 19, -3, -12, 18],\n [-6, 18, 2, 6, 0, -14, 2, 18, 0, -21],\n [22, -22, 15, -17, 21, -8, -16, -21, 7, 6],\n [-11, 11, 7, 13, 12, -21, -20, 19, -11, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, -3, -4, -15, -20, 4, -8, -15, -5, 6],\n [13, -20, -14, -13, 17, -3, -21, -22, 4, -19],\n [14, 9, -5, -9, 22, -8, -19, -4, 1, 7],\n [-10, -12, 5, -12, -22, 19, -19, 15, 11, -11],\n [1, 14, 9, -4, 6, 15, 6, -4, -3, -20],\n [17, -18, 0, -18, 7, 9, 1, 19, 12, 9],\n [22, 21, -1, -2, 5, 11, -7, -12, 10, 21],\n [15, -4, 5, 6, 14, -20, -5, -5, -11, -5],\n [9, 19, 13, -4, -19, -12, -20, 4, -7, 21],\n [-5, 7, 1, -17, 11, -11, 19, 0, 13, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-8, -7, 22, -9, -8, -11, 20, 12, 2, -9],\n [-21, -5, 12, -14, -12, 3, -20, -18, 9, 18],\n [-13, 15, -17, -12, -6, -21, 18, 1, -18, -2],\n [-17, -19, -14, -18, -19, -14, -5, 20, -7, -21],\n [6, 19, 13, -11, 18, 22, 14, 11, 12, 17],\n [-17, 14, 13, -3, -7, -15, 21, -1, -18, -18],\n [22, -12, 20, -4, 16, -6, 14, 15, -5, -14],\n [-6, 18, 10, -3, -5, 1, -10, 17, 5, -20],\n [13, -12, 16, -2, 14, -21, -17, -18, 20, 9],\n [14, 17, -12, -6, -9, -21, 16, -5, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, 6, 3, -22, -6, 16, -21, -8, -1, -3],\n [6, 2, 20, 1, 11, 20, -2, -21, -7, 17],\n [-2, 14, -15, -9, -1, -5, -18, 19, 22, 7],\n [8, -14, 8, 8, 18, -14, 14, -17, 19, 3],\n [-13, -17, 10, 22, 7, 17, 1, 5, 22, 15],\n [6, 21, -8, -15, 0, 20, -14, -12, -17, -11],\n [11, -2, 9, 13, 2, 12, 11, -4, 14, -6],\n [-7, -7, 21, -19, 7, 11, -18, 10, -14, -6],\n [-11, 1, -11, -8, -7, 0, -5, -1, 21, 8],\n [20, -8, -2, -15, 17, 13, 19, 15, -17, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[17, 22, 13, 5, 0, 8, -12, -3, 9, -6],\n [19, 15, -17, -22, 14, -19, 8, -12, -6, -16],\n [12, -21, 17, 14, 14, -13, -11, -6, 3, -18],\n [-18, 15, 4, -18, -15, 8, 10, -2, 12, -2],\n [-8, 13, -21, 7, 5, -6, 21, -3, 17, 6],\n [-18, 2, -13, -4, 18, -22, 11, -9, 2, 3],\n [-2, -7, -13, 9, 21, 22, -3, -14, 11, 8],\n [-4, 8, 7, 1, 10, -5, -2, 8, 16, 19],\n [18, 20, -19, 3, 10, 21, 10, -3, 18, -15],\n [13, -15, 8, -1, 19, -4, -3, 0, 1, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"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, 13, -14, 17, -7, 4, 22, 14, -10, -21],\n [-11, 18, 10, 0, -9, 16, 7, 11, -14, -8],\n [1, 18, 2, 13, 9, -2, 19, 16, -17, 2],\n [-21, 8, 7, -8, -5, 9, -9, -5, 12, -1],\n [-9, 15, -9, 11, -1, -7, -7, -7, 17, 15],\n [-5, 0, 17, -5, -1, 17, 7, 19, 19, -5],\n [-5, 18, -22, 19, -8, -18, 4, -6, 18, 9],\n [15, 3, -21, 5, 22, 0, -3, 13, 19, -1],\n [-12, 5, 22, -1, -6, 8, -12, 13, -9, 12],\n [0, 6, 0, 21, 13, -7, 16, -3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"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, 9, -2, -14, 20, -4, -2, -5, -17, 12],\n [-9, -14, 12, -21, -17, 12, 2, -14, 8, -16],\n [5, -21, -22, 14, 1, 12, -16, 15, 6, -22],\n [7, 9, -13, 11, -12, 14, 4, -13, 15, -1],\n [1, -15, -17, -19, -18, -17, 9, 15, -3, 17],\n [22, 13, -9, -4, -12, 16, -22, 12, -4, 10],\n [9, 13, 1, 20, -16, -16, -18, -9, 22, 3],\n [-22, -10, 0, -3, -16, -17, -14, 5, -13, 12],\n [-16, 2, 7, 20, 3, 21, -11, -10, 17, -19],\n [-22, -17, -21, 4, -5, 19, 6, 10, -20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-19, -5, -15, -1, 18, -1, -4, 5, -21, -14],\n [12, -1, 3, 11, -16, 7, 2, -14, 4, -22],\n [10, -15, 9, 17, -4, 13, 22, -1, 16, 3],\n [-20, -14, 12, -16, -8, -19, 14, 5, -14, 12],\n [2, -14, 10, -6, -11, -14, -18, 3, 22, -4],\n [12, -21, 22, -16, -14, -1, 19, 10, -7, 20],\n [1, -15, 7, 3, 22, 12, 22, -6, 15, -13],\n [18, -6, -16, -21, -12, -20, -3, -10, 0, -6],\n [6, 20, 16, 9, 12, 12, 11, -2, -7, 0],\n [-12, -9, -20, -16, 17, 22, -12, 10, -4, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, 0, 0, 6, -17, 16, -18, 9, 17, 3],\n [-9, -5, -2, 2, -3, 1, -20, -1, -15, 6],\n [-16, -17, -17, -11, -1, 3, 2, -4, 13, 12],\n [-10, 2, 22, 9, 7, -2, 19, 22, 17, 21],\n [-15, 18, 19, -16, -20, 14, -20, -5, 19, -14],\n [1, -16, 10, 2, 19, 11, 15, -2, 15, 17],\n [-5, 16, 10, 5, 2, -9, -3, 16, -3, -16],\n [-19, 8, 7, 14, -2, -22, -20, -10, -16, -17],\n [-17, 11, 9, -7, 15, -15, -2, -12, 0, -17],\n [-8, -12, 4, -8, 22, 15, -19, -9, 22, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -11, 17, -3, 14, -21, -3, -11, 15, 7],\n [-5, -13, -16, 19, -18, 6, 12, 16, -11, -13],\n [14, -21, -20, -9, -3, 22, -19, 3, -8, -14],\n [-20, -21, 16, 18, 7, 14, -6, -20, -14, -15],\n [-14, -6, 1, -15, -9, -7, -5, 1, 16, 4],\n [5, -16, 11, 4, 11, 16, -4, -17, 7, 5],\n [-11, -8, 22, 16, 16, -8, 13, -20, -22, -16],\n [-14, -22, -18, 13, -13, -21, 0, 16, 6, -4],\n [15, -3, -11, -12, 12, -16, 0, -6, -21, -18],\n [-2, -10, -12, 1, 10, 4, 12, -5, -2, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, 9, 20, -12, -20, -2, 20, -9, -17, 6],\n [8, 5, 20, 13, 5, -4, -20, -11, 13, 1],\n [-11, 1, -22, 5, -7, -2, 7, 11, 3, 12],\n [8, -7, 19, 6, 6, -14, -9, -15, -21, -12],\n [-21, -5, -18, -16, 0, -4, -4, -4, 22, 17],\n [5, -12, -12, -14, -9, 11, 6, -2, -18, 10],\n [-14, -20, -9, -5, -11, 0, -9, -7, 14, -3],\n [-3, -8, 18, 2, -6, -11, 22, 19, 16, -16],\n [-15, 1, 2, -2, 10, -13, -1, -4, 6, -20],\n [16, -19, 14, 8, -17, 5, -13, -11, -21, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-22, 12, 1, 11, -3, -7, 7, 16, 2, -18],\n [6, 14, 5, 18, 0, 9, -5, 18, 12, 20],\n [1, 5, 13, -2, -18, 3, 0, 21, 10, 3],\n [-1, -3, -21, 18, -5, -18, 9, -12, -2, -1],\n [-20, -14, -21, 5, 11, -13, -4, 6, -21, -17],\n [21, -16, 13, -15, -4, -13, 10, 14, 15, 4],\n [6, -4, -5, 0, -22, 20, -20, -13, -16, 3],\n [-7, 16, 22, 9, -11, 21, -15, -15, 22, -12],\n [10, 2, -6, 8, -4, 22, -8, 21, 12, 16],\n [-21, 11, 2, 15, -19, -7, 9, -8, 19, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[18, -8, -16, -16, -15, -4, -5, -6, -5, -4],\n [17, -10, -12, -16, 4, 14, -18, -15, -13, 14],\n [3, -8, -7, 6, 5, -13, 17, -19, 17, -9],\n [21, 10, -5, -11, -13, -2, 10, -9, -14, 3],\n [-8, -2, -1, 18, 20, -18, 21, -7, 12, -18],\n [3, 3, -18, 13, 1, -8, 7, -18, 17, -1],\n [10, -18, 9, 0, -13, 13, -6, 4, 22, -15],\n [17, 21, -17, -16, 3, -6, 14, 0, 4, 17],\n [-4, 4, 2, 17, 2, -2, 2, -16, 12, -17],\n [17, -8, 1, -19, -16, 7, -6, 15, 7, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[16, -14, -4, -10, 14, -4, -17, -11, -8, -20],\n [-19, 14, 15, -17, 5, -15, 8, -2, 22, 6],\n [-8, 1, -2, 0, 8, 11, 5, 9, -1, -20],\n [-14, -17, -22, -1, -19, 22, -15, 14, 19, -4],\n [21, -22, 18, 1, -6, 9, -9, -6, 9, 10],\n [7, 11, 5, 1, -9, 11, -22, -1, 10, 21],\n [-5, 16, -11, -13, -21, -21, -17, -3, 15, 5],\n [19, -20, 14, 14, 19, 2, 0, -10, 1, -20],\n [15, 5, 3, -3, 4, -22, -13, -13, -22, 9],\n [9, 20, 4, -10, -6, 5, 2, 13, -21, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[9, -17, 8, -14, 20, -7, 2, 17, 5, -6],\n [8, 0, 8, 3, -19, 16, 20, 20, 20, -8],\n [14, 15, 0, -18, 18, 20, 2, 7, 3, -20],\n [-19, -5, 14, -12, -12, 13, -7, 20, 2, -22],\n [3, 22, 7, -17, 4, -4, 15, 22, 20, -4],\n [16, 21, 9, -22, 2, -10, -13, -5, 13, -1],\n [-17, 4, -15, 1, -3, -1, -14, 17, 16, -4],\n [-22, -12, 18, 19, -13, -22, 4, -6, 21, 21],\n [-6, 16, 20, -21, 0, 18, -13, 19, 7, 12],\n [2, -6, -4, -5, -5, 12, -13, 0, 22, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[21, -14, 9, 3, 6, 19, -4, 6, 12, -11],\n [-15, 2, 4, 20, 22, -17, -10, -12, 15, -17],\n [-18, -16, -4, 20, -17, 2, -14, -3, 2, -15],\n [14, 15, -21, -1, 13, -19, -22, 10, 1, -18],\n [12, 19, 3, 20, 18, 20, 3, 18, -18, 21],\n [-5, 2, 18, 17, 15, -2, 1, 5, -19, -15],\n [10, -20, -3, 12, 16, 20, -16, 4, -18, 14],\n [-22, -1, -16, -15, 21, 7, 5, 3, 11, 9],\n [-1, -3, -9, 0, -20, -4, -9, 17, 16, 14],\n [12, -22, -4, -8, 2, -22, 8, 14, 20, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 18, 20, -18, -8, -21, -11, -16, -21, -15],\n [-14, 4, 5, 14, -8, -4, 7, -10, 22, -17],\n [7, -22, 19, 15, 2, 12, 3, -10, -4, -13],\n [22, -16, -8, 0, 13, 20, 8, -15, 7, 11],\n [10, -22, -7, -12, 4, -1, 17, -4, 21, -17],\n [17, 16, -3, -20, -22, 0, 15, -20, 11, -6],\n [4, 16, 0, 15, -12, -8, 3, -12, -16, -15],\n [-18, -6, 0, -21, 4, -2, -16, 15, 3, 7],\n [-11, -12, -6, -13, -7, -8, -8, -3, -19, 9],\n [-1, 12, -9, 7, 8, -13, -17, 4, -12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-13, -7, 1, -2, 17, 18, 13, 19, 22, 0],\n [-2, 9, -6, -6, -2, -19, 0, 2, 9, -17],\n [-9, 18, 15, 19, 15, 18, 22, -7, 9, -7],\n [-4, 14, 20, -2, -8, 3, 7, 17, -8, 20],\n [-10, 4, 0, 11, 11, 0, 21, -3, -14, -3],\n [16, -9, 3, 4, 11, 6, 9, 18, 22, -18],\n [-19, 0, -2, 10, 18, 1, -7, 9, -4, 3],\n [-20, 12, 16, -5, -16, 9, 1, -7, 1, -19],\n [22, 9, 19, 11, -4, -9, 15, -10, -1, 8],\n [21, 21, 7, 0, -11, 20, -9, 13, 22, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -20, -9, -12, 22, 15, 5, 0, -5, -3],\n [10, -21, 16, 14, 3, -21, -20, -3, -13, 19],\n [-2, 17, -14, -21, 5, -20, -7, -19, 0, 7],\n [15, -10, -17, -13, -6, -15, -14, 11, -6, 20],\n [-1, -20, 18, 17, 6, 16, 4, 16, 17, 14],\n [-20, -4, 11, -9, -2, -21, -13, 19, -6, -21],\n [4, -22, 13, 10, -1, 12, 11, -5, 13, -20],\n [21, -7, -12, -13, 19, -2, 2, 12, -17, 21],\n [-15, 11, 18, -22, -20, 15, 4, -10, 20, -4],\n [-4, -17, -9, -18, 20, 22, 22, 13, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[9, 6, 22, 5, 17, -12, -4, -22, -14, -21],\n [-19, 6, -19, -22, 5, -5, -10, 17, -17, 20],\n [16, -1, 7, 4, -15, 20, 5, -21, -3, -12],\n [-9, 1, -10, -15, 21, -2, -1, -14, 19, 20],\n [-12, -7, -14, -20, 13, 19, -10, -22, 21, -12],\n [1, -18, -21, -6, -6, -3, -8, -19, -12, 0],\n [-22, 19, -19, 15, -21, 22, 4, 11, -10, -5],\n [-12, -18, 6, 2, -9, 18, 15, 18, 14, -12],\n [21, 9, -17, -17, -1, -20, -4, 11, 18, 18],\n [-16, -7, 15, -14, -10, 11, 14, 20, -17, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-19, -18, -17, -10, 1, 5, -10, 19, -5, -16],\n [-19, 8, 1, -1, -2, 19, 3, 7, 12, 0],\n [22, 17, 7, -4, 9, -4, -1, -19, 22, -11],\n [-8, -8, -13, -4, -15, 8, -14, 6, -16, -15],\n [18, -6, -8, -7, -16, 19, -4, 15, 2, -11],\n [9, -13, 1, -19, 20, 14, 22, 19, 16, 20],\n [-19, 13, 14, 2, 18, 7, -22, 6, -7, 14],\n [14, -16, 17, 10, -1, 20, 4, 6, -7, -2],\n [-12, -2, -14, 4, 16, -1, -8, 20, 0, 6],\n [16, -7, -20, -7, -15, 3, 19, -14, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-15, 12, 16, 13, -17, -16, -11, 16, -22, 20],\n [20, 2, -11, 4, 0, -4, -2, -2, 1, -10],\n [19, 13, -8, -22, 11, 19, 8, 9, 13, 6],\n [-13, -2, 13, 1, 4, -2, -5, -19, -5, -14],\n [7, 12, 22, 7, 16, -17, -9, 6, 9, -9],\n [-3, -14, -11, -9, 0, 11, -7, -5, 18, 17],\n [10, -18, 16, -13, -1, 20, 21, 10, 8, -17],\n [13, -20, -19, 4, 15, 2, 14, 4, 18, 13],\n [13, 19, -16, 7, 6, 17, 18, -18, -17, 21],\n [-16, 16, 9, -8, -10, -5, -13, 17, -12, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[17, -21, 4, 22, 21, -15, 15, -7, 1, 0],\n [-9, 4, -13, 5, 2, -21, 22, 10, 12, 18],\n [-10, -18, -18, -1, 11, -22, -6, -14, -13, -8],\n [22, 6, 2, -2, -6, 4, 5, 0, 16, 13],\n [-20, 10, -16, -18, 3, -6, -6, -20, -20, 11],\n [-15, 22, -17, 14, 22, -1, 10, -16, 17, -4],\n [-13, 0, -21, -2, 1, -10, -18, -5, -12, 14],\n [9, 5, -1, 22, 5, -22, -17, -12, 19, 10],\n [-7, -10, -2, 16, 1, 20, 4, 22, 14, -20],\n [-11, -16, -3, -8, -22, -13, -9, -8, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, -13, 14, -17, -17, 5, 15, -9, -10, -10],\n [-13, -7, 16, 12, -8, 0, 14, -15, 3, -1],\n [-18, 11, 4, -4, 20, 20, 12, 22, -3, 15],\n [-10, -5, -5, -22, 9, 2, -2, 4, -12, -22],\n [-4, 9, -15, -4, -7, 12, -21, -11, 6, -13],\n [-1, 11, -2, 14, -18, -17, 9, -20, -13, -18],\n [1, -3, 14, 8, -6, 1, -5, 3, 19, -16],\n [20, -9, 18, -21, 7, -6, -3, -13, 1, 21],\n [-11, 4, -8, -14, -5, -16, 5, 13, -20, 21],\n [-7, 13, -19, 12, -14, -11, -13, 21, 21, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"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, -10, 19, 10, -22, 5, 17, -17, -20, 22],\n [2, 21, -7, 20, -19, -15, 16, -7, 21, 15],\n [0, -17, 20, 21, -7, -7, 0, -7, 13, -11],\n [14, -14, -5, -14, -2, -22, 0, -18, -4, 12],\n [10, -5, 17, -9, -3, -10, -7, 18, 8, 16],\n [12, -3, -22, 17, -10, -16, 22, -1, -16, -3],\n [14, 13, -19, -17, -20, -20, -20, 13, -14, -7],\n [-7, -11, 15, -3, 8, 7, -2, -20, -2, 5],\n [5, -18, -16, -18, -14, -2, -3, 15, 17, 14],\n [-6, 19, 5, 8, 10, 9, 9, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -20, -17, 5, -21, 9, 3, -18, -12, -13],\n [-8, -5, -9, 5, 7, -10, -3, -21, 2, 21],\n [20, -11, 2, -19, 19, -11, -16, 15, 17, 9],\n [20, -17, 4, 12, -2, -3, -4, 10, -19, -4],\n [5, -1, 1, 7, 6, -13, 9, -14, 2, -7],\n [-8, -5, 0, 19, -20, -16, 16, -12, 1, 12],\n [2, 5, -11, 0, -6, 18, 14, -5, -14, 22],\n [12, 13, -5, -3, -2, -3, -17, -14, 20, 6],\n [6, -10, 13, 4, 21, -17, 16, 9, 20, 21],\n [5, 22, -22, 20, 8, 7, -5, 6, 19, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "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, -21, -18, 19, -8, 9, -17, -9, 1],\n [-2, -9, -11, -19, 21, -2, -6, 6, -7, -5],\n [15, 18, 21, -12, 9, 5, -7, 11, 7, 15],\n [-1, -18, -14, -10, 16, 0, 4, 9, 8, 10],\n [19, 3, -5, -11, -20, -18, -9, -11, -19, -7],\n [-12, 13, 15, -21, -10, -15, 21, -2, 3, 15],\n [12, -8, 17, 7, -21, -7, -10, -22, 20, 5],\n [-22, 17, 11, -10, -21, -19, 2, 11, -10, 13],\n [9, -2, 3, -8, 6, 3, -2, -11, -11, -18],\n [19, 3, 9, -21, -15, 4, 14, -15, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "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, -10, 0, -8, 1, 20, 0, -13, 15, -18],\n [-18, 8, 17, -22, -21, 6, -16, 6, -14, 13],\n [-16, 5, -13, -7, -13, 16, 3, 11, 11, 17],\n [-9, -5, -22, -6, -1, 14, -7, -16, -8, -2],\n [-21, 2, -14, -3, -13, -2, -19, 7, 11, 7],\n [-9, -1, -22, -15, -12, -22, -18, 22, -13, 16],\n [-10, -2, 13, 22, 10, 20, 5, -14, 22, -12],\n [17, 6, -16, 4, -1, 8, 7, 5, -3, -8],\n [-8, -11, -6, 0, -17, 22, -7, 4, 0, -22],\n [22, -16, 22, 16, 17, 17, 16, -5, 13, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-21, 3, 9, 0, 17, -5, -4, 1, -19, -21],\n [7, 15, 8, 17, -7, 10, -20, -5, -13, -21],\n [7, 7, 2, 20, 1, 12, -13, 7, 3, 12],\n [1, -3, 16, 17, 12, 16, -13, 4, -8, -8],\n [14, 12, -20, 6, -19, -7, -18, -2, 17, 19],\n [-2, -21, -9, -18, -16, -12, 12, 7, 21, -22],\n [-7, -22, -1, -10, 4, -8, -6, -14, -18, 0],\n [21, 20, -12, 1, -15, 11, 19, 8, -1, -9],\n [-18, -6, -5, -4, -16, 3, 2, -5, 21, -8],\n [6, 19, -22, -19, -14, 13, 9, 1, 14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-8, -3, 17, -21, 2, -10, 4, -10, 5, -8],\n [6, -2, 21, 8, 0, 14, -20, 12, -9, -21],\n [-10, -21, -11, 4, 11, 17, -18, 2, -12, -10],\n [5, -2, 3, 4, 3, -8, -17, -19, -19, 7],\n [-10, -14, 19, -9, 5, 17, -20, 18, 6, 10],\n [-8, 16, -8, -16, 22, -11, 16, -16, 18, -17],\n [3, -14, 1, 7, -7, 4, 10, 0, 22, -4],\n [13, -4, -1, 19, 22, 10, 22, -13, 9, -8],\n [16, -15, 2, -5, -8, 3, 18, 21, -2, -1],\n [11, 14, 14, -9, -19, 1, -21, -22, -21, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "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, 22, -6, -18, 1, -15, 21, -14, -5],\n [-7, 9, 17, 16, 18, 21, 9, 19, -21, 15],\n [20, -19, -18, 14, 14, 3, 20, -14, -8, 1],\n [1, 12, 18, 2, 3, 0, -17, 18, 4, -4],\n [8, 15, 20, 9, -21, -5, 5, -16, 0, 13],\n [1, 5, 2, 16, -19, 22, -4, -19, -10, -22],\n [11, -16, 2, 0, 7, -16, 22, -6, 10, -21],\n [15, 21, -10, 9, -1, -14, -6, -5, 17, 17],\n [4, -12, 5, -15, -5, -10, 10, -8, -1, 15],\n [7, -17, 22, 11, -4, 10, -9, 18, -4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, -13, -21, -21, -2, -11, -13, -11, 16, -21],\n [-22, -21, 0, 5, -6, 17, -2, 21, 11, -14],\n [-6, 19, 22, 9, -18, -9, 2, -1, -18, 15],\n [-14, 8, 18, -2, 13, -22, -1, 0, 0, -8],\n [-22, -17, 17, 12, -6, 0, -3, 5, 14, -5],\n [-16, -3, 1, -7, -10, 5, -16, -8, 0, 0],\n [8, -18, 4, 21, -13, 19, -16, 9, 0, -14],\n [6, 4, 15, -2, 20, -17, 3, -3, -8, 22],\n [15, -3, -8, 6, -17, -7, -22, -17, -7, 10],\n [-16, -13, -15, -2, 3, 14, -5, -19, -3, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[17, -4, 10, 0, -14, 15, 22, 22, -5, -21],\n [-6, -7, 22, 1, 8, -22, 5, 10, 19, 14],\n [16, -19, -22, 10, -13, -20, 14, 22, -2, -14],\n [17, 20, 1, -15, 1, 1, -13, 12, -19, 21],\n [-14, -12, 20, -10, 4, 7, 16, -11, -4, 17],\n [-19, 11, 0, 22, 3, -16, -5, 19, -19, -15],\n [-1, 3, -10, -6, 21, 13, 18, -8, -5, 4],\n [-17, 11, 18, -18, -11, 6, 14, -11, 2, 11],\n [-12, 0, 1, -5, -13, -18, 8, 2, -6, 5],\n [-22, 22, -21, 17, -21, 4, -15, 4, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-19, 21, 15, 8, -18, 2, 5, -4, 14, 19],\n [0, 13, 22, -10, -6, 7, 0, -20, -10, 9],\n [22, 12, -21, -20, 6, -13, -3, 11, -8, 17],\n [22, -22, 3, 9, -21, 9, 18, 6, -3, 0],\n [-11, 21, -13, -4, -13, -4, 3, 1, -14, 6],\n [6, 14, 5, -20, 0, -19, -9, 15, -10, 5],\n [16, 21, -3, 5, 9, -9, -10, -12, 15, 16],\n [19, -8, -14, -20, -18, 5, 19, -8, -20, 12],\n [-16, 7, 1, 8, -9, -7, -19, -20, 12, -14],\n [-19, -4, 1, -12, -8, 13, 8, -15, -21, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-20, -2, -11, -9, 0, -10, -7, -6, -5, -10],\n [3, 22, 17, 16, 8, 17, -6, 9, -22, 12],\n [13, -4, 5, -21, 6, 20, 6, 20, -4, 5],\n [11, 8, 14, -4, 9, 6, -14, -16, -11, 8],\n [-5, 5, -2, -14, 11, 11, 1, -7, 5, 12],\n [-17, 15, 18, -12, -19, -9, -10, -8, -15, 20],\n [1, -12, 12, 2, 0, 22, -16, -18, 9, 5],\n [21, -20, 7, 21, -18, 10, -3, 7, 21, -1],\n [-1, 15, 6, -2, -5, -12, -13, 12, 3, 21],\n [-19, -13, 16, -7, 18, 7, -20, 11, 2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[19, 13, -19, 19, -13, -10, -17, -16, 5, 14],\n [-8, 7, 17, -13, -11, -6, 7, -22, 13, 17],\n [1, 15, -2, 19, 9, -5, -10, 14, 21, -2],\n [-5, 17, 3, -18, -18, 8, 5, -10, -12, -22],\n [1, -10, -5, 1, 6, 5, 15, 22, -1, -3],\n [-12, -3, 18, -10, 1, 20, 1, -6, -18, 7],\n [-9, -8, -14, -9, -13, -1, 8, -10, -6, -22],\n [-9, 21, 16, 12, -22, 4, 22, -1, 11, -14],\n [13, 9, 15, -3, 4, -20, -12, 1, 6, -18],\n [10, -15, -4, -19, 18, 12, 7, -18, 17, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-20, -7, -15, 22, -18, 15, 12, -15, 13, 2],\n [-15, -2, -14, 9, 21, -10, 0, -15, 12, 5],\n [-8, 6, -19, 11, 14, 1, -2, -21, -16, -12],\n [-11, -19, 12, 17, 3, -5, 14, -7, -11, 18],\n [17, 14, -4, -8, -1, -3, 20, -10, 0, 8],\n [3, 22, 9, -2, -6, 6, 6, -1, -4, -9],\n [16, 0, 18, -21, 9, 15, 10, -16, 11, -19],\n [0, -3, -1, 6, 20, 18, 14, -20, -1, -3],\n [2, 11, 19, 6, -13, 16, 14, 17, -3, 15],\n [0, -12, -15, 6, 13, 2, 16, 11, 9, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, -4, 2, 0, -4, -18, -4, 12, -11],\n [16, 2, -18, -11, 4, -19, -4, 22, 1, 19],\n [5, 10, 12, -7, -11, -7, -12, 20, 5, 0],\n [-6, -4, -12, -19, -13, -4, 13, 20, 16, 18],\n [-1, -21, 10, 17, 4, -4, -19, -4, 2, -17],\n [-10, -1, -19, -21, -20, 7, -19, 20, 6, 22],\n [10, -10, 16, 9, 5, 14, 5, 4, 2, 7],\n [-17, 7, -14, -17, 6, 0, -17, -1, -21, 8],\n [-17, 19, -18, -3, -11, 15, 15, -15, 20, 10],\n [16, 17, 8, -20, -4, -15, 7, 8, 6, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, 0, 21, 7, 15, 16, -14, -16, 21, -8],\n [-8, -2, -9, -12, -12, -3, -10, 22, 7, 17],\n [16, -3, 22, 20, 15, -15, 14, 19, 10, 3],\n [21, 16, -15, -5, 16, -9, -5, -2, 0, -19],\n [-13, 20, -12, -3, -4, -22, 8, -21, 18, -18],\n [11, -19, 4, 16, -20, 3, 18, -22, -7, 12],\n [-4, -7, 10, 8, -1, 21, -3, -17, 12, 16],\n [-20, 9, -10, -9, 18, -15, -4, 22, -9, -12],\n [12, 13, -20, 2, -10, -7, 5, 22, 4, -13],\n [-5, -15, -16, -1, 15, -14, 19, 17, 16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[14, 19, 6, 5, -2, 10, 3, 15, -8, -21],\n [-11, 10, -8, 22, -22, 10, -19, 5, -9, 22],\n [-11, -17, -3, -2, -7, -11, -3, 22, 10, -21],\n [11, 3, 10, 19, 7, -22, -15, -22, -13, 9],\n [17, -21, 8, -19, -11, 8, 18, 0, 10, -15],\n [-7, -8, 18, 17, 3, -9, -11, 4, 8, -19],\n [7, -19, 8, 11, -19, -3, -5, -15, 19, -21],\n [-14, -7, -1, -11, -18, 16, -8, 22, -15, 1],\n [-4, 14, -5, -2, 16, -9, -8, -20, 22, -12],\n [-20, 7, -17, -17, 8, -1, -2, 15, 15, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -12, -1, 16, -17, 7, 20, 2, 13, -22],\n [-1, -14, 22, -15, 11, -7, -4, -15, -11, 20],\n [18, 8, 19, 10, -4, 4, 1, 5, -19, -11],\n [0, -3, 17, 5, -22, 18, -12, 21, 8, 18],\n [15, -14, -17, -17, -20, 9, 12, -7, -21, 13],\n [18, -16, 12, 7, 22, 6, 18, -22, 21, -22],\n [18, -16, -20, 13, 16, 8, 2, 1, -22, 15],\n [8, 14, -12, -20, -11, -3, 7, -13, 16, -8],\n [-2, -5, 9, -4, 7, 10, -1, 22, 6, 1],\n [-19, -11, 13, -19, -18, -4, 18, 16, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-11, -13, 6, -2, -10, 0, -17, 8, -14, 1],\n [-7, -12, 13, -22, -2, 21, 13, 14, -17, -9],\n [6, -22, -15, 21, -4, 0, 16, 18, -12, 4],\n [17, 13, 19, -3, 19, -15, 13, 3, 12, -20],\n [-19, 21, 6, 5, -4, 20, 5, -5, -9, 20],\n [-9, 6, -20, 11, -14, 17, -18, 6, 18, -18],\n [22, 20, 20, 21, -10, 3, -14, -19, 16, 8],\n [-18, -16, 5, 17, -9, 1, 19, 15, -18, 11],\n [5, -15, -2, 1, 1, -10, -8, 2, 22, 5],\n [16, -15, 8, -16, 16, -6, 12, -1, -16, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 16, 20, 6, 12, -1, -14, 13, -15, 7],\n [7, 8, -1, 21, 8, 17, 5, -18, -6, -12],\n [-1, 2, -10, 13, 22, 22, -12, -18, -9, -1],\n [-20, 12, 9, 15, 17, 1, 5, -2, 10, 5],\n [16, 13, -13, 14, 17, 2, 22, -6, -19, -13],\n [2, 9, -15, 19, 22, -11, -2, 22, 4, 7],\n [-13, -2, -22, -14, -20, 19, -4, -17, -16, 20],\n [-7, 13, -19, -5, 9, 9, -5, 16, 20, 14],\n [5, 16, -21, 14, 14, -21, -4, -18, 21, -10],\n [-1, -16, -21, -9, 2, 3, -18, -3, -11, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "363", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[8, -6, -7, -13, 12, 10, 15, 12, 4, -16],\n [4, 18, -11, 10, -10, -21, -20, -12, -18, -21],\n [5, -10, 12, 17, -10, -11, -5, -5, -6, 16],\n [-1, -10, 22, 15, -4, 1, -4, -2, 1, 7],\n [5, 12, 15, -6, 11, -14, -10, -9, 3, -2],\n [21, -3, -12, 19, 12, 8, -5, -9, -18, -6],\n [-2, -9, -20, 8, 2, 21, -6, 3, -6, -4],\n [4, -16, 3, -18, -21, -7, 22, -12, 16, 0],\n [12, -17, 14, -22, 10, -5, -20, -4, -13, -3],\n [-12, 9, 17, -3, 9, 20, 14, -1, -19, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-17, 6, -21, 2, 9, 3, 3, 15, -1, -13],\n [0, -19, -7, 19, 10, -10, 21, -10, 10, -9],\n [-15, 3, -1, -22, -7, 21, 6, 0, -18, -2],\n [13, -3, 20, -15, 3, 18, 2, 19, -16, -1],\n [10, -18, 15, -11, 21, -9, -16, 5, -7, 18],\n [-21, 8, 13, -9, 5, 9, 5, -11, -10, -1],\n [19, 6, 7, -8, 17, -19, 10, -14, 15, -7],\n [3, 20, 4, -12, 20, 3, -9, -22, -12, 7],\n [1, -19, -1, -15, -7, 10, 10, -13, -21, 21],\n [-19, 0, 4, 10, 10, 18, -3, -10, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[9, -20, -10, 5, -1, -4, 8, -3, 1, 9],\n [-14, -4, 0, 2, 10, 21, -21, -20, 5, 14],\n [12, -9, 1, 14, -20, 0, 11, -14, -5, -21],\n [-1, 12, 8, 3, -9, 22, 5, -12, 9, -2],\n [0, 1, -11, -20, -17, -11, -3, -17, -3, -9],\n [18, 21, -22, -3, -1, 17, 8, 8, 5, -11],\n [-7, 10, 12, 21, -19, -13, 11, 18, -20, 8],\n [8, -22, -18, -18, -21, -8, -22, -2, 14, -16],\n [-12, 3, 19, -21, 7, -9, -18, 8, 9, 11],\n [-13, 8, 4, -5, -18, -6, -12, -18, 15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 1, 7, -7, 18, -1, -21, -4, 14, -21],\n [-12, 10, -14, 2, -17, -12, 4, -15, 22, 8],\n [4, 21, 18, -18, -8, -21, -8, 8, -3, -20],\n [19, 16, -13, 3, -13, 17, -10, -2, 11, 21],\n [9, -14, 7, -22, -11, 21, 12, 1, 17, 22],\n [-13, 1, 18, -5, -15, 20, -10, -7, -9, -14],\n [-14, -18, -12, -4, 15, -13, -7, 6, -18, -5],\n [19, 19, 21, 12, 13, -1, 1, -11, 16, -11],\n [12, -4, 14, -9, 0, 17, -1, -12, -21, -13],\n [20, -18, 7, -2, 10, 2, -16, 17, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[22, 14, -20, 22, -4, -11, -4, -12, -20, -21],\n [3, -1, -6, 11, -8, -11, -7, -7, 16, -17],\n [-15, 2, -4, -4, -11, -14, 18, 6, 4, -18],\n [3, 7, -9, 10, 12, -12, -19, 10, -17, 5],\n [-13, 13, 3, 7, -1, -18, -21, 10, -7, -16],\n [-2, 12, -1, -1, -17, 10, 16, 20, 2, -5],\n [18, 12, 1, 17, 17, 0, 10, 6, -13, -8],\n [-13, 3, 17, 6, 11, -5, -21, 2, -2, 8],\n [-1, -14, 4, 2, 2, 4, -13, 7, -19, -2],\n [7, 10, 20, 3, -21, 0, 8, -19, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[22, -22, -21, -17, -16, -19, -5, 18, 20, -18],\n [2, -22, 11, -20, -6, 9, 1, -21, -22, 11],\n [-15, 22, 21, -14, 5, -4, -3, -16, 19, 12],\n [-4, -6, 17, -5, -16, 4, 16, 7, 0, -3],\n [0, 3, -9, 8, 4, -14, 0, -13, 0, -13],\n [-21, 14, 17, 15, 15, -22, -5, 12, -16, 21],\n [19, -1, 2, 19, 0, -14, 4, -12, 4, 17],\n [5, -5, 13, 11, -10, 7, 5, -1, 1, 7],\n [22, 15, -3, -17, 10, 15, -8, -8, 9, -9],\n [19, -15, 13, -1, 15, -3, 1, -2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 16, 21, 0, -19, -19, 7, 5, 8, 10],\n [-4, -13, 2, 14, -10, -17, 7, 0, 13, -7],\n [-15, -7, -12, -22, -1, -5, 13, -12, -3, -13],\n [-13, 14, -1, -12, 12, -14, -8, -4, 14, -17],\n [13, 21, -18, -20, -13, -10, -19, 17, 10, 11],\n [13, 10, -2, 16, -18, 22, -10, 17, -6, -13],\n [-13, -21, 15, -2, -22, 7, -5, 12, 16, -1],\n [-20, -17, 13, -7, -20, 13, -12, -6, -4, -15],\n [-9, 3, 2, -13, 9, -8, -19, 5, -19, -10],\n [-11, -8, 6, 0, -10, 15, 12, 17, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-18, -21, 19, 7, 12, -13, -14, -6, 15, 7],\n [18, 12, -16, -11, 19, 11, -20, 10, 17, -10],\n [-12, 17, -3, 8, 10, 11, -14, -16, -14, 19],\n [3, -21, -18, -21, -13, 8, 10, 21, -17, -9],\n [-9, -8, 10, 8, -6, 20, -8, -3, -2, 6],\n [-14, 6, 21, 11, -14, 7, -6, -19, 17, 9],\n [9, -16, 15, 9, -18, 19, -20, -3, -6, -7],\n [-12, -10, -5, -9, 11, -11, -1, -2, 3, 19],\n [16, -21, -7, 11, -12, -4, 7, -16, 4, -1],\n [-6, -8, -14, -11, -15, -21, -7, -20, 8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 18, -21, 7, -10, 14, -9, -22, 9, -17],\n [-1, -12, 0, -9, -9, -3, -16, -4, 3, -1],\n [-17, -10, -13, -4, 8, -13, 14, -10, -6, -18],\n [-2, 16, -3, -16, -8, -8, 0, 10, 21, -21],\n [9, -8, -16, -14, 5, -1, -20, 19, -21, -1],\n [2, 2, 9, 21, -16, 8, 14, -19, 10, -8],\n [-14, -17, 8, 11, 21, 15, -10, 13, 9, -1],\n [6, -12, -17, -18, -22, 16, -13, -13, 1, -16],\n [-1, -2, -1, 10, 21, 2, 8, -7, -8, 6],\n [-4, -6, 3, 13, 13, 12, 17, 0, -14, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "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, -7, 9, 5, 9, -5, 21, 11, 6, -2],\n [-22, -7, 10, -2, 12, 4, -3, 8, -7, -9],\n [9, 18, 9, -21, 22, -1, 14, -6, 9, 15],\n [-6, 11, -16, 6, -6, 1, -15, 0, 10, 6],\n [-4, -18, 14, 0, 3, 1, -2, 10, 3, -13],\n [19, 6, 12, 5, -11, 21, -16, -7, -3, 6],\n [12, 5, -16, -1, -9, 13, -13, -21, -1, -7],\n [12, 17, -12, 20, 20, 10, 11, 10, -4, -3],\n [-13, -4, 20, -11, -13, -16, 17, -12, -7, 10],\n [15, -6, 22, 2, 19, 8, 19, -22, 16, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-14, 20, -21, -22, 21, 16, -18, -11, -9, 16],\n [9, 17, 21, -14, 19, 19, 10, 2, 15, -9],\n [-14, 4, 21, -4, 2, 9, -1, 6, 5, 21],\n [-10, 5, -20, 7, -12, -21, -14, 10, 3, -7],\n [2, -22, -2, -3, -18, -6, 17, 15, -22, -10],\n [-5, -19, -9, -18, 10, 3, -19, 7, -6, 5],\n [-17, 4, 13, -16, -22, -13, -10, 18, 9, -9],\n [10, 7, -14, -17, -13, -12, 16, -3, 2, -11],\n [-1, -11, -9, 19, 13, -9, -21, -21, 20, 20],\n [-17, 2, -20, 0, -14, 8, 5, 2, 12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-21, -8, 20, 17, -7, 0, 12, -15, -16, -2],\n [12, 16, 14, 10, 14, 12, -5, -4, -13, -19],\n [7, 22, 10, -19, -14, -6, 20, 16, 1, 16],\n [-10, 3, -4, -6, 7, 3, -10, -5, -2, 11],\n [-14, 7, 6, 6, -4, -15, 21, -6, -11, -8],\n [-18, 11, -20, -18, 11, -14, 1, -18, 4, -3],\n [22, 18, -21, 0, 11, 6, 20, 12, 7, -20],\n [-13, 11, -22, -17, -17, 20, -7, -22, -18, 2],\n [4, 19, 15, 20, 3, -7, 22, 21, 3, 22],\n [14, 5, 5, 7, -10, 2, 22, -4, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, -9, -13, 11, 17, 0, 17, -2, -3, 9],\n [-9, 1, -5, 7, 5, -9, 19, -2, 11, -18],\n [8, -20, 0, 16, 21, 7, 19, 20, 7, 13],\n [15, -16, -18, -17, -9, -12, 14, -21, 8, 4],\n [-7, -21, 3, -7, -14, -14, -18, 13, -16, 9],\n [6, 14, -20, 7, 17, 8, 4, -17, 6, -14],\n [-3, -12, -4, 16, -13, -18, 16, 0, -17, 8],\n [-5, -2, -8, 8, -13, -17, 1, 10, 5, 5],\n [-13, 0, -8, 14, -9, -9, -16, 13, -5, -8],\n [10, -1, 20, 18, -6, 3, -8, 17, -5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-20, -9, 11, 10, 14, -22, 12, -13, -4, -12],\n [12, -21, -20, -8, 18, 5, -21, 7, 15, -18],\n [-17, -18, -11, -19, 1, 2, 3, 20, 10, -2],\n [0, 14, 14, -11, 14, -2, -10, 20, 10, 21],\n [-17, 20, -11, 15, 7, 14, -5, -7, 22, -16],\n [-22, 5, 21, -20, 20, 16, -13, 22, -9, -8],\n [-17, 16, 22, -7, -5, 12, 2, 10, 10, -4],\n [15, -12, 16, -20, 15, -22, 17, 2, 9, 13],\n [-19, 0, -7, -12, -1, 16, 10, 18, 15, -10],\n [-2, -11, 3, -22, 18, -1, 4, 9, -15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -19, -22, 21, -7, 7, 0, 8, 5, 14],\n [-7, 18, -14, -21, 20, -21, 9, -7, -10, 4],\n [8, 10, -2, -4, -10, -4, 12, 12, 10, -20],\n [-2, 17, 0, 22, 22, -12, -19, -19, -8, 5],\n [13, -15, 1, 11, -8, 0, 4, -9, -21, 12],\n [20, -16, -7, -1, 5, 9, -16, -1, 20, -21],\n [-15, -16, 15, -2, 20, -1, 12, -5, -14, -21],\n [19, 19, -6, 17, -3, -17, -12, -18, -13, 0],\n [10, 17, 13, 16, 11, -6, 3, 4, -20, -4],\n [-15, -6, -22, -16, 13, -20, -4, 19, 4, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[11, -18, 14, -7, -9, 7, 9, 22, -11, 4],\n [3, 6, 0, -1, -3, 15, -7, 8, -20, -2],\n [16, -18, -3, 0, 9, 19, -14, -20, 4, 4],\n [-13, -7, 1, 0, -14, -21, -17, 14, 12, -16],\n [-8, -2, 15, 13, 0, 6, -10, -18, 16, 16],\n [19, 22, 20, -22, -3, 20, -22, 12, 17, 22],\n [-16, 12, 11, -18, 6, 4, -16, -22, -14, -22],\n [4, -6, 9, 18, 7, -8, 19, 5, -20, 5],\n [-18, -21, 15, -7, 21, -6, -11, 3, -16, 1],\n [-7, -5, -15, 4, 3, 8, -5, -21, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[19, -1, 10, -5, -8, 18, -20, 0, -21, 19],\n [-19, 3, -4, -13, -1, -17, -22, 20, -7, -16],\n [1, 12, -9, -19, 18, -8, 21, 0, -4, -9],\n [4, 13, 15, -1, -12, -19, 9, 17, 18, 1],\n [11, -20, 15, -21, 0, 17, -3, -15, 12, 20],\n [-20, 9, 8, 21, 8, -22, -11, -5, 1, 13],\n [6, 2, 0, -20, 7, -6, 22, 7, -4, -18],\n [17, 11, -14, 16, 21, 3, -18, 1, 8, 1],\n [-2, -1, 15, -1, -2, 7, -13, -20, 16, 6],\n [2, -21, -10, 4, 6, -9, -19, -15, -18, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, 1, 21, 20, 11, 5, 1, -18, -10, -5],\n [-6, 7, 15, -4, -1, -5, 3, -8, 5, 7],\n [5, -3, -19, -19, 14, -8, 11, -12, 0, 12],\n [20, 12, -12, -21, -8, 17, 5, 8, 9, 11],\n [-1, 6, -15, -1, -11, 0, 15, -21, -11, -2],\n [-11, 22, 8, -14, -8, 9, 20, -14, 1, -15],\n [5, -5, 20, 14, 13, 14, 9, -2, 16, 6],\n [-5, 0, 10, -14, 21, 20, 15, -19, -7, -20],\n [-15, -7, -21, 22, -4, 1, -7, 17, -21, 9],\n [-22, -5, 16, 9, -14, -20, 1, -12, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 18, -11, -19, 3, -19, -12, -21, 8, -20],\n [2, 11, -22, -18, 16, 8, 13, -20, 15, -11],\n [-7, -15, -12, 22, -9, 4, -5, -15, 10, -19],\n [7, -3, 7, 4, 2, -17, -18, -9, -9, 11],\n [18, 2, 16, -5, -3, 20, -15, 3, -2, 4],\n [9, 19, -6, -22, 4, 13, -12, 18, 18, 12],\n [15, 15, 19, 19, 13, -13, 17, -22, -1, -6],\n [-11, 21, -10, 2, 3, 17, 16, 20, 10, -15],\n [-10, 3, -6, 1, 1, -11, 8, -7, 19, -7],\n [7, 5, -20, 10, 1, 7, 17, 5, 16, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-10, 14, -13, 17, -10, -4, -17, -5, 17, -14],\n [-6, -19, -17, -12, 19, 3, -12, -15, -20, -21],\n [-5, -21, 3, -11, 14, 3, 13, -7, -9, -21],\n [-2, -16, -12, 21, 6, 14, 16, 5, 17, -19],\n [-19, 4, -17, 11, 18, 17, -5, 21, 7, 10],\n [-3, 13, -18, 12, -4, -11, 3, -4, -12, -3],\n [-14, -3, 4, -18, -13, -14, 2, -10, 9, -15],\n [22, 4, -1, 5, -5, 0, 18, 8, 18, 11],\n [-16, -18, -2, -17, 22, 12, 19, 0, -20, 10],\n [15, 0, -7, 2, -7, 2, 19, -16, -15, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-18, -4, -16, -1, 3, 2, -17, -18, 15, 15],\n [-1, 8, -1, -12, 9, -6, 18, -1, -7, 19],\n [-8, -15, -20, -10, 7, 5, -14, -11, 2, 14],\n [-2, 16, 16, -4, -15, 15, -20, -1, -22, 15],\n [-4, -2, -10, 4, -6, -3, 7, 15, -12, 4],\n [15, 5, 3, 16, 10, 9, 2, 1, 17, 4],\n [-1, -3, 10, -18, 6, -18, 16, -6, 6, -12],\n [-1, 8, 16, -22, -8, -4, -13, -14, -10, 22],\n [3, -17, 17, 21, -21, 6, -11, 0, -20, -12],\n [-18, 22, -13, -17, -7, 8, 0, 7, 17, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, 12, -18, -20, 11, -11, 4, -18, 18, -1],\n [-19, 5, -16, 22, 11, -21, -14, -8, 8, 13],\n [18, -8, 10, 8, 4, -21, -14, 20, -22, -4],\n [-14, -21, 14, -22, -11, 3, -13, -22, -22, 20],\n [8, -12, -18, 12, -12, -19, 15, 16, -2, 13],\n [5, -15, -3, 20, -2, 12, 20, 9, 13, 18],\n [-18, 22, -19, -16, 11, -3, -16, 1, -2, -14],\n [-4, -3, 5, 9, 11, -7, 15, -6, -12, -19],\n [17, 22, 17, 19, -5, -17, 9, -18, -8, 22],\n [-7, -6, 14, 20, -8, 12, -15, 12, 13, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-9, 0, -3, -17, 1, 0, 13, -11, -21, 4],\n [9, 6, 17, 17, 21, 10, 6, 10, 13, -6],\n [-13, -22, 20, -6, 19, 5, 15, 13, 22, 4],\n [20, 14, 2, 11, -20, 6, 12, 20, 18, -13],\n [15, 15, -22, -22, 9, -1, -4, 12, -17, 11],\n [-8, 21, 19, 22, -20, 14, -1, 22, 6, -9],\n [7, -8, 6, -9, -20, -1, 10, 0, -16, -3],\n [-16, -6, 9, -8, -10, -20, 2, 9, -7, -22],\n [-20, -3, 5, -1, 13, 18, -22, -9, 22, -8],\n [9, -5, 15, -1, -7, -12, -16, -14, -22, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-15, -12, -18, 6, -17, -11, 20, 16, -16, 21],\n [-11, 10, -4, 13, -4, -2, -4, 20, -14, 22],\n [-1, -4, 14, -12, 2, 12, -18, 22, 8, -9],\n [-10, 11, 11, -5, -17, 19, -2, 17, -18, -21],\n [-17, -15, -21, 0, -3, -19, -8, 7, -3, 1],\n [-14, -2, 15, 18, -10, -18, -9, -16, -17, -11],\n [-7, 9, 19, -12, -19, 6, 11, -14, -13, -15],\n [13, 9, 22, -17, -17, 4, -21, -14, 15, -18],\n [11, -9, -13, -16, -3, -12, -10, -6, 14, 21],\n [13, 10, -13, 11, 22, -10, 2, 21, 10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, -18, -13, 16, 4, 13, 10, 5, 17, 20],\n [-20, 8, 6, 21, 22, 21, 19, -2, 9, 5],\n [-2, 12, 7, -6, 6, -21, 10, -19, 16, 2],\n [-18, -19, 6, 14, -15, -3, 18, -17, 13, 9],\n [-18, 17, -3, 22, -19, 16, -1, 10, 8, 18],\n [6, -18, -13, -12, 14, -1, 1, -2, 13, -7],\n [-21, -8, 18, 3, 7, -21, 6, -17, -22, 17],\n [-12, 0, 3, 8, -8, -14, 11, 16, -6, 12],\n [13, -20, 17, -12, 5, 5, -4, -21, 9, 21],\n [-12, -7, -12, -20, 19, 6, -18, 5, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -17, -20, -1, 18, 16, 9, 7, -16, 2],\n [-21, -15, 10, 5, -13, 15, -5, -10, -2, 10],\n [0, -22, 21, 17, -2, -18, 12, -5, 15, 13],\n [6, 3, 13, 15, -5, 6, 8, 19, -10, 7],\n [-16, 17, -17, -21, -15, -13, 21, 20, -1, -13],\n [12, -4, -19, -4, 18, -3, -19, 3, -20, 7],\n [13, 18, -17, 16, 4, -7, -7, 13, 11, 16],\n [1, 16, -17, -3, -14, -2, -12, 7, -22, 4],\n [-17, 20, -16, -1, 11, -3, 22, 22, -8, -14],\n [-5, 13, 19, 7, -12, 10, 17, -17, 20, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"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, 16, -4, -1, 8, 19, 2, 18, 7, 22],\n [-19, 3, -16, 17, -11, -22, -17, -22, -15, 21],\n [10, -19, 17, -17, 22, -20, -8, -17, -17, 14],\n [4, 19, 18, -18, 16, -6, 0, -6, 18, 0],\n [16, 10, -21, -13, -4, 17, -14, -8, 20, 1],\n [-11, -1, -5, -21, -8, 19, 16, -14, -1, -6],\n [-9, 8, 18, -16, 12, 11, -20, -21, 22, 4],\n [22, -21, 18, -18, -2, -16, 2, 22, -22, -14],\n [-21, -20, 21, 14, 21, -19, -2, 3, 21, 14],\n [-9, -13, 3, -13, 14, -5, 4, -6, -13, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, -4, 21, -7, 0, -11, -4, 2, -20, -10],\n [-2, -1, 6, 20, 2, 0, -11, 0, -18, 6],\n [-18, 16, 12, 12, -6, 7, -21, -8, 0, 19],\n [3, -12, 1, -14, -9, 1, -16, -13, 10, 10],\n [4, -15, -9, -16, -5, 3, 18, -8, 10, -12],\n [-4, 19, -5, -1, 13, -5, -5, -1, 2, 21],\n [8, -14, 15, -4, 2, -8, -18, -12, -10, 11],\n [-15, 2, 4, -12, -5, -13, 10, 13, -6, -18],\n [0, -20, 16, 14, -13, 4, -16, 6, 16, -17],\n [-14, -15, -9, 15, -14, -12, -12, 17, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[13, -20, 22, -4, -15, 5, -22, 17, 7, 18],\n [15, -12, 6, 8, -13, 12, 17, 6, 14, -21],\n [-22, 9, 1, -21, -20, -14, 1, -11, 11, 11],\n [0, -4, 9, 5, 3, 22, -11, 20, 8, -12],\n [17, -19, -5, 6, 16, 8, 5, 4, 7, 19],\n [-12, -9, -19, 13, -22, 21, 16, 14, 10, -2],\n [1, 17, -10, 11, 15, 6, 13, 17, -18, -3],\n [6, -12, -15, 5, 18, -5, 7, -9, -14, -13],\n [2, 4, -21, -20, 6, 14, 4, -19, 12, 4],\n [-4, -13, 3, -16, 4, 7, -11, 17, -18, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[18, -19, -21, 14, 11, -17, 3, -12, 19, -22],\n [11, -2, -13, -18, 3, 21, -4, -2, 11, 6],\n [15, -8, 17, -7, -5, -22, -12, 13, 9, 5],\n [-17, -16, 17, 1, -13, 7, -6, 21, -15, -11],\n [3, -6, 12, 21, -18, 22, -12, -7, 19, 7],\n [17, -17, -3, -3, 1, 4, -20, 1, -13, 2],\n [5, -5, 19, 22, -9, -22, -3, 2, -11, 16],\n [-14, -14, 19, 18, 2, 7, 17, 5, -21, 2],\n [-5, 1, -5, 4, 21, 12, 11, 15, -17, -7],\n [0, 5, -10, -11, -12, -1, 8, 4, 4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, -16, -12, -1, 17, -4, 15, -3, -4, -4],\n [13, 4, -6, -5, -3, 21, 19, 18, -15, 17],\n [-12, 7, -11, 0, -17, 12, -8, 15, 5, -16],\n [-17, 4, -21, -17, 9, 6, 11, -22, -8, -13],\n [-13, -13, 14, 9, 13, 2, -8, -14, -7, 18],\n [-4, 21, -11, 12, 20, -18, 15, -17, -9, -11],\n [-1, 22, 18, -19, 20, -5, 8, 12, -19, -14],\n [22, -8, 19, -2, 9, -14, 9, -7, 22, -18],\n [19, 8, 2, -22, -20, -2, 5, -20, 19, 9],\n [9, 7, -10, 11, -19, -5, 9, -9, 9, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[20, -6, -15, 12, 1, -20, -6, 13, 17, -6],\n [7, 2, -1, 14, -12, -11, -2, -8, -11, -1],\n [16, 12, 19, -7, 10, 20, -9, -5, 21, -7],\n [17, -20, 20, 3, -8, 13, 4, -6, -9, -21],\n [4, 1, 17, 22, 12, -19, 3, 13, -19, 11],\n [-10, 17, 18, -22, -22, -14, -12, -7, 6, 13],\n [-8, 16, -21, -13, -12, 7, 0, -1, 19, 13],\n [6, 22, 9, 10, 16, -14, -22, -5, -1, 14],\n [-9, -1, 10, -17, 4, -17, 21, 18, -7, -21],\n [14, 6, 0, -2, -10, -22, 6, -16, 8, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-1, -7, 5, 21, 16, 2, -9, -2, -4, -10],\n [-21, 13, -9, 11, -5, 1, 7, -4, 13, -2],\n [-4, 3, 12, 17, -19, -2, -20, -18, 20, 6],\n [-4, -6, 11, -3, 5, -14, -20, -13, -2, 18],\n [-19, -1, -16, -11, -12, -1, 6, 4, -3, -9],\n [-16, -8, 5, 20, -13, -20, -11, -10, 16, 21],\n [11, -22, 15, 2, -4, 2, -17, 22, -19, 3],\n [3, 3, -9, 9, 5, -21, 18, 22, -2, -9],\n [14, -21, -18, 15, -21, -22, -1, 18, 2, 7],\n [-14, 14, -13, -8, -20, -15, 2, 13, 20, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[11, 4, -14, -13, 4, 2, -10, -19, -7, -11],\n [2, -7, 16, -21, -14, 21, -10, -9, -11, 12],\n [-1, -2, -20, -1, -14, 17, 19, -20, 8, 14],\n [-17, -9, -4, -5, -16, 13, 6, -20, -10, 13],\n [18, 2, 5, 15, -12, 18, -14, -1, -2, -4],\n [10, -19, 10, 22, -7, 21, -22, -8, -1, 9],\n [14, 0, 10, 17, -1, 17, -11, -5, 9, -20],\n [13, -22, 2, -3, -6, -1, 10, 3, 4, 11],\n [0, -7, -9, 18, -9, 22, 3, 4, 17, -19],\n [-14, 4, 20, 16, -8, 2, -5, 7, 14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-11, -6, 2, -8, 2, -2, -4, 1, -16, -11],\n [16, -12, 10, 2, 16, 11, -12, -7, 9, -8],\n [17, -8, -16, 14, 17, -21, -17, 13, 16, 15],\n [5, -1, 14, -18, -5, -12, -15, -3, -12, 4],\n [6, 2, -4, -21, 19, 16, 21, -21, -16, 8],\n [10, -12, 17, 17, -10, -13, 15, -3, -2, -9],\n [1, 17, -16, -18, -17, 17, 12, -14, 19, -22],\n [16, -3, -17, 9, -10, 16, 17, -2, 14, -11],\n [-17, -8, -2, -2, 5, 13, -6, -16, 0, 22],\n [-1, -13, -5, -21, -11, 22, 16, -1, 20, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[19, -1, -17, 14, -3, -17, -14, 6, 14, -18],\n [-10, 4, 0, 14, 11, 2, 14, 0, 5, 3],\n [-11, 16, -20, -14, -8, -15, 5, 3, -7, 11],\n [-3, -22, 1, 6, -19, -19, 15, -20, 17, -21],\n [6, 5, -11, 21, -8, 18, 8, 14, 9, -1],\n [-20, -6, 6, -11, -9, -15, 18, -21, 11, 1],\n [-3, 20, -13, 17, -16, -22, -13, -18, 17, -2],\n [-14, 6, 8, 22, 4, -17, 20, 8, 18, 22],\n [13, -21, -2, 11, -1, -10, -4, 10, 15, 17],\n [-20, 15, -4, -16, -8, 15, 2, -1, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[13, 14, 19, 19, 19, -16, 2, 17, 18, 1],\n [-18, -2, 17, -3, 6, 14, -3, -5, -19, -12],\n [-1, 20, -9, 22, 5, -19, -7, 15, 0, -10],\n [-3, -18, -4, -2, 19, -18, -9, 13, -17, -18],\n [1, 6, 6, -21, -17, 11, -11, -1, -19, 22],\n [-17, -20, -10, 0, 12, 3, -14, 0, -19, 11],\n [14, -15, 11, 14, -17, -16, 22, 18, 16, 13],\n [-18, -20, -6, -4, 22, -22, 14, -14, -19, 19],\n [-13, 9, -22, 0, -6, 7, 4, -8, 15, -16],\n [10, -18, 16, 11, -20, 9, -21, -7, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-18, -19, -7, -5, 22, -3, -14, -7, 12, 6],\n [7, -3, 19, -1, 0, 13, -1, -22, -2, 20],\n [-4, -15, -18, 17, 6, -5, 6, -8, 22, 8],\n [-8, 22, -20, 21, 21, 19, 10, 1, 15, 1],\n [-10, 4, 10, -4, 2, -17, 10, 2, 0, -6],\n [-2, 20, -3, -11, -10, -5, -1, 1, 10, -20],\n [-6, 16, 9, -6, 21, 2, -15, 20, 12, 6],\n [-11, 13, -14, 3, -1, 8, 21, 7, -8, 10],\n [-20, 11, -6, 21, -18, 7, 20, -8, 16, -15],\n [19, 15, 5, -2, -13, 5, -2, 5, -1, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"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, 15, 1, 5, 22, -10, -14, -14, -2, 1],\n [8, 6, 17, -13, -19, -20, -10, -2, -15, -14],\n [-22, -9, -11, 13, -1, 13, 22, -7, -12, -20],\n [11, 2, 3, -20, -3, 8, -22, 3, 2, -12],\n [-7, -3, 19, 15, -21, 6, -16, 17, 22, 2],\n [-19, 20, 11, 2, -15, 9, -5, 17, -12, 14],\n [16, 13, -13, -17, 22, -7, 2, 11, 8, -15],\n [-6, -9, 7, -5, 13, -2, 8, 10, 0, 15],\n [-18, -8, 7, -7, 17, 6, 5, -17, -18, 15],\n [2, 5, -22, -9, -4, 8, -8, -4, 15, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[8, 14, 3, 18, 2, 17, -15, -19, 8, 9],\n [11, -20, 18, 3, -19, -21, -4, 0, 2, -16],\n [-15, -20, 0, 10, 5, -1, 12, 11, 7, 13],\n [-9, -14, -1, 5, 18, -9, -8, 14, 1, 11],\n [20, 22, 21, -20, 0, -3, 22, -8, 20, -7],\n [-16, 10, -4, -5, 18, -5, -20, -20, 13, -7],\n [20, 0, 0, -8, -14, 17, 15, -5, 15, -17],\n [21, 14, -17, -2, 7, 5, -3, -4, -9, -22],\n [4, 9, 6, 8, 2, -16, 16, -7, 21, -12],\n [-5, 21, 19, -18, -21, -13, 3, 1, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, 15, -17, -11, -14, 19, -15, 8, 18, 9],\n [-16, 9, 19, 2, 10, 5, -12, 8, -13, -21],\n [21, -19, -1, 22, 5, -13, -21, 8, 19, 0],\n [-7, -14, 20, -17, 2, -19, -11, 1, 4, -20],\n [-11, 7, -11, 18, 19, 17, 22, -1, -8, 5],\n [-6, 21, 2, 20, 22, -20, 13, 8, -8, 5],\n [20, 8, 22, -3, 22, -2, 4, -4, 13, -11],\n [12, 10, 13, 18, 0, -10, 7, -13, 18, -3],\n [-17, 8, -4, -20, -13, -13, -2, -21, 22, 16],\n [22, 7, 5, -5, -9, 22, -4, 17, 13, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-11, -3, 11, 13, -2, -4, 18, 18, 20, 19],\n [12, -15, -1, 20, 15, -5, -15, -21, -3, -18],\n [19, 7, -5, 21, 0, -21, 19, 21, 14, 19],\n [9, -22, 16, -22, 21, 8, 16, -15, -20, -11],\n [11, 2, 13, -16, -8, -2, 2, 15, 14, -7],\n [-22, 14, 22, -9, 11, -21, 8, -4, -4, 21],\n [0, 7, -6, -21, -12, -9, 18, 6, -4, 5],\n [-22, -18, 11, -9, -4, 1, 17, -6, -21, 8],\n [-6, -15, -6, 15, 3, 20, 17, 22, 17, -16],\n [1, 7, 3, 7, 12, -21, 21, -19, -18, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[8, 4, 1, 22, -19, 5, -18, 4, 21, -18],\n [-18, -14, 4, -19, 1, 4, -22, 9, -7, 0],\n [5, -3, -6, 13, 22, -15, -5, -10, -14, 14],\n [7, 20, 5, -5, -3, 13, -4, -18, 11, -6],\n [5, 13, 15, 7, -5, -17, 3, -8, -22, -6],\n [8, -21, 13, 12, 4, -20, -3, -15, 6, -15],\n [18, 4, 3, 16, -13, 7, 10, 13, -3, -19],\n [0, 6, 9, 14, 14, 3, -18, 1, 20, -21],\n [-8, 17, -15, 14, 14, -9, -18, -14, -1, 20],\n [21, 21, 7, 10, 15, 14, 22, 15, -16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[20, 17, 9, 13, 19, 18, 22, -4, 8, 7],\n [14, 2, -10, -11, -14, 17, -14, 22, 4, 18],\n [8, -17, 6, 7, 15, -12, 19, -17, 16, 18],\n [8, 12, -11, 22, -17, 22, 3, 14, 9, -19],\n [17, -20, -21, -3, -4, 16, -11, 13, 19, 5],\n [-14, 21, -12, 7, -21, 15, 15, 10, -16, 21],\n [-2, -11, -2, 0, -17, -9, 9, 22, -10, 4],\n [-12, 9, -20, -21, 7, -21, 16, 6, -1, 2],\n [19, -4, -7, -6, 4, 20, -4, 20, 19, 7],\n [-9, 19, 9, 0, 13, -13, 15, 6, -12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-8, 9, 4, 15, -22, 18, -9, -20, 7, 8],\n [-22, -9, 13, 13, 20, 18, 20, -8, 15, 2],\n [21, 22, -9, 1, 20, -21, 11, 0, -15, -18],\n [6, 20, 10, -3, -7, 14, 14, 19, 18, 1],\n [6, 12, -14, -1, -3, 17, -19, 20, 13, -11],\n [0, 16, -15, -13, 0, 6, 22, 9, -9, -7],\n [16, -6, -3, -11, -14, -15, 18, 14, -2, 19],\n [9, 14, -5, 6, -16, 17, 14, -17, -3, -14],\n [-14, -15, -6, 1, 17, 0, 10, -1, -1, 4],\n [-21, 8, -10, -21, -16, -12, 3, -2, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -2, 18, -17, -22, 8, -18, 14, 3, -22],\n [-22, 6, -1, 15, 18, -4, 5, -18, -2, -1],\n [-3, -11, -17, 6, 22, 17, 12, -12, 10, 2],\n [-9, 6, -10, -8, -15, 22, 10, -12, -8, -2],\n [13, -17, 2, 21, -22, 19, 10, 16, 9, -21],\n [2, 17, 10, 15, -12, -4, 2, 5, -13, 8],\n [-7, 19, -5, -1, 12, -11, 19, 5, -14, 7],\n [-5, 22, 1, -4, -9, -21, -12, 3, -15, -20],\n [-8, 22, 17, -10, -7, -1, 10, -21, 22, 6],\n [11, -7, -9, 16, -18, 20, -5, 3, -13, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, -21, 4, -14, -10, -2, 21, -21, -20, -10],\n [-2, 10, -3, 13, -5, 2, 22, 15, 2, 15],\n [-8, -6, 13, 6, 10, 9, -15, 20, -10, -6],\n [-2, -9, 2, 1, 10, -15, 5, -4, -12, -13],\n [-22, -18, -7, -3, -3, 5, -18, -20, 7, 0],\n [11, 5, -22, 4, 11, 8, 9, -16, 20, 15],\n [11, -19, -4, -1, 6, 11, 11, 22, 22, -20],\n [-2, 15, -2, -6, 6, 10, 16, 3, -16, 22],\n [-14, -5, -22, -12, -1, 9, 20, -13, 4, -11],\n [7, -13, -11, 15, -2, 4, -17, 15, -15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-17, 11, 17, -1, 6, -14, -2, 9, -15, 20],\n [-13, 0, -3, -10, -1, 18, -8, 8, 22, 9],\n [22, -10, 2, -2, -19, 19, -8, -2, 19, -15],\n [8, -13, -2, -6, -18, -10, -2, 21, -11, 2],\n [5, -21, -2, 18, -1, -21, 7, -22, -10, -20],\n [-3, -18, -21, 3, 6, -5, -14, -1, 5, -11],\n [14, -5, 11, 19, 19, -20, -18, 0, -10, 1],\n [5, -6, -17, 4, 22, 6, -11, 12, -18, -21],\n [-12, -19, -1, -22, 22, -7, -21, 18, 4, -11],\n [-18, -18, -1, -10, -7, 3, -14, 9, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -8, -14, -7, -17, -15, 10, 9, 13, 19],\n [13, 11, -21, -10, 20, -13, 15, -16, -20, 4],\n [-9, 7, 11, 0, -6, -8, 22, 21, -16, -20],\n [-14, -20, 12, 17, -15, 3, -8, -18, -10, -8],\n [16, -11, 12, -15, -13, 11, -15, -1, -11, -1],\n [4, -5, -4, -18, -7, 18, -13, -4, 21, -22],\n [-1, -6, 12, 16, -14, -18, -14, -12, -9, 17],\n [1, -3, 10, -19, -7, 2, -22, 1, -20, 9],\n [11, 2, 20, -20, -16, 19, 12, 6, 17, 2],\n [5, 1, -18, 4, -13, -11, -5, 15, -15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[7, -14, 20, 2, 7, -21, -6, 22, -16, -1],\n [-13, 3, -10, 19, 5, 13, -12, -14, -7, -6],\n [-18, -18, 15, 8, -21, 4, 20, -4, 20, 2],\n [15, -10, 6, -4, 12, 2, -14, 12, -8, -1],\n [-10, 7, -2, 2, 2, 17, -1, 18, -20, -14],\n [1, 21, 9, -6, 18, 1, -15, -17, -14, -8],\n [1, -12, 8, 22, 22, -10, 7, 2, -11, -2],\n [1, 3, -11, 14, -2, 0, -22, 22, -13, 12],\n [15, 5, -22, -15, 18, 0, -3, 9, 0, -16],\n [-12, -15, 20, -9, -9, 13, 18, 17, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[15, 2, 6, -9, 5, 7, -8, -2, -11, -12],\n [16, -17, -20, 18, -8, 11, -19, 11, 15, 21],\n [16, 18, -17, -1, 14, 9, 5, 3, -19, -13],\n [4, -3, 13, -18, -6, 9, 12, 0, -10, -22],\n [8, -4, 0, 11, -19, 21, 11, 7, -13, -17],\n [-11, -11, -5, 13, 12, 2, 18, -1, 7, 21],\n [6, -16, 17, -20, -2, 22, -3, -14, 18, 13],\n [-9, -5, 10, -21, 14, 8, -1, -14, -3, -3],\n [-22, 7, -4, 13, -9, -22, -18, -13, -14, -9],\n [16, -5, 19, 2, 13, 8, 12, 4, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "328", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-13, -15, 18, 5, 0, -17, -9, 1, -14, 17],\n [15, 2, 15, 7, -1, -21, 2, 1, 14, -20],\n [20, 3, 7, 6, -16, -14, 22, 7, -7, 21],\n [17, -9, 3, 14, -13, 7, -1, 7, 9, -9],\n [0, -6, 13, 6, 1, -12, 18, -8, -1, 4],\n [11, 10, -2, 1, -3, -19, 14, 14, 10, 8],\n [11, -1, 19, 7, -18, 18, 22, 0, -10, -14],\n [-9, -6, 12, -5, -11, 18, -7, 7, -10, -5],\n [-11, 11, 10, -17, -5, -20, -17, 13, -1, -16],\n [7, -21, 9, -8, -1, 15, -15, -15, 16, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 14, -15, -9, -3, 12, 2, -5, -2, 14],\n [8, -17, 19, -3, 5, 18, 13, 17, 3, -10],\n [-19, 11, 14, 11, -7, 0, 0, -8, 2, 6],\n [13, -8, 14, 12, 16, 14, 18, 5, 22, 7],\n [-16, -19, -16, 10, -5, -8, 12, 14, -18, 0],\n [-13, 2, -1, 8, 0, 5, 22, -8, 17, -16],\n [15, 17, -8, -18, -11, -10, -20, -4, 3, 7],\n [5, -8, -5, -16, -9, 1, 1, -12, 16, 20],\n [17, -13, 20, 10, -3, 19, 16, -1, 12, 5],\n [13, 7, -17, -22, -19, 2, 16, -12, 15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-11, 6, 11, -5, -14, -11, -14, -22, -16, 16],\n [19, 11, 9, 5, 3, 13, 17, -9, 22, 8],\n [-7, 16, 19, -12, -12, 15, -11, 19, -14, -1],\n [15, -14, -20, 16, 12, 7, 3, -15, 9, -1],\n [-15, 22, -21, -9, -18, -10, 0, -10, -4, 1],\n [12, -9, -19, 3, -13, 15, 15, 11, 11, -4],\n [-20, 13, -19, 3, -12, -20, -14, -21, -9, -20],\n [-21, -1, 6, 10, 13, -13, 21, 15, -2, 8],\n [12, -20, -4, -1, -3, 13, -4, -19, 9, -15],\n [3, -22, 3, 20, -14, 12, -5, -4, -7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-20, -5, -10, 4, 17, 16, 1, 6, -1, 3],\n [-3, 1, -11, -5, -11, 15, 9, 0, -19, -11],\n [-6, -2, 14, 6, -17, 5, -15, 8, -3, -7],\n [-10, -8, -10, -21, -3, 5, -5, -16, -2, 18],\n [16, -14, 21, -13, 8, 19, -10, -18, 17, 19],\n [15, 20, 13, -21, -17, -10, 6, 21, -9, 7],\n [2, 17, 12, 14, -16, 15, -5, -15, -16, 11],\n [13, 18, -13, 17, 6, -7, 2, 6, -15, -3],\n [13, 4, -10, 3, 19, 2, 5, -14, 3, -11],\n [3, -1, -22, -11, 1, 7, -9, 0, -21, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-17, -4, -2, 22, -3, -2, 17, -19, 2, -16],\n [-16, 10, 3, -6, -15, 3, -8, -3, -4, -16],\n [22, -22, 16, 14, -5, -15, -8, -17, 14, -1],\n [-12, 3, -15, -14, -10, -20, -20, -16, -20, -12],\n [5, 19, 8, -14, 4, -11, -15, 21, 18, -1],\n [-5, 7, -12, -21, 6, 3, -9, 5, 12, -17],\n [13, -11, 11, -17, 14, 14, -15, 14, 17, 10],\n [18, 8, 11, -12, 13, -19, -6, -7, 7, 16],\n [21, -18, 17, 14, 20, 3, 5, -4, -2, 5],\n [-4, 13, -12, -4, -18, -21, 2, 3, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, -3, -5, -7, 5, -11, 17, -17, 1, 20],\n [-17, -6, 19, -4, 5, 6, -16, -4, -15, -15],\n [-18, 20, 11, -2, -19, 21, 13, -18, 0, -4],\n [19, -8, -9, -15, -14, 17, -12, 21, -5, 9],\n [21, 13, 22, -2, 4, 19, -2, -12, 21, 11],\n [-18, 5, -13, -11, 18, -20, -22, 14, 17, -22],\n [-10, 15, -8, -16, 7, 1, -15, -20, -8, 13],\n [18, 20, -9, 4, 7, 18, 21, 14, -17, -4],\n [14, -22, 2, -13, 3, 0, -6, 7, 4, -12],\n [-19, -5, -4, 13, 21, 3, -22, -3, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"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, 9, -22, -22, -20, 17, 9, 13, 20, -15],\n [7, 16, 11, -15, 2, 3, 4, -4, 0, 18],\n [-7, -15, 7, -15, -12, -16, -2, 11, -2, -18],\n [20, -6, -2, -17, 22, -16, -12, -5, 15, -11],\n [-1, -20, -4, 20, 0, 11, -20, 0, -18, 6],\n [11, 21, -18, 6, 22, 1, 16, -2, 9, 20],\n [-18, -5, 15, 12, 15, -7, 12, 1, 13, -18],\n [-14, -19, 10, 4, -1, -12, -18, -13, -20, -8],\n [14, 17, -6, -3, -19, 11, 11, 8, 11, -20],\n [5, 18, 14, 6, -8, 13, 12, 18, -13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[7, -15, 0, -4, 14, 20, 13, -19, 3, 17],\n [4, -10, 21, 11, 10, 3, -3, -15, -7, -18],\n [11, 4, 13, -19, 19, -16, 14, 13, 1, -8],\n [-17, 3, 3, 2, 10, -20, -14, 14, 15, 7],\n [4, -10, 0, -20, 0, 12, 1, 14, -11, -3],\n [-5, -16, 3, -11, 11, 9, 7, -21, -15, 10],\n [19, 7, 22, 19, 22, 5, -10, 1, 10, -18],\n [-17, -19, 19, 20, 11, 6, -2, 3, 9, -1],\n [18, -9, 11, 14, 21, -22, 9, 9, 1, 21],\n [-2, -11, -3, 14, -3, -21, -9, -6, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-8, 11, -15, 19, -20, -12, 4, -14, -8, 9],\n [-12, -20, 3, -16, 5, 16, -19, 7, 15, -9],\n [13, 8, -4, -11, -8, -14, 4, -3, 5, 2],\n [-7, -5, 13, -19, -2, 4, -22, -18, 21, -13],\n [-2, -13, 3, -7, 15, -20, -3, -18, -17, 2],\n [2, -11, -22, 19, -20, -2, -18, -8, -19, -4],\n [-6, -15, 14, 1, -19, 1, -4, 1, 18, 22],\n [-2, -6, -15, 8, -4, -12, 0, 14, 5, 0],\n [-11, -7, -7, -9, -16, -2, -2, 18, 12, 1],\n [-22, -9, -3, 5, -5, -20, 4, -17, -19, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 12, 5, -5, 12, -2, -7, 3, 16, -14],\n [0, -21, -20, 10, 1, 0, -17, -2, -18, -10],\n [17, -10, -4, -14, -20, 8, 16, -10, 18, -12],\n [18, -12, -22, 12, 12, -20, -19, 1, 7, 9],\n [-3, 13, -10, 16, -19, 5, 17, 20, -16, -14],\n [-1, -19, 13, 10, -17, -20, 12, 10, -16, 18],\n [12, -20, 20, -5, -20, 16, 4, -14, -6, 18],\n [19, 22, -18, -19, -9, 6, -12, -1, 19, -18],\n [-11, -2, -8, 1, -10, 9, 3, 17, 3, 13],\n [22, 7, -14, 1, 15, -5, -14, -1, 15, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-16, -11, 13, -12, -20, 4, -16, -21, -13, -20],\n [-6, 20, -22, 11, -10, -9, -6, 11, -6, 18],\n [2, 21, 7, 13, -12, -2, -3, 6, -19, 11],\n [19, 18, -6, -11, -19, 18, -9, -19, 11, -5],\n [-10, -13, -9, -14, 20, -3, -22, 21, 6, -6],\n [-15, -6, -2, 2, -3, 2, -2, -10, -10, 7],\n [-10, 17, -16, 19, -11, -21, -9, 19, -6, -10],\n [-22, -22, 3, -10, 11, 17, -14, -4, 0, 18],\n [5, 7, -16, -9, -21, -11, 20, -21, 5, 5],\n [-11, 7, 17, 17, -1, -5, -9, 2, -13, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -12, 4, -10, -22, 16, -12, -20, -21, 19],\n [1, -3, 17, -8, -17, -3, -1, -21, -8, 11],\n [8, 7, 5, 10, 18, -2, 0, 19, -10, 22],\n [3, -4, 4, 17, -16, 2, 17, 13, -16, -3],\n [1, 5, -18, 13, 8, 10, 1, -13, 15, 21],\n [-18, 8, -14, 9, 18, -18, 4, 5, 20, -11],\n [-18, -15, -6, -15, 11, 0, -5, -13, 16, 18],\n [21, 21, -18, 20, -6, -12, -4, -2, 21, -20],\n [17, 20, -22, 1, 13, -17, -13, 17, 11, 1],\n [0, -3, 15, 12, 11, 13, -7, 0, 21, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -11, 14, -6, -20, 15, 6, 8, 12, 15],\n [3, -10, -4, 9, 4, 16, -10, 11, -4, -4],\n [-20, -20, 3, -17, -10, 15, 4, 18, 1, -13],\n [-7, 0, -11, 5, -10, -5, -21, -6, 0, 0],\n [-22, 20, -9, -11, -9, 21, 15, 18, 21, -7],\n [11, -5, -13, -4, 7, -19, -16, -7, 14, -18],\n [16, 10, 12, 11, 10, 16, -13, -20, 6, 12],\n [8, 16, -8, -22, -4, 14, 4, -2, -16, 20],\n [10, -21, -9, 19, -20, -9, -18, -6, 16, -22],\n [20, 5, 15, -9, -6, -8, -16, 19, -16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, -9, -4, 3, -7, 11, -21, -22, 13, 12],\n [20, 1, -18, 6, 18, -22, -14, 13, -7, -8],\n [-13, 14, -7, 15, 13, -8, -20, -4, 18, 14],\n [-20, -15, 1, -9, 12, -7, -16, 18, 12, -15],\n [-11, -7, -19, 12, 22, 18, 22, 9, -11, -2],\n [-8, 12, -20, -21, -17, -7, 0, 8, 18, 7],\n [-20, -7, -19, 13, 5, 5, -20, 3, 16, -10],\n [-16, -10, -19, -7, 5, -10, 19, -13, -18, 13],\n [-4, 7, 18, 5, 8, 13, 20, -22, -14, -11],\n [0, -11, 19, -14, 3, 7, -3, -7, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-19, 2, -10, 5, 22, -11, 1, 5, -22, 11],\n [-20, -1, -2, 4, -2, -1, -10, 21, -7, 1],\n [-6, -18, 15, 19, 4, 18, 9, 3, -16, 13],\n [-16, 20, 4, 15, 1, 1, 22, 21, 6, 4],\n [11, -2, 22, -22, -13, 7, 5, 19, 7, 5],\n [6, 8, 20, 18, -19, -4, -13, 22, 8, 11],\n [18, 16, 19, 21, 8, -12, 13, 21, 21, 9],\n [0, 17, 16, -20, 5, 2, 5, -4, -4, 19],\n [21, 6, -4, -5, 22, 1, 15, -7, -5, 18],\n [-10, -19, -10, 12, -19, -4, 1, 10, 10, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-20, -20, 7, -5, -21, 9, 20, -14, -21, -3],\n [4, 13, 18, -4, -7, 3, -9, -5, 5, -4],\n [7, 18, -2, -2, 7, 19, 14, 18, 9, 7],\n [-1, 1, -13, 1, -22, 12, -7, -18, 8, 22],\n [14, 2, 20, 2, -20, 15, 9, -3, 7, -21],\n [-18, -4, -3, -1, -12, -5, 4, 8, 12, 21],\n [22, -2, -3, -14, 8, -14, -16, 10, -22, -4],\n [-20, 16, -11, 7, -7, -10, 1, -6, 4, 6],\n [18, -9, -18, 20, 15, -17, 1, 17, 10, -14],\n [19, -20, 0, -2, -1, 22, -15, -3, -9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-15, -4, 22, 15, 13, -17, 11, -13, 8, -12],\n [20, 12, -12, 17, 9, 3, -1, -22, 6, 16],\n [-1, 9, 2, 17, 22, 6, 14, 9, 7, -5],\n [21, -20, -11, -3, -15, 8, 1, -10, -15, 19],\n [-9, -8, -2, -8, 3, 15, 15, 10, -13, -4],\n [-12, -20, 0, -17, 18, 18, 6, -19, -20, -3],\n [20, -15, -17, -18, -15, -15, 12, -4, -13, 12],\n [-14, -15, -15, -15, -3, -16, -1, -6, 21, -18],\n [11, 2, 20, -8, 8, 22, -4, 21, 8, -11],\n [0, 0, 13, -12, -1, 7, -18, 14, -3, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"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, 19, 7, 7, -1, 15, 15, 15, -16, 13],\n [-9, -12, -16, 9, -5, 11, -21, -16, 20, 8],\n [-5, -3, -16, -1, 14, 11, 16, 19, 17, -7],\n [-9, 18, 9, 15, 16, 3, 7, 18, 16, -14],\n [9, -16, -11, 0, -6, -2, -11, -1, 0, -18],\n [-5, 14, 14, -16, -20, -22, -17, -16, 4, 8],\n [-15, -9, -8, -16, -16, 10, 18, -16, -3, -16],\n [-9, -8, -5, -13, 12, 4, 20, -22, 5, 11],\n [-20, -20, -12, -19, 7, 16, 9, -7, -6, -12],\n [13, 9, 12, 4, 11, -18, 2, 5, -5, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -21, 11, -1, -1, 7, 11, -22, 6, -4],\n [-4, 18, 18, 6, 20, 10, -6, 15, -22, 18],\n [10, 13, -1, -5, -6, 9, -3, 0, 5, 3],\n [-16, 18, -3, 18, -12, -16, 15, 4, -14, -19],\n [15, 6, 3, 2, -9, 14, 5, -15, 19, -12],\n [12, 8, 11, 13, -6, -2, 3, 18, 5, -1],\n [18, -20, 5, 13, -21, -3, 17, 13, -15, 16],\n [2, -8, 7, 11, -19, -1, 2, -14, 0, 16],\n [-11, -9, -16, 8, -17, 0, -4, -2, -4, -4],\n [21, 11, 20, -10, 13, 2, 10, -2, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "307", "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, 20, -12, -4, 11, -21, 7, 22, 15, -8],\n [-12, 1, -19, -4, 6, -9, -6, -15, -10, 0],\n [6, -12, -7, 21, 0, -11, 15, 1, 8, 15],\n [13, -22, 3, -6, 13, -6, 14, 4, 2, 7],\n [18, 2, 15, 9, -11, -2, 19, 11, -22, -10],\n [-2, -22, -10, 8, 0, -20, -12, 6, -5, 2],\n [11, -5, -22, 5, -19, -2, -17, -2, 14, 7],\n [-3, 18, 9, 8, 13, 2, -18, -15, -6, -8],\n [-3, 22, 6, 13, 5, -15, -9, 10, 11, 6],\n [-1, -20, 0, -20, -17, 17, 0, -11, -18, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-20, -19, 1, -18, 8, 12, 19, -4, -15, 5],\n [15, 0, -16, 15, -10, 22, -2, 14, -17, -13],\n [4, 3, 19, 5, -7, 5, -20, -22, -20, 7],\n [-4, 10, -15, -4, 13, 14, -18, 11, 15, 4],\n [16, 19, 19, 1, 8, -1, 0, 18, 1, 17],\n [9, 10, 5, -6, 3, -5, -8, 15, -1, -5],\n [-2, -4, -21, 7, 2, 3, 16, -6, -7, 4],\n [-20, 19, 15, 6, -21, 20, 17, -9, -11, 1],\n [5, 16, -5, 2, 14, -17, 22, 7, 8, 11],\n [-4, 5, -15, -12, -7, 3, -22, 8, 4, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-14, 3, -17, -16, -10, -13, 20, 8, 14, -5],\n [-12, -13, 5, -2, 2, -17, 19, -12, 10, -18],\n [11, 9, 20, 1, -10, 20, -17, 11, 2, 18],\n [0, -10, 5, 21, 21, -10, -16, -6, -14, -9],\n [7, 18, 15, 7, 10, 2, 8, 0, 4, 10],\n [-3, 5, -15, -1, 12, 8, 21, 1, -8, 22],\n [8, -18, -1, -6, 5, -20, -4, 15, 4, -6],\n [9, 14, -2, 14, -12, -22, 7, 3, 22, 20],\n [13, 3, 19, 4, 3, 20, -5, 10, 13, 14],\n [11, 3, -1, 1, -11, -12, -2, -7, 13, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "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, -10, -9, 20, 8, -15, -22, 17, -6],\n [18, -10, 4, -10, 17, 4, 9, -11, 20, -10],\n [-7, 11, -17, -5, -6, 16, -9, -16, -17, -11],\n [11, -22, 6, 5, -18, -2, 16, 15, 11, -2],\n [1, -10, 22, 0, 9, -15, -12, -10, -3, -22],\n [-21, -12, 7, -18, -16, 1, 8, 7, 20, -8],\n [13, -13, -22, -16, 21, 3, 20, 20, 7, -22],\n [-8, -3, -1, 2, 13, 14, 22, 4, -4, -4],\n [-7, -2, 10, 19, 8, 11, -8, 13, 3, 7],\n [8, 2, -19, -11, -4, -14, 2, 18, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[20, -17, 12, 9, -9, -17, -5, 8, -7, -20],\n [8, 15, -6, -18, -7, -6, 8, -7, -2, 18],\n [16, 14, 18, -13, 9, 2, 10, 16, 14, 15],\n [15, 5, -8, -15, -22, -13, 12, 10, -7, -9],\n [-18, -7, -2, -12, -16, -15, -6, 7, -9, 21],\n [10, 1, -16, 15, -8, 20, 2, -6, 10, -21],\n [16, -13, -9, -11, -6, -9, -13, 21, 16, 17],\n [6, 22, -17, 17, 8, 14, -14, 20, 22, 10],\n [-16, 15, -15, 11, -6, -6, 7, -5, 16, -8],\n [22, -3, 2, -9, 4, 12, 5, -17, 18, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-9, -7, 21, 13, -18, 9, -12, -1, 20, 17],\n [5, -17, 16, -17, -3, 15, -19, 2, -10, -11],\n [-14, -20, 9, -12, -18, 12, 1, 18, -17, -5],\n [15, -17, -1, 19, 20, -9, -11, 2, -3, -5],\n [1, -8, 8, 19, -22, -8, 11, -21, 13, 0],\n [1, 9, -10, 10, 19, -9, -6, -7, 9, -8],\n [20, 8, -11, 10, -20, -12, 20, -18, 4, -7],\n [12, 17, -7, -7, -1, -19, 9, 4, -8, -4],\n [3, -8, 22, -13, 11, 15, 3, -15, -7, 6],\n [9, -2, 9, 22, -11, 16, -13, -17, 14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[8, 12, -20, -18, 11, 10, 13, -13, 22, -20],\n [-12, -20, 5, 19, 5, -14, 3, 6, -13, 4],\n [22, 9, -5, -5, -1, -6, 2, 3, -18, -14],\n [21, 21, 1, -16, -3, 21, 18, -15, -4, 12],\n [20, 21, 2, -6, 16, 2, 12, 16, 16, -21],\n [-7, 19, -9, 6, 16, -21, -13, -21, 4, -10],\n [-21, 19, -9, -6, 21, 15, 13, 11, 6, 0],\n [0, -7, 21, -16, 22, -22, -4, 22, 10, 11],\n [-22, -11, 2, 0, 2, 8, 1, -13, -21, 10],\n [14, 0, -21, -19, 0, 18, 15, 0, -11, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 6, 18, 5, -8, -13, 11, 6, 8, 0],\n [-5, -16, 4, -14, -3, -2, 5, -20, 22, -13],\n [-6, 12, -2, -14, -6, 9, 15, 5, -5, -17],\n [-17, -6, -13, -21, 10, 20, 2, 15, -22, -7],\n [3, 18, -11, -14, -10, -16, -22, 8, 12, 1],\n [-20, -4, -19, 5, 21, 7, 13, 19, -19, 0],\n [-12, -19, -12, 1, -3, 22, -6, -10, -6, -8],\n [-19, -5, 20, -14, -20, 4, -5, -6, -13, 14],\n [6, -18, -17, 17, 12, -18, -8, 4, 21, 16],\n [10, 1, -2, -21, -4, 22, -5, -13, 22, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[0, 22, 18, -22, -17, -22, -5, 4, 17, 15],\n [22, -6, 3, -10, -13, 15, 3, 8, 0, -3],\n [0, 22, 4, -8, 15, -12, -15, -9, -10, -1],\n [11, -22, 14, 9, -12, -13, 7, -11, 19, 18],\n [11, 2, 13, -19, -2, 7, 15, -11, 16, 2],\n [-4, -21, -1, 7, 13, -20, 0, -19, 5, -9],\n [-17, -17, 18, 14, -16, -10, -22, 1, 11, -13],\n [-17, -19, -15, -8, 22, -11, 16, -17, -2, 9],\n [9, 4, -12, -1, 13, 0, 14, 0, 4, 11],\n [-3, -8, 19, -19, 6, 17, -12, -16, -12, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, 7, 9, 17, 14, -10, -16, 1, -12, 8],\n [21, -9, 21, 3, -22, -17, 8, 20, 20, -11],\n [-22, -17, 6, 7, -10, 7, -11, -13, 16, -13],\n [-5, -17, -15, -3, 18, -7, -21, -12, 1, -4],\n [-19, -20, -8, 17, -19, 20, -6, -14, 2, -22],\n [17, -21, 22, 10, -1, 19, -11, 4, -12, 19],\n [-9, -9, 17, 20, -1, -14, -8, 10, -4, 8],\n [-5, -11, 17, 14, 22, -22, 11, -16, -21, -1],\n [-19, 22, -3, -20, -14, -5, -7, -14, -4, -17],\n [21, -8, -17, -18, 6, 4, 22, 18, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[9, 2, -16, 7, 8, -11, -14, 11, -20, 14],\n [5, -1, 3, -4, -2, 14, -13, -7, 1, 2],\n [3, -22, -19, 14, 20, -9, 1, 4, 20, 4],\n [1, 17, -22, 16, -10, -3, 15, 13, -11, -18],\n [-18, -6, 15, -13, -7, 1, 6, -9, -13, 6],\n [5, -6, -18, -21, 13, 17, 22, 16, -14, 13],\n [-18, -8, -14, 2, 5, 4, 10, 10, 15, -15],\n [-19, 20, 13, 20, 8, -13, 18, 19, -15, 7],\n [-9, 22, 12, -20, 6, -7, -13, -19, -19, -21],\n [-12, -8, -12, 0, 15, 7, -22, 22, 10, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[14, 0, -5, -13, -6, -16, -8, 4, -14, -2],\n [14, 6, 19, 22, 10, -17, 2, 12, -6, 21],\n [4, 20, 17, 2, -11, 20, 14, 17, 21, 15],\n [18, 2, -21, -22, -20, 6, -9, 22, 11, -1],\n [13, -8, 14, -13, -14, 12, 19, -6, -5, 2],\n [12, -7, 22, 2, -7, 18, 1, -11, 12, -14],\n [14, 9, -4, -1, 22, 11, -4, -11, -5, -18],\n [3, 4, -3, -15, -7, -21, 22, -22, -18, 8],\n [0, -2, -11, -19, 14, -12, 19, 17, -14, 3],\n [16, 4, 6, 20, 2, -5, 7, -15, -21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, 16, 3, 6, -18, -9, 12, -17, 0, -6],\n [1, 17, 6, 7, 1, 12, 14, -21, -2, 17],\n [18, -18, 12, 21, 12, -4, -7, 2, -7, 8],\n [10, -6, -2, 12, 0, -7, 15, -9, 17, 18],\n [10, -2, -6, -19, -7, 7, 21, 22, 11, -1],\n [21, 19, 6, -18, -22, 17, 2, -17, 0, 10],\n [-9, 19, 13, -5, 17, 21, -13, 22, 16, -11],\n [15, 0, -16, 22, 2, -10, 15, -4, 22, -1],\n [18, -12, 19, -20, -4, 4, -16, 14, 4, 11],\n [-12, 15, -18, -16, 13, -18, -18, 4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[9, 2, 19, 11, -8, 18, 11, 12, -3, 1],\n [11, 11, 4, -2, 10, 16, 17, 21, 13, 2],\n [-16, -13, -13, 15, 1, 21, -13, 22, 3, 7],\n [4, 21, -4, -22, 10, -12, 11, 15, -7, -22],\n [18, 5, -8, -7, 9, 16, -22, -14, 6, 2],\n [-12, 19, -12, -17, 11, 21, -9, -15, 2, -19],\n [8, -2, 22, 9, -9, 5, 2, 5, -8, 21],\n [-1, -17, -21, -17, 0, 3, -12, -22, 5, -1],\n [18, -10, 18, 13, -1, -19, 21, 18, -5, 15],\n [-6, 2, -6, 6, 22, 21, -15, 6, -8, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -13, 14, -12, 12, 11, 9, -1, -19, -21],\n [10, -14, 12, 15, 8, -9, 8, 10, 21, -7],\n [-3, -9, 12, 22, 10, 6, -15, 11, -9, -9],\n [-8, 19, -3, 5, -19, -16, -21, -14, 0, 13],\n [-11, 0, 8, 19, -12, -22, -10, 16, 6, -17],\n [8, -14, -5, -20, 9, 22, -20, 22, 7, -17],\n [4, -21, -3, -6, 10, -6, 14, 6, -14, -19],\n [17, -10, -17, -14, 3, 16, 18, 19, -9, 11],\n [-19, -2, 8, 20, -2, 20, 6, 1, 22, -7],\n [-14, -2, -21, -21, 14, 14, -18, -17, -15, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "356", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[14, -10, -20, -14, -19, 5, 17, -7, -12, -4],\n [19, -1, 16, -11, 7, 17, 19, -18, 14, 22],\n [9, 11, -11, 20, -21, -16, 9, 17, 12, -17],\n [-1, 2, -10, 0, 22, 21, -14, 19, 14, 14],\n [7, -3, 15, 21, -7, -1, 15, -13, -3, 18],\n [-21, -20, 19, -15, -14, 5, -2, 10, 11, -19],\n [2, 9, -11, -21, -11, 3, -2, 21, 14, 13],\n [-5, 1, 7, -6, -7, 19, -6, 21, -11, 4],\n [-19, 12, -22, -11, 6, -15, -15, -11, 13, 11],\n [13, -19, -12, -20, -13, -11, -14, -2, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 21, -17, 2, 22, -8, -22, 17, -5, 21],\n [8, -3, 21, 2, 10, -13, 6, -4, 5, 4],\n [-4, 20, 8, 12, -9, -17, -14, 18, 4, -6],\n [13, -19, 1, -7, -6, -20, 16, 14, -20, 21],\n [18, 12, -20, -7, -3, 22, -17, 10, 20, 4],\n [7, 12, -5, 7, 20, 3, -8, 9, 12, -11],\n [-2, -11, -22, -12, 2, -14, 16, 20, 4, 6],\n [4, 5, 16, -5, -8, -7, 0, 7, 13, 12],\n [5, -20, -7, -8, -4, -13, -19, -1, -5, -1],\n [19, -7, -20, 21, 12, 18, 16, -7, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-22, 7, 11, 16, 0, 11, 7, 10, -7, 18],\n [7, -20, 22, -21, 3, -5, -21, 17, -20, -6],\n [1, -21, -17, 17, 3, -17, -11, -2, -7, -17],\n [11, -20, 18, -4, 6, 9, -13, 4, 6, -10],\n [-3, 5, 4, -10, 2, 6, -8, 22, 22, 7],\n [15, 9, -16, 12, 10, -11, 0, -18, 20, 21],\n [8, -7, 10, -22, -1, 5, -18, -19, -22, -8],\n [14, 16, 15, 22, 1, 0, -16, 8, -16, -10],\n [-19, -5, 17, -4, -7, -5, -7, 8, 2, -21],\n [5, -7, 13, 22, 17, 12, 1, 12, 7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-12, 22, 11, 15, 16, 1, 6, -19, 18, 7],\n [-9, 1, 15, 11, 13, -8, 12, 6, 13, -19],\n [-8, -12, -8, -2, 12, 0, -13, -19, 22, 2],\n [-21, 15, -4, 1, -15, -17, -3, -9, 17, -17],\n [-11, 18, -16, 22, 7, -7, -15, -9, -3, 5],\n [-17, 7, -19, 13, -20, -13, 15, 4, -5, 22],\n [-12, 13, 17, 12, 21, -10, 0, 20, -14, -19],\n [20, 17, 8, -20, 13, -6, -7, 16, -21, -18],\n [10, -10, -11, -4, -1, 17, -15, 21, -19, -16],\n [-1, -5, -17, -19, 18, 22, -11, 14, -21, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[22, -2, 16, -10, -9, 7, -5, -10, -9, 18],\n [17, 2, 14, 4, 0, -16, -13, 2, 12, 1],\n [19, -12, -3, -13, -2, 5, 5, 4, 10, -19],\n [12, -3, -17, -17, -6, -4, -6, -20, 11, -19],\n [0, -5, 11, 6, 21, -8, 22, -12, 16, -14],\n [12, -13, 17, 15, 6, -17, -4, 3, -14, 18],\n [22, -10, 3, 21, -3, -21, -19, -16, -4, 12],\n [-12, -4, 9, -9, -18, 2, -9, 16, -11, -3],\n [-5, -22, 20, -19, -11, 3, 9, 14, -8, 12],\n [3, -8, -15, 5, 7, 20, 21, -20, -17, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -15, 16, 6, -6, -7, 22, -19, -13, -7],\n [-4, 16, -10, -19, 9, -5, -7, 2, -7, -1],\n [1, 5, 0, -2, -14, -21, 15, 5, 3, 4],\n [2, -2, 15, 2, 15, -12, 5, 13, -19, -4],\n [1, -1, 2, -15, -3, -22, -19, -11, 2, -2],\n [-4, 11, -17, 12, -20, 10, -14, -16, 18, 4],\n [-22, 17, -5, 12, -6, 16, -12, 14, 22, -12],\n [-20, -10, 5, 15, 11, 5, -21, -21, 14, -7],\n [-15, 17, -12, 22, -8, -19, 0, -15, -7, -7],\n [1, -13, 11, -5, -7, 13, -15, -3, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "327", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, -7, 15, -5, 17, 7, 13, 13, 16, 17],\n [18, -22, -6, 5, -16, -3, 19, 1, -22, -5],\n [3, -9, -4, -5, 22, -16, -21, -16, 5, 5],\n [19, -6, 7, -2, 14, -14, 13, -1, -8, -9],\n [4, -5, -13, -1, 0, 19, 18, -18, 2, -22],\n [1, 10, 14, -16, 1, -8, -12, 21, -6, 0],\n [-19, 8, 11, -13, 14, -13, 19, -12, 8, -13],\n [20, 15, 19, -15, -12, -3, 1, -16, -2, 21],\n [-17, 8, -11, 14, -10, 8, -14, 4, -6, -15],\n [4, 17, -8, 16, -17, 9, -15, 12, 8, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 19, 1, -21, 18, -22, -13, 0, 10, 21],\n [14, -12, -3, 3, -21, 2, -19, -4, -10, -4],\n [-10, -11, -21, 14, 0, -4, -20, 1, 0, -19],\n [-5, -11, 12, 4, 20, -9, 8, -20, -18, 6],\n [16, -6, -4, 12, 10, -15, 14, 12, -3, -6],\n [22, -10, -19, 7, -17, -21, -8, 11, -3, -7],\n [20, 6, 4, -22, -10, 17, 9, -20, -9, 5],\n [3, -2, -12, 4, 21, -22, 10, -5, -21, -19],\n [-19, -6, -7, -14, 3, -13, -16, -14, 4, 9],\n [0, 4, 2, 6, 1, -7, -7, 5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-13, 3, -21, -20, 16, -21, 2, 22, -19, -8],\n [-5, -16, 4, -5, -16, 6, 18, 21, 10, -21],\n [-5, 0, -17, 20, 2, -4, -15, 14, 3, 6],\n [5, -16, 13, -8, 10, -18, 6, -6, 22, 4],\n [-6, -19, -11, 0, -12, 13, -11, -14, 1, -5],\n [4, -14, 10, -17, 10, 17, -17, -19, -20, -10],\n [3, 11, -10, -15, -11, -15, -4, 18, -13, 9],\n [-2, 0, 4, 2, -16, 19, 12, -21, 5, -16],\n [19, 17, -11, -6, -1, -14, -20, -1, 13, 16],\n [-5, -6, 4, 12, 9, -20, -10, -6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-7, -1, 2, -22, 4, -9, 5, 13, 20, 9],\n [6, -6, 5, 18, -2, 1, 12, -3, -1, -19],\n [-7, -2, 21, -2, 17, 18, -12, 14, 21, -1],\n [-3, -21, 20, -12, -2, 10, -6, 13, -9, 14],\n [8, -19, -17, -2, -10, 15, -8, -18, 15, 1],\n [-5, 6, 9, -16, 7, 15, 3, -15, 2, 7],\n [1, 7, -18, -19, 19, -14, 10, 6, 8, 21],\n [-4, 22, -21, -3, -11, -2, 8, 13, -3, 21],\n [-3, 22, 13, -5, -17, 10, -13, -5, 11, -8],\n [-20, -15, -12, 9, 19, -6, 7, 20, -15, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-16, -3, -11, -2, 5, 5, -7, -13, -1, -16],\n [-19, 1, 11, 18, -9, 21, -6, 22, -15, 19],\n [-10, -16, -20, 1, 1, -16, 7, -18, 17, -2],\n [-15, -16, 16, -21, 20, -11, 5, 21, -4, 5],\n [12, -11, 5, 3, 15, -17, -4, 4, -14, 18],\n [-13, -13, 10, -5, -13, -16, 17, 9, 20, -17],\n [-4, 18, 20, 11, 20, -18, -4, -9, -13, -12],\n [8, -21, -13, -2, -22, 8, -12, 20, -13, -3],\n [-2, 14, 14, -9, -18, -17, 1, -7, 0, 15],\n [-7, -10, 22, -15, 15, 9, -1, -6, -18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[7, -4, -11, 2, 21, -10, -19, -13, 5, -18],\n [5, 21, 8, -7, 0, 6, -2, -21, 0, -7],\n [-12, -14, -21, -5, -10, 22, -15, -13, 4, -6],\n [1, -2, -22, -7, 20, 10, -17, -11, 9, -12],\n [-5, -21, 9, -3, -2, 13, 15, 4, -12, -5],\n [-6, 11, 22, 3, -17, 20, 7, 16, 9, -6],\n [-10, 18, -10, -17, -1, 10, 10, -19, -9, 12],\n [4, -17, -22, 20, 5, 6, 9, 5, 4, -13],\n [-5, -19, 15, 18, 19, 9, -18, -1, -1, -21],\n [18, 20, 11, -21, 13, 17, -15, 10, 10, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"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, -13, 19, 18, 7, -1, 16, 15, -22],\n [7, -18, 3, 8, 16, 18, -11, -6, -5, -21],\n [1, 5, 16, -13, 10, 1, -12, -15, 4, 3],\n [-11, 12, -8, -2, 14, 7, -18, -6, 3, 11],\n [10, -5, 2, 18, 7, 14, -3, 22, -21, -10],\n [17, 19, -3, -17, -12, 2, 19, -13, 8, 20],\n [-19, 2, 5, 1, 12, 18, -18, 10, -12, -15],\n [-2, 9, -18, 11, -14, 15, 20, 9, -13, -11],\n [12, 16, -5, 0, -11, 8, -12, 11, 4, -2],\n [-13, -10, 22, 2, -10, 18, -17, 12, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 18, -19, -3, -18, -1, 1, 21, -6, -18],\n [3, 13, -15, -14, -6, -15, -18, -13, -9, 4],\n [4, -18, -8, 5, -18, -1, -11, 19, -15, -22],\n [12, -7, 7, 20, 18, -13, 11, -12, -3, 20],\n [-16, -2, -12, 14, 0, 21, 8, -5, 1, -1],\n [14, 21, -22, -17, 15, 6, 20, -12, -7, -17],\n [-22, 12, 1, 15, -20, 17, -21, -8, -1, -19],\n [1, -4, 7, -1, 16, 17, 4, -8, 14, -22],\n [-11, -14, -4, -5, 16, -12, -12, 7, -3, -8],\n [2, -20, 20, 3, 22, 5, -17, 9, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "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, 13, 7, -19, -9, 5, -16, -7, -9, 14],\n [16, 4, 7, -8, 16, 19, -5, -12, -1, -19],\n [-20, 1, -9, -20, 8, 12, 8, -11, -13, -3],\n [-5, 21, 13, -4, -6, 17, -12, -18, 14, 22],\n [13, 22, 21, -9, 5, -14, 15, 6, 2, -15],\n [-4, -21, -17, 7, -21, -4, -10, -15, -14, 0],\n [14, -15, -14, -7, -7, -11, 2, -12, -5, -10],\n [12, -5, 20, 7, 20, 14, 7, -20, 6, 2],\n [-21, -18, 8, -18, -2, 3, -16, 7, 11, 5],\n [-9, -5, 21, -6, 2, -17, -18, -2, 16, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-12, -18, 15, 16, 12, 12, 2, 7, -21, -3],\n [13, 14, -21, 21, 4, 9, -19, 4, 7, -20],\n [22, 4, 15, 13, -22, 12, -11, 12, -5, 14],\n [0, 10, -9, 21, -22, 4, 1, -21, -11, -10],\n [4, -3, 14, 11, -17, -15, -2, 16, -2, 22],\n [-17, 18, 21, 7, -13, -12, -22, -13, 2, -7],\n [-4, -13, -9, -20, -19, 17, 10, -3, -8, -16],\n [21, -20, 4, 14, 6, 3, 4, 2, 17, 20],\n [7, 21, -3, -16, 6, 11, 3, 4, 21, -14],\n [-1, -11, -17, -17, 4, -4, -17, -6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "370", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -2, -13, 20, -15, -9, 8, -5, 7, -5],\n [2, 14, 2, 7, 7, 13, -12, 16, 4, -7],\n [15, 9, 6, -13, 7, -12, -8, 21, 0, 0],\n [-16, -9, -14, 5, -17, 20, 22, -1, -5, 21],\n [15, -1, -14, -5, -2, -8, -14, 19, -21, -9],\n [-2, 20, 22, 11, -16, -8, 16, -11, -16, -18],\n [16, 0, 5, 11, 2, -21, -14, 11, 9, -11],\n [-4, 15, -13, -13, 12, 18, 14, 9, -16, -13],\n [20, 15, 4, 9, -16, 3, -1, -11, 1, 6],\n [9, -7, 3, -17, -22, -10, 15, -17, 15, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "342", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -3, 16, 4, -20, 1, -8, 11, 9, -2],\n [-22, 10, -12, -20, -1, -13, 21, 15, 1, -16],\n [13, -22, -22, 3, -6, -12, -20, -13, -21, 9],\n [-7, 3, 17, 16, -13, 13, 7, -14, -18, -16],\n [13, -22, 4, -11, -7, -15, 2, -10, 18, -13],\n [17, 10, 12, 14, 16, 5, -7, -15, 10, 12],\n [15, -11, -8, -6, 4, -2, -2, -6, 4, -11],\n [21, 13, 5, 2, -14, 14, 0, -12, -22, -7],\n [-10, -3, -7, -7, 12, 9, 0, 2, 20, 5],\n [22, -21, -20, 8, 10, 10, 12, 13, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[21, -12, -17, 2, 11, 12, -2, -5, -15, 11],\n [-9, -4, -3, -19, 15, 9, 3, 5, -11, -13],\n [18, 12, 10, -9, 17, 0, -5, 21, -11, 19],\n [13, 2, 14, 17, -1, -17, -7, 0, -14, 20],\n [12, 6, -9, -18, -2, -17, -22, 8, 22, 18],\n [5, -20, 15, 0, 17, -19, -17, -11, -11, -16],\n [5, 3, -16, -20, -10, 18, -12, 16, 0, -22],\n [11, 8, 10, 13, 13, -9, 14, 9, 5, -22],\n [-16, -7, 9, 1, -9, -8, -22, 5, -4, -16],\n [-5, -10, -5, -19, -19, 4, -7, -9, -9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[22, -9, 19, 22, -17, 20, 15, 4, -12, 8],\n [-20, -22, -7, 21, 4, -20, -15, -7, -21, 6],\n [-7, 6, 8, 19, -12, 9, 1, -4, 9, -13],\n [9, 0, 10, 7, 7, -16, -7, 20, -22, 7],\n [11, 11, 15, 8, -15, -3, 6, 8, -2, 3],\n [8, -3, -1, 17, 3, -6, 2, 14, 4, -20],\n [1, 2, -13, 13, 19, -5, 22, -6, -9, -4],\n [-5, 0, -15, -7, 2, 20, 9, -4, -5, 9],\n [17, -8, -2, -12, 6, 9, -17, -4, -7, -11],\n [-8, -12, 16, -13, 14, 1, 13, -22, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[15, 2, 14, 12, -1, -16, -12, -13, -9, 12],\n [13, -17, -18, 19, -16, -8, -2, -5, -22, -19],\n [-12, -13, 22, -4, 19, 7, 18, 18, -3, 4],\n [-11, -9, 11, 19, 15, -21, 9, -5, -2, -12],\n [7, -4, 17, 7, 12, -19, -2, -18, 13, 4],\n [-16, 8, -3, 2, 15, 2, -6, 14, -8, -13],\n [11, 21, 20, -16, 16, 2, 16, 21, 5, 19],\n [4, 14, 16, 15, 5, 11, 6, 22, -15, -10],\n [14, -20, -9, 9, 0, 0, -10, 18, 16, -2],\n [20, 8, -16, 13, -4, -1, 1, 1, -2, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-10, -17, 5, 9, -10, 11, 9, -9, 9, 22],\n [-18, 12, -19, -9, -5, -12, -4, -21, 11, -20],\n [6, 0, -22, 19, -17, -6, -4, 21, -21, -8],\n [0, -4, 10, -17, -4, 7, -1, -20, -18, 7],\n [-20, 16, 16, 5, -22, -1, 22, 22, 16, -6],\n [19, 5, 7, 17, -15, 4, 18, 22, 2, -10],\n [11, 16, -16, -1, 10, 15, 8, 22, 10, -1],\n [4, 4, -2, 12, -13, 5, 17, 14, 18, 10],\n [-15, 14, 18, 10, -4, 7, -9, -9, 13, -16],\n [20, 11, 9, 19, 10, -9, 2, 5, 19, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[7, 8, 1, -19, -9, -14, 13, -17, 1, 3],\n [11, -22, 0, -6, 13, 14, 22, -3, 3, -12],\n [-3, -22, 21, -10, 13, 21, 15, -10, -9, -11],\n [11, 4, -11, 15, 13, -22, 3, 17, 17, -2],\n [9, 2, -11, 2, 3, 13, -7, -9, 11, 1],\n [-15, 4, 16, -10, 6, 8, 20, -4, -13, 20],\n [17, 11, 20, -22, -4, -22, 1, 2, -19, 1],\n [16, -3, 10, 5, 20, 22, 12, 1, 17, 21],\n [-21, 0, 10, -9, -8, 9, 0, -19, -3, 8],\n [-16, -22, -18, -9, 7, 15, 0, -16, 21, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-7, -14, 16, 11, 8, 22, -16, -21, -17, 21],\n [11, -6, 3, -11, -3, 18, 12, 12, 6, 15],\n [8, 17, -10, 3, -1, -15, 17, -16, -18, -22],\n [22, 17, -12, 9, -16, 6, 7, -2, 16, 21],\n [20, 18, 16, -3, -1, 6, -19, -20, -14, -18],\n [-20, 2, 9, 10, -5, 22, 13, 18, 6, 16],\n [22, -21, -12, 8, -19, 6, -20, -21, 21, 13],\n [-9, -19, 21, 7, -4, -4, 21, 8, -8, 6],\n [-20, -4, -1, -3, -16, -19, -22, 18, -16, -1],\n [14, 7, -14, 4, 15, 0, -11, -10, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "384", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-7, 11, -14, 19, 4, -8, 12, 11, 17, 7],\n [0, -14, 9, 12, 9, 22, -7, 9, 2, 7],\n [14, 14, 12, 22, -15, 17, 13, 2, -5, 16],\n [-13, -22, -19, 3, -12, -8, 9, -8, 5, 0],\n [-20, 9, -3, -9, 12, 17, 19, -14, 1, 18],\n [-19, -11, 1, -22, -9, 8, -13, 10, 13, 19],\n [12, -5, 2, -11, 5, -14, 1, -3, 3, -18],\n [4, 5, 14, 17, -16, -4, -1, -5, -8, 10],\n [16, -18, 17, 14, -18, 14, 20, -16, -21, 7],\n [-12, 14, 16, 10, -14, -12, -11, -13, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -18, 1, 9, 8, 19, 21, -9, -4, 19],\n [1, 9, -11, -2, 13, 2, -9, -15, 6, 2],\n [0, 13, -11, -11, -5, 13, -4, 12, 4, -20],\n [-10, 15, 18, -4, 20, 12, -8, -7, 12, -18],\n [-16, -2, 18, -22, 2, 7, -4, 1, -8, 12],\n [1, 13, -9, -1, 16, -15, -7, -6, -18, 18],\n [12, 14, -5, -2, 19, -22, -6, -15, 6, -3],\n [14, 16, -18, -13, -17, -16, 12, 4, 19, -2],\n [1, 6, 4, 15, -21, 2, -21, 15, -5, 19],\n [-16, -19, 21, 17, 18, -13, 18, 5, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "342", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[13, -7, 10, -13, -2, 4, -2, 4, 9, -18],\n [12, -1, 13, -13, 11, -17, -9, 14, -4, 9],\n [-3, -2, -8, -6, 21, 22, 1, -2, -8, -12],\n [14, 7, -5, 5, -10, 20, -13, 16, -11, 15],\n [18, 17, 3, 21, -4, 0, 13, 4, -7, -16],\n [-10, -11, 4, 10, 8, -12, -6, 15, -21, -20],\n [11, 9, 1, 1, -10, -1, -4, 7, 16, -2],\n [0, -7, 19, -16, -3, 19, -9, 3, -1, 18],\n [13, 3, -11, 8, 17, -19, 17, 4, -14, -11],\n [6, 5, -7, -15, -10, -9, -8, -14, 21, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 2, 18, 3, 22, 6, -5, 13, -3, 10],\n [-3, -20, 20, 11, -17, 8, 12, 9, 19, -14],\n [4, 1, -1, 7, 13, 3, -21, 19, 21, -16],\n [4, -7, 6, -2, 3, -5, -22, -21, -9, 15],\n [-8, 13, 1, 2, -14, -8, 14, -17, 20, 22],\n [-11, 4, -16, 5, -11, 19, 12, -21, 3, -3],\n [2, -2, -22, 5, 15, -10, 7, -13, 22, -1],\n [6, -18, -15, -12, 3, -4, -4, 7, 13, 19],\n [-14, -16, -5, -14, -17, -17, 22, -1, -6, -8],\n [-14, -17, 0, -6, 9, 9, 14, -20, -7, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-20, 18, -9, -9, 7, 17, 4, -6, 16, -14],\n [13, -13, 6, -19, -2, 14, -21, -8, 5, 2],\n [3, -14, 7, -14, -22, -11, 22, -10, -9, -13],\n [-6, -6, 8, 3, 12, 13, -12, -7, 6, 22],\n [-5, -12, -12, -14, 2, 9, 11, -20, -9, 17],\n [2, -7, 13, -14, -19, 22, -21, 2, -1, -18],\n [-2, -13, 0, 4, 7, -19, -17, 3, -13, -18],\n [16, 14, 17, -22, 11, -15, -2, 8, 0, -12],\n [-7, 4, -16, 1, 9, 12, 8, 6, -19, 12],\n [-12, 11, 16, -8, -9, -2, -16, -6, 19, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-9, 15, 6, -13, -6, 9, -3, -6, -16, 16],\n [21, 7, 15, 17, 18, -13, 9, 3, -6, -22],\n [16, 3, 7, -14, 21, 10, 3, 19, -13, 19],\n [9, 16, 19, 10, 4, 20, 6, -4, -5, 12],\n [5, 15, -13, -20, 19, 6, -7, 13, -22, -5],\n [-19, -18, -2, -19, -3, -4, 12, 22, 1, -3],\n [5, 15, 1, -3, 1, -17, 15, 2, 9, -6],\n [-6, -18, -6, -14, -3, -21, -4, -14, 17, -4],\n [22, -19, -17, 13, -12, -2, 19, 2, 7, -5],\n [2, -2, 0, 7, 21, -5, 10, 22, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 0, -22, -8, 5, 19, -3, 13, 20, -7],\n [-18, 20, -8, -21, 1, -10, 0, -11, 10, 21],\n [22, 2, 12, 12, -22, 20, -19, 8, 5, -12],\n [9, -21, 21, -10, -6, -19, 8, 15, -20, 20],\n [-11, 21, -5, 7, -12, 1, -2, 12, -19, 3],\n [-15, 1, 20, 22, -11, -18, -7, 9, 6, 10],\n [18, -9, 2, -15, 4, 12, -1, -16, 13, -11],\n [-14, 22, 12, 16, -4, 5, 6, -15, 20, 4],\n [-18, 6, 12, 10, 9, -2, -13, 19, -7, -12],\n [-4, -10, -8, 19, 13, 9, -4, -8, 15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-10, -3, -8, -16, -1, 20, -3, -4, 4, -15],\n [-5, -13, 18, 12, -8, 0, -11, 4, -17, 1],\n [-1, -14, -13, -20, -17, 3, 22, -9, 13, 19],\n [-4, 16, 0, -18, 21, -8, 7, 10, 15, -4],\n [-18, -14, -16, 1, 18, -7, 14, -13, -2, -2],\n [-8, -10, -16, 17, -15, 20, 18, 15, -21, 14],\n [-1, -19, -16, -22, -4, 7, -21, -10, 5, -9],\n [-20, -7, 2, -20, 11, -20, 18, 6, 17, -4],\n [-3, -2, -3, 5, 4, 21, 2, -21, 20, 1],\n [10, -4, 3, 18, -20, 4, -9, -3, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "342", "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, -19, -21, -21, 2, 0, -2, 22, 2, 4],\n [-12, -9, -6, -8, 8, 11, 13, 17, 21, -10],\n [-5, -6, 22, 21, 16, 5, 3, -9, 14, -12],\n [9, 1, 8, 17, 18, -15, 16, -15, 8, -4],\n [13, 16, 9, -2, 0, 13, -8, -21, -11, 15],\n [-17, 15, -22, 15, 3, 0, -22, -2, -4, 6],\n [3, 11, -6, -5, 9, -19, 7, 8, -5, -18],\n [9, 6, -11, -8, -8, 12, 12, 20, -9, 16],\n [-5, 15, -1, 15, -12, -20, -9, 21, 2, -9],\n [8, 2, 18, -4, -11, -16, -9, 6, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-9, 0, -15, -10, 13, 21, -22, 14, 3, -19],\n [-7, 2, -4, -3, 3, 9, -20, -16, 9, -18],\n [-2, 7, -3, 6, 1, -22, 20, 2, 4, 2],\n [-2, -6, 5, 9, 21, 11, -1, 19, -4, -15],\n [-21, -18, 5, -19, 13, -22, -8, -10, 8, -6],\n [-17, 1, -10, -2, 1, -1, 6, 1, 21, -11],\n [-3, 19, 11, -8, -19, -9, -22, 10, 20, 6],\n [-13, 13, -9, -1, 10, 5, -16, 13, 13, 18],\n [11, 14, -17, 12, 4, 7, 9, -4, -1, -2],\n [-18, -2, 18, -3, 15, 8, 14, -17, 8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"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, -11, -11, 6, -16, -7, -11, -2],\n [-19, 19, -6, 5, 8, -15, 3, 17, 8, -4],\n [-16, -18, -10, -5, -5, -3, 0, 13, 17, 10],\n [-16, 17, -18, 9, -14, 7, 9, 16, -19, 2],\n [-1, -15, -21, 14, 12, 14, -1, -22, 16, 19],\n [10, -19, -14, -15, -1, 19, -2, 18, 5, 14],\n [-21, -6, 8, 22, -10, 22, -5, 1, 8, 10],\n [8, 4, 13, -2, -18, -12, 11, 11, -20, -17],\n [-3, -19, 14, 16, -16, -6, 15, 13, 11, -17],\n [16, -21, -5, 19, 4, 16, 18, -4, 9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[11, 2, 1, 2, -11, 7, -17, 7, 10, -8],\n [6, -9, 2, 22, -18, -21, -7, 16, 15, -6],\n [8, -22, -17, 8, -17, 13, -15, 6, -14, -1],\n [-13, 1, 17, -21, -3, -6, 10, -9, 9, 14],\n [1, 18, -3, -17, 10, 5, -12, 13, -3, -17],\n [-15, -4, -8, -1, -21, 5, 13, 13, 21, -5],\n [-11, -4, 3, 2, 5, -8, -13, 16, 11, -10],\n [-7, 17, 8, -22, 0, -9, 16, 7, 19, -3],\n [2, -12, 3, -2, -18, -16, -11, -21, 16, -2],\n [9, -18, 4, 8, -11, 13, -2, -4, -20, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, 13, -14, 11, 6, -13, -14, 17, -12, -4],\n [-1, -1, -7, -6, 17, -16, 8, -19, 6, -16],\n [20, 7, -20, 2, 11, 10, 8, 1, 15, -19],\n [-13, 2, 14, 20, -22, -6, -16, -9, -22, -17],\n [16, 20, -13, -2, -20, -4, 5, -21, 4, 21],\n [9, -11, -22, 20, 17, 6, -14, -5, 22, 13],\n [-7, 12, 13, -19, 17, 20, 12, -4, -17, 8],\n [4, -20, 13, 13, -21, 14, -8, 14, 0, 21],\n [-17, 10, -18, -2, 5, -2, 1, 5, -12, -1],\n [11, 14, 18, -6, -8, 6, 11, 18, 20, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[4, 15, -8, -2, -19, -5, -16, -7, 12, -11],\n [-16, 18, -13, -22, -11, 4, 5, -5, -22, 0],\n [16, -6, 22, 19, -22, 15, -19, -8, -2, -2],\n [-1, 21, -9, 12, -19, 12, 9, 5, -11, 7],\n [-14, -4, -7, 7, -22, 22, 0, -11, -18, -3],\n [-20, -21, 20, -3, -21, 17, 12, -19, 13, 17],\n [-17, -9, -8, 14, 10, 21, -4, -11, 20, -14],\n [-4, 9, 5, 5, 8, 13, -10, 19, 10, 19],\n [-5, 6, 22, 16, -15, -1, -22, 8, -3, 13],\n [0, -6, 22, -13, -14, -6, -20, 10, -22, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-21, -7, -14, -9, -22, 12, -5, -22, 20, -18],\n [-12, 15, 1, 16, 22, 9, -7, -20, -15, 9],\n [-1, -6, 4, 22, -20, 3, 12, -10, -6, 7],\n [6, -9, 7, 14, 21, 15, -14, 9, -19, -17],\n [-22, 2, 17, 15, -20, -2, -9, 7, -21, -1],\n [-10, 2, 20, -12, -13, 21, 14, 2, 21, 12],\n [-4, 5, 19, 20, -13, -8, 9, -20, 1, -13],\n [21, 7, 18, 10, 22, 2, 16, 16, 2, 15],\n [-11, -19, 5, -3, -13, 8, -4, -21, -19, -8],\n [15, 10, -5, 17, 9, 9, -10, -7, 10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-9, -21, -10, 6, 20, 19, 11, -6, -20, 7],\n [-19, 8, -18, -21, -19, 21, 15, 4, 4, -8],\n [16, 15, -9, -5, 6, -16, 15, 1, 15, -17],\n [-3, 19, 13, -13, -1, 10, 0, 18, 19, -19],\n [-2, -10, 19, -10, -11, 1, 12, -4, -14, -10],\n [-1, 17, 13, 5, 18, -16, 7, 8, -12, 7],\n [-8, -10, 12, 12, -3, 20, 0, 14, -3, -4],\n [21, -5, -19, -15, 7, -3, -15, -18, 18, 11],\n [17, -16, -1, -14, -12, -11, -15, 9, -6, 3],\n [10, 3, -1, -20, 8, -9, -5, 11, 17, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, -11, 16, 10, 9, -2, -9, -21, -16, -8],\n [8, 5, 18, -15, -16, 13, -13, 16, 7, 22],\n [17, 18, 18, -18, -2, -17, -7, -7, 1, -4],\n [-4, 14, 10, -18, -14, -2, -16, 19, 2, -2],\n [21, -10, -2, -13, 1, 4, 10, 3, 13, -6],\n [-2, 22, -21, -8, 21, -21, -16, 13, 20, 9],\n [-20, -20, 10, 22, 2, 14, 13, 12, -4, 22],\n [-4, 10, -5, 4, 7, 8, 16, -20, -1, -13],\n [-15, 11, 19, -5, -11, 9, -21, -6, -11, -16],\n [-8, -21, 4, 3, 2, -11, -6, -22, 8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, 5, 5, -15, -9, -17, -5, 14, -13, 12],\n [12, -6, 4, 1, -13, -6, 22, 10, 10, -6],\n [-5, 21, 15, -16, 3, -22, -12, -13, 8, 2],\n [-22, 20, -20, -22, -16, 20, -9, 0, -6, -9],\n [-14, -2, 22, -21, 9, -15, 13, 3, 14, -8],\n [11, -2, 0, -14, 17, 3, 20, -1, -10, 2],\n [-16, 4, -8, -11, 22, 10, -2, 2, 17, -1],\n [-9, -15, 1, -20, -11, -1, -7, -16, -5, 22],\n [0, 3, 15, -21, -21, -1, 15, 19, 5, -6],\n [-5, -21, 12, -8, -8, 21, 22, 11, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-10, 15, -15, -7, -3, 3, 12, -6, 3, -5],\n [21, -16, 21, 12, -11, 21, 18, -22, 2, -7],\n [-8, -12, 14, 16, -20, 22, 22, 19, 16, -3],\n [0, -8, -5, 16, 12, 6, -3, 19, -8, 9],\n [-11, -11, 2, 11, -15, 1, 22, -22, 2, 11],\n [-9, 13, -17, 22, -14, -22, -14, 1, 16, -5],\n [16, -5, 18, 5, -21, 14, 18, 13, 1, 12],\n [-17, -6, 7, -15, 19, -13, -7, 15, 3, 8],\n [-15, 12, 11, -13, 17, 21, -11, 18, 4, -4],\n [3, -8, 8, 14, -5, 6, 21, 4, 15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "342", "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, 20, -8, -1, 0, -19, 1, -9, 14],\n [-2, 20, 16, -10, -4, 3, 13, 21, 10, 17],\n [-7, -4, 14, -9, 21, 21, 7, 8, -3, 21],\n [20, -16, 19, 14, -21, -1, -10, 15, 8, -22],\n [20, -10, -6, -19, 20, 8, 10, -9, -2, -1],\n [-18, 14, 9, -20, 18, -10, -12, 19, 15, 1],\n [-14, -10, -1, -5, -13, -11, 7, -4, -4, -13],\n [-22, -16, -12, -19, 13, -2, -1, -13, 0, -18],\n [-11, 7, 10, 14, -5, -19, 4, 0, -17, -16],\n [-4, -8, -1, 9, -8, -17, -17, -17, -11, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "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, -19, -17, 19, 14, 15, -9, -4, -16, -5],\n [21, -15, 5, -2, 12, -13, 5, -4, 21, 12],\n [5, -20, 16, 4, -6, -8, 19, 16, -1, -3],\n [4, 12, -18, -21, 18, 22, -3, -16, 13, -15],\n [4, -17, 1, 13, -18, -3, -3, 18, 17, 11],\n [16, -13, -20, 11, 12, 14, 22, 22, 15, 0],\n [14, -2, 4, -22, -14, -20, 15, 13, 11, 7],\n [8, 7, -7, 6, -17, -9, -13, 1, 13, 1],\n [-16, 14, 17, 15, 2, 20, 11, -22, 5, 18],\n [6, 9, -18, 11, 3, -10, -11, -1, -14, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[13, -13, 14, 9, -19, -19, -10, -7, 20, 3],\n [10, -19, 3, -14, 18, -12, -18, 15, 9, 6],\n [15, 17, 5, 1, -4, -22, -18, 0, -4, -21],\n [-21, -14, -5, -7, 16, -14, 21, 0, 10, 15],\n [11, 3, -6, -9, -10, -1, 20, -5, -3, 7],\n [12, 10, -6, 12, -11, -21, 11, -11, 3, 9],\n [-2, -18, 5, 0, 9, -18, 12, -17, -4, 21],\n [17, -17, -9, -20, -12, 16, 18, 1, 20, 22],\n [-5, 8, -13, 3, 6, -21, 7, 16, -13, -11],\n [-3, 18, -4, -17, 0, -4, 8, 10, -21, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-12, 3, -5, -22, 9, -19, -1, 13, 6, 13],\n [10, 16, -9, 14, 22, -18, -1, -18, 14, 15],\n [11, -8, 14, 4, -22, 6, -15, 10, -16, 6],\n [8, 15, -15, 8, 14, -8, 9, 3, -12, 0],\n [11, 10, -6, 10, -21, -19, -11, 6, 19, 19],\n [20, 16, 19, -4, -21, -16, -1, -12, 10, -3],\n [-18, -19, -9, -20, -5, 4, -19, -20, 4, 5],\n [-1, 19, 6, -7, 12, -4, 7, -8, -18, 8],\n [20, 8, -14, -10, 20, -2, 8, -22, 18, -10],\n [11, 13, -7, -13, 15, 18, 11, 2, -22, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -1, -21, 22, -15, 10, -18, -13, -20, -12],\n [7, 5, -18, -11, 21, 22, 6, 3, 6, 6],\n [-9, 13, 12, -15, -7, 20, -18, -7, 18, -10],\n [-15, 3, -18, -14, 15, -21, -16, 7, -6, 21],\n [8, -22, 5, 7, 8, 1, 8, -12, 19, -7],\n [-14, 7, -11, -7, 10, -17, 22, -22, -10, 14],\n [12, 21, 3, 19, -14, -6, 15, 12, 2, -16],\n [18, 8, 9, -4, -6, -17, 2, 10, -4, -8],\n [12, 9, 15, 13, 9, 9, 17, 13, 11, -13],\n [21, 10, 21, -13, 21, 12, -1, 0, -16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-22, -10, -14, -3, -13, 3, 21, -22, 22, -6],\n [-6, 16, 20, -11, 18, -8, -22, 9, -12, -18],\n [-5, -5, 0, -16, 3, -22, 5, -3, 18, 0],\n [9, 15, 16, -5, 10, 2, 9, 5, -10, -4],\n [-20, 4, -6, 20, 6, 21, 21, 10, 5, -3],\n [22, 11, -7, 16, -21, 5, -6, -3, -5, 5],\n [5, -7, 10, -2, -18, 22, 14, -5, -18, 20],\n [-12, -1, 0, 3, 4, -20, 19, -21, -6, -20],\n [-20, 17, -7, -11, -22, -19, -6, -4, -19, 16],\n [-3, 18, 16, -19, -6, -8, 18, 5, -7, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 9, -6, 2, 16, -6, -8, -5, -3, 0],\n [-18, 16, -11, -6, 7, -4, 9, -7, -21, -11],\n [-20, -15, 14, 1, 2, 2, -9, 13, -8, 9],\n [-21, -2, -19, 6, 6, 0, -20, -2, -7, 21],\n [-3, 12, -18, 3, -16, -7, -6, -21, -11, -10],\n [-18, -7, 5, -15, 5, -15, 6, -5, 21, 20],\n [-7, 3, -1, -8, -10, -1, -2, 1, -22, 6],\n [-22, -22, -14, -2, -9, 5, -5, 10, 20, -21],\n [11, 1, -4, -21, -17, -8, -12, -7, -2, 4],\n [-1, -20, -20, -2, 20, -17, 2, 18, 14, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[16, -3, -22, 12, 20, 3, -2, -13, 22, 6],\n [-20, 20, 18, 20, 18, -10, -14, -7, 5, 5],\n [-12, 21, 7, -12, 6, -11, -15, -13, 12, 13],\n [-10, 4, 17, -21, 5, 11, -2, -17, 16, 3],\n [13, 17, -5, 19, 20, 16, -18, 3, -12, -7],\n [-4, -18, -16, -20, 2, -13, -18, 9, 9, -18],\n [20, -4, -11, 8, -6, -1, 18, -1, 3, 8],\n [20, -17, -11, 20, 4, -6, -13, 22, -18, -19],\n [16, -8, -21, -15, -7, -3, 1, 12, -6, -18],\n [-9, -9, 20, 8, -3, -10, -14, 11, -11, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-7, -22, -7, -17, -3, -17, 12, 18, -20, -2],\n [-16, -9, 7, -1, -9, 2, -20, -18, -18, 19],\n [-14, 18, 15, 14, -19, -3, -2, 1, -16, -15],\n [-12, -14, -17, 17, -6, -10, 22, -6, -21, 7],\n [9, 13, -16, -7, -4, -8, -9, 22, -16, 10],\n [11, 1, 12, -2, 1, 14, -7, -6, 6, -5],\n [-12, -20, 19, -5, -7, 18, -22, 20, 20, 4],\n [8, 22, 5, 17, 4, -14, 15, 13, 18, 4],\n [3, 4, -19, 15, -11, -8, 7, -9, -15, 5],\n [8, -21, -8, 17, 20, -15, -18, -19, -11, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-19, -13, 6, 5, 6, -4, 20, -10, 11, -3],\n [-5, 13, -22, 3, -20, 21, -20, -2, -5, 8],\n [13, 21, 8, -15, 2, -3, -12, 17, -22, -2],\n [-6, 5, -5, 6, -13, -14, 11, -3, 8, -20],\n [-22, 10, -15, -5, 7, 10, -1, -6, 19, -14],\n [-1, -13, 10, 16, -20, -6, -14, 17, 13, -4],\n [11, -21, 22, 4, -4, 10, 3, 11, 5, -7],\n [-1, 5, -9, -17, -12, -3, 13, -7, -17, -15],\n [22, 13, -19, 11, -3, 1, 22, -20, 5, 7],\n [6, -2, 19, 4, 2, -20, -22, 0, 20, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[8, 2, 12, 20, -22, -8, 16, 1, 11, -5],\n [2, 13, -22, -14, 18, 8, -1, 15, 18, -21],\n [18, 22, -3, 0, -11, -13, 9, -18, 21, 6],\n [10, 0, 13, -10, -21, -12, 5, 2, 13, -5],\n [16, -14, -21, 13, -6, 10, 12, 10, 9, -3],\n [7, -1, 2, 22, 21, -12, 11, 5, 12, -19],\n [-14, 20, -1, 2, -2, 2, 18, -6, -8, 18],\n [-16, 9, -15, -20, 10, 13, -6, -22, 13, 17],\n [-6, 21, 14, 2, 2, -10, -10, -11, 9, 12],\n [5, 21, -3, 5, 8, 1, -12, 19, -7, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 22, 21, -18, -3, 12, 20, -9, 3, 22],\n [20, 19, 1, 8, -5, 16, -1, -2, 11, 2],\n [17, 7, -17, 22, 2, -18, 6, -1, -20, 7],\n [1, 18, -6, 22, -3, 3, -18, -10, 16, -19],\n [22, -6, 17, 12, 8, -7, 11, 9, 10, -15],\n [7, -20, -6, 1, -7, -3, -13, 1, -16, -3],\n [-10, 6, -13, -14, -16, 21, 10, 1, -7, 9],\n [-19, -9, 6, -1, 0, 3, 3, 21, -1, 21],\n [-20, 19, -6, -9, 22, 7, -10, 3, 17, 9],\n [11, 0, 11, 21, -11, 0, 5, -4, 11, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[11, 19, -7, -16, 4, -3, 12, -6, 5, -15],\n [-19, 10, -1, 8, -22, 18, -9, -16, -15, -15],\n [1, -22, 12, 18, -15, -18, 9, -22, -21, 19],\n [-8, 19, -14, -11, -13, 1, 18, -4, -6, -21],\n [-13, -18, 16, -17, -21, -15, -19, 8, 13, -15],\n [8, -6, 17, -9, -15, 2, -9, 0, 20, 18],\n [-6, -11, -3, 11, -12, 4, -14, -5, 15, 13],\n [5, -3, 19, 6, -19, -8, 18, 21, 5, 17],\n [1, 14, -7, -1, -6, -22, 8, 2, -11, -3],\n [-4, -18, -8, 18, 2, 12, 21, -20, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-7, -8, -18, 19, 19, -10, 5, -13, -7, -21],\n [13, 2, -18, 5, -6, -21, -8, 15, 6, 0],\n [-5, -9, 9, 21, -17, 5, -5, 12, 15, -19],\n [8, -12, -12, 6, -4, -6, -19, 21, -19, -11],\n [-16, -2, 10, 14, -11, -16, -8, 14, -14, 10],\n [15, -7, 8, -8, -21, -10, -18, 10, 9, 19],\n [22, -2, -21, 13, 10, -12, 18, 0, 15, 10],\n [17, -15, 13, 13, 10, 6, 8, 7, -15, 3],\n [0, 20, 3, 19, 15, 16, -21, 3, -5, 4],\n [-6, 22, -8, 20, -16, -6, -4, 4, 17, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, -7, 7, -9, 18, -5, -1, -7, -7, 3],\n [20, -17, -16, -14, 21, 3, -21, 13, -20, -2],\n [21, -20, -14, -11, -15, 14, -2, 14, 17, -20],\n [18, -2, 3, 1, 11, 9, 4, 7, -19, -21],\n [0, 18, -19, 14, -12, 13, 13, -8, 14, -20],\n [7, 0, 10, -22, -22, -20, -14, 9, -10, 22],\n [8, -2, 0, -10, 3, 2, -15, 17, 7, -18],\n [1, -13, -4, 12, -1, 16, 15, -16, 16, -3],\n [17, 9, -21, -8, -13, -2, -8, 11, 12, -18],\n [-4, -16, 21, 19, 19, 13, -5, -17, -19, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-9, 18, 10, -2, -10, -21, -8, -7, 12, 22],\n [-3, -22, -20, -6, -6, 18, -3, -3, -19, -12],\n [-8, 22, 4, 1, -3, 21, -8, -17, -5, -1],\n [-2, 1, -6, -12, -5, 12, 8, 5, 1, 13],\n [22, 1, 10, 7, 14, -10, -7, 20, -14, -10],\n [-16, 12, 21, 3, -14, 12, 1, 10, -2, -1],\n [16, -4, 21, 22, 9, -18, -11, 17, -17, -5],\n [-16, -4, -8, 19, -14, -3, -3, -19, -13, 19],\n [17, -22, 12, 1, 21, -16, -1, 0, -22, 1],\n [-3, 9, 8, 10, 13, -5, 14, 10, 10, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, -14, 19, 8, -16, -8, -19, 16, -15, 1],\n [-15, -18, 0, 20, 11, -8, -4, 2, 16, -19],\n [-15, 6, 19, -10, 15, 13, 14, 19, 22, 20],\n [8, -4, 14, 2, 14, -22, -2, 18, 16, 18],\n [3, 19, -20, 18, -18, 20, 6, 10, -21, -5],\n [-9, 17, 7, 6, 6, -4, 3, 17, -14, 21],\n [-10, 15, 8, -9, 8, -8, 11, -13, -2, 16],\n [2, 14, 17, -3, 22, -16, -5, 18, 21, 3],\n [-6, 19, -16, 5, -2, 14, 0, -13, -6, 15],\n [-22, -12, 10, 8, 21, 1, -3, -18, 19, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[19, -16, 4, -5, 15, 8, -14, -21, 21, 14],\n [22, 6, 11, -8, -14, -7, -21, -22, -14, -3],\n [-21, -22, -13, 0, -4, -5, 1, -1, -3, -12],\n [-14, -8, -7, -10, -17, 2, -8, -5, 20, 10],\n [-9, 11, -21, -3, 19, -7, -20, 7, 0, 16],\n [0, -20, -10, 17, 6, 0, 17, -6, -2, 6],\n [14, -18, -2, -21, 0, -12, -8, 0, -16, 20],\n [11, 15, 18, 21, -17, -7, -21, 9, 20, 15],\n [5, 18, -14, 2, 3, 22, 3, -18, -6, 3],\n [3, 20, -14, 0, 1, 18, -14, -13, -17, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-22, -17, 15, 6, 21, -20, 22, 1, 19, -14],\n [-6, 20, 15, 19, -9, 13, 22, 10, -3, 11],\n [-20, -3, -20, -17, 6, 16, 20, 8, 16, -2],\n [21, -22, 10, -13, 3, -20, -9, -15, 9, 18],\n [13, 4, 10, -2, 3, -9, 20, 13, 5, 5],\n [-2, 18, 6, 15, 11, -22, -3, 3, 4, 0],\n [-16, -1, 14, 12, -19, 6, 14, 13, -20, -21],\n [-18, -5, 11, -8, 17, 21, 18, -22, -1, 2],\n [-6, 10, -6, 15, -18, 14, 20, 20, -12, -11],\n [21, 11, 12, 16, -7, 1, 8, -9, 9, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-10, 15, -6, 21, 13, 19, -5, -4, -16, 7],\n [-11, -12, 6, -20, 11, 11, 8, -1, -21, 4],\n [13, 9, 12, -6, 11, 3, -13, 16, -14, 2],\n [-3, -8, 17, 4, -12, -7, 7, -1, 1, 1],\n [13, -5, -3, -15, -8, -10, 13, -9, 1, 14],\n [1, -5, 9, 12, -3, 19, 9, 14, 14, 10],\n [-22, 5, 4, -6, -8, -9, 8, 11, -20, -11],\n [3, 1, 11, -15, -11, -14, 3, 15, 20, -4],\n [-2, -10, 12, -20, 2, 9, -2, -9, 8, -15],\n [-16, 13, 12, -4, -21, -18, 21, -21, -5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-7, -11, 21, 13, -1, 5, 17, 20, -1, -19],\n [-11, -2, 4, 0, 19, 4, 18, -7, 9, 13],\n [-6, -5, 4, -16, 18, 15, -3, 12, 10, 3],\n [1, 1, 8, 4, -14, -21, -17, 8, 2, -7],\n [22, -17, 0, -18, -6, -14, 3, -10, -16, 17],\n [-5, 14, 22, 1, 9, -16, -3, 22, 11, -4],\n [-9, 9, -14, 13, 3, -3, 6, -7, 8, 1],\n [7, -15, 3, -8, -13, 13, 16, 1, -15, -22],\n [-13, 0, 15, -13, 10, 8, 15, -10, 12, 21],\n [9, -1, -16, -17, 18, -7, -11, -14, 17, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-20, 13, 20, -13, -15, -14, -10, -4, 0, 20],\n [1, -20, 10, 0, -9, -4, 10, 0, 4, -11],\n [-16, 13, -5, -7, -9, -2, 20, 4, 2, 15],\n [-8, -13, 7, 21, -14, 5, -5, -12, 15, -21],\n [-1, 0, -3, 22, 6, 3, 18, -11, 6, -4],\n [11, 4, 7, 14, 8, 5, 2, -17, -16, -17],\n [12, 2, -2, -6, 18, 3, 18, -6, -16, 2],\n [11, 3, -17, -13, -6, -9, -20, -7, -18, 0],\n [4, -18, 14, 15, -5, -11, -2, -16, -6, 19],\n [-14, 18, 1, -12, 2, 14, -16, -6, 18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "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, 22, -14, 22, -15, 22, 4, 0, -13, -21],\n [21, -16, -21, -7, -17, -7, 2, 22, -13, -14],\n [9, 9, -21, -2, -20, 11, 6, 19, -3, 0],\n [14, -15, 21, 13, -9, 0, 4, -8, 12, -1],\n [13, -8, 9, 18, -5, 22, 8, 18, 13, 2],\n [22, -13, 17, -9, 3, -4, 7, 16, -11, 8],\n [22, -5, -21, -9, -3, 16, -3, 11, 11, 14],\n [-20, 12, 10, -4, 8, 21, -1, 4, 15, 5],\n [-2, -3, 15, -10, 6, -2, 19, 10, 9, 5],\n [-9, 19, -1, 14, 11, -6, 10, 10, 15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[16, -16, 2, 7, 18, 10, 16, 5, -5, -13],\n [-21, 20, 20, -9, -10, -22, 9, 2, -13, -8],\n [6, -6, 19, 17, 0, -16, 13, -17, -21, 22],\n [9, 21, -18, -4, -21, 20, 0, 17, -19, -19],\n [-12, 18, -3, -9, 12, 22, -9, -20, -8, -2],\n [-21, -2, -13, 4, -4, -11, -7, -15, 14, 2],\n [1, 17, -5, -2, -15, -4, 7, 4, 13, 13],\n [3, -3, 18, -9, 10, -14, 0, 22, 7, 19],\n [5, 8, 3, 13, 13, -12, -11, 22, -21, 17],\n [-19, 9, 18, 11, -18, -18, -19, 18, -11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, 11, 22, 5, -16, 17, -12, 21, 9, 9],\n [8, -3, -17, -5, -2, -20, 18, 5, 5, 9],\n [16, 1, -16, -4, -22, 10, 10, -12, 0, 22],\n [5, -6, -13, -15, -14, -4, -15, -18, -9, 22],\n [10, 20, 21, 15, -11, -20, 17, 6, -1, 11],\n [-17, 12, 16, -7, 8, 21, -8, -22, 21, -3],\n [0, -3, 9, 2, -15, 10, 22, 7, -20, 1],\n [-11, 8, -16, 17, -6, -13, -8, -2, -2, 6],\n [19, 18, -22, -2, -18, -8, 3, -12, -2, -17],\n [-19, 22, -2, -6, 8, 21, 0, 9, 21, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[11, -17, 15, -1, 10, -12, 0, 21, 13, 5],\n [-4, 20, 20, -10, -10, -15, 20, -10, 12, 4],\n [-12, -2, -15, 19, 3, 7, -1, 16, -13, 3],\n [4, -1, -10, 16, -16, 20, 19, -11, -10, -11],\n [-11, 15, -20, -15, 8, -10, -15, 14, 1, 5],\n [-19, -7, -5, -19, 20, 17, 10, 22, 4, 13],\n [-19, 13, -10, -9, 19, 14, -17, -9, 20, -20],\n [2, 11, -17, 17, -22, -15, -6, -10, -4, 18],\n [12, 10, 22, 22, 21, 10, 19, 16, 15, 15],\n [-14, 14, -22, 13, 19, 15, -21, -13, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "375", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-12, 13, 19, 15, 12, -10, -4, 12, 7, -5],\n [-11, -11, -2, -11, 5, 6, 16, 18, 21, -19],\n [8, 1, 19, -5, 19, 3, 21, -3, -15, 10],\n [-19, 15, -1, 13, 8, -15, -14, -5, 12, 1],\n [-6, -22, 16, 19, -8, -10, 0, 6, 8, 14],\n [5, 9, -16, -9, -9, 9, -14, -17, -8, 7],\n [7, -7, 0, 8, -11, -2, -20, -20, 15, -1],\n [-2, 21, -7, -5, -19, -3, 22, -10, 8, -21],\n [7, 8, 5, -14, -12, 12, 21, 14, -6, 3],\n [-19, 10, -6, 19, -15, 3, 20, -3, 19, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[20, 19, 10, 17, -6, -14, -3, -15, 18, -17],\n [-14, -12, -18, -15, 12, 2, 13, 16, 21, -17],\n [1, -2, 13, -5, -22, 6, -6, -18, -17, 22],\n [-15, 2, -4, 16, -14, 5, 8, -22, 18, -13],\n [-1, -22, -10, -9, 0, 16, 5, 6, 17, 10],\n [-21, 20, 10, 1, -11, 17, 5, 12, -13, 21],\n [11, -18, 18, -5, -17, -12, -22, 0, -19, -16],\n [18, -6, -12, 4, -11, 11, -15, 0, 3, 11],\n [9, -17, -22, -19, 2, -15, 17, -3, -9, 10],\n [-20, -8, 4, -4, -22, 12, 10, -6, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "363", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[16, 3, 4, 1, -6, -12, -1, -15, 19, 9],\n [6, 19, 9, 17, -18, -10, 2, 19, -13, 3],\n [3, -2, 0, 21, -11, 16, 20, 2, -11, 13],\n [9, -5, 19, -3, -21, 10, -6, 13, 7, -14],\n [8, 16, -2, -1, -6, -20, 9, 10, -13, -18],\n [-19, 15, 9, 15, 18, -3, -14, -8, -15, 11],\n [7, -13, -9, 11, -1, -10, 6, 6, -16, 21],\n [-17, 12, 14, -19, -9, -17, -6, 1, -10, -11],\n [6, 1, 11, -9, 4, -18, 17, -14, -7, -10],\n [-8, 13, 2, -7, 21, 21, 8, 14, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 12, 17, -16, 22, 19, 8, -6, 20, -15],\n [0, 21, -5, 19, -11, 7, 13, -8, -5, 2],\n [-10, 1, -6, -22, 14, 4, -3, -5, -14, -13],\n [2, -22, 13, -5, -8, 10, -1, 1, -22, -12],\n [20, 3, 3, -17, 10, -9, 1, 15, 18, -6],\n [-9, -4, -15, 0, 21, -21, -20, -10, -18, -5],\n [-22, 14, -2, 21, -4, 15, 11, -21, -3, 8],\n [-10, -9, 15, -11, -10, 1, 17, 8, -9, 7],\n [4, 13, -17, -17, -8, 1, -10, -16, 22, -2],\n [15, 15, -9, -20, 20, 22, 12, -11, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, -18, 22, -12, 19, 21, -17, -18, -1, -22],\n [-3, 1, -3, 6, 19, 1, -15, 11, -1, 16],\n [10, 7, -17, -10, 21, -4, 3, -6, 14, 4],\n [1, -9, -20, -18, -9, -15, 20, 2, -8, 22],\n [14, 22, -20, 22, -12, -14, -19, -8, 4, 8],\n [-7, 9, 11, -17, 21, -18, 1, -4, 7, -11],\n [-18, 5, 16, 11, -11, 0, -18, 17, 14, -7],\n [-14, 10, 14, 10, -22, 14, -14, -5, 15, -2],\n [21, -9, 16, 16, -17, -20, -5, 14, -3, 6],\n [13, -7, -19, 22, -9, -6, 12, 12, 22, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-13, 6, -11, -14, 3, -2, -22, 13, -4, -17],\n [-5, 14, -15, -12, -18, -2, 17, 20, -2, -3],\n [19, -14, -21, -19, 3, -11, -4, -4, -4, 6],\n [16, 22, 11, -15, -17, 9, 5, -12, 5, 9],\n [18, -15, -3, 1, 4, -12, 0, -1, -18, 11],\n [8, 14, 3, 0, 20, 15, 15, 9, -18, 2],\n [10, -16, -7, 6, -8, -3, -1, -13, -15, 9],\n [5, -14, 8, 0, -4, 9, -13, -3, 12, 8],\n [-12, 20, 17, -13, -14, 19, -13, 14, 14, -16],\n [-3, -3, -15, -6, 15, 2, -10, 22, -10, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[14, 19, 19, -12, -3, -14, 22, 22, 6, 11],\n [-18, 8, 3, 14, 21, -3, -15, -17, -5, -15],\n [2, -21, 5, 19, 2, -3, -17, 14, -7, 12],\n [13, -22, -9, -9, 1, -4, 15, 21, -5, -14],\n [-10, 22, -4, -13, 15, -20, 18, -6, 0, 4],\n [-14, -18, -4, 6, -8, 19, 13, -11, -9, -8],\n [8, -18, 21, -20, 7, -11, -8, 15, 5, 0],\n [-8, -12, 7, -11, -4, 9, -22, -7, -12, 8],\n [10, 13, 7, 15, -19, 2, 11, -6, 10, 7],\n [-10, -11, 9, 0, 6, 11, -4, -11, -19, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "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, 7, 11, 10, 8, 8, -10, 1, -18],\n [-22, 11, -14, -15, 20, 13, 6, 12, -18, -13],\n [15, -13, -12, -15, -19, -5, -3, -20, 21, -8],\n [-15, -17, 13, -3, 9, -17, -7, -21, -5, 22],\n [3, -3, -7, -2, 22, -9, -5, -15, -18, 1],\n [18, 6, -14, 19, -5, -5, 5, 14, -13, -3],\n [15, 18, 0, 20, -3, 0, -18, 4, -14, 20],\n [18, 13, 17, 14, -20, 13, 22, 12, 13, 6],\n [10, 3, -15, -14, -1, -18, 21, 18, 13, 9],\n [7, 21, 22, 20, -6, 7, -14, -19, -11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "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, -16, 16, 21, 19, -15, -14, -17],\n [-4, -1, -3, -3, 4, 4, -16, 1, -15, -20],\n [-12, 13, -21, -22, -16, 1, -11, -15, -10, -17],\n [16, 1, 1, 15, 21, -16, -13, 7, 16, 1],\n [4, 7, -8, -21, -15, -6, -10, -5, -2, 13],\n [-11, 20, -21, -3, 0, -2, 8, -7, -10, -19],\n [-21, -22, 3, 7, 15, -3, 2, -4, 4, -13],\n [18, -6, -21, -6, -16, -7, 4, -22, -1, -1],\n [4, -7, 13, -7, 1, 12, 10, -6, -18, 12],\n [-4, 20, 11, 9, 2, -1, 16, 4, 10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "324", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[7, 3, -8, 13, 22, -11, 18, 22, 20, -11],\n [-19, -20, 14, 15, 9, 3, -19, -22, -18, -21],\n [-12, -14, -15, 16, -8, -14, 19, 7, 6, 2],\n [-1, 11, -1, 7, -13, -18, -18, -21, 7, -1],\n [-10, 16, 2, 4, 4, -2, 8, -8, 15, 16],\n [13, 13, -22, -12, -18, 11, 14, -18, -3, 22],\n [21, 19, -10, -14, -18, 15, 9, 7, 5, 14],\n [5, 20, -17, 18, 21, 6, -19, -5, -8, 2],\n [-19, -9, -6, 11, -4, 6, -1, -9, 13, -21],\n [22, -16, 5, -15, 6, -13, -2, 12, -19, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[15, 2, -3, -16, -16, 9, 9, -1, 2, -17],\n [4, -5, -11, 5, -4, 20, -6, 12, -8, -18],\n [13, 10, -2, 12, 19, 4, 22, 7, 16, 7],\n [22, -2, 3, 1, -1, 14, 20, 3, -1, 10],\n [1, -18, 1, 12, -1, 10, -6, -11, 7, 3],\n [-10, -17, -20, -12, 20, -13, -12, -7, -3, 19],\n [21, -4, -14, 13, -8, 0, -2, 16, -18, -1],\n [8, -8, 5, 15, -8, -4, 12, -5, -13, -8],\n [1, -3, 14, -12, -14, -18, -12, 16, 4, -21],\n [-3, -2, 7, -22, 12, 3, 9, -14, 17, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-7, -11, 13, 14, 4, -16, 7, 1, 7, -3],\n [17, 22, 5, -19, -11, -20, 14, -19, -8, 5],\n [14, -14, -9, 9, -20, -5, -9, 2, 16, 3],\n [-17, 3, 18, -22, -2, -9, -15, 2, -5, -8],\n [19, -3, -7, -16, 6, 8, 6, -6, -18, -5],\n [-9, 8, -5, 2, -12, 3, -18, -7, -15, -10],\n [9, 4, 3, -14, -16, -15, -21, -5, 13, 1],\n [11, 19, 15, -12, -13, 6, 17, -17, -13, 7],\n [5, 6, 2, 13, 4, 11, 11, 9, 21, -19],\n [11, -7, -12, -8, 15, 7, 4, -7, -22, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, 20, -9, 11, -19, -9, -7, -8, 11, -10],\n [-6, 5, -13, -6, -15, -21, -22, -18, 12, -1],\n [20, -7, -14, 13, -14, -9, -13, -1, -7, 18],\n [-20, 5, 7, 6, -22, 5, -1, 9, -12, 3],\n [8, -3, -3, 10, -18, 18, -20, 21, 11, 8],\n [19, -16, 7, -5, -7, -10, 10, -16, 7, -12],\n [-17, -2, 9, -18, 19, 6, 12, -11, 14, 21],\n [-1, -12, 0, 22, -13, 19, 1, -7, -11, 9],\n [1, -19, 19, 10, -5, -6, -2, -22, 21, 2],\n [8, 20, -3, 3, -4, 7, 2, 13, -5, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[4, 10, -17, -16, -22, 15, 12, 0, -7, 11],\n [11, 8, 20, 8, -12, -15, 1, 0, 9, -8],\n [5, -3, -9, 3, 14, -21, 11, 11, 11, -14],\n [21, -20, 7, -4, 8, -7, 20, 1, -8, -1],\n [9, -12, 6, 19, 1, -4, -18, 18, 15, -22],\n [7, -11, -19, -8, -6, -11, -22, -10, 7, -13],\n [13, -17, -14, -21, -17, -12, 3, 5, -10, 15],\n [-11, -4, -5, -4, 5, -11, 9, -10, 0, 13],\n [7, -1, 15, 22, 19, -20, -14, -8, 7, 3],\n [7, -18, 8, -1, 18, -8, 22, 12, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"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, -9, -1, 1, -10, -15, 19, -21, 19, 4],\n [11, 6, 3, 0, 13, -14, -2, 19, 13, -20],\n [-16, 0, 9, 0, -7, -18, -10, -13, -21, -7],\n [-22, -17, -4, 10, 5, -18, -11, 7, -6, -4],\n [17, 19, 2, 12, -14, 9, 16, 15, -8, 22],\n [14, 3, 8, 7, -21, -16, 7, 10, 16, 15],\n [-3, -4, -14, -1, 9, 7, -17, -6, 14, -8],\n [-16, -9, -3, 7, -5, -1, 2, 1, 8, -5],\n [11, -5, -9, -19, -16, -16, -22, 17, 1, 9],\n [-13, -14, 16, -20, 21, 12, -18, -16, -11, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, -6, -9, 12, -22, -1, 5, 0, -5, 22],\n [21, 14, -20, -9, 16, -16, -6, -17, -4, -8],\n [16, -18, -8, 22, 3, 16, 22, -10, 8, -10],\n [0, 17, 9, 14, -19, -6, -3, -12, 19, 10],\n [16, -17, 16, 15, -5, -21, 18, 15, -6, 1],\n [7, 20, 1, -19, -16, -8, 7, 6, 21, 22],\n [-10, 17, 16, 6, 3, 13, 12, -4, -21, -9],\n [-7, 13, 17, 18, 8, 12, -1, -2, 5, -6],\n [-5, 9, 0, -17, 6, -17, 10, 9, -6, -19],\n [8, -1, 4, -2, -3, 11, 0, 21, -7, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-7, -16, -9, -20, 10, 13, 16, 6, 16, -19],\n [16, 17, 18, -1, -8, -19, -5, 21, 0, 15],\n [-19, -19, -5, -22, 9, -2, 15, 3, 18, -2],\n [20, 6, 18, 20, 9, -19, -10, 12, 4, -22],\n [16, -9, 14, 7, -9, -12, 8, 5, 4, -20],\n [-17, 16, -4, 18, 11, 5, -11, 16, -13, 2],\n [0, 3, -4, 15, -3, 22, 21, -5, -12, 2],\n [20, -22, 9, 10, -16, 8, 3, -16, 13, 1],\n [-18, -1, 21, 13, -20, 14, 15, -17, 2, 0],\n [-11, 5, 21, 17, 9, 2, 11, 7, 14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[12, 14, 18, -17, -4, -1, 9, 4, -7, 3],\n [16, -19, -7, -4, 5, -6, 22, -21, -21, 1],\n [4, -19, 13, -3, -11, 5, 6, 10, -5, -11],\n [-13, 1, -6, 20, 9, 2, -16, -3, 6, -4],\n [-12, 10, -8, 8, -10, -4, -17, 5, -1, 5],\n [-7, 10, 18, 22, 3, 0, -22, 6, -15, 19],\n [16, -20, -10, -3, 20, -18, 22, -11, -6, -9],\n [3, 7, 19, 22, 9, 7, -11, 13, -4, 21],\n [2, 10, 19, -2, -21, 14, -2, 3, 9, 4],\n [-6, -19, 16, -8, 10, -9, 3, -21, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-21, -21, -6, -5, -19, -6, 10, 0, -10, -16],\n [18, -22, 17, 19, 8, 13, 2, 22, 18, 17],\n [7, 15, -2, -4, -7, 10, -17, 19, 14, -15],\n [-22, -10, 3, -7, 16, 5, 0, -16, 1, -15],\n [22, -22, -19, 20, 18, -4, -1, 13, -22, -4],\n [6, -4, 20, -17, 2, 16, 0, -22, -8, 2],\n [-19, 22, 21, -22, 17, -2, 20, -13, -21, -6],\n [-10, 4, 18, 5, -13, -13, -14, 11, 16, -19],\n [22, -19, -19, 18, -12, -22, 22, -2, 2, -14],\n [2, -5, -16, 3, -5, -22, -14, -13, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 13, 9, -4, -15, 12, -1, -19, 6, 8],\n [-15, -11, -18, 7, 12, 14, -19, 20, -2, -7],\n [-5, 8, 15, 9, 10, -4, -3, -13, 3, -5],\n [22, 22, -8, 13, -5, 8, -8, 15, 6, 19],\n [-8, -22, 14, 18, 0, -12, 15, -7, 7, 6],\n [18, -20, 17, -6, 3, -14, -6, 14, 8, 8],\n [-12, 15, -1, -20, 5, 9, -19, 17, 15, -12],\n [-22, -7, 11, 22, 9, 21, 10, -12, 13, -10],\n [-3, 2, -17, 14, 3, -19, 22, 3, -5, -10],\n [-15, 10, 20, -7, 19, 16, 8, 17, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-13, 13, 8, 21, 9, -2, -7, 6, 22, -7],\n [-8, -15, -8, -2, -2, -16, -4, -1, 15, -10],\n [3, 21, -1, -16, 12, -20, 12, -7, 22, -7],\n [-21, 15, -6, 15, 1, -1, 0, 21, -4, 21],\n [-1, -6, -21, -9, 5, -10, 15, -6, -14, 17],\n [-9, -21, 19, -2, 12, 7, -6, 16, 2, 21],\n [16, 12, -17, -20, 13, -22, 11, -22, 3, -5],\n [13, -17, -12, 21, 17, 7, -9, -13, 8, 13],\n [-8, 7, -9, 0, -6, 4, 21, -10, -9, 3],\n [20, -12, 15, -22, 1, -3, -15, -15, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "331", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-10, 13, -4, -10, 18, 3, -14, 11, 8, 19],\n [-16, -14, 17, 3, 10, 10, 17, -19, 5, -19],\n [11, 17, -17, 10, -18, -4, -5, -20, 11, -21],\n [-22, 12, -19, 12, -15, 21, 6, 13, -9, 19],\n [7, -16, -10, -1, 22, -21, -15, -2, -3, -12],\n [11, 21, -18, 7, 10, -11, -18, -22, 12, 2],\n [-19, -14, 21, -20, 7, -3, -13, -3, 17, -20],\n [-12, -8, 5, 21, 12, -16, 10, 19, 15, -4],\n [21, 6, -21, 21, -4, -14, -17, -6, -21, 16],\n [-17, -9, 3, -5, -17, -11, 15, -1, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "376", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-14, 19, 9, -13, 4, -9, -14, -14, 3, 9],\n [18, 12, 3, 18, 22, 19, -20, 7, 6, -3],\n [-19, -9, 22, 16, -2, -16, -17, 17, -17, 2],\n [-19, 14, 2, -5, 11, 2, -1, -9, 14, -12],\n [4, 3, 12, -7, 17, -3, -8, -9, -15, 1],\n [10, -7, 4, 5, 21, -9, -14, -10, -1, 7],\n [9, -7, 2, 0, 14, 5, -20, 0, 10, 16],\n [2, 2, 16, -2, 8, 7, 16, 22, 22, 19],\n [11, 15, -16, 4, -10, 6, 0, -15, -2, -10],\n [3, 20, -13, 6, 4, -19, 19, 8, -6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[14, -3, -13, 21, 11, 16, -12, -11, -13, -10],\n [11, 7, -8, -15, 15, 13, 17, -1, -18, 9],\n [-3, 0, 17, -21, -4, 3, 13, -9, -16, -7],\n [-13, 20, -1, 3, -18, -11, 1, 1, -8, 1],\n [1, 19, 3, 11, -5, 20, 14, -17, 22, 2],\n [-6, -7, 6, -22, 22, 19, 22, -3, 3, -2],\n [4, 13, 12, -7, 6, -16, -16, 11, -18, -15],\n [-15, 20, 6, -13, -22, 15, 5, -16, -6, 1],\n [12, -14, 19, -20, 21, -19, 9, 21, -10, 1],\n [-16, -4, 4, 4, -5, 7, 5, 6, -14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[16, -2, 22, 15, -16, 22, 2, 3, -17, -3],\n [-5, -3, 17, -5, -22, 10, 16, 0, -9, 5],\n [-2, 21, 14, -16, -11, 14, 16, 5, -16, 22],\n [-6, 14, -9, 20, -19, -1, -6, 12, 9, 15],\n [8, 2, -13, -21, 4, -11, -7, -7, -20, 2],\n [-5, 16, 19, 17, 9, -20, -15, -18, -3, 21],\n [2, -17, 5, 0, 1, -13, -13, 10, -14, -5],\n [-20, 10, -13, 4, 12, -5, -16, -16, -1, -13],\n [4, 22, -19, -11, -20, 20, -20, 2, 3, 17],\n [-16, 11, -13, -20, 5, -12, 9, -15, -3, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[18, -10, -12, 11, 21, -20, -8, 10, 20, -13],\n [-20, 18, -9, 10, 10, 13, 0, -22, 4, 9],\n [-2, 21, -3, 4, 13, 18, 9, 16, 6, 0],\n [12, -8, 20, -13, -8, 2, -6, 8, -12, -3],\n [8, -7, 13, 16, -12, -3, 3, 3, 19, -17],\n [22, 12, -15, -16, 14, -7, -14, -12, -2, -16],\n [-11, 17, -2, -18, -17, 20, 3, 6, -20, -12],\n [0, 2, -11, -22, -19, -22, -17, 11, 4, 22],\n [-7, -12, -9, 15, -13, -10, 22, 11, 10, 10],\n [16, -10, -6, -14, -10, -7, 14, 7, 16, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[17, -17, -11, -21, 10, -8, -6, 12, 8, 7],\n [15, -7, 19, 22, 17, -6, -16, -18, 17, 4],\n [-22, -21, -19, -22, 6, -2, 19, 12, 11, 16],\n [-21, 2, -17, -15, 12, -4, -14, 10, -15, 15],\n [9, 0, 11, 0, 9, -22, -16, 20, 1, -21],\n [-5, -4, 19, 13, 5, 12, 9, -10, -17, 6],\n [-13, 17, -13, 11, -3, 10, -12, 1, 10, -1],\n [-11, 7, 9, 21, -4, 22, 17, -21, -9, 10],\n [9, 18, -4, -9, -19, -21, -13, 6, -8, 8],\n [10, 6, -12, 22, 17, -14, 6, 14, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "356", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, -5, -21, -1, 14, -3, -19, 3, -3, -1],\n [20, -3, 6, 8, 0, 21, 15, -7, -4, -12],\n [-11, 13, -10, -21, -12, -22, 18, -13, -20, -15],\n [-7, 13, 20, 17, 16, -3, -15, -13, 14, 9],\n [4, 8, -20, 16, -17, -6, -13, -2, 6, 6],\n [-3, -8, -21, 10, -11, -10, 21, 21, 16, 16],\n [15, 22, -2, 18, -7, 11, 4, 20, -20, -14],\n [21, 11, -4, 15, 3, 0, -5, 22, 17, 18],\n [22, 15, -13, 20, -13, -2, 15, 15, -16, -11],\n [18, 10, 2, 5, 1, 8, -5, 0, -16, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-8, 15, 5, 4, -2, 21, 4, 19, 18, -9],\n [-2, -9, 20, -17, -11, 5, 6, 14, 15, -20],\n [10, -11, -11, -12, 5, 12, 11, -1, 16, 0],\n [-11, -4, 8, -10, -4, 13, -1, 21, 7, -19],\n [-10, -3, 16, -17, 21, -11, -7, 22, -6, -15],\n [10, 21, 16, -11, 3, -4, -10, -13, 11, 8],\n [4, -20, 21, -18, -18, 14, -16, 17, 19, -10],\n [11, 13, 11, -20, -13, 20, 12, 14, -17, -2],\n [22, -18, -20, -3, 7, -11, 12, 9, -4, -8],\n [-13, 3, -17, 3, -21, 9, -20, -4, 13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[7, 14, 22, -3, 11, 21, -6, 19, 0, 18],\n [-14, 4, -6, 18, -6, -21, -8, -12, 14, 18],\n [-14, -9, -15, 20, -11, -16, -20, 3, -20, -19],\n [9, -9, -20, -10, -15, 15, -21, 15, 8, 16],\n [4, -6, 12, 1, -22, 6, 3, 21, 12, 21],\n [1, 10, 3, 14, 16, 3, 15, 15, -12, 6],\n [6, -20, -14, 12, -17, -14, -15, 4, 11, 1],\n [-18, -13, -3, -1, -11, 21, 6, 8, -17, -16],\n [10, -8, -10, 1, 7, 10, -3, -4, -4, 15],\n [1, -18, -1, -1, 5, -6, 8, -16, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-16, 6, 22, -15, -19, 17, -7, -7, -1, -12],\n [18, -12, -18, 19, 15, -11, 17, 2, 22, -10],\n [3, -12, 17, 0, -10, 10, 5, -19, 5, 11],\n [-13, -15, -14, -5, -21, -5, 17, -21, -1, -7],\n [14, 9, -13, 18, 11, -7, 11, 14, 17, 11],\n [21, -10, 14, -11, -8, 7, 8, 6, 11, 9],\n [21, 0, -13, -15, -2, -12, -11, 16, -4, 11],\n [15, 11, 3, 17, -7, -4, 6, 22, 15, 13],\n [-2, -13, 0, 21, 21, -16, 15, -18, -4, 10],\n [1, 20, 0, -1, 13, -2, -5, 15, 4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "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, 16, 7, 20, -9, 11, 9, 8, -21, 16],\n [12, 0, -17, -2, 3, 7, 18, 19, 7, -15],\n [16, 10, -13, -5, 13, 18, -12, 21, -15, -22],\n [-15, -18, -22, -20, 4, 22, 0, 21, 16, 17],\n [-12, 22, -12, 13, 15, 8, 1, -4, 9, 17],\n [15, -6, 12, -11, -8, 16, -10, 7, 19, -4],\n [-14, 5, 21, 20, 2, 17, 18, -19, 14, -16],\n [18, -19, 0, 21, 21, -17, 22, -14, -14, -2],\n [-20, -10, 15, -5, 8, 6, -21, 8, 15, -16],\n [17, -13, -10, -22, 14, 2, 7, -21, 13, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-11, -18, -8, 19, -16, -21, -20, -19, -7, 4],\n [-1, -20, -6, -1, -16, 7, -15, -4, -16, -22],\n [-7, 17, 8, 16, 4, -13, 11, -9, -21, 16],\n [-1, 3, 21, -18, 15, -7, -11, 18, 21, 19],\n [-6, 2, 1, -12, -5, 13, -20, -4, -17, 0],\n [17, -16, 21, -14, -21, 22, -12, -20, 19, 7],\n [-15, 14, -2, -15, -12, 18, 11, 16, -7, -16],\n [-19, 9, 14, -1, -16, -10, -5, 19, 11, -10],\n [11, 6, -18, 8, -12, 15, -19, -16, 0, 8],\n [-6, -13, -1, 7, 6, -6, 20, -2, -1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[17, -1, 4, 0, -19, 3, 16, -6, -20, -6],\n [20, 17, -4, 16, -5, 5, -8, 3, 12, -7],\n [-8, -18, 1, -21, 13, 22, 8, 7, -11, 14],\n [-2, -11, 17, 14, 12, -1, 22, 13, -15, 4],\n [4, 13, -16, -20, -19, 1, -15, 22, -10, -14],\n [-3, -3, -18, -18, 12, -22, 19, -8, -6, -11],\n [13, 20, -8, -9, 4, -1, -14, -2, -20, 8],\n [-10, -21, -9, -16, 6, -19, -19, 1, 19, -2],\n [22, 5, 15, -15, 19, -6, -14, -3, -18, 12],\n [18, 6, -11, 9, 8, 8, -22, 20, -18, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-11, -7, -7, -2, 10, 3, -20, 0, 2, -3],\n [13, 12, 20, 10, -18, -19, -15, -12, 20, 4],\n [-13, 22, -3, 9, 4, -5, 3, 12, 5, -22],\n [11, 3, -17, 2, -6, 3, -2, 9, 2, 9],\n [18, -4, -21, 12, -7, -7, 10, 1, 8, 19],\n [0, -6, 10, 14, 13, -4, -2, 16, 17, -4],\n [-15, 3, 18, -5, -9, -5, 14, 5, 10, -17],\n [-16, -18, 4, -15, 15, 10, -11, 14, 14, -8],\n [-6, 14, 19, 6, -20, -12, 3, 17, 22, -17],\n [12, 1, 16, 11, 1, -4, -10, 20, -14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, -2, 9, -11, 6, 10, -22, -19, -10, 0],\n [5, 20, -11, -4, 10, -5, 11, 7, 20, -17],\n [-19, -11, 0, 5, -12, 5, 17, 11, 11, -2],\n [13, 5, 11, 18, 6, 3, -10, 11, -4, -15],\n [6, 20, 17, -7, 5, 7, 0, 6, -3, -6],\n [3, 16, 10, -9, 8, -7, -2, 12, -4, -17],\n [0, 3, -14, -10, 21, -8, 9, 16, 21, -6],\n [22, 6, 17, -5, 11, 2, -11, 22, -8, 20],\n [1, -14, 17, -3, 2, 1, 3, -9, -18, 6],\n [-15, -6, 20, -1, -5, 4, -21, -22, 18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "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, -21, 21, 15, 5, 11, -11, -18, 22],\n [13, -15, 7, -13, -2, 11, 11, -19, -12, -1],\n [18, 0, 11, 7, 2, 1, 2, 7, 16, 21],\n [-7, -13, 8, -12, -14, 13, -4, -18, -11, -13],\n [-9, -3, -3, 21, 13, 2, 18, -18, 18, 4],\n [-21, -11, 5, 21, -10, -2, 20, -15, -11, 18],\n [21, -12, -4, -15, 4, -16, -2, 4, -9, 9],\n [6, 1, 5, 1, -21, 8, -11, -22, -2, 6],\n [7, 19, -22, -1, 19, -15, -10, -9, 19, -22],\n [9, 15, -11, 22, -7, 1, 21, -3, 20, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[9, 4, 11, -1, -20, -6, -9, 4, 16, -3],\n [8, 18, 8, 6, 19, 20, 9, 7, 20, 4],\n [-4, 5, 22, -13, -7, 8, -13, -13, 5, -11],\n [10, 5, -5, 5, 5, 20, 16, -9, -15, 7],\n [13, -20, -13, -14, 17, -10, -1, 1, -16, -10],\n [-17, -13, -12, 6, -7, -3, -2, 6, -9, 18],\n [-7, -14, -17, 15, 6, -5, 1, -6, 13, -2],\n [-4, 0, 4, -12, 3, -12, 20, -1, -4, -15],\n [0, 0, 17, -14, 1, -11, -11, 9, -21, -17],\n [-19, -10, 13, 18, 16, 15, -5, -8, 10, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[7, 13, 2, -19, -5, 22, 10, -3, 19, -2],\n [-22, 11, -14, -22, 4, -8, 1, 2, 11, 21],\n [-13, 7, 22, 18, 2, -20, -1, 17, 1, 4],\n [3, -7, 15, 18, -19, 0, -4, -8, 8, 1],\n [-12, -13, -15, -20, -4, -19, 6, 22, 18, -2],\n [22, -14, -5, -4, -6, 21, 20, 1, -17, 8],\n [4, 11, 4, 4, 12, -11, 6, -17, 14, -16],\n [-17, -4, -9, -2, -9, 17, -9, 9, 3, -20],\n [-8, -2, 7, -9, 16, 14, 18, 5, -21, -1],\n [-16, 21, 9, -7, 13, -21, -6, -20, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[16, 5, 22, 18, -15, 10, -19, -16, -12, 17],\n [-15, -3, 20, 16, 5, -12, -1, 13, -17, -16],\n [-13, 17, -19, -14, 15, -4, 10, 15, -1, 16],\n [-22, -2, -16, -16, -1, -10, 0, -1, 3, -5],\n [-16, -21, -4, -9, 2, 10, 16, -3, 21, -18],\n [-2, -10, -9, -7, 22, 18, 5, -22, -21, -15],\n [-10, 15, -4, -21, 8, -13, -18, 0, 7, 9],\n [-22, 22, 21, 19, -20, 7, 14, 5, -2, -10],\n [17, 3, 17, 7, 1, 15, 18, -18, -7, 19],\n [-7, -13, -5, 15, -6, 18, 17, 8, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "363", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[17, -11, -5, 11, 12, -12, 7, 22, -12, -19],\n [13, -13, 11, 8, 9, 5, 20, 14, 9, 9],\n [-6, 11, 12, 16, -2, 9, 11, 11, -15, -7],\n [12, 0, -1, 8, 6, 15, -4, 22, 13, -14],\n [12, -22, 10, -6, 3, -10, -18, -4, 19, -14],\n [-17, -2, -1, 16, -18, -1, -16, 3, 2, -18],\n [9, -15, -14, 5, -3, -19, -20, 21, 18, 19],\n [-12, 6, 20, -1, -15, 11, 8, -19, -8, -5],\n [-12, 4, -4, -14, 2, -1, 0, 14, -13, -6],\n [-10, -19, 9, 5, 7, 17, -2, -8, -20, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-8, 10, -18, -15, -14, 3, -21, 14, 13, -11],\n [-4, 4, 1, -21, -7, -21, -2, -13, 19, -6],\n [-11, -16, -14, -13, -7, -22, -14, -10, -7, 11],\n [18, 7, -10, -15, -12, 8, 20, -12, -16, -22],\n [0, 9, -8, -5, 5, -9, -10, 11, -3, 1],\n [5, -12, 5, -1, 7, 15, -6, -1, -22, -3],\n [-18, 10, 22, -22, 21, -14, 9, 3, 22, 19],\n [-17, 7, 17, 0, 16, 2, 2, -10, 2, -6],\n [21, 4, -12, -17, -8, 14, 9, 1, -12, 19],\n [6, -15, 14, -13, -13, -22, 22, 0, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-18, 15, 8, 19, 16, -3, 6, 10, 16, 9],\n [2, 21, 4, 0, -21, -19, 2, 22, 0, 18],\n [13, 18, 0, 10, 5, -15, 10, 6, -8, -8],\n [14, -4, 20, -2, 12, 3, 5, -1, 13, -7],\n [-11, 5, -16, 10, 1, -12, -8, -4, -8, -14],\n [-10, 6, 3, 0, -6, -18, -7, 16, 7, -2],\n [-18, 3, 20, 7, -1, 22, -21, 21, -11, 19],\n [4, 3, 22, 21, 2, -4, 4, -6, -17, 0],\n [-5, 20, 21, -21, 22, -4, -19, 10, 11, 9],\n [-5, 21, -14, 14, 13, -20, -5, 17, 2, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[21, -22, 1, 1, 19, 17, -19, 12, 12, -11],\n [0, -1, 3, -19, -16, 0, 8, -16, -1, 16],\n [17, -4, 7, 3, 18, -1, -14, 6, 9, -5],\n [8, 9, -14, 7, 14, 9, -15, 1, -19, -6],\n [-2, -14, -18, -18, 7, -17, 15, -15, 10, -8],\n [14, -14, -20, 8, 16, -16, -7, 5, 12, -8],\n [-16, 12, 8, 15, -15, 15, -7, 11, -22, -4],\n [-9, -4, 0, -19, 11, -21, -11, 0, 20, -5],\n [9, -6, 8, 13, 3, -11, 12, -7, -19, 5],\n [15, 10, 14, -13, 8, -9, -18, -13, 2, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[22, -6, -3, 10, -14, 8, -18, 6, -19, 8],\n [-19, -5, -5, 17, 11, -9, 3, 0, 10, -6],\n [19, 9, 12, 20, 7, -8, -16, -17, -14, -10],\n [17, -5, 12, -22, 1, 13, -7, -5, -20, 19],\n [14, -15, -5, 6, 14, 4, 21, 6, -19, -11],\n [-10, -9, -9, -13, -1, -14, 1, -6, 1, -18],\n [11, 19, -22, 4, 17, -15, -17, -18, -5, -16],\n [13, 10, 11, 9, -20, -22, -2, -10, -15, 21],\n [7, -15, 4, 16, 0, -15, -8, -16, -11, 13],\n [15, 20, 7, -13, -4, -5, 21, -3, -21, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[21, 20, 20, -12, -1, 19, -4, -20, -19, 12],\n [15, -14, -15, 11, 8, 17, -4, 14, 9, 21],\n [21, 5, 18, -5, 2, -13, -18, -8, 2, -3],\n [-13, 15, 18, 5, -17, -12, -4, -7, 9, -21],\n [16, 3, -2, 15, -8, -10, -16, -20, -8, -3],\n [-20, 4, -8, -20, 5, -22, -3, -12, 2, -19],\n [-4, 5, -13, -2, 13, -7, 10, 22, -10, 6],\n [-19, 19, 4, -15, 18, -15, 2, 3, -22, 20],\n [10, -4, -3, -5, 3, 16, -14, 4, -17, -3],\n [15, -22, 15, -7, -19, -20, -1, -14, -15, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-11, -22, -11, -7, -9, 7, 20, -4, -4, -10],\n [21, -13, 6, 5, -10, 22, -8, -6, 0, 20],\n [-13, 13, -9, 9, 11, 8, 16, 9, -7, 3],\n [-6, -1, 13, 12, 0, 2, -18, -17, 3, 15],\n [-17, -4, 20, -4, 8, 14, 0, -11, -10, -1],\n [-20, -11, 14, 8, -10, 0, -10, -17, -20, -16],\n [-13, 8, -19, 21, -17, -5, -16, 11, 0, -15],\n [1, 5, 22, -20, -10, 16, 10, -7, -12, 6],\n [2, -6, 14, -17, -9, -4, 14, 20, -11, -4],\n [-2, 6, 5, -6, -21, -17, 2, -4, -17, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[11, -2, -2, 21, 4, 0, 13, 13, 9, 16],\n [22, -6, -9, -1, -6, 6, 15, 3, 8, 11],\n [4, -6, 0, 11, -5, -2, -3, 9, -11, -19],\n [-14, -12, 7, 22, 3, 9, 5, 17, 14, 19],\n [18, -7, -15, -20, -20, -13, -11, -8, 4, -12],\n [-17, -11, -5, 2, 11, 3, 1, -7, 13, 13],\n [-2, 7, -3, 19, -4, -12, -9, 13, -7, -20],\n [-1, 20, -18, -21, -11, 22, -21, 14, -4, 1],\n [-18, 3, 5, 12, -4, 8, -4, 20, 21, -4],\n [-3, 19, -6, -11, 12, 3, -15, 17, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[22, -1, -10, 19, -8, 0, 5, -10, 9, -12],\n [21, -9, 12, 20, 12, 17, 0, 17, -10, -17],\n [6, 19, -8, -18, 10, 17, -21, 10, 2, 4],\n [2, -18, 20, 17, -19, -9, -6, 18, 4, 13],\n [11, -13, -1, 18, -1, 5, -3, -21, 0, 11],\n [-7, 5, -9, -22, 18, -8, -8, 2, 20, -18],\n [-15, -1, 16, 15, 16, 20, -9, -4, 3, 15],\n [10, -11, 6, -11, 6, 18, 18, -3, 11, 7],\n [6, 16, 17, -21, 3, -22, 5, -15, 8, 16],\n [-4, -10, -7, 0, -12, 1, -13, -18, -11, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 5, -7, -21, 3, -19, 6, -7, -1, 20],\n [-17, 5, -12, 19, -2, 3, 16, -1, 7, 7],\n [10, 17, 7, 14, 7, 3, -17, -19, -8, 13],\n [-20, -7, -7, 17, 4, -17, -2, -10, -14, 18],\n [20, -15, 5, 22, -4, 6, 8, 10, -17, 21],\n [-19, -7, -20, 2, -6, -1, -5, 9, -5, 3],\n [2, 5, 17, 0, -15, -10, 21, -13, 18, -20],\n [-13, -8, 1, -13, -2, 15, 16, 19, 5, 18],\n [-21, 18, -19, 20, -20, 9, 11, -7, -19, -5],\n [5, 19, -17, 20, 19, -22, -7, 14, -14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[13, 11, 8, 11, 14, 11, 22, 14, -22, -8],\n [8, -9, 21, 11, -22, 12, -12, -6, -18, -6],\n [-5, 2, 12, -7, 0, 17, -2, 6, 13, -13],\n [-3, -16, 7, 6, -22, -2, -16, 21, -19, 16],\n [-8, 11, -21, 14, -20, -19, 20, 13, 4, -19],\n [13, -4, 11, -7, 22, 17, -1, 9, -21, -6],\n [0, 21, -11, -10, -13, -19, -16, -21, -8, 13],\n [-14, 1, -17, -16, -7, -6, 7, -15, -20, 2],\n [6, -2, -17, 0, -12, -17, 4, 4, -10, -14],\n [-15, 22, 4, 9, 6, 10, -18, 15, -14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[10, 7, 2, -17, 16, -13, 13, -4, -12, -6],\n [-21, -16, 18, 8, 8, -6, -8, -16, 7, 16],\n [-9, 8, -14, -14, -21, 21, -1, -7, -21, -8],\n [-17, 0, 5, 20, -6, 13, -4, -18, 0, 21],\n [-4, -22, 4, 20, 2, -17, 13, -6, -11, 2],\n [-13, 16, 1, -12, 1, -20, 17, -3, 0, -18],\n [13, -10, 13, -17, -21, 6, -18, -8, -15, 11],\n [14, 3, -14, -15, -9, 2, 11, -20, 9, 13],\n [-18, -8, 5, -5, 22, -12, -13, -19, -3, -18],\n [-22, -10, -1, -10, -8, -14, -20, -21, -11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, 13, 2, -8, -22, -15, 14, -16, 12, 15],\n [22, -7, -6, 15, 7, 14, -5, 13, -11, 5],\n [-12, 20, -17, 3, -7, 15, -14, -5, 10, -4],\n [-14, 21, 19, -14, 21, -18, 0, 19, 11, 15],\n [-1, -18, -22, 3, -5, 3, -8, -21, -8, -12],\n [22, -3, 19, -6, -18, 10, 21, 2, -16, 11],\n [-8, -10, 9, 16, -9, -3, -7, 7, 18, -4],\n [-1, 14, -13, -15, 6, -9, -12, 7, 10, 19],\n [11, 16, 14, 19, 14, -18, 18, 20, -18, -6],\n [-4, 3, -21, -9, 5, -19, -20, -8, -1, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 11, -13, 11, -7, 14, 13, 22, -1, 9],\n [21, -6, -14, 10, 10, -21, -9, 14, 10, -22],\n [-1, 7, 4, 10, -7, -13, 4, 14, -21, 7],\n [20, -4, -4, 12, -12, 9, -7, -6, 6, -3],\n [13, 1, 20, -19, -18, -4, 1, -22, 12, -21],\n [-13, -17, 17, 15, -3, -4, 13, 6, 18, 1],\n [-14, 9, 17, -18, -2, -6, 1, 4, -5, -1],\n [-17, 5, 19, -3, -7, -4, -15, -5, 14, 22],\n [8, 15, -21, 9, -8, -12, -18, 19, 6, -3],\n [-3, -5, -11, -6, -19, -4, 0, 4, 19, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, -19, -19, 1, 0, 13, -12, 10, 15, -18],\n [4, 14, 4, 8, -11, -17, -11, -9, -1, -12],\n [17, 16, 15, -10, -17, -3, -21, -12, -15, 7],\n [4, -19, -16, 1, 9, -4, 19, 12, 19, -20],\n [-5, 14, -1, 10, 15, 16, 11, 0, 12, 6],\n [-21, -9, 21, -15, -22, 5, -20, -16, 11, 9],\n [-14, 12, -4, -8, 8, -7, 14, -16, 12, 6],\n [-21, 11, 12, 8, -11, -22, 6, -22, -22, -8],\n [-20, -9, -13, -20, -3, 13, 4, 13, -12, -20],\n [1, 16, -13, 3, 9, -15, -10, -20, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[19, 6, 4, 7, -9, 18, -8, 19, 21, -9],\n [2, 4, 21, -21, -6, -8, 4, -13, 20, -14],\n [-20, 1, -22, 15, -17, -18, -19, -20, 22, 7],\n [13, 0, -16, 9, 20, -13, 14, 10, 3, 20],\n [22, 8, 7, 0, 6, -15, -7, -14, -19, -4],\n [16, 21, 18, -10, -11, -14, -11, 1, -10, 12],\n [9, 15, -9, -21, -2, 8, 12, -7, 17, 3],\n [15, -20, 14, 13, 15, -21, -1, -20, 17, 19],\n [3, 4, 15, 21, -15, 0, -17, 2, -7, 3],\n [-8, 9, 17, -4, -9, 21, 12, 3, 14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-15, -9, 3, 7, 17, 19, -10, 13, -12, -21],\n [7, 1, -5, 0, -17, -12, -16, 10, -13, -2],\n [-14, 7, 2, 2, 1, -11, -16, 11, -20, -17],\n [4, -4, -15, 13, 16, 13, -5, -16, -22, -18],\n [19, -9, -22, -11, -4, -21, -9, -20, 12, -10],\n [-20, -9, 11, 22, -14, -13, -15, 6, 16, 10],\n [0, -15, 17, 15, 0, 13, 20, -3, -11, 13],\n [-14, 10, -17, 9, -22, 1, 6, -15, -10, 2],\n [6, 1, 4, 3, -3, -19, -1, -16, -5, -13],\n [8, 3, 22, 3, 2, -5, 1, 21, -8, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[20, 2, 12, 1, 17, 15, -2, -22, 3, -13],\n [3, -21, 17, -9, 10, 16, -22, 7, 14, -5],\n [7, 4, 7, 22, 13, -2, -7, -6, -5, 11],\n [-2, -11, 8, -13, 18, -19, -8, 19, 18, 5],\n [-16, -12, 6, 11, 7, 4, 2, 15, 17, 0],\n [6, -12, -19, 13, 8, -13, -7, 7, 12, 21],\n [-6, -18, -20, -7, -19, -14, -19, -2, -13, 8],\n [-6, -7, 16, -17, 7, -8, 20, 8, 7, 14],\n [-7, 21, 13, -21, 5, 17, -6, 18, 15, 13],\n [9, 2, -10, -9, 21, 2, 12, 6, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[17, -6, 2, 0, 9, 8, 0, 15, -6, 6],\n [-21, -12, -7, -6, -2, -2, -17, 22, 0, 9],\n [16, 22, 15, 6, 8, 2, -21, -1, 14, 21],\n [-8, -17, 10, -12, -11, 1, -20, 7, -4, 22],\n [20, -16, -11, 6, -15, -2, -10, 4, -19, 9],\n [1, 18, -14, -13, -12, 10, -16, -12, 22, 5],\n [15, 7, -15, 4, -1, 19, 9, -9, 3, 21],\n [-12, -16, 22, 7, -21, 12, 3, 2, -22, 6],\n [1, 15, -22, 2, 11, 19, 21, -18, 18, -11],\n [-15, 19, -9, -3, 17, -14, -18, -22, -12, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[15, -6, -19, 9, -18, -1, -9, -2, -5, -20],\n [-12, 16, 13, 4, 15, 2, 19, 16, 12, -8],\n [-2, -20, 1, 21, -18, 14, 10, 1, -17, 22],\n [-16, -4, -2, -17, 17, -20, -9, -3, -9, -21],\n [2, -19, 18, 10, -21, 0, 21, -2, -8, 1],\n [-3, 15, 2, -1, -19, -7, 20, -16, 1, 11],\n [16, 6, 21, 3, -9, -3, -16, -5, 20, -13],\n [7, -20, 21, -22, 7, 22, -21, -8, -12, 9],\n [-17, -17, 5, 2, 0, -11, -13, -6, -21, 22],\n [-6, -14, -16, -10, -13, -1, 5, 19, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-22, 4, -19, 1, -9, 14, 0, -18, -3, -1],\n [17, 21, 12, 13, -18, 10, 1, 11, 14, 2],\n [14, 2, -1, 22, -18, -15, 18, 4, 12, -22],\n [-3, -16, 22, -20, 19, -14, -9, -4, 4, -17],\n [-16, 14, 3, -10, 14, 10, 10, 18, -14, -8],\n [-18, 6, -16, 8, 11, -12, 19, -4, -18, 0],\n [-21, 20, -19, -6, 8, 7, -21, 1, -13, 5],\n [20, 9, 10, -5, 1, 14, 7, -18, 0, 7],\n [-19, 18, 1, -20, -8, -22, -13, 22, 3, -11],\n [-22, -21, -12, -11, 5, 10, 19, -20, 18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 14, 5, 8, -16, 15, -18, -4, -10, 16],\n [5, -21, -17, -8, 5, 14, 2, 9, 14, 13],\n [7, 22, 1, -5, -22, -20, -16, 10, -2, -9],\n [14, -20, 14, 2, 10, -10, 10, 6, -4, 3],\n [15, -14, 7, -1, 20, -19, -16, -5, -17, 6],\n [-18, -17, 11, 11, -22, -5, 4, -13, 16, -21],\n [-4, 4, -1, -13, 21, 4, -11, -8, -22, 15],\n [18, 1, -17, 6, -17, 15, -8, -15, 6, -21],\n [-12, -14, -7, 1, 11, 20, 1, 15, 15, 2],\n [18, 10, 21, 20, -6, -16, 4, 13, 18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-8, -17, 13, -18, 22, -18, -21, 20, -5, 9],\n [6, -3, -4, -7, -12, 5, -1, 4, -6, -15],\n [-15, 0, 9, 21, -8, 4, -19, 17, 9, 14],\n [-13, 5, 9, 9, -8, -17, -14, 15, 7, 18],\n [17, -7, 2, -13, 7, -14, 17, -16, 20, 17],\n [-11, -6, 2, -16, -4, -6, 9, 0, 22, 9],\n [3, -15, -1, -15, -18, -11, 4, -3, -12, 13],\n [-21, -13, 19, -16, -11, -7, 8, 4, 9, 19],\n [17, 4, 2, 17, -18, -19, 21, 20, -8, -10],\n [10, -18, -17, 22, 2, 2, -13, -11, -20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 20, 1, 1, 2, 14, -18, -12, 17, 20],\n [-1, -8, -14, -17, 3, -17, 9, 20, -3, 12],\n [20, -20, -5, 12, -13, 13, 7, 3, 7, 8],\n [-19, 1, -22, 3, 6, 15, 13, -14, 19, 9],\n [14, 17, -5, 1, 17, -5, 16, -15, 16, -12],\n [20, 12, 1, -10, 8, 7, 6, 19, -17, -20],\n [5, -13, 11, -22, -11, 13, 9, -12, -22, -17],\n [4, -8, -13, 1, -15, -6, 1, -10, -14, -17],\n [6, 0, -1, -2, -6, 11, 3, 2, 15, -20],\n [-20, -9, 19, -13, -21, -16, -9, -6, -13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[22, 4, -20, 2, -16, -10, 16, 20, 2, 20],\n [6, -4, 16, -1, -21, -1, 12, 11, -18, 4],\n [-5, -20, -2, 1, 3, -3, -10, -17, 3, 20],\n [7, -9, 14, 15, 7, -8, -4, -12, -3, 2],\n [15, 20, 7, 17, 0, 21, -6, -22, 19, -9],\n [16, -5, 18, -7, -13, 21, -14, -9, -21, 19],\n [-2, 19, -21, -17, -12, 18, -20, -12, -19, -8],\n [3, 21, 13, -8, -1, 14, -13, -3, 9, -14],\n [8, 21, 17, 8, 5, -12, 13, 18, -19, -9],\n [6, 5, 2, 0, 10, 7, -14, 15, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[20, -16, 1, 17, -2, 12, 20, -12, -21, -8],\n [-8, -18, 17, -7, 21, -2, 22, -14, -16, 4],\n [-6, -21, 17, 3, 22, -15, 22, 17, -7, -3],\n [9, 9, 12, -8, 19, 9, 7, -4, 1, -21],\n [-2, 19, -7, 17, 16, 13, 18, -21, -7, 6],\n [-16, -8, 0, -18, -22, -18, -10, 3, -10, 9],\n [6, -5, -21, 4, 19, -20, 7, -13, -14, -20],\n [-1, 15, -12, -17, -18, 7, -9, -21, 10, 14],\n [-15, -13, -2, -4, 12, -5, -16, -10, -11, 17],\n [1, -5, 15, -11, -20, 2, 12, -7, 22, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[1, -11, -21, 3, -13, -4, -1, 1, 3, -18],\n [-7, 14, 11, 15, 5, -11, 22, 22, -2, 9],\n [2, -9, 12, -14, 7, 19, 6, 16, 8, -9],\n [-6, 2, 19, 14, 4, -5, 6, -5, -19, -3],\n [-22, 22, 1, 19, 1, -18, 3, -5, 13, -22],\n [-13, -6, 12, -19, 21, 4, -12, -20, 5, -12],\n [-20, 13, -20, 2, -11, -11, 9, 17, -13, -4],\n [20, -16, 1, 16, 9, 0, -4, -20, 2, 2],\n [-17, 10, 10, -8, -3, 20, 19, 9, 1, -20],\n [-19, 21, -17, -4, 3, 2, 2, -13, 15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-18, 19, 21, 12, -18, 12, -20, 18, 9, 13],\n [7, 16, 6, 3, 22, 2, -11, -5, 3, -8],\n [-18, 10, 18, -14, 9, -10, 20, 5, 0, 1],\n [18, 8, -18, -21, 7, -18, -13, 13, 13, -16],\n [6, 9, 4, -22, -3, 11, 13, 3, 0, 10],\n [-22, -20, 12, 12, -10, 10, -10, -1, -18, -6],\n [20, -13, 4, -8, 22, 19, -14, -16, -13, 18],\n [-10, -7, 11, -15, 8, 5, -16, 11, 10, -19],\n [15, 3, -21, 9, 16, 19, 18, -21, 3, 4],\n [-8, -2, 4, 11, -12, 0, -1, 0, -22, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[2, -17, 11, 5, 2, -5, -22, 9, 6, -3],\n [-10, -11, -15, 16, -15, -5, -2, 5, 8, -8],\n [16, 10, 15, 0, -7, 1, -2, -15, 19, -6],\n [-8, -9, -3, 9, -12, 15, 9, -19, 6, -18],\n [20, -11, 20, 16, 0, 10, -7, 21, -12, -15],\n [10, 11, -2, 15, -6, 11, 18, -20, 1, -1],\n [-13, -18, 18, 8, 1, -12, -9, -19, -15, -16],\n [12, 9, -1, -1, 20, 3, 13, 6, -19, 8],\n [-1, -15, -2, -8, -19, 19, -18, 13, -21, -15],\n [-19, -10, -9, -14, 5, 15, -11, 5, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[15, 3, 2, -1, -15, 14, 17, 22, -1, -10],\n [14, -9, -5, 10, -16, -13, 7, 11, 22, -20],\n [17, -11, 13, 8, 0, -15, -22, 12, -8, 5],\n [-11, -22, -12, 14, -21, 22, 12, 22, -15, 8],\n [-2, 22, -20, 2, 18, 5, 5, -21, -15, -22],\n [-2, -8, -15, 17, -1, 16, -3, -10, 3, 16],\n [-16, -12, 8, 11, -12, 1, 2, 10, 6, -2],\n [10, 22, -17, 14, -21, 19, 7, 5, 9, 4],\n [16, -1, -8, 20, 15, 14, 13, 15, -16, 8],\n [21, 7, -9, 11, 4, 0, -20, -18, 19, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-16, 18, -5, 15, -13, 21, 11, 10, 9, 8],\n [5, -19, -8, -21, 0, 0, 12, 4, 3, 11],\n [-10, 17, -13, 16, 3, -19, -5, 12, -6, 4],\n [-15, -10, -1, 13, 20, 7, 12, 22, -19, -10],\n [-17, -5, -15, 18, -3, -2, 9, 9, -21, 19],\n [-21, 18, 9, -1, 3, 18, 22, -13, 16, 22],\n [-18, -11, 18, 18, 9, 17, -5, -13, 0, -22],\n [19, 14, -5, 7, -4, 22, 15, -6, 5, -1],\n [15, 9, 2, -14, 13, 14, -22, 6, -8, 21],\n [6, -2, -11, 3, 22, 8, 12, -9, -16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, -19, -21, 12, 10, 14, 18, -10, -16, 16],\n [4, -20, -6, 2, 7, -9, 6, -18, -16, -4],\n [10, -2, -2, -6, 0, 4, 8, -8, 17, 17],\n [-22, -3, 18, 11, -22, 9, -1, 6, 22, -12],\n [10, 15, -22, 15, -14, -10, 1, 13, -3, 20],\n [22, -22, 12, 20, -3, 17, -22, -17, 18, 3],\n [6, 18, -8, 14, -4, -14, 18, -6, 9, 5],\n [-8, 19, 5, -14, 4, -4, -16, 2, 7, -10],\n [-21, -5, 17, -15, -3, -14, -10, -2, 5, 21],\n [-16, 8, 0, -10, 22, 13, -21, 11, -18, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[11, -21, -3, -15, 0, 14, -7, -1, -15, 20],\n [20, 3, 17, 0, -7, -2, 17, 6, -3, -11],\n [14, 3, -20, -5, -22, -4, -10, 20, 10, 7],\n [-1, 4, -10, -15, -21, -4, 1, -18, -15, -3],\n [12, -21, -17, -7, 13, -21, -9, 15, 3, -3],\n [6, -19, -3, 1, -22, 2, -9, 12, -2, 13],\n [0, -3, 3, 4, 18, -9, 13, -19, 3, 21],\n [17, -7, 20, 16, -3, 1, -13, -21, 22, -14],\n [-5, 19, 7, -20, 6, -16, 2, 1, 20, -17],\n [-8, -8, 17, 4, -2, 22, 9, 9, -11, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-14, -3, -8, -10, -15, -2, 22, 2, 12, 17],\n [7, 8, -17, -12, 19, -15, -15, 16, -11, -20],\n [20, 22, -7, 18, 4, -7, -18, 17, -11, -20],\n [12, 22, -20, 8, 1, 18, 6, 10, 15, -7],\n [10, -13, 7, 11, 12, -16, -17, -8, 9, -21],\n [9, 5, -2, -6, -4, -9, 11, -3, -2, -20],\n [-9, -2, 4, -16, 19, 6, -14, 17, -8, 21],\n [5, 15, -8, -8, 7, 9, 17, -11, -3, 4],\n [-21, 18, -1, 3, 17, -15, 13, 3, 14, -6],\n [-16, -22, 4, 19, 3, 9, -9, -4, -14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[21, -22, -2, -3, 10, 10, -5, 18, -6, -10],\n [20, -14, -22, 0, 17, 11, 13, 22, -9, -2],\n [20, 20, -2, 5, 9, 7, 17, -11, 6, -22],\n [3, -7, -5, 10, 19, 20, 0, -18, -2, -22],\n [8, -5, -2, -16, -22, 0, 4, -21, 11, -7],\n [17, -13, -3, 14, 2, -19, 9, 22, 5, 17],\n [-10, -18, -6, -16, -13, 4, 12, 0, -7, 4],\n [-8, -17, 19, 16, 1, 0, -18, -16, -1, 6],\n [8, 12, 11, -4, 11, 7, -4, -5, -22, 18],\n [-7, 17, 5, -12, 9, 3, -13, 0, 22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -9, -14, -9, 13, 18, -21, -12, -9, 13],\n [12, 19, 2, 10, -14, -10, 20, -13, 10, 22],\n [-14, 17, -10, 1, 17, -6, 10, 0, 4, 21],\n [21, 20, 3, 1, -12, 6, -18, 1, -14, -13],\n [-12, 8, -20, 2, 20, 17, 4, -22, -7, 12],\n [-8, 11, -12, -14, 1, 14, 12, -1, 17, 15],\n [-16, 21, 7, 6, 16, 18, -14, -22, -20, -18],\n [-12, -19, 21, 10, 10, 22, -3, 14, -3, 11],\n [-2, -16, -7, 9, 13, -12, 6, 19, 11, -13],\n [-20, -1, 9, 21, -3, -21, -15, 18, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 3, 12, 17, -18, -8, 19, -9, 14, -5],\n [-11, -20, 17, 10, -19, 17, 3, -2, 22, -7],\n [0, 1, -14, -4, 4, 17, 8, -22, -10, 22],\n [-19, 2, -13, 0, 20, 7, -9, 9, 7, -18],\n [22, -8, -6, 10, -11, 2, -4, 0, 16, -18],\n [17, -2, 13, -9, -17, -4, -19, 1, 3, 19],\n [-4, 9, 19, 22, 12, 17, 19, -21, 10, -13],\n [22, 10, 0, 11, 19, 13, 7, 16, -18, -2],\n [-7, -16, -14, 18, 20, 1, 3, 9, 20, 4],\n [18, -4, -15, 14, -17, -4, 20, 0, -21, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-21, -10, 9, 20, 2, 20, -10, 7, -4, 1],\n [22, 10, -10, 8, 15, -15, 7, -4, 9, 7],\n [15, -6, 11, -7, 14, -17, -21, -18, 19, -4],\n [-22, 15, 2, -7, 7, 7, -13, 17, 1, -2],\n [16, -8, -18, 13, 19, -1, -15, 8, -22, -3],\n [5, 8, 1, 22, -16, -21, -14, -4, 18, 2],\n [0, -13, 0, 10, 20, -4, 11, 14, -20, 22],\n [-16, 20, -22, 13, -22, 18, 7, 9, -4, -13],\n [21, 21, 10, 22, -19, -3, 21, -8, 18, 7],\n [-16, 15, 18, -5, 7, -15, -2, 22, -16, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-18, 9, -7, 17, 3, 4, 16, 5, 10, -21],\n [18, -8, 16, -16, -3, -10, 9, 6, -19, -4],\n [-13, 13, -11, -1, 4, 12, 17, -6, -17, 22],\n [20, -9, 10, 21, 5, 15, -16, -12, 10, -20],\n [-1, -10, 6, -17, 19, 16, 20, 5, -8, 1],\n [20, 3, -22, 3, 8, 0, 9, 21, -22, -5],\n [-6, 21, 5, -22, 13, -18, -18, -21, -12, 12],\n [7, 9, -15, -21, 13, 16, 2, -4, -16, 17],\n [-9, -19, 10, 14, 20, 7, -3, -9, 4, -10],\n [-16, -5, 15, 16, -14, 0, 8, -21, 17, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, 16, -18, 0, 9, 16, -7, -12, -9, -20],\n [-15, -8, -14, -7, 3, 9, -5, -15, 16, 9],\n [-13, -11, -11, -13, 11, 7, 21, 8, 15, 2],\n [1, 10, -14, 2, -3, -6, -17, 13, 18, -3],\n [3, 17, -11, -16, 17, 7, -1, 19, 6, -1],\n [1, -20, 18, 1, 3, -18, -10, 14, -1, 11],\n [16, -20, 9, 1, -14, -20, -1, 1, 15, -13],\n [12, -3, 18, 21, -11, 20, -11, -6, -19, 19],\n [-15, -16, -5, 3, 8, -15, 11, -7, -3, -13],\n [-18, -12, 15, 16, -1, -12, -5, -5, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "325", "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, 17, -13, -6, 18, 22, -15, 8, 17, 3],\n [19, 21, -14, 9, 0, 9, 13, -18, -22, 8],\n [8, -14, 10, 12, 3, -21, 11, -6, -17, 14],\n [8, 5, -2, -12, 18, 13, 16, 22, 4, -3],\n [-3, -21, 14, 4, -5, -10, -5, -12, -9, 21],\n [-19, 16, -10, -4, 20, 16, 2, -8, -3, -6],\n [-22, 6, 21, -4, 7, 2, 5, 14, 19, -12],\n [-7, -5, 18, -14, 5, 4, 15, 21, 0, 20],\n [-1, -19, 9, 1, 15, 5, -17, 10, 8, -13],\n [-11, -16, 1, 5, -12, 9, -3, 5, -22, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-7, 13, -17, -13, 16, 21, -4, -13, 3, 11],\n [18, -22, -13, 10, 3, 11, 14, -10, 15, 7],\n [1, 19, 11, 14, -4, -21, 7, -1, 9, 10],\n [17, -8, -17, 13, 21, -7, -2, 11, 17, 15],\n [12, 10, -15, -11, 16, 22, -5, 17, -2, 4],\n [-11, -17, 8, 11, -16, 8, -19, -6, 6, -20],\n [1, -20, 16, 4, -22, -8, -9, -19, -19, 2],\n [-12, 10, -12, -11, -8, 3, 1, 3, 4, 13],\n [4, 15, -21, 0, -14, -15, 17, 19, -22, -2],\n [3, -8, 20, 2, 16, -7, 12, 0, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[11, -15, 0, -12, 20, 11, -18, 14, 2, 1],\n [1, 19, 11, -5, -11, 19, 16, -8, -11, 6],\n [6, -3, -8, -20, -7, -4, -16, 13, -1, -8],\n [-14, -6, 10, -21, -16, 8, -9, 14, -19, 22],\n [-13, 22, -1, 1, 21, -5, -12, 21, -22, 9],\n [-7, -9, 10, -16, -4, 2, -18, -13, -19, 1],\n [-17, -11, -3, 3, -11, 10, -11, 15, -19, -6],\n [-13, -4, 20, 10, 14, 5, 22, -21, 15, 15],\n [-2, 0, 10, 3, 20, 7, -19, -17, 11, -3],\n [14, -8, 17, 0, 19, -14, 11, 20, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-7, -19, 5, -6, 18, -11, -18, 12, 15, 16],\n [13, 7, -9, -9, -21, 5, -2, -8, 21, 0],\n [-13, 3, 12, 11, -21, 8, 20, 21, 21, 20],\n [-18, -4, 7, -6, 6, -11, -15, -8, 11, 5],\n [-2, -6, 19, -5, 1, 1, -11, -22, 13, 9],\n [-18, 3, -20, 10, 16, -3, -11, 15, -3, -6],\n [20, -15, 20, -10, -14, -4, 3, -18, 19, 22],\n [2, -18, 0, 12, 9, 19, -17, -9, 18, 6],\n [14, -1, -3, -15, 4, -16, 11, 18, 5, 8],\n [-2, -13, 13, -10, 3, 11, -4, -17, -8, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "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, -22, -1, 13, -5, -13, -3, 17, -17],\n [14, -1, -19, -19, -4, 6, 5, 18, -10, 16],\n [5, 7, -1, 0, -5, -6, 8, 5, -15, 9],\n [20, -17, -15, -1, 17, 8, -17, -19, -16, 11],\n [4, -21, -9, 18, 6, 16, -1, -18, 21, -5],\n [-7, 21, -17, -22, -11, 1, -12, 20, 18, 11],\n [6, 9, -2, 17, 10, 10, 5, 21, 13, -22],\n [-11, 10, 21, -18, -21, 13, 1, 20, -2, 7],\n [-8, -14, 9, -15, 0, 4, 19, -15, 6, -12],\n [-2, 21, 16, 7, 10, -20, -10, 13, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-13, 15, 13, 0, -15, -9, 1, -5, 17, 14],\n [2, -3, 2, -6, -19, -2, -3, 22, 18, -6],\n [12, 18, 0, -2, 20, -2, 1, 14, -5, 21],\n [-4, -18, 21, 4, -17, -9, -20, -22, 8, 22],\n [-13, 8, -6, 16, 17, -7, 4, -7, 18, 22],\n [-19, 19, 4, -14, 2, 1, 5, -5, 21, 3],\n [-13, 21, 11, 15, -12, -9, 15, -22, -6, -6],\n [-13, 7, 19, 10, -21, -3, 9, -20, 13, -18],\n [-3, -20, -20, 13, -17, 16, 13, 1, 15, 14],\n [-15, 15, -7, 20, -22, -9, 22, -13, -13, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[17, 18, 8, -19, 20, 0, 18, -11, 22, -15],\n [22, 1, -22, 3, -1, 20, 2, 8, 11, 14],\n [-12, -19, -15, 21, 12, 2, 8, 0, 17, 15],\n [-19, 13, -16, -13, -17, 8, -19, -2, 19, -3],\n [-6, -17, -12, -5, -14, -11, 8, 8, 20, 11],\n [-7, 18, -11, -10, 13, -10, 21, -21, -8, -10],\n [11, 3, -17, -2, 21, 10, -8, 12, 5, 19],\n [-17, 14, 17, -17, -12, -9, -2, -3, -18, 22],\n [-14, 7, 19, 20, 15, 4, -18, -18, 17, -8],\n [-14, 2, -15, -9, 16, 9, 8, 0, 21, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[8, -16, -8, 19, -17, -7, -9, 21, -6, -13],\n [6, 19, -15, -12, -5, 22, -3, -7, 4, 0],\n [-9, -11, 22, 4, -10, -7, 10, 1, -11, -14],\n [-10, 22, -15, -5, 4, 18, 10, -16, -10, -8],\n [11, 17, -3, 14, 18, -6, 6, -2, -9, 6],\n [18, -1, 10, -10, 19, 8, -11, 9, -17, -12],\n [0, -16, -3, -19, -2, 21, 7, 2, 8, -21],\n [-3, 18, -9, 15, 0, -18, -4, -16, -2, 10],\n [-3, -14, 8, -15, -12, -16, -2, 5, -8, -15],\n [-11, -18, -15, 14, -9, -19, 4, -8, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[19, 13, 7, 10, 5, 15, 17, -19, -9, -21],\n [14, -4, -9, -16, -14, 10, 1, 19, 20, -2],\n [21, -22, -2, 17, 1, 15, 21, 18, -19, -17],\n [-20, 11, 2, 4, -5, -18, 1, 9, -2, 21],\n [11, 6, -18, 5, -17, -12, 16, -15, 12, -12],\n [-3, 20, -1, 18, -11, -18, 11, 19, 11, 7],\n [0, 13, 2, -17, 19, 6, -2, -16, 14, 22],\n [18, -14, 13, -22, 8, -3, 5, -4, -22, 6],\n [-13, 13, 0, -5, 6, 5, 21, -16, 8, 15],\n [18, -21, -8, -1, 22, -12, -4, -17, -14, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 20, -20, 22, -10, -8, -18, -18, -21, 15],\n [7, 5, 16, 9, -3, -3, 6, 12, 9, -6],\n [-15, -2, 0, 4, -17, -15, 12, -18, 10, -22],\n [1, 9, 10, 15, -21, 21, -6, -13, 14, 14],\n [-21, -11, 14, 7, -8, 0, -5, 8, 15, 6],\n [-9, 20, 17, 0, 2, 18, 15, 5, 12, 7],\n [4, -15, -4, -22, 22, 21, -3, 7, 6, -15],\n [-9, 15, -20, -20, -9, -2, 12, 21, 21, 20],\n [18, 4, 5, 5, -18, 20, 16, -13, -14, -3],\n [6, 6, 5, -12, -2, 12, 0, 6, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 12, -3, 13, -12, 7, 16, -3, -1, 1],\n [-9, 13, -10, -22, 4, -10, 12, -15, -5, 11],\n [-17, 4, -5, -14, -8, 0, -20, -14, -1, 0],\n [-3, -16, -6, -20, -16, -10, 18, 18, 0, 14],\n [-19, -14, -17, 19, -5, 12, 0, 8, -3, -16],\n [-11, 14, -19, -11, -8, -21, -12, 10, -9, 4],\n [-19, 15, 17, -3, -21, -19, 1, -14, -4, -15],\n [18, 5, -10, -15, -9, -13, -3, -22, -11, 12],\n [-3, -11, -11, 16, 6, -20, -16, 0, -10, -12],\n [2, -3, 4, -17, -17, 16, 18, -14, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-22, -11, -22, 5, 1, -4, -9, -9, 3, -7],\n [1, 9, -17, 22, 7, 0, -4, 2, 2, -21],\n [-13, 18, 4, 21, -15, 18, 20, 10, 20, -4],\n [7, 11, -9, 13, -3, 0, -8, -21, 1, 1],\n [8, -7, -19, 11, -8, -4, -4, 21, 12, -3],\n [16, 18, 6, -8, -3, 9, -10, -16, -7, -13],\n [-21, 15, -5, 11, -2, -2, -22, -8, -13, 12],\n [2, 9, 8, -13, -20, -1, 15, -21, 0, 18],\n [17, 1, 9, 10, 4, -10, 14, 16, 6, 18],\n [2, -4, -22, 12, -7, -15, -16, -2, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-8, 22, -17, 14, -19, -4, -2, 14, 20, -5],\n [19, 13, 14, -8, 15, -21, 19, 8, -17, -4],\n [15, -8, 10, 17, 3, 7, -12, -22, -9, -13],\n [-6, -12, 19, -8, -11, -20, -1, 3, 16, 20],\n [0, -7, -20, 7, -10, -15, 1, -18, -16, 4],\n [-11, 18, 2, 19, 10, -8, 8, -12, 13, -17],\n [22, 3, -15, 16, 14, 14, 7, 15, -7, -8],\n [15, -15, 12, -14, -2, 18, -18, -4, -7, -5],\n [-11, -7, -18, -20, -16, 9, 8, -9, 1, 10],\n [-18, -15, -21, 16, 15, 19, 12, 15, 11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "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, -19, 12, -9, -1, 7, -20, -12, -13, -20],\n [18, -18, -8, -17, -19, 0, 22, -22, 11, -8],\n [-19, 4, -10, 17, 9, -14, 14, 2, -20, 16],\n [17, -7, -6, 4, -13, -22, 6, -5, 9, 14],\n [20, 10, -1, 20, -12, 14, 6, -3, -1, 9],\n [-15, -1, -8, 12, -7, 21, 6, 11, -3, -10],\n [-10, 8, -2, 7, 2, 7, -13, -16, 11, -19],\n [-1, 6, -19, -22, 0, 0, -17, -18, 0, 15],\n [-16, -18, 10, 3, -2, 11, 3, -13, -21, -3],\n [-9, -16, -13, 8, -15, -22, 6, 8, -15, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 3, -13, -5, -21, 14, 6, -21, -20, 1],\n [-14, 20, -9, 20, -12, 20, 1, -9, -5, 13],\n [-10, 11, -4, 18, -12, 3, -18, -2, -14, -11],\n [-22, -9, 3, -16, -7, -8, -19, 7, 0, -1],\n [-8, -6, -21, -15, -17, 16, 5, -18, -2, -3],\n [20, 11, -16, 7, 7, -8, 4, -14, 4, -21],\n [13, 4, 17, 2, 13, 17, -16, -10, 14, -3],\n [-1, -5, -12, -17, -19, -20, -17, -8, -20, -6],\n [7, -1, -21, -7, -1, -12, 13, -11, 17, 12],\n [20, 22, 18, -8, 21, 19, -2, -19, -16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, -17, 16, -6, 13, -21, -6, 6, 4, -16],\n [-12, 3, 16, 9, 0, 17, -16, -22, 2, 8],\n [-17, 5, 8, 13, -7, -8, -1, -5, -15, -13],\n [14, 16, -17, 20, -13, 16, -16, 19, 22, 12],\n [5, 2, 5, -14, -18, -7, 6, 20, 0, -5],\n [3, -18, -15, 17, -4, 14, 5, -19, -3, -1],\n [-11, -22, -15, 18, 4, -2, 22, 10, 15, 10],\n [14, 22, -18, -8, 7, -20, 5, 7, 13, -20],\n [21, 8, -9, -17, -4, -18, 3, 21, -5, 14],\n [22, 13, 8, -5, -14, 3, -21, 9, 19, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-17, -3, -15, 22, -19, 2, 8, -4, -16, 14],\n [7, 4, -6, 9, -4, 2, 6, 2, 9, 14],\n [-12, -19, 8, 13, -19, -21, 16, 10, 21, 4],\n [3, -4, 21, 18, 16, 10, 15, -13, -22, 12],\n [-12, -9, -17, 20, 16, 17, 2, 0, -18, 3],\n [-5, 9, -2, 3, 12, -13, 5, 8, -8, 17],\n [-15, -13, 22, -13, 15, -5, 5, 5, -3, 1],\n [-17, 18, 9, -17, -12, 7, -20, -15, 10, -4],\n [-13, -4, -14, -16, -9, -21, -1, 22, -3, 3],\n [-19, 16, 17, 0, -7, 2, -14, -12, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 13, -9, 0, -7, -3, -20, -17, 6, -19],\n [-22, -15, -3, -7, 8, 9, 11, 6, -11, -19],\n [20, 11, -17, -14, -18, -7, -22, -3, 12, -13],\n [2, 5, 12, 10, 22, -8, -2, 19, 12, 14],\n [-13, -7, -3, -15, 22, 8, -15, -10, 1, -11],\n [22, -6, 18, 13, -11, 13, -10, 12, -18, -10],\n [-15, -12, -15, 8, -11, -12, -6, 4, -10, 13],\n [-10, 18, -1, 21, 1, 7, -10, -15, -18, 20],\n [-17, -16, -1, 7, -8, 14, 18, -3, 8, -18],\n [22, -11, 14, 7, 16, -20, -10, -12, -13, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, 7, 6, 15, 19, 11, 3, -21, 13, -16],\n [13, 17, -9, 4, 3, -3, 12, -12, 3, 12],\n [-18, -7, -12, 10, -14, -1, -18, -3, 20, 11],\n [7, -13, 14, 9, 1, -6, 21, -20, 16, 20],\n [20, 3, -11, 14, 19, -11, 10, 4, -9, -16],\n [19, 21, 15, 19, 21, 4, -13, 19, 20, 18],\n [-14, 21, 11, 18, 6, -5, 6, 7, -10, -1],\n [-7, 22, 9, 17, 3, 8, 21, -4, 19, 11],\n [-17, 12, -12, 14, -1, -10, -7, 3, -1, 19],\n [-10, 0, 9, 0, 20, 9, 15, 5, 10, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 7, -6, 19, 6, -21, 15, 11, 15, -11],\n [-2, 4, 17, -20, 14, 3, -18, -3, 18, -15],\n [20, 5, 6, 18, -21, -21, 15, 15, 20, 0],\n [-13, 22, 5, -4, 5, 8, -21, 6, -9, 5],\n [-22, 21, -7, 14, -2, -9, 20, -6, -8, 8],\n [13, -9, 13, 4, -20, 13, -17, 4, -1, -1],\n [13, 9, 4, -16, 16, -11, -7, 15, -18, 19],\n [12, -14, 6, 4, 9, -13, 2, 19, 15, 2],\n [-19, 20, 18, 21, 0, -13, -17, -10, 8, -18],\n [-19, -20, 7, 0, 14, -5, 12, -18, 18, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[15, -5, -15, -11, 7, -1, -17, 7, -15, 6],\n [8, -18, -12, -6, -10, -3, 8, 3, 5, 2],\n [-5, 22, 9, 6, -20, 12, 15, -8, -20, -2],\n [-20, 12, -15, -20, -12, -21, 10, -15, -11, -4],\n [-5, -2, -1, 20, 7, -5, -17, -22, -14, -7],\n [6, 6, -18, -4, -1, -15, -5, 21, -9, -19],\n [17, 4, 1, 7, -11, 20, -10, 17, 22, -19],\n [3, -22, 4, 0, 19, 15, -12, 16, 19, 21],\n [-2, -1, 5, 15, -17, 2, -19, 11, 3, 16],\n [4, 16, -2, -2, 6, 11, 4, 19, 3, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-3, -15, -5, -18, -19, 20, -18, -7, -14, 2],\n [15, -15, -22, 8, 10, -18, -5, 13, -3, 1],\n [-4, 5, 7, 16, -8, -14, 16, 8, -22, -10],\n [13, -21, 19, 14, 12, 14, -12, -5, -3, -21],\n [1, -7, 0, 15, 21, 6, 7, -19, 6, 21],\n [20, 18, 4, 10, -5, -17, 9, 8, -11, 0],\n [6, -20, 10, 16, 5, -5, 21, -1, -3, -7],\n [-16, -19, 19, 15, 11, 13, -5, 10, -22, 2],\n [22, -9, -12, -15, 19, -7, 16, 14, 8, 19],\n [-5, -16, -19, 9, 8, -13, 7, 12, 22, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[8, 10, -18, -13, 0, -16, 5, -2, 8, 18],\n [4, 6, -13, -15, -14, -12, -1, 17, 3, 14],\n [17, -21, -4, -7, -19, 15, 21, -16, -9, -11],\n [-2, 11, -2, 13, 17, 19, -16, -2, -13, -2],\n [-7, 2, -10, 4, 14, -15, 7, 8, -16, 7],\n [-5, 0, 15, 22, 18, 7, 7, -15, -11, -13],\n [-16, 16, -6, 9, -18, 19, -2, 8, -8, -10],\n [-16, 1, -19, 18, -4, 12, 6, 13, 11, -15],\n [-21, -19, -21, 7, 6, -19, -2, -14, -21, -3],\n [10, -17, 6, -7, 13, -18, 14, -14, 9, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[11, 16, 17, 6, 8, -20, 20, 2, 19, 13],\n [21, -10, 16, -4, -7, 19, 7, 16, 12, -21],\n [-22, 22, -20, 3, 5, 4, -9, 20, 1, 12],\n [11, 1, -17, 8, 6, 13, 6, -10, -15, -8],\n [10, 2, -7, -2, 14, 22, -6, 11, -10, 11],\n [20, -8, 18, -1, -19, 16, 0, -10, -15, -22],\n [18, -6, -6, -15, -20, 6, -1, 20, -21, -21],\n [-6, -14, 10, 6, 6, 21, -17, 20, -17, 14],\n [22, -22, -7, -12, -1, 11, -22, -10, 19, 5],\n [-10, 15, 7, 13, -19, -9, 13, 0, -18, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -15, -12, -16, 0, 22, 18, 4, 8, 17],\n [-21, 21, 8, -15, -22, 2, -6, 7, 1, 8],\n [-10, -8, 3, 9, 22, 12, -7, -14, -4, 17],\n [17, 22, -20, 3, 14, -15, -17, -18, -2, 4],\n [21, 15, -15, -1, 0, 2, -16, -9, 18, 6],\n [-6, -17, 9, -4, 4, 7, 10, 14, 22, -12],\n [18, -13, 6, -1, -3, -4, 1, 5, -21, 17],\n [-5, -5, -21, 0, -8, 2, 22, -5, -2, 9],\n [-4, -5, 1, 19, 7, 6, -2, -2, 18, -21],\n [22, -22, -1, 17, 15, -4, -4, -21, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 22, 0, 5, 5, -18, -5, 7, 1, 14],\n [-7, 6, 7, 2, 15, 16, -22, 17, 16, 16],\n [8, 16, 8, 10, -11, 2, 0, 20, 5, 10],\n [15, 3, 1, -18, 21, -6, 22, 14, -8, -21],\n [11, -3, 7, -7, 21, -19, 8, 3, 18, -11],\n [-21, -15, -9, 1, 20, 17, 18, 2, -16, 9],\n [0, 16, 3, 19, -16, 22, -19, 21, 2, -5],\n [-16, -1, -19, 6, 1, 17, 15, 18, -11, -14],\n [-8, -10, 7, 12, 12, 3, -4, -2, -2, -10],\n [-2, 1, 3, 21, 8, 7, 1, 9, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[15, -5, 18, -11, -2, 0, 5, -6, -8, 0],\n [11, 5, -19, 18, -11, -21, 2, 1, 8, -19],\n [21, 11, -17, 8, 16, 1, 2, -18, -13, -5],\n [6, -12, 7, 20, -18, -17, -9, -7, -9, 10],\n [14, -18, 17, -9, 17, -14, 4, -20, -13, -12],\n [11, -22, -13, -17, -15, 8, -17, 8, 11, 17],\n [6, -20, -1, -11, 15, -4, -16, 0, -10, -19],\n [-2, -9, 13, -16, -10, 12, 10, -12, 16, 2],\n [16, 1, -1, 20, -1, -8, -5, 21, 22, 9],\n [13, -13, -14, 21, 2, -19, 15, 13, 19, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[16, -16, 19, 3, -3, 22, -2, -18, 7, 15],\n [13, 15, 0, 0, -17, 20, 0, -8, -22, 13],\n [16, 5, -13, 10, 1, -17, -9, 9, -4, -17],\n [-3, 2, -3, 15, -12, 9, 6, 7, 6, -1],\n [-12, -3, 18, -9, 4, 15, -19, -16, 7, -13],\n [-16, -18, -19, 13, -8, 16, 15, 13, -21, -8],\n [-3, 11, -10, 2, -9, 18, -14, 12, -1, -18],\n [21, 14, -9, -6, -18, -10, 8, -13, 0, 6],\n [-7, -6, -16, 20, -9, 21, -14, -16, -9, -7],\n [-13, -18, -16, -1, 1, 17, 19, -1, 12, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, -16, -4, 19, -15, 0, -3, 10, -17, -8],\n [-18, -9, -14, 3, 9, 8, -17, -22, -4, -8],\n [11, -4, -12, -5, 1, -14, -12, 20, -19, -5],\n [21, 0, 18, 14, -22, 2, -14, 16, -22, -6],\n [-20, 0, -22, 1, -10, -3, -3, -11, -6, -2],\n [17, 1, 7, 0, 0, -6, -21, 19, 1, 10],\n [22, 21, -8, 9, 19, 11, -1, 8, -8, -3],\n [19, 0, 8, -21, -10, 19, 9, -7, -8, 2],\n [-11, 5, 18, -11, -2, -11, -7, -13, -13, -21],\n [4, 7, 10, -7, -13, -8, 3, -8, -17, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[22, -22, 0, 11, 12, 20, 2, -22, 2, 15],\n [-7, 18, -11, -13, 4, 16, 19, -16, -17, 22],\n [-12, 1, 17, 2, 14, -20, -19, -19, 18, -22],\n [7, -8, 22, 8, 14, -18, 20, -2, 12, -19],\n [-16, 6, 13, 12, 9, 19, -12, 10, 18, -6],\n [-11, -22, 0, -16, -9, 18, 21, 17, -16, -9],\n [11, -21, -3, -6, -13, -18, 10, 14, 13, 21],\n [-12, -2, -19, 2, 18, 12, 12, 12, 16, 10],\n [-10, -19, 21, 17, 15, 19, 22, 7, 4, 12],\n [5, 18, 19, 22, -15, 3, 20, 11, 6, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "414", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-17, -7, -16, -12, -7, -17, 14, -14, -20, 6],\n [-15, 17, -6, 15, 21, -17, -12, -13, -21, 6],\n [-17, -14, -21, -19, 18, 17, 7, -19, -22, 20],\n [-12, -16, -5, -15, 7, -8, -13, -21, 19, -8],\n [-1, 11, -20, -19, 2, -18, -11, 1, -4, 9],\n [-11, 14, 4, -5, 2, 0, -20, -21, -12, 14],\n [7, -10, 17, -17, -11, 16, 20, -15, -14, -19],\n [14, 13, 9, -11, -5, 8, 17, 20, 16, 6],\n [17, 6, 4, -12, 10, 16, -5, 21, -3, 5],\n [-1, 9, -2, 14, 4, 15, 3, 0, 11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-12, 13, 9, 16, 14, 20, -7, 19, 8, 18],\n [-17, -10, 13, -12, -12, -3, 6, -4, 7, -17],\n [-6, -5, 13, -5, 20, -11, 19, -20, -5, -7],\n [16, 20, 5, 19, -14, -3, -5, 2, -2, 22],\n [3, 0, -13, 21, -10, 14, -11, 13, -20, -9],\n [12, 11, 17, 6, 7, -16, -21, -5, 3, -6],\n [-11, 9, 6, -13, 13, -21, 14, -9, -13, 17],\n [-22, 18, -2, -18, -14, -14, -5, -18, -7, 11],\n [-19, -2, 14, 17, 21, -9, 4, -11, 4, 11],\n [-19, 20, 21, -21, 19, 19, 9, -21, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -3, 13, -5, -9, -3, 22, 1, 8, 13],\n [-8, -16, 0, 6, 18, -19, 8, -5, 22, 8],\n [13, -5, -13, -16, 15, 22, 5, -5, 8, -14],\n [20, -7, 17, 2, 14, 7, -21, -18, 19, 7],\n [-4, -9, 4, 7, 22, -9, 8, 13, 16, 7],\n [15, -12, -6, -13, -7, -12, 16, 5, -2, 5],\n [0, -22, -10, -15, -4, 1, 17, 14, 2, 20],\n [3, 19, 4, 9, 21, -20, 18, 20, -14, -22],\n [-5, -20, -9, 9, -19, 14, -2, 19, 4, -18],\n [-20, -1, -3, 18, 21, -21, 20, -22, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -20, 8, 4, -10, 10, 2, -7, 15, 3],\n [-5, -6, 2, 3, -5, -22, -16, 7, 10, 2],\n [2, 4, 12, 20, -5, 7, -9, 12, 11, -3],\n [-8, -16, -10, 13, 17, 11, -10, -19, -10, 21],\n [-10, 0, 6, 10, 0, -20, 9, -20, -11, -19],\n [10, 9, -6, -14, -18, -2, -20, 16, -20, 14],\n [21, 12, 10, -20, -5, -20, 6, 14, -18, -14],\n [-11, -7, 4, -14, 20, -1, -6, -22, -20, -18],\n [-1, -22, -19, -1, 1, 9, -21, 13, -18, -16],\n [13, 17, 20, -15, 13, 20, -11, 5, -21, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, -2, 7, 14, -2, 5, 10, 19, -16, 19],\n [-7, 14, 2, 15, 21, 15, 19, 19, 22, 7],\n [-6, -7, -19, 7, -3, 12, -18, 22, -9, 18],\n [18, 17, 5, -13, 7, 9, -11, 22, -7, 3],\n [12, 18, -7, -6, 0, 19, -1, -2, 11, -18],\n [15, 8, 10, -20, -4, -5, 5, -8, 10, 5],\n [-15, 17, 7, -22, -16, -9, -2, -17, -6, -9],\n [-16, -8, -15, -13, 6, 18, -4, -21, -15, 7],\n [20, 13, -5, -21, -18, -10, 17, -12, -15, 15],\n [-6, -12, 3, 16, 11, -20, 2, 1, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[18, 17, 4, 21, 21, -13, -14, -21, -2, -12],\n [-13, 2, 17, -18, -1, -18, -14, -12, 21, -18],\n [-17, 10, -7, 1, -9, 1, 22, -11, 0, 16],\n [-17, 18, -2, -14, 18, 13, 18, 17, -18, 19],\n [8, 12, 18, -20, -4, -4, -22, -1, -4, 3],\n [-8, -4, 2, 16, 8, 7, 10, -7, 17, -11],\n [5, 7, -17, 19, -9, -18, 13, 0, 9, 8],\n [-9, 9, 4, -22, -14, -7, 12, -13, -7, 7],\n [10, -8, 16, -15, -19, 21, -21, -16, 15, 11],\n [2, -16, 2, -21, 3, 13, 15, 19, -20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-12, 20, -2, 20, -19, -18, -17, -1, 16, -17],\n [-9, -1, -7, 9, 13, -16, 0, -9, -17, 19],\n [2, -20, -10, -20, 8, -20, -6, 16, -21, -18],\n [-14, 6, 12, 17, 13, 12, 7, -8, 6, 2],\n [-12, 14, -19, 20, -11, 9, -18, 19, 19, 14],\n [14, 2, -19, 1, 13, -21, 12, 13, -15, -14],\n [5, 17, 21, -13, -18, 14, 8, 6, -20, 3],\n [8, -21, -8, -10, 5, 21, -9, -11, -8, -2],\n [6, 22, 12, -3, -5, 15, -8, -11, 11, -18],\n [-6, -10, -10, 13, -7, 17, -20, -21, 2, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-12, -12, -13, 5, -12, -16, 6, -22, -8, -16],\n [-19, -20, -3, -20, 6, -3, -13, 12, 3, 7],\n [3, 14, -3, 19, -14, -12, 10, 7, 7, 22],\n [0, 13, 1, 8, 0, 19, 13, 17, 11, -2],\n [3, -16, 2, -20, 20, -5, -17, -10, -21, 17],\n [-10, -22, -21, -19, -10, 7, 21, -11, 10, 15],\n [20, 11, -20, 20, -14, -16, -19, 5, 19, 9],\n [-22, -10, 13, 3, -10, -1, 1, -12, 2, -8],\n [22, 13, 15, 11, 11, 9, 15, 2, -20, 20],\n [6, -2, -14, -2, -2, -16, 9, -1, 19, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[11, -9, 18, -1, 2, -7, 10, -21, 16, 21],\n [-17, 11, 19, 14, -1, -7, -16, -10, -6, -20],\n [-11, -17, -11, -12, 18, -4, 8, -21, 22, 9],\n [-5, -19, -1, -9, -9, 14, 6, 11, -17, 20],\n [-11, 1, 22, 6, -13, 13, 11, 9, 9, -8],\n [-14, 13, -1, -10, 18, 21, -9, 3, 21, 2],\n [-1, 7, -10, 9, 14, -4, 12, 6, -16, 12],\n [16, -17, -9, 5, -22, -2, 4, -1, -12, -14],\n [-13, 20, 16, 8, 9, 8, -15, 17, -18, 8],\n [-16, 22, -9, 2, -2, 6, 22, 8, -19, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "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, -22, 9, -22, -19, -3, 17, 14, -9, -9],\n [-21, -2, 6, -11, -5, 15, 18, 9, 18, -1],\n [13, 19, -11, -2, -15, 5, -1, -7, -11, -6],\n [-2, -16, -3, 13, 18, 21, -10, 18, 6, 20],\n [14, -15, -3, 21, -13, -8, -11, 22, -7, 19],\n [-15, -3, -9, 14, 3, 15, 18, 22, 6, -10],\n [11, -1, 22, 3, 11, 1, -2, 8, -11, 19],\n [1, -2, -19, 2, -15, 13, 11, 4, 5, 6],\n [6, -13, 21, 9, -15, -6, -11, 3, -20, 19],\n [-12, -9, -16, 3, 14, 10, 21, 9, 15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-13, -8, -8, -17, 2, -22, -17, -10, -12, 1],\n [-3, 3, 2, -11, -14, 22, 13, -14, 10, 17],\n [11, 1, 22, 22, 10, 10, 6, 15, -10, -5],\n [12, -21, 2, -17, 2, -3, -9, -19, -15, 11],\n [5, -21, -6, -19, 11, 4, -4, 5, 15, 11],\n [9, 18, 8, -17, -17, 5, -15, -22, -7, 19],\n [-4, -5, 7, -7, 10, 5, -7, -12, -17, -9],\n [13, -1, 17, 0, 8, 5, -4, -1, -22, -20],\n [-15, -10, -22, 6, -10, 19, 6, 7, -7, 18],\n [11, 17, -20, 6, 7, 11, -19, -15, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-13, -9, 8, 12, -21, -21, 12, 11, 6, -17],\n [-19, -22, 12, 3, 6, -12, -19, -1, 10, 11],\n [8, -13, 12, 5, 0, -11, 6, -21, -10, 13],\n [3, -6, 20, 10, -1, -21, -13, 16, 3, 7],\n [-1, -12, -1, 1, 6, -13, 11, 2, -2, 16],\n [-10, -21, -17, -22, 5, -1, -12, 16, -18, -5],\n [-3, -11, -2, 4, 18, 11, -5, 11, -21, -9],\n [16, -22, 5, 18, 4, 7, -1, -11, -22, 10],\n [18, -22, -18, -18, -16, -3, 3, -17, 3, -20],\n [16, -9, -9, -3, 21, -14, -17, -21, 15, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[20, 10, 21, -18, -10, -8, 22, 11, -14, 3],\n [7, -1, 2, 17, -19, 5, 14, -13, -14, 13],\n [-22, 7, -12, 2, -12, 18, -18, 4, 0, -4],\n [-20, -15, 13, -8, -10, 7, 18, -13, 11, 7],\n [2, -17, 14, -6, 13, 17, 9, -1, 10, -1],\n [13, -5, 5, -10, -5, 0, 12, -5, -13, -21],\n [-9, 9, 7, -4, -18, 9, -13, -18, -9, 16],\n [19, 20, -4, -12, 12, 16, 15, -1, 22, 7],\n [7, -12, -1, -13, 20, -4, -8, 12, 12, -22],\n [22, -5, 3, -5, 18, -5, 20, -5, 9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 6, 18, -3, 12, 0, -11, 12, 13, 19],\n [5, 14, -3, 12, -16, 11, -17, -4, 19, -15],\n [7, -21, -7, 1, 2, -10, -14, 7, -14, 17],\n [-16, -7, 15, 9, 6, 20, 17, -8, -12, -14],\n [-7, 2, 9, 22, -13, -13, 7, -3, 18, 11],\n [-22, 9, 17, 8, -12, 18, -4, -16, 6, 19],\n [15, 13, 10, 13, 3, 6, 6, 12, -20, -18],\n [10, -12, -17, -21, -10, -22, 4, 17, 19, -8],\n [12, 7, -17, 11, -2, 9, -3, 12, -14, 14],\n [-17, -13, -14, 10, -7, 9, 15, -3, -3, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-9, -2, -15, 1, -2, 19, 9, -6, 17, -19],\n [19, 0, 13, -1, 2, -19, -13, 1, 12, -9],\n [-3, -9, 16, -14, 11, -3, -20, -11, 16, -11],\n [19, -1, 12, 17, 8, -16, -14, 14, -1, -14],\n [-7, -2, -14, -11, 4, -14, 4, 5, 12, 20],\n [15, 9, 18, -20, -14, -20, 13, -10, 11, 7],\n [-7, 10, 12, -7, 15, 17, -18, -15, 10, 7],\n [-21, 15, 15, -3, -14, -22, -21, -4, -7, 18],\n [-18, 9, -3, 20, -9, -10, 4, 12, 11, -7],\n [5, 20, 12, -8, -20, 4, 4, -19, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-18, 18, 16, 0, 0, -10, 4, -8, -11, -13],\n [15, 5, 20, 12, 15, -3, -11, -20, -21, 5],\n [-1, 12, 22, -14, 0, -6, -9, 9, 17, 13],\n [10, -13, -10, 11, -18, -17, 10, -18, 1, -15],\n [-5, 2, -5, 13, 3, -3, -3, 16, 17, 1],\n [-3, 22, -19, -1, 2, -2, -5, 22, -14, 21],\n [-14, 10, 18, -16, 10, -21, -15, 10, 12, 6],\n [9, -22, 8, 12, 17, 21, 16, -3, 10, 0],\n [-20, -11, -15, 18, -12, 3, 0, 15, -18, 9],\n [-18, -8, 20, 0, 5, -4, -6, -8, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "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, -7, -3, 2, 9, -2, -22, 5, 4],\n [4, 22, 13, -11, -8, -3, 21, -4, 3, -2],\n [14, 20, -13, 5, 3, -10, 2, 8, -3, -8],\n [-5, 17, 0, -20, -12, 4, 14, -11, 10, 5],\n [-17, -17, 21, -2, 2, 13, -5, 21, 16, -18],\n [0, 0, 0, 12, 6, -18, -6, 15, -21, -4],\n [-20, 7, 10, 0, 3, 7, -4, 16, 3, 9],\n [19, 5, -14, 8, -8, 9, -10, -1, 17, -12],\n [10, 1, 17, 21, -17, -7, 7, 7, -9, -16],\n [-20, 8, -13, 10, 15, 14, -8, -19, 14, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "302", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-19, -13, -1, 8, 13, -11, -14, 5, 11, -18],\n [7, -7, -4, -9, 1, -12, -10, -13, 6, 16],\n [4, -22, 9, -5, -19, -7, -5, -2, 2, -13],\n [-16, -22, 10, 10, -4, -16, 22, 18, -9, 15],\n [-16, 20, -20, -12, -15, 3, 15, -20, 6, -11],\n [-5, 20, -16, 7, 19, -7, 22, 2, -19, -19],\n [15, -22, 19, -20, 5, -12, 14, -21, -14, -6],\n [9, 8, -2, -6, 19, -6, 20, 4, 5, 16],\n [-22, -7, -20, -8, -19, 13, 7, 6, 0, -18],\n [-12, -4, -15, 20, -12, -14, 2, 2, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-10, -22, 7, -14, 17, 6, 8, -5, -20, 12],\n [-21, -19, 18, -8, -6, 3, 8, 7, 0, 7],\n [-12, 10, 15, -18, 12, -22, -19, 15, 14, -16],\n [-13, 10, -9, 13, 15, 7, 3, 8, 19, -4],\n [17, -10, 0, -4, -7, 2, 3, -2, -5, -14],\n [1, 17, -6, 7, -19, 5, 18, 17, -14, 13],\n [-15, -1, 2, -17, 3, 19, -21, 8, -11, -4],\n [14, 14, -22, -13, 11, -7, 18, -16, -10, -19],\n [16, 8, -13, -11, 11, 5, -18, 5, -12, 11],\n [-8, -18, -2, 8, 17, -16, 12, -2, 17, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-9, 11, -13, -5, -6, 15, 9, -6, -1, 2],\n [-7, 7, 11, -18, 21, 10, -18, 17, 19, -20],\n [15, -10, -15, 7, -18, 15, 8, -21, -16, -7],\n [-13, 6, 7, -3, 19, 11, -15, 11, 11, 22],\n [13, -16, -9, -3, 14, 10, 8, 10, 3, 3],\n [15, -7, -11, -22, 21, -3, -21, 8, -5, 19],\n [-13, -17, -21, -7, -18, 15, -1, -1, -1, -22],\n [13, -10, -11, -10, -12, -5, -1, -22, -19, -14],\n [-20, -15, -14, -5, -18, -1, 14, -18, 0, -7],\n [-18, 14, 21, 16, -20, 3, -15, -2, -5, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-17, 4, -1, -1, 15, 15, 20, 4, 22, 10],\n [19, 8, 5, 7, 11, 22, -6, 12, 13, -17],\n [22, 6, 0, -9, -14, -8, 15, 2, -3, 20],\n [-1, -16, -5, -6, -9, 3, 17, 9, 6, 17],\n [-16, -14, -11, -20, 9, 10, -8, -14, 21, -6],\n [5, 22, -10, -2, -18, -16, 15, 14, -4, 18],\n [9, 20, -20, 16, 12, 4, 15, -15, -4, 7],\n [17, -13, 7, -14, -1, 8, -13, 13, -13, 4],\n [-8, -4, -12, 9, -3, -8, -19, -6, -22, -4],\n [-18, -5, -6, 19, 18, -19, -4, 8, -20, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, -15, -18, 8, 4, 10, -5, 1, 3, 8],\n [-9, 2, 9, 16, 18, -9, 4, -1, 15, -16],\n [10, 20, 18, 10, 1, 3, 19, 8, 4, -10],\n [8, 9, 0, 14, 17, 22, -7, 16, -15, -5],\n [4, -14, 5, -1, -12, -1, -9, 0, -21, -8],\n [-18, 6, 10, 21, 7, -6, -22, -9, 21, -6],\n [-14, 12, 8, -11, 22, -21, -8, 11, 14, 18],\n [7, -9, 22, -19, -15, 0, -16, -6, -1, 15],\n [3, -15, -1, 17, 22, -1, 17, -18, -14, -3],\n [-1, 11, 12, 13, -4, 5, -16, 18, 15, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, 22, 8, 22, 2, 10, -18, 6, 8, 3],\n [-2, 11, 14, -22, -19, -1, -7, 22, 9, 11],\n [-2, 4, 19, 14, -20, 20, 22, 11, -16, 6],\n [-20, 22, 15, 18, -21, -11, -8, -7, -20, 4],\n [0, 10, 4, 1, 15, 4, 8, -8, 12, 13],\n [1, -6, 22, 11, -22, -3, -17, -18, 6, -17],\n [10, 22, 15, 6, 21, -13, 9, 2, 5, 6],\n [12, 9, 13, -16, -13, 11, 10, 3, -10, 7],\n [9, 10, -17, 13, -21, -16, 7, 3, 2, 10],\n [19, -17, -15, -14, -12, 1, -17, 17, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -16, 17, 17, 4, -13, -14, -13, 7, -14],\n [3, 11, 12, 4, -3, 1, 4, 18, -4, -5],\n [20, 18, -11, 17, -5, -15, 13, 15, -7, -10],\n [3, 3, -2, -2, -15, 10, -17, -21, -15, -17],\n [-17, -1, 2, 8, 12, -18, -1, 2, -5, -14],\n [2, 6, 10, 20, -15, 17, -10, -15, 18, 21],\n [4, -20, 10, 8, 5, -2, 6, 6, -14, -1],\n [-15, 22, -6, 0, 16, 7, -8, -9, 2, -7],\n [-5, 9, 15, -8, 14, 10, -10, -16, -4, -2],\n [14, -14, -19, 8, -16, -10, 17, 13, -15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "314", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, 3, 22, 19, -9, -3, 19, 22, 5, -15],\n [-18, -10, -21, -9, -20, -7, -14, 16, -21, -12],\n [1, 20, 6, -9, 17, -1, 11, 13, 10, 16],\n [20, -5, -1, 2, 14, -18, 9, 13, -14, -9],\n [9, -14, 0, 22, 22, -14, -2, 21, 9, 21],\n [-13, 6, 11, -1, -18, -12, 5, 1, 11, 19],\n [17, -13, 3, 20, 18, -16, 21, -16, -8, 22],\n [-20, 22, 3, -16, -21, -13, 7, -20, 15, 6],\n [2, -19, -18, -17, -4, -5, 15, 13, -11, 1],\n [7, -9, 16, -21, 11, -3, 13, 0, 12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "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, 15, -15, 20, 7, -3, -3, 0, -3, 0],\n [-19, -13, 17, -18, 9, -5, 2, -6, -18, 12],\n [19, -2, 13, -4, 0, -18, 10, -19, 10, 12],\n [19, 3, 14, -1, -12, 3, 18, -10, -9, 18],\n [-16, -7, -3, 22, 20, 4, 11, -1, 15, 14],\n [-20, 4, -16, 12, 22, 0, -21, 1, -21, 13],\n [-6, -12, -16, -21, -8, 8, -17, 14, 6, -19],\n [14, -11, 4, 2, 22, -11, -6, -11, 8, -14],\n [-4, 6, 2, -8, -14, -10, 21, 19, -20, -13],\n [-5, -13, 13, 5, -20, -3, -5, 14, -3, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[11, -1, -2, 10, -7, 19, 12, 13, -22, -11],\n [-10, -15, 8, -18, 21, 13, 2, 22, -10, 12],\n [9, -15, -1, -17, -12, -16, -8, -19, 17, 11],\n [20, 17, -1, 7, -4, 14, 15, 7, 9, -4],\n [2, 14, 22, 0, -11, -14, 14, -6, 12, 18],\n [7, -19, 18, -19, 1, -20, -14, -12, 9, 20],\n [17, 6, 11, 11, -2, 2, -2, -3, 1, -18],\n [18, -21, -14, 20, -15, 9, -16, 15, -3, -8],\n [16, 5, 8, -1, 17, 1, 11, -14, -21, 22],\n [2, -11, -19, 17, -10, 6, 9, 4, 7, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-22, -12, 0, -6, -8, 4, -13, -7, 14, 5],\n [-21, 16, 12, -8, -12, 10, -7, -12, -3, -4],\n [16, 0, -13, -15, -21, -16, 3, 17, -4, -17],\n [10, -12, 13, -11, 5, -14, 0, 17, -17, -4],\n [-3, -5, 4, 10, 6, -14, 22, 21, 4, 16],\n [-12, 19, -15, -9, -10, -16, -8, 15, 21, 20],\n [-5, 13, 8, -19, -10, 16, 7, -4, -19, -22],\n [17, 9, -11, -11, -3, -12, 7, 21, 8, 5],\n [21, 6, 18, -1, 22, 6, -22, -2, 8, 4],\n [12, -15, 17, -15, -17, -8, -2, 14, -17, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, 0, 15, 4, 19, 0, -4, 5, 11, -16],\n [-10, -19, -12, -2, -2, 20, 22, 19, 3, 8],\n [-19, -20, 16, -2, 15, -5, 10, 19, 12, 9],\n [-12, 16, 8, 7, 15, -3, 17, 3, -12, -21],\n [16, -6, 1, 7, 14, -17, 0, 12, 3, 2],\n [13, -2, 19, 20, 0, -22, -13, 2, -1, -15],\n [18, 10, -11, 16, -11, -11, -12, -15, -15, 14],\n [-7, 13, -5, 21, -2, -19, -16, 11, 11, 22],\n [13, 14, 7, 3, -11, -12, 6, -20, -12, -14],\n [3, -15, -2, -15, 19, -17, -5, -17, -2, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, 13, -5, 4, 22, -20, -11, -3, -4, 0],\n [-18, -4, -11, 5, 14, 11, -7, -19, 19, -17],\n [-16, 11, -19, -8, -10, -14, 14, -6, 15, -9],\n [14, 8, -21, -4, -4, -10, -2, 8, 21, 5],\n [-22, 12, -13, -15, -10, -4, -20, -20, 4, -5],\n [12, 21, 11, 7, -15, -2, -4, 20, 17, 7],\n [4, -3, -9, -11, 0, -11, 21, 21, 16, 19],\n [7, 4, 1, -20, 7, 12, 10, 14, 17, -7],\n [-5, -5, -9, 9, -11, 19, -21, 3, 0, 12],\n [10, 18, 2, -19, -2, -19, 8, -8, -19, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[21, -20, -18, -4, 15, 9, -14, -20, 11, 2],\n [-13, 9, -18, 6, -16, -8, -21, -13, -12, 17],\n [-2, -11, -19, 5, 6, -10, -5, 4, -20, 12],\n [16, -1, -6, 5, 15, -7, -18, -1, -6, -12],\n [-1, 21, 21, 13, 18, 21, 19, 17, -20, 4],\n [22, -10, -10, 7, -5, 17, 10, -6, 18, -13],\n [18, 21, 1, 19, 6, -15, 13, -9, 6, -16],\n [2, 19, 7, 5, -13, 11, -7, -13, 6, -8],\n [5, 1, 19, -3, 6, -21, 9, 19, 7, -14],\n [-4, -17, -15, 11, -22, -10, -17, 12, 6, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-13, 8, -15, 18, 16, 5, 8, -10, -16, -22],\n [22, 21, 3, -7, -11, -7, 11, 4, 2, -4],\n [-16, -11, 1, 16, -18, -22, -16, 3, 1, -6],\n [-19, -7, 13, -18, -18, 20, -6, 18, -2, 7],\n [10, 22, 0, 19, 6, 19, 16, 15, -16, 14],\n [-16, -8, 6, -13, -3, 22, -14, -17, -3, -2],\n [-16, 15, 11, -20, 22, -6, 20, -21, 19, -11],\n [-10, 15, 13, -11, 4, 3, 17, -18, 9, 13],\n [22, 15, -7, -13, 14, -8, -12, -14, -5, 10],\n [-14, 18, -8, 13, 13, -22, 5, 10, -22, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-12, 4, -18, -13, 5, -7, 20, 3, 5, -9],\n [-10, -22, 12, -8, 6, 8, -11, -18, 9, -13],\n [-18, 4, 16, -2, -7, 6, -8, 15, -16, -5],\n [-4, -6, -9, 18, -13, 2, 18, 21, -14, -7],\n [1, -2, 11, 16, -16, -16, 5, 12, -13, 15],\n [9, 11, 1, 18, 18, -21, 19, -19, -22, -1],\n [-12, -12, 22, -9, 4, 10, 5, 0, -14, -5],\n [20, 1, 4, 12, -19, -1, -12, -16, 18, 14],\n [11, -11, -19, 22, -21, -22, -5, 0, 11, -19],\n [19, 22, -4, 17, 19, 17, 18, -14, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-22, -11, -13, 4, -4, 17, 9, -1, 2, -12],\n [-12, 3, -7, 6, 7, -12, -22, -17, -10, 4],\n [20, 12, 10, -9, 20, -1, 19, -2, -21, -18],\n [-8, -3, 3, 1, 12, 1, 3, 18, -1, 4],\n [-4, 14, 13, 6, 17, 16, 20, -11, 21, -7],\n [8, -8, 10, -8, 9, -1, -17, 7, 18, -6],\n [21, -21, -7, -11, 22, -11, 16, -6, 19, 18],\n [-17, 18, 3, -22, -7, 17, -7, -7, 16, 6],\n [3, 7, 10, 20, -3, 14, -10, -15, 9, -5],\n [22, 18, -12, 15, 20, -9, 17, 10, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-16, -8, -8, -14, -2, 14, 16, 5, 21, -17],\n [-13, -8, 1, -19, 12, -8, 14, -21, 17, 5],\n [-18, 0, -14, -16, -19, -4, -15, 8, -9, 6],\n [-14, 14, -17, 19, 5, 22, -13, 22, -20, -11],\n [13, -12, -14, -17, -11, 18, -15, 18, -10, 20],\n [-14, -3, 17, -13, 18, 4, -19, -13, -4, -13],\n [0, 13, 18, -14, -21, -4, -15, 3, 13, -12],\n [-20, 7, -5, -6, -14, 7, -7, -15, 18, 3],\n [-18, -18, 1, -9, -18, 13, 2, -6, -17, -16],\n [-8, -17, 9, 19, 17, 4, 17, -18, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "370", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[16, 2, -21, 5, -16, 15, -22, -5, -11, -15],\n [-3, 12, 19, -7, 10, 17, 2, -4, 12, -7],\n [-7, 2, 9, 21, 5, -14, -5, 0, 7, 9],\n [1, -12, 3, -12, -3, 21, -5, 11, 13, -19],\n [-2, 3, -9, 3, -10, 3, 18, -8, 4, 0],\n [-1, -13, -18, -19, 13, -7, 9, -12, 16, 10],\n [12, -19, 0, -20, -3, -22, 10, -13, 21, -20],\n [9, 22, 15, 8, -2, 1, 1, -13, -17, 5],\n [-22, 21, -13, 18, 7, -8, -9, 1, -13, 3],\n [-22, -3, 6, 11, -21, -21, -21, -15, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[22, -6, 7, -15, 19, 6, -4, 14, 1, -5],\n [-13, -7, 18, 19, 21, -18, -8, 0, 8, 7],\n [-16, -3, 16, -20, -20, 8, -16, -22, 4, -22],\n [-17, -3, 16, 21, -20, -21, 9, -3, 13, 4],\n [-3, -4, -2, 20, -3, -18, -3, -11, -13, -1],\n [15, 5, -11, 16, -13, 12, 21, 17, 14, -6],\n [4, 6, 3, -14, -11, 20, 3, 10, 9, -12],\n [6, -15, 2, -3, -2, -19, 13, 20, 6, -4],\n [3, 13, 2, 0, 15, 5, 18, -12, 6, 21],\n [-3, -14, 1, 18, -10, -21, -6, 4, 15, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, -18, -9, 4, 13, 4, -9, -8, 4, -15],\n [-2, 11, 5, 1, -6, -17, 15, -4, -22, 15],\n [3, -18, -19, 2, 22, 22, -1, -10, 0, 10],\n [2, -13, -5, 4, 3, 19, -21, -13, -3, 15],\n [-20, -13, 5, -4, -6, 21, 21, 0, 5, 4],\n [9, 15, -11, -3, -17, -20, -20, 0, -14, 10],\n [13, -11, 3, 14, -13, 21, -12, -4, -18, 1],\n [12, 5, 7, -4, -17, 22, 16, -4, 8, 21],\n [-12, -6, -6, -8, -17, 9, 17, -12, -10, -6],\n [5, -5, 5, -7, 13, 17, -3, 16, 4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "326", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[10, -21, -10, -21, 14, -18, -17, 9, 1, -6],\n [-14, 17, 17, -21, -14, -17, -4, 10, -4, 10],\n [22, 7, 16, -10, -5, -21, -20, -17, 5, -10],\n [-3, 9, 8, -14, -20, 8, -8, -19, -6, 22],\n [8, 6, -12, 9, 17, -20, -22, -15, 18, -6],\n [-15, 20, 10, 3, -21, 6, -8, 7, 21, -11],\n [-21, -2, 6, 6, -7, 8, 10, -21, 21, -19],\n [16, -18, -21, 22, -15, 13, -17, 18, -13, 13],\n [-19, 16, -9, -11, -6, -2, -10, 10, -10, 22],\n [-14, -3, 21, 17, -22, -10, -1, -10, 12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[10, -18, 7, -18, 20, 2, 3, -4, -11, -15],\n [-13, -5, 18, -12, 7, -18, 1, 22, -10, 13],\n [4, 9, -9, 18, -21, -19, -12, 19, 14, 15],\n [14, -10, -14, 19, 4, -21, 4, -11, -11, -20],\n [3, -8, 4, 22, 12, -10, -18, 20, -6, -4],\n [-3, 0, -11, 9, 6, -18, 20, -21, -17, -2],\n [12, -8, -5, -21, -18, 14, 18, -17, 19, -4],\n [-7, -11, 1, -14, -20, -6, 7, 4, 1, 19],\n [16, -16, -14, -7, -12, -14, -22, 21, 12, -3],\n [-15, -16, 14, 14, -3, -18, -11, -2, -3, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -16, -22, 2, -4, -21, -11, 19, 2, 9],\n [20, -5, 8, 21, -14, -2, 16, -16, -10, -3],\n [-10, 5, 14, 2, 22, 3, 21, 10, 17, 17],\n [4, -8, -20, 6, 8, 17, -5, 1, 16, 21],\n [-15, 6, 14, 14, -14, 22, 7, -8, 17, -11],\n [18, 4, 8, -10, -8, -18, 19, 2, -11, -14],\n [3, 14, -14, -18, -16, 18, 8, 21, 14, -16],\n [-18, -6, -12, 14, 13, 4, -22, -22, -9, 5],\n [18, -22, -15, 22, 18, 20, 3, 13, 6, 17],\n [22, -19, 19, -21, 7, -3, 7, -5, 7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-22, -20, 0, 22, 17, -1, 21, -8, 18, -7],\n [4, 9, 11, 19, -11, -5, -5, -19, 11, 16],\n [-4, 20, 22, 8, 8, 19, -3, -3, 9, -3],\n [-7, -4, 8, -10, -3, 20, -11, 3, 12, 18],\n [-13, -11, 1, -14, -18, 8, 11, 22, -12, -14],\n [-1, 17, 5, -7, -13, 11, -8, -5, 22, 8],\n [-18, 10, 6, -20, 0, -13, 9, 4, 13, 1],\n [-3, -20, -18, -20, 17, -17, -8, -17, 0, 7],\n [16, 17, -2, 22, 14, -1, -21, -9, -5, -8],\n [14, -21, 20, -3, -13, -18, 9, -21, 21, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, -5, 17, -19, 9, 13, -19, -6, 19, 10],\n [-1, -5, 4, -8, 2, -13, -7, -19, 8, 9],\n [1, -5, 9, 5, -12, -15, -22, -21, -2, -4],\n [19, 7, 17, 2, -14, 19, 5, 14, 9, 18],\n [-12, -2, 1, -22, -7, 1, -13, 9, 5, 10],\n [15, -1, -22, 12, 22, -11, 2, 5, -6, -7],\n [9, 22, -19, 18, -12, -3, 3, -16, 8, -16],\n [-19, -15, -9, -1, 0, 2, 13, 3, 1, -5],\n [-2, -18, -8, 8, 3, -19, -19, 21, -4, 3],\n [10, -19, 15, 1, 8, 11, 11, -21, 20, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -11, 13, -22, 19, 16, -7, -17, 10, 20],\n [-10, 22, -14, 12, 5, 11, 9, -22, 16, 2],\n [-13, -21, -19, 2, -7, 17, 21, -18, 0, -3],\n [-20, -22, 2, -7, 18, -18, 13, -17, -11, 0],\n [15, -18, -21, -20, 18, -16, 3, -11, 22, -22],\n [-22, 10, 16, -14, -22, -8, 2, 21, 13, -13],\n [8, -3, -18, 5, 11, 16, 15, -7, -8, 18],\n [16, 19, 3, 7, -21, -20, -4, 1, -20, 17],\n [-18, 9, 8, -11, 20, 13, 13, 8, 10, -16],\n [3, 3, -3, 11, 10, -4, -6, 20, 14, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "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, 15, -6, -3, 19, 19, 18, 3, 5, 22],\n [-15, 20, -16, -16, 6, -20, -7, -10, -5, 21],\n [-10, 8, -20, 7, -20, 3, -21, 16, 11, 15],\n [-10, -12, 14, -16, 20, 4, -16, -15, 13, 19],\n [6, -2, 3, -3, 6, -8, 0, -8, -13, -21],\n [7, 14, 4, -6, -20, -15, 20, 14, -19, 1],\n [6, -15, 11, -14, -6, -13, 1, 22, -1, -6],\n [8, 21, -14, -8, 19, 7, -6, -16, 22, 3],\n [-21, 6, -17, 10, 15, -22, -13, 8, 1, -15],\n [5, 5, 21, -15, 6, -4, 6, -8, 8, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[5, -8, -15, 13, 9, 16, 16, -1, -18, -13],\n [8, 14, 0, 9, 1, -19, 20, 15, -8, -12],\n [2, 3, 16, 14, 13, 10, 21, -3, 11, 22],\n [-11, 13, -19, -10, -20, -6, -16, 22, -9, 9],\n [3, 8, 8, -7, -22, 11, 3, 7, 18, -18],\n [1, -13, 15, 12, -21, 6, -4, 15, 19, -9],\n [5, 11, -19, 2, -17, 5, 15, -14, -5, 8],\n [-1, -19, 10, 13, 12, -10, -8, 10, 5, 11],\n [15, -22, 8, -6, -1, 9, 6, -22, 5, 18],\n [-21, 2, -2, 14, 3, 17, -22, 9, -14, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[17, -6, 6, 21, -4, 17, 6, -11, -15, 20],\n [20, 8, -8, 11, 3, 12, 6, 10, 10, 13],\n [-2, 7, -4, 9, -22, 10, 3, 19, 22, 4],\n [5, -3, -15, 3, 8, -18, -12, -2, -15, 3],\n [-11, 20, -10, -13, 6, -15, 19, 15, -22, -14],\n [-19, 10, 19, -2, -16, 9, 16, 5, 3, 14],\n [11, -14, -17, -1, -14, 22, -8, -22, 9, -5],\n [-12, 12, 10, -19, 11, -4, -11, 17, 13, 18],\n [-1, -11, 5, -8, -19, -15, 8, 3, -20, 16],\n [-16, -8, -3, -6, 9, -13, -7, 3, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-11, 16, -20, 1, -21, -19, 0, 0, -15, 19],\n [21, -11, -14, -12, 22, 8, -22, 12, 20, -8],\n [-16, 5, -17, -3, 1, 19, 13, 15, -11, -20],\n [5, -11, -7, 21, -8, 8, -2, -5, -17, -6],\n [0, 12, -5, -12, 0, -6, -17, 1, 14, -7],\n [6, 6, 19, 5, -7, -20, 19, 1, -5, -6],\n [-13, 14, 2, 13, 0, -4, -13, -12, 18, -18],\n [-17, -20, 22, 15, -12, 20, 19, 1, 3, 3],\n [1, 17, -19, -13, 11, 21, 6, 3, -4, -2],\n [-4, 17, 15, -4, -5, -9, 12, -5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, -8, -20, 0, 22, -11, 9, 5, 11, -22],\n [-13, 4, -11, 22, 13, 10, -19, -2, -3, -6],\n [11, -9, -13, -3, 12, -8, 16, 4, -8, -4],\n [3, -11, 1, 13, 10, -18, -14, 17, -9, 13],\n [2, -16, 11, 20, -16, 8, 9, -2, -8, 7],\n [-19, 11, -14, -11, 7, 1, 6, -1, 12, -3],\n [14, 18, -14, -1, -7, -21, 21, 0, 6, -12],\n [12, -1, -20, -11, -22, 20, 3, 11, 6, 10],\n [9, 2, 13, -21, -8, -10, 19, -8, -17, -2],\n [19, 3, 12, 22, -5, -17, -9, -5, 20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-8, 22, 4, 1, -11, -22, -9, 9, -20, -13],\n [3, 8, -13, -22, 9, -4, -22, 3, -18, 3],\n [15, -22, 7, -11, 13, 13, 1, 19, 2, -15],\n [-11, 4, -11, 9, 12, -7, 13, 7, 14, 9],\n [-8, -2, 17, 6, 7, 2, -3, -13, 8, -22],\n [-13, -5, 13, -10, 9, -1, -17, 10, -22, -20],\n [-18, 4, -11, 10, 18, 4, -10, -12, -12, 13],\n [18, -19, 21, -5, -5, 5, -17, 20, -18, -12],\n [-18, -14, 0, -12, -8, 2, -6, 3, -9, 16],\n [-14, 4, 12, 4, -7, -1, 7, 3, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, 17, -22, -11, -6, 2, 6, 19, 5, -4],\n [18, -13, -12, -13, 7, -16, -18, 5, -3, 9],\n [-11, -18, 7, 10, -13, 16, 4, -11, -21, 7],\n [18, -18, 14, -9, 3, -15, 8, -20, 5, -9],\n [-12, 6, 17, -11, 20, -14, 13, -4, -16, -6],\n [0, -11, -16, 2, -9, 8, 2, -12, -12, -16],\n [20, -20, -8, -20, 18, -6, 21, -16, -12, -3],\n [-22, 9, 15, -2, 8, -6, 2, 18, 10, -11],\n [5, 3, 13, -15, 9, 3, -18, 20, 15, -10],\n [-4, -17, 22, -17, -7, 6, -5, 9, 6, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "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, 19, -18, 9, 6, 6, 19, -20, -19, 21],\n [2, -1, 19, -12, -15, 4, 21, -1, -20, 4],\n [-12, 4, -16, 4, -12, 2, 16, -7, -2, 3],\n [4, 22, -6, 8, -9, 0, -21, 3, 3, -1],\n [19, 5, -17, 16, -4, -2, 19, -3, 8, 4],\n [-8, 21, 8, -14, -6, -4, 9, -13, 17, -18],\n [-10, 4, -21, -22, -15, -13, 5, -18, -21, 18],\n [-6, 10, 2, -18, 5, -5, 0, 12, -5, -12],\n [20, 20, -13, -13, 13, -14, 19, -10, 0, -22],\n [-7, -4, -11, -18, -18, -16, 21, -9, 10, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -17, 7, -11, 12, -12, -19, -10, -22, 15],\n [6, -9, -2, 18, 8, 18, -16, -8, 19, -14],\n [6, 1, -8, -2, 18, 1, -16, 1, 0, 2],\n [-15, 11, 12, -1, 11, 5, -22, 21, 14, 7],\n [2, -21, 5, 5, 0, 15, 1, 12, -15, 13],\n [-5, -3, -19, -15, 3, 16, -3, -5, 10, -5],\n [11, -4, 19, 10, -2, -16, -9, 10, -19, 20],\n [-21, 17, 8, 7, -13, -2, 0, 14, -15, -13],\n [2, 10, -6, 1, 19, 7, -22, -6, 5, -10],\n [-13, -22, -3, -16, 9, -2, 3, 22, -16, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[22, 17, 18, 22, 4, 11, -11, -11, -8, -3],\n [-13, 3, -6, -13, -12, -6, -12, -8, -19, 2],\n [13, 8, 6, 8, -14, -22, -20, -19, -4, 18],\n [-1, -15, 2, -19, 22, -9, -18, 6, -2, -8],\n [0, -6, -20, 10, 4, -7, -17, 18, -13, 6],\n [-6, 16, -9, -11, 15, 6, -9, -15, 17, 17],\n [-6, 20, 16, 0, -16, -11, -7, -10, -4, -20],\n [20, -15, 17, -11, 8, 12, -3, 5, -21, 4],\n [-20, -2, -16, 10, 22, 10, 13, -6, -17, -2],\n [15, 11, -11, -11, -5, -17, -10, 8, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[19, -12, 10, -2, 16, 1, 21, -3, -14, 8],\n [5, 15, -18, 14, 18, 11, -13, 9, 14, -6],\n [13, 13, -10, -3, 15, -4, -1, -7, -17, -12],\n [-13, 8, -5, 9, 18, 19, 1, -7, 6, 16],\n [2, 17, 2, 17, 22, -4, -13, -22, 4, -1],\n [5, 12, -20, 15, 3, 21, -18, -13, -16, 7],\n [2, 19, 11, -2, 6, -6, 13, 17, -2, 11],\n [-7, 21, -14, 21, -20, 0, -10, 15, 11, 7],\n [16, 3, 9, -3, 15, -14, 16, -7, 22, 15],\n [-19, -11, 3, -13, -7, -22, -11, -1, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[7, 5, -2, -5, 18, 1, 3, 13, 20, -7],\n [9, -21, -14, -5, 22, -4, 15, -11, -10, 12],\n [-13, -1, -13, 12, 22, -7, 13, -12, -6, 2],\n [-22, -11, -20, -14, -4, -4, -3, -12, 1, -1],\n [-22, 21, 20, -13, -12, -15, -6, -17, -16, 8],\n [14, -19, -16, -7, 2, 13, 12, -9, 13, -14],\n [-12, -22, -14, 2, 17, -8, 1, -15, 6, -16],\n [-5, -20, 1, -3, 8, 3, 15, 20, -15, 9],\n [-15, -18, -7, 4, 16, -22, -18, -20, 22, -6],\n [10, -4, -19, -10, 20, 3, 18, 8, 12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, 7, -6, -10, 15, -16, -14, -2, 7, 14],\n [14, -1, 8, -19, -13, 7, 7, 18, -16, -8],\n [-4, -13, 16, 4, -20, 12, -5, 1, -10, 21],\n [-6, -6, -12, -6, -4, -16, -4, 11, 6, 7],\n [19, 6, 15, -15, -19, 5, -12, -5, -2, 17],\n [9, -6, 11, -6, -8, -3, 16, -12, -4, 9],\n [1, -17, -5, 18, -10, 3, -15, 3, -9, 18],\n [-17, -7, 12, 11, 17, 4, 13, -11, -22, 6],\n [-6, -5, -7, 12, -14, 21, 16, 15, 20, -17],\n [3, -6, 1, -13, 9, -20, -4, 12, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "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, -21, -3, 0, 10, -15, 14, 19, 7, 8],\n [18, -5, 8, 3, 1, -18, -12, 1, -22, -11],\n [15, 0, 21, 2, -11, -20, 1, 3, -8, 8],\n [20, 19, -2, -2, -2, 2, -11, 14, -5, -13],\n [-17, 6, 6, 6, -14, 9, -10, -12, 11, 6],\n [-11, 8, 18, -1, 3, 20, -11, 12, 15, -19],\n [22, -13, -5, -4, -8, 0, 0, -2, 3, 22],\n [11, 18, -10, 2, 21, 10, 5, -10, 4, -15],\n [13, 20, -17, -10, -3, -18, 22, 4, -4, -22],\n [-19, -21, 21, 3, 10, 21, 22, 15, -16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-18, -14, -10, 17, 6, -5, 7, -13, -4, -14],\n [-2, -22, 18, 3, -9, 16, 6, 20, -16, 1],\n [4, 19, -21, -21, -7, -11, 17, 3, -13, -8],\n [2, -19, 3, 0, 14, 19, -19, -22, -22, 16],\n [-20, -8, 20, -5, -2, -15, 2, 9, -17, 17],\n [-3, 6, -18, 12, -4, 16, -11, 10, 12, 19],\n [15, -15, 15, 8, -12, -19, 17, -18, 19, -1],\n [21, -6, -3, 20, -11, 21, -6, 4, 0, -18],\n [5, 14, 7, 22, 6, -9, -15, 4, -17, -16],\n [3, 19, 7, -6, -17, -20, -4, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[12, 12, -18, 15, -17, 6, 0, 22, 14, 9],\n [-22, 11, 21, 5, -16, 14, 6, -4, 21, -4],\n [-3, -8, 1, 18, -15, -16, -4, 5, -11, 3],\n [12, -19, 11, -16, 4, -20, 10, -11, -4, -6],\n [-5, -20, -10, 9, -18, 2, -1, -15, -7, 9],\n [-18, 13, 2, -7, 1, -9, -10, 0, 2, 4],\n [-15, -5, 14, -17, -17, 2, -3, 0, -6, 9],\n [-7, 14, -3, -20, -22, 14, 12, -7, -19, -20],\n [21, -6, 21, 19, 11, 19, 11, -6, 1, 14],\n [-21, -9, -13, -8, 14, -5, 22, -10, 12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[14, -13, 6, 11, 1, 4, -14, -14, -13, -11],\n [-8, -20, 5, -14, 16, 7, 0, 7, -7, 13],\n [7, 14, -7, 5, -3, -9, 22, 6, 14, -4],\n [-6, -22, 6, 6, 1, -4, 20, -13, 13, -6],\n [-6, 9, -7, 0, -7, 9, -21, 17, -17, -13],\n [11, 7, 13, -17, 22, 10, -18, 5, -16, -4],\n [20, 3, 15, 15, 16, -6, -4, 4, 14, -16],\n [15, -6, 6, 21, 16, 21, -6, -8, -7, 10],\n [-12, 10, 9, 22, 5, -3, 6, -7, 7, -6],\n [-9, 1, 14, -10, -5, -16, -12, -6, -4, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}
{"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, -13, -22, -22, 15, 4, 2, 3, 16, -13],\n [13, -15, 10, 6, 11, 4, 19, -19, -18, 19],\n [-12, -22, -10, -3, 11, 10, -9, -11, -12, -22],\n [-15, -5, -18, 8, -20, -1, -17, 1, 4, -2],\n [14, 11, 12, 13, 3, -22, -4, 3, 0, 17],\n [11, 4, -20, 16, -10, 16, -7, -20, 3, -18],\n [-20, 5, 20, 7, 0, -5, -18, -1, 22, -22],\n [4, -9, 18, -14, -19, 2, 8, 9, -21, 14],\n [-21, -9, -8, 2, -13, 5, -15, -9, -3, 19],\n [-10, -4, 11, 3, 14, 1, -2, 1, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-18, 2, 20, 17, -6, 2, 19, 10, -18, -8],\n [19, -8, -22, 20, -5, -17, 11, -21, -6, -18],\n [-3, -9, -11, -19, 18, -13, 16, 7, 14, 3],\n [22, -19, -17, -8, 22, 22, -5, -6, 10, 13],\n [20, 2, 5, -10, 9, -4, 8, -8, 21, 0],\n [17, 4, -22, -1, -15, -18, 1, 10, -11, -19],\n [-8, -14, 19, -10, -13, 19, -9, -22, 4, -1],\n [-1, 3, 1, 7, 17, -6, 0, -13, 10, -15],\n [-18, 11, 4, 8, 2, -21, -3, 20, -20, 18],\n [17, 15, 17, -8, 4, 1, 12, 0, -15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-7, -17, 16, 22, 6, 3, -14, -4, -16, 2],\n [1, 16, 14, 11, 6, 11, -3, -18, 21, 13],\n [7, -3, -12, -2, -3, -17, 22, 3, 0, -18],\n [2, 6, -19, 4, -13, 11, 4, -15, 12, 5],\n [-14, 11, 7, -6, 10, 6, 14, -10, 6, 17],\n [16, -9, -15, 9, -12, 12, -18, 14, 22, -18],\n [-21, 3, 7, -10, 15, 17, 4, -6, -8, 10],\n [7, 9, -16, 16, -7, -12, 14, -9, 0, 8],\n [5, 19, -18, 1, -5, -19, 0, -14, -12, 12],\n [-12, -16, -6, -5, 3, 3, -6, -13, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, 18, 5, -4, -22, 11, 15, 1, 18, 1],\n [-5, -22, -13, -19, -9, -2, 3, 15, -18, -8],\n [1, -13, 12, -6, 9, -14, 8, 18, -8, -20],\n [17, 12, -10, -1, -16, -3, 14, 3, -4, 7],\n [11, 12, 5, 12, 11, -7, 9, -6, 1, -18],\n [-11, -1, -11, 6, 16, 16, 13, -17, -15, -17],\n [7, -4, 7, 2, -13, -21, 20, 1, 5, 11],\n [-20, 3, -1, 9, 20, 13, -9, 14, -20, 5],\n [3, 17, -13, 21, 3, 17, 0, -16, 11, -11],\n [-1, -12, -14, -18, -17, -16, -5, -8, -22, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-14, -16, 21, -14, 21, -12, -20, -10, -18, 9],\n [-1, 20, 3, -20, 18, -15, 1, 17, -10, -12],\n [15, 22, 20, -9, -18, -10, 1, -7, 6, -4],\n [-6, 8, 6, 9, -6, -16, 15, -18, 1, 10],\n [0, -9, 11, -19, -22, -21, 6, -14, 5, 10],\n [0, -3, 8, 22, 3, 8, 9, 12, -8, -8],\n [14, 22, 2, -3, -1, -3, -8, 7, -9, 18],\n [-2, -6, -18, -8, 20, 4, 21, 16, -3, 18],\n [12, -6, -14, 20, 19, -19, -7, -7, 6, 21],\n [9, 9, 15, 16, 17, 15, 16, 18, -7, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-8, -5, -19, 14, 17, -19, -6, -6, 11, -4],\n [-1, 16, 20, -22, -5, 16, 5, -10, 12, -14],\n [-6, 11, -8, -14, 16, -4, -12, 1, -2, -5],\n [3, -19, -21, -6, -22, -10, -13, -6, -2, 20],\n [-14, 8, 12, -13, -8, 22, -21, 15, -20, 3],\n [10, 1, 10, 7, 20, -19, 20, 22, -1, -3],\n [6, -2, 22, -6, -21, 11, -1, -17, 2, -21],\n [20, -6, -14, -3, 14, -8, 3, 2, 8, 7],\n [-13, 15, 22, -2, 1, 11, 5, 14, 1, 6],\n [-6, 16, 1, -6, 14, -17, 19, 14, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, 18, -5, -1, 18, 14, 3, -11, -17, -6],\n [-9, -13, 3, -20, 19, -8, -7, 15, -9, 13],\n [-10, 4, -15, 0, 18, -12, -18, -18, 2, -5],\n [1, -14, 20, -12, -9, 19, -14, -18, 4, -12],\n [5, -14, -10, -4, -15, -19, 21, 2, -16, 4],\n [17, 0, 17, 6, 13, -13, 9, 0, 17, 1],\n [-2, 16, 17, 6, 22, 22, 4, 11, 3, -8],\n [-17, 2, -5, -16, -21, 11, -22, -21, 19, 13],\n [-19, 5, 0, 16, -3, 14, 21, -11, 9, 15],\n [8, -5, 6, 11, 6, 4, 8, 11, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[8, 8, 16, -2, -16, 9, -11, 0, 20, 20],\n [17, -17, 9, 15, -8, 3, -3, -11, 18, 22],\n [3, 7, 6, 7, -10, 18, 20, -1, 20, 18],\n [-6, 0, 2, -17, 14, 3, -2, 12, -17, -1],\n [-6, -12, -19, 21, -13, -6, 15, -5, -4, -1],\n [-8, 21, -4, 2, 14, -5, -11, 9, 3, 3],\n [19, 5, 2, 7, 18, 15, -9, -22, 10, -12],\n [12, -2, -1, -18, 17, -5, 14, 21, 6, -5],\n [-11, -2, 17, 7, 18, -8, 12, 5, -19, 5],\n [7, 4, -7, 9, -11, 21, 13, -8, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "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, -12, 7, 5, 0, -8, -12, 20, -2, 22],\n [16, 8, -8, -6, 2, 1, 22, 13, 10, 21],\n [-19, -22, 15, -12, -2, 2, 5, -17, -17, -1],\n [-8, 10, -6, -11, 8, 12, 11, 9, 0, 15],\n [-18, 17, -21, 8, -11, 16, 19, -3, -9, -12],\n [8, 10, 3, -21, 8, 12, 4, -18, -12, 16],\n [5, -7, 17, 3, 1, -19, -11, -5, -9, -6],\n [21, 18, -7, 19, -3, 20, 5, 18, -22, -7],\n [-19, 9, 6, -15, -21, 1, 18, -9, 21, 20],\n [-22, 10, -12, -3, -8, 5, -2, 0, -14, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, 19, -8, 21, -18, 19, 10, 7, -7, 13],\n [14, 18, 15, 1, 2, 4, -18, -2, 20, 12],\n [-17, -14, 22, 4, -22, 7, -8, 9, -3, -19],\n [11, 15, -3, 5, 16, 2, -12, -15, 11, 4],\n [21, -1, -15, 10, 16, -14, -1, -14, 8, 11],\n [-19, -9, -15, 18, 12, -1, -17, 10, -5, -15],\n [-16, 9, -16, -13, 13, 8, 8, -13, -3, 12],\n [6, 7, 8, 10, 17, -19, 11, -6, 11, 9],\n [10, 14, 8, 3, 8, 8, 5, 15, 21, -13],\n [-15, 13, -4, 5, -18, 1, -16, -3, -21, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-13, -5, 11, -9, -13, 15, 9, -20, -15, -14],\n [-12, -7, 11, 1, 8, -18, 10, 7, 7, -8],\n [16, -7, 3, -11, -4, 12, -3, -2, 14, -8],\n [-7, -7, 0, 21, -19, 6, 14, 1, -15, 21],\n [-18, 20, 6, -13, 21, -14, -1, -13, -3, -3],\n [4, 15, -13, -4, 18, 7, -7, 17, -11, -18],\n [20, -20, 1, 3, 8, -20, -22, -12, 22, -18],\n [-16, 10, -10, 19, 8, -10, -22, 21, 15, 16],\n [10, 19, 12, 16, 19, 19, -14, -17, 18, -14],\n [4, 19, 6, -19, 2, -7, 11, -12, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"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, 16, 22, 22, 5, 20, -18, -7, 5, -21],\n [19, -13, -4, -3, 15, 22, 12, 18, -13, 13],\n [-7, 3, 8, 19, -22, 0, 19, 4, -4, -7],\n [15, -15, -7, -11, -14, -16, 17, 14, 0, 18],\n [-15, 0, -3, -12, -22, 21, -18, -9, -16, 1],\n [16, -19, 4, -16, 1, -14, -22, 11, 17, 8],\n [16, 0, -20, 16, -3, 3, 11, 9, 10, 17],\n [-18, -13, 13, 7, -14, 9, -2, 19, 3, 0],\n [-14, -18, -15, 21, 20, -12, 13, -5, 8, 18],\n [-15, 13, -4, -1, -21, -12, -20, 10, -13, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-20, 16, 14, 11, 5, -9, 5, 7, 7, 4],\n [-21, 14, -10, 16, 19, 5, -3, 16, -5, 11],\n [22, -6, 15, 0, 8, -14, 12, 2, 16, 7],\n [-18, 5, -16, 19, 19, 19, 15, -4, 2, -5],\n [3, 22, -3, -21, 7, -1, 19, 11, 12, -18],\n [-8, 16, -8, 5, -11, -20, -13, 13, -16, 20],\n [-6, -3, 5, -11, -5, 22, 14, -11, -15, 17],\n [18, -4, 13, -17, 5, 21, -22, -4, -20, 13],\n [4, -17, 7, 14, 4, -17, 22, 18, -6, 7],\n [-8, -4, 7, 17, -14, 11, 3, 14, 12, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-21, -10, 20, 20, -14, -2, 18, 21, -22, -3],\n [-18, -11, 20, -2, 16, 0, -15, -1, 3, -4],\n [-8, 14, 18, -2, -10, -16, 2, 10, -20, 16],\n [9, 18, 13, 17, 0, -21, 9, -17, -16, -2],\n [10, -7, -20, 3, 2, -8, -1, 20, 14, -3],\n [6, 14, -4, 17, 8, -9, 20, -8, -22, -11],\n [-12, -14, 21, 10, 4, 11, -22, -13, -10, 6],\n [-18, -12, 4, 16, 13, 4, 20, 16, 2, 16],\n [1, 19, 8, -16, 2, -1, -12, 2, -4, -19],\n [2, 11, 5, -7, -21, 3, -15, 20, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -6, 7, 20, 15, 21, -11, 8, 21, 14],\n [15, -16, -16, 12, 4, 3, 17, 20, -4, -1],\n [-22, 11, 9, 6, -1, -3, 5, 22, 5, -15],\n [-2, -5, 19, -8, -13, 4, -5, -3, 15, 10],\n [7, -20, -22, -13, -22, 10, 6, 12, 14, 8],\n [-16, -3, 20, -1, 19, -11, -13, 15, 8, 17],\n [16, 22, -2, 0, 8, 21, 21, 7, -1, 22],\n [-2, 18, -3, 5, 16, -7, -4, 1, 20, 8],\n [-18, -6, -22, 14, 7, 9, 9, -21, 11, 21],\n [6, -18, 7, 20, 22, -5, -9, 14, -12, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -20, 1, 11, -15, 1, -7, -17, -2, 9],\n [16, -1, -14, -5, -11, -17, 4, 21, 16, -22],\n [-8, -9, -10, -2, 18, -17, -3, -19, 17, -4],\n [20, 17, -13, -18, -21, 8, 21, -3, -17, 20],\n [-4, -5, 7, -16, -6, -19, -20, 2, 7, 13],\n [-9, 18, 0, -7, 5, -11, -15, 7, 18, 15],\n [-17, 16, -18, -20, -13, 7, -7, -12, -20, -8],\n [21, -22, -10, 16, 16, 15, -20, 7, 21, 18],\n [3, -12, -17, -11, -7, -1, -1, 15, -11, 13],\n [-6, 17, 9, 22, 14, -20, 2, -4, 14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "384", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[18, 20, -4, -7, 3, 10, -8, 14, -3, -18],\n [17, 1, -17, -11, -19, 20, -10, -2, -18, -10],\n [-21, 21, -17, 6, 0, 12, -13, -3, 2, 13],\n [-13, 4, -16, -2, -1, -5, -22, 2, -2, 7],\n [9, 12, -9, 16, 19, 2, 6, 17, 9, -12],\n [5, -18, 12, 2, 18, -16, 10, 19, 4, 21],\n [-2, 4, 2, -1, -12, -17, -20, 7, 5, 18],\n [-6, 0, 11, -2, -18, 21, -8, -21, 1, -13],\n [-3, 12, 18, -2, 7, 6, 12, 15, 3, -3],\n [13, 20, 17, -5, -1, -10, -8, -7, 2, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-18, 4, 16, 10, 17, 15, -19, 20, 15, -21],\n [-4, -5, -12, 12, -12, 10, -21, -22, 10, -10],\n [4, -22, 19, 6, 22, 17, -1, 16, -3, 21],\n [17, 22, -21, 18, -6, 18, -18, 3, -10, 11],\n [7, 21, 18, -21, -11, -1, 15, -10, 2, 17],\n [16, 14, -2, -5, -4, -10, 2, -7, 22, 6],\n [-7, -1, 21, -11, 20, 3, 5, 5, 0, 16],\n [7, 13, 15, -9, 8, -11, -12, -19, 2, 20],\n [2, 21, -3, -15, 1, -5, 15, -14, 1, -18],\n [22, -10, -2, -14, -21, -22, -15, 1, 11, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[22, -22, 12, 18, 3, -19, 8, -18, 0, 11],\n [-8, -20, -4, 20, 16, 16, 4, -1, -8, 17],\n [19, -8, 9, 8, 16, -6, -10, 15, 14, -7],\n [5, 11, 9, 1, 14, -18, 21, 0, -2, -22],\n [-10, 21, -15, -22, -8, -13, -22, -9, 22, 19],\n [14, 18, -2, -22, 4, 8, -16, -5, 13, 1],\n [15, 12, -19, -21, 12, -5, -21, 4, 17, -16],\n [18, 8, 18, 11, -16, 22, 6, -15, 10, -20],\n [17, 9, -4, -19, -13, -5, -4, -11, -12, 9],\n [-17, 15, 5, 3, -15, -13, -1, 11, 22, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -17, 8, 13, -12, -5, 11, -20, 18, 15],\n [13, -6, 7, 7, 20, 8, 9, -4, -14, -7],\n [15, -4, 7, 13, -12, -8, 1, 18, -2, 20],\n [-13, 19, 2, 9, 10, 1, -2, 3, -6, -4],\n [-20, -10, -21, 18, 22, 9, 10, 9, 19, 2],\n [-20, 19, -16, 2, 0, 5, -11, -15, 12, 2],\n [7, 9, 13, 9, 2, 3, -15, -18, 20, -21],\n [-4, -20, -11, 16, 9, -17, -15, -18, -10, 8],\n [-10, -22, -19, -3, 6, 9, 10, -9, -4, -20],\n [-12, -14, 5, -21, -10, 12, 8, 20, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-18, 16, 11, 15, 20, -21, 22, 10, 4, -20],\n [-21, 5, 7, 18, 0, 10, -9, -9, -10, -19],\n [-4, 1, 13, -17, -11, -14, -10, 1, -8, 7],\n [9, 9, 11, 12, -5, -4, -8, -1, 2, 1],\n [-17, 13, -13, -11, -18, -3, 14, -5, 17, 10],\n [18, -11, 10, -18, -14, 10, 7, -6, 12, -7],\n [17, -4, -21, -17, 19, 22, -12, -14, 4, -9],\n [12, -3, 9, -15, -12, -21, -18, 7, 21, 18],\n [-12, -7, 2, 19, 2, -12, -22, 10, -22, -14],\n [4, 15, -4, 17, -6, -11, -21, -15, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[20, -2, -4, 11, 7, -3, -5, -2, 13, -16],\n [-18, -14, 22, -5, -22, 13, 22, -9, -15, 14],\n [-3, 8, -16, 18, 15, 21, 20, -8, 12, -6],\n [4, -2, 17, 21, 22, 3, 21, -18, 10, -18],\n [5, -2, -15, -21, 14, -9, 11, 21, 14, -2],\n [4, -5, -18, 11, -5, 12, 3, 6, 18, 5],\n [-17, 3, -5, 7, 10, 9, 3, -1, 11, -11],\n [-1, -2, 1, 2, -21, -22, -13, 11, -18, -6],\n [-22, -9, -2, -17, -12, 16, -3, -3, -2, 1],\n [18, 3, -20, 15, 18, 15, 5, -13, 1, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-16, 0, 0, 1, 8, -1, 4, 15, -18, -5],\n [-15, 12, -6, -11, 16, -1, -17, 7, -21, -18],\n [-21, 12, -18, 8, -6, 4, 8, -13, -11, -5],\n [-10, -15, 12, 21, -19, -16, -2, 22, 21, -8],\n [11, -1, -22, -17, -22, -4, 4, -13, -9, 11],\n [18, 9, -20, -7, 16, 10, -18, 12, -6, 0],\n [3, -16, 18, -16, -8, 7, -3, -20, -1, -16],\n [8, -20, 20, -6, -1, 14, -20, 7, 1, 10],\n [20, -13, -16, -7, 9, -21, -15, -8, -20, -3],\n [11, 18, -19, 0, -15, -13, 15, -18, -13, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-7, 0, -6, 5, -5, 18, -12, 11, -8, -22],\n [10, -14, 21, -6, -8, -19, 14, -17, -17, -4],\n [0, 7, -22, -14, -1, -22, 13, 2, -7, 3],\n [5, -18, -1, -9, -14, -9, -7, 7, 9, -17],\n [-6, -22, -5, -12, -12, 5, -11, 11, -7, -13],\n [16, -15, 3, 19, 19, 19, -9, -14, -4, 11],\n [15, 6, 6, 5, 1, 5, 19, 21, -11, -4],\n [-17, -21, 16, 8, 14, 6, 17, -11, 10, 22],\n [2, 19, -5, 7, -5, -16, -8, 7, -18, -18],\n [10, -17, 17, -19, -10, 19, 3, -3, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[14, 21, -22, 2, 2, -22, -20, 16, -2, 20],\n [2, -2, -20, 17, 6, 12, -1, 0, -10, 11],\n [0, 12, -4, -8, -8, 3, 16, -20, -6, 7],\n [5, 11, -7, 20, 18, -12, 1, 0, 2, 14],\n [-10, -4, 22, 11, -21, -15, -18, -12, -21, 15],\n [9, 1, -11, 15, -7, 1, 18, -6, 9, -3],\n [12, 7, 19, -1, 8, 14, 1, 1, -10, 2],\n [8, 13, -9, -3, 16, 5, 2, 15, 20, -12],\n [-5, 16, -4, -20, 18, 4, 0, 12, 15, 20],\n [-10, 3, -9, 12, 18, -17, 20, -15, 17, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-15, 22, -7, 6, 11, 6, 12, -13, -22, -18],\n [-20, 16, -9, 4, 6, -22, -5, -20, 3, -2],\n [1, 22, -3, 6, -5, -20, 10, -5, 14, -2],\n [21, -4, 0, -3, 1, -4, 3, 10, 9, 12],\n [2, 10, 1, -14, 14, 14, -12, -2, -6, -7],\n [-18, 21, -13, -10, -17, 14, -7, -17, 6, 2],\n [0, -12, 6, -2, 3, 18, 14, -12, 15, 1],\n [-6, -14, -15, 7, -16, 14, 0, -14, -4, 21],\n [-15, -9, 5, 12, -16, -17, 7, 14, -7, 20],\n [-22, 19, -6, -16, 12, -18, 4, 7, 21, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[12, -7, -17, -7, -15, -3, 8, -3, -14, 7],\n [-10, 3, -21, 18, 22, 1, -10, -7, -5, -7],\n [-21, -22, -13, 2, -9, -6, -5, -16, -2, 6],\n [4, -19, -11, -1, 17, 11, 3, 5, -4, 8],\n [-9, 0, -6, 0, -6, -15, 15, -13, 7, -16],\n [-21, -1, -18, -20, -14, -18, -3, 6, -17, -19],\n [13, -2, -6, -8, 4, 16, -4, 20, -20, 5],\n [-1, -17, 8, -18, -10, 11, -13, 17, 17, 21],\n [5, -2, 14, 13, 5, -10, 13, -22, 20, -14],\n [-3, 20, 19, -6, -20, 9, 12, -17, -17, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"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, 16, -22, 17, -7, -3, 1, -8, -13, -11],\n [14, 12, 4, -10, 7, -20, 12, -11, 6, 7],\n [-1, -6, 4, -1, -16, -12, -7, 13, -1, 17],\n [14, -20, 12, 15, 19, 18, 15, 1, 11, 12],\n [-12, -8, -9, 22, -6, -2, 5, 20, 15, -1],\n [11, -22, 0, 9, -19, 18, 20, -17, -7, -13],\n [12, 1, -13, -11, 10, 4, 2, -13, 2, 9],\n [19, 3, -19, -14, 4, -14, 21, 3, -12, 15],\n [9, 7, 16, -14, -12, 0, -6, 9, -12, -1],\n [9, -14, -6, 2, -7, 10, -21, 20, 16, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-11, 20, 11, 2, -9, -14, 7, -11, -13, 1],\n [11, -11, 3, 9, 12, -10, -4, -10, -1, 0],\n [-22, -15, 22, 16, 11, -10, 21, 18, -13, -20],\n [5, 4, -2, -12, 1, -11, -16, 19, 9, -13],\n [5, 3, 6, 4, -13, -19, 19, -1, -13, -19],\n [-16, 0, -20, 1, 14, 7, 18, -11, -2, 20],\n [-6, -20, -8, 13, 9, -14, 17, -1, 13, 9],\n [-18, 18, -19, -18, -16, -12, 16, -17, 6, -6],\n [5, 15, -4, 21, -11, 22, 15, -4, 10, 22],\n [-18, -22, 12, 12, 8, 13, 17, 12, 17, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "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, -10, 7, 17, -6, -14, 16, -1, -8],\n [6, -7, -3, 2, 17, 1, -7, -7, 2, -22],\n [10, -16, 15, 22, 5, 16, 5, 9, 1, -15],\n [21, 9, 5, -20, -16, -17, 6, 22, -9, 22],\n [17, -4, 2, 14, -5, -19, -22, 10, 5, 18],\n [-4, 10, -8, 22, 0, 6, 16, -9, 7, -21],\n [-10, 17, 5, 8, -11, -10, -20, 6, 7, -11],\n [-2, -21, -7, 9, 5, -14, -6, -4, -16, 13],\n [17, -22, 19, 13, 16, -22, 1, -13, -12, 15],\n [-1, 8, -22, 18, -12, -17, 22, -6, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -19, 16, -1, 6, 19, 14, -10, -8, 12],\n [2, -20, -11, -9, 17, 9, -19, 6, 8, 9],\n [1, -12, 7, -4, 13, -17, -21, 16, -4, 17],\n [-5, 18, 13, -3, 14, -22, 0, 15, -3, -19],\n [15, -18, -17, 3, -22, -8, -7, 0, 18, -1],\n [-18, 20, -18, -17, -21, -13, 13, 12, 22, 0],\n [-7, 14, 19, 12, 17, -7, -18, -12, 6, -12],\n [-7, 2, -20, -20, -22, -11, -16, 20, 22, 9],\n [-1, -11, -17, 15, 16, 15, 18, -2, 5, 9],\n [4, -8, 10, 9, 11, -16, -10, 16, -17, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[19, -19, 7, 5, -2, -11, -10, -10, 4, 5],\n [-5, 14, -7, -2, -13, -9, 5, 6, -12, 7],\n [17, 4, -20, -22, 9, 16, -2, -21, -13, 8],\n [-5, -16, -18, 6, -19, -20, -10, -20, -15, -19],\n [19, 12, -11, 1, 15, -4, 13, 12, -5, 17],\n [11, 2, -16, -12, 15, -4, 12, 22, -3, 4],\n [8, 2, -21, 6, 14, 8, 19, -17, -2, 10],\n [-14, -13, -1, 8, -12, -4, 18, -11, 15, -7],\n [-10, 15, -10, -8, -5, -7, 18, 19, 21, -18],\n [4, -21, 18, 4, -22, -9, 12, 0, 20, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"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, 11, 4, 12, -2, 16, -20, 2, -19],\n [-8, -20, -12, 5, -20, -5, -14, -8, 17, -15],\n [17, -9, 15, -10, 16, -13, 21, 7, -18, -1],\n [12, -18, -11, 12, -2, 3, -22, -13, 15, 1],\n [8, 22, 0, -2, -21, 8, -21, 7, 2, -4],\n [-22, 14, 5, -3, -18, 7, 0, 19, 4, 19],\n [-22, -14, -16, 3, -7, -17, 19, 14, 22, -11],\n [1, -6, -21, 8, 14, 19, 6, -22, 21, -9],\n [17, -12, 9, -3, -21, 8, -18, 9, -14, 18],\n [-13, 13, 3, 21, -20, 13, 0, 7, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 20, 13, 2, -3, 15, 10, 10, 15, -22],\n [10, 15, 1, -14, 8, 15, 5, 0, 7, -5],\n [3, 10, -7, 6, -7, 10, 16, 15, 0, 3],\n [-6, 15, 22, 1, 20, -4, 19, 4, -21, -15],\n [-8, 18, -10, 4, -1, -22, -18, 6, -8, 7],\n [-17, -17, 0, -18, -1, 18, -3, -3, 16, 7],\n [-6, 0, 17, -10, 13, 19, -13, 15, 16, 16],\n [-19, -4, 18, 5, 4, 0, -4, -7, 12, -18],\n [1, -18, 6, -17, 18, 18, 21, 14, 6, 10],\n [4, 12, 15, 17, -17, -13, 13, 21, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -7, -22, 12, 6, 15, -10, 17, -11, 0],\n [-7, -9, -7, -17, 13, 1, 4, 2, 17, 13],\n [6, 8, -20, -10, -19, -12, -8, -21, -8, -17],\n [-10, 12, 21, 21, 17, -10, -11, -7, 20, 18],\n [-3, 17, -10, 11, -4, 22, 4, 6, -4, 20],\n [4, -21, 17, 16, -22, -9, -15, 4, 10, 8],\n [7, 2, 13, 15, -22, 8, 12, -2, 11, -6],\n [-14, 6, -15, -4, -17, 1, -17, 17, -20, 8],\n [8, -11, -15, 20, 3, 3, -8, -10, -1, -10],\n [-14, 1, -20, 0, -11, 18, 21, -12, -4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[14, -13, -14, 10, -10, -3, 21, -12, 18, 6],\n [-10, 21, -9, -14, 19, 15, -4, 19, -15, -5],\n [11, 13, -14, -7, -18, -8, 1, 21, 20, 16],\n [2, -7, 19, -1, -7, 10, -18, -16, -5, -17],\n [-11, 21, 10, 11, -2, -5, -9, 19, 7, -20],\n [-10, 14, -4, 14, -10, -8, 3, -17, 4, -11],\n [2, -7, -7, -20, 11, 1, 19, 0, 7, -2],\n [-6, -5, -20, -11, -7, 15, -9, 4, -5, -3],\n [12, -6, -3, -17, 3, -16, 15, -11, -6, -2],\n [-17, 14, 2, -8, -12, -14, -19, -20, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-17, -22, 19, -18, -21, -1, 9, 18, -16, -2],\n [-6, -3, -22, 9, 17, 9, -3, -13, -17, 18],\n [10, -13, 2, 1, 8, 6, -11, 20, 14, 19],\n [-14, 6, -20, -19, -2, -17, -21, 14, -3, 22],\n [10, -9, -3, 20, -21, -16, 14, -11, -7, -6],\n [8, -16, 3, -22, -21, 8, -3, 14, 10, -10],\n [-22, 10, -20, 14, -4, 21, 17, 9, -18, 20],\n [14, -17, 13, 14, -10, -11, -17, 7, 14, 5],\n [-13, 5, -17, -14, 1, -5, -19, 22, 0, 4],\n [-19, -10, -12, -12, -4, 10, -9, -10, -16, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[9, 22, 14, -15, 11, -4, 13, 11, 13, -17],\n [-22, 22, 7, -8, -14, 6, -21, 7, -19, -4],\n [-3, -18, -14, -3, -7, -3, -3, 3, 16, 10],\n [-11, -2, 0, -3, 0, -17, 22, -11, 12, -15],\n [4, -7, 9, 6, -16, -7, 6, 2, 20, 13],\n [-19, 4, 0, 0, 7, 20, 1, -7, -16, 0],\n [15, 8, 19, -4, -19, -17, -4, 4, 6, -11],\n [15, -10, 5, -18, -6, 4, 3, -19, -15, 3],\n [10, -11, -10, -2, 14, 2, 16, -20, -4, -16],\n [-6, -10, 1, 22, -15, -15, 22, -21, 7, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[22, 3, -6, 15, -20, 10, 7, -8, -15, 7],\n [0, -11, 16, -15, -14, -15, 15, 10, 10, 22],\n [-12, 0, 20, 20, 2, -8, -13, -3, -7, 12],\n [11, -2, 17, -22, 2, -9, -4, -15, 18, -8],\n [21, -5, -22, 10, -22, 11, -19, -6, -21, 16],\n [-13, 19, 22, 14, 3, 4, 16, 2, 6, -5],\n [-1, 3, 3, -2, -2, 19, -15, -21, 11, -11],\n [-5, -6, -8, -20, -2, -4, 9, -12, -5, 6],\n [-20, -19, 5, -14, 15, -16, -22, 12, 11, -14],\n [3, -15, -4, 3, -13, 20, 7, 17, 13, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, 19, -10, 14, 7, -8, 12, -20, 6, 1],\n [22, 0, -14, -21, -8, 9, -5, 6, 17, -20],\n [10, -16, 7, 4, 15, 6, 8, -22, 18, 20],\n [4, 4, 6, -18, -20, 6, 18, 16, -10, 10],\n [-3, -20, -17, 20, -6, -19, 10, 10, -17, 18],\n [-9, -16, -17, -20, 14, -1, 15, -15, 1, -10],\n [-10, -22, 18, 13, 9, -18, -16, 22, 9, 5],\n [10, -9, -10, 6, 17, -22, 4, 7, 11, -22],\n [11, -16, -22, 19, -5, 12, -4, -10, 0, -21],\n [-20, -1, 13, -15, 0, -15, 2, 12, -12, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[20, -17, 19, 19, 22, -6, 13, -5, 10, -5],\n [-16, 6, -18, -7, 8, -18, -13, 6, 6, -7],\n [-19, -22, -15, 5, -22, 5, -20, -21, 2, 14],\n [-12, -5, 19, 16, 17, -3, -6, -16, -6, -19],\n [13, 7, -22, 12, -11, -6, -7, 5, 9, 12],\n [-4, 6, 6, -7, -19, -2, 21, -22, -4, 21],\n [3, -11, -6, 14, 5, 13, 6, -18, 15, -20],\n [-8, -20, -10, -18, -2, 18, 0, -1, 11, 18],\n [3, 8, 12, -16, 17, 22, 9, -1, -17, -2],\n [22, 16, 14, 4, -13, -1, 21, -5, -19, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[12, 15, 15, 13, -19, 22, -13, 9, -13, 20],\n [22, -13, -12, 16, -14, -10, 19, -5, 14, -12],\n [5, -17, 10, -9, 6, 16, -8, -18, -1, 8],\n [-4, -5, -17, -14, 7, 8, 12, -6, 19, -7],\n [10, -19, 8, 10, 13, -12, -19, 13, -18, -2],\n [-10, -19, 19, 12, 3, 3, -4, 14, -12, -21],\n [8, -5, -12, 21, -7, -21, 9, -1, 13, -15],\n [13, 20, 2, 17, 21, 8, -19, 16, 22, 20],\n [-13, 4, 18, 15, -6, 22, 15, 2, -6, -10],\n [-2, -8, 1, -16, 22, 15, 17, -1, 19, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, -11, -15, 17, -1, 16, 16, 21, -7, 11],\n [-7, -9, -17, -13, 1, 4, -14, -7, -21, 8],\n [-4, -12, -1, 6, 8, -15, -13, -17, 8, 12],\n [17, 6, -2, 18, -18, -18, 1, -8, 5, 11],\n [-10, 21, 9, -1, 6, -20, -18, -12, 18, 3],\n [-14, 21, -12, -22, 15, 22, 5, 0, 8, -21],\n [-5, -7, 19, -6, -6, 12, 8, 12, 1, 18],\n [14, 7, -5, 4, -7, -3, 18, 5, -2, 18],\n [22, 10, -14, 1, -10, 7, 20, 10, 1, -3],\n [-22, 0, 10, -6, -21, 8, 8, -7, 14, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-16, 13, -22, 7, -5, 19, 16, 3, -12, -22],\n [15, -18, -1, -10, -6, -16, 15, -16, -11, 15],\n [0, -15, -8, 7, -14, 22, -2, 21, -9, -15],\n [13, -14, 3, -3, 15, -17, 11, 0, 16, 10],\n [-2, 18, 3, -18, -14, 22, 10, 2, -6, 17],\n [-4, -12, -15, -17, -17, -15, 1, -4, 18, 4],\n [-3, 1, 15, -18, -7, 16, 10, -13, -18, -4],\n [18, -2, -20, 5, 18, -4, -7, -21, -15, 15],\n [-11, 1, -22, -5, 0, 16, 4, 21, 21, -17],\n [5, 0, 11, 2, -12, -22, 15, -13, -14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-13, -5, -14, 22, 3, 19, -14, 13, -8, 1],\n [17, -21, -19, 15, 8, -3, 16, 22, 3, -18],\n [-19, -1, -17, 14, 8, -18, -16, -18, -19, 4],\n [-14, 14, -21, -4, 16, -6, -6, 17, 1, -10],\n [5, 22, 19, -9, 0, 0, -13, 15, -6, 4],\n [-12, -4, 22, 21, 21, 4, 13, -7, 0, 10],\n [-1, -9, -10, -1, -16, 15, -22, 10, -1, 0],\n [-8, 21, -8, 8, 5, -20, 19, 2, 10, 10],\n [0, 5, -7, 14, -18, 20, -12, -11, -2, -5],\n [-9, 10, -2, 3, 2, 17, 2, 12, -3, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[18, -11, 9, 20, 10, 8, 10, -3, 18, 14],\n [14, 17, -9, 13, -11, 3, 11, -17, -10, -1],\n [12, -4, 14, 0, 9, 21, -12, -19, -11, 16],\n [7, -13, 1, 0, -22, -19, 5, 21, 22, -20],\n [-21, 18, -17, 19, -6, 14, 21, 0, 17, -2],\n [21, 8, -11, 6, 19, -10, 3, 10, 11, -3],\n [-13, -22, 6, -1, -22, 21, -15, -14, 0, -3],\n [11, -7, -1, 0, -22, -9, 0, 15, 17, -15],\n [9, 17, -21, -10, 4, -16, -20, -2, -15, -22],\n [-6, 3, 6, -15, 15, 20, -15, -15, 2, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[19, 22, 4, -1, -20, 15, 1, 10, 12, 17],\n [6, -15, -12, -7, 10, -12, 6, 22, 1, -21],\n [-18, 1, 21, -16, 8, 7, -17, -18, -8, 4],\n [12, -14, 0, -6, 0, 16, 6, 16, 22, -12],\n [-10, -11, -21, 19, -12, -9, -1, -2, 22, 14],\n [13, 2, 20, -20, -21, 4, 10, -5, -12, -16],\n [14, 13, 4, -1, 8, 17, -17, 10, -16, -17],\n [-22, 16, 15, 19, 21, 6, -12, 5, 17, -8],\n [7, 0, -11, 5, 8, 7, 16, -7, 7, -19],\n [10, 10, 5, -2, -8, 3, -9, -8, -21, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[14, -12, -12, 10, -21, 10, -20, -3, 10, 3],\n [11, -9, 6, -21, -15, 4, -15, -16, -12, 16],\n [7, 16, -2, -2, -16, -3, -9, -3, -18, 8],\n [-11, -11, -21, 3, -19, 7, 11, 14, -3, -21],\n [22, 12, -8, -9, 13, 7, 21, 4, -21, -2],\n [-9, 4, -2, 0, 12, -15, -11, 5, 18, 10],\n [10, -14, -8, -13, -21, -20, 0, -13, -4, 18],\n [-5, 12, 18, 20, -14, 8, 7, 14, -11, -6],\n [4, -2, 4, -9, 18, -10, -20, 1, 9, 14],\n [-15, 12, 0, -7, 13, -14, 16, -5, 8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[19, 14, 11, 18, -17, 13, -9, 18, 1, 10],\n [19, -4, 6, -17, -20, -5, -2, 6, 19, 13],\n [8, -15, 9, -7, -1, -21, -8, 17, -6, -10],\n [12, 2, -13, 22, -12, 10, -9, 11, -1, 21],\n [-19, 21, 3, -22, -13, 13, -21, 6, 2, 0],\n [7, 2, -10, 17, 11, 12, -8, 16, 19, -3],\n [20, -1, 2, -9, -4, -1, 0, -22, 16, 7],\n [-18, 7, -16, -10, 8, -16, 6, 2, -10, -8],\n [7, -16, -18, -9, 7, 0, -7, 1, 20, -2],\n [20, 7, -11, 22, 17, 7, 15, -1, -21, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[19, 0, -1, 7, 4, 11, -12, 6, 14, -17],\n [-7, -3, -13, 15, 14, -13, 21, 2, -1, 9],\n [-6, 3, -7, -13, -6, -21, -21, 6, -19, 7],\n [-11, 11, -9, 1, 1, -5, 2, 2, 18, 2],\n [5, 7, 2, 1, 17, 16, -10, -21, 11, -7],\n [1, -21, 6, 16, 16, -6, 0, -11, -10, -18],\n [-8, -21, -17, 13, 0, -10, -21, -18, 17, -7],\n [16, 12, 18, 22, 11, -4, 20, 3, 19, 20],\n [-6, 12, -11, 12, 14, -17, -13, 20, 0, -4],\n [20, -15, -14, -20, 10, -21, 11, 12, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[21, 4, 15, 16, -6, -14, 9, 0, 21, -9],\n [-12, -19, 15, -7, 13, 2, -18, -13, -18, 18],\n [-5, 0, 15, -9, 0, 12, 10, 15, -22, -17],\n [-2, 4, -18, 4, 21, -17, 17, 2, -18, -8],\n [15, -6, -6, 10, -5, 13, -20, 2, 12, 22],\n [-3, 13, 20, 8, -2, 14, 11, 15, 14, -22],\n [8, 0, 20, 15, -12, 16, -3, 14, -16, 12],\n [-21, 10, 17, 1, 16, -13, -14, 20, 10, -2],\n [-9, 0, -11, -1, 5, 4, -13, -5, 1, -20],\n [-19, 7, -2, -1, 5, -14, 21, 18, 18, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[14, -18, -9, -9, -7, 16, 20, -19, 14, -9],\n [18, 0, -14, 1, -12, 5, -4, -4, -11, 11],\n [-11, -20, 7, 12, -8, 20, -1, -14, 5, 6],\n [16, 16, 16, -6, -19, -19, -16, -21, 14, -13],\n [-5, 5, 12, 12, 7, -2, 2, -10, -16, -17],\n [-3, 22, -18, 15, 21, 17, 2, -5, 1, -8],\n [-15, -10, 16, 2, 0, -18, -1, -1, 2, -22],\n [-19, 9, 3, 13, -8, 12, 15, 4, -9, 11],\n [2, 4, -2, 12, -17, 12, 3, -8, -18, 3],\n [10, 2, -6, 21, -3, 19, -21, -15, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "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, -14, -15, -8, 11, -19, 4, 15, -10, 9],\n [12, 13, -13, 0, 0, -19, 21, -18, -19, 7],\n [18, 10, 17, -10, -5, 9, 10, -16, -9, 17],\n [-9, -13, 18, 16, 14, -5, -4, 17, 19, 20],\n [14, -20, -16, -16, 15, -17, -13, 21, 13, 14],\n [4, 22, -22, -22, -2, 14, 5, 16, 13, -21],\n [-21, -19, -21, -22, 17, -5, 18, 11, 4, 13],\n [16, 3, -12, 17, -20, 5, 13, -7, 12, -1],\n [-7, 10, -10, 5, 21, -7, -21, 3, 19, 5],\n [-20, 21, -2, 9, -17, -18, 1, -22, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-15, 22, 2, -12, -11, 22, -15, -13, 12, 15],\n [-2, -5, -5, 3, -3, 2, 8, -5, -7, 22],\n [20, -5, -9, -16, 15, 6, 0, 19, 11, -6],\n [22, -5, -4, -21, 6, -21, -5, 16, 19, 13],\n [13, -2, 10, -21, -13, -8, -11, -20, -19, -14],\n [19, -13, 8, 14, -12, 4, -17, 20, 7, 20],\n [12, 22, -5, -17, -10, 15, -11, -16, -9, -14],\n [12, -16, 16, -2, -4, 4, -21, -9, 14, 10],\n [21, -11, -2, 7, -1, -21, 6, 1, 9, 22],\n [-11, -16, -21, 17, -4, -5, 11, -21, 22, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[17, -4, -17, 18, -6, 0, 17, -14, 14, 15],\n [-2, -2, 4, -12, 16, 7, 5, -3, 22, 15],\n [-19, -5, 6, 13, 4, -22, 12, -18, -17, 13],\n [-18, 21, 9, 16, 22, 8, 17, 22, 21, 19],\n [-13, 8, -15, 4, 6, -9, 0, -19, 11, 18],\n [15, 4, -4, 8, -20, 6, -10, 4, 20, 9],\n [14, -20, 16, -17, -20, -10, -12, 4, -21, 17],\n [21, -11, 17, -11, 0, 8, -13, 12, -17, 2],\n [8, 7, -8, -20, -5, -6, -9, -7, 4, 20],\n [14, 10, -3, 2, -9, 14, -18, 14, -13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, -9, 10, 6, 1, -17, 3, 16, 21, -20],\n [17, 9, 3, -20, -11, -9, -4, -19, -11, 12],\n [0, -20, -20, 16, 19, -7, -10, -4, 5, 15],\n [-14, -6, -16, -15, 14, -11, 5, -21, 5, 2],\n [4, 12, -8, 12, 10, 21, 19, 0, 4, 15],\n [-15, 15, -19, -18, -7, -5, 22, 22, -5, -15],\n [6, -2, 16, 4, -21, -19, -11, -7, 2, 0],\n [-6, 19, -22, -2, 13, -21, 0, 17, -21, 20],\n [-13, 20, -14, 6, 3, 13, 6, -19, -2, 10],\n [8, 5, 13, 10, -19, -19, 10, -9, -14, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, -16, 5, -18, -10, -21, -3, -11, 4, -16],\n [11, -2, -5, -13, 15, 16, 21, -2, -7, -3],\n [17, 1, -2, 21, 8, -13, -3, -9, -4, 7],\n [-7, -1, -3, -17, 22, 20, 10, 18, -4, -18],\n [-16, 11, -3, -8, 15, -22, -18, 11, -2, -9],\n [-6, -11, 4, -17, 16, 2, 4, 22, -21, -1],\n [9, -6, 14, -21, 3, 10, -22, 17, 20, 21],\n [13, 16, 2, -10, 16, 13, -11, -2, 0, -5],\n [-10, -4, 12, 11, -22, -1, 5, -19, 14, -16],\n [-12, -11, 17, 16, 12, 11, -5, -13, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-20, -10, 11, -6, -22, -9, -22, 1, -12, -20],\n [-10, -1, 18, 18, 7, 2, -16, 2, 16, 2],\n [-21, 11, -1, -22, -5, -7, -13, 8, -10, 11],\n [11, 19, -11, 14, 17, -6, 18, -8, -10, -15],\n [-6, -12, 17, -22, 9, 21, -13, 21, -8, -20],\n [-14, -15, -13, -15, -7, -12, 0, -1, 17, -5],\n [16, -20, -15, -18, 4, -18, -4, -6, -5, -21],\n [-16, -7, -16, -5, 21, 3, 6, -7, 16, 7],\n [2, -15, -9, -1, -9, 4, 12, 17, -11, 20],\n [-2, -12, -20, -14, 20, -4, 19, 0, -7, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, -22, -19, 3, 4, 17, -7, 7, 15, 10],\n [-7, 10, -3, 8, 4, 9, -1, 13, 4, 2],\n [-21, 15, 0, -11, 14, 14, -2, 19, -12, -2],\n [14, -19, 3, -3, -16, 15, 4, -6, 9, -13],\n [-12, -5, -21, 12, -17, -20, -16, 12, -10, 15],\n [-21, -21, -15, -14, 11, 16, 8, 6, 13, -1],\n [0, -10, 12, 21, -20, -14, -5, 3, 6, -11],\n [16, 0, -4, 1, 21, 20, 21, 7, 8, -4],\n [-2, -13, -19, -5, 22, 14, -3, 13, 9, 4],\n [18, 1, 6, 1, 6, 16, -5, -13, -14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "317", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-11, -21, 3, -14, -6, 12, -20, -17, 20, 0],\n [12, -8, -15, 9, 11, -12, -20, 6, -13, -5],\n [-5, -11, 4, -4, 18, 10, 2, 21, -21, -21],\n [-18, -1, 10, 21, -18, 5, -9, 17, 20, -13],\n [18, -8, -13, -19, 20, -5, -6, 8, 10, 2],\n [-11, -2, -6, -3, 6, -20, -16, 10, 3, -3],\n [20, 14, 9, 12, -2, 18, -15, -21, -7, 4],\n [13, -13, 5, -6, 2, -8, -5, 5, -21, 17],\n [19, 8, 8, 2, -22, -5, -7, 19, 14, 18],\n [19, 14, -16, -17, -9, -1, 8, 22, -13, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[13, 18, 15, 11, -20, 0, 20, -6, 6, -22],\n [-20, -9, -12, 7, -2, -7, -14, -21, 3, 19],\n [-20, -8, -11, -4, 18, -9, -8, 0, -12, 20],\n [-20, 20, -22, -19, -2, 2, -3, -13, -5, 10],\n [12, 2, -20, -10, 12, 2, -5, 7, 17, 7],\n [1, 3, -22, 10, -15, -11, -15, -12, -9, -5],\n [21, 17, -22, -2, -13, 14, 6, 17, 1, 21],\n [13, -5, -8, 9, 15, 20, 22, -3, 11, -14],\n [18, 11, 12, 4, 19, -5, -2, -5, 4, 8],\n [5, 10, -8, 22, 13, -4, 12, 9, 22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-11, 6, 11, -7, -1, -15, -11, 11, -7, -14],\n [4, 12, -12, -4, 8, -8, 4, 10, -16, 0],\n [13, -1, -22, 4, -12, -11, -2, -15, -10, 14],\n [10, -21, -14, -10, 3, 22, -14, -8, -16, 20],\n [14, -14, -9, 7, -3, 0, -8, 8, -19, 2],\n [-4, 14, 11, -22, 18, 8, 17, 21, 12, 4],\n [-2, -15, -5, 0, 18, 13, 6, -7, -13, -6],\n [-1, 17, -21, 19, 7, 21, 16, 16, 22, -4],\n [-13, -3, 1, -17, 22, -5, -7, 16, 17, 17],\n [-7, 17, -8, 17, -17, 10, -10, -19, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, 10, -18, 17, -19, -16, -7, 14, -12, -18],\n [6, 2, -20, 9, 7, -3, 7, -20, 21, -8],\n [18, -9, 17, -13, -6, -8, 6, 11, 12, -14],\n [-6, -21, 3, 15, 20, 5, 7, 20, -14, 5],\n [-7, 1, -1, -3, -9, 20, 9, -13, -21, -16],\n [-22, 14, -8, -12, -3, 18, 10, 15, -3, -13],\n [9, 13, -11, 2, -14, -6, -9, 1, 18, 22],\n [-20, 18, -7, -5, 16, -9, -13, -13, -17, -20],\n [-1, -21, 16, -11, -22, 14, -10, 9, 2, 15],\n [-18, 14, -5, -13, -4, 11, 7, 9, -12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[7, -22, -17, -9, -20, 16, -8, 8, -4, -1],\n [-16, 4, 12, 20, -18, 12, 13, 14, 0, 13],\n [-19, -21, 14, 12, -19, -19, -17, -6, -19, -1],\n [-2, -11, -16, 5, -10, 20, 20, 10, 17, -10],\n [-19, 2, -3, 15, 12, -14, 7, 16, 0, -12],\n [-8, -1, -6, -11, 12, 11, -22, 9, -19, 1],\n [-16, -11, -1, 12, -2, 6, -6, 5, 19, 18],\n [-6, -19, 18, -17, -8, 21, 1, -15, 18, 4],\n [8, -14, -5, -21, -1, -3, 19, -19, 15, 21],\n [-10, -3, -17, -8, -15, 7, 13, 13, -20, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "366", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, 6, -7, 17, 15, -3, 22, -7, -2, -5],\n [18, 8, -21, 1, -17, -6, 3, 14, -21, 3],\n [21, 14, -22, -21, 10, -12, 7, 11, 4, 20],\n [11, -16, 16, 16, -21, 7, -20, -21, 7, 14],\n [6, 12, 15, -1, 14, -5, 17, 22, 11, 22],\n [15, 7, -21, -3, 21, -7, -19, -10, -9, -14],\n [21, -9, -12, -13, 7, -16, -17, -6, -10, -19],\n [3, 9, -20, -12, -3, 6, -21, 20, -19, 9],\n [-2, -6, 22, -10, 9, -20, 19, 8, 8, -22],\n [5, 0, -18, -22, -7, -12, 13, 14, -7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[7, 21, -19, 18, 15, -15, -15, -2, 17, -15],\n [6, -8, -9, 15, -13, 4, 17, 4, 19, 17],\n [12, 13, -12, -10, 12, -2, 14, 21, -11, 2],\n [5, 21, -5, -13, 16, -20, -18, -11, -9, 22],\n [18, 9, 19, 10, -17, 7, -17, 8, -21, 3],\n [9, -18, 18, 20, -7, -11, -8, -2, 14, -2],\n [2, -6, -15, 7, 10, -21, 10, 5, 3, 18],\n [-22, 12, 20, 16, -3, -10, 8, 15, 0, -11],\n [-17, 1, 11, 10, -16, -9, 13, -7, 0, -5],\n [6, -16, -19, 2, 10, 1, 0, -2, 16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "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, 10, -16, 8, 16, -8, -21],\n [22, -21, -6, 11, 2, -12, 21, -14, -16, -12],\n [-19, 14, 3, 11, -7, 18, 7, -7, -17, 10],\n [-8, -3, -11, 1, 17, 9, 18, 10, -11, -8],\n [-15, -19, 4, 14, -9, 16, -8, -4, -9, -16],\n [-17, 11, 1, 2, 18, 2, -8, 19, -20, 13],\n [-21, -1, 5, 9, 16, 2, -22, 21, 0, -18],\n [12, -12, -8, -18, 15, -19, 21, -13, -14, 10],\n [19, -17, 4, 20, 5, 20, 11, 6, 9, -1],\n [-8, 4, -13, 2, -12, -15, -2, -15, 14, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "342", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 1, -10, 16, -18, -8, 1, -12, -6, -15],\n [19, 1, 15, 4, 19, -16, 1, 4, 14, 22],\n [-20, -1, 15, -1, 17, 6, -13, -6, 19, -16],\n [20, 12, 17, -20, -10, -17, -6, -21, 16, 15],\n [10, 19, 0, 10, 2, -9, 12, 7, -14, 7],\n [-16, -15, -16, 19, 4, 2, 1, 5, 11, -13],\n [13, -8, 15, -20, -11, 10, 3, 18, 18, -17],\n [-20, 4, 18, -9, -12, -6, -7, 20, -22, -17],\n [-8, 10, -16, -15, 19, 7, -16, 17, 22, -9],\n [-20, 3, 21, 11, 7, 7, 6, 14, 21, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-19, -22, -15, -21, -6, 18, 20, 0, -2, 6],\n [-18, 9, -2, -14, -16, -5, -8, 2, -7, -3],\n [22, 14, 11, -18, 10, -22, -16, 19, -19, -19],\n [22, -10, 12, 20, -5, 20, -12, -10, 20, 8],\n [16, 19, -17, 15, -12, -2, 3, -8, 1, -5],\n [-15, 18, 12, 5, 6, -21, -5, -22, -21, 22],\n [22, -9, 5, 21, -2, -3, 11, 11, 16, -19],\n [20, 5, 16, -22, 22, -15, -7, 22, 8, -16],\n [-18, -21, 18, -19, -13, 12, -22, 16, -20, 20],\n [22, 3, -6, 19, -15, 7, -15, 6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -3, 21, -10, 14, -4, -18, 13, 1, 11],\n [-15, -19, 21, 15, -15, -14, 18, 18, 8, 8],\n [17, -16, 2, -10, -18, -5, -16, 15, 19, -8],\n [22, 10, 8, -14, -4, -17, 13, 9, 5, 15],\n [-13, 12, 1, 11, -14, 4, 11, -8, 4, 4],\n [9, 22, 4, 3, 21, -6, -7, 12, 3, 15],\n [7, 19, 14, -9, -5, 5, 17, -7, -21, -3],\n [7, -14, -22, 4, -14, -3, 4, 16, 12, 10],\n [-10, -9, -22, -16, 10, 16, 11, 5, -16, 1],\n [-8, 1, 4, 16, -20, -13, -11, 18, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-13, -6, -14, 19, -8, -19, -2, -16, -15, -3],\n [-16, -17, -14, -9, 13, 6, -20, 22, 8, 1],\n [1, 13, 12, 2, 16, -2, -8, 11, -14, -20],\n [-13, -8, -7, -10, 21, 21, -22, 10, -15, -7],\n [12, -9, 18, 4, 21, -22, 16, 20, 7, 12],\n [-13, 8, -11, 17, 12, 11, 16, 9, -11, 22],\n [5, -4, 1, -3, -1, -12, 5, 22, 17, -3],\n [-18, 17, -16, -1, 14, 18, 6, -11, 6, 13],\n [12, 20, -1, -5, -1, -4, 11, -14, -13, -4],\n [15, -14, 5, 7, 2, -5, 3, -4, 4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-19, 3, 22, -20, 13, -16, -13, 22, -19, -16],\n [-1, 7, -1, 6, -12, -7, 21, -17, 14, -10],\n [10, -15, -12, 10, 10, 21, 17, 4, 16, -5],\n [22, 9, 22, 18, 1, -1, -20, -20, -9, 9],\n [-14, -7, 2, -18, -10, 8, -2, 17, -14, -2],\n [-14, -13, 18, 21, -11, -12, -3, 16, 10, -16],\n [-22, -9, 22, -2, 22, -15, -6, 22, -8, -21],\n [-10, 6, 5, -15, 12, 1, -16, 5, -1, 3],\n [-6, 15, -17, -12, 15, -21, 9, 3, 8, 9],\n [12, -21, -20, 10, -16, -2, 2, -7, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[10, -5, 16, 0, -14, -20, 12, 1, -17, -4],\n [-9, -20, -17, -6, 13, -1, -19, -13, 9, 20],\n [-19, -10, -4, 20, 15, 3, 7, 20, 8, 15],\n [-11, -4, 0, 18, -13, -8, -6, -10, 1, -7],\n [16, 15, 7, 22, 21, -8, -19, 21, -13, 17],\n [9, -2, 6, 7, -16, 19, 6, -13, -1, -6],\n [-5, -18, 16, -6, 11, -19, 18, -15, 3, 2],\n [13, 20, 16, -12, -20, 21, 17, 5, 16, 2],\n [-1, -10, -19, 5, -4, -20, 4, -12, -17, 8],\n [6, -15, -12, -14, 8, -22, -16, -13, -14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, -5, -7, -19, 7, 15, -3, 18, -11, 5],\n [21, -22, -14, 19, 10, -22, 19, -14, -1, -14],\n [-18, -21, -9, -11, 6, -7, -14, 9, 1, -3],\n [-3, 19, 20, -18, -3, -7, -4, -11, -6, 11],\n [4, 18, 3, 11, -2, 19, 18, -20, 18, 13],\n [6, 22, -4, -2, -11, 21, 0, 5, -11, -21],\n [7, -11, 16, 16, -5, 1, -11, -5, -17, -15],\n [-8, 21, -16, 6, 2, -10, 9, -11, 2, -4],\n [19, -7, -11, 12, 13, 1, 10, 13, -19, 12],\n [-15, -15, -16, 17, 2, 12, -8, -5, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 0, 11, -4, -7, -17, 18, -8, -14, 6],\n [19, -21, 10, 15, 0, -10, -3, -16, -6, -2],\n [5, 7, 0, -2, -22, -6, 9, 1, -16, 12],\n [13, -9, -11, 16, 0, -9, 2, -1, 22, 14],\n [6, -15, -12, 7, -1, -8, -2, 2, -10, -16],\n [-5, -11, 3, -18, -15, 13, -18, -1, 0, -15],\n [-4, 11, -17, -6, -6, -8, 16, 14, 8, -1],\n [2, -4, -16, -21, -8, -1, 15, -16, 18, 0],\n [-21, 10, -5, 21, -16, 1, -12, -11, -5, 14],\n [-22, -22, 4, -14, -22, 5, -11, -7, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[18, 0, 12, -7, 19, -15, -7, -17, 13, 8],\n [5, 12, -6, 7, -14, 0, 22, -22, -11, -6],\n [10, -1, -13, 3, -9, 2, -12, -4, 20, 5],\n [4, -12, -1, 2, 7, -4, 16, -16, -17, -14],\n [-5, 8, -17, -1, -14, 8, -1, -2, 12, 6],\n [-2, 12, 0, 17, 21, 0, -5, 0, -22, 21],\n [-3, -7, -14, 2, 15, 2, 15, -16, -7, 12],\n [8, -22, -3, 4, -22, 14, 1, -18, -12, 12],\n [6, 0, -13, 7, 8, 1, -9, -12, -22, 21],\n [3, -3, -21, 10, 22, 22, 22, -6, -17, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "325", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-8, -20, -1, 15, -2, 12, 21, 20, 4, -17],\n [-12, -6, 13, 8, 20, -10, 6, 15, -3, 15],\n [12, 16, -22, 21, -10, 4, -20, -3, 5, -17],\n [-14, 22, 10, -19, -10, 15, -22, 2, -22, 9],\n [19, -4, -6, 16, 18, -11, -3, -1, 22, 8],\n [11, 0, 21, -4, -21, -21, 15, 16, 14, -11],\n [5, -12, 19, 6, -2, 6, 6, 17, 19, -11],\n [-21, 17, 15, 10, 22, -13, 18, -12, -7, -15],\n [-19, 21, 5, -6, -5, -18, -15, -18, 12, 0],\n [-1, -21, 13, -20, 5, 21, 0, -14, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "376", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, -14, -18, 17, 7, 0, 10, -2, -10, 19],\n [18, 18, -11, -1, -19, -14, 8, -21, 13, -12],\n [6, 13, 11, -14, -11, -2, -18, -16, 21, 14],\n [-20, -8, -4, -20, -3, -8, 15, -12, -9, -19],\n [12, -15, -2, 12, -19, 13, -9, 21, -20, -3],\n [-15, -9, -22, -3, -9, 5, 16, 22, -14, 0],\n [-7, 4, 17, -15, 5, -5, 11, -21, 1, -13],\n [17, -15, -18, -20, 10, 7, 16, -16, 22, -2],\n [15, -10, 2, -21, -21, -21, -8, -8, -5, -18],\n [3, 7, -9, -18, 17, -2, 20, -15, -17, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-19, 7, 12, 4, 4, 21, 20, -18, 17, -12],\n [20, 12, -12, 15, 15, -18, 14, 14, 3, 10],\n [10, 0, -16, 9, -14, -7, -14, 21, 20, 5],\n [0, -11, 19, -14, 22, -11, -14, -4, 13, 10],\n [-10, -21, 17, 21, 2, -10, -10, 10, 4, 17],\n [14, -4, -1, -6, -21, -11, 10, 5, 3, 2],\n [5, 8, 21, 8, 4, 21, -22, 12, 10, -22],\n [-14, 10, 21, 14, -8, -8, 6, 18, -2, -5],\n [-7, 6, 18, 4, -8, -14, 5, -21, -2, -12],\n [9, -1, 12, 19, 18, -7, 8, -13, 17, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}