{"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, 25, 2, -12, 16, -19, -6, 12, -8, -4, -16, -16],\n [-3, 26, 9, 13, -3, -24, -5, 26, -25, -3, 17, 3],\n [11, -25, -6, 6, -15, -5, 17, -2, 22, 0, 15, 1],\n [-11, -12, 20, 24, 17, 25, -24, 10, 24, -20, -6, -18],\n [12, -9, -23, -2, -13, 23, -18, -1, 26, -25, -7, 1],\n [20, -20, 17, -19, 20, 8, -13, -10, 9, 23, 13, -23],\n [-25, -21, 15, -23, 2, -9, -1, 17, 7, -17, 9, -13],\n [4, 21, -12, -19, -13, -4, 13, -6, -11, 18, -9, 20],\n [26, -3, -1, -2, 18, 14, 2, -12, 18, -26, -2, -20],\n [-18, -3, -26, 17, -19, -3, -16, 24, -10, -19, 8, 8],\n [6, -22, 15, 12, 14, 1, -20, -18, -19, -15, 7, 6],\n [21, -4, -3, 10, 8, 17, 13, -5, 0, 8, -26, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[10, 20, -13, -24, -26, -22, -1, -13, 12, 0, -18, -12],\n [-12, -1, 15, -14, 24, 5, 12, 22, 25, 5, -23, 3],\n [10, -4, 12, 18, -12, 16, 2, 9, -14, 5, -20, 24],\n [-5, 1, -25, 15, 18, 26, -21, 1, 1, 17, 17, -7],\n [3, -16, 1, -2, 12, 6, -26, 0, 25, -14, 14, -24],\n [12, -21, -19, 0, -18, 10, 6, 24, 15, 17, -3, -12],\n [5, 5, -3, 14, 25, 22, 22, 25, -15, 12, -25, -24],\n [22, 10, 22, -10, 22, -25, -25, 1, -4, 10, 5, 6],\n [-26, -8, -25, 26, 17, -1, 5, -21, 5, -23, -16, -10],\n [11, -3, -22, 25, 7, -21, -5, -16, 21, -11, 6, -18],\n [-21, -11, 2, -24, -7, 9, -8, -1, -24, -8, -7, 5],\n [-20, 25, 14, 6, 13, 12, -9, 13, -26, -16, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[23, -4, 4, 3, 15, 8, -20, -11, -1, 21, 25, 22],\n [-25, -26, 21, -15, -22, 10, 5, -18, 14, 8, -8, 21],\n [-11, -24, -7, -3, 6, -3, 25, -16, 22, -19, 9, 11],\n [13, -7, 8, 21, -2, 8, -2, 2, -9, 19, -9, -25],\n [8, -11, 14, 9, 6, -23, 6, -13, -6, 21, -7, -19],\n [-20, -24, -10, 6, 21, -15, 24, -5, -5, 19, 3, 11],\n [11, 18, 24, -19, 0, 0, 7, -6, 3, 6, 1, 20],\n [6, -22, 21, -8, -23, 8, 22, -10, 17, 1, 3, 2],\n [19, 26, -21, 8, 14, 10, -3, 2, 22, 19, 26, 4],\n [8, 6, 25, -6, 5, -4, 6, -24, -9, -2, 15, 4],\n [-24, 13, 19, -3, 23, 5, 20, -5, -4, -25, 0, 15],\n [-25, -1, -10, 13, 6, -18, 16, 21, 12, 2, 15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[8, 23, -2, -3, -14, -20, 9, 18, -7, -26, -19, 19],\n [-11, -13, -15, 24, -4, -12, 1, 7, -25, 5, -4, -5],\n [24, -2, -5, -5, 22, 25, 15, -21, -12, 16, 10, 6],\n [-19, 26, 17, 17, -22, 12, -23, -21, 18, 5, 25, 3],\n [20, 8, 13, 25, -11, -14, 23, 15, 3, -8, -10, -8],\n [1, -1, 10, -1, 26, -4, -18, -15, 26, -26, -26, 20],\n [7, 5, 21, -2, 13, 18, 26, -26, -11, 12, -22, -5],\n [2, -24, -15, -1, -11, 24, 10, -5, 2, -13, 1, -22],\n [20, 22, 3, 19, 25, -22, -15, -11, -1, -1, 21, -6],\n [12, 9, 6, 3, 10, -4, -17, -22, 9, 7, 25, 4],\n [-17, -8, 5, -26, -22, 18, -23, -11, -3, -11, -25, 22],\n [1, 5, 0, -7, -3, -15, 23, 8, 6, 6, 24, 16]]\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 difference between the largest and smallest singular values:\n[[10, -15, -24, -26, 6, 13, -17, 16, 17, 2, -14, -15],\n [4, 19, -25, 24, 23, 8, -4, -10, -1, -19, 2, -1],\n [-17, -1, 7, 24, 14, -20, -23, 26, 23, 18, -16, 2],\n [9, -2, -6, 9, -17, 10, -18, -3, 8, 22, 8, 21],\n [9, -9, 22, 12, 5, -3, -4, 5, 10, -15, 22, -14],\n [-4, -2, 8, 14, 3, -10, 22, -7, 21, -2, -5, -14],\n [-8, 22, 9, -15, 14, -8, -15, -18, -20, 1, -13, 4],\n [25, -8, 20, -11, 26, -22, 8, -15, -2, 25, -6, 9],\n [26, -4, -11, 12, 18, 26, 15, 12, -13, 4, -22, 8],\n [-4, 2, 16, -16, -9, 20, -15, -18, -17, 17, -10, 11],\n [-20, 19, -14, 13, 15, -18, 23, 0, -25, -22, 2, 10],\n [11, -8, -19, 21, 18, -26, -5, 25, -10, -20, -2, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-23, 9, -21, 4, -8, 17, 12, 0, -17, -1, -8, 12],\n [-24, 18, -14, 23, 1, -7, 1, -19, 14, 12, -26, -24],\n [-14, 1, 22, -2, 6, 11, 26, -21, 17, 18, 5, 18],\n [20, -6, -11, -6, -16, 10, 9, 8, -8, -7, -9, 20],\n [14, 22, -13, -12, 4, -26, 26, -24, -11, -4, -16, -15],\n [-17, 5, -11, -19, 11, -15, -3, 1, 26, -19, 1, 9],\n [-1, -19, 23, 1, 1, 10, 14, 9, 0, -10, -18, 6],\n [26, -7, -14, 1, 21, 2, -14, 19, 8, -21, -9, 24],\n [-22, 20, -2, -25, -17, 3, 23, 18, -22, 6, -26, -9],\n [5, 20, 22, -16, -6, -1, -2, -5, 0, 22, -14, 6],\n [7, 14, 8, -26, -6, 21, -21, 1, -10, -22, 4, -22],\n [11, -24, 26, -4, 10, 26, 10, -17, -17, -8, -10, -6]]\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 largest singular value:\n[[-13, -18, 19, -26, 24, 18, -14, -23, -26, 22, 13, 5],\n [7, 1, 4, -19, 12, -1, 7, -24, 23, -15, -26, 17],\n [-22, 3, 3, -10, 21, 20, -4, -12, 10, -6, -13, -25],\n [-16, 24, 12, 11, 7, 11, 23, 7, -9, 3, -12, 0],\n [24, 7, 25, 11, 6, -3, -12, 3, 15, 24, -10, -22],\n [2, -23, -17, -10, -17, -10, -7, -3, -22, 7, -21, 26],\n [-25, -14, 16, 16, 21, -16, 24, 20, -4, -11, 4, -16],\n [-11, -19, -23, 13, -23, -2, -24, 5, -24, 0, 2, 5],\n [23, 24, -8, -6, -22, -9, 1, 15, -5, -6, -21, -26],\n [-22, 14, -15, -1, 19, 7, 22, -13, -1, 18, 0, -18],\n [-1, 20, -5, 20, 3, 16, 21, -10, -1, 9, -26, -19],\n [22, 8, 25, -12, 20, -5, -13, -1, 1, -4, -13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-25, 18, -1, -13, 24, -20, -24, 20, -4, 19, 16, 20],\n [18, -9, 11, 8, 24, -12, -2, 10, 1, -17, 12, -10],\n [12, -5, -1, 17, -2, -10, -14, -7, -2, -23, -17, -24],\n [14, 18, -9, 20, 9, 20, -5, 7, 20, -19, 13, 22],\n [17, -8, 15, 14, 10, -21, 25, -1, 7, 18, -21, 10],\n [6, 26, -5, -6, -21, -21, 21, -23, 3, -16, 3, 4],\n [-3, -18, -24, 24, 4, 13, 10, 9, -3, 4, -21, -25],\n [-7, 1, -16, -23, -12, -21, 22, 3, 11, 24, -25, -12],\n [-16, -19, -1, 24, 18, 17, -22, -21, -1, -23, -8, -7],\n [6, -7, 22, -15, 20, -26, -1, -13, 11, 10, -16, 9],\n [-14, 16, -24, 6, -21, 23, -17, -22, -4, -17, 17, -25],\n [-14, 13, -25, -7, -26, 10, -18, -10, -18, -16, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[11, 8, 3, 4, 22, -22, 17, 23, -13, 26, -16, -18],\n [7, -15, 8, 8, -26, 13, -5, 2, -19, -16, 14, 10],\n [-13, 3, 8, -6, 10, -22, -8, -13, -1, -23, -2, 18],\n [15, -2, -9, 13, -19, 12, 13, -13, 5, 24, 11, 6],\n [-4, -12, 6, -2, -10, 6, 20, -25, -13, 26, 13, 13],\n [24, 12, 24, -21, -21, -24, -20, 24, -19, 15, 25, -12],\n [20, 2, 6, 25, 3, 12, 0, 9, 2, 11, 6, 10],\n [0, 6, -23, -5, -25, -17, -22, -17, 6, 11, -14, 4],\n [20, 9, 18, -3, 25, -12, 2, -19, -22, 2, 20, -23],\n [-15, 18, -25, 0, 4, 24, 24, 9, 9, -1, 16, 0],\n [-22, -7, -16, -17, 13, 11, -21, -19, -4, 20, -1, 19],\n [16, -15, -1, -14, 13, -9, -2, 6, 20, 13, 16, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[17, 9, 21, -23, -22, 10, -19, 15, 22, 1, 4, -18],\n [24, 2, -13, 13, 14, -5, -16, -4, -26, 19, 10, -6],\n [-1, 19, 9, -4, -26, 24, 13, -12, -6, 20, -18, 26],\n [-18, -17, 25, 26, -1, 14, 8, 25, -2, -1, -16, 11],\n [-25, -20, -9, 0, 7, 0, -10, 16, 17, 24, -3, -2],\n [-20, 25, -21, 26, -3, 6, 22, 2, 16, -5, -1, 1],\n [23, -6, 22, -20, -10, -7, 14, 22, -7, -5, 1, 13],\n [22, -20, -26, 5, -14, 3, -4, 24, -8, 5, 3, 2],\n [22, 18, 2, 3, -11, 13, -8, -9, -26, -13, 24, 20],\n [23, -25, 1, 22, 23, 3, 11, 24, -23, -26, -19, 2],\n [12, -24, 5, -17, -17, -8, 19, 7, 6, -4, 1, 5],\n [23, -20, 2, -19, -26, -24, -3, -4, -19, 20, 10, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[24, 6, 1, 20, -19, 7, 8, 5, -3, -13, 5, 19],\n [16, -11, -23, 25, 10, -6, -13, 4, 21, -9, -20, -17],\n [-20, 6, -4, -6, -8, 21, -8, 9, 2, -9, -25, -26],\n [20, -22, -7, -16, 15, -25, -24, -4, -15, -7, -22, 10],\n [11, 3, -18, 7, 26, 17, 8, 25, -5, 17, -3, -10],\n [-17, 3, 19, -4, 5, -10, 23, 24, -10, -13, -18, 13],\n [-25, 18, -2, 12, -18, -5, 16, 19, -23, -1, 2, 18],\n [7, -4, 10, -16, -21, -9, -6, 15, 9, 14, 11, 7],\n [-10, 10, -2, 11, -15, -4, 26, 15, -5, -6, 0, 4],\n [-21, 0, 13, 7, -15, 18, 26, -20, -17, 18, -10, -1],\n [-6, 1, 19, -25, 16, -26, 24, 26, 9, 24, -1, 2],\n [-6, -16, 13, -16, 9, 22, 12, 13, 8, 7, 20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -22, 6, 9, 20, -7, -8, 8, 25, 16, -10, 18],\n [16, 7, -18, -1, -25, 26, -18, -18, 13, -10, -26, -2],\n [16, 13, 15, -2, 12, 8, -24, 23, 10, 17, 17, 24],\n [3, 11, 7, -15, -8, 10, 17, 22, -10, -17, 22, 20],\n [-15, -11, -3, -8, -19, 4, -6, -10, -4, 10, -11, -21],\n [-19, -2, -9, -2, -15, -12, -1, 14, 18, -1, 20, 5],\n [-17, -11, -20, -10, -4, -1, -6, -5, -20, -13, -12, 26],\n [-20, -18, 24, 21, -19, 23, -4, 2, -9, 4, 3, 25],\n [12, 8, -9, 15, 12, -10, -13, 4, -3, 8, 17, 18],\n [7, -24, 10, 16, 13, -1, -4, 17, 12, -12, 22, -23],\n [2, -5, -2, -14, -9, 6, -11, 18, 15, 17, -25, 8],\n [15, 7, 3, -14, -14, -9, 5, 5, 8, 12, 19, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "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, 2, 26, 17, -11, 17, 20, -17, 3, -2, 12],\n [-7, -22, -26, 3, 22, -24, 18, -13, 3, 23, -23, -9],\n [10, -2, 21, -26, 26, 19, -12, -18, -12, 22, -3, -23],\n [-15, 10, 10, 16, -21, 12, 19, -3, -16, -14, 7, -2],\n [-20, 25, -23, -19, -7, 2, 26, 24, 18, 19, -17, 16],\n [7, -1, 14, 22, -24, -21, -22, -22, 20, -4, 22, -18],\n [8, -7, 22, 15, 8, 23, -9, -10, -3, -24, 5, 8],\n [11, -14, 20, -2, -18, -23, -13, 10, 7, -16, 14, -24],\n [1, 2, -18, -24, -2, 7, -15, 15, -18, -12, 13, -2],\n [-22, -16, 7, -3, -12, 11, -19, -22, 21, -1, -9, -21],\n [10, 21, -14, 1, -22, -14, -10, 23, 13, 18, 5, 2],\n [24, -24, 13, 7, 13, 0, -14, 18, 6, -21, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-11, 13, 1, 6, 21, 14, -14, 16, 18, -2, 26, 15],\n [9, 0, 11, -20, -22, 16, 18, 24, 4, -4, 15, -17],\n [5, 16, 26, 3, 12, 4, -9, 9, -25, -13, -14, 2],\n [-15, 12, -25, 5, -14, 19, 0, 22, 14, -10, 13, 4],\n [7, -3, 18, 8, 21, -21, -8, 3, -20, -17, 14, 5],\n [7, 1, -12, 3, 10, 2, -5, -23, -7, 5, 9, 23],\n [-23, 0, -10, -15, -5, -10, -17, -26, -5, -1, -9, 23],\n [-13, 20, 2, -15, 9, 8, 25, -15, -20, 2, -16, 6],\n [-21, 20, -12, 5, 24, -16, -4, -1, 7, 19, 7, 2],\n [-23, -10, 8, -14, 14, 12, -12, 2, 2, -16, 25, 5],\n [-25, 20, -13, -7, -5, -16, 0, -24, -10, 17, 1, 2],\n [-6, 20, -11, 10, -7, -21, -8, -22, -24, -26, 11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "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, 8, 22, -2, -3, -15, -9, -12, 17, -11, 0, -19],\n [19, -2, -10, 2, 26, -19, -12, 0, 19, 23, 25, -20],\n [-24, 2, 17, 26, -3, -24, -7, 19, -12, -2, 3, -13],\n [-20, -10, 17, -7, 9, -18, 11, 21, -5, 26, 26, -25],\n [-3, -19, -16, -14, -10, -19, -6, -9, 3, -9, 19, 20],\n [4, 11, 5, -16, 18, -2, 6, 11, 14, -19, -16, -5],\n [24, -3, 14, -10, -15, 19, 5, -12, -11, -5, 1, -7],\n [6, -17, 13, 5, 23, 6, -25, 6, 6, 14, -14, 3],\n [6, -14, 25, -1, -5, 12, -25, 11, 12, -1, 19, 23],\n [-12, 7, 15, 17, 22, 13, -16, -24, -21, -18, -21, -18],\n [12, 4, 5, 14, 23, -15, -19, -19, 23, 1, -7, 20],\n [-20, -16, -7, -11, -23, -21, -5, -1, -24, 14, 15, -13]]\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[[-16, -9, -15, -4, -15, -14, -2, 18, 24, -8, 19, 9],\n [18, -19, 2, 26, 5, 24, 17, -9, -21, -9, -8, -5],\n [10, 5, 14, -24, 1, -17, 24, 8, 2, -12, 6, -20],\n [-15, 22, 3, -6, 4, -3, -7, 10, -23, 1, 17, -7],\n [-3, 23, 22, 24, 5, 14, 9, 26, 7, 9, -25, -12],\n [7, 9, -21, 12, 15, 24, 24, -15, -24, 18, -9, 13],\n [-6, -12, 6, 8, -1, -19, 9, 21, 3, -4, 15, 17],\n [-13, -13, -25, 10, -22, 11, 18, 14, 20, -13, 12, -2],\n [-7, -25, 12, -21, -10, -2, 1, -25, 8, 10, -22, -26],\n [13, -15, 9, 18, -4, 20, 4, -16, -17, -24, -13, -11],\n [-17, 2, -17, -15, 3, 14, -26, -22, -7, -19, 16, -15],\n [-26, -7, 1, 16, 10, 20, 10, -15, 10, 22, 22, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 20, -12, -21, 17, -7, 23, -13, -25, -18, 10, -7],\n [-1, 2, -26, 8, -21, 10, 26, -22, 6, 22, 24, -13],\n [-15, 15, -7, 26, 23, -3, 16, 7, -2, 23, 2, 12],\n [4, 20, 16, 23, -4, 17, 11, -7, -4, 18, 25, -11],\n [23, 15, -19, 23, -6, -26, -19, 2, 5, 11, -22, 20],\n [-5, 20, 7, -26, -1, 16, -17, 3, 23, -9, -10, -1],\n [-19, 20, 13, 22, -15, 0, -19, -2, 19, -23, 6, -26],\n [-8, 4, -11, -13, 26, 21, -22, 14, -1, 1, -25, 23],\n [-21, -18, 6, 14, -2, 21, -14, -18, 26, -14, 4, 14],\n [-16, -23, 7, 11, 19, -23, 11, -8, -21, 7, -9, -14],\n [14, -4, -8, 18, -16, -26, -3, -20, -2, -6, -12, -26],\n [-15, -20, -12, -6, -8, 2, -2, 6, 22, 5, 22, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 11, -1, -16, 8, -19, 19, -13, -17, -25, 19, -18],\n [-24, -6, -1, -19, 21, -25, -21, 1, 26, 2, -1, -2],\n [-15, -22, 7, 21, 10, -12, 17, 9, -12, 16, 21, -4],\n [-21, 19, 23, 17, 16, 18, -6, -4, 16, -11, 20, 26],\n [-12, -2, 9, -16, 24, -12, -23, -6, -14, -5, -8, 7],\n [-13, -23, 21, 26, 25, 19, 0, 2, 20, 1, 8, -19],\n [-11, 15, 9, 3, -9, -25, 22, -14, -23, -1, -2, 3],\n [-16, -20, 4, 17, -17, 12, -14, 4, -20, 22, 15, 15],\n [9, -7, -23, -20, -26, 17, 18, 15, 20, -14, -5, -6],\n [-5, 1, -18, -1, -18, -12, -17, -3, 15, -19, -3, -11],\n [22, -1, 0, 10, -23, 23, -3, -8, 9, 12, -17, -2],\n [-9, -8, 9, -17, 6, 23, -22, 20, 22, 8, 17, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "536", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, -6, -10, -5, 21, 10, -12, 8, 1, -20, 5, -16],\n [-17, -18, -13, -14, -2, -25, 8, -20, -6, -9, -24, 15],\n [12, 14, 22, -16, 12, -3, 19, -8, -23, -1, 11, 15],\n [5, 12, 18, 19, 9, 13, 10, 6, 9, -24, -18, -19],\n [6, -21, 14, 12, -23, -14, 22, -25, -22, 17, 0, 5],\n [-6, -19, 11, -19, 23, -24, 17, -24, -5, -21, -25, -4],\n [17, -25, 11, -10, 8, 7, -4, 3, 25, -19, -5, 17],\n [9, -22, -14, 2, 4, 20, -11, 15, 3, -11, -15, -10],\n [-11, -15, -19, -7, -24, -11, 3, 18, -4, 1, 24, 13],\n [-22, -7, 13, 17, -26, 3, -6, -7, -21, -5, -9, -19],\n [12, 5, 6, 26, -11, -15, 11, 25, 7, -13, 9, 6],\n [-4, 23, 18, -25, 14, -6, -25, 0, -18, -26, -16, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[25, -4, -1, -23, -9, -21, 8, -5, 16, -12, -5, 10],\n [25, 15, -15, 20, 22, 15, 11, -9, 18, 8, 3, -3],\n [15, 3, -13, -21, -24, -11, -20, 25, -13, -18, -12, -6],\n [8, -25, 0, -25, 8, -9, -13, -7, -9, -17, -2, -25],\n [-2, 6, 9, 4, -13, -26, 19, -11, 19, 25, -24, 8],\n [14, -21, -2, -14, 26, 7, -19, -6, 7, -23, -2, -12],\n [-23, 18, -15, 5, 5, 1, -14, 4, -13, -7, -9, 2],\n [-21, 5, 2, 16, -25, -4, -8, 4, 24, -22, -8, 7],\n [-17, -2, -25, -16, 23, 4, -12, -18, -4, -8, -18, 8],\n [-6, -18, 1, 19, 24, -20, -11, -11, 6, -23, -23, 12],\n [13, -10, 10, 12, 25, 2, 25, 9, 11, 12, 23, 10],\n [25, 8, -20, 0, 1, -5, -13, -20, 10, -5, -22, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -6, 11, -12, -6, -17, -4, 12, -22, -26, -14, -6],\n [-1, 23, 18, -6, 26, -9, 10, 18, 5, 9, -10, 8],\n [22, -16, -6, 25, 26, -1, -23, 7, 25, 21, -9, 13],\n [8, 14, 2, 25, 2, 11, 15, -6, 15, -14, 22, 14],\n [-10, -18, 14, -26, -25, 21, 2, 6, -17, 23, 13, -6],\n [1, -16, 7, -19, -5, -19, 22, -12, -10, -4, -3, 18],\n [-8, -22, 5, 17, -26, -4, 10, -19, -14, -19, -4, 16],\n [-26, 18, 24, -3, 8, -3, -10, -22, -7, -6, 13, 4],\n [19, 9, -16, 25, -12, -8, -20, 24, 1, 24, 16, -22],\n [-22, 3, 5, -19, -17, 11, 20, 5, 21, 1, -10, 4],\n [-19, 13, -2, -18, -25, -12, 23, -24, 22, 9, -23, -13],\n [14, 14, -2, 23, -17, -6, 9, -15, 0, 13, -25, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[26, 5, 4, -11, 5, 5, 7, -16, -17, -12, -10, 13],\n [-9, -18, -2, 13, -13, -2, 23, -5, 25, 3, -7, -6],\n [17, 5, 24, 19, 22, -6, 8, 5, 3, 12, 22, -15],\n [14, 20, -9, -6, -14, -6, -19, 19, 13, 19, -20, -4],\n [17, 5, -16, -5, -5, 16, -2, -5, 1, 2, -14, -9],\n [-25, 2, -6, -12, 25, 0, 23, 4, -12, 24, -4, -3],\n [17, -14, -5, 16, 10, 6, -24, -8, -4, 2, 3, 12],\n [17, 20, -2, 10, 20, -19, 15, -11, -19, -26, 17, -22],\n [-24, -26, -23, 13, 8, 5, 15, 7, 16, -2, -17, -6],\n [19, 12, 0, 0, -25, 14, 21, -14, -18, 25, 9, -5],\n [15, -1, -15, -10, -13, -13, 7, 26, -7, -16, -11, 24],\n [4, -21, -8, 10, -23, 20, -23, -7, -17, -3, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[10, 11, -6, 13, 12, -6, -17, 11, 19, -23, 18, -7],\n [-10, -20, -23, 2, -13, -24, -3, 10, -11, 25, -23, -3],\n [7, 3, -9, -8, 4, -8, 22, 19, -8, -5, -3, 18],\n [-15, 3, 11, 26, 4, 9, -8, 21, 18, 9, 3, 22],\n [6, -9, 25, 22, 1, 20, -16, 18, 6, -10, -21, -23],\n [-7, 21, 20, 0, -12, -21, 20, -13, -16, 12, -18, -1],\n [-11, -22, 25, -17, 23, -24, -14, 16, 22, 3, 18, -21],\n [-10, 18, 24, 26, -8, 15, 8, 19, -1, 24, -22, 2],\n [10, -7, 22, -6, -17, -22, 9, -21, -1, -23, 12, 12],\n [23, 8, -26, -3, 9, -21, 14, 19, 17, 4, -7, -3],\n [-2, 9, -6, 3, -3, 17, 15, 3, -5, 1, -20, 8],\n [1, -13, -17, -11, -11, 4, 15, -2, -14, -21, 17, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, 9, 16, -7, -9, 16, -6, -23, 23, 6, 0, -20],\n [-21, -12, -9, 5, -16, -7, -3, -12, 21, -20, -6, 15],\n [-1, 17, -13, 10, -6, -9, -22, -24, -4, -1, 10, -3],\n [22, -8, 24, -2, -6, -15, 14, 6, 23, 26, -23, 15],\n [-20, -5, 6, -10, -3, 7, 1, 16, 14, 12, -5, 22],\n [-10, 7, -21, 19, -21, 7, -26, -17, -6, -22, -25, -5],\n [21, -25, -17, 7, -11, 21, 24, 12, -5, -15, -3, 20],\n [13, 11, -17, 8, 24, 22, 5, -20, -6, -7, -1, -23],\n [19, 25, -5, -12, 13, -6, -12, -5, 25, 1, -13, 0],\n [14, 13, 1, -1, 22, -25, -2, -24, -19, 17, 6, 15],\n [25, 8, -21, 12, 25, -4, -2, 23, 16, -8, -22, 24],\n [-16, -15, -17, -19, -3, 1, 14, 9, 10, -6, -19, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538", "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, -12, 21, 19, 13, -9, 15, -7, -21, -15, -25, -20],\n [-11, -24, 18, -24, 0, 23, 16, 13, 11, 6, 1, -26],\n [-19, 10, 5, 21, 16, 10, -23, 3, -21, 19, -8, 5],\n [-18, -15, -16, 19, -11, -26, 18, 26, -6, 3, -14, 7],\n [-23, 1, 11, 4, 0, -22, -2, -24, 6, -23, -2, -7],\n [7, -1, -22, 8, 1, 2, -18, 25, 11, 23, -21, -8],\n [17, -16, -25, 20, 17, 17, -18, -6, -3, 7, -5, -24],\n [-15, 1, 3, -1, 21, -6, 1, -1, 6, -6, 8, 25],\n [7, 14, 24, 20, -9, -16, -4, 21, -5, -10, -22, 17],\n [-16, 3, -12, 0, 8, 6, -7, -11, 7, -25, 8, 13],\n [1, 20, 12, -21, -18, -7, -26, -19, -4, -24, -23, -2],\n [20, 11, -12, -6, 8, 26, 26, 19, 25, -13, 9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "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, 12, -18, 8, -14, -12, -9, 24, 6, -21, 0, -4],\n [0, 7, 19, 11, -13, 9, 26, -19, 8, -8, 3, -13],\n [-7, 22, -2, 13, -3, -13, -1, 11, -4, -5, 21, -8],\n [19, 24, -24, 15, -8, -18, 1, -7, 18, -20, -13, -18],\n [-8, 20, 25, -13, 11, 26, 9, 13, -10, 3, -18, 6],\n [25, -2, -13, -16, 26, 8, 14, -13, 3, 14, -23, -23],\n [1, -19, -25, 14, 19, -5, 14, -11, 2, 22, 21, 3],\n [-15, 8, -16, 19, 23, -6, -6, -22, 21, -7, 10, -24],\n [17, 6, 26, -18, -18, -23, 8, -10, 7, -3, 5, -26],\n [-19, 18, -4, 20, 13, -15, -15, 19, 20, -12, 14, -8],\n [-1, 25, 2, -5, 13, -6, 24, 11, -7, 2, 24, -23],\n [-20, 1, 1, -23, -5, -15, 18, -24, -5, 17, -25, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[7, 0, 14, -26, -19, -4, 11, -21, -5, -2, -9, -10],\n [-15, -21, -1, 0, -19, -8, 15, -26, 2, 18, 22, 8],\n [13, -13, 8, 21, 18, -7, 22, -14, 11, 22, 19, 22],\n [-19, 16, -7, 6, -1, 12, -6, 26, 22, 15, 16, 14],\n [-18, -3, 10, 22, 14, -10, -3, -6, 24, 12, 14, 12],\n [-14, -16, 19, -8, -16, -14, 19, 18, -26, 13, 17, -8],\n [-15, -19, -19, 26, 18, -15, 21, 6, 18, -1, 12, 1],\n [-22, -19, -2, 0, 19, -4, 3, 18, 20, -4, 22, 20],\n [-7, -9, -9, -25, -23, 3, 6, 9, -9, 10, -8, 20],\n [1, 13, -7, 22, 6, -15, 24, -12, 14, 12, -25, 2],\n [14, -17, -25, 24, -16, -14, -17, -13, -9, 24, -18, 12],\n [1, -24, -7, -21, 0, 26, -25, 2, 11, -24, -11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"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, -25, -10, 14, -15, 8, 16, -26, 18, -12, -1, 10],\n [-6, 22, 4, -2, -4, -3, 11, 1, -6, 16, -9, 9],\n [8, 18, -18, 26, 11, 3, 17, 7, 5, -24, -24, 1],\n [17, -12, 14, -4, 13, -16, 21, 5, 9, 6, -3, 12],\n [7, 1, 10, -20, -23, 10, -26, -26, 20, -7, -8, 2],\n [-17, -9, 1, 8, 16, 20, 4, 0, -16, 22, 22, 11],\n [-22, -19, 7, 21, 25, -15, 11, -26, 4, -23, 22, 18],\n [23, -22, 3, -3, -24, -16, 18, -23, -1, 0, 19, 16],\n [0, 15, 24, 23, -21, -12, 26, 3, 15, 10, 10, 15],\n [10, 8, -4, -21, -23, -9, -18, 22, 2, -14, 20, 25],\n [-10, 18, 5, 21, -5, -23, -22, 10, 14, 22, -14, 7],\n [18, -5, 26, -4, 24, -24, 15, 7, 5, 18, 24, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, 19, 17, -6, 17, -16, 12, -23, 24, -26, 1, -3],\n [8, -14, 20, 7, -16, 9, 24, -10, 8, -9, 13, -5],\n [-3, -8, 10, 12, -6, -19, 1, -22, -10, 10, 9, -8],\n [0, 26, 7, -16, 18, 20, -15, -6, -16, 12, 1, -22],\n [-10, -7, 14, 19, -15, -21, -10, 24, -8, -1, 21, 17],\n [17, 25, 5, -21, 9, 11, -16, 6, -3, -4, -12, 0],\n [-16, 24, 23, -10, 24, 26, -13, 0, -9, 1, 24, 20],\n [20, -23, -20, 18, 8, 21, -18, -19, 25, 18, -10, -10],\n [22, 6, 5, -19, -8, 11, -24, -22, -14, 20, 19, 4],\n [-11, 23, 5, -5, 2, -5, 16, -24, -17, 15, -6, -11],\n [-15, -25, 14, -3, 8, 3, 3, 20, 8, -8, 23, -19],\n [-1, 22, 13, -20, 3, -20, -24, -26, 9, -2, 10, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-12, 10, -14, 13, -19, -22, -18, -26, 9, 8, -25, 13],\n [-4, -18, 7, 19, -13, -23, 3, 4, 11, -16, 8, -19],\n [-24, -13, -14, 18, 5, 7, 18, -8, 11, -11, -25, 13],\n [-10, 7, 15, -11, 11, -25, -25, -1, -14, 20, 4, 7],\n [12, -24, -19, -4, -13, 0, 2, 12, 26, 12, -26, -10],\n [14, 3, 26, -14, -6, -8, 26, -8, -2, -5, 4, -10],\n [-4, 5, -17, -17, 9, -19, 25, -7, 5, 23, -13, 23],\n [1, 19, 25, 26, -3, -12, -5, 3, -23, -14, -4, -19],\n [-9, -15, 4, -13, 7, -9, 7, -16, 14, -15, 22, -12],\n [4, 22, 2, -1, -9, 5, -5, 11, -10, -4, -3, 23],\n [-19, 14, -21, -22, 17, 2, 1, -16, -26, 16, -8, -18],\n [0, 7, 17, -23, 9, -9, -12, 24, -14, -8, 22, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[21, -15, 24, 10, -10, -4, -1, 2, 6, 0, -2, -17],\n [20, -4, -6, -6, 16, -14, 10, 6, -3, 17, -16, -10],\n [-23, 20, -2, 3, -18, -6, -7, -8, -8, -15, 10, 15],\n [-10, 10, 21, 12, 1, 14, 8, 20, 21, -9, -13, 8],\n [17, 14, -20, 14, -14, -9, 10, -14, 9, 4, -25, -11],\n [-18, -18, 11, -16, -5, 6, 9, 18, -4, 18, 18, 7],\n [-18, -3, -19, -20, 9, -9, -24, 1, -21, 17, 17, -6],\n [1, 13, -26, 9, -6, 16, 8, -14, 22, -17, 26, 17],\n [20, 26, -17, 19, -14, 10, 11, -3, -25, -5, -10, 9],\n [-13, -17, 8, -2, -24, 20, 11, -10, -15, 25, -3, 2],\n [16, -2, 9, -1, 11, -26, -7, 1, -11, 20, -10, 13],\n [1, -15, 0, 26, 15, 20, 3, 14, 7, 10, -21, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 5, 26, -2, 6, -20, 25, -15, -11, -11, 16, 26],\n [9, -14, -20, 9, 20, 24, -18, 5, -16, -19, 6, -4],\n [-2, -19, 18, -5, -23, 13, -24, 2, 14, 2, 7, 7],\n [1, -14, -12, -4, 17, -1, -23, -1, 13, -18, -22, 5],\n [-7, 23, -16, -12, 5, 1, -5, 14, -10, -1, 17, -20],\n [15, -1, -2, -17, 18, -8, -16, -14, 26, -19, 13, -23],\n [20, 4, 1, -16, 16, -26, 22, 20, 25, 11, -3, 20],\n [4, 14, 19, 23, -1, 22, 23, -22, -7, 25, 14, -16],\n [6, 23, 11, 0, 7, -12, 5, -6, 19, -22, -21, 11],\n [-5, -9, -13, -17, 19, -14, 4, 3, -24, 3, -21, 2],\n [-19, 17, 18, 16, 17, 6, -10, 21, -16, -14, 23, -16],\n [4, 1, 17, -21, 14, -11, -23, 8, 21, -1, -15, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -2, -9, -8, -4, 11, -9, -1, -21, -23, 17, 24],\n [2, 7, -10, 16, 16, 26, -11, -25, 7, -19, -14, 15],\n [-19, 3, 5, 9, 20, 3, -26, 16, 12, -10, -7, -3],\n [23, -5, 2, -5, 17, -18, 10, -17, 9, 10, 1, 1],\n [15, 16, -6, -3, 15, 13, -25, -19, 21, 0, -5, 10],\n [0, 2, -24, 17, -14, 18, -17, 9, -18, 0, 7, 24],\n [-26, 5, -2, 2, -20, 22, -24, -7, -7, 26, 3, 8],\n [8, 22, 12, 0, -1, -13, -10, -9, 18, 25, 2, -7],\n [26, 0, -9, -23, -26, 23, -26, -1, 18, -7, 25, -4],\n [-17, -16, 14, 14, -22, -26, -10, -5, 7, 18, 14, 2],\n [-23, -22, -16, 24, -6, 8, -15, -1, 24, -8, 18, -20],\n [20, -20, -1, 13, -22, -6, -13, -23, -4, 15, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[23, 25, 18, 2, -19, 14, 21, -8, 21, 12, 19, 1],\n [19, 0, -23, -12, 8, 10, -26, -24, 20, -3, 0, 13],\n [9, 7, 2, -3, -3, 15, -23, -24, 7, 22, -4, 26],\n [25, -4, 18, -22, 4, 26, 14, -21, 10, -17, 13, -20],\n [12, 11, -6, -7, -24, 24, -5, 20, -23, 1, -15, 11],\n [24, 9, 20, 14, -22, -14, -4, 23, 3, 10, -2, 21],\n [0, 24, -13, 21, 20, 9, 12, -11, -5, -6, -6, -19],\n [22, -11, 4, 15, -17, 5, 7, -18, -10, -16, 5, -17],\n [-5, -10, -23, 21, 25, 20, -2, -6, 10, 11, 22, -26],\n [-2, 24, 9, -10, 14, -3, -25, 13, -12, 5, 12, -21],\n [-26, 20, -4, 12, -10, 7, 14, 2, -18, -14, -21, -21],\n [-7, 25, 26, -24, -10, 22, -15, 21, 20, 18, -26, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-24, -1, -12, 9, 5, 5, -23, -9, 22, -8, 16, 25],\n [8, 13, -13, 6, -13, 7, -23, -3, 2, -8, -21, 6],\n [22, 13, -8, 26, -26, -22, 0, -11, -21, 13, -14, 21],\n [8, -8, -15, -11, 16, -17, -2, -7, 4, -23, 17, -4],\n [-25, -5, 24, 10, -19, -20, -13, -24, 23, -11, -8, 24],\n [-9, 25, -11, -19, 6, 22, -15, 26, -16, -22, 0, -15],\n [-10, -21, 6, -22, 1, -13, -22, 6, 23, 21, 14, -8],\n [-5, -22, -25, 3, 20, 12, -23, 6, -14, -7, -20, -12],\n [-4, -13, -4, -8, 2, -7, 2, -3, -9, -17, 14, -19],\n [-1, 2, -17, -10, -25, -21, -22, 1, 14, -22, -9, -1],\n [-7, 14, 22, 0, 22, -15, -20, -24, -17, 7, -2, 8],\n [-11, -25, -3, -17, 11, -5, -1, 16, 12, 0, 2, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "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, 0, 14, -7, 17, -8, -7, 8, 20, -25, 3],\n [26, 7, -5, -24, -21, -12, 0, -17, -18, 6, 5, 21],\n [-21, 14, 9, -25, 2, -23, -26, -8, -1, -2, -17, 26],\n [-12, -5, 24, 21, -6, -5, 9, 7, 3, -2, 18, 1],\n [-26, 22, 18, -23, -20, 22, -18, 9, -8, -26, -17, 9],\n [-18, 18, 19, 15, 5, 5, -21, 21, 11, -10, -17, 23],\n [0, 23, 8, 25, -6, -2, 1, 20, -12, -23, 2, -18],\n [0, -1, -8, 1, -10, 16, 14, 15, 23, -7, 18, 13],\n [12, 22, 26, -4, 20, 5, 25, 20, 6, 19, -22, 16],\n [21, 7, 13, -16, 23, -24, 6, -16, -11, -9, 3, 21],\n [-17, -9, 11, -8, 9, -14, 19, -24, -17, 11, -26, 0],\n [19, -19, 24, 19, 15, -10, -18, -21, 16, -2, 12, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 6, 10, -18, -9, -6, -25, 16, 11, 13, 9, 23],\n [16, 10, -12, 1, -9, 7, -5, -16, -14, -23, -5, -20],\n [16, -3, -23, 1, -12, -26, -24, -13, 11, 23, -26, 11],\n [11, -6, 21, 2, -22, 22, -17, 1, -6, 23, -20, -24],\n [18, 20, -7, -8, 8, -23, -22, -26, -23, -15, 0, 15],\n [-4, -2, -6, 25, -3, -2, 18, 19, 5, 5, -22, 9],\n [19, 15, 22, 15, 12, -11, 6, 22, -6, -18, -21, 24],\n [18, 8, 12, -5, 14, -22, 15, -4, -10, -15, -4, -11],\n [-24, 3, -5, -18, 2, 20, 10, -4, -14, 5, 19, 25],\n [20, 21, -4, 18, -10, 13, -6, -25, 10, -21, 17, -9],\n [3, -5, 6, 3, -10, 16, 5, 15, 24, -13, -17, 20],\n [24, 9, 7, -18, 15, 1, -16, -13, 12, 20, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -3, -19, 16, -18, 20, 6, 6, -8, -24, -17, 13],\n [20, 15, -26, 2, 23, 7, 24, -14, -26, 7, 2, 21],\n [20, -14, 21, 22, 26, 2, 12, -3, -1, -10, -20, -14],\n [-22, -1, 22, -24, -20, 22, 12, 26, -26, 22, -10, 16],\n [-2, -24, -12, 2, 26, 16, 5, -1, -11, -2, 1, -18],\n [-26, 2, -5, -11, 14, 24, 17, 24, 14, -20, -13, 2],\n [-8, -8, -25, 14, 18, -12, -24, -16, 26, 19, 3, 13],\n [-9, 24, 21, -25, 5, -19, -5, -21, -15, 20, 13, 9],\n [-12, 1, 25, 22, 18, -9, -25, -14, 18, -12, -7, 2],\n [15, 2, -24, -8, -24, -13, 13, -23, 25, -16, 4, 16],\n [5, 0, 3, 16, -25, 22, -18, 1, 4, 7, -12, 21],\n [-2, 9, -19, -18, 10, 21, 18, 12, 5, 25, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, -8, 17, 2, -20, 1, -18, 1, -21, 2, -10, -11],\n [-4, 4, -24, -6, -1, 9, 15, 10, 26, -5, 15, -15],\n [15, -14, -16, -11, -19, 13, 13, 18, -25, 3, 3, -15],\n [-17, 17, -16, -12, -11, -10, -1, -25, 23, -15, 24, -1],\n [-4, -9, 5, 22, 11, 20, -24, 11, -24, 3, -26, 3],\n [18, 5, 1, -6, 19, -14, 0, 9, -20, -5, -17, 12],\n [26, -12, -12, -23, 5, -4, -21, -3, -7, 10, -7, -15],\n [6, 1, -19, -26, 10, -5, -21, -6, 5, 8, -12, -22],\n [19, 23, 21, -21, -2, 19, 13, 2, -20, 13, -14, 11],\n [-9, -25, -19, -16, 6, 11, 21, 0, -7, -15, 16, 4],\n [0, 5, -17, -24, 18, 0, 8, 4, -12, -11, -14, 22],\n [8, 25, -16, -6, 24, -16, 3, 21, 26, 8, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -13, -3, 23, 22, 5, 9, 5, -12, 16, 8, -24],\n [-11, -22, -6, -17, -8, -2, -23, 2, -8, 16, -25, -17],\n [16, -2, -7, 21, -8, -4, -3, -16, 19, 7, 1, -22],\n [-22, 24, -6, -15, 23, -23, 22, 15, -7, 11, -2, -13],\n [-16, 5, -16, -9, 0, -9, -4, -16, -6, 17, -22, -4],\n [14, -2, 14, -17, -5, -8, -26, -20, -23, -26, -12, 13],\n [-15, -5, -5, 23, 20, -10, 2, 19, -13, 23, -7, 23],\n [21, 6, 16, -12, -15, 13, -7, 3, 11, -24, 1, -1],\n [3, -14, -14, -25, 10, 22, 11, -25, 9, -1, -16, -19],\n [17, 13, 16, -5, -7, -19, 2, 13, -1, 3, -10, -7],\n [25, -11, 19, 16, -20, -11, 18, 20, 21, 0, 26, -4],\n [-3, -18, 8, 24, -7, 10, 15, -10, 20, 4, -19, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 26, 3, 19, -7, 12, 26, -15, 22, -10, 15, 3],\n [2, -8, 19, -16, 7, 23, -20, 17, 7, -7, 23, 11],\n [-3, -17, 5, 25, -12, 10, -7, -24, 10, 13, -19, 13],\n [17, -4, 13, -16, 19, -19, 2, 3, -17, 12, 1, 22],\n [9, -14, 5, 9, 10, -1, -5, -23, 4, -9, 11, -3],\n [-4, -5, -25, 4, -16, 1, 19, 5, -22, 11, -17, 13],\n [19, -3, 8, 17, 21, -4, -10, -26, 4, 4, 15, 15],\n [26, 7, -18, -5, -14, -2, 21, -9, 24, -15, 13, -10],\n [-12, 15, -12, -12, 12, -14, -10, 5, -18, 13, -7, -1],\n [0, -6, -9, -14, -11, -18, -15, 17, 11, -8, -20, 8],\n [21, -9, -11, 12, -23, -2, 5, 13, -14, 18, -10, 22],\n [10, -21, -8, -14, -1, -13, 4, -23, 12, -19, -2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "477", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 11, 11, 1, 26, 3, -24, 1, -24, 18, 7, -11],\n [-5, 5, 11, -19, -19, -21, -13, 5, 8, -17, -24, -15],\n [22, 4, 2, -22, 25, -2, 14, 4, -6, -7, 12, -5],\n [-23, -14, 18, 15, 23, 22, -7, 25, -14, -10, 9, 6],\n [-26, -12, -14, -10, -3, -19, 23, 0, 18, -4, 19, -19],\n [-19, -1, 20, -14, 12, 10, 22, 1, -2, -11, -25, -9],\n [-10, 3, 12, -14, 5, 23, 2, 19, 3, -9, -14, 16],\n [-6, 3, -6, 21, -10, 13, -8, 25, -12, -18, 25, -17],\n [17, 4, 26, -4, 25, 3, 6, 25, -18, 20, -26, 17],\n [8, -16, 7, -11, -18, 5, -12, -15, 6, 18, -13, -19],\n [-19, 0, -15, -26, 16, 13, 15, 24, -16, 12, 16, 4],\n [-10, 6, 5, 2, -6, -6, 13, -4, -21, -5, 23, 11]]\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[[10, 18, 24, -19, 14, 22, 8, 24, -16, -3, 22, -6],\n [24, -25, 13, -8, 12, 1, -10, -21, -8, 11, 1, -25],\n [11, 10, 24, 25, -23, -5, -1, 22, 16, 9, -14, 25],\n [5, -10, 14, 9, 19, -8, 8, 19, 13, 1, -26, 15],\n [-9, 21, 13, 6, -15, -19, -3, -11, 23, -23, 11, 17],\n [0, -18, 20, -11, -15, 4, -3, -13, 18, -2, 7, -24],\n [-3, 15, -18, -1, -7, 13, -17, -8, -24, -3, -22, -24],\n [0, -11, 22, -12, 8, -15, 14, 26, 17, -1, 20, 7],\n [-4, 4, 23, -7, -15, -4, -23, -4, 21, 21, -26, -2],\n [-25, 3, -24, -6, -2, -7, 22, 25, -5, -6, 6, 25],\n [11, -12, 19, 25, -12, 19, -2, -6, -3, -22, -21, 22],\n [16, 21, 17, 20, -4, -23, 0, -9, -6, 1, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[13, -4, -24, 13, 23, -17, -2, 25, 22, -19, -16, -22],\n [18, 26, 10, 18, 11, 2, -22, -18, 21, -25, -26, 13],\n [24, 3, -16, 1, 17, -15, 12, -1, -14, -19, 1, 3],\n [-18, 12, 4, -6, 20, 7, 4, 25, -2, -15, -26, -5],\n [13, 10, 20, -26, -26, 15, 15, -6, -12, -10, -5, 11],\n [8, 18, -11, -19, 20, -10, -10, -1, -14, -10, 11, -10],\n [21, -13, 18, -21, 8, 19, -13, 20, -19, -12, 0, -14],\n [22, 4, 26, 8, -21, -22, -5, 22, -4, -2, 7, -1],\n [20, -22, -1, -7, -21, -21, 23, -9, -23, -10, -13, -13],\n [-14, -20, 17, -12, -8, 16, 20, 17, 8, -10, 8, -8],\n [-7, 9, 8, 5, 21, 17, 13, -3, -10, -20, 16, 23],\n [-26, 8, 5, 9, -14, -21, -13, 10, 21, -12, 20, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[13, -11, 1, -11, -23, 18, -1, 1, 5, 18, -25, 4],\n [-24, -19, -3, -12, 16, 4, -18, 12, 18, -25, -19, -20],\n [17, 24, 12, 15, -11, 8, 3, -17, 11, -9, 23, -22],\n [26, 2, 12, 7, 16, 18, -4, -22, 3, -21, 19, 17],\n [-23, 2, -4, -21, 5, 15, -9, -12, 13, 5, -18, 10],\n [-17, -7, -21, 21, -24, 15, -16, 16, -10, 5, -23, -23],\n [-10, 14, -8, -22, 5, -5, -21, 8, -5, -26, -7, -5],\n [21, -16, -14, 15, -24, -18, -15, -4, -13, 6, -9, 22],\n [14, -18, -4, -17, -8, 20, -22, 20, 25, -4, 3, -2],\n [1, 7, 18, 21, 20, -2, -17, -13, 15, 19, 3, 14],\n [-2, -13, 8, 25, 21, 7, -17, 8, -16, -16, -6, -6],\n [-5, 18, -20, -10, -25, -15, 15, -9, -16, -11, 22, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 8, 26, -1, -11, -21, 17, 16, 20, 20, 21, 15],\n [-15, -14, -23, 12, -25, -1, 0, 0, -12, -19, -20, 20],\n [19, 13, -15, -14, 16, -10, -10, 9, -6, -19, -22, -1],\n [-11, 9, 1, 2, 20, -15, 10, 3, -4, -11, -13, -17],\n [-20, 18, 25, 10, 2, -24, -12, 9, 20, 19, 25, -8],\n [-14, 15, -6, 10, 0, 25, 2, -7, -2, -21, 9, -25],\n [-5, 5, -11, -9, -22, 9, 3, 18, -8, -4, 7, -14],\n [16, 2, 9, -5, 25, 25, 20, 9, -18, 12, 24, -8],\n [11, -21, 25, 20, -12, -7, -18, 5, -23, 23, -9, -22],\n [-7, -4, -16, 10, -5, -23, 2, 17, 7, -14, 15, -18],\n [15, 4, -20, -23, -8, 15, 3, 4, 8, -6, 4, -8],\n [4, 26, 5, -25, 25, -17, -25, -25, -3, -10, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-11, 19, 12, 26, 4, 16, -3, -26, -16, -6, -23, -20],\n [-1, 20, 23, -15, 4, -10, 6, -16, 1, 5, -26, 20],\n [1, 26, 15, -20, -25, 15, -3, -23, 17, -8, -1, -16],\n [13, 23, 16, -16, 18, -24, -15, -24, 15, 0, 22, -25],\n [22, -11, -25, 3, -7, 11, 1, -2, 5, -17, 15, 13],\n [6, -14, 14, 15, 20, 10, -11, 18, -5, -7, 23, 16],\n [0, 14, -11, 7, 5, -1, -2, -25, -15, 13, -18, -15],\n [-1, -18, -17, 5, 7, 21, -7, 12, -25, -26, 24, 9],\n [-3, 0, -25, 4, -13, -25, 2, -12, -15, 10, 1, -7],\n [12, -3, -6, -17, 19, -13, 10, -9, -3, -13, 7, -15],\n [-5, -21, 9, 18, 9, -5, -13, -11, 9, -2, 5, 6],\n [18, 9, -7, -9, 11, -24, -4, 5, 18, -11, -22, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "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, 13, 24, -13, 12, 4, -13, -21, -15, -11, -10, 18],\n [-4, -13, -20, 19, 5, -12, 17, -10, 14, 20, 17, 7],\n [-22, 18, 0, 25, -4, 13, -13, -12, 16, 6, 26, 4],\n [8, -10, 1, -8, 19, -4, 5, 13, -14, -7, 8, -22],\n [-18, 2, -21, -2, 4, -5, -25, 18, -22, 0, -2, -19],\n [-26, -7, 17, -4, 5, -16, 12, 20, -3, -16, 2, -1],\n [-11, 8, -7, 19, -24, -26, 26, 20, -26, -10, -25, 2],\n [-7, -21, -19, 2, 21, 24, 6, -24, 8, -22, 0, 17],\n [-15, -7, 18, -7, -18, 12, -23, 24, -8, 11, 0, 18],\n [16, -14, -14, -5, 1, 25, 20, 26, 18, -5, 16, -8],\n [-19, 25, -19, 15, -1, 21, 24, -1, -4, 16, -14, 1],\n [-18, -7, -8, 21, 12, 24, -15, -12, 4, -13, -16, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[15, 0, -16, 11, 7, 16, -8, -21, 19, 25, 11, 22],\n [15, 1, -26, 8, 13, -19, 25, 20, -20, -16, 12, -23],\n [-2, -15, -1, 11, 19, -15, 16, 24, 26, 10, 19, 26],\n [-3, -11, -14, -2, 25, -23, -16, 5, 22, -20, 19, -16],\n [1, 14, -4, 18, -4, 23, 1, 16, 20, -1, -2, 2],\n [-8, 6, 9, -13, -13, 8, 3, 1, -10, -24, -11, 19],\n [3, 25, 2, 18, -12, 19, -2, 24, 11, 15, 20, 26],\n [25, 11, -4, -2, 15, -20, -5, -10, -9, 22, 14, -17],\n [-17, -20, 21, 23, 11, 0, 25, 6, -26, 17, 26, 7],\n [-23, -10, -23, 16, -1, -23, -26, -20, 3, 23, -18, 8],\n [-19, -3, -8, 9, 23, 25, 16, 0, 5, -13, -9, 1],\n [2, -11, 8, 20, 4, -23, 10, -10, 12, 21, 19, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[21, 12, 14, -23, 3, 3, -5, -16, -25, 17, -15, 3],\n [9, -9, -1, 26, -20, -26, -1, -4, -1, 18, -21, -21],\n [17, -19, -3, -5, -8, 10, -9, 4, 10, 3, 15, 6],\n [-17, 10, -15, 3, 0, 12, -18, -6, -15, 2, 6, 16],\n [26, -12, -25, 25, 12, 26, 17, -9, -24, -20, 16, -9],\n [17, 11, 10, 6, 17, 4, -16, -23, -9, -23, 22, 7],\n [2, -3, -5, -25, 17, -21, 15, -2, -6, -11, 4, -13],\n [12, 1, 5, 1, 24, 22, -18, 18, -5, 5, -22, -4],\n [-22, 15, 26, 5, -17, 12, -12, -20, 2, 20, -24, -8],\n [-17, 1, 2, -12, 8, -21, -15, 20, 11, -14, 2, -8],\n [-24, -19, -19, -7, 20, -23, 24, -6, -24, 18, -19, -4],\n [-11, -14, -24, 21, -18, -13, -14, 26, -20, -12, -20, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[7, 14, -5, -3, 22, 10, 17, -26, -17, 16, -11, 19],\n [-19, 22, -2, 23, -15, -2, -10, -1, 19, 21, -13, 14],\n [9, -4, 16, -21, 20, -22, 16, -2, -9, -14, 16, -13],\n [1, -9, 1, 24, 0, 5, 20, -18, 13, 5, -7, 1],\n [6, -23, 19, 7, 21, -24, -1, -19, -21, -11, -3, 21],\n [12, 3, 18, -14, -22, -2, -7, -9, 20, -9, -25, -17],\n [18, 23, 20, -15, 20, -14, 23, 20, -16, -8, 8, 12],\n [26, -1, 19, -13, 18, 17, -3, 14, -26, 24, 16, -5],\n [-4, -8, -9, -15, 1, 1, 6, -8, 1, 25, 22, 10],\n [-1, 8, 7, 8, 13, -11, 11, -14, -4, -5, -11, 1],\n [21, 8, 18, 19, -19, 17, -5, -6, -1, 13, -6, -2],\n [14, -26, -21, -4, 24, -4, 16, 16, -4, 5, 3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[16, -9, -4, -12, 6, -6, 12, -4, 0, 18, 17, -9],\n [-3, 24, 20, 13, 24, 15, -20, 23, 21, -7, 0, -21],\n [0, -18, 26, 18, 4, -6, -1, 13, 21, 18, -14, 22],\n [-4, -7, 10, 26, 1, -10, 1, 14, -25, -2, 23, 14],\n [-21, -16, 11, -21, 18, -16, -13, -25, 13, -24, 26, 8],\n [6, -3, -8, -9, 22, 25, -3, 18, 8, -26, 9, -2],\n [18, 22, 16, 7, -2, -11, 7, 2, -8, -4, -8, -2],\n [-11, 24, -18, -26, 15, -8, 6, 7, -11, 17, 13, -9],\n [7, -2, 18, -21, -6, -21, 5, 14, 21, 16, 12, 4],\n [15, -17, 3, 25, -9, -3, 25, -18, 4, -12, -23, 13],\n [-18, 18, -18, -1, -23, -10, -11, -12, 8, 25, -22, -22],\n [-7, -12, -9, 20, -25, 2, -14, -23, 15, 18, -17, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "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, -19, -24, 21, 19, -18, 3, 26, -16, 8, 10, 15],\n [-14, 9, -14, -15, 10, -17, -18, 25, -20, -25, -4, 12],\n [13, 12, -6, -4, 2, -13, -1, 24, -22, 4, -2, 4],\n [23, -7, 17, -10, 18, -25, -2, -14, 12, 1, 15, -21],\n [-24, 8, -9, -16, -7, -22, -8, -5, -8, 20, -11, -3],\n [14, -23, -12, -2, 17, 8, -13, 22, -8, 11, 9, -20],\n [3, -8, 22, -2, -11, 20, 13, 24, -19, -9, 1, -11],\n [25, -8, 15, -10, 18, -14, -20, 0, -17, 7, 9, -2],\n [-21, -3, -9, -4, -21, 2, -2, -10, 19, -3, -16, -1],\n [24, 7, 1, -24, -16, 11, -13, 24, -1, 21, -6, 12],\n [3, -19, 24, -7, 21, 5, -5, -20, -18, 18, -26, 2],\n [-19, -23, 8, -24, 18, 13, -20, 0, -26, 0, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, 17, -4, 14, -16, 15, 26, 6, 23, 9, 10, 14],\n [-10, 8, 21, -22, 21, 5, -24, 25, 20, 8, 25, -13],\n [21, 4, 4, -10, -3, 25, -4, -9, 23, -13, 23, -12],\n [-12, -21, 0, -12, 23, 9, -19, -12, -24, 20, -14, 14],\n [7, -3, 13, 5, 5, 3, 25, 22, -14, -26, 7, -12],\n [17, -13, 2, 7, -9, -20, 2, 4, -2, 11, -13, -19],\n [0, -25, -10, 10, -13, -2, 3, 2, -7, -6, 26, -5],\n [8, 10, -11, 23, 22, 16, -10, -11, -25, -23, -6, 12],\n [7, 3, -21, -10, 12, -2, -22, -22, -7, -11, 24, 14],\n [10, 13, -18, -22, 15, -25, -18, 16, 9, -5, -5, -5],\n [7, 2, 11, 19, 6, -9, -20, -26, 6, -26, -3, -23],\n [-23, -9, 0, 16, 5, 6, 1, 15, 14, 9, -21, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "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, -4, 23, 15, -3, 22, -14, -9, -14, 22, 10, 16],\n [12, 15, -10, -12, -9, -4, 24, 3, 7, -23, -24, -20],\n [-9, 15, -20, 13, -21, -5, -26, -23, 19, 22, 25, 23],\n [16, 2, -6, -1, -13, -18, 20, -15, 15, 24, 24, -21],\n [-7, -3, 0, 11, -19, -26, 22, 22, -3, 20, -20, -8],\n [-5, 8, 3, 2, -5, -16, -7, 2, 24, 14, 15, 7],\n [-26, 4, 3, 21, -9, -10, 11, -13, -4, -2, -12, 19],\n [-5, -24, -8, 17, 7, 8, 23, -26, 25, -6, 2, -21],\n [10, -26, 24, -26, 0, -6, 26, -11, 17, 13, -1, -11],\n [1, -26, 9, -17, 16, -10, -4, -20, 17, 26, -20, 17],\n [-12, 7, 19, 18, -23, -13, -13, -11, -20, 5, -8, -25],\n [-17, 23, -10, 10, -15, -21, -5, 5, 14, -7, -26, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[26, -21, -8, -9, -21, 18, 6, -4, -4, -1, -14, -20],\n [-12, 17, 0, -1, 6, -12, 9, 18, 0, -22, -25, 6],\n [-11, -4, 11, -11, -13, 2, -1, 8, -12, -24, -4, 2],\n [7, 6, 14, 14, -4, -20, -24, 5, 4, -9, 16, -20],\n [14, -26, -13, 25, 5, -21, 12, -17, -20, -1, 7, 3],\n [9, -6, -10, 6, -17, 24, 20, 15, 24, -15, -11, 14],\n [5, -12, 0, 1, -10, 19, 23, -25, 9, 23, -20, -14],\n [-12, -2, -4, -5, -1, 6, -16, -17, -2, 10, 21, 16],\n [26, 11, 14, 18, -3, 13, 19, 6, -10, -3, 10, -25],\n [5, -3, -18, -23, -10, -10, 26, 23, 21, 3, 13, -16],\n [-6, -6, -9, 2, -3, -17, 18, -10, -9, 15, 21, -7],\n [10, 18, -9, -10, -18, -13, 22, 2, 4, -23, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "503", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[20, 16, 17, -18, -14, -12, 0, -12, 1, 10, -8, -1],\n [25, -1, -2, -1, -1, 19, 1, 22, -9, 5, 26, -24],\n [-25, 6, 15, -8, -10, 17, 6, -15, 22, -24, 16, 22],\n [-1, 8, -19, 25, 9, 26, -20, 19, 19, 9, -11, -3],\n [-26, 22, -2, -17, -11, -11, -19, 2, 12, 1, -21, -11],\n [-7, -11, -20, 14, -13, 16, -1, -1, -13, -20, 6, -1],\n [18, -7, -24, 25, -23, -1, -16, -25, -13, 17, 3, 22],\n [-15, -1, 17, 6, -14, -13, -3, 7, 17, -1, -6, 1],\n [21, 9, 13, -25, 15, -18, -4, -12, -14, -4, -10, 21],\n [-25, -7, -7, 19, -24, -15, 13, -25, 9, -13, -11, -8],\n [7, 17, 19, -21, -14, 9, -5, -9, -15, 25, 3, 26],\n [24, 13, -20, 5, 21, -8, -21, -7, 0, 26, 16, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[21, -20, -22, -16, -12, -24, -22, -4, 26, 10, -18, -12],\n [-24, 2, -21, -10, -1, -6, -19, -6, -16, 11, -19, 15],\n [-3, 8, -13, -13, -17, -15, 11, 17, 19, 7, 14, -17],\n [-10, -10, -24, 4, 24, -26, -15, 12, -23, 15, -14, 7],\n [15, -6, -5, -23, -9, -22, -8, -25, -15, -10, -17, 7],\n [-21, -19, 24, -16, -15, -18, -25, -19, -16, 26, 9, -17],\n [-6, -7, 21, -19, 9, 2, 15, -15, -13, 21, 23, -6],\n [-5, -6, 17, 23, 3, 12, -7, -3, -4, -20, -18, -26],\n [-1, 11, 11, 17, -5, 17, -17, -21, -10, 24, 23, 11],\n [-3, 24, -17, -19, -6, -21, -6, 12, -3, 6, -9, 1],\n [25, 5, -15, 21, 15, 0, -17, 19, 25, 15, 5, 15],\n [-1, -2, -16, -4, 7, 25, 13, -4, 2, 4, -20, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -6, -25, -9, 20, 6, 10, 7, -7, 8, 24, 23],\n [-9, 19, -3, -19, 3, 17, 26, -17, -4, 25, 22, -16],\n [-25, -1, 9, 6, 20, -14, 13, -2, -23, 15, -8, -9],\n [10, 3, -8, -4, -11, -26, -15, -3, 7, 26, -19, -9],\n [21, -22, -1, 3, -14, -8, 2, -24, -1, 13, -15, -25],\n [-16, 17, 1, -9, -14, 10, -5, -15, -25, 10, -20, -1],\n [-1, -3, -15, -11, -4, 13, -18, 5, -12, 10, -14, -22],\n [-16, -17, 25, -14, 14, 26, 19, 23, -12, 15, -20, 13],\n [1, 5, 8, -12, 21, 9, -6, -21, -26, -23, -16, 17],\n [-1, 10, -4, 2, -6, 21, 18, 18, 22, 0, 12, 13],\n [-14, -4, -11, 3, -23, 13, -11, 4, 26, 15, -2, 17],\n [-15, -1, 10, 21, 6, 1, -18, -15, -22, 25, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-22, 7, 19, 7, -14, 12, 15, 18, 21, -13, -16, 15],\n [11, -23, 26, 6, -20, 14, -19, 10, 24, -17, 16, -12],\n [11, -12, -22, 2, -8, 24, -17, -15, -23, 4, -9, -11],\n [13, 9, -2, -4, -15, 7, 9, 10, -24, -18, 26, -9],\n [16, 8, 7, 14, -13, -23, 2, 14, 18, 23, -12, 1],\n [15, -11, -15, 25, -22, 7, 15, -26, 12, 5, -1, -10],\n [21, 0, -3, 8, 19, 15, 12, -1, 22, 11, -4, -5],\n [-23, 22, -18, -23, -20, -4, -25, 22, -3, 13, 4, 20],\n [4, 20, 13, 21, 24, 16, 7, -3, 22, -1, -11, 20],\n [-14, -12, 0, -23, -11, 3, 17, 3, 9, -24, -5, 22],\n [-5, 23, 23, 22, -15, -6, -23, 4, 17, 4, -4, 26],\n [-7, -12, -4, 1, -11, 10, -6, -12, -10, 23, 10, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "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, 18, -9, -13, 9, 9, -7, 25, -8, 18, 17],\n [-20, 17, 26, -23, 7, -25, -22, -17, 5, 15, 14, -14],\n [12, -22, -17, -17, 11, 0, 24, -6, -19, -26, 1, 22],\n [12, -13, -6, 3, -6, 22, -18, -10, -22, 4, 25, 13],\n [11, 16, -8, 9, 23, 6, -14, -13, 6, 2, 16, 22],\n [9, 17, -17, 4, -21, -26, -20, 0, -6, 1, -11, 19],\n [-4, 25, -7, 11, -2, 1, -22, -6, -9, 20, -21, 2],\n [-8, 6, -26, 18, -24, 15, -6, 8, 14, 13, -24, -2],\n [18, 11, 18, -7, 25, 17, 18, 7, -6, 21, -4, -21],\n [24, 26, -14, 22, -4, -18, -10, -25, -8, -8, -20, 15],\n [15, -7, -18, -10, 0, 20, -25, 9, -8, -10, -22, 12],\n [-9, 26, -20, -10, 12, 9, 13, 18, -23, 11, -2, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"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, -15, -23, -3, 2, -18, -23, 24, -3, -13, -22, -9],\n [15, -8, -15, -9, -10, 3, -3, -16, 8, -4, -10, -26],\n [-12, 5, -18, -12, 1, -3, 8, -5, 0, -8, 18, -15],\n [-7, -26, -6, 22, 18, -26, -17, 20, 5, 12, -5, -9],\n [21, 19, 5, 0, 1, -9, 12, 22, 2, -9, 17, -19],\n [4, 7, -20, 9, -9, 11, -18, -18, 19, -19, 24, 8],\n [-9, -22, -13, 1, 3, -23, 12, -7, -2, 1, -15, -25],\n [16, -13, -5, 4, -4, 21, -7, 11, -23, -12, -3, -2],\n [-26, -20, 4, -15, 15, -22, 17, 23, 15, 11, -15, 12],\n [-9, -25, -17, -12, 3, 17, -10, -23, -20, 14, 4, 24],\n [12, 7, -21, 23, 11, 18, 24, 7, 17, -12, -13, -21],\n [23, 10, 23, 5, -24, -24, -5, -5, -17, 24, -24, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 21, -10, -20, -14, -25, -23, -17, 12, -3, -10, 25],\n [-21, -8, -22, 5, -17, -18, 0, -14, -8, -6, -3, 11],\n [-23, -3, 8, -24, -23, 10, 13, 21, 8, 4, 17, -2],\n [13, -14, -23, 19, -13, -14, 0, -21, -10, 9, 13, 22],\n [8, -10, 14, -25, -14, 25, -25, 25, 1, 16, -1, -5],\n [20, 16, -24, 8, -15, -3, -22, -7, 12, 12, -14, 14],\n [26, 18, -15, -14, -17, 6, 13, -11, 18, 8, -24, -22],\n [-1, -16, -20, 26, -17, 15, 25, 7, -24, -19, 4, -16],\n [18, -20, 18, -25, -21, 14, 5, -7, 7, 23, -11, -2],\n [-15, -20, 12, -10, 18, -16, -21, -4, 0, 19, -21, 11],\n [-25, -5, -7, -2, -12, 22, 2, -19, 10, 22, 25, 6],\n [-5, 23, 20, -22, 12, -9, 11, 26, 10, 3, 24, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "546", "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, -12, 15, 21, 17, -9, -4, 6, -11, 11, 8, 7],\n [1, -25, 3, -14, 14, -11, -22, 1, 26, 12, 18, -7],\n [-3, 0, 3, 18, 0, -1, -20, 15, 20, 26, 11, -22],\n [-4, 1, 7, 26, -12, 5, -1, 21, 4, -8, -18, 2],\n [24, 12, -23, -24, 2, 25, -16, 6, 11, -16, 0, 6],\n [-6, 12, 4, 11, 19, -25, 0, 9, -16, 20, -9, -26],\n [8, 8, 4, 1, 12, -26, -2, 16, 11, -7, -24, 24],\n [-25, -9, 17, -17, -22, -18, -25, 7, 11, 4, -17, 23],\n [-15, 9, -6, 22, 20, -21, 21, 22, -24, -17, -22, 19],\n [-1, -6, 18, -1, 11, 17, -1, -19, -22, -12, -11, -26],\n [-11, 10, -24, 25, 20, 4, -14, -11, 16, -6, -25, 0],\n [11, -1, 11, 19, -2, -16, -19, -19, 6, 26, -20, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "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, -19, 24, -6, -7, -19, 19, 4, 23, 2, 21, -18],\n [-12, 3, -1, -17, 2, -11, 9, -7, 18, 10, -5, -20],\n [-4, 14, 13, 2, -11, 11, 1, 21, 11, 4, -13, 26],\n [6, -18, 0, -3, -14, -1, 2, 24, 22, 16, 1, 1],\n [-19, -4, 2, -22, 15, -20, 15, 9, 14, 0, 19, -25],\n [-2, -18, 26, 0, -26, -4, -17, 15, 25, -2, -24, -21],\n [-21, 26, -25, -9, -4, -25, -15, -5, 10, -7, 12, -3],\n [21, -7, -26, -26, -10, -26, 26, 25, 18, 3, 14, 20],\n [-24, 19, -16, -3, -5, 17, 18, -1, -14, -26, -3, -17],\n [8, -3, 1, 9, -11, 13, -11, -10, 24, -12, -11, -12],\n [7, -16, -26, -12, -1, 24, -23, 16, -22, 8, -14, -17],\n [-16, -9, 7, 12, 14, 15, 23, -4, -20, 12, -24, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"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, 22, -1, 6, 10, 21, -12, -25, 14, -20, 5, -23],\n [-7, 23, 26, 9, 5, 1, -14, -26, 8, 21, 3, 9],\n [-2, -11, -8, -26, -22, 24, -5, -3, 16, 18, 25, 10],\n [26, 9, 9, -23, 9, 25, 26, -9, 23, -11, 14, -9],\n [-5, -25, -6, 9, 17, 12, 20, 12, 2, -1, -6, -10],\n [-11, 4, 24, -18, 4, -13, 22, 10, -25, 25, 21, 19],\n [-13, 6, 8, 12, 20, 24, -7, -25, 24, 14, -8, 10],\n [-9, -11, -23, -15, 2, -20, -13, -15, 8, -22, -10, 15],\n [5, -17, 16, -10, -22, 18, 15, -18, 22, 6, 9, 9],\n [-9, -18, 2, 23, -13, -2, -12, -21, 15, 2, -12, 2],\n [-23, -9, 23, 22, 17, 12, -11, -16, -13, -24, 24, 23],\n [15, 11, 18, 15, -9, -7, 21, -2, 11, -14, -23, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, 1, 25, 10, -19, 17, 7, 17, -22, -22, 4, 18],\n [-18, 15, 5, 6, -24, 3, 23, -15, 2, -24, -1, 3],\n [-18, -1, -25, -24, 19, -23, -2, 24, -14, 12, 17, 8],\n [-4, -18, -25, 14, 17, 4, 17, 20, -25, 5, -9, -14],\n [19, -22, 15, 17, -17, 16, -2, 7, 10, 3, -20, -21],\n [-24, -14, -24, -1, -3, 26, -21, 16, 22, 15, -15, 22],\n [9, -25, -16, 12, 7, -1, -9, -6, 9, 13, 25, 19],\n [17, -5, 26, 3, 23, 16, 3, -19, 7, 20, -18, 24],\n [-7, 13, -2, -8, -22, -16, -12, -19, -8, -4, 0, 13],\n [5, -1, 0, -8, 23, 15, 2, 12, 14, 6, -8, 10],\n [-8, 6, 20, -11, -4, -20, -1, 5, -15, -19, -22, 15],\n [1, 26, -22, 22, -1, -22, -5, -12, -14, 1, 6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-4, 6, 16, -9, 23, 26, 3, -1, -11, -14, 12, 6],\n [-1, 21, -26, 22, 11, -25, 22, -21, 19, 23, 11, 15],\n [-3, -9, 0, 14, -19, 1, -17, -10, 2, -21, -13, -5],\n [-21, -1, 12, -15, 8, -13, -5, 24, -4, 21, -20, 13],\n [23, -2, -14, -6, 14, -17, 26, -18, -12, 25, -25, -2],\n [-14, 7, 24, 7, 8, 11, -24, 15, -21, 21, 22, -8],\n [-24, -9, 12, -18, 25, -15, -22, -24, -16, 3, -23, -22],\n [-26, 0, 1, 2, -9, -15, -14, 14, -25, 10, 18, -11],\n [21, -3, 8, -5, 9, -16, 19, 2, 8, 21, -12, 4],\n [15, 14, 16, -11, -17, 22, 5, 24, -25, -3, -4, -25],\n [11, 4, 24, 13, -1, 2, -24, -13, -2, 21, -26, 26],\n [-24, -1, -9, -18, 11, -4, -6, -26, -6, 0, 15, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "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, 9, 1, 18, -10, 13, 25, -24, -15, 12, -15, -25],\n [19, -5, -4, 3, -22, -18, -6, -16, -22, 8, 0, 22],\n [-25, -3, 4, 6, 12, 3, 19, 10, 24, 1, 4, -16],\n [-4, -25, 13, 14, 0, 8, -25, 12, 10, -6, -22, 25],\n [18, -6, 2, -7, 11, -7, 23, -2, -25, 5, -1, -21],\n [14, -24, 6, -26, 24, -22, -14, -8, -15, 21, -2, 24],\n [8, -15, 3, -22, 7, -5, 12, -14, 20, -24, 26, -7],\n [4, -22, -3, 13, 6, -19, -3, 23, -7, -11, 23, 25],\n [-15, -14, 18, 15, 12, -2, 19, 5, -3, 21, 20, 17],\n [-18, 13, 23, -4, 23, -14, 5, 23, -12, 9, 22, -22],\n [-5, -11, 14, -17, -3, -9, 22, -9, -20, -23, -1, -22],\n [-11, 8, -1, -9, 2, -4, 26, -13, -12, 22, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -10, -4, 16, -10, -13, 2, -7, 3, -8, 26, 12],\n [-14, -9, -4, 19, 6, 12, 13, -9, -18, 6, 5, -10],\n [-8, 0, -21, 8, 10, 7, -7, -2, -23, -17, -17, -3],\n [-6, -16, 0, -11, -1, 3, 22, -11, -20, -11, 8, -11],\n [13, -15, 8, 22, -6, 23, 16, 9, 21, -10, 5, 14],\n [-21, -3, 0, -7, -2, -25, -18, 1, 26, 11, -24, -7],\n [-21, 12, 6, -26, 10, -21, 18, 7, 20, -12, 18, -1],\n [-13, -20, 19, 4, -3, 4, 2, 15, 5, -10, -13, 13],\n [9, 21, -3, 18, 0, -2, 5, 25, -9, 19, -9, 10],\n [-1, -18, 8, -19, -7, 15, -5, -8, 3, 26, 1, 8],\n [16, -16, 4, 22, 21, 12, 9, 3, -4, -8, -15, -12],\n [4, 16, 10, 10, -12, 2, 23, 16, -1, 17, -25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-12, 25, -23, -5, 23, 11, -4, -1, 24, -16, 1, -25],\n [-19, 2, -16, 10, -9, 23, -13, -17, 8, -18, 8, -16],\n [17, -15, -24, 26, 12, -13, 1, -16, 12, -2, -6, -17],\n [16, -12, -8, 21, -5, -6, 25, 17, 5, 23, -4, -14],\n [-22, -23, 1, -13, -19, -18, 24, 8, 10, -6, -9, 6],\n [-19, 24, 22, -10, 16, 4, 7, -21, -5, -13, -24, -15],\n [9, -15, 18, -25, -25, -12, -4, 2, -10, 5, -20, 3],\n [1, -13, 17, 3, -10, 5, 19, -21, 24, -3, -21, 0],\n [-9, -3, 10, -3, 11, 7, 13, 20, -12, -16, -5, -3],\n [-26, -9, 17, -15, 16, 1, 13, -20, -4, -6, 7, -16],\n [-5, 15, 8, 25, 2, 15, 1, -9, -13, -9, 1, -3],\n [-19, 15, 18, 26, -19, -23, 0, 9, -22, 6, 22, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "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, 12, 20, -1, 10, 7, -20, 13, 1, 12, 12],\n [1, -13, 26, 23, 11, -23, 15, -9, 17, 21, -2, -20],\n [11, 1, -22, -24, 17, 4, 20, 15, -7, -8, 21, -16],\n [13, -24, -4, -20, -4, -20, 19, 7, 15, -8, -18, 21],\n [24, -9, 14, 21, 18, 15, -2, 25, -13, 17, -2, -8],\n [12, -12, -11, 0, 13, -17, -23, 24, -8, 1, -6, 20],\n [-13, 6, 21, -17, -8, 3, -5, -24, 10, 14, -9, -16],\n [21, -25, -15, -21, 16, 13, 17, 2, 3, -25, -18, 20],\n [-25, 2, 6, -17, 7, 17, -19, 10, 6, 20, -21, 17],\n [13, 18, -8, 5, 0, -26, 16, 25, 6, 13, 5, -22],\n [-10, -19, 15, 7, -18, -4, 8, 23, -20, -12, 26, -7],\n [23, -2, -24, 19, -3, 7, 19, -5, -16, 21, -19, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "559", "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, 8, 22, 19, 11, -19, 10, 0, 1, 13, 7, 5],\n [-12, 17, -10, 6, 20, 19, 25, -11, 2, -18, 6, 22],\n [2, -14, -6, -6, -22, -17, -21, 24, -14, -26, -7, 20],\n [19, -19, -17, -18, 22, 14, -24, -16, -15, -17, -2, 22],\n [22, -2, -16, 9, 12, 26, -1, -13, 12, 13, -26, -23],\n [3, -15, 8, -14, 25, 4, 11, 16, -4, -23, 25, -11],\n [-20, -5, 2, -16, 6, 2, 12, -15, -20, 12, 15, 21],\n [-1, 13, -18, 14, 7, 18, -14, 9, -2, -3, 17, -10],\n [-25, -14, 4, 2, 23, 1, 0, -12, 4, 13, -12, 6],\n [-7, 15, -15, 10, -18, -4, -19, 5, 21, -13, 0, -2],\n [-14, -6, 18, 4, 10, 21, 16, -22, -14, 1, 16, -2],\n [24, 8, 20, 12, -20, 11, 5, -24, 18, 12, 10, 23]]\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[[-5, -19, -10, 25, 0, 6, 19, -10, 15, -15, 21, 19],\n [0, 21, -19, -4, 15, 22, 2, 23, -7, -11, -10, -11],\n [-8, -19, 11, 11, 26, 2, 14, 9, -1, 4, 17, -15],\n [-10, -12, -18, 12, 15, 21, -15, 5, -2, 12, -9, -12],\n [5, -21, 17, 16, 25, 8, 7, 11, -22, -9, -11, -19],\n [-2, 5, -1, 25, -5, 4, 16, -17, -15, 26, 1, -21],\n [-7, -22, -4, -18, 2, -11, 19, -5, -19, -7, 24, -13],\n [12, 10, 23, 7, -16, 13, 6, 4, 17, 7, 23, -20],\n [22, -4, 19, -20, -2, -24, 11, -7, 7, 22, 17, 17],\n [3, -10, -17, 8, -7, -9, 18, 17, 0, 22, 9, -4],\n [5, -17, -16, 11, -21, 14, 20, 7, 9, 10, -10, 13],\n [13, -15, -6, 13, -8, -24, -9, 26, 24, -8, 20, -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 difference between the largest and smallest singular values:\n[[-11, -19, 21, -9, 25, 21, 16, 12, 22, 22, -15, 18],\n [-17, -20, 19, -26, 22, 9, -6, 10, 25, -3, -2, -20],\n [15, -10, 2, 3, -20, 6, -20, -3, -16, -18, -15, 8],\n [-23, 9, 1, -14, -4, -8, 15, 10, 12, -3, -11, 6],\n [-15, 7, -20, -16, 4, 2, -14, 4, -25, 12, -12, -16],\n [7, 12, -23, -16, 2, -25, -11, 12, -14, 10, -10, -6],\n [17, -8, -20, 11, -19, -14, 10, -25, 14, -16, -3, -21],\n [-1, -20, 12, -8, -21, 16, 2, 16, 12, -25, -8, -23],\n [-21, 22, 10, 1, 3, -20, -18, -2, 6, -26, 24, -21],\n [-9, -17, 1, -16, 6, -26, -14, 10, -7, -26, 25, -24],\n [-9, 14, -13, 4, 0, -10, 19, 2, 9, 10, -1, 26],\n [-10, -5, -2, -25, -5, -22, -23, 9, -21, 25, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "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, -2, -1, 12, -7, 6, -13, 9, -10, -6, 19, -11],\n [19, -11, -7, 2, 1, -19, -3, -24, -2, -8, 6, -25],\n [-12, -5, -17, -9, -5, 19, 22, 0, -14, 6, -22, -1],\n [-14, 0, -13, -3, -24, 20, 24, 22, 3, 8, 21, -13],\n [-15, 1, 17, 2, 16, -10, 13, 22, -6, -4, -7, -16],\n [7, -17, -17, 16, -21, 9, -3, -15, 16, -4, 0, 18],\n [10, -21, -26, -21, 23, -5, 14, -3, -2, -12, -1, -19],\n [24, -3, 21, 11, -21, 8, 15, -26, 19, 9, -15, 11],\n [-16, -15, 15, 23, 12, -20, -16, 9, 25, 4, 6, -14],\n [-9, 14, -3, -18, 4, 14, -17, -25, 11, -12, -24, 16],\n [4, -21, -24, -16, -12, 18, 25, 1, -17, 11, 20, 23],\n [23, -20, -12, -9, -9, 25, 14, -3, -25, 13, -7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[16, -1, -20, 11, 3, 15, -22, -16, -26, 7, -26, -8],\n [-25, -6, -7, -4, -6, -3, -23, -15, -5, -7, -9, -26],\n [3, 6, -3, -13, 9, -22, -16, -3, 4, -14, -11, -3],\n [-14, -3, -1, -25, -11, 11, 19, -26, 22, -16, 24, 8],\n [16, 2, 10, -10, 12, 15, 1, 2, 16, -24, 25, -17],\n [15, -13, -15, 20, 15, 3, 5, 5, 15, 5, -1, 24],\n [-26, 15, -25, -10, 3, 12, -20, 25, 0, -18, -5, 7],\n [19, 22, -26, -18, -7, 26, -8, 9, 13, 18, -23, -18],\n [14, -5, -9, -15, 15, 16, 12, -18, -21, -8, 21, 20],\n [-20, -11, -22, -11, -26, 24, 10, 12, -8, 10, -10, -1],\n [-5, -19, 6, -25, 3, 20, -7, -9, 16, -17, -3, -23],\n [10, -23, -14, -2, -14, -9, -3, -25, 21, 6, -8, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[1, 8, 12, -17, -26, 15, -6, -18, 20, -12, 8, -22],\n [14, -5, 14, -4, -20, -4, 17, -2, 0, 14, -21, 7],\n [-18, 22, 6, 24, -21, 10, 4, 7, 14, 2, -13, 9],\n [9, 26, -12, -19, -1, 9, 21, -6, 1, -23, -11, -5],\n [-15, -11, 24, 13, 11, 15, 10, 2, -9, -17, 15, 12],\n [-9, -26, 12, -6, -26, -12, -23, -7, -17, -4, 14, 7],\n [19, 21, 6, 7, 12, -17, -7, -26, -14, -26, -22, -11],\n [-12, 22, 1, 4, -4, 21, 18, 16, -10, 22, 7, -14],\n [-13, -16, 1, 15, 5, 8, 4, -10, 20, -18, -17, -19],\n [-6, -14, 23, -22, -21, 3, 4, -10, -16, -7, 21, -18],\n [-25, 10, -26, -23, 9, -2, -24, -18, -5, -4, -15, -17],\n [7, 16, -17, 3, -5, -21, 23, -25, 3, -25, 5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-11, -15, -26, 26, -19, 21, 23, -14, -12, 26, 17, -19],\n [-17, 19, -22, 23, -8, 20, 11, -16, 26, 16, -7, -7],\n [-6, -9, 23, -17, 7, -1, 3, -18, 19, 24, 4, 15],\n [-23, -21, -13, -23, -1, 20, 21, 12, -10, -8, 24, 22],\n [-21, 2, -16, -11, 3, -2, 13, -16, -20, -1, -5, -2],\n [-8, 4, -1, 15, 14, 9, -4, 20, -14, -2, -25, -25],\n [-11, -18, 1, -14, 8, 14, -14, 4, -6, 5, 7, -19],\n [14, 21, -25, 11, 5, 13, 1, 10, 14, -26, 14, -17],\n [-23, 8, -17, 20, -16, -13, 11, -15, 18, -10, -11, 8],\n [-25, -16, 14, -24, 2, -9, -7, 20, -13, 7, 22, 4],\n [13, 15, -9, 3, -2, -8, -19, 1, -19, 4, -24, -24],\n [17, -5, -10, 9, -10, -13, 24, -18, 3, -6, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "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, -16, -7, 8, 26, 20, 19, -16, 25, -19, -23, 0],\n [17, 13, 11, 20, 3, 17, 21, 21, 0, -6, 25, -7],\n [-23, -16, -14, -18, -23, -15, -18, -14, 21, -1, 11, 15],\n [-14, 12, 1, -8, -3, -8, 22, -14, -14, 1, 26, -25],\n [-17, -5, -14, -18, 6, -13, 21, -7, -12, 5, 6, -10],\n [-3, 3, -14, 20, 21, -11, -25, -10, 5, 16, -19, 25],\n [-24, -15, -7, -11, -13, -11, 26, 22, 16, 22, 24, 6],\n [3, -15, -12, -9, 1, -4, -13, 3, 6, 18, -12, -20],\n [-12, 25, 15, 19, 11, 19, 17, -16, 2, 4, -2, 25],\n [-3, -8, -25, -5, -7, 6, -19, -2, 19, -18, 7, -4],\n [-22, -2, -19, -11, 21, 18, 25, -12, -26, -5, -24, 11],\n [-13, 9, -9, 20, 14, -9, -24, -17, 22, 12, 20, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 0, -16, 22, -22, -20, -8, 2, -12, 8, 20, 10],\n [-15, 3, -7, 10, -24, -18, 14, 12, -1, -25, -4, -4],\n [-6, -11, -18, -14, 1, 0, 24, 25, -10, 11, 9, -26],\n [-9, 24, -18, -14, 13, 18, -12, 16, 17, 19, -23, 6],\n [-3, 9, 24, 14, -17, 9, -7, 14, 18, 17, -16, -15],\n [-9, 3, 17, 21, 10, -7, -2, -15, -6, -2, -16, -18],\n [23, -2, 8, 25, 5, 22, -13, -26, -10, -2, -19, -22],\n [-22, 14, 8, -8, -4, -18, 3, 23, -11, 6, -25, -13],\n [19, -26, -1, -2, -11, -12, -1, 20, 17, -11, -13, 2],\n [-3, 20, -12, -8, -19, 7, -25, 0, -17, 8, -4, 22],\n [-19, 1, -4, -23, -13, 26, 15, 2, -26, -23, 5, 6],\n [22, -1, -10, 12, -4, 5, 25, -12, -14, -25, -8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, -3, -16, -5, -12, -17, 14, 0, -18, 25, 1, -26],\n [-10, 4, 17, -17, 10, 2, -9, 20, 11, 12, 22, -21],\n [13, -15, 26, -13, 17, -17, -7, -12, 4, -20, 14, -17],\n [-17, 21, 12, 1, 3, 10, -24, 23, 16, -12, -6, 25],\n [10, -15, -23, 20, -18, 12, 15, 1, -4, 18, 13, 17],\n [-5, -3, 24, -1, 3, 6, -11, -5, 22, 23, 16, -9],\n [-20, 23, -1, -19, -21, 3, 12, -4, 5, -5, 15, 16],\n [18, -18, 4, -20, -18, -14, -24, 8, 6, -6, 4, 25],\n [7, 5, 8, -12, 5, -21, 18, -6, 6, 5, 25, -8],\n [6, 1, 4, -6, 7, -12, -13, -8, 16, -12, -21, 25],\n [-18, 10, -7, 7, 11, -1, -9, 1, 24, -18, 5, 26],\n [-21, -13, 1, -3, -14, 16, -15, 24, -8, -6, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-3, -1, 18, 1, 19, -9, 17, 9, 15, 2, -10, -23],\n [17, 18, 2, -23, -17, -2, 4, -24, 20, -25, -2, 22],\n [-21, -1, -19, 8, 0, -2, -9, -26, 21, 12, -24, -23],\n [14, 10, 24, -12, -19, 11, 23, -8, 20, -1, 12, -17],\n [11, -13, 22, 14, -8, 3, -22, 4, -20, -8, 4, 25],\n [12, -3, 7, -4, 21, 18, 13, -21, 11, 14, 9, 0],\n [-16, -22, -10, 25, -20, 0, 20, -12, 19, -14, -16, 18],\n [-1, -5, 1, -3, 2, -18, 15, -23, 22, 19, -9, 16],\n [-11, 6, 2, 12, -17, -18, 4, 1, -24, -13, -2, -12],\n [-25, -3, -13, 21, -20, 9, 23, -3, 0, 10, 11, 3],\n [0, 12, -12, -1, -26, -23, 2, -26, 16, 23, 19, -5],\n [-16, -17, -10, 9, 20, -1, 21, -6, -14, -18, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-21, -26, -21, -14, -5, 4, -5, 10, 20, 0, 23, 25],\n [-13, 20, -22, 9, 5, 7, -20, 15, 21, -17, 23, -10],\n [3, -6, -14, -26, -26, 20, 6, 11, -2, -1, -14, 1],\n [6, 10, 14, 3, 22, 21, -19, 22, 20, -26, -15, -22],\n [-3, -21, -2, -26, -2, -26, 5, 15, 15, -24, 22, -8],\n [16, 2, 23, -25, -18, -10, 19, 9, -10, 22, -15, -7],\n [23, -24, 16, 23, -23, -10, 23, 10, 19, 15, -12, 6],\n [-11, -16, -7, 11, -3, -11, 3, 7, -26, -3, -3, -18],\n [-5, -15, -10, -2, 1, -12, 3, 24, 0, -5, -17, 4],\n [0, -15, 19, 4, 5, 5, 14, 18, 8, 26, 19, -6],\n [-17, -11, -20, -23, 0, 25, -2, 4, -16, 21, -7, 9],\n [-10, 18, -16, 3, 8, 14, 11, -5, 26, 16, 21, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"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, 10, 19, 22, 8, -23, -11, -11, -6, -1, 9, -8],\n [-10, 18, -1, -5, 1, -26, 17, 9, 16, 10, -25, -10],\n [13, 11, -6, -18, -14, -16, -11, -11, -25, 15, 17, -19],\n [16, 15, -14, -10, 12, -3, -24, 3, 25, -14, -8, -20],\n [-18, -8, 18, 13, -5, -9, -4, -25, 23, 23, -16, 4],\n [6, -13, -11, -16, 6, -20, 4, 21, 19, 20, -13, 1],\n [26, 16, -11, -8, -10, -1, -21, 16, 22, -18, 23, -10],\n [4, -15, -4, -22, 16, 9, 9, -24, -3, -10, 12, -1],\n [-23, 18, -15, -26, -6, -8, -6, 25, -9, 16, 25, -24],\n [22, 17, 5, -17, 13, -12, -22, -23, 1, 26, 25, 24],\n [26, -23, -12, -10, 17, -24, -17, 20, 15, -4, -9, -26],\n [8, 26, 4, 17, -26, -24, -24, 10, -8, 2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[9, 2, -1, -23, 22, -13, 23, 0, 6, -5, 21, -24],\n [-4, -6, 14, -4, -23, -6, 10, 16, 4, -6, -1, 14],\n [8, 11, -3, -16, 14, 2, 20, -24, -26, 25, -8, 19],\n [22, -5, -13, 22, -13, 17, -11, 6, -14, 11, 22, -15],\n [24, 11, 12, 6, 6, 2, -22, -21, 4, -11, 4, -2],\n [21, 19, 6, -14, 25, -17, -3, -17, 14, 4, -14, -24],\n [23, 25, 7, 22, 1, -8, -4, 18, 5, -14, 6, 7],\n [6, -22, -24, -20, -3, -5, 18, -4, 3, -9, 5, 26],\n [-20, 6, -22, 22, 1, -19, -12, 25, -23, 7, -22, 6],\n [-22, 11, 7, -1, -26, -23, 12, -1, 6, 6, -19, -7],\n [-11, -6, 18, -1, -4, -9, 4, 25, 15, -15, -26, 15],\n [-18, -24, 24, -1, -18, 15, 24, -11, -3, 23, -13, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[7, 6, 23, -3, -18, -14, -25, -20, 21, -6, -8, -2],\n [20, -5, -16, 6, 5, -6, 12, -7, -19, 15, 10, -18],\n [-2, -2, 6, -25, -8, 19, -7, 15, 14, 15, 2, -21],\n [-10, -2, 11, -23, 3, -7, -24, -4, 24, -9, -1, 9],\n [-19, -10, 4, 10, 18, 6, 0, 18, -23, -5, -1, 5],\n [-3, 19, 8, 10, 5, -20, 6, 4, -15, -16, -3, -19],\n [5, 11, -5, 7, -8, 25, -7, -13, 6, -17, -11, -23],\n [0, 1, 16, -11, 25, 6, 21, -8, -6, -5, -18, -18],\n [-18, 0, -10, 17, 18, -19, -11, -9, 6, -26, -15, -21],\n [14, -22, -11, -9, 22, -9, -26, -8, -19, -24, -2, -22],\n [13, -8, -9, 23, 26, 4, 6, 20, -9, 12, -11, -11],\n [20, 11, 14, -20, -13, 16, 26, 21, -2, 5, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-11, 25, 2, -11, -15, -10, 10, 0, -2, -14, -19, -22],\n [-15, 14, -24, 8, 6, -5, 23, 17, -18, 14, -9, 23],\n [2, 12, 0, 9, 18, -10, 7, 19, -24, -22, -13, -24],\n [-4, 12, 3, 23, 18, -4, 0, -17, -2, -14, -11, 14],\n [7, 10, -5, -10, -4, 9, 22, -18, 25, -25, 5, 23],\n [26, -5, 16, -14, -19, -26, -10, -15, -23, 26, -14, 4],\n [14, -20, -4, -3, -22, -22, -10, 3, -18, -21, -2, -8],\n [-11, -6, -25, -17, -11, 10, -12, -14, -14, 5, 18, 20],\n [19, -19, 16, -9, 9, -1, -17, 4, 6, 2, -22, -14],\n [-26, -4, 13, -24, -24, -20, 9, 8, -12, 13, -24, 2],\n [3, 12, -9, -16, 16, 22, 11, 13, -26, 2, -17, 1],\n [4, -8, -24, 9, 16, -12, 6, 14, 16, 24, 18, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-11, 9, 6, -7, -14, 6, -22, 10, -13, 0, -4, -13],\n [13, -23, 12, 25, -8, 20, -23, 3, -8, 4, 4, -18],\n [26, -14, -13, 19, -17, 21, 4, 10, -4, 0, -21, -1],\n [-25, 18, -14, 24, 23, -8, -26, 13, 5, -5, 21, 2],\n [-25, 13, 11, 21, -16, -10, 24, 16, -19, -5, -23, -16],\n [-19, -18, -1, -25, -11, 4, -21, 26, -6, -1, -8, 1],\n [-19, -13, -3, 21, 17, 10, -1, 4, 24, 5, 23, 14],\n [-25, -2, 25, 17, -25, 15, -26, 9, -15, -18, 9, 14],\n [1, 11, 6, 15, 19, -5, -2, -9, -21, -9, 25, -11],\n [-12, 21, -19, -14, 16, -20, -10, 23, 5, -5, 24, -14],\n [20, -4, 2, -5, -26, 2, 21, -22, 8, -17, -8, 10],\n [-20, 19, 8, 18, -14, -17, -25, -21, -19, 9, -2, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[20, 13, -20, 19, -4, -8, 19, -5, -14, -6, -26, -8],\n [6, -23, 15, -24, 0, 25, 14, 8, 1, -21, -21, 17],\n [-4, 6, -11, -3, -22, 14, 15, -14, 20, -15, -22, 10],\n [4, 1, 1, 3, -9, 17, 0, 8, -1, 12, 22, 24],\n [-9, 6, -2, 4, 10, -25, 6, 12, 16, 16, 5, -9],\n [-10, 7, 12, -20, 15, 26, 8, 3, -15, 8, -16, 17],\n [-23, -2, 21, 5, -7, 23, 4, -23, 11, 26, 20, -26],\n [-24, 10, -5, -10, -13, 14, 8, -14, 8, 16, -25, 20],\n [-14, 24, -11, -9, -20, 18, 9, 14, 3, 15, 14, -20],\n [-12, 13, -8, 16, 10, -25, 15, 21, -14, 13, 14, 16],\n [16, 4, -11, 15, 17, -21, 1, 5, 17, -17, 23, -9],\n [-23, -18, -20, 23, -19, 16, -20, 14, 13, -24, -10, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-12, 19, 2, 23, 21, 25, -5, -23, 25, -21, 11, -1],\n [-16, -1, -10, -3, 1, 8, 4, -14, 8, -11, -12, 16],\n [-9, 20, 10, 21, 21, 22, 14, 0, 8, 25, 18, 8],\n [1, 12, 11, -18, -15, -12, -6, 25, 8, 15, 6, 24],\n [-8, -4, -14, 17, -26, 24, 2, -3, -11, -2, -4, 1],\n [20, -11, 16, 11, -16, -24, -12, -26, -20, -26, 22, 5],\n [-18, 2, -1, -4, 18, 16, 2, 25, 11, 6, -20, -15],\n [4, 5, -7, 24, -10, 9, -24, -26, 23, 0, 26, 20],\n [13, 6, -7, -13, 9, -22, -4, 18, -12, -21, 6, -8],\n [-14, 2, -21, -12, -11, -3, -4, 21, -17, 14, 14, 22],\n [-10, 22, 17, 18, 3, 17, 19, -17, -8, 2, -25, 9],\n [-8, -20, -1, -12, 20, 11, -24, 11, -11, -25, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "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, 3, 16, -20, 9, 2, -3, 25, 12, -23, 2, 17],\n [-22, 2, 3, 2, -1, -8, -1, 10, 0, 3, 24, 26],\n [3, -24, 16, -20, 22, -18, 26, 14, 15, -14, -12, -22],\n [2, 8, 0, 0, -19, 5, -7, -17, -14, 2, 8, -19],\n [2, 4, 14, 3, -5, -6, -15, -16, -25, 23, 14, -25],\n [7, -24, -11, 24, -23, -4, 23, -7, -2, 3, -9, 15],\n [-16, 2, -10, -1, -4, 25, 21, -7, 18, -25, -3, 4],\n [0, -25, -13, -23, 22, -14, 9, 8, 17, -19, -25, -21],\n [4, -17, 17, -6, 15, -17, -4, -24, 5, -7, -17, 2],\n [14, 25, 24, 19, 7, 10, -7, -19, -20, -21, -16, 17],\n [-9, 24, 15, 2, -2, -6, 19, -24, -9, -3, 20, 11],\n [-17, 0, -15, -20, -10, -26, 23, -1, -12, 24, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[20, 4, 8, -26, -19, -15, -8, -2, 5, -15, -14, 1],\n [-26, 24, -21, -19, -23, -22, -2, -5, 1, 12, -4, -23],\n [25, -23, 20, -6, 10, 14, -25, -20, 22, -11, -10, -7],\n [-4, 7, -16, 7, 6, -1, -25, -4, 14, -5, 7, -12],\n [-17, -12, 15, 2, -4, -10, -18, 23, 9, -18, -11, 9],\n [21, 24, 6, 4, -21, -17, -11, -23, -5, -14, -11, 25],\n [2, -21, -1, -16, -3, 2, -24, 25, -17, -26, 25, 16],\n [-1, -15, -13, -2, -19, 16, -23, 1, -20, -17, 24, 9],\n [-25, -1, 26, 23, -13, -11, 16, 15, -10, 19, -5, -23],\n [-8, -25, 12, -18, -8, -11, -2, 21, -9, -4, 26, -6],\n [-16, 12, 14, -23, -2, 5, 3, 18, -1, 9, 24, 7],\n [-18, -15, -25, 11, -22, -22, 25, -5, -22, -23, -18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-5, 0, -17, -11, 15, 15, 24, -17, -21, 22, -22, -21],\n [20, -2, 24, 23, -23, 13, 21, 5, 24, 25, 8, -17],\n [7, 9, -21, 16, 19, -11, 26, -8, 7, -2, 4, 22],\n [14, -10, 20, 3, 12, 4, -8, 8, 2, -26, -23, 1],\n [-9, -1, 13, -8, -21, -26, -19, 6, 24, 16, -6, -3],\n [-2, 20, 16, -8, 2, 26, -17, -15, 6, -20, -10, -17],\n [4, -21, -10, 23, 10, -9, -1, 22, -11, -19, -3, -14],\n [2, 5, -3, -11, -16, 5, -21, 8, 6, -9, 10, -14],\n [-17, 10, -1, 19, -10, -26, -2, 7, 12, -17, -7, -20],\n [-11, 10, 2, -15, -10, 21, -7, -1, 21, -8, 20, -15],\n [-6, 15, 7, -20, 18, 8, -12, -26, -1, 8, -2, 15],\n [-12, -5, -21, 25, -12, -3, -6, -20, 2, 5, 5, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-22, -23, -5, -9, 8, -10, 23, 23, -3, -25, -14, -12],\n [-22, -24, 10, 10, 10, -24, 8, 25, -4, 1, 3, -9],\n [25, 9, 6, -1, 21, 13, -10, 13, -20, -19, 26, 4],\n [-15, 21, 4, 17, -8, -17, 12, -15, -7, 10, 21, 14],\n [-20, 25, -13, -16, -20, 2, -17, 2, -18, 9, 21, -17],\n [-8, 4, -10, -18, 18, 6, 7, 18, -3, -18, -20, -11],\n [-8, 12, -21, 23, 24, -16, -15, 15, -14, -15, -6, -17],\n [-7, 23, 9, 1, -3, -22, 10, -15, 8, 13, -25, 23],\n [14, 18, 12, 15, -18, -5, 20, -22, -15, -26, 17, -5],\n [11, 24, -8, -11, 4, 24, -24, -4, 15, -9, -1, -14],\n [-9, -24, -4, -24, -2, 0, 17, 0, 25, 12, -2, -3],\n [-19, -18, 19, 10, 3, 26, -8, 26, -11, -3, 17, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, 13, 12, 20, -21, -22, -13, 26, 18, 15, 23, -23],\n [-19, -3, -16, -10, 23, -6, -1, 16, 21, 17, 18, 0],\n [-11, -1, 26, 6, 4, 21, 20, -21, 17, -19, -20, 7],\n [17, 26, -13, -11, 16, 25, -18, -17, -10, -15, -21, -8],\n [16, 14, 26, 2, -21, -2, -3, -2, -11, 25, -11, -21],\n [10, -6, -23, 7, 1, 11, 14, 1, -10, -13, -20, -5],\n [24, -26, 2, 25, 4, 3, -12, -9, 8, 23, 3, 7],\n [15, -16, 0, -3, 8, 12, -19, 24, -9, -14, 18, -3],\n [24, -4, -15, 22, 3, 4, 1, -5, 17, 1, -14, -2],\n [17, 24, 19, -20, 18, -21, -3, -8, -8, 9, 24, -18],\n [21, 9, 11, 13, 2, -3, 21, -22, 26, 15, 18, -1],\n [-13, 12, 2, 25, -21, -20, 10, 26, -9, -4, 17, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-26, -23, 24, 17, 20, 8, -4, 0, -1, 25, -19, 16],\n [-11, 14, -24, 5, -22, -7, -13, 5, -1, 20, -21, 9],\n [13, 24, -22, -14, 5, -11, -26, -14, -16, 26, -19, -2],\n [13, 5, -3, 1, -13, 18, -24, 9, 0, -7, 20, -12],\n [0, 26, 18, 14, 1, -2, 15, 17, 19, 6, 19, -13],\n [-19, 21, -13, -26, -11, -9, -20, -12, -3, 22, 24, -14],\n [-18, -12, 8, -3, 6, -11, -19, 2, -4, 18, 4, 13],\n [22, -13, 26, 3, 26, 12, 0, 20, -11, 24, -21, 6],\n [17, -9, -11, -15, -7, 18, 13, 2, 3, -1, -5, 6],\n [26, 12, 20, 2, -5, 18, -14, -18, -3, -12, 9, -14],\n [0, 17, 10, -20, -19, 10, 14, -13, -15, 9, 25, 13],\n [-10, 13, 26, 2, 0, -26, 25, 7, -23, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-20, -26, 14, -24, 17, 24, -12, 4, -11, -17, 2, -21],\n [2, -10, 26, -5, -3, -10, -6, 24, 23, -16, -20, 15],\n [12, -22, 17, 21, -6, -9, 8, -7, -12, -22, -14, 24],\n [-15, -6, 10, -21, -20, -1, 15, 21, -19, -18, 0, -23],\n [-6, 4, -6, 13, -2, 12, -12, 26, 8, 22, 16, 14],\n [10, 15, 20, 1, -13, -23, 26, -7, 7, -15, 6, -3],\n [-7, -22, 11, 3, -3, 16, 13, -20, 9, 11, -11, 25],\n [-12, 19, -4, -15, 2, 17, 21, -12, 2, 18, 16, 22],\n [-6, -12, -13, 15, 17, -11, -12, 15, -23, 0, -4, 2],\n [14, 26, 25, -18, 26, 25, 16, 16, -20, 26, 15, -23],\n [-22, -22, -16, 14, 1, -11, 14, 3, -23, -25, 19, -24],\n [23, -6, -21, 16, 26, -9, 17, -22, -18, -7, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-9, -8, -24, -18, 9, 4, 22, -10, -4, 7, 14, 14],\n [-22, -12, 20, -24, -8, 1, -24, 11, -23, -3, 4, 18],\n [18, -16, 10, -26, -18, -10, -26, -24, 20, -1, 26, 4],\n [-1, -4, 3, -17, -19, 17, -2, -5, -12, 14, -17, -7],\n [14, 20, -4, 26, 26, -26, -25, -8, -13, -19, 11, -15],\n [-1, 0, 2, -12, 19, 26, -26, 16, 1, -24, 24, -9],\n [25, 7, 5, 2, -2, -1, 12, -19, -8, 20, 15, -5],\n [2, 6, 11, 18, 19, 8, 16, -24, -8, -17, 0, -12],\n [-16, 20, -1, -3, -14, 5, 10, -23, -14, -18, 22, 7],\n [10, 21, -20, -26, -15, -6, -16, 17, 24, 17, 17, -13],\n [7, 7, -2, -23, 25, -1, -11, -17, 18, -25, 8, -8],\n [-21, -8, 26, 25, 24, -19, -13, -17, -24, 11, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, -4, -9, 19, -8, 1, -1, -17, 20, -23, -25, -24],\n [-20, -11, 4, -17, -8, 1, -10, 1, -8, 10, -4, -7],\n [-14, -14, 16, -16, 21, -12, -10, 23, 1, -8, -23, -5],\n [-5, 10, 12, 7, 6, 17, 15, 13, 6, -15, -25, 1],\n [-17, -5, -10, -1, -24, -20, 17, -19, -7, -15, 8, -10],\n [1, 14, -17, -5, 11, 6, -5, 17, 10, -14, 0, -12],\n [-5, 3, 16, 13, 10, 7, 17, 7, 21, 26, 8, 15],\n [-8, -19, 12, 6, 17, 1, 10, 21, -2, 9, -10, -3],\n [-6, -25, 4, 17, 6, 3, -15, 17, -15, 24, 22, 25],\n [-3, -3, -16, -14, 0, -19, -17, -19, -7, -19, -18, -20],\n [-13, 1, -25, 16, -19, -14, -6, 20, 1, 8, -4, 19],\n [-12, -25, 24, -15, 25, 9, -24, -22, -24, 20, -8, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"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, 10, -10, -13, 1, 0, -17, -24, 9, 11, -2, -5],\n [21, 12, 20, 3, -6, 3, 1, 4, 25, -1, 16, -5],\n [-6, -26, 10, -14, -6, 19, -18, -10, 20, -6, 4, 12],\n [-5, -15, -21, 26, -11, -1, -22, -18, 19, 13, -13, 17],\n [15, 3, 25, 25, -1, 26, 18, 2, -8, 20, -19, -4],\n [26, 15, 8, 4, 26, 8, 5, -22, -11, -10, 5, 11],\n [5, 25, -7, 21, -25, -7, 20, -9, -26, 2, 2, -8],\n [17, 13, -21, 17, 12, 23, 19, -19, -3, -7, -13, -22],\n [14, 13, 7, -11, 18, -20, -11, -20, 0, -13, -13, 17],\n [6, 6, 17, -7, 26, 20, 9, -20, 5, 21, -24, 12],\n [2, -3, -5, -21, 21, -3, 13, -4, 11, -17, -11, -16],\n [5, 18, -21, -3, 6, 26, 24, -15, 0, 11, -9, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[12, -14, 26, 13, 3, 26, 22, 14, 25, -14, 7, 9],\n [3, -2, -25, 9, -9, -22, -8, 15, -9, 5, -6, -17],\n [10, 22, -5, -14, -10, -18, -3, 17, -13, 19, -19, 10],\n [-8, 1, 19, 14, 3, -20, -1, 13, 19, 19, -16, -13],\n [-6, -19, -24, 1, 2, -4, -9, 8, -14, -15, 20, 23],\n [-22, 12, -16, -16, 20, 15, 20, 4, 4, -14, -13, 22],\n [18, 15, -2, 6, 6, -12, -11, 17, 11, -21, 17, -2],\n [-12, -23, -23, 3, 7, 0, 4, 5, 17, 12, 25, -18],\n [14, -19, -13, 6, -4, -6, -15, -25, -14, -23, -7, 23],\n [24, 21, -13, 3, 2, -19, -15, 14, 11, -1, 23, -25],\n [13, -13, -21, 15, 13, 4, -10, -2, 5, -15, 22, -14],\n [-8, 17, 21, -2, 4, 10, -2, -11, 11, 16, 22, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-13, -21, -2, -4, 16, -15, -14, 9, 12, 7, -21, 11],\n [23, 25, 13, -19, -19, 13, 6, 7, 17, -12, 9, 8],\n [19, -5, -4, 13, 18, 24, -5, -22, 4, -14, 1, -7],\n [6, -11, 2, -4, -3, 7, -20, 11, 10, -23, 7, 15],\n [-5, -22, 23, 15, -4, -12, 4, -18, 16, 26, -2, -2],\n [22, -6, -18, 21, 11, -5, 16, -4, 22, -23, 2, -12],\n [-26, 3, 2, -7, 6, 14, 17, 9, -5, -14, -20, -19],\n [1, 18, 16, -18, -2, -11, -17, -16, 4, -15, 4, -13],\n [24, 17, 5, 23, 26, -10, 8, -26, 2, 24, -23, -4],\n [1, -11, -15, 26, -6, 18, -10, 13, -14, 25, 5, 10],\n [23, -12, -15, 22, -12, 7, -21, -10, 21, 22, -7, -18],\n [-22, -4, 6, 11, -13, -10, -8, 6, -26, -14, 19, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-21, -21, 6, 3, 19, 8, -4, -17, 24, -8, 24, 1],\n [-4, -23, -7, -8, 15, 0, 7, -23, 11, -20, 21, -20],\n [23, 25, -1, -1, -8, -18, -7, 15, 18, 23, -11, -10],\n [-5, -14, -15, -17, -26, 5, 3, -19, -6, -5, -9, -25],\n [21, 17, -18, -24, -1, -6, 3, 1, 9, -1, 7, -19],\n [-17, 21, 16, 23, -13, 13, -12, -10, 26, -9, 5, 11],\n [-4, 19, -4, 8, 12, -12, 26, -3, 1, -11, -11, 13],\n [12, -21, -25, -14, 17, 20, -18, 7, -10, 0, 2, 10],\n [16, -5, 24, -3, -20, 7, 21, -15, -4, -12, 6, -14],\n [-4, 11, 5, 18, 23, 8, -26, 20, 18, -22, -14, -22],\n [5, 24, -6, -3, -9, -6, -17, -3, 13, 20, -6, -2],\n [25, -4, -5, -23, 7, -21, 1, 4, 8, 12, 15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-21, -11, -25, -3, -10, 18, -26, -21, -22, 18, 23, 2],\n [-15, 12, 20, -24, 21, -26, 0, 21, -3, 17, -8, -19],\n [17, 20, -25, 3, 3, 22, 12, 18, 5, -26, 11, -14],\n [-16, -17, 21, -1, -7, -10, -10, -23, -22, -4, 19, 25],\n [-17, 19, 1, 6, 16, -1, 23, 21, 2, 0, -9, 13],\n [-17, 15, -22, -17, 23, -6, -3, 11, -24, 13, 4, 14],\n [10, -25, -25, 12, 22, 15, 17, 7, 15, -7, 6, -23],\n [18, 17, -16, 15, 20, -22, -2, 22, 10, 7, -18, -21],\n [-9, -13, -8, -13, 13, -10, 8, 2, 15, -10, 16, -19],\n [-26, 18, 26, 9, -20, 19, -22, -3, 1, 16, -10, 10],\n [-7, -24, 10, -1, -12, 24, 21, -19, -14, 21, -24, -26],\n [-18, 4, 14, -1, -10, 7, -18, 24, -14, -22, 14, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-26, -2, 20, -23, 9, 25, -17, 1, -21, 0, -15, 25],\n [21, -24, 19, 6, -17, 4, -12, -20, 9, -13, 21, -13],\n [-24, 22, 26, 19, 23, -24, -5, -8, 8, -15, -22, -17],\n [14, 6, -14, 8, 24, 5, -16, 21, 11, -3, 8, -8],\n [-21, 13, 18, 17, 15, 8, -23, 6, -14, 9, 16, -8],\n [16, -15, -16, -21, -15, 0, 14, -2, 15, -24, -24, -7],\n [1, -4, 21, -24, 15, -3, 16, 13, -21, -7, -16, 5],\n [0, -6, 17, 21, 23, -14, -5, 8, 20, -5, 1, -6],\n [19, -9, 4, 19, 10, -6, -13, -2, 0, 13, -4, 4],\n [20, 2, 20, 3, 24, -1, -7, 11, -8, 0, -2, 13],\n [11, 25, -4, 2, -12, -24, -17, -12, -11, -10, -8, -16],\n [21, -22, -22, -13, 23, -1, -19, -22, -20, -11, -13, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "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, -23, 9, 21, -10, 20, 9, -21, -11, 2, 9, 11],\n [10, 21, 21, -17, 14, 9, 2, -13, -23, 17, 15, 9],\n [23, 18, -14, 19, -9, 6, -6, -11, -12, -22, -21, 11],\n [-24, 21, -15, 9, 6, 9, 6, 4, -6, 0, 0, -19],\n [10, 5, -1, -25, -15, -5, -10, -20, 16, -23, 10, 11],\n [5, -16, -26, -2, 15, 25, -3, 26, 16, -10, -19, 18],\n [0, 25, -9, 0, -5, -11, -25, -22, -9, -24, 0, -10],\n [-11, -21, 24, -20, 23, -13, 11, 13, -12, 20, 20, 21],\n [6, 16, 0, 2, 10, -22, 2, 5, 26, -21, -25, -21],\n [19, 16, -23, 2, -2, -18, -24, -1, 21, 16, 0, 9],\n [5, -26, 26, -11, 24, 21, -16, -1, 13, -26, -1, 1],\n [26, -18, 17, -5, -19, 22, 15, 0, 12, -8, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, -3, -3, -8, 23, 20, -25, -13, 26, 5, 15, 5],\n [1, 21, 12, 13, 15, 20, 13, -14, -15, -19, -12, -1],\n [-15, 16, 24, 19, 0, -9, 18, 9, 22, 24, 0, -18],\n [12, -26, -20, -1, -20, 25, -20, -19, -11, -24, 18, -17],\n [23, -20, -6, 26, 10, 4, -4, 0, -5, 12, 0, 22],\n [-23, -3, -4, 21, -8, 15, -24, 0, -24, 1, -10, 4],\n [-17, 22, -5, 3, 22, -6, 9, 26, -4, 11, -15, -2],\n [-7, 22, 22, 15, -20, 2, 21, 2, -14, -24, -25, -11],\n [3, 11, -21, 18, -20, -22, -20, 7, 5, 22, -14, 3],\n [-2, -6, -6, 1, 21, -7, 7, -22, -9, 12, 16, -16],\n [-10, 21, 18, -5, 10, -7, 21, 21, 21, 19, -21, 7],\n [-13, 21, -4, -7, -14, 20, 17, 14, 5, -1, 23, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-13, 25, 9, -19, 13, -5, -5, -11, 0, -17, -2, 4],\n [-6, 0, -10, 6, 4, 23, 15, -1, -6, 9, -26, -23],\n [-23, -1, -23, 22, -18, 3, 24, 18, -23, -22, 18, -4],\n [-11, -5, 10, -19, 21, 6, 11, 16, -11, -22, -11, -20],\n [24, -26, -18, -9, 18, 20, -24, -3, 1, -17, -18, -14],\n [21, 8, -4, 20, -10, 19, -20, 25, -11, 26, 13, 9],\n [-7, -3, 20, -22, 18, -21, 1, -22, 22, 12, 11, -25],\n [16, 12, -6, 13, 10, -9, 21, 19, -15, -10, 10, 19],\n [11, -12, -20, -13, 23, -26, 11, -24, 10, 17, 4, 16],\n [-14, 21, -9, -10, -10, -16, -7, -17, 2, 21, 7, -10],\n [25, 15, -14, 17, 20, 12, 0, 26, -1, 1, -14, -15],\n [17, 1, -25, 10, 7, -4, 25, 18, 2, 8, -16, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 24, -16, -18, -13, -18, 12, 21, -24, 2, -8, 9],\n [5, -20, 1, 17, -9, -22, -4, -5, -1, 15, -15, 13],\n [-8, 20, -26, -24, 0, -9, 23, 3, -25, -22, 2, 6],\n [15, -7, 3, 15, -22, 23, -6, -12, -7, -19, 22, 4],\n [-15, -6, 3, 0, 17, -1, 6, -1, -1, 9, 13, -26],\n [-12, 23, -26, -16, -25, -26, 4, 17, -11, -5, 15, -9],\n [20, -10, 3, -17, 8, -6, -11, -21, -24, 14, 16, -6],\n [-14, -9, -3, 0, -23, -5, -3, 13, 18, -17, -25, 13],\n [-21, 21, -9, -10, 11, 18, -4, 19, 3, -6, -17, 16],\n [-14, -15, -18, -23, 12, -3, 7, 12, 14, -22, -12, 23],\n [-23, 24, 25, 12, -19, 22, 18, -3, 26, 1, 16, 0],\n [-26, 7, -10, 10, 11, -1, -3, 12, -6, 3, 20, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "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, -14, 10, -24, 5, 8, -8, -13, 21, -5, -10, -23],\n [18, 13, -8, 10, -25, -12, -25, -16, 18, -4, -17, -24],\n [-22, -24, 11, -14, 15, -8, 13, 23, 8, -3, -3, -10],\n [13, -17, -25, 17, -4, -21, -25, -6, 8, 22, 2, -20],\n [2, 26, 10, -4, 6, -19, -15, 19, 21, -17, -12, 26],\n [-3, -1, 20, 15, 26, 12, -24, -25, -21, -6, -18, -17],\n [9, -24, 14, -3, -5, 22, -13, 15, 18, 17, 0, 6],\n [-5, 2, -8, -8, -21, 18, -8, -14, -1, -5, -6, 9],\n [-25, 20, 17, 3, 0, -20, -7, 23, 4, -4, -14, -10],\n [-23, -13, -7, -14, -24, -1, -1, -9, 5, -13, 20, -24],\n [-26, -1, -3, 22, 8, -13, -24, -14, 20, 23, -13, -6],\n [-1, -24, 24, 13, -23, 9, 24, 16, -26, 13, 20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-20, 26, 25, 25, -16, 0, -13, -5, -11, 19, -15, 22],\n [19, -17, -3, 19, -9, -5, -18, -10, 11, 13, -14, 23],\n [10, -21, -6, 24, 9, -20, 9, -2, -16, 17, -13, 18],\n [2, -17, 23, 21, -22, -19, 19, -22, -3, 13, -1, -21],\n [-11, 9, -15, -16, -24, 17, 10, -21, -8, -9, -11, -4],\n [16, 10, -18, -24, -19, 11, -23, -15, 17, 4, -2, 26],\n [-11, 15, -13, -14, 14, -20, -15, 10, 23, -23, -25, 8],\n [17, -24, -23, 11, -15, -8, -17, -26, -10, -11, -18, 26],\n [-18, -18, -15, 14, -12, -25, -16, -16, -19, 5, -21, 26],\n [-7, 12, 8, -19, 23, 22, 16, 7, 26, -8, -20, 4],\n [-9, 13, -13, 12, 26, 9, -10, 10, 17, -18, -7, 18],\n [1, 23, -7, 14, 9, 26, 0, -19, 5, -26, -10, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-7, 18, 5, -25, 5, 18, -18, 3, -7, 11, -26, -22],\n [8, 9, -26, -13, -18, 3, -3, -23, 23, -13, -2, -23],\n [-2, -17, 8, -20, 15, -14, -23, 23, 16, 9, -13, -9],\n [-19, 5, 0, 15, 10, -4, -20, -15, -2, -24, -1, -23],\n [15, 9, -12, 5, 2, -17, -6, -11, 20, -8, 2, 25],\n [24, -9, 17, -11, -26, 21, -25, -12, 12, 1, -26, -22],\n [15, -5, 26, 9, 19, -14, -26, -11, 14, -5, 5, -11],\n [24, -12, 19, 25, 15, 26, -15, -26, 26, -10, 14, 24],\n [23, 1, -20, -18, -5, -1, 26, -15, -20, 19, 20, -12],\n [11, -6, -13, -25, -19, 18, -21, 10, 10, 6, 14, -21],\n [25, -1, 12, 14, 10, -13, 10, -19, 12, -14, -14, 13],\n [16, 1, -9, -8, 11, 5, -5, -25, -14, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "549", "dataset": "MATH"}
{"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, -3, -25, 3, -10, 13, 7, 11, -5, -22, 21],\n [13, 24, -11, -14, -1, 4, 25, 12, 21, -4, 21, -15],\n [-13, -9, 0, 1, -9, -11, 25, -11, -14, 2, -18, -1],\n [1, 14, -14, 9, -18, 20, -13, 24, -15, 26, 5, 11],\n [-24, 25, -11, -7, 5, -4, -10, -11, 11, -19, -8, 3],\n [7, -13, -5, 17, -10, -12, 23, 21, 5, -14, -6, 22],\n [13, 6, 0, 8, -11, 1, 7, 20, -26, 14, 21, 4],\n [9, 17, 6, 6, 12, -9, -4, -4, -12, -1, 3, -2],\n [18, -11, 12, 21, 18, -13, -10, -15, 2, 5, -3, 25],\n [-14, -7, -12, 26, -23, 7, 1, 23, -25, 20, 3, -1],\n [24, 20, -1, -7, 15, 1, -7, -16, -17, -4, 10, 14],\n [25, -8, 18, -9, 22, 0, -21, -17, -25, -3, 11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"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, 26, 18, 23, 12, -25, 19, -22, 23, -16, -17, 16],\n [-25, -12, 12, 14, 10, -20, -7, 7, 8, 7, 26, -5],\n [4, -4, -8, -23, -3, -7, 12, 1, 12, -10, -8, 21],\n [8, 5, 20, 19, 20, 19, 12, 8, 3, -10, 15, 20],\n [2, -21, -10, -10, -13, -3, 23, 10, 13, 12, 5, 9],\n [23, 10, 21, -13, 0, -8, 4, 19, -18, 11, -10, -8],\n [17, -23, 21, -16, -5, -23, -10, -19, 19, 7, -16, 4],\n [-16, 11, 26, -6, 19, 3, -17, -1, 0, -19, 12, -19],\n [-19, 7, -11, 14, -14, -4, -15, 0, -5, 5, 22, 0],\n [-25, 18, 6, -1, 1, -8, 16, -22, 6, -7, 3, 18],\n [-19, 11, -10, 17, -26, -24, 19, -1, 4, -19, 16, 19],\n [-19, 8, 12, 1, 24, -23, -11, -14, -7, 24, -22, 10]]\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[[-7, -3, 9, 7, 18, 21, 7, -8, -10, -22, -2, -9],\n [26, 23, -19, 0, -12, 18, -14, -11, -5, -7, -14, -7],\n [-25, 8, 20, -8, 18, 10, -21, -13, -23, -5, 24, 12],\n [9, 7, 0, -20, -24, 20, 6, -25, 15, -11, -2, -12],\n [-3, -12, 4, -13, -13, -21, -13, -10, -9, -7, 24, -10],\n [-11, 13, 12, 25, 5, 17, -18, 0, 19, 25, 6, -17],\n [-10, 22, 22, 9, -10, -9, 25, -4, 7, -19, -14, -4],\n [-7, -5, 20, 25, -4, 14, 8, -24, 7, 6, 19, -10],\n [18, -8, 3, -4, -12, -13, -25, 12, 22, -9, -21, 5],\n [-6, 13, 1, 0, -25, 6, -11, 12, -5, 16, 20, -14],\n [-25, -13, 11, 14, 1, -20, -9, 14, 9, 14, 9, 17],\n [-23, 3, -3, -7, 19, 4, -3, -20, -1, -14, -19, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "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, -14, 2, -7, -13, 5, 23, 0, -2, 25, -23, -6],\n [-9, 12, -12, 26, 11, 21, 25, -3, -19, 1, -6, -11],\n [-11, 8, -10, -18, 8, 25, 2, 12, -9, -15, -8, 21],\n [-5, 22, 25, -12, -26, -25, -19, -5, -2, -25, 24, -18],\n [-18, -14, -21, 3, -12, 24, 26, -12, 23, -20, -16, 13],\n [11, 13, -25, 24, 21, 12, -17, 17, -10, -20, 13, 12],\n [-23, 8, 24, 20, 9, 4, -2, 14, -14, -9, -6, 21],\n [-26, 9, 23, -19, 25, 21, -6, 16, 25, 26, 26, -6],\n [0, -8, -4, 24, 23, 24, 16, 8, 13, 25, 24, 15],\n [21, -22, 25, 14, -19, -16, -11, 12, 20, -3, -6, 25],\n [-4, 22, 11, 20, -19, -20, -25, 3, -14, -4, 2, 11],\n [10, -7, 6, 2, 23, -12, -4, 15, -24, 10, 2, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-19, -5, 26, 2, -25, 14, 22, 23, 18, -26, 17, -7],\n [25, -6, 10, -19, 0, 20, 8, -21, 18, 17, -8, -9],\n [-26, -2, 0, -20, 17, 15, 2, 4, 17, 16, 9, -8],\n [-21, -2, 4, -18, -7, -17, 10, 0, -14, 14, -25, 23],\n [-6, 6, -3, 26, 17, 15, 7, -18, -25, 3, -5, 19],\n [-16, 16, -10, 9, -14, -20, -11, 6, 18, -26, -16, -21],\n [-7, 8, 17, 10, 14, -1, -15, 3, 1, 0, 15, -8],\n [-22, -22, 14, 0, 1, -1, 0, 25, 22, 15, -6, -26],\n [1, 21, -12, -10, -1, -7, -2, -14, 6, -2, -19, -22],\n [-21, -4, 25, 3, -13, -4, -16, 4, -21, -16, -14, -15],\n [-25, 26, 8, 9, -10, 1, 1, -5, 11, -20, -12, 5],\n [-16, -3, -24, 3, -21, -25, -13, 14, -9, 24, 17, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-14, -1, 17, -15, -9, -18, 22, -6, 21, 22, 26, 13],\n [16, -3, 7, -19, 17, 26, 6, -4, -14, 26, 22, -13],\n [-13, -11, 22, 11, 12, -1, -1, -26, 5, -12, 25, -6],\n [-9, 3, -14, -3, 3, -25, -8, 20, 17, 20, -2, 23],\n [-13, -21, -15, -7, -4, 3, 3, 11, 3, 14, 3, 9],\n [22, 7, -11, -3, -13, -1, -19, -13, 4, -25, 21, -23],\n [-26, -7, -13, 13, -2, -2, -24, -22, 11, -1, 13, 11],\n [11, -23, -20, 3, 3, -8, 12, 8, 13, 6, 6, -13],\n [11, -17, 1, -13, 9, 11, -11, -6, 1, 6, -21, 14],\n [-12, 17, -24, 16, 20, 8, -13, -25, 2, -23, -1, 24],\n [-15, -25, -10, 8, -17, 21, -5, 14, 16, -6, -12, 8],\n [21, -6, -6, -6, 17, 5, -22, 12, -18, 26, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "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, 17, 25, 7, -17, 24, 14, -3, 13, -3, 5, 6],\n [11, 17, 24, 22, 7, -16, 4, -9, -4, -5, 16, -9],\n [13, 20, 14, 20, 12, -7, -14, 18, -26, 25, -23, -3],\n [9, 9, 18, -25, 1, -1, -4, -12, 9, 0, -21, 8],\n [12, 11, 8, 9, -17, 3, 26, 14, 11, 2, 25, 16],\n [12, 23, -23, -22, -23, 9, 18, -11, -2, -13, -16, 2],\n [7, -5, -13, -3, 12, -1, 16, 9, 12, -11, 11, 5],\n [-21, 7, -19, 3, 0, -20, 0, -2, 19, 14, -12, -2],\n [-5, -9, -15, -4, 24, 18, 12, -2, -17, 3, -17, 7],\n [19, -14, 2, 11, 14, 18, -18, -14, 10, -13, 10, -18],\n [-19, 12, 13, -24, 20, 13, 6, 5, -20, -8, 7, -13],\n [23, 20, 19, -8, 24, -1, -10, 1, -8, 0, 21, 25]]\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[[-8, 6, 24, -20, 2, 16, -22, 3, 22, 16, -19, 15],\n [-15, 15, -14, -1, -9, 15, 24, 25, 22, -7, -11, 10],\n [-24, 0, -12, 7, 18, -5, 13, -4, 22, -23, 24, 14],\n [-4, 20, -18, -3, -6, 14, 19, 26, -11, -2, -1, 22],\n [18, -18, -12, 12, 6, -26, -22, -18, 17, -21, 1, 18],\n [-1, 1, 13, -12, -21, 0, 11, -23, -16, -6, 3, -9],\n [8, -24, -15, 0, 26, 3, -6, 11, -6, 11, 13, -12],\n [-9, 25, 2, 21, 11, -6, -10, 14, 24, -9, 10, 11],\n [-15, -16, 21, 25, 22, -7, -18, -26, -24, -6, -4, -18],\n [-8, 18, 19, 25, -8, -4, 0, 0, 12, 9, -15, 0],\n [19, 7, 6, 1, 4, 5, 23, -7, 13, 8, 4, 4],\n [11, -5, 18, 14, -18, 25, -18, -12, -14, -5, -11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-25, -1, -13, 11, 7, -19, 9, -6, 19, 16, 1, 19],\n [17, 21, -21, -7, 4, 6, 17, -20, -19, -18, -25, -10],\n [25, 18, 10, 15, 17, -10, 26, 11, 8, 20, 12, 3],\n [-21, -23, 24, 10, 8, -18, -21, -14, -5, 1, 3, 25],\n [9, -25, 9, -19, 18, 15, 23, -18, -26, -14, 23, -12],\n [5, 7, 16, 4, -13, 20, -13, 21, 2, 20, -8, 0],\n [-18, 10, 10, 16, 1, 25, -3, 1, 9, 25, -9, -2],\n [8, -23, -13, 12, -1, -19, -3, -11, -7, -12, -20, -10],\n [-5, -5, -15, -9, 19, 20, -12, 10, -11, -22, -25, 25],\n [1, 14, 0, 4, 14, 9, 20, 16, -26, 23, 2, -26],\n [-19, -11, 1, -5, -9, -5, 14, -15, -8, -2, 23, -22],\n [7, 12, -17, 20, -20, 10, 20, 25, 25, -12, 15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, -1, 19, -1, -17, -10, 26, -13, -25, 21, -14, 0],\n [-18, -20, 21, -17, -18, -5, -4, -20, 21, -18, 0, -3],\n [2, -10, -7, -20, 16, 13, -20, 1, -8, -7, 17, 12],\n [13, -20, -21, -2, 14, -14, 12, 13, -5, 22, -10, 21],\n [-5, 7, -19, 22, 18, -9, -3, 15, -25, -25, 0, -13],\n [21, 12, 26, 26, -15, 5, 1, 1, 19, -2, -23, -1],\n [9, 23, -24, -26, -10, -20, 21, -22, -8, 12, 19, 7],\n [8, 22, -11, 13, 23, 20, 12, 0, 14, 11, 23, 23],\n [-2, -1, -13, -13, -13, -2, 9, -23, 20, -12, 5, -9],\n [-13, -26, 15, -7, -17, -17, -3, 7, 1, 0, 13, -26],\n [6, -23, -20, -18, -11, -22, 7, -4, 16, 23, -2, 24],\n [-14, -3, -16, 25, 24, -10, 10, -14, 0, -7, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -19, 2, 13, -8, -21, 17, 12, 21, 14, -6, -5],\n [15, -17, -17, 25, 2, -11, -26, -10, 3, -1, 26, 19],\n [-8, 26, -6, -10, 19, 13, -6, 26, 14, 13, 18, 22],\n [-8, -20, -10, -26, 10, -21, -1, -25, 5, 21, -22, 10],\n [4, -15, 8, 3, 21, -21, -12, -12, -11, -7, -14, 17],\n [15, 19, 4, 7, 2, -24, -18, -16, -16, -2, -5, 15],\n [19, -18, -7, -6, -17, -5, 2, -18, -22, 13, -16, -26],\n [26, 15, -26, 12, 19, -22, 22, -5, -1, 26, -21, 5],\n [21, -16, -17, 20, 12, 7, 4, -15, 24, 17, -11, 11],\n [-24, -25, 25, -22, -16, -2, 8, 8, -5, 10, -5, -16],\n [5, 8, 4, 18, 26, -19, -7, 15, 7, -23, -9, 24],\n [-23, -7, -18, -11, -1, 11, -2, -23, 14, 18, 14, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[26, -8, -13, -6, -12, -24, 10, 26, 23, 19, -11, -13],\n [-18, 20, -20, -13, -21, -6, -12, 25, -19, 7, 13, -26],\n [5, 22, 24, -22, 3, -5, -7, -11, -20, -20, 23, 23],\n [-25, 20, -13, 4, 23, 14, -13, -22, -16, 13, -22, 2],\n [-16, -22, 22, 5, 9, -12, -8, -5, 7, -10, -15, -2],\n [-10, -17, 1, -9, 24, -9, 18, 5, -13, -11, 23, -9],\n [-11, -10, -20, -15, 7, -17, -22, -6, -24, -8, 18, 17],\n [8, -21, -13, -23, 18, 24, -9, 2, 8, 25, 11, -11],\n [-7, -3, 8, 17, 24, -8, -23, 6, -25, -14, 18, 3],\n [7, 3, 24, -3, 21, 17, 6, 14, 22, -17, -9, -8],\n [-20, -8, -3, -12, 14, 15, -4, 25, 25, -23, 11, -23],\n [-22, 14, 17, -4, 13, 26, 10, -16, -16, -14, -13, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-2, -9, 24, 17, 17, -9, -17, -20, 23, 17, -13, -12],\n [-11, -25, 3, 3, -9, 4, 17, 21, -14, -7, 22, 23],\n [8, -4, 15, 6, 11, 8, 24, 9, -7, -24, -19, 13],\n [5, 2, -20, -25, -6, -21, 1, 21, 15, 9, 5, 18],\n [15, 26, 19, -18, -16, -4, 23, -16, 22, -25, -24, -16],\n [23, 8, -12, 16, -16, 4, 1, 1, 5, -2, -7, 1],\n [-2, -16, -8, 1, -26, -22, -17, 15, 19, 7, 9, -25],\n [-9, -14, 24, -22, -7, -25, -16, 3, 5, 5, 23, 11],\n [1, -17, -5, -10, -5, 16, -8, -10, -3, 9, 5, 19],\n [25, 9, 1, -13, 9, -21, -18, -6, -15, 3, 4, 13],\n [-23, 4, 0, -2, -22, -21, -22, 24, 0, -19, -18, -12],\n [9, 14, -20, 5, -19, 20, 24, -12, 10, -8, 12, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-8, 1, -10, 15, -8, 4, -16, -12, -17, 16, -4, -24],\n [-24, -9, -2, 16, -7, 2, -5, 23, -12, 12, -17, -6],\n [25, 2, 5, -17, -14, 20, -4, 23, -4, 4, -23, 25],\n [22, -24, -6, 26, -25, -23, -26, -12, 6, -21, -20, -8],\n [17, -26, 12, -8, 18, -1, 17, -15, -5, -14, 1, -13],\n [-5, 3, 17, -7, 17, 0, 11, 15, 25, 14, 7, 12],\n [14, 17, 10, -26, -12, 5, -19, 6, -9, 18, 2, 5],\n [6, -22, -9, 21, -17, 9, 6, -4, 13, -22, 7, -3],\n [-10, 4, -20, -10, 1, 11, -5, -12, 10, -12, 23, 23],\n [-2, 26, -6, 11, -25, 0, 22, 5, -6, -23, 17, -8],\n [-25, -1, 7, -13, -12, -7, 7, 9, -8, -18, -20, 3],\n [-14, 0, 17, 8, -14, -12, 19, -18, 18, -4, 9, 26]]\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[[13, -24, 7, -8, 1, -4, 13, 22, 18, -20, 14, -15],\n [-13, 19, -12, -24, -12, 24, -3, 25, 19, -19, -22, 24],\n [-23, -13, -11, -7, -3, -21, 4, -21, 8, -12, 2, -24],\n [-16, -24, 1, -17, 23, 6, 21, -11, -17, 6, 9, -24],\n [-22, -15, 17, -14, -3, 17, 5, -11, 5, 18, 10, 9],\n [-6, 20, -15, 24, -6, 24, -6, 16, 26, -21, -18, -26],\n [-15, -13, -21, -26, -5, 7, -16, -24, 15, -21, -21, -7],\n [-6, -25, -1, 4, -1, 5, -17, -4, -21, -4, 1, 22],\n [3, -13, 10, 5, 22, 7, 14, 17, 24, -5, 4, -20],\n [14, -6, -11, -7, 16, 17, 20, 23, -8, 21, 5, -12],\n [-22, -16, -12, 2, 23, 18, -23, 22, 9, 21, -4, -12],\n [19, 17, -24, 5, -17, 13, 11, -5, -13, -10, -6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[21, -12, -12, -26, -3, -15, -17, 19, 15, 15, 25, 4],\n [-16, -11, -18, 20, -13, -8, 4, -18, 9, 26, 12, -1],\n [-19, -3, -19, -8, 20, 21, 3, -5, -18, 17, 21, -23],\n [10, -19, -26, 1, -21, 20, 9, 26, -16, -22, 23, -3],\n [20, -9, -7, 1, -14, -22, 3, -26, -5, -9, 19, -22],\n [4, -21, 0, -2, 2, 1, -11, 26, -15, -7, -9, 7],\n [26, -4, 18, 0, 22, -10, 21, -6, 23, 13, 4, -24],\n [-10, 23, -1, -4, -21, 1, -19, 18, -19, -8, 11, 2],\n [-4, 20, 5, -17, 0, 22, -26, 12, 2, 18, -24, 24],\n [20, 10, 4, -16, -5, -9, 8, -21, -24, -22, -18, 1],\n [-8, 1, 0, -14, 11, 16, 26, -6, 0, 19, -21, 11],\n [22, -16, 20, 14, 26, -10, 12, -20, 3, -6, -26, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -19, -22, 3, 24, -19, 22, -8, 17, 3, -12, 9],\n [17, 0, -14, -13, 10, 21, 3, 12, 20, -14, -11, 17],\n [-20, 21, 0, 18, 8, -12, 1, 8, -20, 23, 19, 23],\n [24, 19, -7, 5, 11, 13, 5, -1, 12, -7, -9, 23],\n [-12, 25, -5, 24, -5, 26, -6, -25, 13, 26, 16, -9],\n [-4, -14, 14, -18, 22, -20, 14, -26, -25, -23, -13, 5],\n [9, -25, 13, 23, 24, -13, -7, -2, 15, 22, -19, 1],\n [19, -6, -4, 5, -19, 4, 10, -11, 13, 15, 0, 13],\n [14, -9, 8, 22, 25, -12, 26, 0, -10, 13, -25, 22],\n [23, 4, 10, 14, 14, 7, 7, 24, -24, -10, -13, -13],\n [19, 11, 8, -26, 21, 2, -23, 6, -10, 1, 23, -1],\n [-19, 7, -9, 4, 0, -11, -17, 13, -15, -5, -11, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-16, -7, 24, -26, 0, -24, -15, 3, -18, 26, 10, -26],\n [15, 22, -23, -12, 24, 0, -19, -4, -12, 0, 4, 12],\n [20, -19, 3, 15, -9, -23, 20, 16, -5, -24, -12, 8],\n [20, 11, 6, -13, 21, -26, 26, 22, -1, -19, 23, -11],\n [11, -17, 15, 10, -1, 1, -15, -7, 22, -13, 19, 8],\n [2, -15, 25, -9, 17, -25, -25, -10, -17, -9, -5, -8],\n [26, -26, -3, 9, -2, 9, 4, 4, -25, -8, 26, -15],\n [-17, 4, 18, -5, -4, 25, -4, -12, -1, -24, -4, -7],\n [18, 13, 12, -19, -9, 14, -21, 0, 9, -12, 10, -22],\n [12, -18, -20, 14, -7, -17, -1, -23, 11, -3, -13, 14],\n [-26, -10, 18, -3, 0, -20, -18, 16, 8, -15, -6, -24],\n [-12, -6, -17, 6, 19, 25, -21, -25, 2, 13, 6, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-23, 2, 10, -7, 14, -4, 18, -9, 22, -2, -26, -12],\n [7, 21, -7, 10, 0, -5, 24, -22, 7, 12, -24, -10],\n [-3, -3, -24, 18, -20, -2, -24, -12, 2, 23, 2, -17],\n [5, -4, 12, -18, 10, 25, 13, -13, -23, -7, 1, -13],\n [17, 7, -14, 4, 6, 25, 12, 1, -2, 5, -18, 1],\n [4, -10, 26, -4, -14, -17, -11, -21, 21, -16, 25, -24],\n [1, 14, -12, -14, 15, 25, 18, -10, -20, 1, 11, -14],\n [-10, -12, 9, 1, -12, 19, 26, -16, 4, -23, 8, 7],\n [25, 0, -17, 3, 18, -7, 2, 26, 2, -4, 23, -6],\n [21, 16, -17, 14, -15, 3, 24, 6, -9, -13, -5, -6],\n [-26, 22, 16, 25, -12, 9, 20, -5, 5, 19, 6, 14],\n [12, -4, 16, -25, -25, 11, 24, 2, 25, 19, -24, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-20, 9, 2, 10, 22, 9, -4, 18, -11, 21, 4, 7],\n [23, -26, -9, 13, 16, -12, 21, 22, -10, 17, -17, -7],\n [-21, -19, 18, 7, 5, 24, 15, -23, 17, 23, 12, -7],\n [-3, -3, -1, -2, 9, -20, -17, 20, -15, -26, 25, 23],\n [-2, -11, -22, -8, -23, -21, -1, 22, 12, 12, -18, 18],\n [25, -13, 21, -18, -12, 10, 23, 26, -7, -19, 5, 20],\n [-6, 14, -8, 2, 4, -21, -23, 16, 2, 15, -24, -26],\n [17, -12, 20, -6, 19, 4, -20, -10, -8, 12, -24, 3],\n [8, 2, 23, 25, -13, 8, 1, 3, -1, -20, 12, 4],\n [-22, 8, 23, 20, 25, -13, 9, 0, -3, 13, 2, 26],\n [18, -5, -19, -12, 22, -22, 25, -23, -16, -9, 15, 22],\n [3, -12, -21, 26, -11, 20, 13, -18, 16, 7, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[9, 0, -18, -22, 24, -5, 4, -24, 3, -6, 8, -21],\n [1, 5, 15, 10, -2, 5, 8, -5, -3, 12, 3, 23],\n [5, 4, -4, 13, 6, -2, 9, -3, 4, 12, 19, -14],\n [-17, -4, -9, 5, 6, 9, 1, -11, -11, -9, -19, 15],\n [-11, -16, -21, -26, -15, 11, 1, 18, -10, -26, 5, -19],\n [13, 16, 19, -3, -17, 20, 12, 12, -17, 9, -2, 23],\n [-17, -8, 19, 18, -12, -11, -25, 2, -23, 26, 23, 2],\n [4, -10, -17, 0, 26, 14, -12, 17, 4, -6, 14, 19],\n [18, -1, 11, 24, 9, 25, -10, 24, -24, -13, 22, -14],\n [14, 0, -26, -10, 21, 23, 7, -13, -10, -24, 7, 13],\n [-2, -25, 7, -1, 4, -18, 3, -7, -6, 2, -2, 11],\n [17, -2, -18, 12, 17, -1, 10, -11, 10, -15, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "478", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-7, -18, -4, 12, 2, 4, -8, -7, -4, 16, 0, 3],\n [-6, 17, 8, 22, -20, -5, -17, -4, -12, 3, 7, -14],\n [-23, -9, -4, 6, 7, 7, 9, 8, -10, 1, -13, 7],\n [21, -16, -14, 6, -25, 7, 26, 2, 10, -23, -15, -1],\n [1, -24, -7, -17, 25, -9, 26, 26, 26, 0, 4, 0],\n [15, -26, -21, -16, 7, 12, -7, 26, -6, -6, -9, -6],\n [-8, -23, -14, -9, 25, 2, -2, -14, 0, -8, 22, -26],\n [11, -8, 25, -26, 13, -10, -6, -5, -12, 23, 12, 21],\n [12, 5, 22, -23, 17, 18, 5, -23, 26, -26, 6, -20],\n [-18, -26, -11, -9, 20, -21, -25, -18, -23, 18, -4, 16],\n [18, 16, 24, -19, 12, -2, -11, 8, -10, -9, 0, -12],\n [-10, 16, -22, -11, -12, 15, 19, 7, 21, -8, -19, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "521", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-17, -22, 25, 21, 26, -1, -5, 17, -4, -14, -18, 22],\n [-7, 1, 17, 10, -3, 17, 6, -7, 21, 3, 17, -18],\n [18, 22, -10, 9, -13, -8, -20, -24, 6, 17, 5, 20],\n [-16, 15, -25, -1, -23, -10, -10, 1, 3, 13, -4, 19],\n [-3, 2, -23, 11, 2, -8, 0, 2, 9, 8, 25, -21],\n [-4, 12, 19, 17, 21, 25, -19, -25, -14, 13, -6, 4],\n [25, 21, 9, 21, 25, 11, 0, 9, 21, -4, -6, -14],\n [10, 20, -1, 13, -20, 19, 12, -5, 12, -4, 3, -9],\n [15, -9, 19, -17, 12, 3, -1, -20, -20, -22, -26, 19],\n [-9, -14, -2, 13, -19, -17, 5, -10, 11, -12, -12, 21],\n [13, 24, -7, -12, 8, -21, 3, -19, 4, 21, 20, 5],\n [18, 25, -12, -9, -14, -3, 13, -13, 1, -16, -21, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-26, -2, -25, 5, -14, 6, 5, -3, 0, -23, -3, -4],\n [2, 7, -6, 3, -1, -7, -11, -24, 22, 10, 13, 17],\n [-2, -4, 17, -26, 6, -12, -10, 7, -10, 25, 14, 17],\n [-23, -14, -23, -20, 19, -18, -4, 6, 6, -7, -23, -26],\n [15, 7, 0, -6, -3, -12, 8, -2, -18, -10, -6, -14],\n [-24, -23, -23, 16, 1, -20, -1, -16, -3, 16, -17, 10],\n [-14, 17, 15, 12, -8, 24, -8, -15, 25, -5, 20, 10],\n [3, 19, -15, 2, -6, -16, 10, 21, -9, 17, 0, 10],\n [21, -15, -4, 7, 11, -4, 26, -2, -23, 3, 3, -14],\n [15, 22, -13, 20, -19, -3, -9, 8, -2, -10, 5, -3],\n [-20, -14, 0, 21, -22, 9, -1, 15, 18, 4, -17, 19],\n [-1, -5, -15, 5, 0, 6, 26, 25, -7, 12, 14, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "486", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -13, 17, 13, 26, -5, -9, 21, 2, 16, -11, 19],\n [8, 26, 7, -24, -23, -22, -17, 25, 2, 5, 4, -25],\n [-15, 0, -22, 10, 0, -4, 6, -23, -6, -3, 17, 4],\n [17, 21, -3, 22, 26, -17, 22, 22, 23, -25, 4, -2],\n [-23, 24, -16, -10, 17, -25, -21, -18, -22, -7, 2, -6],\n [-18, 1, -19, 4, -7, 0, -19, -6, 1, -4, -21, -24],\n [-22, -18, -20, -23, 12, -22, -16, -12, 7, -14, 21, -20],\n [13, -21, 12, 23, 3, -5, -2, 1, -7, 12, -24, -22],\n [-26, -12, -1, -24, 13, 14, 20, 15, 7, 25, -22, 4],\n [24, -14, 16, -26, -5, -12, -1, -9, 21, -18, -26, 16],\n [-18, -4, 16, 18, -25, -13, 11, 13, -9, -11, 26, 2],\n [17, -16, -21, -24, -13, -25, 5, 4, -16, -5, -24, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 6, -3, -26, 17, -12, 10, 0, 11, 21, 0, 17],\n [-15, -24, 3, 5, -4, -25, -20, 7, 5, 26, 12, 5],\n [16, 16, -13, -24, 19, 5, 16, 9, -10, 21, -24, -17],\n [26, 20, 13, -9, -24, 12, -17, 25, -18, 19, 19, -16],\n [6, 9, -1, 0, 11, -5, -1, -5, -22, 8, -25, 8],\n [-18, 24, 24, 22, -9, 16, -15, -24, -9, 11, -20, 6],\n [-21, -9, 18, -5, 24, 12, 24, -18, 8, -4, -15, 25],\n [-3, 23, 13, -18, -14, 13, 15, -10, -20, -10, 23, -3],\n [-25, 8, 1, -8, 6, -6, 26, -17, 26, 19, 18, -18],\n [11, -21, 24, 26, 15, 8, -9, 26, -8, -22, -2, -16],\n [-17, -10, 9, -1, 4, 5, -6, -9, -9, -26, -13, -19],\n [-25, 24, -12, 7, 9, -26, 24, -6, 15, -26, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[20, 9, 12, 3, -20, -5, 23, 18, -17, -19, 0, -17],\n [-13, 19, 25, -16, -21, -6, 6, -8, 12, -3, -9, 8],\n [25, 16, 10, -8, 26, -3, 7, -5, -23, -17, -25, -19],\n [6, 11, 16, 1, -17, 18, -26, 7, -24, -18, -22, 15],\n [-17, -15, -9, -6, -6, -26, -24, -22, -2, 22, -19, -10],\n [-18, 5, -21, 22, 13, -6, -20, -20, 20, 12, 0, -19],\n [-18, 1, -12, -25, -20, 20, -9, -5, 23, -17, 23, 6],\n [-20, -24, -13, 17, 19, 9, -14, -11, -11, -22, 25, -2],\n [11, 11, 23, 11, 12, 21, 14, -1, -14, 17, 24, -1],\n [-26, -19, -23, -6, -5, 24, 26, 10, 22, -24, -8, -26],\n [2, -4, 6, 25, 14, -4, -22, -20, -21, 22, -5, 22],\n [-14, -15, -23, -19, 10, 4, 10, 18, -1, 16, -19, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "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, 18, 2, -22, 1, 26, 13, -10, -4, 18, -18, -25],\n [5, 24, 25, 22, 4, -20, 3, -24, 24, 24, -18, -17],\n [19, 23, 20, -1, -26, 3, 11, -12, -2, -21, -9, -26],\n [-24, -10, 21, -19, 22, 13, -10, -2, 14, -15, 2, -2],\n [24, 9, 26, -2, 2, -16, -23, -13, 19, 11, -10, -25],\n [-19, 9, -17, -20, 9, -11, -13, -11, -2, 14, -23, 2],\n [-21, -26, 12, -26, 24, 13, -24, -26, -26, 12, -6, 18],\n [3, 5, 6, 21, -5, 3, 19, -23, -4, 17, -2, -15],\n [-10, 26, -12, -17, 8, 25, 25, 2, -15, -26, -26, -17],\n [-9, 20, -25, 22, -19, -5, -5, -1, -1, -18, -6, 4],\n [25, 16, -21, -13, 6, -20, -3, -18, -16, -4, 21, 24],\n [-25, -12, 8, 9, 25, 1, 12, 17, -23, -17, -21, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[19, 8, 22, 16, -17, 26, 5, 15, 15, -24, -1, -12],\n [-10, 0, -9, 24, -8, -15, -3, -22, -3, 0, 21, 3],\n [-12, 20, 11, 17, 7, 0, -7, 14, 5, -23, -22, 26],\n [-19, -5, 15, -20, -5, 19, 3, 10, -11, -12, -22, -24],\n [-4, -17, -22, -4, -12, -9, -2, -19, 4, -6, -25, -5],\n [-19, -4, 5, -19, -23, 3, -8, -4, -9, 26, 2, -4],\n [6, 25, 20, -9, 17, 6, -20, 24, 1, -26, 12, 7],\n [12, -8, 4, -14, -3, -22, -4, -8, -26, 6, 23, 6],\n [5, 1, 10, 14, -15, -18, 23, -16, 6, -8, 15, 7],\n [-20, 4, 25, -25, -8, 11, 5, -17, 14, -19, -1, 3],\n [-16, 14, -7, -7, -18, -19, -12, 7, -3, 6, 14, 14],\n [18, 13, 0, -6, -22, 8, -6, -23, 22, 21, -11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 25, 8, -21, 6, -6, -11, 20, 12, 7, 15, -12],\n [-21, -25, -3, 22, 1, -26, -26, 1, 9, -7, 21, -19],\n [-26, -1, 24, 16, 22, -2, -17, -15, 14, -20, -15, 20],\n [13, -10, -22, -13, 7, 21, -10, 8, -26, 23, 23, 9],\n [-12, -8, 24, 15, -22, -8, 16, 12, -22, 25, -15, -8],\n [20, -15, 9, -15, -9, 22, 24, 21, 16, 7, 21, 6],\n [22, -9, 2, 18, -22, -2, -3, 2, 11, 6, -17, 10],\n [6, -4, -16, -3, -3, -20, 23, -6, -7, 26, -17, -2],\n [20, 9, 21, 20, -12, 17, 13, 13, 23, -21, 10, -25],\n [-15, -23, -4, -14, -10, 4, -11, 14, -1, 1, -26, 20],\n [-15, 10, 23, -7, -25, 9, -12, 11, -5, 17, 23, 5],\n [-7, 9, 6, -12, 23, 19, -24, 2, 20, 0, -22, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 8, -20, -21, -1, -26, -8, -20, 9, -15, -7, -4],\n [-2, 3, 2, 4, -9, 14, -8, -23, -26, 14, -12, -19],\n [-12, -12, 23, 12, -5, -9, -11, -25, 9, -7, -11, -24],\n [3, -25, 8, -1, -22, -25, 24, -7, 7, 7, -7, 23],\n [-2, -7, -2, 26, -13, 20, 17, 16, 16, 12, -15, 21],\n [-22, -25, -11, 3, 20, 16, 11, 18, 24, 15, -3, 24],\n [3, 10, 26, 12, -16, -13, -4, 26, -11, 23, -6, -23],\n [6, 20, -13, -8, -22, 9, 4, 18, -9, 17, 4, 3],\n [-6, 20, 3, 14, -23, -22, 14, 18, -17, 0, -11, 3],\n [-14, 9, -6, 18, 26, 13, 18, -12, -7, -7, 18, -22],\n [5, -21, 3, -1, 10, -14, 2, -22, -2, -14, -3, 4],\n [-7, -19, -18, -6, 24, -7, -12, -1, 15, -16, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"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, 0, 3, -8, 7, 11, -4, 26, -26, -24, -24, 1],\n [-13, 25, 3, -22, 22, -12, 11, -13, -13, 22, -19, -19],\n [-8, 5, 4, 2, 14, -16, 18, -14, 0, -8, -1, 26],\n [24, 10, 21, -18, 1, 5, 25, -24, 24, 5, -22, -19],\n [-13, -24, -3, -14, 16, 2, -19, 24, 15, 4, -1, -9],\n [-9, -20, 21, 11, 21, -11, 6, 24, -24, 11, -23, 9],\n [-23, 15, -18, 13, 24, -10, -10, 6, -7, -13, -5, 25],\n [0, 16, -24, -3, 3, -19, -5, -2, -17, 22, 2, 13],\n [-26, 25, -6, 12, -3, -18, 17, -1, -18, -7, 8, 9],\n [15, 9, -18, -5, -26, -22, -18, 10, 11, -8, -19, 15],\n [16, 5, -14, -7, 9, 16, 17, 10, 3, -17, 4, -2],\n [2, -3, 12, -6, 14, -18, 15, 15, -25, -23, -19, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-13, 22, -14, -6, -3, 23, -9, 18, 13, -1, 5, 17],\n [26, 6, 25, 4, -9, 8, -15, 24, -2, 18, 4, -17],\n [20, 25, 7, 24, -24, 19, 12, -19, 5, 16, 2, -5],\n [-7, -21, 16, 22, 2, 15, -10, 4, 26, 7, 11, 10],\n [-23, -25, -15, 8, -21, 19, -19, -6, 26, 19, 8, 21],\n [-12, -20, -12, 18, -21, 20, -10, -23, -5, 5, -5, 0],\n [19, -12, 17, 24, -5, 1, 15, 11, -18, 7, 9, -18],\n [-12, 18, -7, -19, 1, 24, -8, -11, -16, 15, -19, 6],\n [-17, -9, 8, 16, 23, -24, 13, 0, 1, 19, -21, 20],\n [-13, -20, -17, -12, 4, 2, 15, -10, 24, 2, 22, 17],\n [-12, -1, -15, -2, 14, -22, -23, 17, 21, 14, 4, -24],\n [26, -24, -1, 23, -10, -17, -25, -3, -16, -3, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[5, -4, 7, 14, -8, -25, 24, -25, -12, -6, 8, -22],\n [16, 0, -3, -20, -21, 19, 6, 22, -10, 19, 15, 3],\n [-19, 13, 19, -20, -21, -23, -26, -12, 4, -2, 20, 6],\n [25, 8, -22, -22, 9, -10, 26, 25, -13, 2, -19, 7],\n [13, -26, 2, 9, 24, 10, 2, -22, 26, 5, 25, -3],\n [-8, -15, 25, -26, -20, -10, 7, 16, -20, -10, -24, 2],\n [-5, 11, 16, 2, 23, 23, 15, -22, 3, -4, -6, -1],\n [20, -6, -7, -4, -23, -6, -6, -26, -12, -10, 24, -13],\n [-8, 23, 7, -21, 18, 22, -21, 26, -22, -20, 6, -14],\n [24, -26, -14, 16, 0, -20, 25, -24, -2, 6, 13, -10],\n [18, -13, 10, -4, -3, 2, 11, 0, 11, 26, 13, 18],\n [23, -4, 4, 9, -10, 10, -24, 9, -22, 19, -12, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[22, -21, -17, 5, -4, 21, -10, 19, -7, 17, 14, -12],\n [17, 19, -5, 23, 25, -21, -23, -4, 17, 18, -8, 18],\n [4, 17, 25, -24, 1, -24, -13, -9, 0, 24, -17, 22],\n [-12, -8, -18, -23, -12, 24, 21, -19, 22, 26, -26, -20],\n [26, 4, -9, -15, 21, 3, 6, 20, -20, 1, 22, -24],\n [16, -21, 4, 11, -12, -20, 16, 3, 0, -10, -9, -5],\n [26, -1, 24, 0, 13, -3, 25, -19, -6, 2, 16, -6],\n [-24, 4, 0, 19, 0, -18, 6, 6, -1, 1, 17, 16],\n [4, 26, -26, -7, -15, -10, -12, 7, 23, -11, -23, -19],\n [7, 19, -2, -12, 1, -18, -25, -10, -17, -18, 4, -25],\n [-3, -8, -10, 16, 22, -17, 23, 1, 11, 21, 1, 23],\n [25, 23, -26, -24, -12, 25, -17, -6, 10, -12, -4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"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, -17, -18, 17, 12, -22, -2, 15, -1, -19, -5, 25],\n [-2, 21, -15, -18, -17, 21, -17, -18, -1, 8, 0, 4],\n [-8, 16, 11, -21, -12, 2, 20, 18, -22, -13, 26, -25],\n [-4, 17, 25, 19, -8, -3, -7, 20, 0, 25, -3, -10],\n [-2, 19, 4, 1, 23, 1, -5, -22, 17, 15, -19, 11],\n [1, 20, -15, -2, 11, 17, -12, 17, 14, 24, 26, 7],\n [18, -14, -19, -14, 9, -21, 11, 5, -6, 17, 17, 22],\n [-20, -1, -12, 22, 15, -4, 25, 11, 14, -12, 21, 26],\n [13, -11, 5, 10, -9, -7, 19, -25, -4, 3, -24, 19],\n [12, 20, 22, -26, 14, -5, 2, -13, 21, 1, -6, 18],\n [5, -21, -26, -6, -23, -24, 22, 3, 4, 7, -8, -7],\n [-4, 13, -2, -12, 11, -4, 25, -25, -12, 25, 17, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"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, -13, 0, -13, 8, 6, 25, -26, 7, -8, -3, 15],\n [-23, 9, -14, 5, -18, 12, -11, 23, -24, 25, -7, -17],\n [-5, 21, -24, -16, -2, 15, 21, -19, -18, -12, 5, 26],\n [-24, -23, 3, -14, 17, -6, 14, 19, -8, 12, 21, -5],\n [-7, 10, 4, -17, -9, 16, 12, 19, -7, -9, -16, -5],\n [17, -9, 7, -4, -26, -17, 26, -26, 11, 12, 22, -18],\n [4, -20, -10, 8, 21, 10, 25, -9, 6, -23, -4, -16],\n [25, -18, 3, -19, 13, -22, -15, -26, -12, -2, -9, 11],\n [15, 19, 26, -1, 13, -24, -5, -1, -8, 17, 17, 20],\n [12, 9, -6, 14, 21, -1, -14, 9, -3, 14, -1, -6],\n [-9, -12, -12, -21, 16, 4, 1, -19, 2, -6, -10, 22],\n [-3, 23, 9, 4, 20, 7, -25, 15, -24, 3, -19, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-20, -15, -8, -1, 1, -12, -13, 21, -13, -24, 23, 2],\n [-21, 22, -4, 1, -13, -13, -7, -14, 0, 8, 18, -25],\n [14, 18, 13, 21, -3, 2, -24, 18, -23, 23, -25, -7],\n [26, -12, 22, 5, 15, -26, 11, 8, 24, -20, 18, -14],\n [22, -26, -13, 2, -24, 19, -3, -26, 21, -17, -14, 9],\n [-18, -13, 9, -17, 13, -4, 8, -20, 15, 8, -25, -12],\n [-18, 20, -10, 12, 25, -9, -12, -9, -3, -4, -15, -4],\n [-6, -1, -19, 3, 7, -25, -22, 4, 6, -23, -21, -4],\n [18, -8, 16, 18, -19, 12, -14, -26, -21, -20, 21, 0],\n [-12, 25, 7, -4, 21, 22, -3, -12, 8, -23, 17, 10],\n [-10, 4, 11, -17, 23, 0, 15, -21, -21, 25, -12, -23],\n [21, 13, -20, 24, 22, 26, 18, 20, -1, 4, -25, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "594", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[15, -14, -9, 3, -16, -14, 24, -3, 2, -22, 8, -8],\n [-14, -22, 17, -13, 11, -5, -18, 22, 13, -1, 18, -22],\n [2, -5, 22, -24, 1, 11, -13, 20, -13, 16, -16, -18],\n [11, 20, 17, -21, -26, -2, -11, 25, -12, 7, -10, -24],\n [-24, 10, -10, 22, 25, 11, -26, -20, -1, 20, 12, -8],\n [25, 3, 16, -13, -14, -7, -1, 0, -2, -18, 14, 21],\n [-15, -17, -21, 23, 7, 25, 14, -8, -21, -25, -12, -10],\n [-11, 1, -6, -19, -17, -17, 23, -17, -18, 1, -3, -8],\n [6, -23, -24, 15, -15, -9, -4, -7, -21, 26, 7, 15],\n [-25, 3, -18, 0, 15, 7, 13, -3, 22, -10, 2, 9],\n [23, -15, 4, 22, -18, -8, 19, 19, -10, -25, 13, -22],\n [12, 21, -11, -10, 0, -20, 25, -19, -19, -4, 5, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "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, -9, 11, -15, -12, 1, 11, 23, 4, 25, -18, -19],\n [19, -8, 24, -19, 7, -23, 4, 11, -24, 8, -8, 16],\n [2, -17, -15, 19, 3, 3, -9, -3, 5, -18, 20, -3],\n [-1, -24, -4, -16, -17, 23, 9, -14, 2, 11, 26, -14],\n [-1, -7, -22, -7, -13, 18, -13, -19, 21, -14, -3, -12],\n [24, -26, -5, 7, 23, 24, 13, -24, -1, -13, 14, -19],\n [22, -11, 15, -6, -17, -2, 11, -5, 22, 21, 20, 19],\n [-23, -23, 3, -25, 2, 16, 9, -6, -6, 21, -6, -23],\n [-26, -1, 24, -25, -18, 18, -9, 21, 21, 15, 14, -16],\n [-2, -1, 9, 15, 8, 11, -24, 14, 8, 23, 13, -5],\n [-19, -12, 18, -20, -8, 13, 15, -10, -26, 18, 2, -14],\n [21, 2, 14, 15, -21, -22, 7, -16, -18, 11, 13, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-18, -19, 17, 13, -24, -14, -8, 7, 5, 22, -11, 9],\n [-9, -13, 3, -25, -14, 0, 26, 25, -10, 4, -12, -7],\n [-22, -20, -9, -16, 5, 23, 0, -1, 10, 18, 1, 23],\n [-25, -7, -23, -14, -3, 21, 11, 13, 21, 18, 2, 9],\n [-25, 14, -9, 22, -19, -12, 14, -10, -4, -25, -21, 2],\n [0, 10, 22, 7, -9, 15, -17, 11, 17, -10, -14, 25],\n [21, 15, 0, 26, -25, 7, 4, -4, -20, 11, 6, -15],\n [18, -15, -8, -18, -17, -10, 23, 13, 12, 14, -17, -15],\n [-12, 4, -12, 1, -23, 9, -26, 17, 7, 20, -10, 12],\n [11, 17, 24, 6, -6, -1, 19, 9, -22, 6, -26, 26],\n [-21, 10, -25, 26, -22, -1, 14, 24, 26, 20, -14, -15],\n [-22, -25, -23, 0, 23, 26, -17, -14, 17, -25, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[19, -17, -5, 13, -2, -12, -14, -19, -6, -6, -5, 19],\n [6, 18, 0, 13, 23, -5, 3, -18, 18, 8, -9, 15],\n [-22, 0, -21, 5, -19, 12, -6, -9, -13, -12, 15, -1],\n [26, 17, 5, 12, 1, 12, 16, 5, -14, -12, -9, 12],\n [-21, -16, 5, 13, -7, 6, 13, -19, 24, 8, -22, 8],\n [20, -13, -6, 20, -3, -10, -9, 7, -15, -11, -23, -2],\n [7, 1, 19, -16, -14, 4, -2, 12, -17, -3, -26, 26],\n [-2, 1, 9, -9, -21, -25, -24, 19, -19, 4, 21, -8],\n [23, -21, -13, -24, 21, -26, 17, 3, 19, -8, -8, -18],\n [-20, 19, 10, 23, 14, 26, -20, -18, -23, -2, 22, -15],\n [-21, -9, 13, -6, -12, -24, -25, 14, 13, -23, 5, -25],\n [19, 2, -25, 7, 0, 12, 17, 11, -9, 9, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525", "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, -7, -6, -4, 3, -2, 4, 0, 7, -19, -8, 14],\n [-1, 1, -23, 4, -11, 24, -17, 11, 21, -17, 18, -18],\n [12, 9, 24, 9, -8, -8, -15, -14, -2, 9, -2, 1],\n [15, 26, 12, 3, -22, -10, -9, 16, 20, -6, -5, 12],\n [23, -21, 23, -11, -25, 24, -26, 3, 16, 25, 10, 21],\n [-4, -26, -8, 19, -24, -25, 10, -10, 1, -9, 6, -12],\n [-5, 14, 0, 10, 5, 18, -8, 1, 1, -17, -7, -2],\n [-6, -13, -5, 26, -1, 17, -16, -20, -10, -9, -20, -7],\n [11, -16, 17, -11, 24, 0, 24, -16, -11, -4, -15, 13],\n [-24, -25, 11, 21, 25, -3, 2, 20, 19, 7, -7, -9],\n [-13, -9, -25, -26, -7, 7, 14, 14, 21, -16, 0, -4],\n [11, 17, -24, -15, 3, 4, -4, -26, 14, -7, -21, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[8, -23, 2, -17, 24, 2, 11, -26, 13, -19, 11, -10],\n [-8, 6, -12, 18, 4, -6, -24, -25, 8, 14, -11, 18],\n [24, 23, -6, -15, 1, -15, 6, -7, 13, 22, -6, 25],\n [12, 14, 22, 15, 9, -5, -1, -20, -20, -19, -1, -3],\n [-3, 13, 21, -15, 20, -19, -18, -24, -6, 4, 21, 20],\n [-3, -23, -7, -11, -17, 16, -1, 2, -22, -16, 2, 18],\n [-12, -21, 21, -12, 16, -7, 7, -25, 17, -11, -8, 7],\n [22, -13, -3, 1, 21, 5, 10, -17, 22, 18, 21, -18],\n [-3, 9, 2, 2, 21, -4, 0, 4, 16, -20, 22, 18],\n [-23, -13, 15, 15, -17, 17, 7, -1, -4, -18, 10, -19],\n [26, -13, -20, -20, -18, -24, -13, -10, 23, 17, -5, 19],\n [-1, 1, 18, -13, -18, 24, -1, -25, -16, -10, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[12, -9, -14, -22, 23, -4, -3, 2, 21, 20, -19, -1],\n [-12, -26, 1, 22, 20, 19, -13, 15, 7, 4, -21, 22],\n [-22, 4, 10, -12, -12, 25, 16, -22, 1, 6, -16, 16],\n [-21, -4, 13, -25, -12, -4, -5, -18, 20, 13, 3, -11],\n [19, 20, 25, 3, 18, -18, -26, 11, -19, 25, -9, 0],\n [-9, 5, 22, 5, 26, 21, 18, 9, 9, -6, 19, 5],\n [4, 10, -11, 19, 19, -13, -3, -2, 19, 24, 8, -10],\n [19, 15, 18, -23, -16, 20, -12, 3, -3, -25, 16, 7],\n [-4, 4, 10, -14, 6, -20, 5, -20, 15, 11, 25, 17],\n [-14, -3, 1, 5, 16, -9, 7, 21, 7, 24, 11, -26],\n [16, 23, 15, 4, 23, -26, 24, -11, 12, -12, 6, -4],\n [26, 14, 7, -10, -2, 15, -21, 4, -22, 13, 13, 3]]\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 sum of all singular values:\n[[-22, -15, -20, 18, -14, 22, -23, 23, 15, -24, -15, -26],\n [0, 16, 23, -14, -10, -19, 5, -7, 24, -10, 7, 8],\n [8, 11, 15, -3, -9, 23, 19, 21, 12, 6, 22, -4],\n [-2, 10, 0, -26, -6, 22, -17, 4, 17, -2, -7, -25],\n [21, -12, 1, -14, 23, 25, -13, 23, -25, 7, 8, 10],\n [-2, 21, -12, -15, -18, 4, -13, 2, 26, 21, 16, 11],\n [15, -19, 21, -24, -25, -11, -8, 3, 14, -11, 4, 1],\n [-23, -17, 24, 18, -9, 20, 5, 3, 9, -18, 9, 2],\n [-11, 1, -6, 20, -25, 19, 8, 1, 9, 4, 6, -4],\n [14, -10, 19, 22, -26, 15, -4, 21, 0, -2, 5, -8],\n [-3, -24, -15, 8, -12, -10, 23, 5, -20, -8, -20, -22],\n [13, -6, 21, 21, 24, 20, -20, 10, -4, -16, -17, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[14, 6, -7, 6, 13, 8, 7, 9, 0, -8, 16, -22],\n [2, -17, 13, -14, 2, -22, -15, -14, -5, 13, -12, -14],\n [-26, 11, 16, 18, 26, 25, -26, -16, 16, 13, -5, 8],\n [24, 17, -21, 1, 4, -19, -22, 15, 21, 17, -10, 11],\n [-18, -17, -7, -13, -13, -1, 2, 22, 0, -2, -11, 9],\n [7, -11, 6, -24, -4, -16, 21, -9, 20, 14, 17, 2],\n [23, -22, -3, 2, 2, -1, 13, -24, -25, -2, -8, 13],\n [-25, -8, -26, 0, 18, 25, 22, 8, 14, -22, 11, -23],\n [-10, 26, -6, 26, 21, 4, 21, -5, -16, 7, 22, -12],\n [23, -17, 11, 5, 26, 21, 4, 10, 17, 1, 4, -21],\n [-13, -4, -11, -2, 12, -25, 11, 14, 12, 7, 24, 13],\n [16, -2, 9, -11, -9, -14, 10, 0, 7, -16, -26, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "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, -22, -9, -13, -14, 5, -20, -19, 23, -20, 25, 22],\n [-11, 16, 4, 24, 0, 6, 26, 2, -19, 6, 14, -8],\n [-6, 14, -6, -2, 15, -4, -16, 6, -7, -2, -1, 13],\n [25, -15, 5, 6, -17, -23, -12, 24, -21, 0, -22, -22],\n [-9, 1, 8, -5, 7, -23, -9, 14, 24, -1, 15, -5],\n [20, 6, 16, -13, 4, -17, 24, -3, -6, 21, -19, 5],\n [4, 7, -4, -2, -20, -8, -20, 20, -19, -13, -26, -14],\n [-24, 26, 1, 11, 24, -12, 9, 26, -24, -23, -22, 23],\n [-1, -2, -17, -19, -15, -24, 0, 23, -4, 13, 6, -13],\n [-4, 4, -14, -15, 8, -9, -6, 18, 20, 15, -26, 11],\n [14, 15, 20, -18, -4, -13, -16, -20, 4, -3, -1, 3],\n [7, 19, 11, -22, -22, -8, 24, 11, 1, -1, 15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[19, 22, 3, -24, 1, 6, 15, -24, -22, -8, 15, 21],\n [-26, 11, -18, -22, 19, 15, 7, 10, 6, -2, 15, 2],\n [-2, -18, -24, -12, -23, 18, 11, -7, 22, -4, 10, 20],\n [-19, 10, 18, 6, 6, -20, -5, -22, 19, -12, -6, -2],\n [-10, 23, -20, 23, -8, 25, -20, 13, 18, 23, -3, -16],\n [14, -26, 5, 13, 26, 17, -25, -12, -6, -3, 23, -10],\n [20, 25, 25, -18, 8, -7, -8, -9, -7, 3, 13, -26],\n [-3, -3, 20, -8, 3, -1, 15, 17, 11, 2, -14, -23],\n [18, -10, 6, -22, 1, -3, -10, 23, 12, 21, 13, 17],\n [19, 24, -16, -15, -14, -19, -26, -18, 1, -25, -13, -14],\n [21, -25, -23, -15, 21, -17, -24, -23, -21, -4, -22, 23],\n [-24, -17, 16, -8, -13, -6, 16, 1, -6, 9, -3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-10, -5, -8, 18, -17, -16, 11, -25, 6, 16, 4, 21],\n [8, 10, 20, 20, 9, -4, 9, 13, 12, -1, -2, -10],\n [-12, 10, 18, -23, -5, -10, -5, -10, -13, -13, -10, -19],\n [7, -1, 18, 3, -5, -11, 3, -11, 11, -3, 9, 8],\n [-21, -23, -9, -21, -1, 10, 0, 14, -16, 11, -11, -8],\n [16, 26, -12, -1, 14, 4, -8, 24, -3, -18, -4, -23],\n [-17, -18, -8, -12, 24, 7, 15, -8, 22, 25, -6, 7],\n [24, -10, -9, -10, -25, 24, -26, 16, -17, 10, 21, -22],\n [-15, 9, 4, 11, 24, -18, 17, -1, -12, -11, -14, -2],\n [3, 26, -20, 25, -23, 16, 13, 11, 3, -17, 3, 12],\n [-20, 9, 8, -3, 12, 9, 18, -7, 22, 5, 12, 22],\n [-1, -1, 9, 16, 8, 16, 8, -15, 6, 9, -13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[19, 18, 18, -3, -12, 4, -10, -15, -5, -4, -1, -13],\n [-15, 23, -23, 19, 24, -14, -9, 16, 1, 11, 14, 17],\n [-8, 19, 20, 16, 11, 19, -24, -8, -7, -2, -16, -10],\n [22, 8, -13, 12, -8, -24, 7, 22, 14, -5, 11, 0],\n [-6, 14, 4, 0, 10, -25, 20, -18, -8, 15, 9, -17],\n [13, 18, 12, -20, -23, -12, -15, 21, -21, -18, 8, -19],\n [-20, -23, -14, -8, -20, -17, -2, 17, 8, -2, 2, -15],\n [24, 20, 13, -15, 25, -21, -17, -25, 18, -2, -20, 13],\n [-4, 21, -16, 9, 22, 21, 24, -4, 16, -20, 0, -14],\n [24, -10, 5, -1, -5, -14, -15, -20, -26, 6, 25, -13],\n [20, 16, 14, -10, -23, 25, 24, 12, -26, 14, 18, -3],\n [7, 7, -3, -12, -10, -14, -20, -18, 17, 8, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "557", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[12, -4, -1, -26, -13, 5, 24, 21, -17, -26, -22, -24],\n [22, 23, 26, 0, 24, -5, -9, -11, -25, 20, -14, 18],\n [-11, -19, 16, -19, -17, 6, 4, -15, -18, 10, -18, 21],\n [-9, 3, 5, 13, -4, -16, -7, -8, 9, 25, -1, -17],\n [-3, -14, 25, 19, 26, 7, 2, 9, -20, 24, 3, -10],\n [21, -14, -3, 4, 0, 23, -6, 17, -26, -12, -24, -21],\n [-13, 11, 6, 25, 11, -19, -1, -12, -13, 21, -7, 21],\n [-8, 6, 9, -3, -17, 25, 23, 7, 9, 20, 9, -11],\n [-12, -9, -20, 20, -5, 5, 16, -8, 13, -26, 8, -22],\n [23, -15, -15, -6, -8, -18, 16, 22, 21, 9, 15, 20],\n [24, 5, 8, 4, 26, 5, 10, 5, 16, 10, 12, 11],\n [3, 5, 18, -25, 24, -16, -7, 10, -18, 11, 22, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "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, -20, -22, 20, 15, -3, 21, 14, -20, -16, -18, 22],\n [3, 14, -24, -5, 13, 24, -7, 5, 21, -20, -20, -7],\n [-2, 18, 8, 17, -3, 13, -14, 25, 21, 12, -23, -15],\n [-10, -26, -10, -25, -21, 17, -16, 26, 16, -9, 13, -2],\n [12, 1, 19, -11, -15, 14, 25, 2, -4, -6, -11, 26],\n [24, 21, 14, 18, -1, 10, -5, 24, -17, -20, -18, -2],\n [19, -12, -14, 15, 19, -1, -6, -4, 17, 1, 24, 11],\n [-15, -3, -14, 13, 21, -25, 12, -15, 12, 24, -13, 3],\n [14, 23, 16, 21, -8, 4, 16, 23, 16, -2, -23, 23],\n [24, -14, 9, 15, 10, -24, -11, -1, 13, 12, -8, 19],\n [-12, 5, 22, -6, -26, -21, 0, -4, 20, 4, -15, -6],\n [25, -25, -22, -18, -7, 19, -9, -5, -19, 7, -18, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"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, 0, -11, -6, -22, 2, 20, 10, 16, -5, -13],\n [-8, 8, -3, 15, -21, -24, 7, 18, 23, -25, -12, 10],\n [-12, 5, -6, -10, 7, 5, 23, 20, 25, -4, 8, 10],\n [16, 14, 10, 6, -2, 19, 10, 13, -6, 19, 21, 11],\n [13, 7, -8, 0, -18, -22, -22, -2, -1, -8, 3, 9],\n [21, 21, -11, -20, -9, -6, 4, -26, -24, 4, -2, 26],\n [-19, -26, -20, -20, -19, -8, -10, -16, 20, 14, 22, -16],\n [11, 14, 23, 25, -25, -23, 23, 1, 6, -16, -24, 13],\n [-22, 25, -6, -5, 10, -16, 17, -5, 14, 26, -14, 25],\n [-24, -14, 1, -16, -16, -6, 25, -6, -20, -10, 21, -13],\n [6, -16, -14, -26, 7, -18, -14, 10, 3, 14, 18, 10],\n [20, -20, -13, 21, -21, 7, -11, 24, 10, 9, 19, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "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, -3, -24, -23, 5, -26, 7, 18, -18, -15, -17, -17],\n [23, 17, 21, -4, -21, -3, -3, -6, 15, 4, 20, 14],\n [3, 7, -9, -15, 8, -20, 14, 13, -2, -21, -26, 19],\n [-11, 21, -23, 2, 11, 20, 1, -5, -19, 5, 6, -14],\n [0, -9, -9, -14, -5, -13, -16, 12, 23, 26, -5, 9],\n [-10, 24, 5, -13, 15, 2, -21, 23, -23, -16, 18, 13],\n [-17, 1, -16, 8, -12, -19, -7, 23, -6, -26, 2, -3],\n [3, 13, 8, 6, -7, -11, -18, 4, -10, 4, 21, -4],\n [-21, 3, -20, 21, 13, 15, 19, -16, 7, -15, 25, 25],\n [18, 20, 0, -15, -14, -19, -11, 2, 8, 2, 4, -14],\n [-15, 24, -25, 6, -19, 14, 13, 26, 22, 14, 5, 11],\n [1, -12, -4, -3, -14, -6, -15, -14, 12, -4, 23, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"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, 1, -13, -10, -3, 26, 7, 24, 21, -5, -17, -19],\n [-6, 10, -20, -1, -14, -11, 3, 4, -22, 5, -11, 20],\n [-18, -5, 17, 13, 18, 10, -13, -11, 16, -7, 17, -12],\n [17, -1, -18, -26, 8, 17, -7, 18, -21, 15, -17, 21],\n [6, -11, 9, -21, -8, 4, -25, -9, 15, 1, -23, -26],\n [20, 15, 23, -11, 18, 20, -25, 25, 9, -26, 12, -4],\n [-1, -16, 15, -26, -16, -3, -17, -13, -13, -20, -4, 16],\n [-5, 9, 0, -25, 12, 24, 19, -8, -20, -15, -24, 20],\n [-22, -19, -13, 9, -20, -20, 23, 19, 5, -19, -15, -17],\n [-13, -18, 11, 3, -22, -26, -26, -7, 22, -16, -1, 17],\n [-24, -21, 16, 18, -16, -19, 2, -17, 7, -3, 19, 21],\n [-10, 5, -16, 7, -3, -22, 2, 21, 21, 7, -11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[10, -19, 2, 25, 19, -2, 15, -4, 7, -24, 3, 23],\n [26, 7, 5, 26, 2, -18, -25, 12, -20, 19, -22, -19],\n [5, -9, 11, 19, -9, 22, 14, 18, -11, -6, -17, 15],\n [-23, 17, -19, 20, 26, -8, 20, 13, 13, 24, -18, 3],\n [-10, 13, 17, -12, -23, -21, -11, -1, 10, -4, -14, 20],\n [-10, 0, 25, -5, 10, -8, 12, 8, -14, -13, 21, 4],\n [18, -25, 19, 25, 12, 10, -13, -18, -17, -20, 1, 19],\n [-2, 19, 1, -25, -10, 25, -23, -14, -9, -24, 24, 10],\n [6, 14, -3, -19, 8, -25, 6, -15, -5, -14, -17, -10],\n [16, -22, -18, -14, 25, -4, 3, 16, -23, -6, 16, -18],\n [-20, -11, -4, -4, 4, -22, -21, 24, -26, 21, 1, -9],\n [-3, -14, 6, -17, -20, 10, 5, 18, -5, -11, -3, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-13, -16, -8, -4, 7, 13, -14, 12, 17, 1, 13, -11],\n [23, 24, 1, -23, 1, -15, -11, 26, 22, 9, -7, -1],\n [-1, -5, -18, -22, -10, 22, 7, -25, 26, -20, 9, -14],\n [-7, 3, 3, -16, 4, -24, -25, 21, -24, -12, -10, 21],\n [25, -20, 21, -22, 7, 6, 18, -11, 10, -24, 20, 21],\n [16, 24, 23, -6, 14, -19, -5, 24, -22, -10, 10, -13],\n [12, 14, 1, 4, -10, 8, 13, -5, 18, 21, 26, 2],\n [-17, -9, 8, 17, -11, 23, 22, -20, 3, -8, -4, -19],\n [-10, -6, -1, 1, 12, 6, 13, -8, 2, -7, -7, -17],\n [-15, 6, -2, -2, 26, -23, -23, -18, -12, -1, -12, -1],\n [1, -20, 5, -15, 8, 25, 5, -18, -13, -14, 17, 6],\n [5, -8, 3, -11, -15, -17, -25, -9, -14, 2, -3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-15, 2, -5, 9, -26, 16, 13, 7, 7, 21, 6, -23],\n [11, 3, 26, 25, 19, -7, -1, -12, -20, -20, 23, 2],\n [-4, 7, -7, -12, 6, 26, -10, -7, -14, 17, -3, 20],\n [10, -20, -19, -4, -13, -23, -6, 19, -17, -5, 3, 3],\n [-11, -16, -5, 2, -2, -13, -13, -25, -14, -24, 3, -9],\n [9, -6, 26, -8, -11, 1, -23, 24, -12, -26, 21, 20],\n [-11, -7, 6, -10, -22, -22, 12, -14, 17, 9, 3, -23],\n [-4, -6, -6, -21, -3, 20, 26, 4, -8, 11, -15, -13],\n [23, -15, -12, -8, 1, 13, 14, -22, -22, -21, -4, -24],\n [10, 6, 16, -6, -7, -26, 12, 20, -10, 2, -19, -1],\n [1, 7, -1, -14, 17, 10, -14, 11, -2, 20, -4, -5],\n [-6, 3, -16, -23, 6, 20, -15, -18, 5, -16, 10, -3]]\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[[-20, -19, 6, -2, -26, -24, 13, 1, 16, 6, 19, -26],\n [11, 26, 0, 11, 8, -17, -15, -17, 7, -3, 1, -5],\n [18, -11, -14, 9, 9, 16, -4, -13, 5, -24, 0, -8],\n [-5, -26, -22, 22, 6, 24, -8, 9, 24, -21, -12, 9],\n [6, -3, 0, 22, -16, 22, -4, 6, 14, 19, 20, 2],\n [4, -26, 7, -9, -9, -21, 25, 13, -26, 20, 15, 3],\n [-23, 5, -17, 16, -22, -18, -22, -16, 8, 0, -23, -17],\n [12, 6, 11, -19, 22, -3, 12, 6, 14, 16, -8, -25],\n [-16, 8, -10, 15, -24, -5, 8, -6, -2, 12, -25, -26],\n [-20, -7, 16, -21, 9, 24, -6, 24, 19, 8, 9, -19],\n [23, -23, 16, -11, -24, -20, -25, -26, -26, 11, 24, -20],\n [-3, -22, -6, 1, -9, -3, 5, 18, 6, -17, -18, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, 6, -20, -23, 1, -4, 26, 5, 17, -11, 19, -17],\n [-13, 12, 9, 7, -3, -9, -11, 14, 10, 14, -2, -19],\n [-3, -7, 21, 3, -7, -9, -23, 21, 9, -21, -24, -9],\n [20, 13, -9, -4, 8, -21, -1, -6, -3, -12, 0, 5],\n [-15, -22, -20, -5, 0, -12, 12, 18, 8, -1, -4, -14],\n [-1, -24, 2, -25, 1, -4, 9, 22, -21, -16, 11, 7],\n [-10, -24, 17, 19, 7, -5, 2, 2, -22, -17, -17, 26],\n [-18, -6, -14, -17, 11, -16, -23, 19, 4, 22, 25, 7],\n [15, 8, 12, 12, 6, -19, 5, 6, -19, 19, -13, 7],\n [-19, 24, 15, -20, -14, -6, 20, 5, -16, -13, -16, -25],\n [7, 17, 20, -10, -13, -2, 21, 0, -19, -10, -22, -15],\n [11, -9, -1, 4, 10, -21, 14, -12, 15, 22, -1, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "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, 14, 20, -13, -26, -10, 6, 2, 26, 18, 4, -19],\n [3, -14, -11, -25, 18, -9, 8, 18, -8, -14, 24, -23],\n [-8, 23, -2, 11, 24, 4, 9, -23, 12, -20, -11, 21],\n [-22, 20, -4, 9, 5, -3, -2, 18, 1, -8, -20, 17],\n [14, -10, -25, -11, 12, -9, 12, -26, -24, -6, 3, -16],\n [-5, 20, -2, -24, 3, -3, 18, 9, -4, -19, -23, 23],\n [12, 16, 4, 2, 9, -14, 14, -18, -6, 24, -24, -2],\n [-2, -15, 2, -16, 25, -16, 22, -1, 26, -13, -11, -17],\n [4, 4, 9, -17, -1, -7, 17, -18, -12, -18, -20, -1],\n [-3, -15, -7, -13, -5, -11, 2, 5, -8, 8, 16, 5],\n [26, -7, 24, 13, -7, -19, 8, 15, -14, 14, -21, 20],\n [-11, -22, 26, 18, 24, 7, -21, 6, -12, -12, -13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-22, 25, -1, 21, -10, 16, 20, 25, -11, 8, 11, 26],\n [-4, -14, 6, 2, 26, 19, 7, 7, 0, -12, 23, -18],\n [-1, -24, 9, 20, -22, -7, -7, -22, -17, -11, -2, 17],\n [-2, 3, -13, -5, 16, 1, 3, -8, 11, 15, -7, 8],\n [-5, -12, -16, 7, -3, -21, -10, 1, 23, 4, 9, -18],\n [-17, -6, 7, 4, 2, 16, 16, -16, 6, 19, -26, -6],\n [-4, -18, -26, -6, -5, -23, -26, 24, -17, -12, 25, 9],\n [2, 25, 19, -22, 2, 20, 20, 0, -2, -11, -11, 9],\n [-2, 14, -26, -22, 14, -7, -22, 9, 2, 21, 7, 21],\n [-9, -25, -11, 2, 6, -11, 8, 20, 16, 15, -10, -23],\n [22, -23, 24, -2, 6, -13, -3, -16, -2, 1, -20, 22],\n [9, -17, 22, 9, 4, -8, -9, 22, -21, 1, -20, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "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, 14, 23, 7, -2, -10, 26, 6, -4, -18, -21, -25],\n [11, -18, -24, -11, -2, -3, 20, 2, 17, 13, -1, 11],\n [8, -4, -23, 15, -13, 26, 20, 12, -20, -19, 15, 24],\n [-8, -25, 20, -26, 15, 11, -14, 15, 17, -3, 5, 3],\n [-21, 11, 6, 17, -4, -17, 19, -12, -4, 9, -26, -19],\n [-24, -13, -10, 7, 20, -21, -22, 19, 24, 14, 13, 2],\n [8, -9, 13, 21, 3, -12, 26, -12, -11, 6, -17, -8],\n [10, 23, -24, 9, -23, -16, 14, 6, 1, 5, -11, -18],\n [-16, -21, 22, 0, -15, -5, 13, 21, 10, -6, 6, -10],\n [2, 26, 13, -17, -9, 20, 25, -14, 0, -17, 5, 14],\n [18, -24, -5, 0, -24, 6, -25, -16, 19, -17, 12, 6],\n [-20, -12, -1, -16, 11, 0, 12, -20, -26, -17, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[3, 3, -19, -3, -8, -24, -12, 9, -21, 15, 23, 21],\n [-9, 11, -8, 22, 23, 3, -14, 12, 25, -15, 7, -15],\n [17, -3, -23, 9, 23, 21, -13, -10, 22, -24, 11, -4],\n [-14, -18, -6, 14, -19, -10, -11, -11, 1, 24, -11, 19],\n [25, 19, -13, 19, 17, 11, -7, 18, 21, 14, 7, 2],\n [-24, -17, -7, -25, 0, 5, -17, 13, -10, 6, -21, 12],\n [20, -9, -18, -19, -2, 4, 15, -23, -7, 1, 13, -26],\n [13, 17, -4, 20, -14, -11, -1, 4, 23, -26, -10, -11],\n [10, 25, 26, -17, 11, 17, 4, -17, 22, 7, 24, 25],\n [-21, 1, 1, -14, 14, -15, 23, 13, 23, -25, -19, 15],\n [-18, 23, -19, 24, -24, -18, -14, -18, 4, -2, 25, 17],\n [18, -19, 20, 4, 18, 26, 18, 4, -10, 20, -8, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "576", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[19, 3, -17, 22, 2, 13, -9, -15, 22, -4, -16, -18],\n [-3, -2, -2, 20, -18, -15, -16, 22, 11, 1, -19, -17],\n [-2, 20, 9, 23, 16, -18, 14, -19, -24, 26, -9, 19],\n [8, -10, 9, 26, 1, 23, -12, -8, -5, -21, 20, -20],\n [17, 21, -18, -7, 10, -16, -25, -5, 21, 9, -22, -20],\n [-21, -5, -17, 19, 13, 19, 19, -7, 1, -4, 8, -26],\n [2, -18, -18, -5, -25, -11, 13, -21, -14, 6, -8, -12],\n [6, -17, -26, -15, 16, 2, -10, -23, 2, -20, 17, -14],\n [-22, -21, 7, 26, -20, 19, 1, 19, -17, -23, -24, -2],\n [-4, 0, -13, 11, 5, -4, 20, 13, 10, -24, 8, -14],\n [7, -3, -26, -15, -19, -8, -18, 1, -13, 0, -9, 15],\n [14, -21, 6, 10, 15, -2, -14, -4, 9, 6, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[9, -10, -17, -4, 17, -25, 8, -13, 20, 18, 14, -25],\n [-8, -11, 16, 17, -2, -26, -25, 21, 0, -25, 3, 24],\n [-17, -8, 15, -11, -14, 21, 23, -19, 23, 4, 18, -2],\n [12, -6, 23, 11, 14, 2, -21, -9, 22, 17, 8, 0],\n [-22, -20, -17, -17, 24, 1, 9, -17, 23, 8, 26, 8],\n [10, 21, -7, -14, -16, 18, -8, 1, 11, 18, -23, 10],\n [-8, 10, 26, -13, 4, 1, 9, 17, 11, -8, 15, -26],\n [-4, 1, 21, -23, 14, -9, 22, 20, 24, 12, -2, -9],\n [-21, -8, 26, -15, -2, 8, -26, -22, -26, -19, 12, 20],\n [16, -9, 19, -18, -22, -23, 17, 2, -26, 3, 18, -26],\n [-24, -5, -19, -9, -2, 21, 25, -7, 4, 3, -11, -25],\n [-10, -17, -20, 15, 24, 25, -18, -10, -18, -18, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[12, -16, -19, -2, 19, -25, -17, 26, -3, 21, -11, -8],\n [4, -16, -21, -21, 5, 12, 21, -14, -24, 14, 8, 11],\n [-10, -24, 7, -15, -3, -21, 15, -16, 21, 0, 21, -3],\n [-9, 0, 14, -6, 24, 7, 6, 21, -9, -24, -3, -26],\n [-21, -8, -5, 24, 16, -19, -22, 25, -18, 20, -6, 1],\n [19, -23, -3, -19, 25, -10, 7, -7, -11, -17, 7, 16],\n [-17, 3, 3, 24, -2, 19, 16, 14, -20, 20, -7, -10],\n [-24, 20, 19, 13, 9, -1, -17, 7, -13, -19, 0, -17],\n [23, -12, 10, -5, 18, 23, 4, -25, 18, 4, -13, -17],\n [3, 9, 20, 13, -12, -13, 4, 2, 0, -6, -18, -7],\n [8, -12, -3, 22, -11, 9, -16, -19, -24, -8, 19, 14],\n [-24, 9, -2, 9, -16, 24, -11, -10, 15, -3, -10, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-7, -5, -21, -20, -13, -16, -15, 19, -22, -22, -7, -12],\n [-1, 6, 3, -3, -4, -18, -24, 9, 21, -20, -5, -13],\n [21, 2, 23, -11, 21, 7, -17, -20, -2, 0, -12, 5],\n [1, -18, -20, -11, -1, 8, -10, -4, -19, -25, 4, 25],\n [5, 2, -24, -19, -25, 4, 24, 22, 10, -7, 2, -10],\n [-17, 14, -5, -21, 16, 7, 4, -15, -15, -11, -2, -5],\n [0, -3, -15, 26, -9, 18, 20, -11, -23, -15, 22, 6],\n [-5, -9, 21, 6, 0, 15, -8, 21, -13, -2, 7, -3],\n [11, -4, -22, 17, 9, -3, 9, -22, 12, -21, 18, 9],\n [18, -23, -17, 25, -26, -6, 13, 12, 10, -24, 20, 4],\n [0, -10, -4, -14, 20, 0, 24, -7, 19, 26, -14, 17],\n [-3, 14, -24, 16, -17, -26, 22, -14, -13, 6, -25, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[12, 14, 4, -23, 7, -8, 10, -18, -3, -14, 17, 3],\n [-8, 14, -17, 24, 15, 17, -13, 13, 21, 22, -7, -23],\n [11, 17, 23, 12, -22, 15, 5, -21, -13, -21, -13, -15],\n [0, -1, -15, -19, -17, -11, 25, -1, -19, 14, 18, 2],\n [-7, -10, -8, -10, 12, -26, 25, 2, -13, -10, -14, 2],\n [7, 0, 19, 6, 2, 10, 12, -8, 19, -3, -13, 20],\n [10, -22, 26, -3, 7, 23, 4, 3, -18, 0, 1, 15],\n [-1, -9, 9, -19, -9, -7, 5, 2, 22, 21, -9, -20],\n [-26, 1, 6, 23, -23, -7, 26, 25, 9, 4, 11, 1],\n [-24, -21, 18, -4, -20, 9, -26, -21, -3, 10, 18, 24],\n [9, -3, 11, 18, 2, 10, 18, 5, -2, -17, 8, -2],\n [0, 18, 5, -15, -23, 15, -1, -24, -10, -18, 2, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "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, 14, 26, -7, 14, 7, 24, 1, 21, 8, -11, -6],\n [-14, 8, 15, 5, 23, 11, -21, 23, 11, 11, -14, 19],\n [26, 12, -14, 20, -15, 26, 6, 1, -24, -9, -1, 13],\n [-25, -23, 23, 1, 1, -2, -1, 18, 20, -25, 15, 7],\n [3, -6, 17, 10, 17, -4, 6, -25, 0, 21, -5, 7],\n [-11, -7, -1, -11, -21, 18, 17, -4, 15, 10, -19, -21],\n [10, 25, -5, -21, 5, -10, 11, -10, 10, -4, 22, 22],\n [-14, 5, -5, -20, -5, -6, -21, -13, -11, -24, -18, 20],\n [-6, 23, 3, 3, 15, 15, 5, -4, -24, -26, -24, 10],\n [-20, -24, 9, 22, -24, -23, 4, -25, -13, 10, 4, 26],\n [-25, 4, 20, 16, -5, -17, 25, 3, 6, -8, 19, -2],\n [19, -26, 5, -2, 14, -10, -13, 18, -14, 11, 12, -25]]\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 difference between the largest and smallest singular values:\n[[5, 5, 13, -21, -2, -24, -9, 23, 11, 16, -24, 21],\n [-22, -3, 7, 20, 21, 12, 21, -3, 9, 1, 21, 22],\n [7, -11, 9, -20, -9, -21, 23, 1, 12, 7, 24, 14],\n [2, -23, -13, -22, -2, 12, -19, -12, -8, -16, -7, 9],\n [-9, -13, 11, -2, -11, -9, -26, 13, -26, -26, 24, -6],\n [-2, 0, -17, 23, -15, 1, 22, 5, 6, -19, 15, -1],\n [15, 23, 14, -25, 8, 7, -21, 4, -4, -15, 24, 1],\n [-12, -8, -15, 23, 21, -25, -16, 17, 10, 11, -2, 16],\n [-6, 15, 9, -18, -15, -17, 19, -22, 6, -22, -11, 10],\n [10, 2, -9, 2, -21, 26, -9, 5, 15, 20, 4, -16],\n [-1, 1, 0, -8, 18, 0, -7, -24, -11, 12, 17, 2],\n [-12, 3, 13, 22, -26, 2, 26, 3, 13, 19, 5, -17]]\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[[0, 24, -19, 24, 9, 15, 8, 9, 21, 9, -2, -7],\n [25, 18, 26, -10, -4, -2, 21, 22, 4, -21, 8, 25],\n [-23, 13, -7, 14, -26, 18, -1, 7, -17, -4, 24, 22],\n [-3, -14, 2, 19, 0, 4, 16, -17, 4, 12, -17, -3],\n [6, -13, 8, 18, 7, -10, -6, 5, -24, -12, -19, 5],\n [11, -1, 3, -18, 5, -16, -5, 7, 14, -9, -8, -9],\n [10, -9, -15, -23, 20, 16, 0, 24, -22, -21, -14, -4],\n [15, -2, 19, -23, 25, 5, 17, -12, -1, 15, -16, -18],\n [-16, -25, 18, 0, -1, -19, -6, -6, -19, -26, 11, -14],\n [-18, 1, -21, 20, -4, 21, 9, -10, -18, -15, -5, 24],\n [25, -15, -21, 17, -18, 25, 10, 26, -24, 7, -19, -17],\n [20, 14, 15, 16, -18, -13, 10, 0, 14, 5, -23, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[24, 6, -6, -26, 17, -16, -26, 19, -16, -20, -25, -12],\n [-19, 25, 20, -1, 13, 15, 24, 8, 25, 19, 14, 14],\n [-6, 11, -19, 16, 5, -19, 17, -17, -4, -23, 21, 25],\n [11, 3, 14, -4, -22, -6, -21, 22, -10, -2, -3, -5],\n [-14, -10, -13, 7, -1, -8, -1, -24, -25, 1, -25, -5],\n [-20, -23, 22, 11, 12, -7, -21, -18, 25, 4, -1, 9],\n [-1, 1, -22, 24, -17, -9, -12, 6, -22, 10, 13, -5],\n [-5, -5, 25, -12, -10, 24, 18, 1, -5, -6, 15, -10],\n [-22, -9, -10, -23, -20, -2, 10, 13, 13, 16, -18, -8],\n [24, -18, -4, 4, 5, 25, 4, -10, 21, 12, -5, 8],\n [3, 26, 24, 13, 10, -1, -21, 7, 5, -2, 24, -14],\n [11, 11, -25, -22, -16, -16, -3, -13, 18, 3, 13, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"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, 8, -6, -22, 11, -25, 13, 10, 22, 7, -16, 9],\n [-16, -18, -21, 7, 20, 10, 5, -15, 18, 5, -10, -23],\n [15, 6, 16, 21, 16, -18, 7, 12, 24, 3, 23, -7],\n [12, -4, 14, 17, 8, -4, 21, 12, -4, 10, -4, 12],\n [1, -8, 22, 21, 3, -6, -3, -6, -1, 24, 23, 24],\n [9, -1, 6, 9, -23, -18, -19, -25, 2, -4, -21, 16],\n [9, 19, -6, -5, -18, 7, -1, -26, 9, 17, -22, 14],\n [-5, -23, 21, -25, -11, -11, 26, -5, 16, -26, -12, -3],\n [-23, -9, -10, -20, 23, 18, 25, 25, -17, -26, -25, 22],\n [-5, 5, 2, 8, -10, -15, -3, 3, 17, 3, -7, 15],\n [-20, 15, 23, 11, -20, 22, 3, -15, 22, 4, -9, 19],\n [16, -25, 26, 6, -16, 7, -11, 8, 25, 6, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-19, 24, -1, 6, -1, 10, 3, 4, 6, -16, 26, 14],\n [-22, -25, -14, -9, -1, -2, 17, -13, -22, 15, 25, -25],\n [-23, -15, -16, -23, 16, -18, -17, 0, -21, -12, 15, 4],\n [-5, 26, -21, 6, 2, -6, 25, 3, -6, 9, -5, 19],\n [-7, -5, 25, 13, -16, 20, 4, 24, 13, -14, -9, -5],\n [-10, 11, -2, 5, -12, -14, -1, 23, -16, -14, 6, 23],\n [10, 11, -26, 12, 0, 9, 5, 14, -12, 4, -21, -2],\n [22, 25, -9, -5, 4, 9, -18, 19, -24, 6, 0, 16],\n [-26, 17, -18, -22, -12, 23, -18, 18, 1, -14, -3, 18],\n [-17, 15, -5, 12, -5, 10, 25, 12, -7, -17, -17, -1],\n [-2, 26, 1, -14, -12, -21, 25, -15, -8, 5, -16, 11],\n [6, -25, -12, 9, -22, -12, 16, -17, -10, 7, 25, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-17, 25, 3, -24, 24, 10, -24, 13, -22, 1, 17, -13],\n [12, -16, -19, 10, -19, -15, -12, -8, 21, 19, 1, -20],\n [13, -20, 3, -9, -3, -21, 24, -23, -24, 22, 24, 20],\n [-21, -1, 17, 24, 11, -16, 25, 2, -7, -17, -1, 21],\n [0, 23, -13, 9, -15, 25, -4, -6, -19, 12, -18, -3],\n [4, -2, -10, 15, 2, -24, -6, -19, -13, 12, -11, -9],\n [4, -16, 11, -7, 26, 19, 26, 18, -23, -7, 4, -7],\n [-16, 23, -26, 17, -9, 12, 17, 6, 9, -9, 20, 4],\n [8, 12, 11, -12, 20, -21, -19, 13, -5, -26, -14, -3],\n [-6, 18, 16, -23, -20, -15, -14, 17, -11, -21, -13, 24],\n [21, 4, 9, 10, 14, 8, -17, -10, 24, 15, 3, 17],\n [-20, -9, -8, -12, 12, 17, -5, 12, 15, 3, -7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "559", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[15, -2, -4, -22, 23, 14, 3, 21, 12, 0, 15, 10],\n [-20, -22, -12, 24, 15, -19, -18, -16, -5, 7, 8, -14],\n [-16, 5, 15, -12, 11, -26, 19, 23, -3, 16, 13, -5],\n [-24, -13, -25, 5, 21, 11, 6, 19, 15, -21, 14, 12],\n [-2, 7, -16, 19, 10, 14, -20, 19, 21, -5, 21, 12],\n [-17, -6, -21, 22, -26, 7, -13, 9, 0, -18, -21, 4],\n [-10, 26, 16, 9, -6, 0, 14, 1, -11, 8, 9, 8],\n [18, -8, -6, 6, -4, -21, 5, -5, -24, 8, -11, 15],\n [-2, -10, 12, -14, 1, -16, -17, 12, -3, 11, -3, 6],\n [-10, 17, 9, 8, -21, -11, 18, 1, 14, 5, -1, -16],\n [25, -2, 4, -6, 18, 24, -24, -15, 24, 13, 19, 14],\n [-2, -10, 11, 9, 9, -8, 17, -25, -10, 3, 20, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[8, 25, 9, 6, -26, -9, -23, 20, 0, -2, 1, 26],\n [-5, 15, -2, -10, 17, 25, -15, -11, 10, -11, -10, 4],\n [-12, -14, 13, 0, -6, -25, -19, 15, -20, -17, -23, 16],\n [14, 9, 8, 16, -24, -9, 24, 19, 16, -3, 5, 7],\n [-25, -25, -17, -4, -12, -15, 16, -10, -9, -13, -10, -12],\n [-15, -11, 5, -4, 11, 7, 7, -11, 7, 13, -20, 6],\n [-23, 16, 25, -20, -9, -23, 22, -16, 16, -7, -16, -12],\n [19, -10, 7, 23, 21, -15, 15, 1, 21, 8, -19, 0],\n [-5, -3, -25, 4, -5, -26, -13, -2, 9, 9, 14, -24],\n [-22, -26, -8, 6, 15, 3, -15, -17, 7, -11, 13, 19],\n [2, -12, 21, -16, 17, 7, 9, 3, 8, -18, -9, -8],\n [12, -23, -21, 24, 6, 5, -11, -16, -5, 9, 23, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 4, 2, -22, 11, -2, 7, -15, -5, -18, -7, 2],\n [17, 2, 18, 0, -10, -22, 25, 18, -14, 15, -12, -12],\n [-9, 23, -25, -4, 16, -14, 16, -23, 20, -2, -16, 23],\n [21, 15, -15, -14, -18, 26, 18, 11, -21, 16, 24, 16],\n [-17, -4, -12, 18, -4, 13, 10, 7, -11, 18, 24, 14],\n [20, 5, 11, 13, 19, -22, -10, -5, 12, 14, 21, -9],\n [1, -14, 23, 15, -26, 26, 23, -8, 7, -23, 16, -24],\n [14, -17, 1, 7, 12, 20, -8, 15, 25, 19, 9, 16],\n [-24, -4, -10, -20, -1, 16, -9, 19, 19, -21, 4, 2],\n [-18, 8, -10, -15, 9, 25, 21, -3, -17, 3, 2, 12],\n [-17, 12, 1, -9, 14, 23, -10, -16, -26, -10, 9, 9],\n [19, -18, 18, 1, 21, 6, -24, 24, -19, 23, -21, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-21, 2, 10, -15, -18, 14, 22, -8, -10, 21, 17, 5],\n [8, -13, 22, -11, -6, -15, -3, 7, -19, 17, -6, 21],\n [-19, 1, -11, -17, 25, -12, -23, -1, -12, 9, 5, 16],\n [11, -23, 14, -18, 8, 1, 10, 20, -18, -25, -24, 26],\n [17, 21, -22, -17, 1, -12, -13, 19, -4, -14, -11, 3],\n [13, -19, -10, 3, -10, 8, -26, 22, -3, 21, 22, -2],\n [-25, -2, -13, 12, 24, 6, -10, 4, -17, -21, 12, -2],\n [11, 10, 3, 7, -9, -3, 22, 0, 0, 12, -6, -8],\n [12, -4, 12, 21, 17, 20, -12, 16, -25, 8, 24, -7],\n [1, -12, -11, 6, 20, -15, 12, 12, 16, -7, 2, 16],\n [22, -24, 21, -22, -25, -4, -1, -1, -20, -17, -22, 20],\n [-15, 5, 15, 4, -5, -10, -7, -7, 16, -19, 20, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"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, -4, 11, 26, 1, -14, 2, -19, -16, 20, 18, -9],\n [23, -2, 22, -5, 18, 8, 2, -6, -20, -15, 9, -3],\n [5, 0, 5, 5, 5, -1, -16, 19, -9, 12, -22, -11],\n [-16, 8, 21, -16, 15, -4, 7, 21, -10, -17, -9, 17],\n [-19, -1, -24, 25, -3, -24, 11, -25, 8, -10, -18, 9],\n [-5, 4, 7, -3, -18, 19, 16, -25, -6, 7, 0, 10],\n [-20, -5, -23, -13, 7, -4, 17, 15, -2, -26, 24, 21],\n [-12, 5, -13, 14, -6, 20, -20, 9, -6, 23, 13, -15],\n [-12, -12, -10, 7, 17, 8, 12, 11, -13, -22, 3, -23],\n [-12, 12, 8, 18, -17, -25, 17, -3, 1, -5, 17, 5],\n [4, -8, 24, -6, -24, -21, 5, -25, -3, 18, 0, -18],\n [-14, -13, 24, -16, -13, -11, -17, -7, -11, 7, -11, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[26, 1, -9, -1, 11, -20, 18, 7, 20, 22, 18, -20],\n [6, 8, 25, 23, 12, -6, 22, 1, 5, 17, -11, -17],\n [-4, 21, 25, 23, -12, 16, 23, -21, 6, 12, -15, 25],\n [9, 4, -17, 26, 7, 14, -17, 25, -16, -13, -24, 6],\n [-20, -23, 12, 21, -17, -12, -11, 11, -23, -23, 9, 0],\n [-5, -5, -10, 18, 7, 5, 25, -21, 6, -19, 23, 26],\n [9, -22, -22, 20, -17, 13, -20, -15, 3, -2, 1, 16],\n [-14, 20, 22, -5, -9, 0, -19, -21, -16, 2, 14, -22],\n [-20, -5, 20, 26, -23, 5, -8, 18, 6, -26, 19, 14],\n [17, 23, 14, -19, 5, 3, 19, 1, 14, 25, 5, -2],\n [7, 6, -14, -2, 15, 13, 12, 17, 22, 17, 21, -17],\n [4, 17, -16, -2, 19, 25, 18, 7, -7, -20, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "557", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 25, -15, -22, -15, 2, 8, -7, 10, -26, -11, 3],\n [-18, 15, -17, -14, 21, -7, 2, -23, 19, 22, 1, 10],\n [-14, -24, 10, 21, -8, 1, -8, -10, -9, -9, -4, 13],\n [23, -18, 2, 24, 15, 2, -25, -10, 18, 4, 1, 16],\n [21, 25, 12, 3, 8, 21, 24, -7, -11, 7, -13, -1],\n [-7, 15, 24, -3, 16, -9, 16, -18, -8, -7, 15, 3],\n [-1, 4, 8, -24, 13, 2, -21, 25, -26, 25, -3, 11],\n [7, 24, -20, -16, -16, 9, -7, -11, -22, -3, 3, 3],\n [12, 21, 20, 10, 6, -7, -5, 14, -6, 10, 0, 11],\n [8, 11, 13, -21, 5, -11, 1, -11, 0, 26, -24, 22],\n [-6, 11, 11, 3, -5, -8, 4, -7, 20, -8, -25, 13],\n [12, 0, -19, 18, 0, -12, -15, 20, -13, -20, -10, -1]]\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[[10, -7, -17, -8, -9, 3, 3, -2, -3, -17, -25, 11],\n [5, 8, 24, 10, -20, -20, 0, -17, 6, 16, -20, -21],\n [-21, -14, 21, -14, -25, -8, 24, -8, 23, 11, -25, 24],\n [-1, -21, -7, -4, -12, -21, 1, 8, -16, -19, 23, 22],\n [24, 24, -3, -6, 22, 9, -20, -22, 2, -11, -21, -13],\n [25, -25, -2, 4, 23, 23, -14, -9, -10, 18, 1, -15],\n [8, -5, 12, -26, 10, -6, -26, -23, 5, -26, -14, 19],\n [20, -10, -15, -20, 24, -24, 23, -1, 4, 9, -1, -24],\n [17, 1, 17, -10, 11, 20, 3, -25, -19, -13, 10, 8],\n [15, 12, -16, -12, -25, 10, 16, 5, 13, -14, 16, -10],\n [-12, 6, 24, -11, 24, -14, -5, -4, 9, 16, 23, 23],\n [-17, -10, 3, -14, 3, 19, 3, -20, -17, 8, -25, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-8, 12, 10, -24, -2, 7, -5, 11, -13, 12, -25, 5],\n [16, 26, -24, 14, -19, -1, 5, -16, 23, -26, -12, -23],\n [-23, 1, -17, -16, 23, -4, 20, -24, 12, 12, -10, -5],\n [25, 0, -11, -11, 13, -24, 25, 20, 6, 15, -25, 12],\n [19, 21, 0, -12, -20, 18, 15, -18, 14, -21, -15, 3],\n [-7, -7, 19, 0, -7, -20, 13, 13, 3, -19, -25, -13],\n [-17, 23, -9, -9, -11, 25, -22, 25, 4, 10, -7, -4],\n [5, 15, -10, -14, 22, 23, -14, -10, -12, -1, 17, 1],\n [15, 18, 3, 16, 8, -5, -17, -16, 11, 6, -21, 10],\n [-20, 17, -15, -20, -25, -26, -4, -2, -9, 17, -20, 24],\n [-24, 2, -17, 16, -22, 7, -19, -13, 13, -21, -26, 6],\n [13, -16, 23, -3, -17, 17, 25, -4, -11, 10, -11, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[4, -21, 3, 10, -26, 24, 15, -2, 19, -6, 8, 11],\n [-22, 22, 23, -15, -22, -18, 17, 25, -18, 8, -26, 20],\n [-17, 19, 12, 9, 10, 25, 21, 8, -10, -14, -21, 10],\n [21, 5, -16, -10, -22, -21, -17, 26, 6, 3, -6, 15],\n [-10, 0, -24, 2, -25, 2, 22, 9, 7, 10, 15, -26],\n [-1, -26, -23, 12, -13, 19, -9, 7, -26, 26, -5, -11],\n [-5, 23, -11, 1, 1, -5, -21, -2, 15, -25, -20, 26],\n [-10, 8, -7, 17, -25, -20, 5, 22, -8, -15, -18, 0],\n [-13, -25, -6, -23, 24, -6, 21, -5, 22, -25, -10, -8],\n [13, -3, -7, 11, -15, -2, -4, 23, 7, 5, 24, -3],\n [15, -2, -24, -2, 1, -15, -1, 21, 17, -19, -22, -16],\n [15, 8, 0, 14, 17, 11, -8, 21, 26, 5, 19, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "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, -9, -17, 5, -9, -15, 24, -19, 6, 19, 11, -13],\n [-25, -18, 17, -22, 7, -8, -20, 12, 15, -10, -1, 19],\n [0, 16, 1, -7, -21, -19, 5, -8, 5, -8, -3, -3],\n [-10, -9, -15, 14, -4, 21, -9, -11, -11, 9, -4, -5],\n [12, 6, -3, -7, 6, 4, 13, -19, -17, -26, -6, -2],\n [5, 26, 19, 19, -17, 24, 21, -18, -7, 21, -7, 13],\n [-20, -16, -6, 11, 20, -8, 19, -12, -21, -17, 19, -11],\n [18, -16, 8, -19, 1, -24, -25, 26, -13, 25, 2, 26],\n [20, -24, -26, -12, -7, -5, 7, 23, 6, -18, -24, -25],\n [-23, -11, 6, -18, 13, 11, 25, -9, -11, -19, -4, 9],\n [-24, -12, 11, 6, -9, -4, 16, -24, 3, 18, -10, 23],\n [5, 19, -20, 12, -13, -12, 17, -15, -19, -11, 14, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[19, -3, 2, -11, -22, -22, 25, 3, 26, 23, 23, -22],\n [16, -14, 8, 22, -2, 23, -13, 17, 19, -1, -9, -7],\n [7, -20, 20, -17, -12, -10, -16, 7, 0, -6, 4, 23],\n [-23, 14, 22, -10, 22, 21, -7, -2, 13, -4, -12, 6],\n [-8, -12, 14, -22, -11, 18, 21, 5, -5, 16, 5, -14],\n [11, -1, 25, -10, -22, 22, 6, 0, -22, 10, -20, 21],\n [-9, 4, -21, -25, -14, 15, 26, 25, -16, -1, -6, -25],\n [13, 24, -7, -10, -11, 15, -22, -13, -3, 24, -23, 25],\n [21, -3, 20, -18, -24, -18, -9, 9, -8, -3, -23, -18],\n [6, -26, 25, 24, 8, -17, -15, -9, -13, -17, -17, -9],\n [-3, -26, 3, -12, -19, 8, -9, 14, -11, -6, -12, -22],\n [18, 25, -20, 21, -20, 0, -2, -5, 21, -14, -10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[17, -14, -1, -18, -22, 12, 6, -23, 1, -1, -23, -11],\n [10, -5, 9, 11, 8, -2, -19, -10, -9, 23, -15, 6],\n [-4, -15, -16, -14, 8, 0, -2, 13, -24, 22, -2, 18],\n [-17, -10, -24, 18, -5, 11, -13, 0, 15, -7, 21, -9],\n [-14, 15, -21, -17, 10, 2, -21, 12, -16, 21, -2, 17],\n [17, 3, -7, 10, -11, 4, 2, -21, 2, 5, -18, 10],\n [26, -4, -11, -9, -8, 17, -25, -17, -15, 19, -9, -8],\n [11, 10, 0, 21, -13, 18, 26, 7, -25, 17, 6, -8],\n [0, 21, 3, -20, 0, -6, -20, 21, -2, 11, -9, 6],\n [6, 5, -2, -13, 11, 11, -23, 17, -9, -17, 8, 8],\n [13, -4, -2, -26, -9, -12, -2, 5, 26, -7, -10, -16],\n [-14, -2, -7, -2, 15, 18, 22, 4, 26, -26, 25, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"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, 1, -6, 3, -24, 7, -21, 16, 2, -24, 6, -16],\n [18, -22, 23, 5, 20, -9, 20, -7, 25, 25, 12, 22],\n [13, 1, -14, -1, -11, -2, -17, 2, 19, 11, -7, -1],\n [5, 12, 11, 22, 26, -3, 4, 13, -15, 9, -17, -21],\n [-20, 26, 4, 0, -19, -24, 13, 20, -6, -26, 18, 23],\n [-12, -20, -12, -2, -24, 3, -13, 25, -23, 9, -24, -22],\n [-2, 4, -16, -19, -1, -25, 1, 21, -17, 23, 12, 10],\n [12, -6, 1, 11, 6, -16, 18, 17, -26, 26, 20, 6],\n [-24, -1, -12, 14, -13, -4, -19, 9, -7, 25, -21, 6],\n [1, 23, 11, 3, 19, 16, -10, -18, 1, -20, 19, 1],\n [-10, 13, 21, 17, 17, -22, -22, -13, -21, -20, 26, -10],\n [-18, 4, -5, 18, -18, -11, 9, 7, 18, -14, -8, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "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, -11, 1, -8, 13, -21, -23, 3, 12, 4, 19],\n [0, 18, -6, 10, -18, 8, 15, 20, 25, -6, -10, -3],\n [4, -21, 8, 23, 10, -14, -2, 5, -26, 22, 8, -8],\n [26, 25, -15, 13, 13, 20, 16, -7, 6, 2, -11, -13],\n [-20, -21, -6, 9, -5, 13, -8, -2, -24, 9, 18, 26],\n [7, -16, 21, 15, 20, 0, 15, -25, -21, 19, -25, 15],\n [-10, 13, 21, -13, -17, 18, 6, 15, -15, 5, 22, -3],\n [-13, -22, 24, -22, 20, 5, 18, 22, 6, 19, -23, 3],\n [14, -10, -24, -14, 17, 21, 9, -9, -4, 8, 22, 6],\n [24, 9, -10, 12, 7, -15, -22, 21, 13, 0, 13, -14],\n [-1, -13, 5, -16, 11, -11, -5, 20, -11, -14, -15, -9],\n [2, -9, 19, -25, -25, -24, 2, -19, -16, -15, 5, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-18, -3, 22, -11, -10, 20, 25, -5, -20, -17, 2, 9],\n [-3, 19, -13, -13, -2, 19, -5, 25, 23, 20, -4, 5],\n [-1, 24, 0, 18, -15, -8, -8, 25, 7, 5, 2, -6],\n [8, 15, -22, -15, -20, 14, -25, -2, -17, 11, 17, -21],\n [0, 8, -17, -18, -7, 10, 8, 10, 13, -19, 19, 4],\n [22, 16, -11, 1, -21, 5, 1, -16, 15, -4, 3, -18],\n [1, -3, 1, -3, -12, 12, 23, 6, 20, 7, -5, 2],\n [7, 15, 25, 20, -17, 24, 18, 3, -16, 7, -6, -14],\n [-2, -6, -26, -22, 26, -5, -20, -14, 18, 25, -4, -6],\n [-21, -7, -15, 13, -18, 23, 1, -16, 25, 5, -16, -3],\n [-12, 14, 8, -10, -2, 22, 8, -8, 14, 4, -10, 23],\n [-4, 20, -26, -17, -19, 15, -1, 7, -8, -13, -19, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-26, 21, -2, -3, 20, -7, 3, -22, -24, 5, -10, 15],\n [-22, -16, 11, -23, 12, -8, 12, 19, 22, -4, -10, -14],\n [0, -26, -25, -9, 9, 18, 6, 9, -25, -23, -11, -23],\n [-18, 22, -6, -4, 25, 26, -25, -24, -4, -1, 20, -20],\n [9, 17, 6, 22, 9, -23, -4, -2, 14, -1, 1, 1],\n [-6, -17, 0, 24, 24, -12, -10, 12, 8, -22, -11, -4],\n [12, 21, -18, 6, 8, 13, 23, -3, -3, 23, -3, -8],\n [12, -2, 25, 4, 11, -2, 0, 5, -16, -22, 17, 6],\n [-8, 16, 20, -11, 8, -16, -16, -17, 7, 25, -22, -4],\n [-2, 2, 13, -14, 20, 5, 7, -15, -3, 13, -6, 2],\n [24, -4, 6, -19, 15, -14, -22, 14, -17, -13, -3, -16],\n [19, -24, 2, 26, 21, 25, 3, 22, 10, -20, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-16, 17, -2, -3, -25, 0, -8, 2, 10, -16, -8, 1],\n [12, -6, -1, -5, -21, -16, -13, 9, 13, 14, -25, 16],\n [-7, -5, 12, -23, 2, 19, -3, -26, -3, 3, -15, -8],\n [10, 13, 16, -23, -12, -7, 17, -7, -6, -17, 3, -3],\n [21, 13, 25, 13, 11, -24, 2, -19, 2, -17, -22, -16],\n [-23, 22, 8, 23, 13, -15, -6, -11, -13, -6, 21, 0],\n [9, -26, -26, -5, -12, 25, -7, -24, -13, -18, -8, 13],\n [7, -23, 6, 16, 10, -25, 0, 18, -10, 22, 23, 26],\n [4, 14, -21, 25, 4, -24, 13, -24, 6, 25, -14, -6],\n [10, -11, -6, 21, 17, -14, -23, 4, -18, 21, 6, 10],\n [26, 10, -3, -2, 24, 14, 2, 13, 24, 23, 20, 9],\n [-12, 18, -9, -7, -22, -9, 13, -26, -8, -4, -1, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 7, -8, 21, -9, -25, 0, -21, 12, -21, -21, 4],\n [14, 13, 3, -6, 14, 17, -9, -4, 11, -4, 1, 9],\n [-2, -20, -9, -7, -22, -9, 15, 13, 6, -12, 8, 20],\n [19, -26, -6, -19, -20, 14, 23, 17, 13, 13, 3, 11],\n [8, -25, 19, -19, 11, -23, 10, -6, -14, -18, 18, 2],\n [14, -3, -11, -15, -25, -8, 3, -11, -3, -14, -22, -4],\n [11, 4, 26, -10, 22, 22, -24, -1, -14, 17, 11, -5],\n [-6, 2, 18, 19, 12, -22, -13, -9, -23, 6, 12, -7],\n [-14, 9, 18, -23, 8, -19, 25, 13, 22, 20, 9, -21],\n [-5, -21, 15, 9, -18, -11, 12, 19, 11, 6, -9, -15],\n [0, 20, -26, -12, 20, 0, -11, -6, -26, 2, -24, -15],\n [1, 12, 10, 4, 4, 6, 6, 20, 13, -16, 19, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -14, 24, 17, -8, 9, 1, -23, -24, 11, 10, 16],\n [-2, 14, 8, 2, 14, 2, -15, 8, -7, -10, 26, -15],\n [23, 9, -17, -9, 3, -19, 14, 24, -14, 4, -21, -20],\n [-6, 11, 16, 22, 24, 1, 17, -6, -6, -3, 0, 0],\n [-14, 23, 2, 12, 1, 10, 2, 21, -5, 9, 3, 1],\n [-4, 6, -23, -24, 5, -23, -26, -15, -14, 7, 2, -18],\n [4, -20, -14, -25, 6, 23, -20, -9, 24, -19, -15, 16],\n [3, -18, 1, -23, 12, -10, -16, -25, -4, 23, -5, -1],\n [-15, 5, -18, 16, -22, -1, -20, 2, 6, -3, -2, 4],\n [2, -22, 11, 18, -16, 5, -19, -7, 7, 20, 15, -19],\n [-25, -6, -12, -21, -22, -24, 16, 16, -11, 8, -18, 8],\n [-8, 16, 19, 7, 12, -17, -17, -7, -26, -21, 26, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-25, 11, 6, -24, 9, -14, 8, -12, 18, -5, 16, -23],\n [-10, -22, -6, -3, 4, 13, 26, 3, 15, -20, 22, -20],\n [0, -3, -8, 14, 7, -5, 25, 24, 0, -21, -17, 18],\n [4, -2, -25, -17, -17, -1, -22, -5, -23, 7, -20, 23],\n [-10, -16, 26, 23, -19, 1, 17, 6, 25, -2, -6, -15],\n [-1, 2, 11, 8, 10, 19, 17, 18, 18, 2, 22, -3],\n [-12, -21, 5, 17, 7, 9, -7, 26, -15, 8, 22, 11],\n [-10, 0, -10, -16, 12, -25, 24, -25, 2, 18, -3, -3],\n [-11, 4, 22, 16, -18, 0, 14, -13, 18, -2, 16, 17],\n [-5, 8, 6, 0, 13, -1, -8, 18, 12, 18, -1, -21],\n [-24, -21, 1, -24, -14, -14, -14, -26, 13, 10, 4, 25],\n [-10, -18, 18, -14, 10, -13, -16, -2, 4, -13, -20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[22, 9, 15, 15, 20, 25, 17, 14, -24, 20, 17, -1],\n [20, -1, -26, -12, -16, 10, -20, -15, 25, 11, -24, 15],\n [26, -1, 3, 5, 9, 18, 24, 10, -9, -26, 26, -6],\n [1, 21, -11, 21, 1, -5, -8, 21, -26, 4, 25, 25],\n [15, 7, 19, 13, -21, 1, -24, 4, -11, -10, 17, 0],\n [24, -3, -7, 5, 8, -14, 21, 16, -7, 21, 25, -25],\n [-23, 0, -2, -23, 5, -10, -26, 6, 3, -22, -15, 11],\n [5, 11, -10, 18, 13, 5, -3, -15, 20, 4, -8, 2],\n [-6, -1, 25, 1, -10, -18, -6, 23, 7, -16, -7, 22],\n [26, 23, 20, 12, -11, 2, -26, -9, -5, -19, -20, -2],\n [3, 7, 17, 21, 14, 25, -16, -12, 8, -4, 26, 18],\n [-6, 1, -14, 7, 11, -21, 17, -23, -22, 13, -21, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -24, -4, -19, -8, 26, -16, 23, -17, 1, -7, 17],\n [25, 1, 2, -19, -8, 26, 21, -6, -9, -18, -23, 14],\n [-2, 7, -18, -18, -9, -16, -14, 11, -18, -11, -23, 7],\n [-20, -12, 11, -16, 5, 0, 3, 25, -10, 9, -8, -20],\n [16, 18, -6, 1, -24, -13, -25, 2, -9, 10, 18, 18],\n [-3, 19, -15, 26, 18, 5, -9, -14, -23, -4, -17, -22],\n [23, 13, -13, 7, 1, -19, -11, 4, -20, -24, 2, 9],\n [12, -23, -18, -10, 22, -7, -13, 19, 2, -14, 9, 18],\n [26, -10, 20, 23, 16, -23, -7, -16, 15, -5, 18, -19],\n [1, 18, 14, 3, 6, 6, 20, 9, 0, -7, 6, -2],\n [17, 16, -8, 20, -6, 15, 6, -24, -13, -12, 6, 15],\n [-5, -26, 4, 20, 8, 26, -7, 5, -15, 24, -11, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "516", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-13, -9, 3, 6, 7, 17, 22, 7, 22, 26, -20, -21],\n [-21, -5, -19, 10, -12, -1, 12, -24, -17, -24, 3, 19],\n [-5, -24, -26, 6, -8, 9, 7, 4, 16, -3, -15, -14],\n [-11, -11, 24, 25, 26, -7, 14, 21, 0, 12, -14, -23],\n [5, 18, 13, 7, 12, 16, -10, -3, 2, 19, 1, 18],\n [20, -5, 1, 26, -2, 14, -24, -14, 4, -14, 14, -9],\n [10, 16, 7, -10, 25, -6, 9, 23, 25, 13, -8, -15],\n [1, -16, 21, 10, 1, 8, 17, -12, -11, 18, -20, 20],\n [-24, 4, -15, -19, -2, 17, 23, 8, -15, -6, -1, -25],\n [-13, 19, -23, -10, 20, 21, -22, -3, 22, -20, -4, 20],\n [-10, -15, -16, 24, -16, 7, 20, 10, 23, 2, 26, 26],\n [21, 9, 0, 15, -5, -25, 20, 9, 21, 3, -20, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-24, -10, 14, 5, -19, -4, 11, 3, -12, -17, 11, -12],\n [3, 19, -1, 24, 18, -13, -24, 9, -1, -13, 4, -13],\n [13, -17, -18, 19, 13, 16, 15, -9, 9, 9, -15, 23],\n [13, -24, -9, -20, 4, -26, 4, -14, 2, -24, 2, 8],\n [-12, -6, -8, 1, -23, 18, -14, -12, 24, 21, 12, 5],\n [-24, 3, -7, -25, 23, -2, -16, -26, 21, 22, 21, -17],\n [-10, 3, 8, 23, -8, 19, 26, 7, 5, -15, 16, -10],\n [-21, 24, -14, 12, -5, -16, -20, 18, 18, -6, -26, 3],\n [-8, 24, 20, 19, 2, 8, 26, -7, 9, 12, -26, -4],\n [4, 24, 8, 25, 20, 18, -5, 19, -20, 6, 18, 9],\n [17, -20, 0, -25, -10, -26, 19, 3, -5, 1, 26, 6],\n [-1, 8, -16, -20, 1, -2, 14, 4, -24, 6, 24, 7]]\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 largest singular value:\n[[-6, 10, 22, -8, 10, -6, -13, -17, 26, -20, 2, 13],\n [-19, 12, -14, 19, -8, -16, -25, 22, -21, 2, 14, 24],\n [-22, 14, 3, 12, 9, 0, 23, -9, 25, 22, 9, -11],\n [-22, -18, 7, 7, 9, 4, 25, -7, -10, -7, 1, -6],\n [-8, -24, 3, -22, 15, -21, -24, 22, 15, -3, 17, -26],\n [23, 24, 25, 9, -12, 14, 11, 17, -9, -4, 20, 2],\n [24, 14, -5, -3, 18, 21, -14, 6, 23, -5, 8, -10],\n [-5, -22, -2, -21, 26, -10, 4, -10, 6, 12, 21, 10],\n [21, -23, 16, -13, -14, 0, -3, 0, -19, 26, 25, 20],\n [23, 12, -6, 24, 14, -16, 4, 0, 15, 19, 21, 0],\n [-19, 6, -15, 8, 7, -11, 9, -25, -15, 0, -10, -7],\n [-6, 3, 15, -7, -19, -9, -9, -9, -25, -15, 5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-19, 24, -17, -16, -13, -1, 20, 3, 15, -23, 12, -16],\n [-3, -5, -24, 10, -25, -15, -6, -22, -20, -23, 16, 14],\n [9, -5, 2, -18, -1, -15, 21, -26, -19, 6, 25, 24],\n [-23, -13, 2, -13, -18, -18, -1, 22, 20, 15, -10, 14],\n [-23, 19, -24, 2, -2, -6, -15, -26, -26, 18, 19, 21],\n [-20, -17, -12, 13, -16, 19, 18, -4, -14, 0, 14, -10],\n [23, 24, -14, -15, 2, -6, -7, -7, 4, -19, -3, -16],\n [12, 6, 15, -12, -23, -26, 5, -16, 3, 10, -8, 24],\n [9, 7, -20, 18, -7, 26, -15, 5, -25, -5, 14, 21],\n [13, -3, 23, 4, -23, -3, 16, -10, 13, -8, 13, 11],\n [7, 20, 6, -21, 24, 9, -14, 20, -18, 8, 7, -11],\n [-9, -9, 11, 23, 16, 5, -20, -4, -4, 19, -9, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545", "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, 13, -3, -13, 23, -22, 19, -5, -5, -17, -1, -12],\n [11, 14, 15, 22, -26, -13, 9, 4, 1, 7, 8, 12],\n [-4, 19, 17, -8, -9, -12, -26, -2, -1, 8, -12, -23],\n [-12, 15, 11, 18, 12, -26, -5, -16, 19, 11, 10, 24],\n [-1, 24, 0, -14, -20, -19, 19, 24, 24, -4, -1, 17],\n [0, -18, 19, 11, 20, -14, -20, -16, -17, 6, 12, 23],\n [-24, 14, 2, 10, 18, -11, -11, 17, 23, 16, 22, -20],\n [-12, 11, -21, -9, -8, 25, 24, -25, -24, 19, -2, 9],\n [22, 1, 11, 1, 5, 24, 14, 9, 12, 9, 16, -4],\n [-25, -17, -21, -19, -12, 18, 2, 1, -5, 7, -7, 6],\n [-12, -20, -3, -1, 23, -17, -12, 10, -3, -16, 13, -6],\n [13, 11, -12, -12, 10, 18, -13, 16, 25, -6, 17, -7]]\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 largest singular value:\n[[6, -24, 13, -4, 17, 20, -4, 0, 8, -2, 5, -5],\n [-19, 24, 25, 11, -9, 1, 1, -16, -15, -25, 10, -23],\n [14, 18, 18, 20, 7, -4, -14, -20, 5, -4, 22, -19],\n [23, 20, 20, 10, 7, 21, 2, 10, -4, 11, 2, 17],\n [-22, 25, 13, -16, -13, 22, 15, -25, 8, 18, 22, 8],\n [15, 1, -19, 5, -23, 18, -20, 12, 21, 0, 10, -10],\n [-17, -23, -4, -13, -22, -25, 19, -3, -9, 0, -3, 2],\n [-16, 21, -9, 21, 26, -23, 6, -13, 17, 15, 5, 24],\n [-23, -7, -6, -24, -2, -23, 20, -16, -11, 9, -21, 4],\n [13, -14, -4, 25, -23, 10, 15, 10, 17, 6, 15, 2],\n [10, -8, 24, -7, 5, 17, -11, -22, 22, 19, -15, 18],\n [-6, -13, 10, -5, 3, -4, -22, 2, 3, -9, 19, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[25, -26, 12, -10, -24, 15, -20, 0, 1, 17, 4, -12],\n [26, 21, -19, -21, 1, -23, 3, 16, -10, 7, -21, 9],\n [8, 12, 12, -11, -25, -19, -12, 0, -11, -26, -17, -20],\n [21, -17, -15, -10, 18, -15, -12, 19, 24, 5, 5, 24],\n [-1, -13, 23, -1, -22, 25, 11, 23, 19, -23, 1, -26],\n [-14, 16, -24, 22, 23, -2, 15, -11, -6, -14, 25, 17],\n [9, -19, 17, -8, 20, -11, -15, -7, -9, -15, 21, -2],\n [25, -16, -5, 25, 19, 7, -14, 19, 11, -15, 12, 9],\n [1, 0, 12, -14, 16, 13, 0, 24, 4, -25, 26, -9],\n [-1, 26, 15, 4, 11, -5, 9, -8, -13, -13, 23, 2],\n [-10, 23, 23, 10, -18, -26, -23, -20, -16, -13, 15, -8],\n [13, -24, -19, 2, 23, 10, 25, 16, -18, -8, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, 21, -2, 18, 11, 21, 23, -10, 17, 6, 12, -13],\n [1, -9, 6, 25, 15, -12, -16, 9, -12, 26, 21, 3],\n [-12, 22, -4, 16, 23, 21, -12, 2, -16, 18, -9, 13],\n [4, -18, -5, -16, -10, 6, -16, 12, -19, 24, -23, 9],\n [-8, -3, 14, 22, -9, 6, 19, 9, -17, -13, -20, -15],\n [-5, 0, 21, 10, -16, 9, -14, 5, -19, -20, 16, 16],\n [-10, -5, 19, 7, -7, 26, -19, -5, 0, 7, -6, -12],\n [-22, 11, -10, -19, -8, -22, -4, -8, -13, -17, 4, -14],\n [-5, 10, 12, -17, 4, 16, 8, -14, 3, 7, 9, 8],\n [20, -23, 26, -23, 20, -21, 1, 3, 0, -22, 17, 12],\n [8, 12, 17, -12, -8, 3, 11, 5, 13, 2, -21, -1],\n [0, 8, 1, -22, 14, 21, -11, 14, -9, -14, 16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "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, -17, -21, -11, -2, 17, -23, 10, 7, -8, 6],\n [-23, 17, 7, -15, 4, -11, -25, 22, -25, 9, -21, -4],\n [12, 20, 25, 17, 10, 19, -11, 16, 17, -8, 22, -3],\n [0, -20, 3, 14, -13, 25, 17, -12, -15, 26, 26, 2],\n [-4, -14, -18, -3, 12, 3, -26, -17, 11, 20, -12, -18],\n [-14, -4, 6, -18, -24, 3, -18, 25, -2, 20, -3, 5],\n [-20, 9, -2, -7, -10, 9, -1, -8, 10, 21, -24, 16],\n [1, -5, 20, -8, 26, 19, -11, -21, 10, 4, 26, 22],\n [21, 7, 4, -16, 9, -21, 0, -20, 22, 5, -19, 6],\n [20, 25, 17, -12, 0, 3, -5, 20, 2, 14, 21, 3],\n [-25, -12, 20, 0, -20, 0, -6, -14, -10, -16, -17, 6],\n [-13, 10, -19, 6, -20, 7, -20, -20, 14, 9, -20, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, 18, 16, 14, -13, 13, 26, -13, -6, 22, 0, 19],\n [-1, 0, -3, -22, 15, 11, 1, 15, 16, 5, -3, -21],\n [-17, 19, 25, -24, -20, 2, 7, -20, -10, -14, -6, 4],\n [-18, 18, 20, -14, -10, -19, -18, -18, 13, 21, 25, 3],\n [-20, -10, 12, 11, -22, -10, 13, -26, -11, -10, 3, 4],\n [8, 18, -19, 21, 3, 12, -6, -12, 7, 0, -25, -17],\n [-22, 0, -23, 20, -14, -10, -6, -4, 6, 23, -12, -13],\n [-18, 17, 10, 3, 2, -4, 7, -20, 26, -18, 23, -23],\n [-25, 0, 6, 5, 17, 18, 19, 10, 0, 1, -24, 9],\n [22, 24, 16, -19, 17, 23, 23, 14, 10, 26, 22, 18],\n [11, -5, -13, -12, 19, -23, -9, -26, -15, 14, 15, 26],\n [23, -10, -8, 9, 21, -20, -18, -19, -2, -20, 15, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, -10, -15, 19, 4, -15, -25, -15, 0, 19, -20, -14],\n [26, 9, -26, 22, 8, 3, 4, -10, -19, -24, -17, 7],\n [-5, -23, 5, 2, 19, -16, 19, -14, -23, -25, 7, 16],\n [-5, -22, -18, -7, -6, -10, -15, 1, -9, -24, -22, 26],\n [25, -13, 21, -1, -8, 14, -10, 12, 15, -23, 15, 8],\n [-3, 14, -14, 6, -12, -12, 4, 16, 1, -17, -20, 6],\n [-20, -22, -1, -11, -19, -5, 7, 13, 1, 19, 9, 20],\n [-20, 25, 13, 16, 1, -25, -18, -21, -26, -24, -17, 10],\n [17, -4, 6, -18, 26, -14, 1, 24, -20, -1, -11, 13],\n [-1, 24, 12, 5, 9, 15, -26, 22, -6, -14, 24, -1],\n [18, -18, 10, -4, -26, -25, 16, 1, 9, 4, 14, -22],\n [10, -2, -19, 7, 12, 22, 5, -16, 20, -2, -24, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[23, 25, 5, 25, 8, 5, 7, 10, 25, -22, 18, 1],\n [1, -19, 0, -11, -9, -2, 21, -26, -19, -6, 7, -3],\n [10, -1, 20, -13, 2, 3, -24, -20, 9, -16, 5, -15],\n [-12, 11, -3, -26, -9, 19, -20, 15, 14, -25, 13, 4],\n [6, 25, 3, 4, 7, -20, -2, -11, -5, 9, 26, 0],\n [-10, -23, 8, 14, -5, 20, 25, 8, 17, -12, 25, 13],\n [17, -6, -14, 20, -16, 22, 26, 0, 4, 17, 5, 25],\n [3, -9, -11, 8, -18, 12, 24, 10, 24, -17, 25, -15],\n [-19, -24, -8, -16, -19, -1, 18, -4, -17, -9, -15, 12],\n [-1, -16, -17, -24, -20, -23, 13, -19, 11, -14, -15, 8],\n [11, 24, 16, 9, 20, -25, -12, 22, 7, 12, -1, 21],\n [-22, 21, -2, 24, 7, 20, -23, 7, 0, 15, 2, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-9, -23, -26, 23, -7, -21, -7, -7, 19, 0, -1, 5],\n [-17, -9, 14, -15, -17, -3, -3, 26, 24, 11, 19, -2],\n [-19, -13, 16, 4, -3, -11, -7, 11, 20, -12, -13, 26],\n [-15, 7, -19, -8, 19, -22, 0, 14, -14, 5, 4, 14],\n [19, 10, -25, -20, 21, -16, -16, -4, 4, 17, 18, -19],\n [5, 21, -6, 4, -26, -14, -16, 2, -23, 9, -12, -24],\n [24, 2, -6, -25, -21, 4, -3, 13, -10, -22, -25, -15],\n [-22, 15, 14, -7, -19, -26, -21, -16, -24, 4, 1, 20],\n [16, -22, -1, -11, 26, 4, 1, -20, 11, -18, 12, 8],\n [16, 0, -15, 26, -2, 16, 2, 4, 7, 6, 0, -25],\n [-13, -14, -3, -22, 7, -4, -8, 3, 22, 16, -11, 25],\n [23, 25, 13, 7, 22, -16, -13, 21, 20, -12, 8, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 17, -5, -4, -3, 8, 24, -17, -19, 21, 21, -15],\n [2, 2, -4, -1, 10, 5, 25, 11, -21, -19, -10, -15],\n [-5, -13, 7, -8, -21, -9, 9, 10, 11, -12, 11, 13],\n [-18, 26, -21, -25, -11, 25, -26, 3, 21, 6, -26, 12],\n [-11, -10, 21, 21, 11, -9, -5, -5, 8, 4, 13, 0],\n [9, -23, 22, -22, -2, 4, -13, 3, 20, -15, 0, 18],\n [-3, 3, -9, -13, -8, -5, -1, -20, 1, 11, -22, 9],\n [-9, -13, 21, -4, 25, -13, 5, -22, -5, 1, 16, -15],\n [-9, 9, 4, -14, -7, 18, 9, -20, -4, 7, 26, 23],\n [5, -6, -21, -11, 8, 20, 26, -7, 15, 14, -16, 5],\n [-13, -3, 17, 12, 16, 4, -10, -2, -18, -5, 18, 21],\n [8, 10, -10, 1, -26, 26, -18, 22, -14, 20, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[26, 4, -19, -19, 7, -4, -17, 10, 21, -2, 24, 6],\n [18, -23, -20, 6, -25, 21, 19, 5, -22, 19, -10, -15],\n [25, -15, 8, -6, -6, -25, 26, -6, -12, -16, -17, -9],\n [-4, 4, -1, 26, -25, 12, -20, -3, 12, 5, -1, -4],\n [-13, 2, -2, 4, -25, -25, -4, 20, -16, 2, 15, 8],\n [22, -18, 5, 3, -12, -13, 24, -10, -5, 25, 3, -10],\n [-11, 25, -19, 12, 4, -15, 6, -15, -2, 11, 21, -9],\n [-8, -24, 8, -22, 8, 24, 0, 10, 19, -6, -11, 1],\n [-2, 6, -10, 16, 3, 14, 26, -23, -25, -18, 4, -2],\n [10, 9, -22, -3, -3, 2, 23, 18, 4, 10, -8, -4],\n [8, 23, -21, -21, 10, 3, -26, -19, 1, -2, 6, 26],\n [11, 25, -13, -16, -25, 26, 3, 3, -23, -14, -20, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-24, -18, -13, 25, -16, 10, -13, -8, -19, -20, -20, -24],\n [-24, -9, 18, 6, 10, 1, 9, -11, -12, 2, -9, 22],\n [19, 19, -8, 2, -21, 18, 23, 20, 0, -20, 0, -8],\n [-10, 14, -16, -22, -25, 20, -15, 15, 15, 25, -16, -17],\n [1, -20, -13, -14, -22, 24, 15, -19, 23, -26, -22, -16],\n [25, 16, 21, -17, -12, 12, 20, 2, -2, 21, -21, -16],\n [-10, -12, -11, -25, 9, -8, 11, 23, -6, -16, 14, -24],\n [7, -9, -12, -2, 23, 24, -12, 3, -10, -9, 4, 23],\n [16, -9, 8, -14, -13, 9, -9, -22, -13, -2, 17, 12],\n [-15, 13, 26, 26, 1, 8, -26, -24, 16, 23, -20, -18],\n [9, -4, -3, -17, 23, 21, -15, -8, 5, -3, -5, -24],\n [13, 0, -8, -18, 24, 22, -14, -25, 9, 2, -16, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-23, -23, 25, -26, -2, -1, -16, -4, -25, -8, 2, 13],\n [25, -23, -11, 20, 10, 0, -22, -12, -4, 22, -24, -9],\n [16, -1, -21, 17, -10, 19, 11, 15, 21, 23, 0, -7],\n [-21, 24, 8, -15, 21, -24, 21, -23, 25, 18, -23, -23],\n [12, -6, 17, -25, -11, -20, -8, 16, 6, -18, 10, -10],\n [0, 6, 22, -15, 18, -16, -14, 4, -14, 11, -1, 4],\n [-5, -21, -7, -6, -17, -8, 8, -1, -20, 10, -19, -22],\n [17, 9, 24, 1, 23, -24, 12, -19, -12, 26, 0, 22],\n [24, 9, -11, -1, 18, 17, -23, -15, -10, 14, 17, -1],\n [4, -12, 25, 7, 2, -18, -13, 9, -23, 11, 10, -3],\n [-10, -14, -7, -10, 24, 0, 6, -6, -10, -5, -2, -24],\n [0, 0, 19, -15, -12, 11, -7, -5, -25, -23, 18, -14]]\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[[5, -5, -2, 0, -10, -21, 16, 24, -11, -19, 6, -17],\n [7, -8, -13, -24, 14, -4, 13, -16, 20, -21, 7, -26],\n [8, -2, 2, -4, -9, -13, -10, -25, 4, -8, 5, 1],\n [14, -19, 15, 14, 13, 12, -5, -3, 11, -25, 14, 14],\n [-8, 14, -25, 1, 5, -8, -11, 3, -5, -13, 25, -26],\n [18, -25, -5, 19, 6, -12, 23, 14, -5, 13, 12, 14],\n [14, -16, -23, -20, -6, -20, -23, -15, 0, -10, -7, 4],\n [-1, 4, 8, -18, -22, 25, 21, -19, -6, -11, 24, -11],\n [-9, 20, 1, -9, -13, 21, 10, 13, -11, -6, -26, -16],\n [-16, -25, 5, -8, -22, -24, 1, -1, -4, 3, -19, 9],\n [2, -14, -2, -5, 19, 6, 10, 26, -20, -4, -21, -12],\n [-12, 13, 7, -13, 2, -11, 2, -4, -17, 20, -23, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "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, 7, -23, -7, 1, 1, -21, -13, 8, 20, -26, -8],\n [-26, -14, -19, -9, 8, -4, 23, 25, -1, 14, 11, -7],\n [-25, -1, 9, -2, 3, -9, -20, 0, -16, 10, -19, -16],\n [-3, 3, 3, 25, 25, -12, 8, 12, -3, -19, 16, 15],\n [-7, 14, 20, -1, 25, -3, -5, -22, -12, 9, 10, 2],\n [-12, 0, 22, -19, 2, -8, 4, -18, -17, 10, -17, 6],\n [-2, -23, 26, -22, -4, 12, -22, 25, -19, -10, -26, 23],\n [-15, 8, 25, -13, 21, -9, -17, -12, 15, 6, -8, 7],\n [18, -2, -11, -19, 8, -6, -8, 19, -16, 17, -16, -16],\n [-5, -6, 0, -9, 15, 21, 13, 11, 3, 24, 18, 20],\n [18, 6, -6, -25, -14, -25, 16, 18, 4, -17, -4, -5],\n [20, 2, 6, 4, -13, -17, -9, -16, 12, 20, -24, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, 4, -19, 16, 21, -25, -5, -22, -20, -7, 1, -14],\n [-25, 5, -1, -24, 14, 15, -14, -6, 18, 10, -4, -20],\n [-10, 1, 20, 3, -22, -3, -20, 7, 23, 15, 6, 0],\n [-13, -8, 21, 24, 11, -15, -24, -20, 8, -2, 22, -12],\n [-8, -8, -4, -16, -6, 25, 7, 12, 24, -20, 15, 17],\n [0, 23, -4, 11, -7, 0, 26, -19, 10, -24, -25, -5],\n [-21, 12, 13, 9, 17, -3, -15, -10, -5, -8, -18, -15],\n [5, 26, 4, -10, -4, -17, 3, -8, -1, -1, -16, -7],\n [18, -23, 20, -15, -2, -17, -5, -20, -3, -25, 5, -6],\n [-20, -19, 26, 24, 11, -6, -19, -2, 1, 1, 4, 25],\n [9, -2, 25, 14, 10, 11, 24, -15, 10, 10, 4, -9],\n [-1, -21, -18, -16, 4, 19, -25, 2, 19, 24, 15, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 9, -20, -14, 15, -17, 9, -11, -12, 26, 16, -8],\n [-6, 8, -12, 21, -13, 2, -22, 22, -9, 24, -26, 0],\n [0, -2, 14, -6, -13, 25, 26, -7, 1, -6, -4, -16],\n [-25, -7, -3, -2, 10, -5, -3, -12, -15, 19, 4, 16],\n [4, 26, 3, 14, -7, -19, 17, 3, 8, -6, 20, 13],\n [1, 12, -10, -15, 25, 23, -9, 20, 1, -24, 24, -12],\n [-11, -5, 22, 4, 4, -26, -16, -21, -4, -18, 25, -11],\n [11, 17, -8, 18, -14, 5, 9, -18, 19, 19, 22, 10],\n [4, 4, -8, -25, 18, 5, 16, 7, -26, -6, -24, 0],\n [17, -20, 6, -18, 3, -9, -1, -7, 11, 14, 4, -19],\n [-4, 23, -2, 20, -26, 19, -9, -8, 24, 15, 25, 26],\n [-21, -10, 19, 18, -19, 15, -18, 10, 0, 9, -21, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "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, -23, -5, 13, 0, 10, -25, -18, -16, -7, 25, 16],\n [12, -13, -1, 11, 3, 9, 11, 8, -21, -24, -26, 26],\n [-9, -4, 5, 2, -4, 9, -21, -10, -9, 4, -21, 7],\n [17, 17, 0, 9, 21, 25, 15, -2, -17, 12, 19, 12],\n [-15, -16, 22, 16, 26, -24, 24, -5, -23, -19, -13, -7],\n [-3, -13, 1, -11, 5, 20, -15, -11, 25, -8, -22, -15],\n [2, -22, 15, -10, 20, -19, 13, 13, 3, -17, -7, 18],\n [-11, 14, -11, 15, -24, -4, -5, 1, 19, 18, 9, -23],\n [11, -3, -8, -16, 13, 19, 13, 19, 12, 26, -9, -15],\n [-13, 20, -9, 17, 15, -15, 13, 0, -21, -3, 24, 6],\n [18, -11, 23, -15, 4, 10, 26, -14, -19, 11, -24, -7],\n [-23, 17, 18, -25, 24, 9, -4, 18, -8, 13, -19, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[16, -9, 9, -3, -26, -26, 19, 9, -16, -9, -11, -10],\n [-3, 7, -23, 8, -12, -25, 24, 4, -18, -17, 26, -2],\n [24, -22, -13, 15, 21, 11, 13, -25, -9, 2, 26, 26],\n [26, -7, -19, 10, 22, 21, -1, 10, 22, -23, 6, -5],\n [-21, 6, 1, -3, -23, -25, -14, 19, 22, -16, 8, 12],\n [-17, 16, -17, -19, -22, -4, 7, 20, 5, -11, -23, 1],\n [21, 17, -13, -15, -6, 21, -11, 17, -25, -4, 2, 19],\n [16, -18, -20, 2, 17, -10, -18, -21, 17, -7, -17, -18],\n [-15, 6, 5, 7, -8, 6, 21, -11, 23, 23, -4, -1],\n [18, 17, 14, 10, -18, 3, -14, 21, 15, -11, 19, -25],\n [4, 24, 16, -8, -16, -13, 20, -2, -20, -12, 3, 4],\n [-3, -2, -19, 3, 9, 23, -13, 2, 0, 26, 23, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[7, -6, 11, -16, 6, -12, -15, -3, 23, 10, -16, 26],\n [-8, -26, -10, 13, -11, -1, 16, 24, 16, -12, -19, 3],\n [-13, 6, 15, -20, -9, -15, -25, 23, 2, -6, -20, 25],\n [0, -15, -7, -13, -17, 14, -4, 3, 20, 4, 25, -17],\n [-8, -8, 17, -4, 17, 14, 5, -7, -23, 6, 21, -26],\n [-14, -24, -15, 2, 4, 14, 9, -25, -5, -5, 14, 4],\n [25, 18, -13, 2, 8, 23, -18, 20, 5, 0, -17, -2],\n [22, 18, 6, -16, 10, -18, -20, -20, 7, -8, -7, 23],\n [15, -2, -22, 21, 2, 0, -2, 10, -12, 21, -23, -13],\n [22, -10, -6, -11, -1, -18, -25, 16, -12, 8, -3, 21],\n [26, 24, 11, -13, 10, 10, -21, -9, -5, -9, 24, -25],\n [5, -10, -26, -18, -14, 9, 10, 3, 4, -4, 23, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "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, -2, 9, -1, -1, 18, -14, -10, 13, -23, -4, 8],\n [-16, -15, -18, -12, 18, 10, -22, -8, -16, -18, 8, 23],\n [0, -14, -15, -18, 15, 1, -14, -7, 25, -14, 0, -1],\n [2, 2, -5, -18, -3, 15, -8, 11, 4, 12, -12, 5],\n [24, 19, 21, 19, 2, 25, 7, -18, 8, -21, 10, -13],\n [20, 23, 22, -18, -8, -4, 14, 1, -11, -1, 11, 13],\n [-2, 8, -22, -20, -4, -2, -26, -5, 26, -23, 1, 21],\n [-13, 6, -23, 15, -16, 12, 5, -23, -26, -1, 6, -10],\n [0, 15, -22, -20, -2, -19, 7, 14, -23, -15, 4, -16],\n [10, 17, 26, 9, 18, -5, -26, 23, -23, 9, -19, -2],\n [1, 25, 11, 9, 9, 16, 14, 19, -23, -14, 11, 18],\n [-2, -24, 5, 12, -26, -16, -25, -22, -5, 19, -14, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 20, 4, 8, 11, 14, 8, 18, -14, -20, -22, 2],\n [-19, -19, -20, -8, 12, -4, 9, 15, 5, 18, -23, 3],\n [24, 15, 12, -22, -24, -5, 1, -5, -5, 7, 2, 16],\n [15, -14, -20, -17, 1, -23, 5, -5, -7, 21, -7, -21],\n [-18, 1, -14, 4, 12, 23, -13, -5, 10, 18, -3, -19],\n [-12, 24, 14, -21, -4, -2, 4, 19, 2, -4, -17, -18],\n [22, -14, 5, 22, 24, 18, 14, -26, -26, 10, 13, -9],\n [9, 4, -26, 20, 25, 9, -18, -5, 1, -1, 25, -17],\n [20, -24, -25, 10, 4, 6, 5, 16, -15, -24, 21, -1],\n [-13, -15, 25, -1, -11, 26, -19, 22, 22, 1, -20, -12],\n [14, 9, -19, -17, -12, -9, 19, 10, 14, 18, 24, 16],\n [17, 8, -25, -5, -12, 10, 12, 9, -22, 21, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "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, 9, 11, -9, 8, -2, -5, 4, 10, 7, -4, -11],\n [-21, -12, -9, 11, -14, -3, -14, -26, 21, 9, 22, -9],\n [21, 6, 11, 16, -21, -10, -23, -13, 3, 19, -7, -19],\n [-25, 10, -23, -17, -7, 26, 8, 21, -17, 1, -12, 9],\n [-26, -5, 0, 2, -12, -17, -7, -5, 23, 21, 26, -18],\n [24, 5, -10, 15, -8, 13, 0, 24, 10, 7, 20, 22],\n [-17, 3, -6, -6, 7, -18, 7, 23, -15, 20, -6, -7],\n [-21, 23, 18, 9, -15, 14, 4, -25, -11, -26, -23, 20],\n [25, -26, 25, 20, 8, -14, 23, 18, 15, 4, -7, -20],\n [13, 6, 1, 23, 17, 23, 17, -7, 5, -18, 7, -13],\n [-23, 2, -12, -10, -8, 11, -18, 0, 22, -12, 10, 1],\n [23, -23, -6, 7, -8, 10, -23, 10, 24, 5, 18, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-15, 14, -11, -13, -26, 25, 5, -6, -23, -18, 24, 19],\n [-5, -15, 3, 3, 5, 9, -20, -10, -26, -13, 20, 17],\n [17, 11, -1, 0, 18, -11, 19, -20, 5, -2, 4, -11],\n [14, -13, -2, 3, -20, -15, -24, 0, 19, -8, 16, 10],\n [18, 15, -20, 22, -11, 5, -19, 22, -14, -16, -7, -9],\n [10, -21, -7, 5, 19, 17, 2, -23, -20, 16, -7, 7],\n [9, -20, 6, -12, 25, 5, -5, 13, 2, -2, -22, -13],\n [23, 8, -25, -2, -11, 19, -11, -16, 22, 8, -4, -22],\n [8, 2, 20, -22, -24, -21, -4, 19, -25, -9, 3, 11],\n [-22, 19, 22, -16, -26, -17, 14, 25, 17, -1, 6, 0],\n [23, -15, -25, -26, -26, 6, -5, -15, 12, 9, -6, -7],\n [9, -1, 20, 4, -26, 11, -13, -1, 19, 15, -20, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -8, -18, 8, -23, 18, 15, 5, 19, -21, 1, 1],\n [13, 24, 2, 15, -22, -22, 10, 14, 1, 14, 20, -18],\n [2, -13, 11, 25, 13, 7, 10, 22, 15, -13, -9, 6],\n [7, 1, 9, 18, 21, 10, -4, 15, -10, -16, 5, 10],\n [-12, -23, 12, 3, -17, -4, -3, 9, 25, -22, 10, 16],\n [-8, 10, 26, -19, -20, 13, -14, 10, 0, -9, -3, 14],\n [-25, -11, -13, -10, -21, 8, -10, 18, 11, 13, -21, 21],\n [11, 22, -6, 8, -4, -15, 2, 0, -21, -6, -20, 16],\n [14, -11, -22, -12, -6, -23, -22, -20, 8, 9, -12, 1],\n [-25, -22, -20, -5, 22, 4, 5, -19, 14, 15, -16, -26],\n [20, 13, -8, 17, 11, 15, 10, -20, 12, -2, -5, 0],\n [14, 20, 11, 21, 12, -12, -25, -19, 17, 16, -21, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 18, -4, 21, 13, -10, -14, -23, -7, 15, -2, -5],\n [25, 21, -10, 13, -16, -2, -22, -6, -1, -11, 13, -6],\n [21, 5, -23, 11, 26, -19, -18, 18, -10, 14, -14, -18],\n [-21, 0, 15, 10, 12, 16, -3, -18, 15, -16, 8, 2],\n [-19, -10, -20, -15, 21, -12, 26, 2, 18, 23, 23, -3],\n [10, -13, -16, 8, -10, 0, 17, -24, -25, -23, -9, -7],\n [-6, -13, -19, -25, -1, -8, 15, 1, 2, -22, 16, 1],\n [14, 21, -1, -22, -12, 19, -18, 5, 25, -1, 10, -12],\n [14, -23, 26, 26, 9, -7, 0, -6, -5, -20, 20, 4],\n [-10, 23, -20, -8, 1, -17, 0, -14, -25, -5, -7, 16],\n [-22, -21, 8, -26, 8, -24, 9, -20, 2, -12, -16, -9],\n [17, -23, -3, -16, -21, 24, -9, -12, -24, -10, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "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, -8, -18, 13, 17, 4, 0, 20, -2, -20, 26, 21],\n [-20, -7, 26, 17, 22, 16, 9, -8, -25, 7, -10, -3],\n [-18, -26, 15, 1, -12, -6, -12, -4, 26, -25, 19, 9],\n [23, -18, -25, -25, -9, -10, 14, -19, 7, 7, -22, 17],\n [2, 1, -11, -13, 25, -25, 13, -23, 25, 14, 25, 4],\n [-1, 0, 24, 7, 4, 21, -16, -19, -15, 8, 18, 7],\n [-14, 0, -19, 20, -6, 14, -16, -5, -6, 1, -24, -20],\n [-13, -12, -18, 25, 16, -20, -15, -8, 0, -9, -14, 16],\n [-26, 11, -6, 7, -14, 18, 24, 14, 24, -4, -26, -4],\n [1, 5, -19, -1, -13, -3, 21, 2, -23, -9, -13, 0],\n [14, 20, -24, 3, 9, -4, -9, 19, 20, 13, -17, -15],\n [26, 14, -19, 5, -10, 14, 18, -13, 10, -18, -1, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[24, -3, -4, 4, 12, 17, -25, 23, -9, -11, 2, -16],\n [-25, -13, -23, 12, 7, 26, 19, 12, -18, 13, 14, -20],\n [24, -10, -4, 18, -16, -5, -9, 22, 1, -11, 15, -23],\n [9, -5, -16, -6, 13, 14, -11, 15, -18, 8, 7, -18],\n [-14, -21, -23, 19, 1, -16, 7, 8, -22, 12, -16, -15],\n [16, -8, -14, -23, -13, 17, -25, -19, -5, 24, -14, -6],\n [-6, 1, 6, 2, 10, -5, -1, -16, -16, 18, 7, -8],\n [21, 10, -13, 2, -8, 10, -6, -3, -1, 14, -15, 21],\n [-8, 20, 22, 3, -12, -24, 22, -14, -18, -14, -11, 24],\n [-13, -19, -8, 5, 8, -4, -6, -9, 21, -13, -11, -3],\n [22, 25, 5, -16, 18, -16, -23, -1, 19, -22, 9, 6],\n [-13, 5, -20, -17, -25, -17, 8, -6, 13, 15, -19, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "503", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, -18, 14, 3, -23, 8, -13, -13, 26, 21, 10, -7],\n [2, -4, 20, -6, 4, 5, 14, -20, -14, -4, -19, -15],\n [9, -11, -1, 2, 2, -21, 10, 6, 4, 19, 14, -9],\n [11, 20, 4, -11, 13, 24, 10, -13, 12, -23, 3, 26],\n [6, 9, 3, -13, -4, 21, 1, -20, 15, -17, -23, 17],\n [11, -14, -6, 6, 13, 1, -4, 5, 21, -22, -1, 12],\n [-1, -24, -3, 26, 7, 7, -7, 3, 15, -7, 14, -9],\n [11, -7, -21, 15, -2, 14, 14, -24, 17, 16, 19, -8],\n [-17, 24, -22, -5, -18, 6, -12, -3, 3, 9, 12, -21],\n [-12, 11, 12, 25, -5, -24, 26, 2, 2, 4, 18, -25],\n [8, 18, -18, -5, -8, 23, 10, -17, 19, -6, -10, -24],\n [-20, 14, 10, 9, -24, -14, 14, 3, -4, -20, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "486", "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, -17, 6, -7, 2, 2, 26, -6, -26, 24, 7, 17],\n [5, 18, -13, 10, 8, -3, 22, -26, 19, -21, 22, -23],\n [11, -26, 14, 4, 9, -18, 14, 18, -4, 4, 2, 22],\n [-6, -24, -1, -21, -7, 20, 19, -14, 14, -4, -12, 19],\n [4, -23, -16, -25, -11, 24, 4, 21, 12, 16, 17, -23],\n [21, 1, -11, 12, -2, -14, -22, 3, -26, -22, -13, -16],\n [7, 2, -9, -12, 19, -2, 3, 18, -25, 24, 13, 0],\n [22, -12, 5, -7, 26, -13, 0, -24, 22, -24, -14, -2],\n [-9, -26, 12, -22, -25, 3, -10, 2, 26, 15, -23, -18],\n [-6, 16, -15, -15, 23, -23, 1, -18, 13, 24, 5, -14],\n [7, -8, -13, -22, 0, 1, -1, -17, -3, -10, 25, -11],\n [-10, -26, -6, 20, 22, 16, -5, -22, 9, -6, -18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[21, -15, -9, 8, -12, 23, 17, 3, 18, 6, 9, 13],\n [24, 26, 3, -1, -6, 10, 16, 4, -10, -10, 7, -3],\n [6, -23, -18, -25, 8, 11, 18, -12, 16, 15, -24, 4],\n [25, 14, 15, 26, -4, -15, -19, 26, -6, -6, 5, -10],\n [10, -3, -19, -9, -16, -17, -1, 20, -21, 24, -10, -4],\n [15, 10, 1, -11, -15, -6, -3, 1, 10, -6, 6, -25],\n [10, -8, 1, -12, -26, 16, 1, 23, 8, 5, 1, -18],\n [-3, -23, 18, 14, -24, 21, -5, 13, 12, 22, -2, 21],\n [26, -5, 23, 21, 20, 7, -7, 9, 10, 12, 0, 20],\n [22, 5, 15, 25, 2, 14, 21, 5, -3, -24, 0, -18],\n [13, -4, -20, -10, 10, -20, 3, -14, -9, 4, -5, -13],\n [-9, 8, -10, -8, 4, 12, 26, 9, -12, 2, 13, -11]]\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 difference between the largest and smallest singular values:\n[[6, -2, -11, 3, 7, -25, 13, 17, 16, 11, 24, -9],\n [-22, 20, 13, -21, -15, 24, -15, -15, -18, 15, -5, 22],\n [23, -11, -23, 23, -24, -11, -13, 14, 11, -23, -25, -17],\n [-16, 12, -1, 10, -1, -23, -1, 11, 1, -25, -25, -11],\n [-4, -4, -14, -6, 12, -2, 10, 22, -14, -12, 1, -24],\n [-4, -23, 20, 23, -24, 12, -19, 16, -2, 14, 25, -15],\n [-22, 6, 19, -2, -2, 8, -12, 15, -1, -17, -3, 8],\n [2, 11, -22, -3, -8, 19, 22, 17, -18, -1, -2, 8],\n [23, 9, -13, -21, 5, -1, -12, 22, 4, 10, 11, 26],\n [10, -8, -13, 9, 10, -16, 0, -25, -5, -25, -7, 17],\n [21, -10, -23, -13, -20, -12, 3, -11, 13, -25, -8, -26],\n [4, -23, 0, 26, -2, -5, 16, -17, 23, 6, 22, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[17, 3, 3, -11, -18, -10, 8, 23, 20, -12, 21, 1],\n [-7, 6, 6, 9, -14, -23, -4, -19, -14, -3, 13, 19],\n [3, 3, -2, 6, -18, -1, -3, 6, 12, -2, 25, 18],\n [-12, 14, 21, 22, 14, -21, -7, 17, -11, -6, -12, 12],\n [15, -23, -3, -24, 23, -26, 3, -14, -9, 13, -16, 15],\n [2, -23, -2, 9, 9, 17, 13, 1, 18, -19, -6, 8],\n [17, -9, 20, -2, 19, 14, -22, 20, -19, -4, -24, 17],\n [10, 4, 2, 14, -7, -24, -4, 13, -6, -14, -19, -22],\n [-2, 12, 10, 14, -22, -19, 17, -23, 14, -5, -13, -8],\n [-14, 8, -23, 6, -5, -26, -16, -11, -23, 2, 12, 17],\n [11, -3, 25, -18, -19, -13, -12, 26, -5, 10, -12, -21],\n [-26, -7, 14, 9, -25, -21, -25, -24, -20, -7, 22, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[14, 24, -22, -2, 11, -9, -26, -2, -10, 19, -12, -22],\n [-10, -6, 26, -4, 16, -17, -10, -26, 10, 21, -20, -15],\n [13, 23, -26, -7, 17, 4, -23, -1, -15, -5, -26, -26],\n [-24, 26, -15, -6, -14, -14, 26, 14, -9, 6, -21, -2],\n [-4, -3, 10, -1, -23, 11, 8, 22, -16, 9, -2, -7],\n [-26, 3, -23, -4, 8, 15, -5, 4, -26, -23, -8, 3],\n [-26, 21, -8, 25, -6, -5, 23, -25, -21, -6, 6, -8],\n [0, 10, 2, 1, 7, -26, 21, -2, -6, 7, -1, 9],\n [8, -4, -10, 20, 15, -15, 17, -7, 12, 0, 15, 10],\n [-7, 25, -16, 1, -25, -3, -11, -15, -11, 9, -25, -2],\n [2, 1, -17, 18, -4, 5, 4, -8, -12, 6, -10, 25],\n [9, -7, -18, 11, -24, -25, -9, -4, -8, -20, 8, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "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, -7, -8, 14, -11, 11, -6, 2, 17, 11, 18, -3],\n [10, 2, 4, 18, 25, 12, -15, 3, 26, -23, 3, -22],\n [-11, 0, -23, -19, 21, -19, -10, 19, 17, -24, 0, 25],\n [7, 18, -6, 16, -3, 17, 23, 14, 2, 12, -21, -13],\n [23, -13, 10, 25, -3, -14, -26, -15, 24, 15, -3, 10],\n [-7, -21, -15, -6, -24, 0, 19, 26, 9, -10, 22, 19],\n [-12, 12, -23, -10, 11, -16, -15, 20, 5, 0, 17, 16],\n [0, 22, 13, 17, 2, -18, 16, -24, 12, 2, -6, 8],\n [26, 21, -17, -4, 12, -2, -3, -7, -12, -6, 26, 15],\n [-15, -9, -4, 14, 2, 14, 9, -22, 12, -1, 12, -16],\n [15, -16, -9, -15, -11, 0, 9, -10, 22, -6, 10, 4],\n [18, 8, 0, -4, 5, -10, -16, -26, 1, -9, 22, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-7, -20, 10, -11, 12, 18, 18, 20, -4, 5, 22, -10],\n [-8, 15, 7, -13, -24, 12, -2, -16, 22, -12, -8, 16],\n [-12, -12, 11, -12, -18, -22, -8, -3, 2, -22, -5, -14],\n [23, 25, 22, 20, 19, 2, -11, 9, -10, -7, -13, 23],\n [-21, -5, 13, -18, 5, -3, 6, -14, 8, -21, 22, 13],\n [3, 11, -11, -26, 15, -9, -5, -1, -13, 10, 22, -13],\n [-1, 23, 9, 25, -4, -25, 12, -20, 12, 18, 24, -5],\n [1, 11, -7, 22, -9, -3, 6, 18, -1, -8, 21, 15],\n [-14, -17, -13, -18, 26, -16, -24, 13, -15, 8, 12, 19],\n [12, 5, 12, -13, 17, -26, 0, 10, 16, -26, 18, 2],\n [-3, -10, 8, 4, 15, 5, -8, 4, 12, -7, 1, -24],\n [5, -5, 17, 15, 26, 17, -12, 11, -8, 4, -1, -22]]\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 largest singular value:\n[[-7, -25, -6, 24, 24, 9, 1, -7, 10, 12, 9, -16],\n [-24, 10, -7, 5, 20, -2, -6, 23, -11, 21, 15, -26],\n [-4, 16, 22, -3, 20, -2, -20, 11, 20, 20, 12, 8],\n [-13, -18, -24, 11, -7, 14, 6, 14, 17, 5, 9, -1],\n [21, -22, 22, 3, -10, -21, -12, -26, -14, 21, 7, 3],\n [-8, -25, 26, 17, -15, 13, 17, -3, -16, -25, -26, 1],\n [-23, 14, 3, -20, -5, -1, 2, -2, -17, -7, -13, 6],\n [-22, 18, -21, -5, -10, -12, 12, 13, 1, 26, -25, -9],\n [0, -6, -4, -20, 25, 21, -8, -18, -15, 19, 3, -20],\n [-25, -10, -16, 23, -15, -24, -6, -13, -12, 24, 15, 14],\n [-17, 25, 9, 24, -17, -10, 17, -2, 0, 6, -16, -14],\n [-26, 4, 6, -6, -11, 12, -4, -17, 21, 6, -5, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-21, 20, 9, 20, -17, -11, -14, 24, -7, -23, -7, -5],\n [2, -11, 16, 20, 16, -4, 3, 3, 16, -24, -3, 22],\n [10, -14, 15, 5, 10, -15, -19, -3, 17, -11, 5, 7],\n [8, 5, 23, -10, -25, -1, 17, -10, 11, 22, -25, -19],\n [19, -21, -18, -26, -22, 12, -18, -13, 0, -18, 9, 2],\n [-7, -12, 9, -24, 26, -4, 19, -18, 3, -8, 11, -24],\n [23, 21, -24, 7, -25, 0, -4, 15, 5, 20, 8, 13],\n [-9, 0, -16, 12, -8, -2, -20, 4, -25, 11, -22, -13],\n [-9, 9, -23, -3, -14, -6, 6, -7, -22, -3, 8, 3],\n [1, 26, 24, 18, -20, 15, 8, 3, 7, 12, -18, 26],\n [-15, 2, -17, 0, -8, -14, 15, 10, 5, -12, -6, -24],\n [-19, -21, 2, -8, -10, -17, 6, -14, 0, 15, -15, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-17, -6, -4, -26, 6, 25, -1, -12, -5, -2, -26, -1],\n [-6, 14, -3, 12, -11, 5, -11, -14, 15, 5, 23, 14],\n [17, -3, -14, -16, -12, -17, 15, 14, -24, -11, 17, -10],\n [-2, 3, 20, 8, 10, -14, -3, 11, -1, -18, -8, 1],\n [-20, 18, -5, 3, 10, -11, 9, -22, 2, 25, 24, -4],\n [-21, 9, 6, 22, 14, -11, 7, 16, -1, 10, -14, 25],\n [-10, 5, 5, 1, 2, -2, 20, -5, 0, 17, 11, -7],\n [18, 23, -3, 20, 20, -19, 24, -13, 12, -13, -22, 20],\n [-6, -12, 9, 6, -10, -7, -26, -11, 18, -9, -17, -4],\n [-9, 22, -18, 19, 26, 3, -14, 25, 25, 4, 19, 16],\n [-14, 5, -10, -24, -26, 26, -22, 5, -2, 18, -22, 10],\n [-4, -15, 7, -4, -11, 22, -22, 17, 20, 1, -21, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "506", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[16, 3, -1, -10, -18, -11, 22, 25, -9, -14, 2, 16],\n [18, -3, 18, 17, 19, -14, -2, 14, 19, -26, -18, -23],\n [1, -15, -3, 19, -18, 8, 11, 8, 6, 26, 8, 19],\n [-7, -25, 17, -1, 15, -14, 3, 25, 5, 9, -8, -5],\n [-26, -16, -1, 21, -8, -8, -15, -24, -9, 22, -22, 21],\n [-3, -13, 24, 11, -24, -21, -15, 25, -16, 12, -1, -26],\n [-11, 21, 22, 20, 26, -18, -22, 25, -19, -6, 6, 12],\n [16, -7, 26, 18, -5, -14, 12, -16, -9, 3, 6, 17],\n [-24, -26, 9, -21, 10, 2, -16, 25, -14, -16, 11, 24],\n [-2, -12, 26, -14, 15, 6, -14, 11, 26, -3, -7, 17],\n [-10, 23, -3, -1, 13, 5, 2, -13, 10, -5, 7, 0],\n [1, -5, 16, -24, -5, 21, -6, -11, -18, -14, -17, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "572", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-6, 22, 15, 13, -20, 19, -5, -9, -6, 24, 23, -13],\n [-17, 6, -18, -9, -14, -10, -4, -2, -11, -3, 4, -16],\n [-4, 14, 12, -5, 6, 14, 15, 21, 26, -9, -13, 1],\n [-16, -3, 9, -8, -14, 6, 26, -8, 20, 25, 5, -12],\n [-16, -4, -22, -5, 15, -9, -20, 6, -24, 1, -26, 22],\n [20, 10, -5, 21, 17, -8, -13, -24, -8, 6, -6, -26],\n [-1, -17, 8, -14, -21, 16, -21, 8, -11, 14, -19, -24],\n [-22, -6, 4, -13, 10, -8, 10, 26, -7, 25, -25, -20],\n [6, 26, 23, 15, -21, -20, 17, -9, 16, 2, -8, -2],\n [-23, 24, -14, 5, 0, 24, 7, 1, -18, -19, -6, 19],\n [3, 2, -18, -14, -9, 11, -5, 4, 8, 15, 15, -17],\n [-18, 4, 17, 13, -3, 14, 22, -19, 23, -7, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, 15, 6, 1, 26, -26, 14, 25, 8, -3, -21, -20],\n [-18, 10, -11, 7, 8, 8, -7, -4, 15, 8, 20, 19],\n [-4, -23, -17, 16, -16, 13, -18, 13, -15, -10, 5, -4],\n [-12, 24, 1, 25, 11, -22, 13, -9, 26, -6, -12, -24],\n [19, -1, -12, 18, 26, -7, -6, -1, 14, -4, 22, 24],\n [-2, -23, 25, -17, -5, -24, -8, 4, -18, 2, 10, 19],\n [-20, 26, 11, -3, -19, 7, -1, 1, 1, 19, -20, -24],\n [25, -5, 11, 26, 19, 17, -9, -15, 4, 12, -22, 17],\n [14, 2, 16, 9, -13, 17, -9, -20, -4, 6, 18, -11],\n [10, 24, -2, -18, 1, -18, -15, -9, 0, -1, -1, -17],\n [-10, 24, 5, -3, 16, 21, -19, 3, -1, -3, 0, -12],\n [1, -16, 12, -25, 24, -18, 23, 18, -4, 6, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-13, 5, 22, -5, -7, 6, -22, -7, -13, 0, -1, 5],\n [3, 0, -1, -9, 18, -4, 17, 20, -3, -23, 14, -24],\n [16, 3, 20, -11, -20, 12, -5, 14, 4, 22, -14, 14],\n [14, 25, 2, 1, 17, 26, -8, -4, 20, 23, -19, -2],\n [11, 11, 8, -1, -24, -25, -22, -7, -15, 11, -11, 10],\n [11, 9, 19, 2, 8, 22, 10, -6, -6, 1, -21, -7],\n [9, -14, 13, -16, -3, -8, -4, 4, 10, 10, -24, 7],\n [2, -24, -12, -20, -24, 20, 16, -11, 18, 7, -7, 17],\n [26, 12, 6, -13, 15, 8, -16, -7, 3, 26, 1, -12],\n [11, 23, -14, 20, 8, 20, -3, -26, 15, -3, 0, -9],\n [-1, 2, -19, 17, -1, -22, 6, 13, -22, 22, 20, 9],\n [-14, -10, -14, -2, -25, -3, 9, -2, 7, -15, -8, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[15, 3, 10, 16, -26, -24, 22, -1, -12, 19, 20, 21],\n [1, -23, -8, -3, 13, -21, -11, 5, 3, 8, -19, -22],\n [10, -15, -2, 6, 12, -3, -16, 15, 8, 13, -26, -19],\n [-4, -7, 5, -16, -20, 3, 21, 12, -14, 15, 22, -24],\n [-20, 16, -14, 10, -2, -4, 24, 20, 6, -22, 5, 3],\n [4, -14, 15, -22, -4, -26, -17, 23, 0, -19, 25, -24],\n [-8, 24, -25, 22, 4, 21, 26, -17, 26, -11, 10, -7],\n [-24, 8, 7, -6, 9, 5, -9, 7, 11, -24, 26, -24],\n [0, -25, -24, -10, 19, 12, 26, 11, 13, -8, -8, 17],\n [-22, -22, -13, 0, 22, 21, 9, 13, 8, -6, -22, -3],\n [12, 23, -3, 13, 16, 19, 23, -14, 11, 18, -26, 16],\n [12, -17, -25, -11, 10, -11, -4, -1, -11, 0, 20, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 6, 5, -18, -16, 10, -21, 3, 13, -12, 21, 3],\n [-9, -15, -23, -11, -4, -16, -3, -5, 12, -12, 22, -12],\n [-17, 1, 9, -10, 9, -5, -4, 2, -5, -16, 9, 17],\n [2, 15, 5, -13, -9, 11, 10, 7, 18, -4, 5, 19],\n [-24, 16, -5, -4, -23, -14, 5, 2, 13, 13, 18, -17],\n [-14, 18, -10, 11, -25, -10, 17, -1, 11, 10, -22, -2],\n [-18, 1, -5, 2, 8, -7, -22, 12, 17, 5, 12, -17],\n [13, -10, 10, -12, -18, 5, -4, -16, -14, -9, 22, -18],\n [15, -22, 16, -5, 5, 20, -25, -6, 1, 25, -3, -3],\n [-13, 10, 0, -3, -21, -1, -12, 2, 9, -17, 1, 24],\n [-18, -6, -17, -23, -23, -21, -1, 13, -11, -19, 1, -11],\n [11, 22, -26, -8, 23, -10, 22, 1, 17, -15, -21, -20]]\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[[-19, -24, 22, -6, -19, 1, 3, 5, -16, -7, 23, -11],\n [-2, 18, -18, 24, 12, 22, 13, 13, -24, -11, -15, -12],\n [26, -23, -4, 0, 12, 16, 10, -14, 16, 10, 13, -6],\n [2, 2, 22, -16, 24, 23, 1, -17, -22, -2, 6, -10],\n [22, 6, -2, 6, -18, 0, -2, -23, -18, 19, -12, -11],\n [-11, -14, -13, -5, -6, -18, 14, 26, -23, -17, 8, 26],\n [-18, 24, 21, -11, 22, -9, -17, -6, 24, -12, -12, -16],\n [13, 21, 15, 14, 20, 10, -7, 7, -5, 21, -9, -11],\n [-22, -26, -8, -17, -6, -14, -3, -4, -4, -16, 20, -25],\n [-21, 26, -16, -12, -18, -15, 9, 1, -4, 0, -3, -13],\n [8, 0, -6, 22, -14, -19, 17, 17, 17, 7, 15, -4],\n [-18, -26, 9, 19, -11, -2, -9, 7, 11, -24, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-14, -10, -13, 3, -5, 16, 21, 16, 2, 23, -25, 26],\n [-19, -13, 7, -14, -17, -19, -20, -14, -1, 5, -8, -12],\n [-25, 10, -8, 6, 12, 23, 6, -26, 12, 1, -10, -21],\n [25, 17, -7, 20, -14, -15, 3, -6, -25, 26, -9, 1],\n [-23, 15, 16, 26, -21, 11, -18, -7, 18, 3, 10, 11],\n [-23, 11, 23, -14, 8, 3, 15, -23, -2, 4, 20, -15],\n [-12, 26, -1, -17, -15, -5, 13, 26, -6, 8, -20, -9],\n [0, 8, 20, -25, 5, -12, 18, -3, -7, -17, -3, -3],\n [-3, 13, 21, 21, 7, 14, 13, -16, -1, -26, 3, 26],\n [16, -9, -1, 26, 20, -18, -18, -26, -20, 17, 15, 24],\n [-11, 11, -16, 24, -2, 2, -8, -9, 20, 2, -11, 19],\n [13, -19, 7, -21, 18, 18, 26, 3, 17, 7, -6, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "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, 22, -21, 12, -21, 26, -23, 26, -18, -22, -17, 20],\n [-19, -4, -23, 10, -20, -21, 18, 24, 15, -12, 8, 23],\n [5, -13, 8, -16, -17, -10, -14, 7, 18, 24, -22, 21],\n [-17, 5, -15, 25, -14, -6, 21, 26, 6, 14, 21, 24],\n [20, 23, 5, -15, 19, 8, 9, 11, 21, 1, -14, -15],\n [-5, 17, -25, 2, -14, 8, -14, 7, -8, -18, 25, 4],\n [6, 0, 18, -25, -12, -8, 4, -11, 16, -12, -21, -13],\n [0, 11, -8, 10, 16, -23, -1, -18, 14, 22, 13, -12],\n [14, 10, -23, -1, 25, -9, 14, 26, 8, 14, 14, 2],\n [26, -3, -23, -6, 12, -20, -4, 13, -6, -26, 14, -2],\n [4, 17, 11, 18, -22, 26, 4, 24, -26, 3, -9, -19],\n [-1, 13, -12, -8, -17, -3, -11, 16, 4, 17, -11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -7, 8, -18, 13, -17, 18, -9, 18, 18, -12, 18],\n [3, 21, 5, 13, 0, 0, -8, -17, 17, 19, -21, 26],\n [-3, -18, 0, -20, -21, 6, -6, 19, 11, 17, -10, 4],\n [10, -16, 1, -22, -15, -24, 14, 11, -25, -1, -25, -15],\n [13, -25, 14, -11, 3, 20, 19, 25, 9, -23, -16, 26],\n [-3, -9, 0, 10, -25, -12, -16, 0, 22, 21, 20, -4],\n [8, 25, 3, 20, -3, -8, 2, -14, 21, -4, -15, 22],\n [21, 14, 2, -21, 24, -4, 4, 18, -6, -3, -19, 17],\n [-18, -5, -23, -14, 7, -24, 10, 1, -1, 23, 26, 19],\n [7, -12, -19, 21, 8, -3, 25, 25, 10, -23, -15, -8],\n [-12, 3, 18, 10, -15, -8, 7, -20, 1, 1, 2, 10],\n [-7, -16, 23, 23, 12, 15, -4, 25, 19, -7, -7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-25, -14, -14, 14, 22, -12, 4, -4, 26, -5, -11, 15],\n [2, -7, 1, 0, 17, 2, -22, 25, 22, 15, 11, 26],\n [25, 11, 17, 26, 24, -25, 18, -7, 16, 20, -14, -1],\n [8, 19, -19, 1, 14, -12, 23, -19, -16, 2, -22, 20],\n [20, -20, 26, -9, 1, -15, -15, 9, 2, -16, 26, -21],\n [-6, -17, 5, 20, 6, -10, -24, 16, -9, -17, 26, 14],\n [12, 16, -19, 7, 10, 14, 6, 22, -17, 13, -9, -2],\n [15, 14, 9, -25, -8, -17, 22, -24, 26, -8, 24, -1],\n [24, 24, 20, -2, 23, -10, -17, 19, 24, 23, -16, -16],\n [-15, 13, 21, -19, -3, -13, -4, 23, 26, 9, -10, 18],\n [-22, -24, -18, -7, 23, -7, 24, -8, -6, -11, 6, -22],\n [-3, -12, -1, 17, -2, 1, 6, 19, -9, -9, 11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 22, 23, -12, 17, -14, 25, 7, -23, 8, -8, 4],\n [-2, 13, -15, -15, 15, -2, 6, 10, 1, 25, 16, -18],\n [-13, -24, -22, -1, 26, 14, -9, 11, -6, 12, -11, 13],\n [-4, 2, -17, -22, -16, 2, 26, 18, 0, 25, 7, -13],\n [14, 15, -17, 15, 24, -16, -16, 8, -8, -3, -26, -15],\n [20, -13, -24, 25, 18, 23, 5, -11, 11, -17, -10, 22],\n [13, -23, -12, 6, 12, -17, -20, 6, -10, -15, -10, 20],\n [-11, -13, -24, 24, 17, 24, 23, 3, 19, 25, 14, 8],\n [-1, -15, 4, 25, -10, 10, -19, -8, -1, -23, -12, 24],\n [20, -13, 3, 21, 15, -3, 19, 25, 16, 7, -8, -24],\n [-23, -16, -14, 23, -9, -8, 17, 6, 11, -24, 22, 8],\n [-26, 8, 9, 11, 12, -2, 13, -14, -23, -21, -16, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "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, 7, 13, 25, -18, 9, 22, 12, 15, 10, 15, 17],\n [-6, -7, 11, -26, 8, 1, -20, 16, 17, -18, -26, 9],\n [7, 7, -10, 26, 5, -25, 9, -2, 16, 24, -1, 18],\n [-1, -6, -9, 2, 24, -3, 20, 1, -15, -16, 0, -4],\n [6, -11, 1, 1, 18, 11, -21, 15, 2, 7, -24, -21],\n [21, 11, -14, 9, -12, -21, 6, 14, -15, 16, -14, 6],\n [24, 1, 26, 9, -22, -2, -10, 10, -8, 8, 16, 7],\n [19, -21, -8, -26, -20, 7, -8, 6, -1, 14, 26, 22],\n [15, 0, 11, -1, 8, -7, -3, 20, -6, -1, -7, -21],\n [-24, -17, -15, 6, -5, -11, -10, -17, -15, -8, 13, -4],\n [13, -17, -17, 23, -17, 12, 3, -23, -26, 16, -8, -22],\n [3, -1, 13, 7, -25, -3, -13, 14, 15, -14, 2, -26]]\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[[19, 7, -23, 1, -8, -26, 9, 16, -14, 23, 15, -22],\n [6, -13, -11, 5, 23, 0, 8, -24, -23, -20, -14, 14],\n [-24, -10, 20, -17, 20, -26, 1, 26, -17, -20, 12, -24],\n [-20, -18, 13, 8, -1, -22, -14, 18, 3, 13, 23, 12],\n [-17, 15, -4, -16, -15, -14, 13, 22, 19, 22, 24, -11],\n [-18, 25, -17, 2, -18, 6, -3, 8, -16, 12, 23, -14],\n [-4, -2, 23, -11, 21, -6, -17, 14, 13, -8, 8, 1],\n [14, -25, 24, 3, 13, 23, 13, -22, 11, 15, -12, 9],\n [-24, -3, 14, 21, 21, 20, 14, 22, 26, -15, -19, -13],\n [-9, 17, 19, -7, -4, -22, -26, 18, 19, -25, -11, -22],\n [-5, -26, -15, -8, -5, 15, 17, 24, 21, -10, -14, 12],\n [1, -24, -22, 9, -12, -10, 17, 19, 2, -23, 5, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575", "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, -23, -14, -7, 20, -9, 22, 24, 15, 10, -15],\n [-2, 3, -12, 9, -19, 1, 25, -5, 22, 11, -11, -22],\n [19, 7, 22, 11, -16, -25, -2, -2, -26, 4, -22, 13],\n [-23, 24, -22, -22, -11, -9, 16, -10, 8, -9, -23, 24],\n [4, 4, -18, 4, -22, 9, -11, 15, 14, -11, -7, 3],\n [-1, 22, 4, 23, -12, 25, 14, 11, 11, 16, -7, 8],\n [-4, 17, 20, 12, -2, 23, -5, 20, -19, -18, -12, 21],\n [-7, 8, 10, -24, 7, 7, 9, 8, -18, 3, -1, -15],\n [-3, 14, -8, 17, -11, -1, -4, 6, 15, 3, -4, -17],\n [9, 4, 16, -5, 16, 16, 11, 20, -25, 26, -4, 8],\n [10, 5, 16, 26, -15, 8, 14, -24, 7, 11, -3, 11],\n [-10, 13, -26, -19, -12, 23, 18, -2, -19, 25, 5, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-14, 19, -12, -21, 6, -20, 6, 20, 2, 11, 10, 17],\n [5, -24, -7, -13, 1, 11, -23, -12, -10, 10, -3, 11],\n [15, 14, 9, 14, -19, -24, 3, -5, 25, 6, -2, 25],\n [3, 10, -24, -23, 2, 5, -4, -8, -12, 24, -11, -4],\n [13, 19, 10, -26, -8, 10, 8, 3, -10, 12, 22, -1],\n [-14, -5, 19, -4, 17, 16, 6, 0, 8, -15, -18, 7],\n [-13, 10, -24, 17, 17, -6, -20, 6, 8, -16, 18, 5],\n [-5, 15, -8, 9, 10, -16, 14, -14, 1, 22, -12, -14],\n [26, 16, 6, -19, 5, 10, 21, -23, 24, -9, -4, 2],\n [-25, -14, -11, -19, -8, 5, -24, 24, 22, 5, 14, -6],\n [-2, 26, -10, -2, 6, 4, 9, -4, 20, 17, -2, 22],\n [17, 21, 3, -14, 16, 20, 2, -11, 11, 0, -1, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[20, 10, -24, -1, 7, 6, -12, -25, 1, -7, 11, 17],\n [26, -11, 19, -23, -19, 17, 19, -7, -1, 5, -14, -22],\n [17, 15, 26, 24, -14, 14, -16, 10, 5, 18, 15, -9],\n [2, -12, -7, 17, 9, -22, 13, 10, 6, -9, -8, 24],\n [5, 15, -5, 14, -26, -2, -7, 8, 18, -21, -21, 23],\n [10, 22, -24, 10, 4, 8, 18, -12, -10, -12, -22, -5],\n [19, -16, 1, -13, 12, -24, 25, 15, -16, 3, 11, -22],\n [25, -5, -14, 17, 24, 24, -6, 10, -2, 25, -6, 1],\n [14, -23, 2, 20, 8, -4, -20, 25, 25, 19, 19, -18],\n [-4, -24, -18, 26, -23, 22, -2, -21, 21, -9, 18, -20],\n [8, 4, 11, 5, 8, 1, 17, -22, 3, -5, -10, -17],\n [-20, -23, 15, 0, -20, -4, -16, 26, -19, -19, 10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "577", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-20, -5, 9, -25, -3, 24, -25, 21, -15, 20, 15, -1],\n [11, 18, -21, -4, -25, -1, -13, -9, 11, 5, 24, -13],\n [3, -14, 13, 4, 10, 18, 11, -5, 1, -8, 16, -11],\n [-22, 17, 22, -25, -17, 20, -8, -7, 2, -2, -10, 24],\n [24, -14, 18, -11, 26, 8, 9, 12, -24, -18, 13, 23],\n [26, 19, 25, 2, -22, -24, -17, 4, -16, -10, 13, 14],\n [-19, 25, -25, -23, -11, 14, 14, -6, -22, 8, -13, -12],\n [-21, -11, -4, 4, 15, 19, -15, 14, -8, -15, 18, -14],\n [22, -25, -7, 4, -18, -6, -19, 12, 10, 2, -8, 8],\n [18, 11, -1, -16, 9, 8, -23, -24, 18, 20, -15, 5],\n [20, -1, 16, 16, -14, 17, 11, 2, 25, 24, -8, 8],\n [21, 14, 0, 19, 4, -24, 8, -3, 25, -20, 24, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "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, -26, 17, 26, -21, 12, 7, -9, -2, -12, 20, 5],\n [15, 22, 23, -9, 4, 2, -12, -4, 11, 14, -16, -12],\n [-4, -24, -8, -26, -3, 22, -16, 3, 23, -16, 12, -26],\n [-15, -23, -2, -19, -12, 16, 3, 13, 5, 17, 8, -6],\n [4, 9, 0, 17, -19, -4, -4, 15, 6, -14, 12, 25],\n [8, -11, -15, 4, -22, 23, 13, 17, -2, -6, -24, 21],\n [-17, -4, -10, 15, 8, -2, -25, 0, 19, -18, 22, -23],\n [-1, 5, 2, -5, 20, -14, -4, 4, 24, 14, 9, 26],\n [13, 4, -12, -13, 8, -3, 3, 3, 0, 22, 13, -13],\n [18, 20, -16, 20, 17, -1, -6, -18, 20, -26, 17, -21],\n [-26, -5, 24, -14, 11, 22, 18, 14, 13, 4, -12, 23],\n [-25, 26, 4, -1, -25, -16, 6, -9, -6, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[12, -6, 22, -11, -20, -5, -20, -25, 10, -13, -19, 2],\n [17, -20, 11, 18, -5, 17, -10, -11, 6, 12, 8, 11],\n [5, 26, -24, -24, -19, 19, 4, -18, -22, 1, -12, 22],\n [0, 15, 4, 13, -9, 11, 22, -23, -6, 20, 15, -4],\n [18, -5, -26, -2, 14, 1, 10, -16, -5, -2, 26, -6],\n [9, -7, -11, 1, 2, 23, -1, 13, -25, 22, -17, -14],\n [-12, -18, 0, -19, -21, 9, 23, -3, -24, -1, 9, -6],\n [-14, 25, -16, -19, 19, 19, 21, -13, 6, -25, 25, -26],\n [-16, -21, 5, -12, -15, 10, 2, 17, -5, 19, -13, -8],\n [-22, 8, -2, 23, 11, -18, -20, 26, -9, -25, 25, -17],\n [17, -25, 18, -19, -20, 8, -4, -19, -6, 6, 20, -26],\n [-15, -16, 21, 3, -23, 7, -4, 5, -24, 1, -23, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-15, -3, 6, -24, -23, 3, -21, 22, 3, -19, -9, -11],\n [26, -21, -3, 24, 1, 5, -2, 1, -6, -19, 9, -18],\n [13, -6, 24, -26, 26, 26, -23, -17, -1, 13, -24, 17],\n [-18, 5, -24, -23, -21, -18, -1, -25, -25, 23, -6, -5],\n [-24, 8, 23, 11, 6, -12, -16, -17, 9, -13, -25, 18],\n [21, 17, 10, 24, 2, 8, 26, -7, -6, 7, 22, 26],\n [16, 6, -8, -19, 4, -16, -19, -2, 22, -7, 11, -20],\n [26, -14, 12, 16, -17, -19, 15, 16, -7, -10, -16, -11],\n [10, 15, 5, -1, 25, 10, 25, -18, 8, -24, 4, 15],\n [-20, -25, -2, 13, -15, 3, 3, 2, 14, -16, 24, 25],\n [-4, -10, -14, 6, -26, 13, -14, 11, -24, -11, 15, -20],\n [26, -24, -13, -11, -23, 4, -14, 0, -26, -2, 10, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "591", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[17, -16, -18, -20, -13, 3, -3, -24, 21, 12, 0, -26],\n [11, -1, -21, 15, -15, 24, 11, 19, 8, -17, -18, -4],\n [3, 25, 24, -5, 20, -18, -8, -19, -23, -22, -8, 19],\n [-9, 2, -8, -21, -22, 16, -22, -19, 0, 10, 16, 18],\n [11, 10, -9, -1, 15, -11, -5, 19, -4, 20, -24, -24],\n [-15, -4, 20, -16, 15, 25, 20, 23, 19, 2, -21, 19],\n [-11, 7, 24, 10, -16, -16, 26, -2, -8, 5, 23, -19],\n [-15, 14, 8, -21, -6, 26, -1, -26, -10, 8, 0, 23],\n [23, -25, 9, -26, -17, 4, 10, -22, 14, 19, 26, -14],\n [18, -3, 0, -26, 22, -7, -19, -24, 22, 5, 17, -2],\n [-2, 23, -13, 16, 0, 21, 5, 0, -23, 23, 12, -16],\n [21, 21, -24, -2, -3, -18, -19, 12, 4, -10, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-23, -23, 10, -19, 15, 22, -21, -18, 15, -19, 5, -12],\n [-9, -4, -22, 23, 0, 6, -25, 15, 11, 1, -3, 24],\n [-6, 4, -16, 23, 1, 21, 13, -23, 16, 15, -11, -15],\n [-5, 8, 16, -11, -3, 8, 1, 15, 2, -6, 21, -2],\n [12, 4, -12, 20, 15, 8, 11, 23, -5, -22, 21, -14],\n [5, -24, -12, 0, 25, 0, 3, -21, -2, 1, -5, -23],\n [-12, -1, -9, -18, 25, -23, 21, 23, -22, 18, -21, 24],\n [-15, 4, 20, -18, -20, 2, -13, 24, -7, 21, 5, -5],\n [9, 17, -9, 13, 22, -2, 4, 8, -1, -23, 15, 21],\n [-7, 7, -15, -11, 15, -22, 17, 8, 17, 0, -26, 7],\n [16, 5, 17, 12, 6, 4, -14, 18, -25, 3, -17, -4],\n [6, 12, 18, 2, 3, 7, 25, 12, -10, -5, -22, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 5, -3, -16, -16, -10, 5, -8, 0, 5, -2, 1],\n [13, 25, 0, -13, 15, 12, -25, -10, -26, 18, 5, -8],\n [-13, 4, -9, 25, -13, 20, -13, -3, -22, -11, -22, -14],\n [-11, -12, 4, -22, -6, 3, -4, 11, 2, -14, 5, 21],\n [15, 0, 7, 18, 22, 6, -23, -9, -21, 1, 17, 0],\n [-1, -7, -14, 1, 7, 22, -4, -17, 24, 3, -5, -22],\n [26, 17, 23, -18, 16, -23, 15, -26, 7, 14, -1, -9],\n [-11, -4, 19, 9, -1, -25, 17, 25, -22, 2, -23, 20],\n [8, -5, 22, -19, 17, -6, -19, 25, 25, -22, -6, 0],\n [11, -22, -6, -19, -5, -9, -23, -23, 10, -12, 11, 0],\n [-6, 21, 19, 19, 21, -23, -16, -8, -8, 0, 13, 15],\n [1, -22, 21, -2, -24, -1, -17, -3, 2, 18, -20, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"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, 19, 0, 15, -18, 17, -24, -14, -21, 11, -6, -8],\n [-2, 12, -23, -5, -22, -26, 23, -10, -18, -18, 26, -3],\n [-17, -7, -10, -14, 2, 9, -4, 0, -9, -9, -18, -24],\n [-20, -12, 3, -18, 14, 0, 9, -9, 4, -10, 26, -21],\n [12, -2, 15, 15, 11, 11, 4, 24, 2, 13, -18, -26],\n [-11, 11, -4, -19, 20, -15, -17, -11, 20, 16, -3, 12],\n [-19, -16, 14, -1, -20, -12, -12, 21, -24, -11, -12, -2],\n [6, -13, -3, -16, -24, -18, -21, 4, -11, -16, 23, -10],\n [22, -24, -8, -3, 20, 15, -19, 22, 9, 13, -25, -4],\n [13, 3, -2, -20, 1, 14, 23, -10, 5, -26, 0, 17],\n [9, 22, -20, -24, 3, -26, 24, 7, 11, 16, 26, 9],\n [6, 16, -11, 11, -16, -19, 25, -26, -13, 3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[7, 11, -1, 14, -13, 13, 8, 15, -9, -7, -18, 14],\n [24, 18, 6, 22, -23, -23, 21, -11, 20, -1, -21, 10],\n [-5, 15, 12, -20, 15, 3, -17, -12, -21, -3, -25, 13],\n [25, -12, 26, -6, -9, -22, -2, 9, -17, 24, 19, -4],\n [-3, 18, -17, -21, -14, -6, 5, 16, -12, -25, -12, 24],\n [-10, -7, 23, -21, -12, -10, -1, -5, -18, -15, -5, -4],\n [10, -13, -3, -19, -1, 5, 1, 5, -5, 22, -18, -24],\n [-2, 12, -15, 2, -24, 14, 19, -4, -4, -9, -16, 9],\n [-1, -19, 1, -9, -14, 9, 15, 13, 17, 24, -15, -5],\n [-25, 13, 1, -14, 6, -24, 7, -4, 5, -7, 1, -19],\n [-24, 3, -2, 26, 3, 2, 20, 3, 7, -2, -10, -3],\n [11, 1, 6, 9, 24, -20, -4, 19, -1, -13, 15, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -20, 21, 9, 12, -12, 22, -24, 21, -25, -20, -11],\n [-6, -18, -15, 2, -3, 6, -13, 16, -9, -22, -12, -20],\n [-2, -13, 25, 13, 9, 8, 17, 23, -3, -12, -16, -3],\n [-16, 17, 24, -10, -21, -6, -19, -12, 25, 5, -17, 1],\n [-12, -15, 16, -9, 10, 17, -3, 10, 2, -17, -13, -11],\n [10, -16, 24, -1, 13, -8, 25, -9, 3, 5, -4, 26],\n [-15, -14, -6, -6, 2, 2, 23, 0, 2, -12, 20, -15],\n [14, -8, -15, -4, -22, -1, 26, 25, -17, -5, 12, -4],\n [-16, 1, 4, -19, 26, 12, 21, 1, -11, 19, 20, 25],\n [4, 14, 21, -11, -22, 8, 26, -2, -14, 2, 0, 13],\n [-10, 10, 11, 2, 7, 3, 4, -5, 19, -2, -23, 8],\n [14, 23, 17, -18, -1, 0, 0, -9, 3, 18, 19, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[15, -24, 2, -20, -9, -11, 22, 5, 11, -2, 17, 5],\n [-8, -24, 8, 23, 2, -16, -21, -8, 10, 18, 0, -22],\n [-1, 8, -8, -10, 8, 20, 22, -14, -13, 3, 21, 16],\n [-10, 10, 26, -12, -9, 21, -13, -13, 18, 6, 11, -16],\n [-16, 21, -1, -24, -2, -10, -5, 2, 19, -1, 7, -1],\n [-18, 13, -16, -20, 3, -25, 3, -23, -13, -14, -2, -14],\n [-14, 10, 17, -21, -1, -13, -19, -3, -5, 13, 12, 22],\n [-6, 16, -1, -17, -14, 15, 26, -13, -18, -20, 12, 4],\n [23, -11, -19, 21, 24, -12, -2, 20, 11, 14, -12, -2],\n [-20, -1, -19, -9, -6, -11, 20, -24, -26, -14, 5, -15],\n [4, 14, -25, 14, -19, -2, -22, 18, -25, 15, 11, 12],\n [-24, 19, 21, 11, -5, 13, 6, 25, 5, 20, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-24, -21, 22, -14, 4, -10, -6, -11, -10, 5, -26, 21],\n [11, -19, -26, -25, 20, 10, -3, 0, -7, 20, -6, 15],\n [10, 8, 11, 26, -12, 23, 19, 15, 3, -23, 16, 25],\n [12, -12, -4, 14, -12, -1, -15, -9, -21, -9, 23, -3],\n [11, 1, -12, -8, -22, -23, -10, 26, -17, -15, -22, -20],\n [17, -4, -25, 3, 25, 22, 18, 10, -22, -7, -1, 17],\n [17, 12, -21, 2, -17, 24, -11, 7, 4, 9, 14, -22],\n [6, 16, -8, 5, -4, -24, -26, 9, 14, 1, 21, 12],\n [-22, -14, -16, 19, -5, 22, -4, -15, 26, 26, -6, -8],\n [-22, -3, 3, -19, -25, 22, 7, -4, -24, 25, -3, -9],\n [20, 10, 22, 4, -13, -26, -13, 14, -22, 4, 4, 3],\n [9, -26, -24, -7, 16, 21, 16, -6, 3, 15, 17, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-22, -17, -3, 18, 24, 12, 21, -21, -17, 15, 16, -17],\n [-2, -13, 20, 12, -14, -16, 12, -16, 19, 22, -11, 6],\n [14, 14, 5, -17, 24, -12, -11, 16, 0, 22, 24, 18],\n [5, -21, 20, 21, 9, -19, -2, -20, -10, 21, 3, -25],\n [-10, -23, -1, -13, -19, -22, -22, -22, 0, -22, -24, 11],\n [3, -26, -19, -14, -7, -21, 23, 23, 21, -19, 3, 22],\n [13, -12, -17, 6, -18, 22, 25, 6, -18, -13, 5, 10],\n [-21, -22, -23, 21, -11, -17, 4, 4, -13, -14, -23, 19],\n [-1, -3, -18, 8, 15, -12, -3, 4, -8, -25, -25, 14],\n [9, 10, 7, 12, -8, 11, -4, -11, 19, 17, -21, -1],\n [-5, 18, 20, -3, 19, 13, -6, 3, 25, -16, 26, -18],\n [-15, -1, 11, 24, -24, 6, -12, 20, -22, -3, -16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -17, 25, 16, 1, 12, -10, 17, -1, -2, 9, -15],\n [-24, 23, 2, 17, -3, -8, -14, -11, 13, 0, -21, 15],\n [-17, 11, -19, -9, 5, -10, 15, -25, 17, -7, -17, -18],\n [21, 12, 14, -2, -2, -3, -21, 3, -17, 12, 4, -9],\n [16, 6, 26, -8, -4, -22, -1, 2, -3, -21, 12, -23],\n [21, 15, -1, -12, -14, 13, -5, -14, 12, -10, 9, 12],\n [21, -2, 7, -6, -2, -2, -5, -4, -2, -13, -13, -1],\n [13, 3, -1, 11, -5, 12, 12, 7, -2, 9, -14, 2],\n [15, -18, -12, 4, 17, 0, 4, -17, 24, 26, 10, -20],\n [5, 25, -16, 21, 18, 1, -23, 21, 18, 4, 2, 6],\n [-23, 20, -1, 26, 4, 4, 0, -2, 21, 9, 22, 4],\n [16, 10, 18, 17, -4, 8, -23, 1, 15, 14, 15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-26, -15, 16, 26, 13, -1, 19, 19, 25, -4, 22, -5],\n [24, 25, 1, 26, 26, -10, -21, -13, 23, -10, 11, -22],\n [-14, 21, 26, -18, 17, 15, -1, -14, -8, 21, -10, -11],\n [3, 5, -13, 21, -12, -15, 10, -16, -22, -16, 7, -8],\n [-1, -1, -10, 4, -8, 17, -7, -4, -2, 1, 10, -15],\n [21, -26, -25, -17, 7, 5, -2, -17, 23, -26, 5, 10],\n [-15, 22, 24, -9, 3, -14, -24, -6, 15, -13, 13, -17],\n [-25, 18, 10, -16, -26, -1, 15, -14, 1, 9, -6, -17],\n [-15, 19, 0, -24, 1, -25, 1, 24, 4, 16, -6, -20],\n [23, 4, -13, 12, 12, -18, -4, -15, 2, 11, 12, -5],\n [-23, 21, -20, 13, -19, 25, 8, -18, 24, -14, 12, -7],\n [-6, 20, -8, -25, 17, 13, 3, -4, 13, -14, 6, 5]]\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[[1, -3, 15, 1, 3, 26, 14, 2, 7, 24, -5, -2],\n [-13, -17, -17, -19, -13, 18, 11, 5, 26, 18, 5, -24],\n [-7, -14, -4, -8, -11, 9, 8, 20, 20, 23, -20, 25],\n [10, -19, -2, -4, -17, 3, 6, -16, 8, 0, 26, -24],\n [20, 22, 23, -19, -14, 15, -24, -7, 19, 18, 8, -14],\n [-7, -3, -18, 3, -2, -11, -19, 17, 1, -15, 24, -3],\n [22, 2, -12, -9, -20, -14, -8, 21, 16, -22, -1, -25],\n [6, 21, 10, -2, -2, 12, 3, 14, -23, -8, 0, 25],\n [20, 12, -3, 23, 10, 26, -2, 2, 4, 18, 8, 1],\n [11, 17, 26, 23, 23, -23, 1, 25, 4, -4, -13, 1],\n [-13, -26, 16, 5, 14, -9, -22, 15, -12, 15, -11, 9],\n [9, 13, 3, 11, -4, -16, -2, 18, 24, 16, -25, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[20, -3, -14, 15, 10, 3, -16, -4, 19, 1, 2, 25],\n [-12, 18, -24, -18, -19, 20, 6, 7, -18, 26, -10, 14],\n [-26, 13, -22, 3, -16, 1, 11, -10, 23, -4, -9, 10],\n [0, -2, -22, -8, 0, -14, -20, -1, -13, 0, -19, 4],\n [8, 0, -23, 15, -23, -9, -4, 5, -15, 25, -7, 20],\n [18, -15, -19, -5, 0, 14, 25, 14, -10, 5, 6, 4],\n [-21, 12, -18, 15, 5, 9, -11, -15, 14, -24, 0, 0],\n [-18, -10, 19, -22, -1, -6, -26, -26, 8, -18, -4, 11],\n [14, -23, 25, -8, 10, -22, 1, 19, 15, 21, -4, 11],\n [25, -4, 19, -9, 2, 1, -18, 12, 23, -17, -25, -14],\n [11, 0, 14, -7, 13, -17, -11, -12, -14, 23, 11, -7],\n [-3, 14, 23, -20, -4, -3, 2, -22, 16, 18, 8, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[9, 24, -9, -21, -4, -17, -20, 17, -19, -14, 3, -9],\n [-13, -16, 15, 11, -14, 15, 17, 6, 23, -14, -2, -3],\n [2, 9, -21, -9, 1, -22, -9, 10, -20, -18, 8, -15],\n [25, 19, 13, 17, 12, -3, -18, -15, 9, 10, -18, 12],\n [19, 25, -5, -10, 6, 20, -3, -12, 2, 5, 6, 2],\n [-12, 0, 7, -23, 22, 21, -9, -6, 21, -19, -21, -7],\n [-25, 24, 18, -5, -6, -21, 5, -21, -14, -26, -5, 26],\n [-3, 14, 3, -5, 17, -15, -1, -23, -8, -11, -15, 6],\n [-6, 9, -18, 12, 15, 18, -19, -7, -17, 5, 1, -17],\n [-19, 25, 20, 6, 20, 22, -14, 17, 8, 24, 2, -22],\n [-24, 26, 10, 14, -21, 21, 15, -11, 8, -9, -16, 24],\n [-4, 20, -16, 2, 15, 0, -18, 8, -18, -9, 17, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "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, 9, -26, 0, 18, 13, 11, 2, 13, -8, -3, 17],\n [-26, 9, -4, -14, 3, 22, 24, 24, 10, -16, -20, 8],\n [-16, 22, 16, 20, 24, 13, 21, -6, 20, -24, 3, -3],\n [11, -24, 10, 6, -5, 4, 19, -15, 18, -13, -15, 0],\n [-14, -3, 11, 26, 20, 21, -18, -19, 10, -12, -20, -3],\n [22, -11, -3, 16, -20, 16, 1, -25, 7, 11, -24, -26],\n [4, -4, -7, -11, 19, 5, -10, -9, -23, 8, 13, 9],\n [-4, -12, -14, -13, -13, 10, -22, -5, 1, 18, -23, 23],\n [11, 2, 10, 8, -7, 8, 8, -7, -25, 25, -9, 3],\n [15, 26, 2, 12, 25, -5, 2, 19, -17, -7, -11, -21],\n [-10, -21, -5, -9, 5, 1, 15, -17, 14, -5, 1, -12],\n [16, 2, -20, 23, 7, 5, -25, -1, 18, -16, -2, -8]]\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 sum of all singular values:\n[[-7, 6, -10, 25, 3, -9, 5, 13, 18, -23, 5, -8],\n [-24, 11, 1, 11, -21, 13, -10, 15, -22, -8, 16, 15],\n [8, -5, -3, -17, -25, 1, 14, 10, 26, -10, -21, 16],\n [-22, 12, -20, 5, -23, -6, 15, 5, -9, 6, -13, -21],\n [-16, 19, -7, 2, 8, -11, 21, -20, 13, 9, 17, 17],\n [4, 15, 17, 16, 16, 20, -21, 2, 0, 16, -25, -5],\n [-18, -16, -11, 18, -14, -9, 26, -2, 6, 25, -17, 3],\n [24, 22, -26, 6, 22, -12, 2, -25, -16, 26, 7, 25],\n [14, -8, -25, 21, -7, 14, 25, 4, 26, -23, 2, 3],\n [-14, -12, -7, 7, 1, -7, 23, -2, 0, 3, 14, -7],\n [-26, 8, 22, 16, -3, -2, 13, 26, -15, -16, 3, -14],\n [20, -2, 25, -2, -10, -15, 24, 25, -16, -17, -10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-11, 25, -7, 22, -22, 14, 5, 0, -23, 14, 21, -20],\n [19, -13, 12, -3, 21, -9, 11, 12, 24, 13, -26, -10],\n [-1, 24, -5, 12, -9, 11, 1, -6, 11, 6, 3, 15],\n [-19, 3, 12, -18, 6, 16, 2, 4, -24, 23, 11, -16],\n [-22, 4, -7, -23, -19, 15, 8, -14, 22, -22, 13, -8],\n [-9, 6, -23, -9, 19, -3, 16, 2, 4, 1, -18, 18],\n [-1, 22, 20, -25, -21, 2, -1, 1, -20, 7, 18, -17],\n [21, 14, 13, 20, -5, 0, 12, -5, -8, 9, -18, -8],\n [-25, 1, 12, -5, 24, -21, 20, -20, -21, 6, -13, -26],\n [-2, -21, 1, -9, 0, 22, -25, 13, -6, -4, -25, -11],\n [-23, 7, -22, 22, 7, -5, 19, -7, 12, 20, 23, -14],\n [17, 7, 17, -21, 2, 6, 26, -26, 20, 21, -20, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -13, 24, -3, -8, 0, -4, 18, -6, 17, 2, -26],\n [4, 0, 17, 9, 0, -12, -2, 21, -12, 13, -8, 20],\n [23, -16, 14, 6, 14, -4, -15, -25, 16, -6, -13, 7],\n [-12, -6, -4, -6, 23, -13, -6, -15, 15, 19, 20, -22],\n [-25, -5, -21, 17, -25, 2, 9, -20, -11, 6, 6, -13],\n [16, -15, 16, -21, -15, 26, 4, -15, -17, 13, 0, 25],\n [24, -20, 19, 9, 6, 0, -19, -22, -19, 13, -6, -3],\n [-20, -8, 4, 9, 0, 2, -4, -7, -21, -15, 23, -15],\n [23, -24, 15, 12, 8, -8, 18, -23, 4, 15, 11, 6],\n [-21, -19, 1, -12, 4, -19, -21, 2, 24, 19, 7, -20],\n [13, -17, -14, -5, -6, 25, -26, 14, 15, 25, -25, 25],\n [2, -16, 10, 23, -20, 8, 3, -11, -12, 13, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[10, -24, 2, 10, -18, 0, 5, 21, 19, 23, 12, 4],\n [20, -1, 13, -24, -16, 25, 2, 0, 23, 20, -17, 8],\n [20, -4, -21, -16, 16, 24, 0, 4, 3, -24, -14, 13],\n [-6, 16, -16, 18, -24, 11, 4, -3, 15, 24, -15, 19],\n [16, 0, -6, -2, 3, 3, -17, -24, -14, 0, -9, 18],\n [-3, 19, -13, 12, 17, -23, -11, 24, -17, 21, 10, 0],\n [21, -26, -22, -14, 18, -24, -10, -8, 10, -22, 20, 15],\n [17, -3, 16, 6, -6, -24, -23, 24, 5, -3, 25, 8],\n [-9, -24, 12, -1, 26, -3, -26, 24, 23, 7, -15, -10],\n [-6, -6, -24, 17, 1, -2, 17, -21, 15, 3, 5, -5],\n [11, -13, 7, 16, 20, -1, 13, -14, 3, -8, 15, 14],\n [23, 12, -24, 4, -15, -12, 26, 18, 11, 13, -13, 8]]\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[[-11, 23, -3, -10, -9, 15, -10, -11, -6, -3, 7, 25],\n [9, 16, 0, 12, -10, -2, 24, 11, 15, -6, -23, -2],\n [3, 6, 12, -1, -2, 26, -11, 22, -3, -22, 15, 12],\n [-14, 3, -20, 20, -10, 0, 8, -22, 15, -22, -3, -20],\n [-20, -13, -12, -22, 10, -23, 3, -7, 26, -1, -18, 3],\n [17, 21, -5, 13, 14, 17, 3, -7, 1, -20, 26, -23],\n [1, 8, 6, -20, -18, 7, 12, 15, 7, -14, 2, 8],\n [18, -17, 3, 17, -1, 8, 1, 2, 25, -21, -24, 2],\n [-25, -5, 19, 20, 23, 0, 24, -5, -17, 25, 22, 22],\n [-8, -3, 0, 9, 16, -10, -17, -10, 17, -17, -17, 11],\n [-10, -1, -1, 24, 7, -23, 23, 0, -6, 9, 11, 19],\n [4, -20, 17, 7, -9, -3, -14, -14, -2, -22, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "514", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[17, 19, 6, -3, -17, -2, 14, -17, 12, -11, 1, -15],\n [17, 5, 24, 2, 18, 26, 23, 0, -1, -24, -1, 12],\n [-26, 8, 26, 0, 19, -23, -8, -5, -21, 25, -18, -16],\n [-5, 20, -18, 2, 16, -17, 7, 4, -5, 19, -23, -25],\n [-22, 19, -12, -8, 11, -12, 19, -19, -7, -15, -23, 26],\n [11, 16, 12, 9, -12, -26, 4, -18, -4, 25, -1, 13],\n [17, 12, -9, 6, 14, 12, -13, -26, -14, 25, -12, 10],\n [-22, -13, -13, 19, -22, -16, 5, 24, -22, 9, -12, 26],\n [-20, -22, 3, -12, 3, -13, -3, -3, 8, -22, -15, -7],\n [19, -22, 9, -6, 21, 12, -24, 2, -2, 0, 9, 25],\n [-5, 11, 8, -26, -24, -3, -19, 21, 12, -9, 14, -24],\n [-9, -11, 5, 26, -26, 26, -1, 25, 21, -15, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[14, 26, -14, -15, -14, -9, -8, -8, 24, -21, 21, -20],\n [-20, 1, 1, -8, -11, -10, -5, -8, 21, 2, 21, -8],\n [20, 8, 20, -2, 21, -7, 10, -8, 15, -14, 20, -15],\n [22, -12, -23, -12, -10, 0, -16, -4, -12, 25, 4, 26],\n [-1, -20, -14, -14, 25, -7, 7, -17, 23, 25, 10, 25],\n [24, 0, 7, 9, -11, -6, -11, -10, -12, -14, 6, -22],\n [0, 25, -26, 17, 3, -4, -12, 9, -8, 3, -11, -9],\n [-1, -10, -16, 25, 18, 2, -18, 22, -10, 0, 10, -5],\n [-19, -24, 11, 8, 5, -19, 17, 0, 5, 9, 7, -2],\n [4, 15, 20, -14, -12, 24, 23, -14, 25, 25, 6, 4],\n [-2, 21, 13, -4, 11, -24, 25, -11, -25, -4, 7, 3],\n [20, -17, -26, -5, 25, 20, 6, -2, -5, -11, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, -22, 26, 10, -4, 15, 0, -15, -17, 7, 6, -11],\n [2, -9, 0, -20, 9, 0, -17, -17, -16, 3, -24, 2],\n [-13, -14, -8, -2, -17, -12, 1, 13, 22, 11, -20, -13],\n [3, 13, -15, 1, 23, -13, -26, -23, 22, -9, 24, 9],\n [5, 1, 1, 11, 5, -19, -2, 20, -7, 6, 3, 10],\n [-11, 26, -2, 11, 26, 15, -17, -22, -19, 6, 10, -26],\n [4, -20, 20, -4, -3, -13, -4, -18, -19, -19, -24, 5],\n [25, -23, 22, 11, -25, -18, 19, -26, 22, -16, 2, -1],\n [0, 11, 2, 6, 1, 4, -8, 21, -1, 23, 2, -16],\n [14, 5, -6, 11, 7, 13, -5, 21, 0, -19, 13, 19],\n [4, -26, 12, 7, 20, -3, 1, 23, -23, -9, 2, -4],\n [10, 0, -11, 18, 0, -18, -22, -19, -9, 8, -21, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508", "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, 19, -1, 24, 12, -3, -17, -12, 11, -7, 2, -21],\n [21, -18, 24, 23, -22, 21, 12, -8, -22, -7, -16, 23],\n [0, 2, -20, 23, -24, -22, -14, -11, -15, 12, 0, 18],\n [6, -12, -6, 17, -10, 25, 10, 22, -12, -7, -8, -26],\n [-23, -24, -19, 14, 17, -22, -18, -26, 16, 3, -20, -5],\n [-7, 2, 0, -2, 19, 8, 0, -16, -10, 4, -9, -8],\n [23, 11, 2, -12, -20, 10, 10, -20, -5, -15, -19, -9],\n [1, -9, 4, -10, -4, -16, -12, 3, 25, 4, -21, -15],\n [-4, 12, 13, 9, 8, -24, 15, 1, -12, -14, -8, 13],\n [-9, 4, 10, -6, 12, -22, 24, -10, -8, -23, -1, -3],\n [12, 11, 19, -8, 3, -1, 25, -16, 12, -24, 25, -5],\n [-10, -16, 20, 12, 20, 0, 22, 16, 2, -15, -14, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -16, 14, 16, 9, -25, -4, 9, -13, 10, 22, 0],\n [-15, 2, -21, 17, 20, -4, 24, -17, 7, 17, -15, 5],\n [-1, -20, 5, 6, -9, 8, -7, 4, -22, 5, 25, 20],\n [15, -8, -26, -20, -5, 23, 7, 24, -17, 20, 15, -1],\n [5, 15, 0, -15, 13, -4, -13, 7, -10, -21, 0, -19],\n [6, 8, 20, -10, -1, -20, 19, -3, -2, 8, -1, 23],\n [-22, 25, 20, 11, 8, 3, 23, -2, -3, 3, -7, -24],\n [5, -19, 24, 23, 20, -4, 19, -11, 8, -2, -12, 24],\n [-19, 7, -2, 22, 17, -8, 16, 23, -14, 19, -15, -12],\n [-4, 26, 13, -25, 13, -4, -22, 7, -17, 0, 15, -23],\n [-23, -19, -21, -2, 0, 20, 23, 26, 13, -7, 0, -20],\n [-4, -7, 22, 24, 7, 2, 17, 24, -22, 0, -15, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[10, 7, 3, 9, -21, 5, 5, -18, -5, -17, 2, -16],\n [1, -25, -6, 4, 14, 25, -10, 0, 3, 14, -19, 10],\n [-22, -1, -21, -11, -26, -18, -6, -20, 16, -12, -3, -22],\n [24, 11, 2, 19, 25, 19, -16, -23, -17, 7, -23, 25],\n [-17, 6, 19, -9, -15, 24, -4, 17, -2, 10, -23, -14],\n [-9, 2, 17, 3, 21, 11, 1, -20, -3, 14, -17, 10],\n [0, -6, 9, 16, 24, 2, -20, -14, 18, 26, -4, 23],\n [-2, 14, 18, -14, 10, 3, -1, -15, -26, -9, -6, 26],\n [-3, -10, 15, -18, 25, 13, 1, -12, -14, 1, 26, -10],\n [-18, -6, 3, -16, 3, 9, -2, -20, -7, 8, -17, 8],\n [-26, -13, 18, -22, 13, 17, 11, 7, -3, -23, 0, -22],\n [16, -14, 13, -6, 10, 5, 11, 4, 5, -12, 21, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "494", "dataset": "MATH"}
{"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, -20, 11, 4, 17, -1, 9, 19, 16, -1, 17, -25],\n [16, 18, 16, -18, 26, 21, -22, 0, -15, 8, 2, -11],\n [-8, 22, 16, 26, 24, 0, -9, 14, -14, 3, -1, -21],\n [-24, -4, -15, 14, 14, -12, -26, 23, 20, -19, 4, -16],\n [-10, 0, 4, 0, -13, 24, -4, -22, 3, 7, 20, -8],\n [4, -11, 18, 0, -1, 12, 2, 22, 24, 12, 17, 18],\n [2, 18, 19, 20, 4, -25, -21, -18, -12, -7, 21, -25],\n [-24, 25, 26, 3, -19, 13, -6, 12, 16, -14, 13, 14],\n [21, 10, 5, -13, -26, 0, -3, 24, 22, -5, -13, 18],\n [-19, 0, -24, 6, 24, 20, -6, 5, 13, 14, 18, 17],\n [14, 5, 25, -3, -16, 10, 24, -6, -9, -16, 0, 16],\n [11, -26, 2, -6, 2, -18, -20, 11, 4, 0, 15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "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, -12, -22, -7, 11, 10, -10, 23, -23, -6, 7],\n [13, -22, -23, -5, -13, -23, -19, -24, 19, 2, -1, 23],\n [3, -15, -12, 25, 25, 14, -25, -26, 20, 20, 1, 13],\n [8, 7, -23, -9, -15, 23, -6, -17, -6, 13, -2, 23],\n [-10, 24, -21, -13, 10, 13, 13, -9, 3, -18, -13, 19],\n [25, 19, -10, 7, 19, -5, 26, 5, -15, -11, -5, 11],\n [23, 12, -25, 18, -19, 17, -26, 14, 13, 14, -22, 18],\n [19, 9, -10, 14, 3, 25, -12, -7, 9, -25, 18, -23],\n [23, -3, 21, 15, -25, 19, -25, 23, -26, -14, -21, -5],\n [-10, 22, -5, 16, -21, 25, -24, 19, -21, -10, 8, 22],\n [24, 23, 10, 20, 8, -4, -19, -20, 23, -17, -1, -17],\n [-8, -4, 4, 6, -25, 1, 5, 6, -18, 2, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "595", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-9, -20, -13, 2, 23, 25, -8, -22, 14, 23, 18, -22],\n [25, -12, -1, -3, -8, -7, 16, -18, 26, 1, -11, -16],\n [7, -2, 13, -6, -22, -16, 16, -18, -16, 10, 14, -26],\n [-1, -17, 13, -8, -11, 18, 10, 23, 14, -23, -13, 3],\n [-20, -15, -3, 12, 16, -5, 20, 3, 12, -7, -1, 22],\n [-22, 13, 15, -21, 26, 7, -22, -17, 1, -24, -14, 21],\n [20, -25, 8, 25, 23, 25, 25, 20, 1, 10, -4, 16],\n [-4, 8, 14, 12, 5, -25, 20, 17, 21, -11, -11, 24],\n [-24, 1, 2, -7, 9, 6, -5, -19, 20, -3, 26, 10],\n [-7, -15, -7, -7, -23, 3, 4, -5, -12, 11, 10, 1],\n [-16, -13, -16, -18, -3, -17, 11, 16, 14, 10, 15, 5],\n [-7, -13, 11, -23, -3, 5, 26, -17, 16, -11, 12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-9, -2, -20, 26, 20, 24, -9, 20, -9, -24, -26, 6],\n [-20, -17, 17, -19, 5, -4, -10, -13, -10, -2, -6, -21],\n [-7, 22, -7, -1, 5, -19, 18, 21, 17, 2, -10, -9],\n [13, -9, -16, 18, -15, -12, -1, -24, -24, 11, 8, -18],\n [16, 13, -23, -7, -12, 2, -22, 12, 13, -20, -19, 5],\n [9, 6, 10, 5, 16, 9, 7, 22, -2, 17, 5, -25],\n [-18, 11, 2, 11, -9, -5, 8, -12, -20, -14, 15, 9],\n [-11, 14, -6, 1, -17, -8, -10, -26, -14, 9, 20, 15],\n [-7, 14, 13, 25, -21, -4, 15, -3, 25, 22, -22, 5],\n [19, -10, -16, 0, -23, -4, -4, 22, 7, -6, -5, -26],\n [5, 1, -9, -20, 11, -21, -13, 3, 17, 19, -13, 17],\n [14, -18, 4, -25, -9, -22, -1, -4, -15, -13, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[20, -12, 8, 25, -8, -12, 24, -19, -4, -14, -4, 4],\n [3, 15, -25, -16, -2, 2, -5, -8, -18, 14, 11, 2],\n [-17, -5, -3, -19, 20, -21, -20, -7, -10, 9, -19, -14],\n [-3, 19, 23, 4, -4, -10, 23, 19, -3, 16, -17, 4],\n [18, -7, -11, -13, -24, 3, -9, -21, -7, 8, -8, -1],\n [8, -15, -19, 10, 22, -17, -6, 22, 14, 18, 15, 2],\n [4, 13, -20, 7, 7, 3, -23, 14, 3, -2, -13, -3],\n [16, 4, 26, 12, 1, -2, -8, -23, 7, 5, -2, -5],\n [26, 1, 24, 26, -9, 26, -20, -16, 15, -16, -18, 8],\n [10, -4, 6, -26, -7, -22, 2, -1, 24, 11, -24, -6],\n [-14, 4, -10, 8, -4, -24, 26, 18, -25, -24, -7, 21],\n [26, 17, -18, 21, -23, -2, 25, 23, -26, 12, 25, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[13, 13, -3, -18, 19, -7, -22, -7, -6, -25, -6, 15],\n [-3, -18, 12, 3, -9, 17, 16, -17, 18, 14, 21, -6],\n [-5, -10, -22, -21, -17, 16, -25, -20, 19, -23, 10, -8],\n [26, 1, -7, 3, 15, 11, -25, -24, 20, 15, 22, 12],\n [-2, -25, 12, -12, -24, -22, 13, 9, 23, 24, 13, 11],\n [10, 0, -22, -10, 11, 18, 14, -15, 15, 4, 6, 16],\n [2, 11, -24, 11, 14, 13, 3, 20, -5, 11, 5, 16],\n [-17, 5, 16, -23, 2, 18, -19, -7, 20, -20, -26, -2],\n [-1, -18, -4, 13, -25, -1, -13, 17, 4, -1, 22, -8],\n [11, 26, -22, -21, 8, -11, 4, -9, -13, -2, -12, -1],\n [9, -16, 10, 14, 10, -20, -9, 23, -7, -25, -1, -4],\n [5, -14, -14, -10, -2, -5, 0, -10, -1, 11, -13, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "514", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-13, -15, -22, 10, -23, 2, -2, 18, -23, 23, -11, 23],\n [-25, -4, -23, -7, -10, 25, -21, -9, -7, 12, 18, 14],\n [7, 13, 19, -3, -9, 3, -26, -4, 2, 14, 14, 5],\n [-25, 21, 9, 18, -10, 16, -25, -23, 17, 7, -26, -4],\n [-21, -11, -25, 19, 25, -15, 0, -8, 1, 8, 24, 16],\n [-23, 22, 22, -20, 10, 24, -2, 26, 24, 14, -10, 14],\n [-13, 10, -25, -3, -12, 21, 24, 6, -15, -8, 25, 20],\n [-22, -26, 16, -18, 12, 7, 2, 22, 21, 21, 19, -25],\n [-8, 1, 8, 13, 26, 24, 21, -5, -23, -19, -26, 9],\n [-20, -2, 2, -26, -9, -23, -7, 19, -19, 0, 23, 12],\n [8, -2, 26, -13, 17, 20, 13, 4, -22, -10, -17, 16],\n [-11, 21, -23, -22, 15, 19, 14, 23, -7, -21, -16, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-10, 14, -24, -11, 25, 9, -1, -3, 20, 7, -7, -10],\n [24, -7, -11, 24, 26, 22, -23, -9, 9, 26, 8, 3],\n [-9, -6, 25, 5, -22, 14, -4, 3, 0, -12, 14, -13],\n [-6, 7, -1, -2, 23, 18, 4, 26, 21, -21, 21, -23],\n [-3, 15, 4, -8, -16, 2, -22, -9, -24, 13, -16, -6],\n [3, -8, 26, -2, 8, -15, 20, -1, 21, -22, -8, 0],\n [11, 2, -15, -8, -18, -9, 2, -24, -4, 3, 19, -3],\n [26, 10, 10, -23, 1, -11, -14, -19, 26, 21, -2, -25],\n [3, 13, -24, -4, 2, 14, 3, -16, -6, 0, -3, 25],\n [4, 3, -26, -26, -19, 21, 15, 7, -11, 0, -23, -8],\n [2, 14, -24, -16, -19, 12, 6, -19, -2, -3, -1, -1],\n [-10, 0, 2, 16, 12, -18, -13, -22, 23, 3, 1, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, -19, -12, 1, 9, 6, -21, 24, -15, -20, 18, 1],\n [-20, 14, -26, 26, -3, 18, -8, 26, 5, 3, -26, 5],\n [-7, -6, -8, 3, 23, 1, 5, 3, -4, 0, 10, -1],\n [-24, 4, -25, -17, 11, -8, 4, 2, -2, 5, -10, 24],\n [18, 22, -4, -9, -16, 25, -7, -14, -3, 16, -7, 24],\n [15, 1, 8, -6, -21, -20, 2, 26, -4, 25, -22, -5],\n [-18, 5, -17, 19, 16, 22, 1, -16, -20, 3, 16, 18],\n [24, 11, 7, 19, 1, 5, -11, 12, -26, 7, 14, -4],\n [23, 26, -7, -9, -9, 15, 13, -6, -19, 7, 23, -16],\n [16, 24, 16, -17, -19, 20, -19, -8, -26, 25, -24, 26],\n [17, 5, 21, -11, 3, 22, 1, 1, -11, 14, 24, 6],\n [-2, -9, -1, -21, 11, 17, -24, 16, -21, -13, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -14, -26, 11, -13, -10, -14, -14, -18, -21, -21, 3],\n [10, 26, 19, -13, -23, 7, -25, -10, 15, -13, 24, -10],\n [3, 16, 2, -20, -18, 19, -4, 9, -13, -7, 25, -10],\n [5, -2, 24, 3, 22, 0, 0, 19, 4, 18, -1, -13],\n [21, -6, 1, -12, 3, -2, 24, -16, 17, -16, 1, -22],\n [1, -19, -1, -21, 5, 21, 5, -15, -21, -14, 12, 13],\n [17, 7, -4, 14, 18, -10, 18, 21, -26, -20, -14, -13],\n [26, -10, 3, 21, 20, 22, 7, 0, -2, 17, 8, -18],\n [-21, -1, 11, 12, 0, 13, 4, -24, -3, -12, -21, -16],\n [3, 8, 21, 11, 16, 13, 2, -4, 15, 15, -24, -1],\n [-13, -8, -6, -6, -18, -14, 14, 26, 17, 19, 10, 11],\n [18, 18, -3, 11, 19, -16, 2, 18, 17, 21, 11, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, 25, 21, -1, -1, -15, -9, -18, -24, -17, 16, -25],\n [-19, 25, 16, -9, 25, 12, 4, -13, 12, 6, 2, 17],\n [6, 8, -25, 8, 5, 9, 19, 23, -4, -22, 20, -11],\n [13, -3, 26, 13, 1, -2, -20, 11, -20, 24, -5, -5],\n [0, 6, 18, 5, 12, 5, -26, -17, 18, -23, 2, -20],\n [11, -21, 26, -16, -18, 3, -5, 12, -18, 11, 24, 19],\n [6, -1, -11, -18, -4, -12, -8, 15, -11, -2, 8, 24],\n [-14, 19, -20, 7, -13, -4, -4, -10, -14, 0, -25, 10],\n [3, -23, 3, -24, -13, -16, 13, -4, 14, 21, 5, -24],\n [15, -26, -18, 21, -18, -15, -26, -11, 3, -19, 19, 19],\n [-17, 6, 11, 14, 24, -5, -11, -8, -16, 26, -16, -13],\n [12, -1, 17, -7, -7, -22, -26, -16, 20, -17, 20, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "546", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, 20, 7, -14, 17, -2, -4, 9, -15, 20, 18, -25],\n [-7, -11, -13, 26, -25, 22, -11, -23, 16, -14, 11, 22],\n [-26, -18, -6, -9, 16, 5, 19, 7, -7, 16, -25, -23],\n [18, 11, -20, -5, -7, 8, -23, 26, -7, 8, 6, 24],\n [-6, 18, -13, 4, -5, 21, 3, 2, 9, 22, 15, 2],\n [-20, 5, -14, -14, -13, -21, -11, 14, 25, 21, -6, 26],\n [17, -11, -22, -3, 16, -26, -17, 16, 20, 8, 4, -12],\n [-16, -18, -25, 17, 25, 3, -11, 21, 26, -26, 21, -21],\n [19, -16, 6, 25, -10, 24, 7, 19, 13, -2, -5, -1],\n [0, 11, -18, 10, -22, -9, -5, 19, -15, 17, -5, -21],\n [9, 0, 20, -12, -10, -24, -17, -2, -6, 13, -18, -3],\n [5, -24, 6, 16, 18, -15, 2, -6, 12, 7, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"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, -24, -23, -10, 23, -10, -8, -23, 2, -10, -5, -25],\n [15, -15, 18, -16, 26, 13, 2, -7, -22, -2, 7, -15],\n [1, 7, -21, -8, -15, -2, -14, -10, -15, -24, -3, -19],\n [21, 9, -1, 18, -19, 5, 5, -26, -24, -26, -12, 23],\n [-7, -24, -12, 10, -6, 15, 12, -4, 13, 8, -9, -10],\n [4, 21, -1, -5, 18, 9, 8, -16, 0, 7, -9, 0],\n [-23, -10, -21, 15, -16, -22, -9, -2, -17, 14, -11, -17],\n [-17, 9, -6, -13, -19, -26, -11, -1, 22, 15, -21, 12],\n [23, -25, 26, -18, -22, 13, -22, 20, -19, -22, -22, 25],\n [-10, -18, 7, 6, -5, -6, 16, -12, -26, -20, -4, 24],\n [20, -21, -7, -1, 15, -15, -14, 20, 24, 22, -14, -25],\n [5, 23, 4, -16, 10, -23, 7, -11, 4, -2, 12, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-19, 7, -12, -22, -8, -17, -18, 2, 25, 13, 10, -8],\n [-14, 19, 13, -11, 3, -22, 6, -8, -8, -10, -3, 26],\n [1, 15, 10, -5, 12, -11, 8, 0, -15, 19, 1, 25],\n [-26, 12, -9, -4, -5, -23, 21, -16, -9, 21, -20, -6],\n [8, 10, 23, 3, -10, 6, -11, -12, -14, 12, -24, -3],\n [-4, 18, 21, -26, 5, 6, 21, 3, -25, -9, 26, 3],\n [-9, -22, -22, -19, -18, 5, -13, -14, -9, -23, 23, -5],\n [-7, -12, -20, -14, 7, 14, 3, -22, -26, 4, 24, -7],\n [-8, 2, 18, 11, -17, 2, 4, -16, -4, 3, -2, -11],\n [-4, 6, 24, 10, 1, 0, -21, 11, 10, -21, -2, -14],\n [6, 6, -2, -13, 13, 14, 15, 11, -18, -9, -12, -23],\n [7, 11, -10, -20, 5, -4, -7, 20, 26, -25, -6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "493", "dataset": "MATH"}
{"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, 22, 0, 23, 21, -17, -19, -6, -5, -14, 21, 13],\n [-15, -10, 21, -18, 24, 22, 13, -15, -18, 3, -21, -2],\n [1, -17, 14, 1, 2, 9, -16, -6, 11, -1, -9, -23],\n [17, 14, -12, -4, 14, -21, 16, -20, 19, 21, -12, 25],\n [-18, 24, 3, 17, 16, 1, 3, -19, 8, 24, 8, -1],\n [3, 8, 11, -16, -7, 19, 4, 7, -15, 21, 1, -24],\n [26, 21, 15, 25, -22, -14, -15, -26, 25, 16, -8, 2],\n [20, 23, 21, 12, 15, -2, -11, -10, 1, 12, 16, 22],\n [-22, -26, -24, 21, -3, 2, -12, -23, 17, -26, 22, -12],\n [-3, 25, 4, -7, -17, -16, -9, 7, 1, 11, -11, -3],\n [12, 24, -15, 23, 15, -20, 9, -10, 22, -23, 26, 10],\n [6, -8, -1, -16, 4, -26, 13, 9, 2, -2, 20, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"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, -24, -9, -20, 1, -10, -2, -9, 25, 13, 16, -24],\n [-2, -20, 20, -17, 17, 17, 24, -8, -12, -6, -6, 10],\n [1, 18, 5, 14, 0, -4, -17, 13, 14, -21, -3, -9],\n [-17, -12, 18, 16, 7, -19, 23, 8, 0, -2, -24, -6],\n [12, 5, 23, 26, -6, -18, 23, -26, -23, -23, 22, -1],\n [7, 0, -12, 18, 5, 14, -20, 17, 17, -13, -4, 20],\n [-26, 5, 14, -1, 21, -18, -11, 4, -25, 5, -17, -2],\n [-9, 18, 7, 2, 18, -3, -24, -12, -24, 4, -17, 11],\n [-5, -13, -18, -9, -19, 11, -12, 19, -12, 25, -21, -15],\n [15, -8, 13, -22, 0, -17, 16, 25, 19, -13, 7, 22],\n [-12, 2, -1, 0, -24, -24, 8, 8, 23, -21, -13, -1],\n [-24, 6, 15, -14, 2, -18, 5, -5, -5, 7, -17, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-15, 24, -24, -8, 6, 20, -1, -14, -20, 7, -5, -7],\n [16, -4, 21, -13, 3, -4, 20, 25, -8, 12, 14, 9],\n [-21, -4, -17, 8, -6, 5, 3, 6, -21, -22, -12, 16],\n [25, -2, -14, -21, 10, -25, -10, -3, -15, 17, -13, -20],\n [-1, 5, 2, 19, 12, -18, -13, 26, -10, 22, -2, 26],\n [3, 18, 2, 2, -9, 4, -8, -10, -21, -15, 11, -24],\n [20, 8, 20, 6, 26, 2, -24, -22, -13, 9, 1, 14],\n [5, -9, 15, 13, -14, -25, 25, -2, -7, -20, -16, -22],\n [2, -9, -19, 0, 15, -25, 8, -1, -4, -22, -11, 15],\n [-16, -8, -11, 5, -15, -25, 16, -5, -1, 6, -3, -22],\n [-6, 19, -9, 12, -22, -19, -6, 20, -22, -14, -8, 2],\n [-25, 10, -1, 2, -22, 5, 11, 21, -25, -22, 20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[24, 8, -8, -12, 8, -19, 20, -26, 11, -5, -10, -11],\n [18, -26, -24, -21, 25, 26, -24, 20, 3, 20, -16, 0],\n [-5, -21, 11, 14, 19, 4, 16, -21, 23, -7, 20, 14],\n [-16, -25, 4, 11, -1, 0, 19, 19, 4, -3, -14, -2],\n [10, 14, -2, 2, 4, 16, 12, -25, -15, -22, 0, 7],\n [-13, -20, 10, 9, -17, 2, -11, 11, -6, 11, 14, 6],\n [2, 21, -10, -14, -21, -25, -19, 5, 9, -18, -4, -20],\n [4, -6, -26, 19, -25, 13, -16, 10, -9, 17, 26, -3],\n [25, -8, -22, 2, 12, -25, -10, 18, -16, 10, -14, 2],\n [5, 18, 13, 16, -19, -17, -2, -16, 1, 6, 12, -1],\n [-19, 11, -1, 5, 19, 1, 25, -20, 8, -25, -5, 23],\n [-5, -24, 19, 23, 18, -19, -23, -12, 17, 19, 25, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-15, 2, -18, 15, 13, -7, 7, -1, 21, -6, -4, -9],\n [25, -3, 15, 2, 11, 11, 25, -14, 5, -8, -10, -25],\n [-9, 12, 0, -13, -12, -19, -18, -6, 16, 8, 25, -13],\n [0, -19, 8, -9, -13, 25, -19, 22, -19, 10, 17, -25],\n [-10, -14, -13, 14, 14, -18, 0, -7, 11, -15, 15, -5],\n [10, 23, 12, 4, -14, -26, 11, 26, 26, 13, -18, 12],\n [-17, 2, 13, 3, -25, -9, 1, 20, 5, -3, 11, -13],\n [-2, -2, 5, 0, 5, 4, 23, -3, 8, 3, 6, 6],\n [19, 0, 6, 6, -23, 3, 17, -12, 2, 1, 5, 9],\n [3, 15, 16, 11, 15, -15, -24, -12, 21, -17, -5, -4],\n [-16, -11, 22, 19, -11, -13, -21, 15, -10, 4, 15, 26],\n [-17, 19, -7, 22, -18, -12, 12, -25, -23, 25, -3, -9]]\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[[-16, 10, -1, -19, -5, 25, -22, -25, -22, 8, 5, 17],\n [-8, 12, 24, -23, -4, 19, -8, -1, 23, -1, -20, 5],\n [20, 26, 6, 17, -1, -3, 24, -4, 11, -1, 18, 4],\n [-21, 18, 4, 20, 21, 13, 18, 18, 25, 25, -15, 24],\n [-10, -1, -24, -12, 22, 11, -3, 24, 3, 17, 9, 26],\n [17, 0, -5, -25, -20, -11, -3, 3, 17, 21, 19, -26],\n [0, -18, -20, -22, 3, 15, 0, -17, -2, -9, -20, 4],\n [5, 23, 18, -16, -17, -5, 4, 14, 20, -13, -24, -3],\n [-13, 26, -11, 1, 8, 13, -25, 7, -9, -20, 22, 11],\n [15, -20, -23, 16, -11, 22, -21, -7, 4, -8, 25, -5],\n [-6, -9, 5, 20, 7, 24, 0, 11, 17, 3, 6, 0],\n [-4, 16, -8, 4, -23, 26, -8, 26, 11, 13, -5, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -17, -17, 3, -17, 9, -9, 17, 16, 21, -8, 16],\n [-4, -23, -15, 22, -3, -14, -23, 0, 11, 12, -19, -1],\n [7, -18, -17, 24, -26, 21, 23, -19, -17, 16, 22, -2],\n [4, 12, -24, 12, 11, 8, -19, -26, -22, 24, 0, 18],\n [-1, 16, -1, -16, 7, 14, -25, -6, 24, -1, -15, -18],\n [14, -4, 15, -22, -18, 23, -17, 22, -17, -13, 9, -17],\n [23, 10, 14, 11, 21, -5, -4, -11, -16, 26, 20, 24],\n [8, 21, 26, -7, 10, 14, -22, 9, -14, 25, -10, -1],\n [25, 17, 25, -7, 12, 6, 3, -11, -20, 3, -25, -15],\n [16, 13, -26, -24, -19, -1, 13, -16, -6, -22, 13, -1],\n [-6, -18, -10, 10, 24, 24, -25, 24, 20, 13, 1, 0],\n [13, -26, 19, -16, 12, -9, 0, 20, -17, 9, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-26, -13, -7, 25, -18, 18, 0, 22, 25, -23, 10, -9],\n [4, 22, 26, 12, -17, -18, 1, 1, -14, -9, -15, -19],\n [-4, 23, -22, -20, -12, -24, -9, 11, -1, 11, 25, 6],\n [-6, -10, 16, -25, -2, 14, -8, 11, -2, 12, -23, -24],\n [7, 15, -17, 22, 0, 21, -1, 0, -26, 17, -7, 25],\n [-2, -17, -26, -11, -16, -23, 8, -14, -6, -12, -17, 11],\n [-16, 5, 6, -7, 9, 3, -17, -12, 2, -26, -6, -12],\n [-24, 6, 11, -8, -23, -15, -2, 7, -10, -21, -15, -12],\n [-10, -26, -13, -25, -23, 25, -25, -1, 19, 23, 13, 25],\n [6, 21, 12, -21, 3, -5, 0, -8, -17, -21, -1, 15],\n [24, -24, 25, -24, 25, -21, 22, 23, -17, 11, -14, 11],\n [-15, 19, 22, 0, -19, -22, 9, 11, 16, 3, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -13, -17, -16, 8, -4, -19, -6, 10, 1, 25, 4],\n [26, 1, 15, 0, 13, -6, -18, 2, -12, 6, 10, 20],\n [9, 24, 1, -17, -4, 1, 7, -22, -9, -21, 15, 20],\n [-4, 1, 14, -14, 23, -2, -20, -25, -11, -25, 9, -25],\n [22, 11, -17, -13, 0, -12, -6, -15, 24, 16, 6, 13],\n [-5, 11, 17, 25, 21, -9, 17, 25, -25, 2, -20, 4],\n [14, -9, -18, -19, 6, -22, 21, -13, -14, -16, -7, -4],\n [18, 0, -12, 3, -11, 18, 13, -9, 24, 20, 15, -4],\n [9, 11, -19, 12, 2, -15, -9, 23, -8, 9, 6, -22],\n [12, 1, -1, 16, -6, -4, -6, -16, 15, 12, -11, 6],\n [0, -26, 17, -11, -22, 19, -9, 14, 7, 17, -2, 15],\n [7, -12, -23, 24, -23, -2, 14, -14, 15, 19, -2, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "511", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[8, 25, 21, -18, -13, -5, 21, -18, -3, -4, 10, 18],\n [-12, 9, -13, 25, -7, 12, 9, 0, -10, -1, 14, -23],\n [-24, -8, 14, 13, 12, -20, 9, -8, -15, -7, 11, -15],\n [2, 3, -7, -23, -25, 20, 3, -4, -21, -9, 26, -5],\n [10, -23, 16, -16, 14, 8, -16, 7, -18, 4, 15, 5],\n [16, 8, 22, -16, -10, 24, 9, -25, -3, 19, -12, 1],\n [-24, 2, 25, 18, -14, 23, -5, 25, 26, 4, -20, 21],\n [21, -1, 4, 11, 11, -23, 8, 6, -24, -8, -18, 19],\n [-8, -8, -1, -14, -5, 21, -19, -3, -1, 21, 14, 14],\n [-24, -20, 25, 23, -25, 6, -15, 21, -15, 26, -17, 14],\n [26, 0, -9, -23, 13, -4, -6, 9, 3, 21, -6, -4],\n [-6, -19, 12, -14, 13, -5, -20, -3, -22, 23, -1, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538", "dataset": "MATH"}
{"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, 13, 11, -16, 21, 3, -23, -25, -14, 12, -10],\n [-4, 18, -17, -14, 15, 12, 15, 2, -11, -24, 9, -23],\n [9, -11, 14, -21, 15, 1, 9, -4, -15, 15, 4, -15],\n [5, -2, 24, 2, -8, -5, -3, 6, 9, 18, 13, 19],\n [-11, -25, -19, -14, 3, -26, -15, 22, -20, 21, -13, 15],\n [8, 1, -15, 13, 21, -3, -26, -10, 11, 1, 6, -3],\n [20, 18, -21, -6, 18, -23, 6, -17, 9, -14, 9, 21],\n [-18, 4, -23, -7, -19, 0, 9, -18, 16, -3, 10, 14],\n [13, 3, -1, -23, 25, -26, -7, 1, 18, -3, 1, 1],\n [-22, 5, 25, 3, -6, 15, -11, -19, -15, 5, -2, -24],\n [-1, 9, -10, 0, 26, 25, -5, 18, 11, 8, 19, -20],\n [-24, -21, -14, 19, -12, -1, 21, 6, -12, 12, 14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-13, -8, 1, -3, 23, 14, 6, -15, -17, -20, 19, -26],\n [-12, -26, 18, -7, -25, -24, 9, -11, 2, 17, 9, 17],\n [12, 25, -24, 10, 17, -15, -7, -4, -5, 5, -20, -5],\n [17, -25, -13, -11, -3, -20, -23, 25, 10, 19, 14, -22],\n [-25, -22, -24, 15, -19, -1, -17, 7, 19, 9, 26, -15],\n [-7, 2, -13, 21, -22, 21, 0, -23, 2, -24, 6, 3],\n [9, -18, -26, 21, -4, -24, 5, -3, -21, -14, 22, -12],\n [26, 3, -15, 13, 21, 8, 1, -23, -20, 20, 16, -11],\n [-5, 19, 18, 14, -2, 23, -24, 25, -5, 4, 10, -5],\n [0, -25, -5, 26, -10, 21, -7, -3, 18, 4, 25, 16],\n [-19, 26, -22, -25, -23, 8, 7, -24, 21, -7, -18, -21],\n [20, -22, 14, 11, 8, 4, -14, -1, -5, 5, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-11, 20, -21, 19, -16, 25, -17, -11, -15, -20, 12, 0],\n [-3, 23, -12, -21, -8, -19, 25, 20, 9, 23, -14, 6],\n [5, 1, 13, 24, 22, -17, 6, -26, -6, -22, -26, 26],\n [-6, -2, -7, 18, -18, -11, 1, 13, 19, 22, 9, 12],\n [22, -3, -11, -13, 21, 7, -3, 20, -16, 18, 9, -26],\n [20, -15, -6, -18, 12, -24, -11, -23, -1, 19, -14, -7],\n [-8, 0, -25, -17, -2, -8, -12, 12, 20, 22, -3, -11],\n [-10, -11, -9, 22, -23, -25, 22, 22, 4, -25, -25, -12],\n [21, 16, 2, 7, 13, 5, -6, 3, -3, 17, -13, 1],\n [-13, 17, 7, -13, -2, -15, 14, 13, -7, 21, 15, -20],\n [-12, -18, -23, 4, -4, -21, 1, -15, 20, 24, -5, -3],\n [7, -8, -3, -7, 25, 7, 20, 0, 17, 2, -26, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, 16, 12, 18, 19, -20, 16, -7, -7, -2, 16, -6],\n [-18, 0, 1, -2, 9, 7, -25, -18, -8, -12, 26, -6],\n [23, -11, -25, -1, 17, 2, 6, 7, 19, 0, -20, 22],\n [-12, -10, -18, -14, 5, -25, 5, 20, -7, 16, -8, 19],\n [0, 9, 3, -16, -11, -1, 3, -25, 7, 14, -5, 4],\n [26, -6, 9, 13, -4, -1, -9, -12, 7, -5, 1, 16],\n [22, -20, 13, 15, -3, 8, -14, 22, -14, 4, -8, 2],\n [-5, 14, -6, -11, 3, -22, 14, 14, -21, -6, 15, 23],\n [-16, -3, 1, -12, 12, 19, 13, 24, 20, -8, 23, -10],\n [-24, -24, 12, 1, 4, 15, 22, 20, -19, -10, 8, 9],\n [0, 13, 18, 6, 23, -16, -6, -21, 21, -6, 24, 1],\n [-10, -9, -16, 19, 17, -2, 3, 25, -2, -20, 22, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[19, 0, -1, -14, -3, -15, -13, -18, 4, -23, -8, -26],\n [2, 18, -21, -26, -2, 0, -5, -10, 2, -24, -10, -25],\n [5, -5, 12, 6, 26, -5, 20, -23, 11, 26, -14, -4],\n [-14, -7, 6, 7, 11, 2, 5, -16, -9, 18, -6, -15],\n [25, 12, -7, -20, 0, -20, -25, 16, 6, -6, 2, 5],\n [18, -15, -14, 12, 17, 22, 13, -24, 12, 24, 25, -19],\n [19, 19, -25, -21, 21, 14, 26, -12, 24, 20, -15, 14],\n [21, 5, -21, 25, 0, 20, -14, 26, -4, -17, -13, -24],\n [-15, -2, -26, 5, -3, 26, 21, 15, -18, 23, -26, 15],\n [12, -17, 17, 16, 14, 3, -22, -23, 25, 18, -19, -11],\n [-26, 22, -12, -3, -12, 23, -21, -25, -22, 24, 12, 14],\n [7, 12, 5, 2, 2, -3, 19, 4, -3, -12, -15, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "557", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-23, -14, 14, 17, -17, 14, 26, -4, -20, -15, 21, -12],\n [-20, -19, -20, 16, -23, 23, 24, -20, 18, 14, 3, -9],\n [3, -20, 25, 21, -4, 10, -20, 11, 2, 7, 12, 26],\n [14, 18, 22, 22, 20, -9, 20, 16, -2, 0, 0, -15],\n [-4, -10, 17, -20, -3, -20, 2, 26, 1, -4, -17, -11],\n [16, 21, 7, -2, -25, 23, -22, -13, 4, 13, -21, 1],\n [-18, -21, 26, -10, 13, 8, -15, 18, -9, 16, 7, 19],\n [-26, -12, -9, -5, -9, 22, -26, 19, -7, 21, 9, 11],\n [-2, -11, -7, 11, 20, 6, -20, -4, -16, 6, 13, 19],\n [-22, 18, 20, 14, -19, 24, -10, 24, -9, 23, 0, 4],\n [-23, -25, -22, -10, 12, 5, 2, -11, -26, -15, -8, -18],\n [21, -20, 3, -12, 17, -23, -21, 11, 20, 8, -25, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-19, 24, 26, 3, 21, -8, 3, 4, -11, 11, -5, 6],\n [23, -5, -19, 10, -15, 23, -22, -2, 2, -14, 26, -1],\n [-5, 2, -15, 21, 19, 16, 1, -18, -17, 21, 24, 15],\n [-1, 26, 9, 26, 13, -16, -21, -23, 26, 0, -3, -22],\n [23, -24, -20, -3, -5, -15, 8, -10, -24, -16, -21, 16],\n [9, -10, -5, -26, 17, -24, -11, 8, -13, 22, 24, -20],\n [-1, 16, 21, 4, -3, -8, 10, -26, -2, -17, -9, 15],\n [-26, 2, -14, -23, -15, 21, -8, -1, 17, 11, -11, 17],\n [-2, -17, 10, 1, 1, -2, -2, 24, -15, -19, 9, 12],\n [-3, -4, 10, -16, -10, 1, 26, -24, -25, 24, 2, 7],\n [-13, 6, 21, 20, -9, 2, -25, -16, 4, 26, 22, -14],\n [17, -1, 7, 26, 23, -17, -15, 22, -5, 19, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"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, -3, -2, 8, -19, -22, -5, 1, -15, 6, 26, -11],\n [-1, -15, -4, 22, -1, 14, -14, -4, 4, 9, 0, 9],\n [20, 15, -4, 11, -24, 3, 5, -12, 11, -16, -25, -1],\n [7, -26, -16, -22, -1, -21, 8, 25, -22, 25, -18, 1],\n [-8, -22, -4, 17, 17, -11, -20, -13, -5, -18, 20, -4],\n [16, -23, 16, -1, 14, -21, 4, -10, -18, 0, -21, -21],\n [-23, 25, 16, -24, -3, -9, 5, 21, -6, 21, 2, 5],\n [-2, -15, 19, -18, -20, -13, -7, -7, -17, -16, 12, -8],\n [-8, 26, 16, -21, -19, -26, -4, 13, 10, -17, -25, 9],\n [-25, -12, -7, 15, -6, 3, -3, -25, 11, -5, 2, -13],\n [-22, -3, -1, -25, 19, 18, 7, -4, 14, 8, -12, -24],\n [-15, 11, 24, -10, 11, 0, -8, 22, 21, -6, 13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"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, -8, 4, 13, -7, -12, 13, 8, 21, 8, 6, 13],\n [14, 17, -9, -10, -19, -7, -16, 3, 0, 12, -13, 15],\n [-12, -15, -7, -10, 13, -1, -13, -2, -1, 20, -2, -2],\n [0, 16, -15, -7, -11, -2, 0, 25, -9, -17, 24, 23],\n [3, -26, -23, -4, -20, 3, -1, -26, 2, -2, 13, -1],\n [-10, 4, -19, -22, -26, -12, 9, -20, 19, 17, 26, 0],\n [8, 0, -7, -9, 13, -25, 3, 11, 3, -20, 12, -14],\n [6, 13, 3, 3, -4, 18, -3, -7, 1, -8, 22, -14],\n [-11, -12, -16, -15, -5, -2, -24, -3, -2, -18, 1, 19],\n [3, -20, -16, -17, -24, -8, -25, -10, 2, -25, 26, -11],\n [22, -17, -23, 16, -1, 22, -3, -15, -6, 15, -11, 9],\n [8, -18, -21, 17, -26, -13, -3, -17, -9, 18, -18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-8, 9, -24, 11, -18, -17, -18, -10, 15, 11, 21, 22],\n [16, -7, -20, -23, -17, -6, -13, -2, -10, 1, -13, 25],\n [-14, 7, 14, -24, -23, 17, -12, -7, -19, 23, -22, -25],\n [1, -5, -18, 1, 19, -26, 25, 9, 22, 15, -25, 11],\n [-1, 4, 24, 14, 24, -8, 4, -18, -24, 11, -21, 22],\n [18, 18, -20, 14, -2, -2, 23, -26, -5, -7, -14, 13],\n [-6, -4, 14, 6, -18, 2, 25, 5, -16, 25, 9, 2],\n [21, 4, -13, 25, 26, 23, -2, -1, -5, -18, 6, -4],\n [8, -7, 6, 8, 19, 3, 19, 3, -5, 18, -26, -12],\n [-2, -7, -20, -11, 25, -4, -6, -26, 20, -7, 20, -8],\n [-21, 11, 5, -26, 3, -11, 0, -9, -14, 17, 23, 1],\n [-17, -13, 25, 2, -16, 23, 0, 17, -10, -24, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "559", "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, -26, -21, 24, -23, -5, -14, 17, 3, 13, 25, -1],\n [12, 26, 12, -20, -13, -1, -9, 24, -3, 25, 24, -2],\n [23, 5, -21, -11, -24, -6, 5, -25, 20, -7, -16, 24],\n [-9, -16, 8, 9, 11, -15, 4, 26, 9, 3, 17, -23],\n [-25, 17, -14, -1, 2, 21, 9, 1, -19, -22, 5, 3],\n [-13, 20, 16, -17, -17, -21, -11, -1, -6, 9, 14, 15],\n [3, -22, -17, 21, 4, -16, 11, -20, -15, 18, 22, 14],\n [-19, 1, -11, 26, -24, 10, 5, -6, 18, -9, 26, 21],\n [19, -16, 23, -19, -15, 24, 25, -25, 14, -5, -18, -13],\n [-12, -16, -14, 1, -2, 10, -21, 10, 6, -2, 23, -4],\n [-19, -10, 4, -1, -16, 3, -16, -24, 13, 13, 26, -6],\n [8, 1, -5, 15, 24, 19, -9, -4, -1, 8, 2, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[19, -16, 15, 19, -26, -11, -2, 11, -9, -11, -8, -11],\n [-22, 0, 17, -21, 7, -11, 26, -4, 16, 17, 5, 16],\n [-4, -7, -8, 2, -19, 2, -9, -22, -15, -17, 20, 10],\n [-10, 5, -23, 4, -1, -15, -9, -19, 5, -7, 22, 13],\n [-14, -4, -24, 8, 12, 23, -6, -20, -1, -4, 5, -25],\n [12, -25, 12, 19, -12, -11, -1, -19, -11, -6, 12, -16],\n [-3, 9, -9, -4, -14, 22, 17, 23, 15, 12, 17, 17],\n [18, -26, -20, 21, 21, -6, -11, 21, -13, 16, 24, 16],\n [-25, 4, 12, -18, 14, -13, -17, 21, -3, 23, 6, 7],\n [-7, 1, -23, 7, -23, -21, -5, -23, 23, -22, -16, 18],\n [8, -8, 25, -16, -16, 26, 0, -25, 20, -19, 7, 13],\n [-7, -4, -12, 21, -14, 4, 22, 19, -13, -26, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[8, -12, -22, 10, -23, 19, -7, 12, -5, -3, 20, -16],\n [19, -21, 0, -17, 12, -17, 19, -1, 10, 6, 24, -19],\n [24, 22, 24, 1, 21, 9, 13, -2, 9, -14, -20, -26],\n [-18, 1, 9, 19, 3, -18, 3, 8, 20, 0, 2, -22],\n [-26, 16, 24, -22, 2, -10, 24, 22, 10, -3, 25, 0],\n [-18, 11, 26, -14, -1, 26, -16, -3, 6, 22, -21, 8],\n [-11, -14, 17, -16, -4, -25, 3, -8, 13, 18, 19, 20],\n [22, -12, 26, 15, 6, 17, 14, -22, -5, 0, 20, 8],\n [-8, 12, -20, 12, 7, 7, 0, 17, -22, -23, -20, 21],\n [-24, -6, 7, 22, -18, -7, 13, -15, 12, 19, 1, 21],\n [6, -17, -16, -20, -9, -8, -13, -10, -4, -8, 18, -24],\n [7, -2, 14, 4, 12, -13, 10, 25, 20, -7, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[25, 4, -20, -22, -23, -16, -8, 11, -7, 0, 2, -9],\n [10, 25, 20, 26, -2, -7, -21, 9, 22, -12, -9, 11],\n [-2, -7, -5, 24, -15, 14, 13, 20, 6, 2, -25, -1],\n [5, -24, 3, -8, -17, -2, 19, -8, 16, -6, -21, 24],\n [-13, -19, -25, -9, -5, 3, 9, 1, 8, -25, 9, -9],\n [16, -18, 1, -19, 26, -19, -22, -14, -20, -6, 2, 10],\n [18, 25, 21, -13, 10, 24, -23, -5, -16, 7, 18, -11],\n [-18, -11, 12, -11, 4, 4, -14, -22, 20, 12, -9, -7],\n [-25, 13, 3, -17, 15, -16, 26, 2, 26, 13, -11, 21],\n [1, -10, 11, 23, 22, 17, -12, 4, -20, 19, 3, 9],\n [22, -1, -16, -21, 15, 2, 1, -12, 2, -21, 21, -15],\n [24, -11, 19, 11, -18, -5, 6, -1, 13, -20, 19, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[13, 16, -3, 14, 24, 12, 11, 23, 10, -8, 16, -22],\n [3, -2, 3, -2, -18, 0, -3, 13, 16, 11, -12, 11],\n [-1, 3, -16, 2, -12, 17, -18, 15, 2, -12, -10, -11],\n [-5, 13, 22, 16, -16, 11, -2, 3, -25, -26, 25, 11],\n [10, -18, -22, 23, -3, 0, 3, 24, -12, 20, -18, 19],\n [10, 3, 22, -12, -7, 22, -2, -18, 18, -5, -14, 10],\n [1, -13, 3, 12, -22, -15, 8, 14, 15, -26, 19, -26],\n [15, 16, -7, 7, 7, -3, 1, -16, -19, 8, 14, -11],\n [-11, 15, -21, -7, 25, 25, -16, -19, -7, 5, 6, -21],\n [1, -19, -13, -24, -25, -5, 6, 16, -6, -21, 13, -20],\n [-21, 23, 17, -19, -3, 0, 26, 24, 1, -22, -8, -18],\n [-2, 17, 20, 18, -14, 26, 26, 10, -25, 24, 13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "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, -21, -2, 12, 19, 4, 11, -11, 0, 3, -23, 12],\n [-11, 9, -20, -6, -25, -19, 15, 0, -25, -21, -23, -6],\n [-26, 11, -15, 0, -13, -12, -3, -9, -10, -18, 20, -9],\n [26, -9, -22, 21, -18, 8, 17, 19, -26, 14, -18, 5],\n [-7, -14, 13, -16, 19, 21, 16, 24, 15, -1, 13, -16],\n [-2, 13, -2, -7, 15, 22, -16, 17, -17, 25, 22, -24],\n [12, 0, 8, 22, 13, 4, -6, -5, -8, -13, 10, 24],\n [18, 23, -4, -1, 16, 17, 13, -15, -26, 23, 7, 17],\n [-8, -4, -20, -20, -26, -9, -19, -2, 15, 2, -4, 2],\n [-26, -12, -12, 1, 9, 15, 13, 5, 19, -14, -6, 22],\n [12, 11, -18, -7, -7, -19, -13, -7, 8, 18, -6, 14],\n [26, 14, -5, 16, -21, 17, 0, -23, -23, 1, 0, -10]]\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[[12, 11, 25, 2, 13, -20, -19, 14, 6, 5, 8, -9],\n [24, 16, -11, -9, 11, -2, 7, -23, -22, 26, -13, -26],\n [-5, 19, -6, -14, 21, 9, 2, 11, -18, 6, -5, -10],\n [-4, 9, -21, 21, 12, 2, 0, -22, -18, -3, -8, 6],\n [3, 13, 25, -23, 5, 22, -26, 7, -6, 4, -13, -1],\n [-5, 7, 6, -14, 5, -19, -5, 14, -7, -6, 7, 22],\n [3, -21, 8, 0, -7, 22, 11, 13, -13, -17, 25, 15],\n [-12, 13, 16, 21, -24, -12, 18, 4, -16, 19, 12, -8],\n [-12, 11, -7, -5, -20, -13, -23, -18, 12, -2, 20, 8],\n [10, 22, 0, 1, -3, 6, 6, -11, -4, 19, -16, 19],\n [13, -8, 7, -4, -17, 10, 20, -26, -25, 24, -5, -10],\n [20, -3, 23, -6, 13, 2, 26, -13, -19, 3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[13, 24, -14, 1, 3, -22, -17, 12, -18, -13, 11, -17],\n [6, -16, 13, -21, -10, 9, -21, 20, -17, 22, 15, -22],\n [-8, -20, -3, 24, 15, -8, -16, -24, 3, 16, 11, -21],\n [20, 8, -5, -16, -19, 0, 2, -19, -4, 2, -11, 8],\n [-19, -19, 18, 6, 15, -22, 10, -10, -5, -13, 11, 5],\n [-13, 17, -7, -5, 3, 6, -22, -9, 19, -20, 2, 20],\n [-18, 20, 21, 14, -20, -20, 22, 16, -21, 19, 20, 26],\n [13, 0, -23, -26, -21, 4, -26, 26, -22, -8, -22, -22],\n [22, 4, 17, -20, -12, 24, 26, -14, -15, -8, -14, 0],\n [11, 6, -21, -14, -14, -14, -7, 9, 10, 18, -18, -10],\n [8, 25, -9, -2, -12, -4, -26, 14, 11, -9, -26, 12],\n [-17, 4, 11, -20, 11, -19, 7, -18, -2, 0, 14, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "552", "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, -18, -10, 8, 21, -11, -25, 16, 4, -11, 20, 6],\n [-6, -10, 8, 24, 25, -20, 2, -16, 3, -9, 19, -11],\n [-21, -25, 16, 16, -17, -23, 22, -17, -18, 18, 16, 15],\n [-3, -22, 8, -23, 8, 15, -14, 10, 5, 18, -26, -16],\n [-1, -24, 22, 24, -14, 5, 21, 23, -4, 25, -4, 24],\n [3, -21, -20, 20, 3, 10, 21, 5, -21, 8, 5, -15],\n [-23, 5, 8, 21, -11, 24, -12, 14, 25, -25, -21, -13],\n [14, 2, 15, -1, -9, 20, -23, 10, 26, 11, -2, 20],\n [25, 2, 7, -11, 10, 3, -4, 9, 1, -26, -19, 26],\n [15, -12, 7, -8, 17, 3, -17, 17, 26, 0, -7, -2],\n [-18, 13, 7, -6, -3, -20, -23, 24, -19, -14, -6, 8],\n [-22, 25, -19, -25, -3, 15, -11, -23, 3, 19, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "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, -14, 10, 22, 22, -16, -8, -9, -10, -16, -12, -19],\n [17, 2, -10, -1, -22, -23, -3, -16, 3, 13, 21, 21],\n [8, 17, 18, 6, 9, -6, 11, -22, -22, -6, -2, -17],\n [-8, 5, -9, 7, 21, -12, -3, -22, 26, 5, -18, -22],\n [-22, 14, 14, 7, -20, -1, -26, 25, 7, -1, 5, -15],\n [-21, -7, -8, -11, -23, 5, -9, -22, 23, -21, -13, 25],\n [22, -9, 26, -17, -4, 24, -9, -23, 25, 5, 20, -21],\n [-1, -21, 8, 14, 16, -22, -13, -25, 24, 13, -14, 24],\n [-22, 20, 9, 9, 23, -8, -7, -5, 4, 14, 20, 17],\n [-23, -24, 10, -2, 22, 10, -23, 26, 12, -20, -20, 22],\n [-2, -12, -20, 20, 25, -23, 7, 18, 17, 15, -8, 20],\n [22, 26, 11, 0, -22, 26, -14, 19, -13, 3, 20, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-17, 5, -26, -3, 2, 16, -20, 4, -10, 3, -2, 1],\n [9, -20, 8, -7, -13, 23, 23, 3, -26, 11, 14, -2],\n [7, -19, -7, 3, -23, -6, 0, -17, -4, 6, -16, 14],\n [-8, -16, -23, -4, -22, 26, 22, 23, -22, -9, -10, -24],\n [16, 22, -19, 13, -4, -4, -25, 12, -6, 25, -3, 26],\n [11, -7, 23, 12, 23, 0, 17, 12, -20, 6, 2, -17],\n [-17, -15, -24, -24, -14, 18, 4, 0, -21, 0, 8, 20],\n [-18, 26, -21, -21, 13, -1, 16, -8, -11, 14, -4, -16],\n [-11, 2, 11, 22, 21, -7, -6, 1, 23, 6, 23, 13],\n [-1, -17, 7, -18, 9, -16, -17, 19, -20, 24, 11, -11],\n [24, -1, 5, 4, 24, 5, 18, -15, 0, -5, -12, -19],\n [-23, 25, -19, -4, 26, -11, 21, 7, -5, 22, -4, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "537", "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, -20, 10, -1, 1, -23, 22, 5, 11, 19, -18],\n [9, -1, -16, -7, 26, 21, 21, 21, 11, -12, 8, -18],\n [6, -16, -5, -21, 10, 23, -6, -15, -20, -25, 12, 14],\n [-3, -1, -2, -7, 13, 14, 15, 17, -25, 15, 8, 6],\n [-10, -5, -26, 10, 3, 19, -21, 14, -13, 9, 6, 11],\n [12, 26, -21, -1, -3, 6, -19, 17, 16, 7, 7, -3],\n [-25, -19, 26, -2, 3, 5, 3, -20, 21, -3, -18, -11],\n [-25, 8, 7, -5, -8, 22, 25, -6, -15, -16, 25, -8],\n [-21, 15, -13, 6, 20, 11, -14, -1, -13, 18, -3, 21],\n [-26, 19, 18, 3, -17, -17, 1, -23, -13, -15, 11, 20],\n [10, -17, 14, 0, 15, -15, -5, -23, 2, 9, 18, -13],\n [-15, 18, -7, 18, -4, -5, 7, -6, 24, -18, -17, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-17, 25, 18, 25, 3, 6, -25, 22, 5, 18, -10, 1],\n [18, -10, 24, -13, 25, -17, 7, -13, -10, 10, -5, -9],\n [8, 21, 24, -9, 25, 3, 10, 13, -21, -12, 8, -1],\n [14, 0, 3, -16, 25, -3, -13, -4, -18, 15, 20, -9],\n [26, 24, 12, -8, -22, 26, -9, 6, 17, 11, -14, 22],\n [-18, -1, 26, -26, -15, -3, -26, -23, -20, 25, 1, 10],\n [25, -22, 12, 5, 22, 4, 17, -12, -24, 22, 19, 20],\n [20, -12, 24, 16, -9, -6, -17, -6, -1, 14, -24, -26],\n [-6, -16, -11, 8, -6, 14, -16, 4, 22, -26, 14, 5],\n [-24, 5, 15, -22, 16, 10, -15, -13, 17, 24, -18, -20],\n [-11, 1, -20, -13, 5, -19, 0, 26, 23, -24, 0, 3],\n [7, -1, 10, 13, 24, -5, 5, 14, -25, 20, -19, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "588", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-20, -8, 6, -25, -24, 1, -13, -12, -6, -13, 13, -9],\n [22, 12, -7, -26, -18, -18, 16, 24, 11, 12, 2, -12],\n [-7, 11, 14, 3, 20, -1, -21, 12, -10, -21, 1, -18],\n [0, 8, 19, -21, -23, -11, -4, 21, -4, 2, 14, -23],\n [13, 13, -3, -21, 13, -21, -13, -13, 23, 18, 20, 8],\n [-21, -4, -7, -10, -7, 21, -21, 13, 1, -14, 2, 18],\n [-7, -10, 26, 8, 18, 12, 25, 10, 16, -4, -9, 9],\n [-7, -20, 9, 15, -26, 22, 10, 22, 8, 14, -24, 8],\n [2, -18, 10, 15, 20, -2, -15, 11, -20, -20, -23, 18],\n [20, 4, 23, 23, 12, -17, 21, -4, -1, -4, 2, -19],\n [-8, 2, 16, 26, -21, 2, -3, -17, 24, -13, 25, -21],\n [-23, 25, -12, 10, 21, 12, 1, -25, -14, -25, 14, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[25, -22, -24, -25, -13, 13, 25, 17, 22, 2, 21, 11],\n [-21, 23, 7, -19, 19, -25, -1, -10, -3, 4, -11, 23],\n [-6, 11, -1, -10, 23, 19, 15, -23, 23, 16, 21, -23],\n [-8, 11, -2, -19, -9, 24, -9, 21, -20, -10, -24, -5],\n [-12, 4, 9, -1, 21, -13, -10, -18, -20, 19, 0, 1],\n [-15, -10, -18, 17, 17, -19, 0, 15, -15, 10, -7, -26],\n [-18, 20, -3, 7, 9, -23, 2, -4, 8, -11, -19, 0],\n [12, -15, 17, -23, 20, -2, -21, -24, 12, -3, -6, -21],\n [6, -19, 6, 21, -24, -25, 11, 13, 12, 12, -3, -6],\n [24, -9, 8, -16, -16, -24, -4, -26, -4, -5, 15, 3],\n [-25, -10, 14, 23, -7, -18, -16, -10, -13, -9, -9, 17],\n [23, -19, 2, -19, -1, 1, -19, -7, 20, -19, -13, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[13, -10, 24, -1, -21, -10, -23, -2, -20, -10, -5, 1],\n [23, -21, 3, -17, 23, 12, -13, 19, 15, -5, 14, -1],\n [-17, -25, -24, 21, 15, -16, -17, -15, -13, 3, 14, -14],\n [3, 11, -16, -26, 0, 20, 12, 16, 22, 10, -18, 21],\n [16, -1, -2, -10, -21, -12, -24, 4, 1, -18, 17, 24],\n [-9, 21, 13, 5, -8, -22, 17, -21, -15, 20, 15, -10],\n [12, -20, 26, -16, 7, 26, -25, -13, -9, 21, 16, -18],\n [12, -23, 21, -13, -16, 3, 13, 16, 0, 2, 25, 5],\n [22, 3, -1, 3, 24, -17, -15, 6, 7, -9, 12, -11],\n [18, -23, -17, 1, 14, -9, -18, -5, -17, 13, -4, 16],\n [-14, -3, -14, 21, 18, -2, 17, 20, 2, -11, 13, -21],\n [-19, 7, -9, 16, 5, 22, -17, 7, -4, -8, -7, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[25, 7, 11, -10, 17, -22, -25, 14, 7, -7, 19, 20],\n [-25, 1, -9, 17, 12, 21, 24, 8, -12, 20, 12, 13],\n [12, -24, -8, -4, -8, -9, 3, 12, -8, -22, -14, 7],\n [-3, -9, -23, 9, -19, 16, -26, 14, 11, 9, 11, -14],\n [-5, 2, -18, 0, 19, 17, -23, 13, -10, 10, -24, -23],\n [13, -11, -16, 0, -1, 4, 7, -19, 12, -26, -25, 0],\n [18, 16, -24, 7, -11, -26, -20, 8, -5, 21, 5, -1],\n [-21, 19, -16, 4, -6, 24, -5, -26, -6, 18, -7, -18],\n [0, 2, 16, 6, 18, 25, -26, -24, 5, -7, -10, 10],\n [11, 22, -17, 16, 18, 2, 15, 19, 5, -14, 4, -23],\n [25, 22, -9, -16, 15, 26, -9, 24, 14, 10, 6, 10],\n [-24, -26, -8, -21, -17, 10, -15, 17, -10, 0, -25, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "569", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 19, 17, 1, 18, 10, 10, -10, -22, -8, -23, 12],\n [22, 16, 11, 18, 17, 3, 5, 10, 0, 5, 15, -16],\n [14, -14, 8, -10, 3, -9, 10, 21, 3, -1, -11, -16],\n [-23, 14, -12, -15, 0, 21, -23, 8, -6, 9, -25, 24],\n [12, 1, 7, 6, 23, -19, -19, 15, 23, -5, 0, 1],\n [-16, 0, -26, 12, 1, 0, -19, 19, -3, 24, 13, 24],\n [9, -3, 15, -5, -17, -23, -19, 12, -12, -19, 2, 15],\n [12, 24, 8, 14, 21, -13, 5, -20, 17, 6, 21, 8],\n [0, -26, -21, -25, -20, -19, 18, 2, -11, 2, 4, -5],\n [26, -17, -23, -2, 26, -14, -10, 13, -19, -4, -20, 5],\n [-3, -26, 20, 20, 24, 9, 0, -21, 15, 4, -15, -1],\n [-2, -23, -21, 19, -14, -2, 4, -5, 26, 8, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-24, 10, 18, -1, 20, -10, 11, 23, 8, 14, -19, 25],\n [-16, -3, 16, -19, 3, -26, 7, -7, 9, 7, 7, -14],\n [26, 25, -21, 9, -2, 0, 20, 4, -24, 1, -23, -10],\n [11, 7, -7, -14, 20, -22, -3, 24, 11, -10, 4, 1],\n [-26, -25, 6, 13, 2, -23, -9, -3, 5, -18, 20, -11],\n [-6, 3, -24, 6, 4, 18, -13, -21, -22, 2, 10, 9],\n [-6, -15, 19, -4, -13, 16, 15, -17, 0, 14, -25, -13],\n [-20, -10, -7, -19, -7, 9, -22, -14, 12, 11, -10, -21],\n [-8, -2, -24, 14, 26, 1, -1, 20, -19, -12, -26, 13],\n [-4, 9, 15, -11, 23, -23, -19, 9, -17, 25, 3, 9],\n [-11, 3, 17, -17, -16, 7, -11, -8, 17, -23, 22, 17],\n [4, 21, 8, 7, -1, 12, -21, 6, 20, 0, -15, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-19, -18, -26, -22, -20, -9, 13, -3, -1, -17, 13, 17],\n [21, -15, -5, 0, -24, -9, -22, -13, -2, 25, 4, -6],\n [21, 11, 21, -7, -13, -7, 10, 19, 3, 16, 26, 14],\n [-7, -20, -22, 4, 2, -12, -2, -14, 17, -3, -12, -3],\n [-1, -8, -3, -8, 15, -10, 21, -22, -23, -5, -17, -6],\n [-2, -21, 3, 2, -16, -16, 21, 19, 0, -8, -5, 1],\n [-23, 10, -8, -10, 23, 13, 9, -4, 23, 1, -16, -13],\n [-14, -3, -11, 1, 3, 17, 14, 12, 15, 0, -10, 23],\n [-1, -20, 8, -12, -11, -6, -10, 18, -1, 8, -7, -7],\n [-4, -22, -18, -4, -9, 2, -16, 16, 21, -19, 0, -25],\n [-4, -6, -17, 11, -23, -6, 10, 16, -15, 21, 25, 26],\n [19, -13, 25, -7, 20, -19, 0, 10, 14, -6, 21, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[17, 12, 22, -12, 20, -15, 26, 7, -19, 10, 3, -24],\n [3, 2, -26, -11, 15, 4, -17, 3, 16, -1, -15, 13],\n [-22, -18, -16, 20, -4, -10, 16, -14, -10, -4, 12, -18],\n [-9, -9, 3, 15, 17, -1, -9, -6, 14, 14, 15, 6],\n [16, -13, -17, 1, -13, -8, -1, -17, -10, 7, -13, -1],\n [23, 7, 25, -8, -3, 4, 13, -21, -7, 12, 18, 7],\n [-5, -20, 6, -21, -11, -19, 18, -4, -9, -13, 23, 9],\n [-12, -22, 26, 19, 21, -12, -16, -25, -4, -3, -9, -23],\n [-12, -15, -24, 5, 9, -6, 21, -21, -25, -18, -15, 17],\n [-3, -13, 22, 14, -15, 0, -17, 16, -25, 4, 1, -11],\n [-26, -5, -26, 4, -5, 7, -15, -4, 1, 25, 23, -15],\n [0, -4, -26, 16, -25, 17, 4, -25, 22, -2, 11, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-8, 1, -21, 12, -8, 25, -10, -21, -12, -5, 14, 7],\n [-22, 26, -4, -22, 17, -17, -23, -15, 20, -17, 3, 23],\n [-3, -22, -14, 9, -18, -9, 8, 4, -3, 16, -23, 14],\n [-1, 17, 15, -17, 14, 15, -18, -26, -11, 19, -14, 11],\n [-13, 13, -4, -9, 1, -7, -26, -15, 0, 16, -14, -23],\n [-2, -21, 18, -5, 18, 11, 9, 26, -24, -12, -16, 7],\n [0, -4, -10, -4, 7, -6, 6, -22, 25, -10, -26, -20],\n [-24, -1, -11, -11, 17, 14, -13, 17, -1, 0, 21, -10],\n [17, -23, -10, 6, 3, -6, -10, -16, 24, 3, -9, -7],\n [7, 14, 1, -18, 17, 4, 18, -11, 4, 2, -14, -4],\n [-13, 12, -25, -15, 1, 5, 22, -3, 10, 2, 25, 15],\n [-9, -24, -14, -14, 15, 2, -25, 1, 21, -23, 24, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"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, 14, -22, -19, 7, -2, 0, 25, 25, -20, 9, 5],\n [-6, 20, -9, -25, 19, 15, -22, 17, 15, 23, 11, 1],\n [4, 17, -3, 6, 12, -15, 12, -18, 25, -12, -4, 17],\n [18, -5, 9, -17, 1, 8, 2, -22, -23, 24, -12, 3],\n [-1, -4, 12, 2, -5, 8, 21, 20, -9, 8, 19, 6],\n [-20, 7, -17, -3, -2, 21, 17, 0, 23, -21, 22, -19],\n [-6, 14, -8, 7, 12, 16, -4, -14, 15, 20, 26, 12],\n [1, -21, -15, -24, 21, -7, 14, 15, 18, -19, -1, 11],\n [1, 8, 17, 14, 14, 16, 11, -25, -20, 14, -2, 24],\n [23, 5, -15, 26, -16, -17, 8, 17, -23, 15, -25, 17],\n [1, 16, 19, 20, -13, 17, 2, -25, 7, 6, -7, 20],\n [3, 15, -1, -7, -26, -26, -2, 6, -4, -16, 17, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-13, -26, 6, -21, -4, -1, -24, 19, -21, 13, 25, -2],\n [20, -10, 1, 5, 2, -4, 14, -11, 5, -1, 6, 21],\n [-8, 14, -10, 11, -13, -9, -6, 19, 12, 15, 21, 12],\n [1, -7, -21, -1, -21, 12, -1, -10, 13, -25, 24, -6],\n [-20, 17, -7, -24, 9, 16, 17, 24, -8, 3, -16, -14],\n [6, 11, 21, -25, 19, -4, 23, 22, -7, 23, 24, 3],\n [-12, -25, 3, -2, -23, -26, -19, 25, -13, -16, -3, -3],\n [5, -2, 19, 1, -11, 15, 12, -11, 9, -15, -15, 7],\n [11, -7, 20, -12, -5, -11, -3, -24, -26, 26, 17, 20],\n [24, 11, 24, -10, 14, -6, 18, 20, 21, -14, -25, -25],\n [16, -2, 1, 21, 22, -1, 8, 1, 6, -9, -13, 14],\n [-18, 17, 3, -24, 7, 6, 0, -18, -14, 3, 26, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[24, 15, -1, -22, 19, 0, -12, 1, -24, 14, -26, -26],\n [24, -21, -16, 23, 19, -11, 6, -3, 5, -17, -2, -17],\n [-14, -26, 8, -13, -6, 21, 25, 11, -26, -7, -22, 13],\n [17, 5, -26, 18, 14, 25, 13, 18, -25, 4, 20, 19],\n [24, -1, -18, 24, 3, 19, -19, -22, 12, -23, 13, 9],\n [-6, 6, -1, 13, 12, -16, -6, 21, -5, 22, 10, -20],\n [15, -14, -7, -12, 11, 7, 9, 26, 19, -2, 2, 20],\n [1, -13, -23, 11, -20, -14, -10, 2, -10, 9, -8, -1],\n [25, 18, -18, -25, -7, -4, -9, -1, 25, -2, -10, 12],\n [22, -17, -2, 19, 1, -1, -15, 17, 22, -8, -4, -13],\n [-10, -12, -6, 11, 3, -8, 5, 2, -5, -7, 11, 11],\n [9, -26, -8, 16, -1, -20, 7, 9, -21, 10, -5, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "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, 16, 2, 23, 25, -10, -14, -10, -17, -2, -9, 22],\n [17, -12, 0, -8, -12, 18, -20, 16, 13, 25, -11, -3],\n [-4, -16, -3, -22, 12, 21, 3, -11, -7, 2, -10, -8],\n [-1, -12, -2, -12, -7, 3, -6, 20, 8, 17, -21, 25],\n [10, -16, -4, 17, 12, -18, -9, 19, 9, 13, 21, 9],\n [1, -8, 3, 11, 24, -12, 17, -15, -25, -18, 8, -26],\n [19, 4, 1, 18, 10, -20, 19, -11, 23, -13, 6, -21],\n [-6, -17, 5, -21, -25, 12, 22, 0, -13, -4, 12, -6],\n [14, 24, 3, -2, 26, -3, -16, 8, -23, 10, 9, -14],\n [-18, 1, 19, -11, -21, 0, -17, -4, -6, -1, 18, -24],\n [16, 8, -20, 0, 15, 6, -23, -1, -19, -7, -10, -22],\n [22, -18, -19, -20, 10, 9, -24, -19, -22, -22, -10, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[0, 13, 12, 22, -15, 1, -23, 25, 1, -2, 23, 9],\n [15, -24, 4, 10, -15, 10, 10, -23, 3, 11, 15, 11],\n [0, -5, -26, 21, 16, 11, -7, -9, -21, 22, -15, -10],\n [26, -5, -9, -17, -3, -7, -15, -23, 15, -22, -1, 9],\n [-11, -22, -1, -8, -21, -3, 4, 4, 26, -20, -17, 12],\n [-5, -13, 1, 15, 25, -5, 5, -16, -13, 4, 17, -23],\n [18, -5, 2, 8, -14, -7, -8, -12, 24, -1, -7, 9],\n [-21, -12, -23, -21, -25, 9, 23, -12, -15, 13, 17, 14],\n [-20, -5, -19, 25, 15, -16, -25, 3, -23, 26, -2, -6],\n [-2, -18, -19, -22, 19, 1, -25, -6, 22, -19, 7, -4],\n [-12, 0, -25, 1, -16, 19, -6, 15, 5, 5, -20, -5],\n [-13, -14, -6, -5, 7, -17, -26, -26, -3, -24, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[24, 14, -14, -23, 25, -4, -21, 7, 14, -9, 9, -1],\n [6, 6, -2, 25, -10, 24, -24, -5, 22, 8, -23, 1],\n [-14, 3, 20, -15, -24, -6, 13, -26, -9, -14, -20, -14],\n [-10, 18, 5, 2, 18, 3, -16, -13, 26, -17, -19, 4],\n [-21, -8, -8, -15, 26, 12, 23, 25, -9, -24, -18, -21],\n [-26, 15, 13, 2, 22, 8, 8, 3, 8, 12, -5, 16],\n [1, -9, 5, -22, 7, 4, 19, 6, -23, -13, -12, -7],\n [-7, 22, 8, -23, -9, -3, 0, 6, -2, -22, -9, 18],\n [19, -7, 8, -21, 0, 1, -16, -18, 25, 1, -8, 12],\n [-6, 4, 15, -20, 10, -2, 1, 9, -10, -1, 1, 10],\n [-10, 22, -10, 6, 7, -4, 3, 0, 24, -18, -7, -4],\n [20, -8, 10, 18, -23, -14, 11, -15, -18, -12, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "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, -22, -2, -3, 10, 26, 4, 19, 7, 14, -13],\n [0, 20, -23, -4, 11, 19, -22, 0, 16, 26, -13, -20],\n [19, 18, -9, 5, -25, 14, 16, -7, 2, 16, -1, 11],\n [-26, -22, -13, -2, 21, -18, 3, -8, 25, 13, -19, -11],\n [23, -19, -4, -18, 5, 10, 7, 26, 19, -9, 18, 17],\n [-12, 26, -12, 2, -4, -4, -26, -5, -20, 18, 5, 1],\n [23, 5, 6, 16, -14, 25, 1, -18, 21, 16, -24, -10],\n [7, 5, -18, 14, 21, -26, 22, 15, -7, -22, 13, 18],\n [-6, -22, -23, -19, -2, -20, 10, 15, 5, -10, 1, -21],\n [15, 21, 15, 9, -25, 4, -26, -24, -14, 4, 2, 17],\n [6, 26, -17, 11, -18, -26, 17, 10, 5, 6, -25, 19],\n [-25, -22, -17, 25, 11, 10, -25, 14, 15, 13, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[10, 26, -9, 0, -7, 23, 7, 17, -19, -23, 3, 25],\n [9, -18, 14, -15, -13, 8, -21, 20, -4, 24, -23, -26],\n [-18, 21, -18, 17, 19, -12, -3, 26, 21, -19, 1, 15],\n [19, -10, 8, 4, -23, 21, -13, -2, 19, 21, 13, 23],\n [-20, 4, 8, 11, -7, -11, -5, 9, -8, -25, -23, 7],\n [-20, 20, 22, -13, 16, 5, -10, 10, -13, -10, 5, 25],\n [26, -25, 12, -23, 13, 3, 3, 6, 15, -26, 6, 9],\n [22, 4, 10, -13, -21, -20, 13, -3, 23, -23, -2, -24],\n [1, -4, 9, 21, -14, -5, -2, 16, -3, 16, 10, 25],\n [6, -13, -3, -5, 25, 24, 10, 25, -4, -21, -8, -15],\n [-1, 2, -13, -10, 3, -20, -6, -26, 22, 11, -23, 19],\n [-19, -9, 25, 18, -19, 4, 4, 1, 21, 10, -24, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "584", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-12, -23, 8, 7, 9, -21, -23, 22, 3, 12, -9, -5],\n [-17, 22, 2, -4, -23, -8, -1, -20, -14, -24, 13, -16],\n [-11, -7, 24, -4, -4, 5, 14, 15, 11, -24, 25, -19],\n [11, 13, -13, -19, -16, 15, 15, 16, 6, -12, 10, -13],\n [-1, 25, -19, 22, -23, 9, -9, 0, -8, -24, -18, 12],\n [-25, -18, -21, 11, 1, 21, 7, 2, 21, -24, -11, 17],\n [8, -16, 16, -4, 3, 21, -22, 25, -19, 16, 16, 23],\n [24, -17, 1, 9, -17, -13, 11, 10, 20, -22, -21, 3],\n [-8, 25, 22, -13, -16, 19, -22, 18, 4, 17, 5, -3],\n [24, -17, -14, 20, 25, -14, 9, -5, -18, -8, 25, -20],\n [-12, -10, 19, -13, 14, 21, -25, -13, -23, -24, -24, -16],\n [-22, 21, 2, 1, -4, 3, -4, 24, 14, -5, 16, -15]]\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[[0, 13, 19, 22, 25, -12, 20, -4, 17, 14, 17, -8],\n [17, -16, 11, 13, 16, -24, -11, 5, 11, -18, 14, 11],\n [-22, -26, 8, 8, -15, 9, -6, 21, 16, -19, 0, -18],\n [1, 3, -13, -4, 2, -1, -5, -12, 24, -18, -1, -10],\n [-18, -24, -11, -14, -1, -10, 5, -3, 9, 26, -5, -18],\n [-5, 14, 23, 19, -7, -24, 9, 6, -9, 9, -17, 9],\n [-6, -2, 22, 13, 24, -18, 21, 0, -12, 25, 5, 21],\n [26, 17, 23, 12, -11, 1, 24, -21, -21, 11, 20, -25],\n [14, 13, -20, 0, 1, -11, 20, -18, 25, -12, 7, -7],\n [-13, -16, 3, -24, -25, 23, -13, 2, -22, 17, 19, -21],\n [-19, 12, 12, 17, 2, 12, 17, 0, -11, 0, 12, 13],\n [-26, 18, 24, 6, 23, 12, 0, -10, -12, -5, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-4, 9, 22, 12, 21, 22, -7, 20, -18, 26, -4, 18],\n [-20, 4, 24, -16, 13, -10, 9, -1, 9, -9, 4, 22],\n [8, 14, 1, -1, -21, 7, 1, 17, 20, -18, 2, 7],\n [-15, -11, -20, 4, 6, 26, -20, -24, -7, -22, -24, 20],\n [11, -12, 8, -4, 6, -25, 9, -6, -13, -13, 15, -16],\n [-23, 20, 25, 3, 9, -7, 25, -11, 7, 18, -19, 18],\n [-7, -6, 13, 3, 9, -22, -6, 11, -4, -8, -17, 0],\n [8, -14, -18, -10, 4, 15, 17, 18, -3, 15, 24, 26],\n [-8, 22, 3, -22, -19, 10, 20, 9, -2, 18, 22, -22],\n [6, -5, 20, 15, -2, 16, 23, 2, 18, 25, 3, 21],\n [24, 3, 17, 19, 4, 7, 1, -17, -23, 6, -10, -16],\n [-20, -10, 1, -10, 14, -17, -1, -21, -10, -11, 12, 24]]\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, -23, -7, 22, 14, -16, -4, 6, 4, -20, -5, -22],\n [10, -26, -21, 18, 20, -23, 3, 3, -10, -3, 4, 1],\n [18, 16, -23, 12, -8, -3, -20, 19, 26, 21, 26, -18],\n [-5, -25, 0, -11, -22, -15, 25, -1, -12, -24, -18, 1],\n [12, 9, -2, 14, 1, 20, -6, 2, -2, 3, 12, -16],\n [-8, -16, -2, -26, 5, -6, 18, -14, 7, -10, 24, 20],\n [-8, -17, 15, -18, 24, -16, 11, 4, -25, -3, 15, 20],\n [-22, 23, 3, 12, 8, 26, 21, -10, 4, -25, -11, -6],\n [3, 25, -26, -13, -11, -18, 22, -19, -18, 7, 18, 6],\n [-5, 3, -20, -9, -6, -22, -20, -15, -10, -3, 10, 17],\n [-8, 18, -11, -2, 0, 24, 15, 17, -20, 19, 15, -19],\n [-12, -11, -19, 9, 5, -10, 9, -5, 5, -16, 18, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -13, 1, 12, -15, 0, -26, -17, 6, -11, 12, 25],\n [-21, -2, 23, -7, 9, -4, -11, -26, 26, 3, 0, 25],\n [-25, 21, -6, -18, 20, -3, 21, 14, 12, 15, -20, 3],\n [18, -25, -15, -14, -24, 16, 13, 16, -9, 12, 17, -21],\n [15, 25, 0, -12, 25, -12, -8, 11, 24, 20, -7, -7],\n [-9, 7, 12, 10, 8, 11, 11, -26, 24, -15, -22, 0],\n [12, -7, 13, -8, 11, -12, -21, -18, 9, 21, -4, -17],\n [-26, -16, 22, 23, -7, 1, -5, -7, 20, 11, -11, -25],\n [-2, 0, -24, -4, 5, -10, 13, -7, 3, 1, 20, 18],\n [26, -4, -8, -2, -3, -26, 1, 2, 17, 23, 23, 8],\n [23, -10, -16, 10, -20, -1, -4, -9, 2, 12, 23, 7],\n [11, -19, -6, -6, 22, 9, -10, -11, 26, -12, -12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-10, 24, -26, -14, 11, -17, 6, -1, -15, -8, -12, 26],\n [-22, -25, 24, -13, 2, 14, -26, -14, 22, 5, 7, -13],\n [25, 11, 11, 23, 24, 14, -12, 12, -21, 2, 10, -8],\n [25, -26, -6, 12, -9, 0, 1, -19, 4, -15, 15, -21],\n [-1, -11, 3, -8, -9, -3, 18, -7, -20, -20, -11, 15],\n [20, -13, -15, 2, -12, -19, 12, 26, -18, 19, 1, 0],\n [-20, 17, -13, -16, 5, 24, 1, -21, 8, -21, -3, -18],\n [-25, 11, -13, 24, 4, 3, 0, 9, 19, 4, 26, 15],\n [-21, 16, 18, -9, 25, -13, -7, 25, -16, 26, 10, 13],\n [-23, 17, -21, -4, -19, 3, 9, 25, 15, -16, 20, -22],\n [-24, -12, -25, -25, -19, 19, 3, 14, -22, 3, 17, -17],\n [6, -3, -8, 3, -2, -16, 22, 8, -26, -10, 4, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "558", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, 25, -1, 9, -22, 20, -13, 24, -12, -15, 23, 19],\n [15, -19, 4, -1, 2, -23, 23, 1, -2, 13, 5, 9],\n [-16, 10, -17, 11, 9, 23, 26, 0, -10, -20, -18, 8],\n [-18, 9, 3, 4, -8, 14, -4, -7, -21, 16, -3, 20],\n [-5, -21, 25, -3, 15, -5, -9, -11, 9, 25, -14, 10],\n [25, -3, -8, 23, -7, 0, -10, -11, -26, -6, 0, -26],\n [3, -7, -3, 19, -25, -12, 2, 8, -14, -8, -26, 18],\n [20, -11, 16, -24, 13, -21, 4, -22, -1, 1, -12, -18],\n [-5, 10, -6, 15, 2, -1, -21, -16, 9, -7, 17, -7],\n [0, -21, 6, 3, 23, 7, -22, -11, -15, -15, -16, 25],\n [24, -6, -20, 7, 2, -21, 9, 7, 22, -19, 10, -17],\n [-11, -25, -8, -20, -25, 18, -4, 4, -23, -11, -17, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 1, 19, -15, -14, 25, 13, -10, -9, 26, -17, 1],\n [-14, 7, 22, -21, -15, 2, -14, -1, -23, -12, -11, 26],\n [-8, 20, -1, 5, -21, 25, -21, -22, -25, 25, -25, 10],\n [-24, -21, 4, 16, -22, 23, 19, -17, 0, -3, -5, -2],\n [-24, -11, 3, 21, 16, -23, 16, 13, -11, 13, 14, 19],\n [-19, -3, -11, 0, -25, -7, 24, -7, -7, -8, 24, -9],\n [-14, -10, 6, 26, 1, -22, 1, -2, -7, -6, -14, -21],\n [2, 15, -18, 2, 11, -26, 3, 23, 5, -4, 12, -17],\n [17, -6, -1, -12, -10, 8, -2, -12, 6, -16, -3, -21],\n [1, 2, 21, -6, -15, -5, 0, -6, -12, -9, -17, -5],\n [17, -7, -8, 1, 10, 23, 24, 17, -26, 7, 8, -1],\n [3, -15, -13, 12, -23, -15, -3, 13, 4, -26, 10, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "511", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-12, -14, 2, 18, -23, -12, 17, 13, 21, -15, -2, 0],\n [-21, -4, -12, 12, -22, -4, -12, -2, 3, 17, 16, -23],\n [-14, 23, 13, 12, -4, -11, 8, -11, 21, -20, 18, -14],\n [26, 24, 23, 2, 12, -7, 23, 2, -9, -5, 9, 14],\n [26, 21, 9, -19, -24, 2, -18, -19, 3, -15, 19, 1],\n [15, 26, 22, 16, -17, -14, -25, -26, -5, 6, -11, 15],\n [2, -17, 12, -20, -26, -1, 18, -22, 8, -14, 0, -15],\n [3, 23, 5, 4, -22, 10, -25, 11, -20, -26, -24, -7],\n [-25, 15, 16, -6, 18, 5, 21, -7, 16, 23, 4, 16],\n [6, -3, -9, -7, 5, -22, -25, -1, -2, 23, -5, 12],\n [-5, -16, -16, 18, -23, 6, -9, 4, 17, 1, 15, -5],\n [13, -24, -20, -7, 16, -20, -20, 2, -1, 14, -24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "539", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-10, 13, -7, 7, 26, 25, 6, -11, -4, -23, 14, 13],\n [6, -19, -22, 6, -2, -20, 20, -20, 6, 14, 6, 2],\n [17, 12, 14, 5, 10, 17, 2, -5, -25, 23, -18, 2],\n [6, -17, 1, 19, 26, 19, 12, -15, -5, -21, 18, 13],\n [-4, 26, 7, 15, 11, -11, -17, 20, -6, 25, -17, -16],\n [-6, -2, 7, 4, 0, -2, 15, 5, 26, 17, -16, 20],\n [-1, 9, 10, 6, 6, 15, 9, -14, -13, 24, 10, 16],\n [13, -26, -22, 3, 26, -9, 18, 10, 12, -15, 7, 18],\n [-13, 11, -11, 15, -16, 6, -12, 21, 15, -17, -24, -16],\n [-16, -11, 11, 3, 14, -26, 11, 23, 18, 7, -8, 7],\n [9, -23, -17, -10, -11, -6, 1, -19, 2, -21, 3, -25],\n [20, 4, -2, -4, 16, -6, -11, -23, 16, 19, -19, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[26, 0, 24, 9, 9, -3, -21, 16, 6, -25, 14, -11],\n [11, -18, 24, -22, 26, -17, 3, -20, 2, -25, -7, -23],\n [1, -19, 8, -25, 14, 1, -16, 9, -18, 11, -26, 0],\n [-24, 12, -18, 13, 1, -6, 1, 18, -3, -9, 24, -18],\n [-1, -3, 25, -21, 26, -15, 9, -18, -17, -24, 22, 2],\n [-20, -1, -19, 16, -14, 8, -8, 19, -5, -11, -12, -25],\n [11, -6, 3, -20, 4, 14, 14, 22, 8, -23, 7, -26],\n [-17, 3, 5, -24, -17, -18, -10, 20, -24, 0, 26, 8],\n [-23, -23, 22, 5, 11, -16, 17, 12, 18, -21, 8, 26],\n [19, 5, 19, -4, 15, 10, -1, 7, 11, -16, 23, -6],\n [16, -3, -12, -24, -25, -20, -22, 26, 18, 13, 2, 14],\n [5, 3, -19, 5, 15, -25, -17, 16, 16, 10, 19, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "566", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[25, -4, 7, -9, 6, 6, -10, -21, -14, -6, 4, -6],\n [6, 1, -21, -19, -14, 7, 13, -5, -26, -14, -26, -17],\n [-22, -7, -14, 10, -17, -24, 7, 7, 3, 10, -23, 7],\n [5, -6, 14, -3, -18, 14, -3, -2, 9, -19, 23, 14],\n [2, -2, 8, 11, 1, -8, 5, 10, 22, 24, 1, 8],\n [-19, 14, -4, 13, 19, -4, 5, -17, -10, 8, 8, -24],\n [9, 2, 22, 19, 0, 4, 7, -15, 10, -2, -25, 3],\n [17, -18, -4, -18, -7, -26, 12, -4, -9, 15, 5, 20],\n [-18, -16, -26, -16, 6, 3, -22, 23, -26, -17, -14, 0],\n [-19, 1, 18, 25, -25, 26, -15, 0, -14, -5, 13, -12],\n [4, -20, 12, 22, 24, 8, -20, -15, -13, 7, 12, 21],\n [-18, 6, -15, 7, 0, -5, -9, 19, 17, -9, 10, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-23, 18, -11, -5, 21, 24, 9, -7, 4, 25, 6, -14],\n [25, -7, 14, 15, 11, -5, 12, -4, 21, 22, 6, 14],\n [3, -13, 20, 9, -19, 20, -5, -23, 24, 8, -19, 7],\n [-5, -2, -2, 13, 13, -10, -11, 21, 21, 12, -12, -10],\n [8, 6, 13, 12, -9, 3, -4, 10, 20, -20, -17, -11],\n [1, -4, 7, -9, 20, -4, 24, -7, 4, -13, -4, -25],\n [2, 23, -18, 6, 21, 17, -15, -8, 15, -7, 10, 4],\n [8, 14, -6, 20, 19, 16, -14, 12, 0, -2, -25, 8],\n [25, -19, 6, -2, -6, 9, -14, 19, -18, 8, 19, 9],\n [22, 20, 17, 19, 24, -17, -22, 4, -3, 5, 22, 22],\n [-24, -11, 14, 22, -7, 17, -3, 7, 25, 21, -4, 26],\n [11, -25, 14, -22, -9, 26, 23, 2, -17, 15, 15, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "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, -4, 3, -21, 17, 9, -7, -11, 1, -1, -5, -16],\n [-26, -22, 22, 16, 19, 14, 15, 9, -25, -21, 0, -1],\n [8, -14, -15, -9, 11, 15, -21, 1, 1, -2, -22, -12],\n [20, 17, -18, 18, 21, 26, -25, 22, -18, -1, -4, 24],\n [1, -21, -23, 3, 20, -9, 3, 0, 17, 4, 17, 25],\n [22, 12, 3, 25, 10, -15, -10, 7, 1, -23, 7, 19],\n [-13, -14, 22, 22, 23, -24, -6, -11, 24, 11, -1, -21],\n [-9, 14, 23, -21, 14, 23, -2, 21, -3, 3, -4, 18],\n [16, -19, 22, -18, -21, 6, 6, 18, -20, 15, -9, -21],\n [18, 10, -6, -1, -12, 17, 3, -16, -19, -22, -19, -22],\n [-17, -12, 11, 23, -24, 14, -17, -20, 24, -3, -1, 7],\n [-19, 12, -22, 9, 16, -1, -17, 6, 9, 4, 11, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-2, 18, -14, -26, 9, 9, 23, -3, 0, -9, 23, 20],\n [23, -12, -10, 2, -22, -16, -11, 25, 7, -10, 6, 23],\n [22, 4, -9, 24, -2, -22, 3, 18, -4, 11, 18, -9],\n [5, 3, 2, 9, -18, -4, -24, -5, 13, 18, 4, -5],\n [-16, 15, 16, -24, -13, 19, -8, 4, 9, 5, -1, -26],\n [-25, -21, 18, -13, 1, 6, -2, 13, -9, 19, 7, -15],\n [0, -3, 6, 26, -12, 16, 5, 23, -10, 8, 20, 18],\n [8, -14, -18, -17, -26, 7, 19, 10, -2, -5, -17, -1],\n [-8, 13, 18, 14, 23, -23, 13, -22, 2, 11, 25, -22],\n [-26, 1, -8, 9, -26, 2, 24, 9, 5, -13, 5, 19],\n [-18, -8, -16, 21, 24, -23, 14, -2, -10, 20, -19, 18],\n [-26, -25, -17, 0, 26, 0, -14, -16, -13, 5, -11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[11, 7, -1, -22, -8, 12, 1, 1, -10, 10, 17, -8],\n [0, 23, -15, -24, -23, 20, 20, -16, 7, -9, 8, -9],\n [19, -21, 7, 6, -19, 15, -7, 23, -7, 16, -9, 0],\n [21, -22, -20, -5, 7, 16, -14, 25, 5, -3, -11, -13],\n [12, -20, 17, -15, -7, 6, -21, 13, 0, -14, -22, -3],\n [-17, 19, 5, -18, 22, 8, 17, -15, -16, 9, -19, -17],\n [-13, 3, -26, -15, -22, -13, 9, -10, -5, 4, -1, -14],\n [-24, 16, -16, -22, 11, -23, 5, -17, -17, 17, -9, 20],\n [-4, -9, 8, -24, -26, -10, 15, -21, -16, -13, 22, 1],\n [12, 9, -16, 24, 14, 26, 13, 25, -23, 21, -21, 11],\n [-8, 4, -25, 16, -2, 23, 14, 21, -16, 19, 13, 18],\n [15, 17, -6, -24, -25, -16, -3, 23, -3, -6, -2, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[13, 16, 20, -4, -3, -6, -25, -4, 24, -12, -1, -1],\n [1, -1, 18, -25, 8, 5, 3, 19, -7, -14, 0, -4],\n [-11, 4, -15, 6, 11, 18, 5, -25, 23, 22, 24, -4],\n [5, -12, 13, 14, 13, -19, 16, 23, 22, -5, 11, 7],\n [-26, -17, 13, -11, -3, 19, -3, 21, -13, -1, 12, -9],\n [-7, 14, 9, -3, -1, 2, 21, -5, -16, 14, 22, -16],\n [25, -24, -6, -16, -19, 4, -17, -21, -10, 11, -20, 5],\n [-14, -21, -24, 0, 18, 15, -1, -23, 10, -6, 24, 1],\n [-9, 5, 12, 26, 6, -1, -10, 25, 2, -7, 3, 23],\n [-22, -21, 15, 24, -17, -21, -17, 15, -6, 17, -23, -14],\n [-17, -11, -8, -21, -1, -18, 19, -17, 13, -24, 22, -8],\n [8, 19, -21, 2, -8, 23, 17, -12, 11, -6, 17, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "531", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[12, -4, -7, 15, 23, -25, 18, 5, 20, 1, -23, -20],\n [-24, -2, 21, -18, -4, -4, 22, -1, 13, -9, -3, 0],\n [18, -25, -26, 21, -11, 16, -3, 9, -16, -1, -21, -1],\n [2, 16, -26, -18, 0, -20, 26, -24, -18, -25, -17, -10],\n [4, -26, -9, -21, 11, 14, 15, 20, -23, 13, -23, 8],\n [-23, -26, 14, 16, 4, 26, -8, -6, 3, 25, -20, -22],\n [-25, 24, -24, -12, 12, 10, -17, -18, -4, -13, 18, 6],\n [-11, -7, -19, 22, 11, 7, 4, 18, -19, -2, 14, -14],\n [-9, 23, 14, 7, 9, 23, -10, -15, -11, -14, -16, -13],\n [15, 1, 26, 24, -3, 26, -10, -18, 19, 3, 10, -24],\n [-19, -9, 3, -24, 7, 16, 1, 10, -2, 3, -20, 19],\n [2, 24, -25, -1, 14, 15, 24, 22, -20, -9, -21, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[13, 0, 14, -3, 6, 4, 7, -5, -3, 9, 1, -7],\n [-9, 15, 5, 6, -17, -18, -2, -14, 20, 23, 18, -22],\n [4, 4, 7, -1, -20, 14, 24, 19, 22, 25, -7, 16],\n [-5, -22, -15, -6, -18, 2, 0, -10, 13, -3, 0, -19],\n [17, 2, -8, -17, -3, 7, 13, 4, 19, 24, -23, 14],\n [18, 4, -18, -1, -14, 21, -1, -26, 13, -18, 4, -3],\n [18, 22, -5, -18, 12, -4, -7, 15, -6, 0, -22, -10],\n [7, -18, 7, -17, 17, -25, 20, -2, -24, 7, -20, 1],\n [-18, -16, 2, -11, 12, 2, -14, 8, -16, 8, 20, -19],\n [-20, -22, -21, 24, 8, 3, -16, 11, 0, -6, -13, 22],\n [8, 2, -3, 9, 14, 18, 5, -21, -17, -7, -7, -1],\n [-6, 18, -4, 19, -15, -14, -17, -20, 10, -15, -2, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "483", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[13, -1, 13, 24, -22, -19, 15, 18, -18, 12, -7, 25],\n [24, -16, 13, -5, -11, 15, 11, 15, -17, -2, -8, -23],\n [-8, -24, -10, -13, -17, -21, 4, 4, 21, -18, 26, -15],\n [17, 19, -1, -25, 15, -23, 5, 1, -21, 3, 1, -14],\n [19, 9, -17, -17, -22, 2, 9, -15, -5, 19, 12, -25],\n [-13, -17, 21, -24, -19, -10, -23, -6, 3, -8, -12, -7],\n [15, 3, -17, -4, -3, -15, -18, -12, 2, -9, -7, -26],\n [-24, -19, 12, 4, 20, -19, -12, -5, 5, -22, 17, 17],\n [-18, 26, 14, -12, 20, 25, 17, 10, 6, -5, 24, -16],\n [23, -21, -10, 19, 17, -22, 12, 21, -18, 2, -4, 20],\n [9, 4, -7, -4, -20, 19, 9, -23, -3, -13, -2, -20],\n [-12, 17, 19, -14, -8, -15, 21, -1, 21, 6, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-21, -2, 26, -10, 16, 9, 23, 25, 19, -18, 1, 8],\n [-24, -16, -7, -4, 3, 10, 9, 17, -15, 9, 8, 7],\n [-23, -3, 9, 1, 12, -25, 16, -22, 1, -14, 9, -18],\n [12, 3, 0, -14, 15, 12, 23, 1, -9, 7, -6, -26],\n [18, -4, 7, 9, -18, -19, 23, 3, 21, 9, 9, -9],\n [-25, 26, -16, 25, 9, 4, 4, -3, 19, -6, 5, 22],\n [3, -19, 6, 24, 24, 26, 12, -26, 6, 15, -14, -5],\n [-22, -15, 2, -24, 24, 9, 20, 18, -16, -1, -25, 2],\n [14, 2, 17, 9, -8, -17, -16, -20, -14, 14, 17, -25],\n [3, -5, 26, -26, 0, -20, -26, -2, 21, -23, 3, -19],\n [22, -6, 24, -23, -23, -19, 15, -1, 2, -11, -8, -26],\n [10, 7, 2, 0, 21, 18, 3, -21, 9, 12, -25, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-13, -19, -24, 8, 0, 7, 1, 4, -10, -8, 15, 17],\n [-16, -18, 3, 18, -21, -13, 4, -16, -22, 4, -25, 12],\n [-10, 11, 19, 9, -24, 16, 2, 6, -13, 11, 2, -4],\n [-10, 22, -16, 1, -20, 18, 13, -19, 14, 2, -2, -20],\n [-5, -18, -16, 7, 0, 23, -5, -24, 23, 21, 13, -19],\n [-21, -2, -25, -11, 26, 14, 24, -6, -12, 7, 20, 16],\n [-7, 17, 4, -12, 21, 1, -21, -24, 11, -4, -24, 26],\n [18, 17, -19, -25, -20, -10, -20, 6, 9, 20, -23, 17],\n [-11, -6, -9, 19, 19, 1, 16, -11, 20, -5, -21, 3],\n [18, 1, -10, 9, -15, 23, 13, -15, 9, 13, 2, -25],\n [2, 3, 9, 17, -2, -6, -5, -17, 4, 20, -18, 14],\n [12, 7, 12, 14, 23, -4, -15, -20, 5, -8, -5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-19, 3, 24, -21, -25, 7, 2, 13, 15, 26, 26, 16],\n [25, -7, -24, 21, 8, -19, 24, -15, 23, 18, 16, 5],\n [2, 18, -6, -24, 11, 0, -24, -26, 19, -7, -20, 14],\n [-26, -17, 18, -15, -23, -20, -17, -5, -2, 2, 12, -12],\n [-8, 12, 19, 26, 19, -9, 15, -24, -21, -5, 14, 19],\n [26, 4, -6, -19, -26, -24, 2, -21, 6, -9, 15, 22],\n [26, -26, -5, 4, -4, -19, 2, 17, 24, 19, -8, 22],\n [-11, -8, 10, -5, -8, -23, -22, -22, -2, -3, -26, 23],\n [1, 20, -6, -8, -4, -13, -21, 5, 23, 5, -19, 10],\n [-5, -19, 11, -17, -24, -14, 12, 3, -23, 18, -21, -11],\n [-5, 0, -6, 2, -26, 3, -3, -14, 3, -1, 7, -7],\n [24, -21, 16, 22, -18, 10, 10, -11, -23, 5, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, 18, -10, 14, -2, 18, -11, -7, 15, -17, 25, 21],\n [-4, 25, 6, 16, -14, -2, 23, 10, 9, -3, -21, -12],\n [7, -23, -13, -23, 1, 2, -9, -7, 21, 14, 5, -19],\n [16, 19, 22, -14, 13, 19, 16, -18, 13, 19, 20, 6],\n [-15, 10, -2, 19, -2, -11, 24, -11, 12, 8, -4, -19],\n [26, 26, 19, 25, -24, -3, 16, -5, -13, -5, 7, 9],\n [4, -6, -22, -8, 15, 26, -6, -25, 26, -24, 20, 24],\n [26, 3, 7, -2, 8, 2, -15, -4, 1, 19, -10, -11],\n [22, -18, -24, -5, 4, -13, -24, 11, -4, -6, 24, -3],\n [5, 18, -22, 6, 17, 20, -8, 7, -24, 12, 1, -16],\n [-17, 13, -25, 19, 18, 12, 0, 26, -18, 12, -26, 6],\n [11, 6, 21, -24, 5, -14, -6, -23, -10, 15, -23, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-15, -1, 18, 9, -11, 24, -20, 6, 21, -25, 6, -13],\n [-7, 10, 0, 20, 15, -6, -25, 16, -11, -8, -23, -17],\n [-5, -15, -25, -25, 14, 17, 7, -9, -11, -8, 20, -2],\n [3, 21, -21, 0, -12, 4, 17, -5, -15, -17, -6, 20],\n [4, 9, -17, -8, -4, 19, -17, 22, 0, 16, 23, -25],\n [-16, -19, -8, -11, -23, -13, -5, -10, 16, -1, 8, 9],\n [26, 18, 22, 3, 25, -6, -7, 15, -1, -15, -19, 8],\n [2, 26, 15, -20, -17, 12, 23, -7, 1, -13, -15, -19],\n [-20, -22, -26, 20, -18, 17, -9, 16, 15, -17, 23, -26],\n [-7, 16, 2, -25, -1, -16, -2, 7, 14, -26, 4, 11],\n [-5, -25, 20, -26, -3, 23, 9, 18, 9, 20, 7, -18],\n [-15, 19, -7, -23, -12, -23, -22, -17, 17, 17, 13, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "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, -26, -9, 25, 4, 19, 22, -21, -21, 15, -8, 5],\n [15, 3, -1, -24, 6, 23, 4, 20, -7, -23, 5, -9],\n [-17, -5, 24, -10, 15, -23, 10, -20, 24, 24, -19, -26],\n [-19, -8, -10, 14, 25, 21, -18, 24, -11, 26, 18, 24],\n [10, 0, -25, 9, -15, 23, 8, 4, 26, -8, -1, 9],\n [-23, 21, 16, 4, -14, 26, 16, 12, 19, -23, 13, 17],\n [-14, 14, -18, -25, 8, 26, -15, -10, -23, -13, -6, 14],\n [-19, 6, 18, 1, -24, -13, -8, -21, 9, -7, -26, -17],\n [-14, -15, -16, 9, -10, 20, 26, 2, -24, 2, -17, 26],\n [19, -8, 26, -23, 19, 11, -15, 4, -25, 22, -26, -10],\n [-2, -22, 21, -13, 25, -17, -6, -2, 8, -24, -9, 23],\n [9, 12, 6, 21, -10, 13, -21, 7, -1, 15, 4, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[24, 1, 9, -14, -6, -1, 24, 4, -11, 4, -14, 3],\n [5, -22, -15, 12, 14, 10, -23, 15, 21, 16, 2, 14],\n [-22, -16, 3, -18, 22, 1, -5, -16, -6, -21, -1, -11],\n [24, -13, 8, 15, 26, 9, -5, 26, -25, -14, -16, -15],\n [6, -5, 26, -18, 17, -20, -10, -17, 11, 12, 24, 19],\n [-2, 0, 3, 3, 16, 7, 6, 5, 15, -15, 14, -4],\n [2, 16, -26, -7, -17, -8, -4, -6, 16, 8, 21, 5],\n [-17, -25, 24, 9, 21, -21, 16, -10, -12, 9, -3, 13],\n [2, 23, -13, -25, 21, -5, 20, 26, -21, -18, -15, 15],\n [12, -22, 13, 17, -26, -17, -16, 0, -4, -7, -22, -14],\n [23, -17, 26, 22, 24, 9, 14, 23, -11, -20, 5, -2],\n [17, -1, 9, 26, 1, 17, -15, -1, -23, 17, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 4, 3, -24, -11, 7, 11, 1, 22, 17, 14, 21],\n [-20, -19, -20, 26, 10, -20, 23, -9, 21, 12, -6, 7],\n [22, 0, -19, 7, -9, 24, 25, 14, -15, -5, 24, 13],\n [-5, -19, 15, 1, 23, 20, 5, -16, -6, -1, -13, -12],\n [-13, -15, 9, -24, 17, -20, 12, 24, 19, -26, 12, -2],\n [4, -5, -17, -9, -14, -19, -18, -12, -19, 6, 8, -8],\n [3, -18, -8, 20, 19, -1, -26, -24, 7, -2, 3, -26],\n [-9, 6, -18, -20, 3, -14, -10, -14, -14, 15, 11, 10],\n [-17, -13, 16, -22, 9, 8, 19, 18, -4, -22, 17, 1],\n [-4, 15, 7, 4, -20, -20, -23, 17, 5, 1, -23, 12],\n [25, 18, -19, -13, 3, -24, -25, -17, -21, -20, -11, -21],\n [-11, 0, -15, -5, -12, -5, 8, 21, 23, -12, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[22, -25, -25, 22, -8, -22, -23, 1, -9, 13, 14, 23],\n [4, -5, -16, 21, -11, -23, -6, 14, 18, -2, -7, -19],\n [16, 26, -18, -9, 4, 25, 8, 3, -9, -8, 14, -3],\n [23, -5, 21, -13, -8, 2, -5, 3, -12, -6, -1, 9],\n [-15, -20, -16, 12, -7, 8, -23, -25, -7, 20, -7, -15],\n [26, -10, -9, 13, -3, -19, 10, 14, 3, -7, 25, -4],\n [10, -17, 6, -3, 9, -11, 23, 1, -15, -7, 20, -9],\n [10, -1, 19, -20, 16, 20, -6, 16, 5, -20, 26, -4],\n [-7, -7, 5, -1, 9, -3, -26, 26, 1, -1, 7, -1],\n [9, -22, -25, 5, 7, 23, 3, -3, 1, 19, -24, 26],\n [23, -17, -21, 7, 4, 25, 16, 23, 19, 25, -14, 12],\n [26, -7, 5, -17, -1, -8, 2, -14, 7, -7, 17, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-9, 7, 21, -19, -11, 13, -4, 5, -14, -1, 11, -26],\n [-25, 12, -14, 0, -23, 14, 24, -7, -24, -4, -25, -11],\n [-17, 1, 17, -9, -25, -13, 17, -7, 13, -4, -20, 18],\n [20, -13, 10, -19, 23, -22, -4, 14, -17, 22, 0, 8],\n [-26, -20, 20, 24, -19, -16, 7, 25, 1, 7, 16, -7],\n [1, 22, 15, 10, -24, -18, 25, -5, -2, -25, -4, 24],\n [-10, -2, -15, 0, -7, -18, -4, 9, 1, 23, 21, 2],\n [26, 15, 5, -15, 3, -16, 10, -7, -16, 21, 20, 11],\n [18, -11, 8, 23, -26, -2, 22, 0, 25, 5, -21, 14],\n [9, 12, -4, 2, 3, -5, -16, -1, -4, -24, 21, -21],\n [-20, 17, 12, 24, -5, 21, 23, 15, 6, 13, -24, 3],\n [21, -3, -24, -25, 17, 13, -8, -3, 23, -7, 20, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[23, 4, 23, 14, 4, 10, 16, 2, -23, -17, 9, 8],\n [21, -6, 16, 14, -26, 15, -15, -3, -25, 20, -7, -11],\n [7, -14, -9, 2, 24, 16, -13, 3, 8, -18, 10, 19],\n [12, -15, -6, -9, -16, 0, -3, 14, 16, 23, 7, -7],\n [-14, 20, -19, 10, -22, -20, 17, 25, -15, 14, -23, 13],\n [-8, -26, 16, -14, 23, 26, 25, 15, 18, -2, 17, 18],\n [7, 8, -10, -1, -6, 24, -15, -11, 25, -7, -17, -4],\n [20, 3, -19, 24, -22, -15, 15, -13, -15, -3, 18, 26],\n [26, -10, -26, 15, 10, -16, 15, -21, -12, 14, 13, -4],\n [-4, 11, 11, 22, -15, -20, 10, -11, 11, 13, 8, 13],\n [2, 12, -10, 24, -1, -7, 19, -2, 11, 12, 10, -8],\n [-6, 5, 1, 12, 14, -15, 20, -12, 1, -6, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[25, -1, -12, 10, -15, -23, 8, 4, 0, 5, 6, -14],\n [10, 17, -25, 11, 10, 23, -22, -9, 21, -10, -25, 22],\n [15, 8, -13, 24, -15, 6, -20, 12, 18, -18, -22, -23],\n [5, -22, 25, 17, -19, -14, -23, 25, -16, -12, 19, -9],\n [-7, -26, -26, -16, 2, 2, -3, -7, 3, 11, -22, 18],\n [-17, -21, -23, -23, -20, 21, 6, -18, -1, 24, 25, 20],\n [14, -6, 25, -5, 6, 6, 21, -22, -6, 0, 14, -26],\n [24, -11, 8, 9, 17, 5, 2, 12, 20, -4, -12, -1],\n [10, -2, -25, -15, -8, 5, -4, -22, -2, 8, 2, 11],\n [18, -7, 20, 9, 25, -20, -5, -9, 26, -6, -5, 12],\n [-15, -16, -15, -1, 3, -12, -19, 16, 26, -9, -17, -19],\n [11, 8, -7, -15, 22, -24, -7, 23, -15, -3, -11, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-8, 14, -13, 25, -13, -5, -23, 20, 25, 7, -9, 7],\n [-9, 13, 4, 15, -7, 9, 15, -17, -24, -6, 9, -17],\n [-20, -5, -4, -15, 12, -14, 13, -14, 6, 4, 21, 24],\n [1, -8, -6, 5, -1, -14, 2, -20, 20, -1, -21, 5],\n [9, -4, 25, -16, -6, -8, 7, 22, 20, 25, 23, 17],\n [8, 22, 4, 19, 2, -21, 9, 26, 4, 5, 13, -7],\n [-5, -24, -19, 18, -8, 4, 5, -12, 12, 4, -24, 24],\n [5, -17, 1, 0, 21, 19, 13, 16, 4, 24, 7, -22],\n [-16, -20, -19, -10, 17, 23, 12, 14, 24, -13, -3, 3],\n [24, 25, 23, -12, 26, 26, -23, -14, -22, 4, -15, 3],\n [22, -17, 3, -1, 17, -21, 0, -7, 1, -7, -15, 18],\n [-6, 3, 22, 25, -17, 24, -22, 10, -19, 3, -10, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -11, 5, 0, 24, -21, 15, -11, 18, -24, 13, -7],\n [13, -20, -16, 2, 25, -24, -6, 26, 5, 3, 12, -16],\n [-10, -2, 23, -2, -18, 18, 2, -12, -8, -12, 12, 8],\n [13, -14, -11, -24, 26, 4, -26, 8, -11, -26, 23, -13],\n [-20, -4, 8, 2, -5, -11, 2, -21, -9, 2, -2, 18],\n [-25, 17, 5, 9, 5, 14, -7, 10, 15, 11, 6, 25],\n [-22, -21, -5, -6, -8, 16, -12, 7, 20, -20, -10, 17],\n [17, -22, 25, 12, -25, 0, 18, -3, 14, 20, 1, 20],\n [-26, 26, 25, -6, 1, -24, 3, -26, 24, 25, 18, 20],\n [18, -9, 22, 6, -12, -3, 9, 7, -1, 24, 13, -5],\n [-11, 13, 15, -11, -22, 24, -21, 15, -3, 3, 10, 5],\n [26, -8, 24, 18, 1, 20, -19, 16, -26, -23, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 0, 0, -14, 12, 0, 12, 11, -19, -15, -3, -9],\n [-12, -11, 6, -17, 20, -3, 18, -8, 0, 18, 14, 4],\n [-6, -11, -4, -13, -4, 14, -9, 9, -15, 10, -16, -22],\n [24, -6, 5, 2, -20, 9, 13, 0, -21, 11, -23, 19],\n [8, -17, 11, 23, 3, 15, -18, -11, 25, -23, -1, 2],\n [1, -16, 1, 17, 5, -3, 24, 15, 12, -20, -9, -24],\n [17, 19, -7, 7, 3, -18, -17, -21, -10, -12, 6, -14],\n [15, 17, -5, -11, 7, -24, -19, -7, 20, -3, 24, -9],\n [-4, -26, 24, -25, -22, -9, -11, -17, 26, 2, 8, -2],\n [15, -3, -14, -6, 15, 16, 12, 7, -8, 1, 0, 23],\n [-1, -16, 22, 8, -7, -15, 1, -25, -26, -18, -5, 24],\n [13, 0, -18, -20, 9, 21, 11, 23, -25, 16, -22, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[10, 8, 24, -19, 16, -24, -24, -26, -3, 18, 3, 15],\n [-1, 11, 16, 13, 24, 16, 11, 17, 23, -24, -14, 9],\n [14, 21, -15, -7, 12, 17, -19, 26, 20, -25, -16, -6],\n [10, -21, -8, 3, 19, 12, 17, 22, 9, -7, -17, -3],\n [6, 2, 3, 9, 18, -21, 20, -13, -24, -3, -8, 11],\n [7, -18, 3, 5, -14, -9, 17, 26, -5, -23, -4, -20],\n [17, -16, 12, 15, 14, 7, -22, 15, -2, 1, -13, 0],\n [-11, 0, -25, -8, -4, 14, -13, 20, 24, -1, -19, 0],\n [20, 13, 1, -23, 11, -16, 17, -3, 1, 14, -9, 22],\n [-6, -1, -24, -14, 11, 1, -13, -26, 1, 9, 23, -16],\n [16, 13, -23, 7, -26, -17, -10, -20, 12, -14, -5, -26],\n [1, 6, -14, -26, 11, -2, 15, -6, 6, 10, 7, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -24, -9, -4, -19, -18, -25, -25, 0, 21, 12, 9],\n [-22, -26, -5, -17, 18, -3, -12, 6, 23, -4, -13, -9],\n [-2, -5, 17, 17, 10, -20, -1, -3, -14, 14, -21, -6],\n [-20, -9, -12, -19, 25, -11, 22, -24, 18, -18, 25, 20],\n [-1, -1, 3, 0, -11, 21, 24, -23, 24, -8, 7, -21],\n [18, -12, -17, 15, 9, 19, 13, -21, 17, 13, -21, -12],\n [2, -2, -8, -13, -24, 23, 15, 19, -13, 12, 12, -6],\n [-16, 23, -17, -12, 3, 17, -10, 2, -10, 6, 11, -6],\n [20, 24, -13, -17, 15, -4, 12, 12, -13, 20, -5, 25],\n [14, 1, 20, -18, -4, -20, -3, 16, 10, -18, 11, -20],\n [-4, -2, 19, 24, -5, 16, -20, -21, 9, 19, -5, 8],\n [22, 20, 6, -6, -16, -14, -24, -14, 23, 14, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[13, 7, 5, -4, -3, -26, -3, -24, -10, -20, -17, -8],\n [-3, -18, 23, -12, 22, -5, -10, -8, -18, 11, -8, -19],\n [-21, 22, 11, 18, -6, 2, 7, -15, 12, 5, -21, -10],\n [5, -19, 11, 2, 4, -8, 26, -18, 25, 1, 21, 23],\n [24, 12, 13, 26, 4, -8, 6, -1, 18, -26, -16, -25],\n [26, 8, -14, 12, 7, 7, 8, 5, 18, -15, 6, -9],\n [-22, -8, 4, 0, 15, 11, 23, -12, 19, 21, -23, -8],\n [-6, 13, -26, -7, -5, -14, 14, -26, -12, -12, -13, -22],\n [22, -21, 14, 4, 25, -1, -2, 24, 26, 22, 12, 13],\n [-12, -21, -26, 14, -20, 25, 24, -23, -26, 14, -25, 21],\n [7, 8, 19, -14, -10, -17, -24, -23, -2, 10, 16, 11],\n [2, -26, 24, 3, 12, -17, 2, 17, 5, 17, -26, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "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, -15, -25, -18, -15, -2, 9, 17, 23, 8, -5, 6],\n [23, -6, 13, 24, -5, 1, -23, -1, -4, 21, 22, -4],\n [14, -19, 25, 5, 24, 12, 17, -26, 3, 1, -10, -4],\n [11, -3, -5, -22, -2, 25, -20, -5, 17, 10, 7, 9],\n [22, 13, -7, 10, -10, 25, -23, 26, 23, -9, 1, 23],\n [-11, 16, -19, 17, -9, 23, 2, 13, -11, 3, 22, 7],\n [3, -6, -5, 20, -2, -5, 1, 12, 6, -25, -23, -11],\n [-15, -10, 9, -11, 12, -4, -19, -18, -13, -18, 20, 26],\n [-1, 9, -24, -17, -2, -23, 3, 23, -16, 24, -8, 23],\n [-14, 9, -24, 21, -13, -17, 11, 13, 0, -3, -11, -17],\n [26, 0, -20, 24, 1, -1, -9, -14, -19, 0, -13, 14],\n [17, -21, -7, 1, -4, -15, -3, 24, 17, -5, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-20, -12, 21, 3, -23, -21, 21, 20, -25, 4, -3, 8],\n [20, 4, -2, -19, -15, -25, -12, 13, 5, -16, -10, -6],\n [-5, 6, 25, 2, -12, -6, -25, 15, 25, 11, -24, -2],\n [-14, -3, 4, -12, -21, 14, -17, -18, 23, 14, 23, 14],\n [-22, 18, 17, 14, -8, -7, 6, 16, 10, 4, 12, -14],\n [11, 18, -21, 20, -19, 16, -17, 14, -23, -13, -23, -3],\n [20, -6, -17, 19, -2, -21, -11, 17, 1, 9, 6, 3],\n [9, -2, -14, 12, -12, 11, 3, -13, 23, -23, -26, -24],\n [18, 23, 9, -23, 16, -13, -2, 12, -24, -20, -19, 17],\n [-20, 21, -2, -10, -1, -23, 22, -9, -23, -10, 20, -10],\n [18, -2, -24, -15, 0, -10, -5, 12, 12, 16, 21, 9],\n [-11, 10, 24, 2, -13, -20, 14, 1, -14, -11, -6, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[12, 8, 25, -12, 26, -1, 19, -20, -9, -2, 10, -6],\n [25, -19, -7, -9, 26, -8, 25, -24, 11, -9, 0, -12],\n [19, -6, -5, -19, -16, 16, -15, 21, 12, 0, 8, -25],\n [8, 4, -19, -7, -19, -23, 4, 5, -14, -5, -1, -10],\n [2, 0, -5, -9, -22, -15, -25, 15, -20, 20, -1, 12],\n [-12, 21, 6, 20, -24, 15, 21, -25, -10, -26, 9, 16],\n [-10, -25, 6, 2, -21, 16, 9, -3, -16, -22, 3, -17],\n [10, 0, 0, -3, -24, 11, -1, 18, 21, 12, -9, -24],\n [11, 15, 21, -2, -14, -2, -3, 14, -11, 16, 14, 15],\n [-16, -6, 4, -12, 26, 18, 22, 9, 16, -26, 1, 6],\n [-24, -12, 6, 5, -4, -1, 21, -10, -18, -22, 2, -21],\n [20, 14, 8, 24, -6, 18, 18, -4, 8, 25, 19, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[15, -18, -14, 16, 7, -11, -22, -26, 13, -5, 21, 19],\n [-1, 7, 23, -6, -20, -2, -15, 4, 20, 0, -5, 7],\n [-10, -16, 2, 7, 24, 10, 22, 21, -1, 18, 18, 18],\n [5, 10, -22, -7, 24, -20, 16, -4, -26, 12, -24, 18],\n [-24, -21, 4, 0, 2, -12, 9, -22, -24, 24, -2, 5],\n [-6, 21, -10, -18, -1, -5, 14, 19, -4, -16, -17, -4],\n [-22, -1, -23, 16, 0, 11, 7, -24, 23, 5, -1, -9],\n [-20, 26, 18, -14, -21, 8, 4, 15, 26, 10, 16, -23],\n [15, -23, 18, -19, 11, -16, -25, -9, -9, -5, -15, -10],\n [24, -10, 9, 2, 22, -11, 14, -16, 17, 16, 18, -5],\n [3, -19, 19, -9, 19, -11, 20, -7, 12, -19, 3, 11],\n [2, -14, -10, 13, 16, -10, -18, -25, 15, -3, -6, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-25, -22, -10, -3, -19, 3, 23, -5, -3, -1, -19, -15],\n [-13, 3, 8, 4, 1, 19, 0, 9, -26, 14, -13, -17],\n [23, 15, -20, 13, -13, 9, 0, -16, 15, 22, 10, 15],\n [-17, -20, -10, 25, -15, 10, 10, 9, -20, -3, 7, -26],\n [2, -1, -17, -26, 18, -10, 14, 9, -18, 12, -4, 2],\n [-25, -9, 1, 26, 20, 15, 22, -20, -16, -20, 16, -3],\n [-12, 4, 24, -8, -17, 21, 25, -19, -26, -25, 2, 15],\n [-17, 15, -18, 23, 4, 5, -25, -3, 10, 26, 16, -21],\n [-19, 13, -2, 15, 16, 24, -2, 19, -16, 8, -26, 26],\n [-4, -24, 14, -26, 17, -15, 11, 13, 4, 2, 8, 1],\n [-6, -16, -1, -16, -22, -20, 24, 4, 12, 15, -19, 26],\n [0, -6, 3, -13, -26, 18, -3, -21, -21, 26, -22, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[17, -12, 8, 21, 23, 14, -19, 16, 8, -22, 4, 15],\n [4, 10, -19, -21, -4, 26, -11, 17, 22, -19, -23, 5],\n [26, 22, -24, 23, -11, 7, -14, 6, -5, 4, -3, -24],\n [6, 3, -1, 7, 24, -5, 3, 8, -2, 1, 6, -4],\n [-1, -18, -19, 10, 6, -12, 22, 20, -19, -6, -24, -18],\n [25, -13, 11, 0, -7, -23, -3, 0, -15, 1, 8, -3],\n [4, -24, 3, 0, 26, -10, -21, 20, 16, -9, 8, 0],\n [-10, -16, 11, 10, 15, 7, 20, 5, 16, 19, 19, 8],\n [1, -5, -11, 19, 15, 13, -15, -22, -1, -1, -14, -3],\n [17, -24, 5, -4, 22, 25, 10, 11, 18, 11, -14, -12],\n [-25, -16, -11, -9, 7, -17, -14, 5, -19, -20, 21, -10],\n [14, 0, -19, 2, 25, 10, 0, 10, -3, 18, -11, -1]]\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[[4, 0, -1, 16, -12, 22, -12, -4, -2, 17, -23, 9],\n [26, -11, 20, 13, -6, 25, 13, 16, 26, -10, -24, -20],\n [-15, -26, 16, 10, -21, 19, 22, -4, -2, -2, -24, -23],\n [3, 6, 2, -23, -13, -6, -20, -6, -20, -26, 7, -4],\n [-24, -9, 16, -15, -13, 14, 1, 15, 18, -3, -3, -24],\n [-18, -3, -25, 13, 1, -20, -18, 18, 12, 12, 6, 7],\n [-6, 2, 0, -10, 15, 20, 21, -4, 26, 18, -6, -19],\n [-18, 6, -23, -9, 5, 3, -2, 6, 8, 15, 7, 23],\n [-25, -14, 26, 14, -4, -4, 4, -25, -25, -22, -13, -4],\n [8, 19, -26, 14, 21, 22, 13, -12, 3, -6, -19, -20],\n [14, 7, 15, 10, 21, 26, 5, 6, -21, 15, -17, -1],\n [24, 18, -1, -8, 8, 18, -23, -2, -19, -15, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-10, -2, 6, 0, -25, -18, 6, -8, 22, -22, 20, -7],\n [-3, 4, 17, -23, 5, 20, 8, -13, 9, 24, -21, -10],\n [-9, -19, 24, 25, -15, -10, 4, 24, -26, -16, 15, -11],\n [10, 22, 1, -18, -19, -2, -17, 13, -24, -4, -4, 17],\n [-23, 23, -4, -18, 26, -23, 7, 12, -9, 7, 7, 15],\n [-24, -8, 7, -1, 8, 14, 16, 4, 16, 0, -24, 10],\n [-15, 20, -4, -10, -11, -10, -12, -1, 18, -25, -10, -26],\n [3, 5, 3, 15, -23, 15, 17, 5, 8, -26, -8, 6],\n [-8, 9, 0, -14, 0, 19, -13, -3, 8, -8, -2, -16],\n [-18, -21, 9, 10, 2, -18, 6, -4, -12, -16, -4, -1],\n [-26, 3, -10, 20, 19, 14, -4, 9, 14, -22, 8, 23],\n [-18, -23, -20, -26, -11, -2, -21, 11, -13, 10, -16, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[25, 15, -26, 26, 9, -19, 5, 6, -19, -13, -3, 22],\n [14, 2, -2, -21, -26, -4, 14, 6, -13, 1, 2, 16],\n [13, -4, 17, 11, 22, 16, -17, 0, -19, 17, 26, -23],\n [-6, -6, 3, -14, -24, -7, 9, 13, -22, -5, -25, -2],\n [13, -3, -22, -11, 26, -12, 24, -14, -16, -11, -9, -2],\n [20, 11, 13, -23, 26, 21, -6, -16, 25, 7, 3, -23],\n [-13, -16, -23, -1, -24, 10, 11, 14, -23, -1, 12, 18],\n [15, 17, 15, -16, -16, 11, 11, -7, -1, 11, -15, 2],\n [-13, 23, -2, 24, 15, 15, 12, -1, -17, -13, -22, -5],\n [-16, 2, -20, 25, -9, 4, 16, -7, 8, -20, 3, -23],\n [24, 3, 3, 3, 26, -9, 16, 19, -17, -13, 9, -4],\n [-15, -15, 7, -1, -21, 10, 24, 26, -12, 15, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[13, 20, -4, 9, -14, 4, 10, -1, 16, 21, 25, -9],\n [20, 6, 13, 5, -23, 14, -8, -20, 20, 8, -1, 17],\n [-4, 7, 24, -20, -16, 24, -19, -14, 5, 14, 7, -9],\n [-12, 16, -3, 20, -6, -9, -13, 26, -8, -14, -11, -25],\n [7, 22, -1, -5, -7, 2, -9, 2, 15, 17, 0, 8],\n [2, -21, 25, 10, -2, -6, 4, 13, 23, -11, -13, -21],\n [-16, 0, 11, -22, -12, 11, 26, -11, -9, 26, 6, 8],\n [25, -3, 8, -20, -13, 23, 3, -3, -12, -14, -8, 2],\n [-5, -25, 12, -14, 9, 11, -9, 24, -12, 8, 25, -10],\n [21, -14, -5, 25, 13, -6, -1, 19, -23, -20, -17, -12],\n [-1, -11, 13, 7, -10, 11, -11, 7, 2, 26, -9, -16],\n [-15, 10, -25, -9, 11, 6, -18, -12, 1, -19, 19, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[12, 25, -19, 15, 23, 23, -8, -23, 0, -14, 11, -6],\n [-1, 18, -4, 3, 4, 4, -11, 25, 15, 14, -20, -10],\n [-3, -7, 12, 0, -25, 24, -26, 7, 0, 10, 23, -21],\n [11, 0, 21, -11, 8, 0, 8, 9, 11, 1, -24, 14],\n [4, -24, 11, 26, 25, -3, -1, 14, 20, 1, -18, 10],\n [26, 0, 21, -24, 14, 22, 1, 5, 8, -20, -20, -6],\n [5, 11, -7, -19, -23, -1, -12, -21, 21, 5, -22, 17],\n [19, -21, -24, 2, -8, -17, -20, 18, -26, -26, -10, -5],\n [9, -13, -21, 3, 19, 20, 6, -7, -11, -23, 7, -26],\n [-14, 21, -19, -5, -23, 7, 18, 10, -4, -7, 26, -3],\n [0, -14, -22, -11, 11, 21, 2, -1, -5, -3, -14, 16],\n [-6, -26, -23, -24, 23, -4, -11, 18, -14, 12, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563", "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, -12, -22, 22, -5, -5, -16, -3, 18, -17, 20, 7],\n [-16, 16, 2, -5, 6, -19, 22, 5, 13, 18, -4, -22],\n [4, 2, -21, 25, -2, -2, 4, -13, -10, -11, 1, -18],\n [24, -25, -23, -7, 14, 9, 10, -21, 25, -26, 18, 23],\n [-24, 25, 10, 18, 15, -24, 16, 6, -12, -23, -12, -20],\n [20, -23, -24, -4, -13, -21, 6, -18, -15, 23, 8, 26],\n [4, 24, -24, 19, 9, -14, -14, 7, -6, 7, 15, 16],\n [1, 20, 8, -13, -9, -8, -8, 6, 24, 8, -7, 2],\n [-19, -2, -10, -26, 11, 22, 26, 3, 1, 6, -14, -3],\n [17, 10, -5, 25, -14, 13, -15, 14, 22, 19, -20, 9],\n [2, 2, -1, 0, -3, 4, -20, -10, 22, 6, 7, -9],\n [14, -22, -26, -20, 7, -24, 9, 8, 24, -15, -12, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -11, 2, -21, 22, 10, -4, -14, 17, -26, -15, 0],\n [-2, -5, 7, -9, 14, -11, 2, 3, 3, -7, 20, -5],\n [15, 7, -23, 23, 4, 24, 23, -13, -19, 10, -22, -19],\n [-16, 2, -6, 12, -14, 22, -8, -24, 7, 11, -8, 5],\n [20, 9, 24, 12, 25, 26, -13, -20, -7, 5, 19, 4],\n [-5, -22, 4, -12, 17, -10, 26, 10, -8, -17, 17, 7],\n [22, -2, 10, 1, -12, -7, -14, -7, 16, 4, -9, 14],\n [21, 1, 20, -23, -3, 17, 18, -18, 20, 23, 25, 5],\n [5, 12, -6, 17, 15, 12, 19, 0, 20, 9, -19, -8],\n [2, -8, -22, -5, 8, -17, -12, -25, 26, 15, -5, 21],\n [8, 12, -8, 20, -15, 7, 18, -7, 24, -20, -3, -24],\n [-21, 6, 26, 7, 6, 2, -4, -23, -22, 7, -11, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[20, 16, 15, -24, 16, 22, 15, 22, -13, 6, 1, 14],\n [-12, -23, -7, 26, -2, 8, 25, 26, 12, 26, -5, 8],\n [20, 1, -17, -11, 22, -4, -8, -26, -26, 26, 19, -1],\n [7, -25, 1, -7, 15, 20, 0, 1, 4, 20, -20, -19],\n [5, -16, 21, -1, -2, -20, -7, 14, 24, 3, -26, -9],\n [-19, 2, 13, -5, 5, 13, -13, -25, 8, -20, -24, -12],\n [16, 7, -5, -9, 19, -9, 7, 9, 19, 12, 20, 11],\n [10, 25, -9, 16, 13, 2, -15, -9, 4, -12, 13, 3],\n [9, 1, 26, -12, 16, 6, -25, -19, 21, 6, 8, -9],\n [-1, 21, -6, 1, -7, 25, 18, -7, -23, 9, 7, 18],\n [-14, 4, 25, 12, -20, -10, 15, -15, 3, 21, 7, -5],\n [-6, -18, -15, -10, -11, -22, -8, 1, -10, -5, 8, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "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, -8, 20, 23, -1, 17, 17, 8, 16, -4, -17, -5],\n [20, -16, -1, -26, 25, 9, 26, -6, -19, -7, 18, -10],\n [-12, -6, -26, -24, 4, 4, -6, -4, -10, -5, -5, 9],\n [-19, 20, -19, -13, 11, -3, -5, -12, -7, 0, 1, -5],\n [4, -18, -4, -22, 18, 12, -10, 13, -22, -20, -19, -20],\n [-5, 17, 11, 26, -6, -23, 5, 2, 3, -24, -22, -8],\n [-19, 10, 4, 0, -14, 15, -21, -26, 3, -16, 25, 14],\n [4, -11, -12, -22, -12, -26, -12, 9, 21, 12, -19, 26],\n [-5, 0, 7, 3, -15, -25, 19, 24, 25, 11, -5, 24],\n [-10, 8, 25, 15, 18, 25, -4, 2, 2, 23, -8, -10],\n [-19, 23, -20, -16, -24, -25, -8, 1, 1, -2, -16, 13],\n [16, -25, -15, 14, 11, -15, 23, -2, 10, 4, -10, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "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, -25, -11, -26, 25, 7, 18, 21, -26, 24, 9],\n [25, -24, 7, -15, 18, 0, 23, 10, -2, -15, 24, 6],\n [-18, -26, 23, -4, 1, -24, 11, 9, 17, 17, -22, 2],\n [26, -14, 17, -23, -21, 24, 11, -21, -16, 0, 19, 8],\n [13, -23, 0, -11, -9, -20, -16, -19, 25, -21, 21, -22],\n [-21, 11, -25, 4, 12, 5, -18, -12, -6, 19, 26, 1],\n [18, 0, -22, -10, 10, -3, 4, 8, 14, 14, -23, -7],\n [16, -10, 19, -17, 10, -6, -6, 22, -11, 6, -17, 17],\n [-9, 6, 2, 4, -3, -15, -7, -21, -19, -13, -22, 9],\n [21, 11, -24, 9, -5, -19, -13, -20, -23, -8, 16, 20],\n [-3, -11, -21, 17, -19, -2, 5, -2, -17, 16, 14, -10],\n [19, -24, -18, 25, -9, 22, 3, -22, 25, 5, 26, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -3, 11, -24, -11, -12, -2, -19, 14, -23, 5, 18],\n [8, 26, 3, 12, 21, 22, 3, -10, -8, 25, 4, -10],\n [-25, 10, 21, 2, 3, 16, -5, 11, -16, 6, -8, -24],\n [13, -5, -9, 18, 3, -26, -7, 22, -22, -15, -16, -3],\n [-9, -19, 2, -5, 18, -25, -4, -11, 17, -19, -23, -13],\n [-18, -16, 21, 11, 17, 24, -11, -14, 9, 17, 9, -10],\n [-13, 2, -10, -26, -7, 6, -25, -10, -4, -5, -26, -15],\n [-14, -13, -17, -15, -5, -9, 12, -8, 3, -12, 12, -13],\n [-18, -22, 6, 21, -22, -3, -19, -8, 25, -15, -19, -19],\n [11, -7, 2, 14, 7, -9, -26, -16, 20, 17, 8, 24],\n [25, 5, 24, 15, -11, -21, -18, 13, -5, 21, -19, 5],\n [-1, -9, 10, 25, -15, 11, 7, -23, -11, -3, -13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[24, 4, -23, 23, 17, 7, 11, 11, -24, -19, -15, 8],\n [-25, 26, 2, -4, 6, 23, -9, 13, -5, -13, 2, 18],\n [-12, -12, 18, -23, 9, -22, -24, -15, -7, 17, -7, 12],\n [12, -26, 17, -24, 20, -18, -7, -18, 4, 19, 1, 8],\n [13, 11, 17, -25, -24, -13, -10, 8, -23, 20, 3, 12],\n [24, -13, 21, 0, -14, -7, 22, 22, -3, -17, -20, 25],\n [-10, -5, 17, -16, 15, -4, -5, 13, 20, -9, 18, -1],\n [21, 3, -14, -23, 16, 0, 24, 13, -17, 17, 1, -6],\n [25, -16, -7, 26, 9, -8, 25, -17, -12, 18, 18, 26],\n [-9, -20, 3, -13, 10, 14, 3, 0, 22, 10, 21, 14],\n [-10, 3, -9, -24, 1, 10, 3, -6, 22, -7, -5, 9],\n [9, -6, -3, -6, -20, -19, -5, -5, 3, 7, 2, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "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, 7, 11, -17, -18, 5, -22, 8, -16, 15],\n [-11, 0, -7, 24, -26, -1, -16, -12, 12, 13, 21, -9],\n [-3, 1, -2, -4, -16, 6, -11, 9, -4, -21, 16, -3],\n [11, 15, -21, -17, -5, -4, -22, 1, -18, 12, 22, 17],\n [1, -2, 16, 11, 0, -3, 16, 16, 19, -11, -25, -25],\n [-22, 19, -6, -17, 15, -9, -1, -7, 14, 9, 22, -6],\n [-25, 19, 6, -4, 12, 4, -23, 14, -24, 10, 26, -17],\n [15, 5, 9, 22, 0, 26, 22, -8, 11, -26, -1, 19],\n [-14, 8, -25, -5, 12, 1, 17, -25, -16, 21, 10, -1],\n [1, -1, -10, -24, -13, -11, 22, 24, 9, 1, 1, 26],\n [25, 25, -2, -18, -16, 10, 16, 18, -6, -25, 7, 15],\n [-14, -22, -16, 2, 20, 1, 1, -22, -7, 10, 12, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[5, 2, -25, -26, -7, -26, -23, -12, 20, 3, -21, 11],\n [-26, -20, -22, 22, -20, 9, -24, -15, -12, -7, 14, -6],\n [5, -15, 10, 13, 20, -20, 24, 18, 4, -26, -16, 18],\n [7, -8, -16, 6, 6, -19, 18, -19, 7, 13, 0, 2],\n [-13, 7, 18, 10, -26, -18, 25, -17, 3, 16, -9, -10],\n [-21, -16, -3, 9, 6, 6, -9, -22, 4, -11, -25, -18],\n [-25, 10, -7, -10, -2, -8, 15, -19, 25, -16, -14, -14],\n [-18, -22, -9, 13, 25, -13, 7, -5, 21, 6, -3, 2],\n [-14, 23, 0, -26, -20, -23, -17, 13, 8, 12, -11, 0],\n [-7, -17, 18, 6, -20, 15, 17, 19, -5, 16, -10, -18],\n [13, -17, 9, 4, 4, -22, -9, -21, 15, 23, 1, 16],\n [-3, -22, 1, -24, -9, -23, 13, 22, 15, 5, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 6, -25, -16, 20, 6, 14, 13, -26, 15, -10, 23],\n [-11, -25, 22, -23, 5, -20, 2, -18, 8, 25, 26, -22],\n [23, -6, -10, 12, -13, 5, -12, -6, -13, 14, -11, 24],\n [-26, 13, -9, 7, -1, 9, -6, -26, 0, 24, -16, 11],\n [24, -13, 1, 0, -5, -6, -3, -8, -3, -1, -2, 18],\n [17, 2, -17, 24, -16, -3, -3, -15, -20, 13, -10, 8],\n [-21, -15, -12, 5, -4, -20, 11, 4, 2, 17, 1, -15],\n [0, -23, -6, -18, 22, 7, 10, -6, -4, -3, -17, 11],\n [-21, -6, 10, 2, 13, -6, -5, 8, 19, -22, -12, 14],\n [20, -8, -11, 13, 20, 16, -4, -23, -6, -3, 15, -1],\n [15, -25, 13, -19, -18, -25, -13, -7, -25, -23, 8, -13],\n [-6, 21, -12, 12, 23, -7, -21, 1, 26, 21, 16, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[1, 7, -13, -18, -4, 17, 8, -5, -22, 14, 2, 8],\n [23, 7, -23, 18, 22, -18, 24, -13, 18, -22, 23, 20],\n [0, -16, 3, 24, 10, 12, 7, 24, -3, -11, 3, -3],\n [-24, 2, 15, -15, 0, 2, -25, 2, 13, -18, 25, 17],\n [1, 10, -4, -14, -22, 5, 1, -12, -3, 5, -6, -22],\n [10, 9, 1, 5, -4, -11, 23, -17, 2, 25, 0, 8],\n [15, 18, -3, -4, -24, 9, 18, -13, -23, 17, 21, 15],\n [5, -7, -10, 2, 12, 5, -23, -3, 17, 15, -25, -13],\n [13, 15, 11, 7, 19, 16, -25, 9, -21, 9, -5, -22],\n [11, 14, -5, 21, -16, 16, 4, 26, 26, 15, 2, 6],\n [-5, 22, 0, -19, 21, -21, 19, -2, 7, -18, 9, 4],\n [-8, 22, -26, -3, 7, -10, 7, 8, 9, -14, -2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "513", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 10, 19, 11, -26, 21, -21, 18, 18, -16, -11, -5],\n [19, -16, 10, -1, -1, 15, -6, -1, -12, 12, 8, -16],\n [-18, 15, -4, -23, 3, 1, -2, -5, -2, 25, -1, 23],\n [2, 19, 14, 5, -1, 1, -7, 21, -25, -4, 12, -22],\n [-6, -5, 22, -16, 3, 1, 9, -10, -6, 10, 9, -2],\n [-3, 3, 15, 8, -6, -21, -6, -19, -22, 13, -17, 4],\n [3, 24, -6, 9, 0, 11, 8, 5, -1, -23, 0, 9],\n [10, 0, 20, 21, -21, -9, -1, 17, -3, 25, -20, 17],\n [-13, -14, -1, 16, 16, -25, 19, 20, -4, 1, -26, 5],\n [-15, 19, 23, 26, 8, -1, 4, -15, 2, -22, 8, -20],\n [-11, 5, 25, -10, -6, 0, 13, 20, 25, -12, -4, -19],\n [-2, -16, -6, -17, 23, -18, 21, -26, -5, -21, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-14, -5, -21, 14, 19, -3, -6, 12, -4, -22, -20, -24],\n [-14, -15, -21, 7, -12, 20, -9, 22, -24, -5, 8, 1],\n [14, 15, -15, -26, 9, 3, 26, -4, 10, 1, 22, 26],\n [-22, 9, 20, -17, -22, -13, -3, 1, -6, 18, 24, 13],\n [-15, -7, 24, 5, 24, 11, 13, 15, -6, -10, -26, 24],\n [17, 1, -25, -10, 12, -13, -13, 17, 21, -9, 13, 7],\n [16, -26, 15, -9, 21, 7, -4, 22, -11, -8, 10, -21],\n [-3, -10, 21, -11, 12, 21, 14, -21, -11, -18, 2, -23],\n [-1, 11, -1, -13, 8, 22, 16, -3, -19, 13, -2, -23],\n [-12, -11, -16, 1, -20, 23, 11, -3, 4, -23, 10, 8],\n [-21, 19, 6, 25, 5, 19, 11, 8, -10, 5, -13, -8],\n [-3, 12, -16, -20, 18, -3, 26, -3, -13, -3, -16, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "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, 15, -25, -3, 18, -17, 5, -10, -17, -5, -21],\n [0, -7, -26, -10, -26, 10, -12, -26, -10, 19, 18, 16],\n [17, 11, 16, -25, -9, -15, 2, -4, 20, -18, -19, 23],\n [-11, -4, 26, 2, -17, -15, 25, -15, 3, -17, -13, -23],\n [20, -7, 14, 12, -20, 3, 25, 14, -3, -17, 25, 18],\n [11, 9, -10, -6, 19, -24, -26, -9, -25, 13, 21, -23],\n [5, -8, -7, 15, 22, 22, 26, -20, -18, -20, 0, -6],\n [8, -3, 5, -15, -4, 9, 22, 2, -24, 16, -19, 7],\n [-13, 9, 21, 19, 5, -20, -17, -15, 13, -4, -16, 25],\n [-14, -15, -20, 26, 17, -17, -20, 24, 0, -20, 23, -3],\n [-4, -2, 17, 9, 6, 10, 15, 12, 25, -20, 3, 4],\n [18, 19, 10, -6, 7, 19, -6, 13, -7, 7, -19, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[25, 3, 2, -22, 3, -15, 12, 0, 26, -14, 20, -17],\n [9, 4, -11, 12, 18, 9, -1, 17, -7, 7, 10, -19],\n [-23, 2, 4, -25, -2, 11, -24, 19, 15, 16, -22, -5],\n [-11, -18, 26, 21, -18, 22, -15, 20, 15, -23, 22, -9],\n [-9, 15, 16, 26, 6, 15, -24, 11, -10, -15, -16, -10],\n [8, 14, 23, -21, 8, -21, 5, -16, 16, 12, -14, -14],\n [12, 19, 7, -24, 5, -23, 13, 26, -26, -18, 22, 23],\n [-20, 0, -24, -5, -11, -19, -22, 22, 3, 1, 24, 0],\n [23, -5, 3, 10, -20, 23, 3, -14, -5, -16, -22, -5],\n [-12, 26, 12, 10, 4, 2, 12, -10, 14, -21, 14, -10],\n [7, -4, 25, 3, -14, 3, 22, 26, -7, -21, 4, -8],\n [-21, 7, 1, -14, 25, -17, 14, 18, -20, -9, -5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "573", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[9, -19, -15, 13, 21, 6, -3, 15, 12, -13, 22, 24],\n [-22, -8, -24, -26, 13, 14, 10, 6, 22, 19, -10, -18],\n [4, 8, -24, -14, 25, 10, 11, -13, -21, 2, 22, -18],\n [9, -4, -12, 23, 20, 23, -20, 20, -2, 10, -4, -16],\n [19, -19, 9, 15, 12, -26, 25, 17, -14, -11, 19, -14],\n [10, -13, -14, 19, -15, 1, -5, -7, 20, -8, -16, 3],\n [-1, -12, 3, 2, 5, 26, 3, 17, 24, -11, 9, -9],\n [14, 21, 12, 1, -8, -16, -10, -6, 10, 17, 24, 7],\n [6, 2, -23, 5, -16, -1, -9, 26, 5, 0, -11, -17],\n [17, 7, 6, -17, 15, -1, 15, -2, -25, -1, -7, -24],\n [5, -26, -3, 23, 16, 17, 6, 11, 21, 25, 8, -10],\n [21, 16, 21, 17, 6, -16, -4, 11, 5, -8, -15, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "539", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-25, -17, -8, 1, 20, -19, 16, -4, 21, 18, 3, 1],\n [-14, 10, -15, -17, 24, -10, -26, -5, -12, -11, -7, -17],\n [15, -1, 22, -4, -10, 7, 14, -5, -23, -20, -22, 4],\n [-8, -23, 23, -5, -24, -4, -23, 19, -3, -13, 22, 14],\n [24, -24, 20, -6, -1, -26, 3, 24, -23, -13, -9, -15],\n [11, 15, 9, -11, -26, -24, 12, 8, -12, 11, -11, -10],\n [7, -17, -16, 1, 0, 11, -9, 20, 21, 3, -14, -11],\n [-25, -7, -15, 2, 19, -19, 11, 19, 20, -7, 8, 12],\n [4, -11, -4, 7, 5, -10, 16, -3, 8, -4, -19, -4],\n [-6, -8, 4, 23, -20, 21, -3, 19, -19, -14, -24, 7],\n [-14, 5, 8, -6, -26, -25, 15, 16, -1, -24, -3, -1],\n [-19, 20, 10, -19, -9, -9, -15, 9, 13, -25, -7, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[13, 17, 7, 22, 19, 19, -21, 13, -17, -3, -9, 6],\n [12, -20, 18, 21, 17, 2, -8, 11, 12, -2, -10, 24],\n [10, -24, -3, -9, 22, -1, -6, -16, 14, -10, 24, 18],\n [11, -6, -23, 5, -9, 17, 1, 9, 10, 17, 23, -1],\n [22, -3, -17, 11, 22, -19, -25, 17, 8, 25, -6, 0],\n [-4, 5, -1, -20, 6, -10, -19, 15, -10, 21, 15, 20],\n [21, -9, 9, 12, 17, -4, -15, -4, 26, 6, 26, 1],\n [17, -4, -20, 20, -25, -26, -23, -19, 22, 2, -9, 10],\n [4, -21, 17, -3, 21, 14, -12, 13, -15, 19, 22, -13],\n [0, 25, 10, -14, 11, 19, 11, -24, -11, -15, -13, 7],\n [23, 4, 12, -22, -15, -1, -10, 17, 26, -16, 6, 14],\n [13, 19, -23, 5, 4, -16, -10, 0, -19, -6, 6, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-22, 5, -2, -19, 0, -1, 13, 2, -18, -9, -20, 15],\n [-6, -11, -24, 5, -17, 5, -19, 5, 23, -23, 2, -15],\n [26, 10, 9, 24, -8, 10, 20, 4, 17, -1, 18, -21],\n [2, -10, -7, 15, 19, 20, -17, -21, 21, 5, -25, -17],\n [10, 0, 14, -8, 24, 14, -11, 24, -7, 9, -22, -9],\n [-19, -14, 14, -17, 9, -8, 4, 9, 2, 18, -4, 5],\n [22, -16, -25, 5, -22, 4, -14, -5, 8, -8, 2, -4],\n [-8, -11, 4, -11, -1, -24, -4, -18, 24, -3, 6, -13],\n [1, -3, 16, 23, 25, -20, 11, 17, -2, -25, 18, 25],\n [-26, -4, 20, 25, 13, -9, 20, -19, 7, 16, -19, 2],\n [-14, -26, 2, 23, 10, -26, 17, -22, 26, 21, 23, -25],\n [20, -5, 3, -16, 2, 15, -24, 18, -14, -24, -17, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "dataset": "MATH"}
{"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, -4, -10, -26, -12, 26, -25, -9, 12, -5, 1, 3],\n [-14, -24, -24, 18, 26, -1, -23, -11, 1, -19, 13, -11],\n [4, -4, -25, -18, 0, 18, -5, 17, 7, -18, 6, 11],\n [7, 8, 20, -1, -20, 18, 21, 18, 0, -15, -10, -6],\n [16, -5, -1, 12, -14, 15, 15, 18, -4, 24, 3, -10],\n [0, -7, -20, -23, 22, 4, 3, 4, -23, -9, -7, 13],\n [13, 26, 21, 20, 23, -4, 24, 11, -18, -11, -6, -18],\n [25, -2, 22, 9, 20, 16, -13, -10, 1, 18, 14, 21],\n [-19, -13, -12, 12, -2, -16, 2, -24, 12, -5, 10, 14],\n [-7, -8, -14, 0, -8, -11, -25, -26, -24, -3, 17, 11],\n [-25, -11, 2, 10, 17, -23, -13, -10, 17, 18, -10, -7],\n [20, 2, 14, -1, 15, 11, -10, -15, 1, -18, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-11, 21, 4, 0, 2, -26, 0, 26, 5, -16, 26, 8],\n [-25, 19, -26, -21, -20, -25, -25, 20, 26, -22, -14, -8],\n [-8, 20, -26, 8, -9, 22, 5, 5, 26, -19, -16, -7],\n [-19, 1, -6, 11, 11, -21, -25, -17, 15, -18, -24, -25],\n [9, -19, -18, -1, 7, 21, 3, 11, -19, -24, -16, -2],\n [25, -22, -15, 3, 0, 16, -22, -7, 25, -6, -24, 14],\n [23, 17, -23, -3, -20, -3, 25, -16, -25, 17, 14, -21],\n [-20, 11, -9, 18, -18, 26, 1, -8, -23, -23, -14, 1],\n [-16, 26, -25, -21, -15, 13, 10, -3, 25, -18, -1, -23],\n [14, 17, -23, 22, 25, 7, -5, -14, -12, 13, 11, 14],\n [16, 17, 26, -25, -25, 16, -19, 11, -9, 2, -16, -21],\n [-18, -5, 19, 24, -2, 4, -6, 11, 25, -8, -17, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "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, -15, -8, -25, -12, 11, -19, 19, 8, 11, 16, 3],\n [-18, 3, 22, -8, 2, -25, 1, -19, -2, -17, -5, 8],\n [15, -3, -1, 4, -4, -25, 12, 6, -3, -15, 10, -18],\n [17, 16, 17, -24, 17, -4, -3, 6, 3, 11, 16, -25],\n [13, -5, -16, -15, -8, -7, -18, 16, -9, 14, 20, -9],\n [13, 9, 0, -14, 20, -19, 21, 16, -4, -14, -20, 23],\n [13, -25, -24, 15, 12, -4, -20, -23, 26, -19, 5, -8],\n [-15, -17, -13, 0, 17, -6, -7, -23, -8, 2, -20, 26],\n [6, -19, -16, 6, -2, 6, 9, -1, 9, -16, 3, 6],\n [-17, 2, -2, 5, -23, 12, 7, -5, -14, 24, 9, -21],\n [-10, -1, -3, -18, -25, -7, 0, -21, 23, 0, -3, -12],\n [21, 6, 15, -17, -6, -21, 3, -4, 9, 19, 22, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 7, 3, -9, -10, 18, 24, 15, -6, -3, -23, 22],\n [21, -2, 24, -3, 19, 25, 0, 4, 20, 24, 8, 25],\n [-7, -11, 4, -20, -9, -19, 0, -13, -9, -26, 4, -7],\n [-21, 18, -26, -8, 12, 0, -11, -13, 7, -20, -7, 4],\n [-5, -7, -12, -2, 19, -26, -10, -11, 10, -6, 0, 8],\n [-3, 25, 24, -25, 19, 26, -2, -8, 18, -14, 2, 5],\n [-21, -18, 25, -26, -3, -17, 8, -21, 21, -7, 11, -15],\n [-24, -9, -6, 8, 10, -8, -2, -9, 13, 3, 15, 24],\n [15, 26, 7, -17, -5, 23, -23, -24, 22, 22, 1, -5],\n [-15, 22, -14, 14, 6, 20, -8, 14, -10, 20, 7, -23],\n [12, -19, 6, -26, -22, 5, 13, -26, 8, -5, 2, -10],\n [3, 8, -26, -23, -18, 18, 5, -22, -13, 24, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[19, -5, 0, -2, 9, -23, 5, -18, -25, 15, 23, 12],\n [26, 19, 26, -2, 20, -17, 10, -2, 13, 26, 2, 10],\n [-22, -13, 6, 0, -22, 24, 17, -12, -24, -26, -3, -15],\n [18, -13, 15, -7, -13, -13, 18, 26, 8, -8, -7, 15],\n [17, -4, 7, -26, -23, 13, -10, -1, -13, 19, 24, 5],\n [9, -7, -11, 24, -8, 18, 12, -3, -13, 2, 15, -13],\n [25, -16, -16, 20, 13, -3, -5, 22, -6, -21, -13, -18],\n [8, 17, 9, -2, -12, 18, 1, 23, -13, -14, 14, 4],\n [-22, -8, -19, -14, 14, -10, 5, -22, -18, 16, 7, 18],\n [-26, 13, -12, 5, 7, 8, 26, 22, 23, 1, -10, 19],\n [-16, -4, -1, 19, -22, -1, -21, 24, 16, 7, 15, -14],\n [-2, -25, -13, -10, 14, 13, 13, 12, -2, 0, 21, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, 22, 6, 0, 18, 4, 21, 11, -12, 17, 13, -26],\n [-16, -12, 6, 21, 5, -2, 12, 6, 2, 7, -19, -16],\n [-14, -22, 23, -8, -6, -24, -1, 6, 3, -5, -22, -8],\n [-18, -3, 12, -15, 19, 21, 18, 0, 23, 15, 26, -6],\n [11, 8, 5, 9, 6, 16, -10, -22, 17, -7, -4, 12],\n [-23, -1, 3, 21, 20, 19, 2, 7, -17, -7, -3, 7],\n [10, -14, -4, -17, -5, 18, -13, -2, -9, -7, 1, -19],\n [-22, -6, -7, 17, -11, -7, 24, -2, -20, -2, 9, 24],\n [-17, 13, -11, -23, -17, 24, 21, 4, -15, -7, 5, -25],\n [-16, -7, -4, -14, 8, -10, -17, 13, 11, -13, -8, 5],\n [6, 16, -2, -2, -13, 18, 17, 11, 9, -3, 14, 12],\n [12, -14, -25, 7, -12, 21, -25, 25, -2, -22, 7, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"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, 16, -19, 22, -13, 2, 3, 10, -23, 8, -20],\n [-1, 5, 16, 6, -3, 23, -26, 2, 21, 18, 11, 11],\n [-6, -4, 19, -22, 3, 13, -9, -21, -22, 15, -9, -14],\n [-7, 11, -6, -23, -14, -9, -14, -14, 12, 10, 8, 11],\n [13, 0, -1, -15, -25, 16, -7, 8, -17, -19, 13, 19],\n [9, 4, -12, 15, -9, -12, -8, -3, 8, -25, -14, 18],\n [-18, 8, -25, 19, -11, 19, 9, -25, -11, -19, -26, -9],\n [14, -1, 17, -22, -6, 8, 13, 1, -1, 5, 21, 23],\n [17, 17, -6, -23, 15, 14, 9, -3, 6, -22, -24, -16],\n [18, 5, -5, -16, 11, -5, -23, 12, -24, -17, 10, -8],\n [-9, 1, 4, -10, -3, -26, -22, 5, 26, -10, -6, 14],\n [16, -5, 12, 12, 7, -13, -11, -22, -9, -23, 17, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 18, 0, -21, -16, 20, -6, -10, 4, 7, -14, -4],\n [-26, -23, 3, 4, 20, -11, 16, -24, -15, -15, -16, -11],\n [2, 26, -6, 18, 17, 15, 16, 23, -22, 25, -14, -10],\n [-15, -10, -26, -19, -11, -12, -8, -2, 4, 15, -25, -2],\n [4, -23, -23, 25, -15, -10, -6, 2, -5, 9, 13, -11],\n [-12, 3, 19, 24, -16, -14, -4, 13, 14, 7, -7, -25],\n [-19, -9, -20, 16, 4, -5, 1, -2, 25, -26, 5, -2],\n [21, -11, 2, 15, -3, -10, 15, -21, -13, -1, 1, 20],\n [9, 4, 0, -25, -8, 1, 18, 17, -6, 18, -12, 7],\n [13, -24, -26, -3, 16, 0, -18, -3, -10, 1, 12, -23],\n [2, 18, 1, 10, 2, 17, 25, 2, -22, -16, -25, -23],\n [-17, 12, 17, -19, -4, 0, -4, 21, 7, 8, -10, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[23, -17, -25, -10, 4, -11, -3, -20, -8, -11, 6, 9],\n [18, -17, 16, 24, -12, 16, -24, -25, 16, 15, 8, 0],\n [-22, -12, 9, 22, 6, -26, -15, 15, 14, -18, 25, -7],\n [3, -13, -4, 2, 24, 15, 8, 25, 0, 22, 0, 3],\n [-24, -15, 20, 4, 10, 0, 20, 25, -3, 21, 14, 13],\n [-16, 0, -18, -11, -13, 20, 3, 19, -3, 15, -14, 6],\n [-18, 22, -1, 22, 15, 18, 23, -14, -6, 2, 1, -3],\n [-14, 15, -7, 12, -20, 14, 21, -12, -2, 8, -14, 16],\n [-19, -6, 26, -21, -17, 22, 25, 14, -6, -13, 25, 18],\n [6, -2, -8, -18, 22, 20, 25, 10, 9, 9, -12, -22],\n [-10, 3, -20, -21, -12, 25, 19, -17, -21, 15, 25, 14],\n [-14, -13, -26, 6, -8, -18, 10, 22, 21, -15, -22, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[25, -16, 24, 26, 11, -17, -12, 23, 26, 12, 1, -24],\n [-11, 18, -10, 9, -8, -23, -2, 0, -15, 0, -23, -3],\n [-10, -1, -9, -5, -21, -8, 10, 7, -16, -3, 18, 10],\n [-4, 13, 16, -23, -9, 3, -12, 10, -4, -15, -23, -23],\n [25, 14, 14, -13, -19, -4, -26, -16, 0, -23, 2, -10],\n [22, -8, 18, 24, 22, -3, 25, 17, 25, 19, 14, 17],\n [5, 4, 22, -11, 5, 17, 15, 7, 8, 10, -11, -6],\n [-14, -9, -25, 6, 14, -9, 1, 10, 8, 10, -15, 13],\n [-19, -2, -20, -25, 6, 6, 13, 22, -4, -22, -13, -19],\n [-7, -9, -4, 2, -20, -3, 19, -2, -13, 11, -24, 26],\n [19, -13, -24, 15, -18, 26, -20, -1, -20, -20, 17, 9],\n [25, -14, -24, -7, -18, 26, -5, 25, 18, 6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "537", "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, 25, -1, 5, 1, 3, 13, -10, -9, -2, -23, -1],\n [4, -15, 21, -9, -17, 9, -25, -2, 20, -18, 20, 5],\n [-22, 24, -24, -10, -14, -24, 1, -23, -9, 8, -13, -11],\n [-15, -16, -25, 6, -14, 3, -1, 23, -9, -14, -23, 6],\n [-12, -10, -21, -22, 6, -11, 19, -3, -22, -24, 8, 0],\n [-15, 23, 14, -2, -10, 22, -7, 1, 23, 8, 23, -12],\n [6, -24, -20, -17, 14, -1, 14, 13, -21, 6, -11, -3],\n [3, -17, -16, 17, -5, -24, 11, 13, -4, 18, -8, 13],\n [26, -14, 9, -24, -5, -2, -7, 1, -24, -5, 17, 10],\n [11, -9, -7, 19, -22, 16, -18, 2, -10, -15, -1, 6],\n [6, 9, 2, -5, -9, -10, 17, 25, -3, -5, 17, -22],\n [-26, -8, 3, 12, -12, 19, 8, -22, -21, -2, -16, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "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, 7, 17, -13, -18, -7, -11, -10, -10, 7, 15, -16],\n [8, 7, 9, -19, -8, 25, 23, 6, -4, -25, -19, 2],\n [15, 24, -20, 22, 2, 4, 3, 8, -2, 20, -23, 22],\n [16, 11, -10, -17, -26, -9, 19, -8, 23, 5, 4, 6],\n [-5, -26, 14, 19, 8, 17, 22, -10, 7, 2, -21, -26],\n [0, -15, -23, -11, 25, -16, 25, -7, -1, 1, 15, -19],\n [-25, 13, -1, 0, 6, -20, 19, 9, -6, 22, 7, -4],\n [7, 13, -20, -1, 13, 25, 22, -10, 4, 12, -2, 10],\n [-12, -25, -16, 5, 3, -10, -3, 18, -23, 23, 19, 5],\n [-8, -24, -23, -2, -18, -6, -4, 19, 2, 3, -2, 22],\n [2, 7, -13, -5, 21, 24, -11, -16, -13, -20, -22, 13],\n [2, -10, 3, -2, -13, 15, -5, 17, -22, 13, 1, -15]]\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[[9, -14, -6, 5, 22, -6, 10, 11, -18, 10, -25, -24],\n [16, -17, 8, -18, 13, 21, 5, -6, 7, -2, 15, 5],\n [19, 10, -5, -2, -26, 18, 9, -6, 14, -11, 5, -6],\n [26, 1, -8, -13, -4, -3, -7, 5, 13, -17, 25, -26],\n [4, 25, 10, -12, 13, 4, 1, -17, -21, -12, 20, 0],\n [-17, -6, -8, -23, -5, 11, -12, -21, 23, -16, 17, 3],\n [13, -3, -5, 3, 19, -23, 23, -21, 11, -1, -8, -25],\n [-23, -22, 20, 8, 2, -11, 18, -15, -6, -18, -16, -19],\n [-1, 5, 12, -23, 7, 1, -2, 24, 17, 8, -8, 8],\n [24, 24, 12, 2, -13, -6, 9, 11, -13, 13, 23, -12],\n [24, 23, 3, 20, -15, 23, -22, 0, -12, -1, -18, 13],\n [13, 8, -14, 18, 17, 20, 19, 6, 7, -23, -14, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[26, 18, -26, -16, 23, -18, 11, -4, -14, -22, -2, -17],\n [-22, -5, 15, -2, 10, -7, 1, -6, -16, 2, -22, 10],\n [22, 26, -22, 6, 18, 9, -19, 25, -21, -12, -12, 26],\n [21, -18, -22, -1, -4, -11, 12, 8, -17, 0, -11, -6],\n [-15, -18, -11, -18, 2, -4, 12, 16, 22, -3, -5, 4],\n [-17, 20, 15, 0, 7, 21, 12, -3, -6, -12, -10, 18],\n [-8, 26, -2, 13, -5, 14, 24, 22, 15, -13, 1, -15],\n [0, 25, -3, -5, 12, 14, 23, 12, 9, -4, -19, 1],\n [23, 2, -12, 12, -19, 1, 6, -16, 15, 10, -2, 7],\n [-5, -25, 24, -11, -16, -13, 5, -5, -22, 9, -4, -8],\n [2, 15, -4, -18, -9, 4, 10, -10, -9, 0, -6, -26],\n [5, -13, 19, -13, 6, 9, 12, -15, 18, -2, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[7, -13, 3, 17, -14, -13, 2, -1, -24, -2, 0, 18],\n [13, -11, 11, -16, 2, 20, 24, -3, 2, 7, -16, -7],\n [-7, -18, -4, 9, 22, 0, -3, 13, -2, -2, 21, 6],\n [4, -17, 12, -12, -26, -11, -6, -25, -24, -12, 5, 23],\n [20, 0, 9, 8, 12, -3, 25, 24, -19, -20, -23, 3],\n [-17, -2, 15, 20, 5, 5, 23, 5, -17, -18, -2, -2],\n [14, -11, 22, -11, 3, 11, -22, -20, -14, -19, 6, -17],\n [25, -7, 5, 2, -26, 0, -7, -13, -12, -21, 25, -25],\n [2, 12, 5, 25, 24, -22, -5, 1, 5, 2, 13, -24],\n [4, -14, -21, -6, -13, -2, -20, 16, -5, 5, 14, 5],\n [15, 25, 3, -10, 13, 11, -6, -1, 16, -24, 11, -10],\n [12, -21, -6, 18, 19, 24, 13, -14, 25, -18, -22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523", "dataset": "MATH"}
{"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, 11, 17, 17, 11, 4, -23, -14, 17, -12, 13, -14],\n [16, 16, 16, -1, -8, 26, 22, -26, -14, -2, -7, 14],\n [-4, -3, 16, 14, 22, 12, 13, 3, 7, 19, -17, 14],\n [-26, -15, 19, 24, 2, -16, 14, -10, -7, 11, -21, -7],\n [-17, -17, 4, -1, -10, 26, -13, -22, -24, 16, 24, -7],\n [24, 19, -12, -24, -24, -4, -18, -16, 20, 22, 17, 22],\n [14, -14, -19, -5, 11, 0, -1, -4, 12, 4, 2, -26],\n [-17, 20, 19, -23, 4, -23, 2, -18, -12, 17, 14, -24],\n [-12, 26, -16, -21, 20, -20, 24, 19, -23, -6, -26, -4],\n [-14, 16, 1, 2, -9, -4, 1, -18, 26, 16, -21, -11],\n [10, -26, -5, 19, -4, -6, 24, 4, 11, 1, 17, 0],\n [12, 15, 15, -14, 5, -20, 24, 6, 20, 19, -14, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-20, -15, 13, -12, 22, -6, -15, -14, 13, 15, 12, -25],\n [2, 21, 2, 9, 11, -20, 3, -4, 24, 1, -4, 9],\n [15, 2, -23, -7, -22, 19, -16, -25, 14, 17, -3, 6],\n [-5, 20, -21, -3, 2, 22, 5, 26, 20, 3, 19, 24],\n [14, -24, -2, 1, -12, -10, -25, 0, 9, -13, 16, 5],\n [-15, -4, -11, 17, -25, -20, -6, 4, -4, -2, 8, 8],\n [18, -20, -22, 5, 26, -22, -2, 4, -7, -5, 11, -14],\n [12, -25, -5, -18, 24, -25, 18, 5, -19, -11, 6, -16],\n [5, -19, 5, -6, -2, -7, -26, -6, -20, -2, -18, -5],\n [-25, 26, -8, -21, -22, 18, -17, -26, -1, -1, -9, -6],\n [19, -15, 11, -13, 22, 5, 12, 8, -10, -17, 8, -11],\n [-21, -23, 25, -18, 2, -20, -11, -21, 17, -24, 17, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-13, -13, -18, 9, -4, 25, -12, -20, -7, -8, -21, 24],\n [12, -26, -20, 8, -2, 11, -4, -2, 11, -16, 7, 4],\n [11, 23, 19, -15, -18, -14, -7, -6, -5, -26, 13, 14],\n [-10, 18, -23, -21, 18, 22, -8, 3, -4, 5, 2, -19],\n [-6, -10, -10, -6, -12, 0, -2, 6, -25, 25, 15, -11],\n [9, -19, -11, -20, -22, -4, -19, -24, 8, 23, 9, 9],\n [-12, 3, -12, 2, -23, 7, -4, 8, 1, 4, 15, 6],\n [-9, -22, -18, -7, 11, 24, -18, -9, -12, -12, -13, 8],\n [13, 24, 16, 9, 20, 15, -7, -16, 14, -10, 14, -2],\n [2, -4, -18, -2, 14, -4, -25, 18, -26, 11, -21, 21],\n [17, -12, -20, -25, 3, 2, -15, 25, 7, 3, 9, 8],\n [-25, 23, -24, 15, -15, -23, 25, -20, -7, -8, -19, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, -12, -19, -9, 2, 19, 24, 9, -24, -18, -17, 13],\n [-7, -25, -26, 0, -23, 21, 10, 5, -9, -13, 18, 21],\n [-12, 24, -23, -8, -3, 3, -14, -16, 1, 23, -16, -26],\n [20, 15, -23, 11, 7, 22, -15, -3, 10, 5, -8, 2],\n [11, 22, 2, -8, -7, 26, -24, 13, -22, -4, -22, 3],\n [5, -3, 22, 24, 24, 15, 8, 5, 18, 21, 17, -5],\n [-6, 1, 22, 7, -11, -16, 6, 17, 11, -8, 1, 2],\n [10, 26, -24, -9, -9, -15, -9, 5, 15, 9, 25, -8],\n [-23, -16, -24, 0, 20, -11, 17, -9, 3, -3, -21, 20],\n [7, -15, 15, -4, 9, 13, -12, 24, -11, 18, 20, -13],\n [-12, -15, 16, 26, 8, -2, -13, -25, -9, 8, -18, -16],\n [-1, -24, -22, 5, 14, -17, 11, -21, -16, -10, -25, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "536", "dataset": "MATH"}
{"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, 23, -22, -6, -21, -23, -18, -22, -23, -18, -9, 16],\n [-11, -25, 2, 21, 24, 15, 9, -15, 14, 18, 10, 7],\n [8, 13, -21, 10, 9, -7, -11, -19, 17, -5, -22, -22],\n [18, -16, 16, -8, 12, -10, 10, 11, -9, 23, -18, 23],\n [24, -10, 14, 6, -7, -9, -3, -14, 13, 1, 19, -24],\n [9, -16, 12, -6, 10, -25, -21, 25, -22, 20, 16, 5],\n [10, 23, 13, -16, -10, -13, -25, 12, -9, 6, 3, -12],\n [2, -1, -26, -10, 12, 21, -25, -12, -5, -7, 2, -2],\n [16, -3, 7, 16, -6, 21, -25, 24, -11, 13, -6, 25],\n [10, -19, -13, 19, -5, -9, -22, 15, 20, 18, 3, 4],\n [-18, 4, 4, 14, 24, -18, 10, -21, 15, -1, -17, -21],\n [26, 6, 25, 18, 3, 13, -3, 1, 18, 11, 2, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "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, -19, -4, 16, -18, 24, -16, -21, 20, 22, -15],\n [7, -6, 5, 9, -2, 8, 7, -8, 10, -10, -11, -11],\n [17, -23, 22, 3, 24, 7, -22, 6, 19, -18, -10, -15],\n [-3, 25, -15, -12, -11, -4, -9, -5, 19, 17, 4, 16],\n [-12, 26, -6, -19, 22, 13, 9, 15, 11, -21, -10, 13],\n [18, 20, 9, 1, 20, -4, 4, 19, -16, -7, 5, -10],\n [15, 11, -21, -26, 10, -23, 4, -16, -10, -20, 25, 8],\n [-25, 13, 10, 10, -17, -15, -10, 19, -1, -22, -22, 11],\n [20, 0, -22, -19, 4, 6, -6, 8, -6, 24, -12, 9],\n [-25, 3, 1, -10, 17, -7, 13, 2, -22, -2, -17, -8],\n [14, 21, -26, 20, 7, -13, -2, -1, -6, -11, -17, 5],\n [17, 18, -7, -18, 7, 4, -8, 20, 4, 3, 20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "519", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -9, -6, 4, 12, 15, 14, 24, 16, -23, -1, 6],\n [17, 6, 22, -7, 14, -19, 9, -19, 4, -5, 15, 23],\n [20, -8, -7, -4, -3, 16, -3, 9, -18, 13, -11, 0],\n [18, 10, -14, 24, -25, -15, 14, 6, -4, -13, 12, 22],\n [3, 19, 22, 7, -18, -12, -3, 21, 14, -2, 9, 5],\n [20, -6, 15, 12, -21, 20, -2, -25, 4, 3, -12, -9],\n [5, -13, -9, 8, 25, -5, -13, 11, -13, 7, -5, -11],\n [21, 26, 22, -11, -11, 13, 11, -9, -4, 19, 21, 13],\n [-9, 19, 22, -5, 13, 3, 21, 15, 15, 26, -9, 26],\n [-9, 14, 26, -26, 21, 15, -12, -22, 0, -10, 14, 5],\n [11, -1, -25, 1, 18, -4, 23, -7, 9, 15, -5, -16],\n [1, 18, -5, -10, 4, -16, 9, -13, 8, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "507", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 9, -11, 12, -7, -2, -8, -1, 5, 23, -6, -18],\n [16, -8, 22, -6, -9, -21, 8, -13, -18, 8, -25, 24],\n [-21, 8, -2, -18, 23, 4, -20, 1, -25, -26, 10, -3],\n [8, -20, 11, 2, -26, 24, 3, 25, 19, 5, -17, 7],\n [-16, 21, 22, 10, 0, 23, 21, -17, 11, -5, -3, -19],\n [-21, -23, -22, -21, 20, 5, 11, 24, -7, 13, 18, 9],\n [22, -13, 23, 20, -8, -16, 12, -26, 8, -8, 6, 5],\n [9, -3, 16, -20, -20, 19, 20, -22, -13, 18, 25, -1],\n [23, -26, -14, -4, -7, -20, -21, -18, 1, -17, 8, -20],\n [-2, 3, 16, -1, 17, -15, -14, 13, -23, 26, 25, -26],\n [-21, -25, 19, 0, -9, 15, 2, 26, 6, -24, -7, -23],\n [-9, -19, -5, 14, -5, -8, 1, -25, -18, 8, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "580", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, -20, 3, 22, -2, 22, -18, 0, -26, 6, -19, 22],\n [5, 13, -8, 9, 23, 18, -5, 12, -1, -24, 19, -18],\n [8, -20, -12, -23, 10, 1, -18, 8, 21, 21, 24, -2],\n [-18, 25, 6, -10, -15, -18, -22, 20, -1, 18, -8, 8],\n [-25, 18, -20, -18, -5, 15, 6, -11, 16, -3, -19, 3],\n [-1, 18, 21, 8, 18, -10, 26, 11, -17, 14, 23, -10],\n [-20, -25, -16, 23, -24, 19, -7, -14, -4, -10, 2, 16],\n [12, 5, 8, 8, 7, -6, -11, -4, -16, -13, -24, -20],\n [13, 18, 24, -16, 6, -8, 18, 22, 14, 24, 24, -4],\n [-4, 2, -21, 12, -22, 5, 13, -1, -13, -9, -6, -2],\n [-7, -3, -24, -5, -19, 19, 19, 2, -20, -21, -21, -15],\n [-5, 20, -1, -2, -8, 9, 8, -14, -2, 21, 18, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[3, -6, 15, 18, 13, 17, -19, 14, 15, -20, -24, 10],\n [-24, -9, 24, 15, -18, -3, -20, 6, -2, 15, 7, 11],\n [-6, 11, 13, -9, 12, 23, 6, 1, -2, -13, -7, 12],\n [-7, -20, -23, 4, 3, 10, -6, -26, 25, -24, -14, -20],\n [-21, -21, 7, 5, -11, 11, -19, -6, -16, 23, -4, -21],\n [19, -12, -16, 0, -12, 18, 11, -23, -13, 18, -17, 2],\n [-15, 13, -7, 10, -25, -7, -15, 11, 3, 20, -9, 23],\n [-17, -20, 15, -22, 21, 2, 24, 8, 12, 24, -15, -17],\n [10, -25, -24, -13, 20, -7, 18, 22, 25, -23, 24, -1],\n [20, -12, -18, -24, -25, 12, 14, 3, 10, -10, -24, -18],\n [-19, -18, -10, -3, -19, 26, -13, -11, -9, 22, -3, 12],\n [25, 20, 0, 1, -20, 7, 0, 7, 12, -8, -21, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "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, -12, 18, 12, 12, -12, 9, -24, -26, -20, -18],\n [-26, -22, 20, 9, -17, -25, -4, 12, 2, -8, 11, 20],\n [-7, -15, -16, 8, 25, 22, -20, -4, 23, -10, 21, -25],\n [-22, -6, -14, -16, -3, 6, 0, 8, -9, -6, -23, 14],\n [5, 16, 22, -16, -24, 24, 25, -6, 16, -13, -21, 24],\n [26, 2, 4, 20, 1, 16, 23, 9, 1, -8, -24, -15],\n [9, -3, -15, -3, -26, 1, -11, -6, 3, 7, -1, 8],\n [4, -11, 15, 2, 2, -18, -13, -19, -25, -16, -25, 20],\n [-9, -22, -20, -4, -8, -8, 21, -8, 22, 18, 13, 1],\n [-16, 23, -16, -18, -13, 7, 2, 22, -6, 21, -22, 6],\n [-18, -24, -13, -9, -15, -4, -13, -11, 10, -7, -7, -12],\n [14, -2, -10, -15, 18, 15, 12, 26, -20, -19, -3, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, -6, 23, 6, -17, -5, -8, 2, -24, 12, -23, 10],\n [4, -21, 1, -17, -15, 19, -25, -24, -26, 8, -3, 20],\n [21, 25, 7, -7, -11, 3, 20, 12, -2, -22, 2, 10],\n [1, 26, 14, -4, 5, 19, 24, -9, 14, 8, 16, -3],\n [20, 1, 9, -6, -22, -1, 23, -4, 17, 6, -1, -5],\n [-7, -25, 14, -9, -22, 5, 19, -16, -6, -5, -24, -18],\n [-25, 19, 1, 7, 26, -17, -8, 2, -25, 21, -21, 17],\n [-20, 9, -19, -8, -17, 6, 10, 11, 0, 2, -8, -9],\n [24, 24, -4, -26, 25, 16, -24, -17, -20, 22, -1, -11],\n [12, 18, 5, -15, 17, -19, -19, 18, -16, 6, -2, -10],\n [4, -8, 18, -12, 17, 26, 22, 8, 12, -25, 7, -2],\n [11, -23, -11, 5, -12, 15, -13, 14, -12, -20, -20, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "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, -9, -10, -9, -8, 26, 13, -14, -16, 24, -20, 0],\n [10, -22, -19, -17, 10, -1, -12, -11, 2, 1, -17, 13],\n [24, -23, 19, 13, 26, -13, 17, 6, 24, -9, -15, -17],\n [-6, 6, -13, -18, -1, -12, -6, -5, 19, 14, 16, -22],\n [17, -11, 25, 8, -22, -1, -1, 24, -22, 23, 9, -3],\n [-12, 3, -22, 13, 21, -5, 6, -22, 5, 23, 21, -4],\n [-17, 9, 23, -10, 26, 0, 18, -19, 13, 17, 23, -21],\n [-20, -1, -10, 10, -4, 0, 24, 13, -8, 0, -2, 13],\n [-2, -6, -2, 24, -20, 8, -21, 13, 23, -12, -3, 22],\n [-23, -20, 3, -10, 11, 3, 18, 12, -18, -8, 25, -14],\n [20, 22, 10, -8, -21, -15, -12, 20, -24, -23, 10, 11],\n [-21, 22, 1, -19, 24, 25, 4, -6, 18, 2, -12, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-3, -6, 22, -4, 4, 7, 1, 5, -5, -24, -18, -21],\n [-26, -5, 24, -23, 18, 25, -19, 10, 15, 25, -8, 17],\n [-26, 14, -3, 21, -10, 5, 23, -13, -10, 5, 6, 3],\n [26, 20, 24, 7, 1, -3, -13, 7, 20, -26, -5, 6],\n [17, 20, -9, 20, 12, -15, -17, -25, -25, -21, -7, 11],\n [1, 15, -24, 21, 10, 10, 15, -2, -4, -14, -3, -24],\n [23, 24, 11, 1, -1, -7, 0, -26, -17, -17, -26, 5],\n [24, 5, 16, 0, -14, -10, 1, -2, 25, 23, 9, 20],\n [-25, 5, 5, -21, 4, -18, 16, 25, -11, -2, 13, 1],\n [-10, 4, -4, 4, -1, -23, 12, 16, 16, 16, 26, 26],\n [-12, 10, 11, -4, -22, 14, 16, -2, 3, -1, -24, 25],\n [-23, 20, -9, 10, -16, -16, 9, -11, 16, -2, -26, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[18, 3, 24, -21, 0, 25, -8, 11, 18, 16, -8, 12],\n [17, 5, 21, -26, -2, 20, -14, -17, -9, 9, -5, -21],\n [0, -19, -3, -7, -5, -18, 13, 23, 12, -8, 23, -26],\n [-16, 14, 15, -17, -26, 0, -10, 17, 17, 24, -10, 12],\n [16, -25, 21, -4, 14, -17, 26, 15, 3, 8, -2, -10],\n [19, -8, -9, -9, 19, 8, -17, -4, 18, -5, 17, -18],\n [5, -1, 2, 15, -8, 21, 2, 26, 8, -15, -19, -2],\n [0, 20, 16, 18, -21, -14, -16, 11, -21, -22, -20, -8],\n [16, -21, -2, -18, -7, -2, 23, -19, 23, 10, 11, -25],\n [-5, 9, 24, -23, 21, -26, 21, 6, -3, 22, -22, 21],\n [8, 15, 23, 26, 23, -1, 22, 16, 14, 16, -1, 14],\n [22, 25, -22, 17, -9, -2, 21, 14, 13, 11, 22, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, -3, 1, 19, -23, -19, 22, 6, -24, 22, -7, 8],\n [12, 16, 20, -20, 0, -22, 22, 10, -26, -5, -20, 22],\n [-19, 17, 3, 1, -1, 7, 22, 5, -5, -7, -13, -4],\n [-24, -8, -13, 13, 12, 10, 8, -26, -8, -12, -2, -26],\n [4, 10, 25, 16, 19, -5, 23, -7, 14, 20, 16, -22],\n [-12, -25, -15, -20, -25, -19, -18, 0, 1, 10, -12, -8],\n [3, 24, -14, 18, -21, 3, -26, 15, 11, -2, 8, -1],\n [-14, -8, -17, 18, -20, -12, -4, 9, 16, 4, -19, 3],\n [7, 6, -26, -11, 23, -16, 0, -5, 13, -8, 17, -21],\n [21, 13, 12, -7, -24, -26, -4, 11, -24, 24, 7, -10],\n [21, 0, 26, 12, -4, 11, -16, -12, -1, -16, -20, 20],\n [21, -19, -22, -10, -4, -25, 0, -6, -20, 26, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "536", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, -15, 21, -16, -10, -17, 21, -11, -12, -12, -7, -23],\n [5, -5, 8, -13, 3, 4, -17, -21, 0, -16, 9, -17],\n [-11, -3, -6, 13, 14, 9, 22, 15, 18, -4, -6, 5],\n [26, -10, 24, -10, -6, -23, -4, -2, 5, -21, -13, 14],\n [11, 15, 11, 14, 18, -11, 5, -11, -8, 10, 16, -6],\n [-12, -1, 3, 13, -12, 16, -14, 0, -4, 7, 7, -4],\n [17, -7, -18, -7, 20, 12, -13, 22, -1, 0, 7, 2],\n [5, 14, 18, -22, -23, -4, -6, 6, 14, -3, -11, 5],\n [-8, -1, -24, 8, 12, -9, 25, -20, 5, -3, -11, 26],\n [-3, -23, 18, 5, 15, 7, -8, -13, 11, -14, -5, 4],\n [17, 17, 3, -4, -15, 16, -13, 9, 18, -19, -3, -24],\n [-13, 24, 23, -16, 18, 11, 1, -4, -9, -7, 6, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475", "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, 10, -1, 24, -25, -24, -7, -17, 15, -6, 13, -18],\n [-25, 1, -24, -11, -23, -4, 3, 11, -14, -21, -17, -10],\n [-19, -18, 7, -10, 25, 16, 23, -5, -24, 14, 13, 2],\n [12, 0, 12, 26, 13, 25, 10, -24, -8, 7, -13, -6],\n [-25, -17, 25, 15, -10, -25, 0, -26, 23, 9, 6, -5],\n [22, 8, 7, -9, 9, -24, 17, -11, -16, -17, 24, 15],\n [-6, -2, 8, -21, 19, 17, -19, 7, 14, 19, -26, -24],\n [25, 11, 0, 25, -14, 16, 20, 23, -8, -8, -21, 20],\n [26, -13, -22, 16, 25, 18, 18, 9, -18, -4, 5, 2],\n [18, 1, 13, 25, -16, -8, -26, -18, -25, -23, 2, -23],\n [-26, 1, -9, 19, -14, 13, -21, 22, 16, 20, 12, -5],\n [3, 0, -19, 16, 1, 26, -25, -7, -16, -13, -3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-19, 17, -6, -5, -18, 15, 16, -16, -11, 23, 26, -18],\n [-24, 9, 25, 24, 15, -14, -26, 17, -16, -3, -22, -25],\n [-10, -10, -7, -12, -23, -16, -4, -26, 15, 23, 20, 24],\n [-23, 11, -25, 18, 0, 7, -14, 20, -9, -16, -22, 2],\n [-2, -13, 21, 19, 14, 11, 14, 10, -16, 17, 5, 22],\n [-21, 25, -21, 20, 22, -5, -24, -8, 7, 14, 14, -20],\n [-11, 11, -18, -14, 7, 19, 10, 16, 20, -21, 11, 21],\n [25, -23, -22, -21, -14, 19, -3, 1, -14, 15, 22, -9],\n [-20, -23, 4, -3, -5, -6, 21, 15, -1, 3, 26, 25],\n [24, 8, 24, -4, 18, 13, 23, 3, -8, 5, 23, -8],\n [-5, -23, 18, -15, -12, -12, -17, -8, 26, -19, 24, 4],\n [-18, 2, -20, -19, 14, -10, -12, -11, -20, 15, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -15, 5, 20, -17, -3, 23, -23, 16, 10, 18, 15],\n [12, 16, -23, 9, 10, -2, 14, 3, -26, 2, -11, 10],\n [10, -20, 13, 24, 6, 23, -5, 16, 0, 2, -11, -6],\n [-16, -6, -18, 0, 12, -5, -12, 16, -4, 24, 2, 12],\n [-11, -24, -11, -19, -1, 15, -18, 8, -20, -19, 8, 21],\n [19, 12, 9, -21, -20, -15, 12, -26, 23, 16, 16, 22],\n [-2, -15, 0, -4, -8, -6, 23, -6, -3, -14, 15, 24],\n [9, -12, 23, -26, 24, 7, 15, 4, 23, 5, 9, 2],\n [-17, -6, 9, -3, 0, -6, -9, 25, -23, 20, -9, -18],\n [25, 22, 3, 8, 18, 3, 12, 19, -21, -13, 19, 2],\n [5, -13, -7, 23, -18, -15, -13, -4, 21, 7, -11, -9],\n [14, 13, 6, -22, 12, -17, -5, 16, 17, 6, 4, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[9, -24, -23, 0, 11, -2, 10, 0, 14, 9, 19, 20],\n [9, 19, 15, -20, 3, 23, 25, 20, 2, 13, 14, -22],\n [-21, 17, -20, 12, 5, -12, 24, -14, -9, -17, 13, -16],\n [13, 13, 20, -25, 0, 25, 18, 23, 17, -19, 22, 11],\n [-11, -3, -4, -13, 0, -17, 1, -2, -25, 18, 6, 23],\n [19, 8, 20, 14, -14, -22, -22, -5, 7, -26, -10, 24],\n [22, -18, -17, -12, 18, 2, 26, -2, -6, -10, 0, 1],\n [-4, 12, 9, -24, 6, -20, -22, -1, -10, -10, 20, -24],\n [-24, 7, -19, 18, -21, 10, 18, -5, 6, 23, -20, 22],\n [13, -8, 21, 19, 25, -17, -4, -25, -6, -3, 21, -14],\n [-22, -9, 25, -16, 10, 5, 1, -5, 18, 1, -26, -21],\n [-16, 15, 6, -11, -14, -6, 21, 20, 12, 19, -3, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, 18, 10, 23, -24, -15, -20, -7, -12, -26, 24, -17],\n [-13, -12, 7, 22, -2, 4, -17, 10, -21, -21, 1, 11],\n [-13, -14, -14, -17, -11, 12, 8, -12, -4, 10, -19, -1],\n [-5, -22, 7, 0, -8, 16, 16, 8, 18, -7, 24, 20],\n [11, -14, -9, -9, -26, 5, 26, -2, -6, 0, -16, 21],\n [-26, -8, 5, -19, -8, -11, 8, -25, -15, 2, -17, -5],\n [7, -6, 10, -22, -21, 5, -24, -17, -22, -3, -7, 10],\n [4, 20, -10, 22, -3, -9, -1, 15, -20, 16, -13, 14],\n [22, -25, 3, 22, -10, -7, -17, -3, 17, -15, 0, -12],\n [-18, -9, 21, -20, 1, 19, 9, -24, 17, -11, 9, -23],\n [8, -18, 19, -15, -17, 19, 17, 17, -25, -8, -14, 15],\n [26, 6, -26, 1, 13, -21, 25, -24, 18, -2, 17, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545", "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, -23, -19, 12, -11, 17, 11, -4, -21, 16, 17],\n [-11, -11, -4, -11, 9, -15, 10, -18, -9, -18, 21, -6],\n [-26, -4, -22, -8, 8, 6, 19, -9, 13, -13, -7, 25],\n [-14, 26, -11, 14, 4, 12, 8, -7, -26, 13, 19, -14],\n [-20, 18, -5, -20, -7, 25, 10, 9, -23, -21, 19, -24],\n [-24, -24, 9, -18, -11, 24, -11, -15, 11, -7, 26, 4],\n [3, -6, -24, -6, 1, 1, -22, -20, -22, -18, 20, -6],\n [-7, 11, 13, 25, 10, -10, 15, 1, 4, 6, 5, 5],\n [21, -4, -6, -2, 6, -24, -21, 22, 1, -25, 5, -1],\n [-22, -16, -17, -12, -9, 22, -13, 1, 3, -14, -7, -25],\n [-2, 17, 16, 24, -15, -2, -23, 15, -15, -20, 11, 13],\n [5, 16, -21, 26, 0, 8, -6, -7, -8, 6, -23, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[25, 22, 1, -5, 24, -3, 19, 3, 2, -17, 26, 5],\n [-18, -2, -11, -12, 21, -9, 26, -4, 15, -24, -20, 12],\n [25, -16, -3, 8, 23, -2, 1, -15, -4, -10, 14, 10],\n [-9, -18, 18, 8, 9, -9, -7, -6, 20, -7, -21, -18],\n [16, 2, 2, -14, 9, 0, 20, 22, 17, -21, 12, 5],\n [22, 16, 17, 1, 18, -26, 23, 24, 16, 4, 3, -9],\n [2, 15, 11, -4, -5, -25, -22, 15, -12, 5, 19, -21],\n [-13, -3, -6, -13, -15, -23, 17, -6, -10, 2, 24, -11],\n [-9, 11, 14, 24, 17, -16, 5, 1, -11, 7, 23, 3],\n [11, -5, -22, -18, -14, 12, -4, 0, 5, 4, 6, 15],\n [-1, -9, -15, -24, -22, -13, 20, -15, -23, -11, -16, 9],\n [11, 21, -25, -14, -19, 17, -6, -1, 11, 8, -12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[3, -25, -11, -14, -26, 16, 1, -26, 13, 7, -14, 26],\n [-25, -23, -2, 7, -14, 9, 5, -6, -1, -12, 2, -1],\n [-6, -15, -15, -22, 15, -1, 5, -25, -19, 0, 10, -19],\n [-3, -14, 2, -14, -4, 20, -12, -3, 16, -4, -17, 11],\n [-22, -22, 4, 13, -26, -25, 22, 2, -20, 2, -18, 9],\n [-20, 1, -17, -11, -17, 12, -1, 7, 7, 13, -13, -9],\n [-26, -10, 22, -5, 10, -11, -20, -12, 24, -6, -25, 21],\n [-2, -18, -7, 23, -17, 25, -6, -23, 3, 7, 3, -13],\n [-5, -26, -19, -16, -26, -22, 18, 22, -17, 12, -14, -6],\n [9, 26, 18, 6, 16, 1, 26, -18, 18, -16, 13, 2],\n [-20, 0, -5, 4, 3, 1, -7, -12, -12, 26, -15, -10],\n [-4, -21, 18, -11, 0, -4, -26, 18, -20, 18, 12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[23, 22, 21, 22, 13, 12, -9, 9, -5, -25, 21, -1],\n [23, 5, -4, 13, 19, -9, -8, -3, -23, 19, -25, 3],\n [22, 11, 4, 13, -11, 26, 6, 23, -24, -9, -17, -25],\n [24, 3, 3, -2, 16, 24, -3, 8, -17, 21, 3, -1],\n [8, -3, 24, -7, 26, 12, 22, 13, 8, 12, -17, 0],\n [24, -12, -12, 10, 8, -24, 2, -23, 20, -11, -22, -6],\n [13, 15, -6, -25, -13, -22, -20, -16, 8, 3, 17, 19],\n [-26, -11, 20, -26, -5, -14, 0, -12, -10, -18, -22, -4],\n [17, 22, 16, -16, -3, -19, 20, 7, 15, 26, 4, -5],\n [-13, -22, -10, -9, -8, -20, -1, -2, -9, 17, -12, 2],\n [19, 15, 22, -26, -23, -18, 9, 24, 5, -3, 10, -9],\n [-12, -7, 13, -25, -2, -14, 0, -14, 1, 19, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, 17, 4, -4, 10, -24, 23, 8, -13, -25, 23, -14],\n [-25, -15, 0, 7, 13, -22, -2, -16, -14, 1, -6, 22],\n [21, 24, -1, 0, -1, -12, 23, -21, -23, -23, 3, -14],\n [-18, 15, -13, 1, 13, -24, 14, 2, 6, -12, 20, 12],\n [-12, -20, 18, -15, 23, 12, -20, 20, 14, -21, -1, -18],\n [24, -3, 25, 3, -11, 21, 0, 6, -4, 18, -8, 9],\n [-8, -5, 15, 18, 6, 18, -17, 20, 5, -12, 12, 19],\n [-19, 24, -2, -9, -12, -1, 14, 17, -6, -5, 19, 7],\n [10, 10, -13, -23, -3, -25, -26, -25, -14, 0, 25, -10],\n [18, -10, -22, -3, -19, 17, -18, -9, -11, 24, 5, 13],\n [12, 26, 14, 17, 19, 5, 15, 21, -25, 11, 16, -23],\n [-22, 10, 22, 10, -1, 16, -18, -12, -3, -3, 8, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "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, -2, -1, -4, -21, 14, 0, -8, 4, 11, 16, 5],\n [-25, -9, 1, -20, -4, 26, 9, -3, 1, -2, 12, 22],\n [-23, 18, 25, -8, -23, -14, -26, 7, -20, -2, -4, 3],\n [22, -20, 18, -10, 6, -25, 11, 17, -14, 25, 25, 5],\n [-5, -18, -10, -9, 13, 13, 0, -16, 1, -19, 23, -9],\n [-14, 6, -12, -5, 11, 3, -21, 18, 7, -8, 22, 6],\n [-13, 21, 20, 14, -8, 13, -12, -17, -25, 23, 25, -25],\n [-6, -15, -17, -15, 12, -25, -26, -25, -4, 1, 26, -10],\n [25, 13, -6, 17, 7, -18, -10, 22, 15, 18, 5, -22],\n [-13, 19, 20, -2, -5, -22, 11, -18, 4, 14, -6, 9],\n [-26, -5, -4, -4, -12, 19, -26, -21, 13, 8, -10, -4],\n [-7, 1, 10, -9, -20, 22, 20, -7, -3, -11, -14, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-20, -12, -4, -4, 4, -22, 0, 17, -17, 24, 15, -20],\n [5, -4, 20, -18, 2, 0, 11, -6, 16, -21, -1, -7],\n [-12, 18, 11, -7, 26, -12, 2, -21, -11, -26, -21, -11],\n [6, -20, -17, 26, -19, -6, -1, 10, -9, -23, -7, 21],\n [15, 21, 13, -8, 6, -4, -18, 11, 18, 18, -9, 19],\n [-25, 21, -10, -11, 19, 18, 21, -3, 4, -26, 1, 22],\n [6, 15, 10, 12, -23, -26, 6, -17, -24, 10, 18, -6],\n [-18, 13, 16, -3, 19, -19, -3, -3, 26, -17, 8, -23],\n [17, -18, -16, 16, 21, -14, 0, 3, 19, 12, -15, -8],\n [13, -23, 22, 7, -4, 18, -1, 26, -20, -9, 15, -23],\n [26, -19, -5, 26, -1, -14, 19, 26, -10, 17, 9, 14],\n [20, -12, -9, 0, -21, 7, 14, -22, -15, 2, 10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-2, 20, 7, -16, -4, -3, 24, 22, -9, -17, -22, 4],\n [-2, 26, -10, 1, -26, 18, -25, 22, 20, 13, -25, 0],\n [-19, 0, 10, -10, -23, 17, 23, 11, 4, -22, -2, 1],\n [-8, 10, 15, -4, 24, 9, 18, -14, -10, 23, 24, 3],\n [-4, 22, -24, -14, 5, 18, 8, -25, 20, -24, 21, 2],\n [-17, -7, 7, -12, 13, 18, -26, -1, 5, -25, 5, 14],\n [2, 25, -7, -4, 24, -15, 17, -17, -8, 25, -17, -8],\n [-1, -3, -18, 2, 2, 10, 1, -24, -4, 24, -23, -13],\n [11, -14, 1, 12, 17, -7, 1, 5, -13, -14, -16, 11],\n [12, 15, -12, -18, -24, -22, 1, 15, -12, -24, 26, 23],\n [8, -20, 3, -3, 26, 4, -13, -11, 24, -23, -24, 8],\n [-18, -23, -8, -3, -16, -12, 9, 4, -19, -25, 23, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "558", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-24, -6, 24, -15, -13, -4, -14, -11, -10, -9, -14, -1],\n [18, 13, 12, 4, 13, -10, 5, -26, 8, 9, -8, 1],\n [-25, 2, 16, 2, 16, -8, 1, 7, 4, 10, -8, 5],\n [2, -18, -20, -15, 24, 4, -9, 1, 23, -6, -18, 7],\n [7, 20, -3, -11, 1, 19, 24, 20, 8, -21, 11, 26],\n [25, 14, -16, -23, -13, -14, -12, 22, -19, 16, -3, -16],\n [21, 8, -2, -4, 20, 18, -20, -22, 5, 1, 17, -24],\n [3, 17, -22, 24, 24, 6, -7, 3, 17, -5, -5, 11],\n [2, -6, -9, 26, 21, -16, -17, 8, -1, 23, 17, 19],\n [-23, -17, 12, -11, 14, 3, -24, 7, -2, 11, 15, 9],\n [-23, 15, -17, -14, -21, -20, 1, 10, -12, 3, 13, -17],\n [-15, -10, 21, 3, -26, 9, 13, -3, 11, -6, 15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, -14, 10, 17, -6, -9, 13, 19, 20, -1, -22, -22],\n [4, 1, 22, -14, 22, -16, -26, -3, -14, -9, -3, 2],\n [1, 11, 18, 26, -5, -7, -16, 24, -7, 14, -14, 20],\n [-3, 16, -3, 21, -10, -22, 3, -13, -12, -18, -13, -17],\n [-5, 4, -14, -10, -26, -13, 17, 12, 8, 26, -26, 0],\n [18, -5, 7, -18, 23, 9, 21, 5, 11, -7, 0, -24],\n [-16, -3, 2, -22, 6, -19, -8, -23, 14, 8, 3, -22],\n [21, 13, 11, -24, -11, -19, 18, -22, 11, 8, -19, 9],\n [-2, 26, 22, -19, -6, 24, 19, -18, 5, 17, -14, -4],\n [-19, 8, 1, -12, 25, 2, 24, -23, 7, 10, -3, -6],\n [-25, -20, -16, -15, -23, 8, 13, -1, -9, 10, -11, -15],\n [14, 13, 10, 25, -8, -12, -5, -7, 16, 25, -14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, -1, 18, 5, -6, -10, 2, 26, 2, 21, -5, 22],\n [-8, -13, 12, -4, 14, -25, 24, 5, 11, 6, -20, 21],\n [7, -23, -4, -7, -5, 19, 2, 16, 14, 10, -24, -5],\n [-7, -2, 7, 15, 26, 2, -17, 12, 20, 10, 13, 23],\n [-7, 11, -4, -16, -19, 2, 9, -2, 12, 7, 20, 5],\n [14, -4, -6, -8, -2, -4, -8, -22, -8, 8, -15, 12],\n [-2, -22, -15, 0, -23, 25, -8, 18, 20, -3, 15, 1],\n [6, 8, 23, -11, -15, -11, -16, 16, 1, -4, 19, -10],\n [-8, -16, -23, -17, -8, 9, 16, 12, 25, 14, -5, -25],\n [6, 13, 0, -8, 21, 19, -23, -8, -2, -21, 20, -14],\n [24, -5, -23, -25, -24, 19, 3, -23, 21, 16, 2, 18],\n [6, -14, 20, 12, 5, 1, 10, 1, 0, -2, 3, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[3, -18, -21, 2, -4, -21, -5, -25, 4, 26, -21, 15],\n [-22, -7, -15, 11, 11, -19, 22, 23, 16, 6, 12, 13],\n [4, -24, -8, 21, -19, 3, 4, 2, -21, -25, -4, 17],\n [3, 26, 11, 19, 12, -18, -20, 20, 17, 22, -12, -12],\n [-6, -13, -16, -16, -7, -14, 18, 3, 13, 12, -7, 18],\n [16, 24, 11, -19, 24, 10, 15, 6, -1, 17, 12, -19],\n [-9, 12, -13, 25, -9, -6, -4, -23, -17, 16, -16, -7],\n [-8, -26, 4, -25, 14, 22, -22, 7, -23, 0, 12, 26],\n [22, -24, -1, 14, -26, 25, 26, -11, 8, -8, -11, 6],\n [4, -5, 17, -7, -21, 8, 12, -24, 5, -14, 21, -13],\n [14, -19, 20, -8, 18, -13, -16, 23, 8, 9, -24, -2],\n [-14, -11, 1, 18, 0, -17, -9, -19, -20, 22, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[20, -18, 15, 13, 12, 2, 10, 23, 21, 20, 15, 2],\n [1, -6, 6, -1, 11, -12, -25, -15, 6, -12, 18, -26],\n [6, -23, 1, 26, -13, 26, 22, 18, -15, -21, 24, -7],\n [21, -6, -11, -15, 25, -7, 18, 6, 23, -25, 7, -1],\n [6, 15, 3, -26, 19, -19, -26, 19, -17, 5, 24, 13],\n [-25, 4, -23, -15, 4, 14, -4, 6, -19, 22, -11, -12],\n [14, 13, 25, -1, -13, -15, 0, 20, 4, -23, 3, -23],\n [4, 7, -23, -7, -9, 20, -19, 15, -25, -18, -11, -5],\n [-15, -22, 12, -12, 18, -19, -3, 24, -8, 10, 26, -9],\n [-6, 22, 12, -13, -12, 22, -24, 18, -16, -24, 3, -21],\n [-21, 4, -5, -6, 11, 11, -21, 2, 19, -16, 21, -5],\n [24, 12, -21, 3, 16, -2, 9, -26, -5, -18, 18, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578", "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, -11, -8, -19, -15, 16, 14, 4, 15, 6, -8, 0],\n [-3, 22, 1, -23, -15, -4, -7, 13, 1, 21, -26, 14],\n [-16, 17, 4, 14, 11, -18, -21, -21, 25, -24, 5, 8],\n [-11, -25, 9, 14, -20, 8, 3, 18, 19, 2, 14, -26],\n [17, -26, 14, -20, -24, 9, 12, 4, -2, 20, -3, -26],\n [11, 4, 10, -16, 22, -24, -15, -7, 3, -17, 12, -12],\n [-6, -9, 5, -8, 3, 6, -5, 18, 2, -3, -23, 23],\n [-15, 9, -23, -22, -8, 14, 12, 4, -20, -15, -17, 2],\n [25, -6, -14, -4, -21, 4, -18, 24, -3, -11, -16, 9],\n [-26, -6, 17, 9, 10, -21, -13, 2, -26, -19, 20, 17],\n [-8, -4, 12, 14, -16, 0, 13, 9, 15, -7, 15, -19],\n [19, 9, 25, -1, 8, -24, -23, 17, 2, 23, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[16, 1, -9, -13, 16, -13, 2, -24, 7, -18, 13, -22],\n [2, 14, -22, 26, 18, 16, 16, 25, 17, 24, -14, -1],\n [-18, -23, 12, 4, -22, -20, 1, 13, -13, -3, 15, 11],\n [-22, 20, 21, 7, 1, 20, -19, -6, -3, -3, -14, 22],\n [-12, 19, -2, 24, 18, 26, 1, 12, -19, 4, -20, 24],\n [20, 12, -10, 26, 23, 24, 8, -5, -20, 26, -17, 1],\n [12, 16, 2, 8, 26, -5, -18, 9, -19, 3, 3, 4],\n [-5, 17, 4, 13, 20, 1, 19, -22, -10, 25, -16, -5],\n [20, -2, -14, 9, 18, 18, -16, -22, -13, -5, -24, 23],\n [8, 5, 11, 13, -3, 1, -6, 22, 6, 1, 12, 23],\n [9, -17, 10, 13, -2, 18, -10, 26, -23, -17, 26, -2],\n [5, -19, 15, 18, -15, -6, 18, 0, 3, -17, -6, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "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, -24, 22, 26, 15, -8, -21, -20, 16, -11, 9, -23],\n [-9, 5, 5, -9, 12, 16, 10, 26, 1, 23, 12, -25],\n [10, 10, 24, -25, -8, -22, 17, -14, -5, 25, -20, -25],\n [-13, -2, -1, -22, -7, -15, 9, 4, -10, -11, -17, 8],\n [6, 11, 8, 24, 0, -20, 0, 14, -15, 19, 6, -14],\n [26, -25, -24, -16, -22, -25, 19, 1, -14, 19, 8, 13],\n [-14, -15, -9, -9, -10, 12, -5, -14, 18, 11, 26, -8],\n [-3, -8, -6, -3, 3, 1, 21, 8, 19, 26, 11, -10],\n [21, 7, -18, -14, -13, -1, 25, -6, 17, -7, -16, 24],\n [15, 23, 8, 21, 4, -9, -13, 22, -22, -10, -6, -13],\n [-24, 4, -2, 20, 17, -10, -1, -10, -8, 0, -20, -1],\n [-22, -25, -11, 18, -16, 12, -4, 8, -21, 10, -26, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "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, -24, -8, -17, -7, -16, 5, 13, -7, 5, 16, 10],\n [-5, -23, -14, -21, 2, -25, -2, 5, -1, -1, 11, -5],\n [-17, -4, -23, -11, 15, 6, -14, 19, 17, -14, 6, -13],\n [-19, -1, -5, 19, -26, 22, -11, 17, 2, 25, -4, -22],\n [-6, 23, 9, -7, 16, -19, -1, 14, -2, 25, 15, -20],\n [24, -5, 6, -22, 11, -15, 17, 26, -13, -20, 1, 25],\n [26, 25, 19, -11, 14, -25, 22, 4, 9, -13, 19, 1],\n [20, 5, 1, -15, -14, -5, 15, 21, 2, 3, -12, 13],\n [-23, 6, 19, -18, 24, 11, -11, -1, 16, 26, 0, -16],\n [19, 16, -1, -13, -26, -16, 3, -3, 23, 22, -23, -5],\n [19, -19, 20, -11, 6, 6, -17, -25, 17, -23, -4, 24],\n [0, 6, 6, 14, -7, -14, -16, -8, 26, 22, 5, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[25, -14, 1, -5, -8, 4, -7, 26, -3, 5, -18, 24],\n [-8, -4, -2, 6, 22, 19, 17, -25, -24, 1, 10, 8],\n [-13, -3, 23, 10, -24, -4, 7, -18, -9, -25, -5, 24],\n [8, 4, -1, 23, -13, 18, 21, 26, 1, -16, 5, -6],\n [-4, -3, -15, -24, -21, 21, -15, 26, -7, -21, -7, -13],\n [14, 22, 17, -26, -7, -5, 13, 4, 4, 1, -15, -11],\n [6, 8, 17, -23, -17, 7, 14, -24, 4, 25, 4, 25],\n [-26, -22, -22, -25, -12, -26, -6, 10, -20, -16, -1, 15],\n [-25, 3, -13, 26, -22, 4, 21, 5, 7, -17, 4, 0],\n [-9, -22, -10, -16, -22, 26, 11, 21, 10, -6, -3, 3],\n [-11, 22, 14, -5, -25, -8, 22, 10, -25, -16, 6, -18],\n [-2, -21, -16, 0, -19, 18, 4, 0, 17, 14, 20, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "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, -25, -12, 4, -7, -24, 15, 12, -17, -1, -17, 13],\n [-14, -6, 7, 17, 5, -18, 3, -26, 26, -15, 17, 8],\n [-3, 13, 18, 22, 25, -17, 20, -3, 14, -9, -19, 19],\n [16, -14, -11, -13, -18, -18, 24, -22, 20, -16, -8, 11],\n [-17, -11, 2, -22, -9, 24, 15, 15, 17, 26, 8, 9],\n [-5, -3, -15, 12, -15, 8, 23, -8, 10, -13, -4, 13],\n [-5, 20, 21, 23, -16, -25, -17, 16, -22, 3, -6, 22],\n [6, -2, 19, 20, -20, 13, 1, -11, 18, 10, -24, 18],\n [-8, -15, -8, 22, -16, -24, -25, 19, -1, -5, 26, -10],\n [7, 23, -12, -15, -11, -11, 12, -21, 19, -19, 25, -2],\n [-8, -8, -15, -18, 14, 2, 0, -22, -1, 3, -13, 6],\n [8, -16, 26, -23, 25, 6, -21, 1, -17, 9, 22, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, -5, 26, -22, -25, 6, -11, -20, -6, 8, 19, -5],\n [24, 21, -5, -21, 6, 12, 16, -2, -9, 14, 8, -3],\n [13, 13, -4, 6, 2, -17, -12, -17, -1, 13, 26, 2],\n [7, -9, -25, -2, -6, 24, 4, -5, -18, 0, -2, -2],\n [0, -17, 3, -23, -6, 3, 6, 16, -1, -25, -4, 4],\n [-23, 20, -7, -2, 18, -26, -25, -21, -20, 24, -23, -9],\n [14, 26, 16, -22, -2, -26, 7, -24, -10, 5, -3, -25],\n [-26, 7, -19, 18, 19, 26, 17, -18, 1, -8, -7, -20],\n [15, 8, -8, -10, 13, -9, -20, 0, 12, 3, -4, -7],\n [-4, -1, 21, 20, -13, 21, 4, 0, -18, -4, 26, -17],\n [20, -4, -17, -25, 10, 13, 11, 11, -26, 21, -9, 8],\n [-20, 17, 15, -5, 26, -2, 15, -4, -18, 0, -16, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538", "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, 13, 1, -9, 9, 7, -14, 19, 25, 3, 1, -5],\n [-3, 20, 3, 18, 11, -7, -21, 6, 20, 11, -12, -12],\n [5, -13, 15, -19, 9, -5, 11, -7, -3, -6, 1, 22],\n [-4, -3, 12, 17, -4, -23, 19, -23, 3, 21, 1, 4],\n [6, 23, -8, 26, -17, -2, 10, -14, -21, 3, -4, 9],\n [-11, -19, -11, -16, -26, -5, -9, 9, -16, -7, -17, 21],\n [-17, 10, 23, -5, -16, 8, -18, -12, 24, -8, 10, -21],\n [9, 17, -22, -24, -17, -14, -23, 13, 6, 25, 7, 9],\n [26, 6, -6, 12, -22, 18, -14, 13, -10, -17, -17, -25],\n [11, -6, -26, 3, -9, 8, 26, 12, 21, -5, -24, -21],\n [9, -11, -24, 9, -16, -10, -8, -19, -13, -1, 21, -2],\n [24, 21, -17, 5, -12, -23, 1, -23, -14, -15, -12, 2]]\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[[-4, -14, 11, 19, 8, 13, -15, 3, 19, -22, -25, 15],\n [3, 8, -17, -18, -10, 11, 3, 14, 8, -20, -15, 23],\n [15, 7, 22, -24, 6, 13, -14, -16, 13, -7, 4, 6],\n [7, 23, 23, -18, -20, -18, 15, -1, -25, -22, 22, -25],\n [25, -17, 4, 6, 17, 20, -21, -13, -13, -12, 6, 4],\n [-10, 16, -12, -7, 21, -6, 2, -18, 2, 17, 7, 20],\n [-18, 21, 3, -10, 25, -23, 13, 5, 5, -20, 11, 5],\n [-22, 15, -24, -7, -10, -11, -16, -14, -9, -13, 7, -15],\n [-5, -6, -1, 15, 12, -25, 23, 22, -11, 7, -16, -8],\n [3, -20, 0, -5, -10, -12, -18, -15, -19, -25, 22, 21],\n [-11, -24, 24, 21, 4, 16, -1, 14, 19, -25, 3, -14],\n [10, 25, -13, -26, 5, -21, -5, -16, 22, -4, -13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "552", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-7, -20, -8, -1, -5, -21, -14, -17, -8, 4, -17, 10],\n [-14, -10, -22, -6, 12, -7, -20, -12, -12, 26, -4, 6],\n [17, -25, 23, 5, -12, -20, -18, 1, -5, -24, 26, 15],\n [-25, -5, -2, -2, 5, 17, -20, 4, 10, -23, 6, -12],\n [-18, -21, 19, 4, 7, 17, 11, -14, 9, 5, -5, 21],\n [2, -16, -21, -22, -26, 24, 12, 23, -17, -17, 22, -3],\n [-20, -5, -6, -5, 6, 17, -2, 4, 22, -11, 25, -12],\n [2, -8, 25, -10, -1, 9, 9, 8, 13, -4, -18, 7],\n [24, -9, -11, 5, 1, 5, 23, -9, 17, 7, 2, -6],\n [-26, -11, 22, 6, -6, 8, 0, -7, 4, -11, 26, -13],\n [21, 5, 14, 5, 26, 26, -25, 18, -5, 10, 26, 25],\n [-10, 5, 11, -10, 7, -20, 2, -10, -3, -19, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "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, -8, -22, 10, -4, -1, -3, -6, 6, -1, -17, 15],\n [2, 8, 1, -15, 17, -20, -11, -7, 2, 8, 1, -20],\n [-5, -13, 9, -17, -25, -5, -11, 8, 20, 13, 21, -16],\n [16, 16, 6, 7, 25, 6, -8, -7, -17, -8, 26, 16],\n [-15, -17, -20, 13, -16, 23, -11, 6, 11, -10, 18, -2],\n [15, 4, 15, -26, 12, -7, -18, 16, 25, -25, -26, 17],\n [12, 24, -22, -15, -13, 12, 5, 13, 19, 17, -18, 15],\n [15, 6, -2, 11, -13, -18, 0, 17, -8, -2, 25, 5],\n [-5, 2, 1, 17, -14, 1, -24, 3, -16, -25, 23, 23],\n [-18, 6, -1, -11, -2, -26, -6, -7, -22, -10, 13, 11],\n [-26, -14, -9, -23, 20, -13, 21, -22, 6, -1, -23, 3],\n [-10, 1, -21, 0, 9, -20, -26, -17, -14, 14, 5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 3, -18, -21, -17, -16, 12, -7, -2, -15, -5, -15],\n [-13, 15, 21, 9, -13, -25, -25, 16, 16, -21, -2, -24],\n [-4, -18, 4, 1, -2, 8, -26, -25, -12, 16, 13, -11],\n [-4, 22, 8, -19, -20, -6, 8, 12, 10, 6, 10, 8],\n [-9, -8, -17, -23, 3, 18, 6, -23, -18, -10, 16, 12],\n [-3, 12, -14, -1, -8, -10, 23, 3, -1, -14, 22, -9],\n [-6, 25, 7, 24, 20, -18, 3, 2, 2, 19, -8, -19],\n [17, -10, -15, -12, -22, 7, 25, 23, -24, -22, 7, -18],\n [-3, -22, 0, 22, 26, -7, 20, 18, 14, -25, -4, 7],\n [2, 16, 8, 3, -24, -17, 7, -26, -21, -21, 16, -11],\n [-26, -22, -2, 0, 15, 26, 11, 16, -1, -11, 25, 18],\n [17, 23, -1, 18, 10, 1, 1, 3, -14, -2, 18, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-8, -14, -16, 21, -4, -13, -17, 7, 13, -4, 13, -6],\n [-7, 5, -13, -3, 19, -9, 20, 3, 1, 21, -13, 15],\n [-6, 7, -22, 4, -24, -4, 12, 17, 3, 15, 16, 3],\n [22, 9, 11, -20, -22, -21, 22, -13, -16, 10, -25, 4],\n [19, 0, -11, -25, 22, -1, -11, -18, 25, 25, -18, -22],\n [9, -20, 5, 2, 10, -24, 3, 13, 4, 21, 0, -21],\n [2, -18, -7, 23, -16, -8, 12, -17, -22, 12, -4, -21],\n [4, -9, -6, -12, 4, -17, -21, -3, 6, 1, 1, -17],\n [-4, -12, 19, 21, 10, -13, 21, -13, -20, 24, 9, -9],\n [26, -12, 22, 6, 20, 21, -5, 16, 14, -10, -1, -12],\n [13, -9, -19, -24, 24, -13, 7, 6, 10, 22, -26, 26],\n [21, 8, -17, -8, -16, 8, -25, -24, -12, 25, 14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "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, -25, 3, 11, -22, -21, -22, -15, -23, -3, -2, -1],\n [19, 19, 16, 6, -6, -4, 10, 10, -15, 10, -6, -14],\n [16, 26, 6, 17, -21, 16, -15, 11, 3, 10, -9, -11],\n [18, -20, 19, -26, 26, 1, 26, 17, -24, 23, 16, 25],\n [12, -17, 24, 18, -13, -12, -21, 12, 18, -11, 20, -9],\n [8, 21, -2, 6, 6, -8, 11, -16, 12, -24, 11, -26],\n [13, -2, 5, 19, 9, -23, -4, -11, -16, -5, 12, 6],\n [14, 11, -14, -6, -15, 24, -1, 22, 26, -26, 14, -5],\n [0, 5, -19, 7, -9, -23, -26, 26, 17, -11, 3, -4],\n [4, 1, 23, 10, -11, 14, -18, -25, 19, 16, -25, 5],\n [-11, 26, 24, -14, 22, 0, 4, 6, -6, -8, 21, -14],\n [-8, 8, 8, 6, -24, 21, -6, 13, -4, 21, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, -23, -23, -12, 1, 9, -19, -3, 7, -12, -4, 0],\n [-13, 26, -25, 8, 16, -20, -11, -5, 1, 5, -20, -5],\n [16, -25, -19, -20, 11, 21, -6, 16, -5, 8, -9, -18],\n [22, -25, 15, 15, -10, 13, -7, -21, -16, -22, -17, -4],\n [6, 13, 9, 12, 24, 20, 7, -10, -1, 26, 21, 0],\n [19, -24, -8, -19, -10, 23, -26, -20, 9, -24, -8, 15],\n [0, -24, 7, -22, 22, 10, 19, -11, -13, 3, 5, 24],\n [18, -15, 0, -1, 21, 2, -4, 22, -5, -7, 11, 19],\n [-11, 4, -24, -6, 24, 12, -22, -7, -4, 5, 15, -18],\n [-24, 0, 0, -17, -11, -3, -4, -18, -25, -21, 10, 8],\n [-20, -12, -6, 11, 9, -4, 2, -14, -22, 20, 12, 12],\n [15, 18, 16, -26, -7, 16, -26, 8, 13, 18, -20, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[25, 7, 23, -22, 2, 23, 21, 0, -20, -26, -18, 20],\n [-26, 0, -10, 5, 14, 3, -12, 15, 1, 25, -24, 1],\n [-22, -25, 11, -11, 17, -10, -15, -1, 22, -20, -3, -11],\n [-9, -19, 0, -1, 4, -9, -25, 14, -4, 21, 22, 15],\n [-5, 6, 26, -9, -12, 14, -24, 21, -4, 20, -25, 15],\n [-23, -1, -8, 22, -17, -5, 26, -21, -26, 16, -11, 25],\n [-20, -3, 8, -13, -23, 14, -12, 17, 21, -4, -8, -13],\n [0, 9, 11, -5, -16, -23, 5, 13, 14, -3, 7, 25],\n [-24, 11, -25, -4, 13, -7, -19, 8, 22, 16, -24, 5],\n [4, 17, 19, 4, -26, -15, -9, -3, 9, 2, -2, -4],\n [-24, 3, -10, 18, 22, 3, 22, -8, -22, 13, 7, -18],\n [12, 21, 17, -1, 26, -22, -3, 4, -3, -6, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -6, 3, 22, 20, -17, -24, 12, 2, -2, -25, -14],\n [0, 2, -13, -23, -19, -22, 17, 0, -3, 17, 16, 7],\n [1, -3, -22, -14, -9, -10, 3, 11, -8, -5, 22, 22],\n [-9, -1, -12, 1, 3, 1, -7, -23, -23, 10, -12, 7],\n [-16, -4, 8, 16, 8, -16, -25, 25, 25, -12, 13, 1],\n [4, 5, 7, 23, -5, 2, 26, -19, -5, -15, -4, 11],\n [-25, -15, -6, -15, 18, 4, -18, -12, 5, 16, -18, -3],\n [-19, 25, 1, -9, 16, 10, 9, 26, 10, 5, -6, 12],\n [22, 2, -9, -4, 6, 21, -18, 17, 24, 16, 11, -23],\n [-11, -24, -19, -11, -25, 18, -8, -3, -11, 24, 13, -25],\n [5, -26, 22, -9, 12, 5, -18, -24, -3, -16, 1, -11],\n [2, 14, -15, 19, -23, -1, -23, -16, -25, 4, 23, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-2, 7, -26, -22, 12, 25, 4, 9, -24, 11, -15, -11],\n [-19, -16, 18, -13, 0, -9, -19, 6, -23, 22, 3, -7],\n [3, 0, -2, -21, -22, -13, 24, -13, 7, 14, -2, 12],\n [-9, -7, 16, -19, -1, -6, 0, 5, 15, 23, -10, 22],\n [-26, 0, 9, -16, 14, 14, 8, 11, 11, 15, 15, 22],\n [20, 9, -17, 13, -26, -5, -10, -15, 17, -14, -2, -1],\n [19, 13, 19, 12, 22, 16, 6, -19, -14, -1, -10, -3],\n [-3, -15, 4, -11, 15, -11, 3, 1, -24, 6, 24, -3],\n [3, 13, 21, 1, 20, 12, -25, -14, 10, -17, 13, -14],\n [-8, -21, -9, 13, -18, -10, -23, 23, -21, -16, 15, -1],\n [-16, -19, 26, -24, -25, -9, -25, -1, -15, 10, -1, 9],\n [-11, -13, -25, -6, -20, 26, -16, 17, 2, 10, 21, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 13, -23, -23, 0, -21, 7, 14, 13, -9, 17, 21],\n [3, 6, -7, 9, 19, 23, -22, 8, -8, -15, -1, -8],\n [25, -16, 26, -7, -18, -7, 0, -22, -17, -18, -2, -14],\n [5, -19, 18, 0, -5, 1, -9, -4, 14, 4, 14, 7],\n [-20, -22, -6, -21, 18, 23, 8, 15, -4, -24, 6, 11],\n [-4, -11, -2, 22, -11, -2, 15, -20, -19, -24, -22, -8],\n [-20, 23, -5, -1, 23, -2, -21, -22, 11, 11, -5, 4],\n [-5, -16, 5, -10, 14, -5, -11, 15, -12, -19, 19, 21],\n [24, -24, -14, 3, 1, -18, -15, -2, 10, -6, 24, 12],\n [12, -8, -19, 11, -24, -5, -26, 11, 25, 25, -8, -6],\n [-14, 0, -10, 23, -7, 3, 11, -16, 0, 11, 1, -1],\n [12, 6, 5, -2, -3, 13, 0, 19, -5, -7, 6, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[2, -22, 19, 12, -10, 2, -16, -5, 4, 12, -26, -12],\n [-8, -17, -18, -14, 18, -1, -21, 13, 17, -25, 2, 21],\n [-15, -4, 23, -24, 23, -16, -22, 18, -17, 26, 20, -21],\n [-11, 4, -4, 3, 13, -7, -2, 8, -22, 20, -24, 20],\n [7, -15, 0, -22, 14, -5, -23, 26, 1, -20, 21, 18],\n [7, -25, -18, -12, 4, 9, 22, 14, -12, 6, 4, 0],\n [-25, -18, 16, 24, -26, -8, -18, -25, 10, 22, -26, 19],\n [-15, -1, -17, 24, 20, -26, -26, 16, 4, -16, -22, 8],\n [-16, -23, 11, 23, 12, -6, 9, 19, 1, -19, -7, 16],\n [19, -6, 8, 16, 5, 9, 14, -22, 18, 25, -23, -20],\n [7, -7, 24, -20, 25, -3, -6, -18, -8, -7, 1, 5],\n [7, 26, -11, 11, 24, 23, -10, -16, -23, 13, 23, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[26, 13, 15, -9, 23, 22, 21, -21, 19, 5, -22, -12],\n [18, -11, 21, -10, 10, 16, -12, 8, -19, 8, 9, 0],\n [-13, -4, -7, -21, -3, -4, 9, -15, -25, 0, 5, 2],\n [23, 19, 13, 13, 17, 6, 2, 6, 9, -10, -17, -26],\n [16, 26, -10, 15, 1, 11, 9, 18, 0, 16, 10, 19],\n [-2, 7, -24, 2, 8, 16, 14, 24, -17, 26, 11, 11],\n [-26, -26, 5, -5, -8, 8, -21, 7, -12, 17, 26, 15],\n [24, 26, 18, -24, 23, 25, 10, -5, 18, 2, -13, 3],\n [-12, 23, 2, -13, 24, -24, -5, 6, -4, -20, -7, -20],\n [-10, 5, -12, -14, 20, -24, -2, 22, 5, -11, -26, 19],\n [-24, -7, 1, -5, 9, 14, 26, -26, -13, 18, -12, 5],\n [-9, 21, 11, -5, -11, -16, -20, -18, -26, 15, -19, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-22, 2, -21, -15, 16, 12, -20, 17, -15, 6, -8, 26],\n [9, -8, -6, -8, 16, -18, 18, -5, -8, 10, -16, -2],\n [8, -22, 18, 4, -13, -14, 7, 7, -9, -21, 24, 15],\n [-6, 13, -22, -25, -21, 23, -19, -25, -4, -7, -23, -12],\n [3, -7, -3, -18, 25, -6, 11, 14, -14, -22, 19, -13],\n [23, -20, -21, -15, 19, 24, -11, 24, 5, 15, -16, -23],\n [2, 25, 7, -18, -17, -19, 9, 5, 18, -21, -21, 0],\n [-25, -18, 11, -22, 7, -13, -17, 20, 22, -20, -7, -16],\n [-14, 26, -10, 10, 17, 9, 6, -17, 7, 18, -14, -2],\n [17, 6, -17, 25, -3, -22, -17, 12, 20, 0, 23, 25],\n [9, 6, 1, 13, 16, -24, 4, 2, 17, 18, 25, 23],\n [17, 15, -6, 5, 1, -6, 20, 8, 3, 20, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[21, -25, 6, -23, 22, 12, -2, -22, -23, 25, 25, 2],\n [10, -19, -7, 14, -21, 9, 5, -22, 13, -7, 18, -23],\n [12, -5, 6, 4, 14, 2, -22, -17, -16, 23, 10, -5],\n [-3, -6, 9, 24, -11, -25, -12, 14, 22, -1, 3, -25],\n [2, -21, -26, 13, -16, 25, -4, -1, 4, -12, -18, 7],\n [12, -10, 8, 9, -24, 13, -16, 1, 21, 1, 19, -8],\n [-25, 5, 17, -16, -11, -16, -24, 15, 2, -22, 1, 4],\n [-14, -2, -21, 25, -24, -5, 14, 26, 12, 5, 3, -20],\n [-2, -25, -19, 23, 6, 1, -17, 11, -9, -14, -6, 6],\n [-4, -26, 17, 13, -6, -22, 8, -9, 11, 9, 20, 2],\n [-1, 9, 11, 23, -9, 2, 4, 15, -14, 25, 23, 3],\n [-20, 13, -21, -25, -19, -17, 22, 17, 16, 22, 21, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-17, 25, 8, -8, -23, -8, 14, -7, 22, -23, 22, -1],\n [-24, 25, 3, 9, 14, -21, 24, 12, 0, -11, 20, -11],\n [19, 9, 7, 12, -3, 12, -21, -7, -18, 22, -6, -16],\n [21, 3, -26, 0, 21, 22, -21, 16, -20, 21, -5, 7],\n [-7, 18, 18, -12, 20, -18, -9, 19, 19, 9, 19, 15],\n [3, -16, 6, 19, 13, -21, 16, 19, 12, -5, 12, 26],\n [-8, -5, 4, 15, -2, 14, 23, 22, 3, 18, -23, 26],\n [-1, -20, 13, 21, -15, -26, -21, -26, -19, 17, 21, 6],\n [-23, 24, 23, 13, -21, 18, 25, -24, -12, -21, -21, 10],\n [24, 0, 15, 14, 19, -22, 12, -10, -4, -10, 14, -4],\n [12, 6, -25, -17, -8, 13, -18, -12, 16, -3, -15, -5],\n [-9, -25, -12, 15, 12, -18, -5, -10, -13, 4, 14, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "561", "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, 8, 7, -24, -25, 18, 0, 18, -25, 25, 24, 14],\n [-22, -6, -20, -2, 18, -26, -18, -25, -24, 17, 10, 17],\n [-23, -6, -1, 26, 17, 10, -13, 19, -17, -1, -17, 10],\n [-9, 0, -10, -17, -16, 20, -3, -8, 17, -11, -4, -15],\n [-8, -2, -24, -14, -6, -5, 20, 2, 22, 16, -2, -4],\n [-15, 22, -4, -22, 2, -22, 12, 8, 8, -10, 3, -25],\n [-12, 24, -4, 15, -1, -16, -3, -18, -13, -3, -20, -17],\n [6, 6, 19, 0, -19, -13, -20, -9, -1, 14, -12, 6],\n [-16, -8, 15, -9, -5, 9, -9, -9, -5, -2, 25, 17],\n [4, -18, 23, 11, -8, 25, -2, -12, -22, -16, -14, 7],\n [-19, -2, 0, -16, -9, -17, 6, 9, -10, 22, -22, -4],\n [-24, 12, 10, -17, 0, -20, 22, 2, 22, 12, -21, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"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, -13, 11, -18, 25, -16, -16, 13, 8, -16, 9, -24],\n [18, -8, -19, 26, 1, 26, 26, -26, 26, 13, 3, 14],\n [11, -16, 2, 4, -17, 8, 13, 2, 10, -25, 21, -26],\n [5, -3, -25, -24, -18, 22, -3, -15, 7, 7, -4, -8],\n [25, 5, 22, 1, -1, 22, 18, -15, 16, 4, -16, 13],\n [23, -23, -9, 2, 20, 12, 20, 4, 24, 1, 0, 26],\n [3, 22, 15, -16, -13, -23, 9, -26, 17, 12, 10, 6],\n [-6, -3, 13, 23, -14, 22, 7, 11, 2, 26, 9, 13],\n [20, -22, -7, 2, -16, -19, 1, 22, 14, -9, 3, -13],\n [-18, -17, -2, 25, 0, -25, -24, 2, 10, 0, -23, 8],\n [0, -8, -17, -1, -20, 0, 3, -15, 13, -22, -14, 14],\n [-23, -25, 10, 7, 23, -21, -1, -16, 15, -26, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-17, -22, -1, 17, -8, -6, 7, 2, 11, -12, 13, -11],\n [24, -9, 22, -26, -16, 9, 5, 1, -21, -20, 13, -3],\n [-17, 3, -10, 17, -19, -15, -1, -10, 8, 19, 17, -22],\n [18, -16, -11, 15, 3, 13, -21, -7, -7, -3, 0, -24],\n [-3, 25, -17, -2, 1, -9, 15, 18, -13, -26, -7, 20],\n [-2, -15, 21, 12, 19, -18, -18, 15, 14, -2, 3, 21],\n [13, 1, -25, -2, -9, -3, -9, 0, 17, 8, 7, 11],\n [-21, 22, -11, -4, 1, -14, -15, -16, 20, 22, 25, -5],\n [4, 0, 0, 13, -1, -20, -16, 26, -5, 13, -8, 11],\n [-7, -8, -8, 9, 20, 0, -10, -9, -7, 17, 15, 14],\n [-19, 13, -16, 3, -15, -4, -21, 8, -12, 11, 1, -20],\n [-21, 0, -25, -21, 5, 2, 7, -26, -12, -17, -17, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, 5, 9, -2, -12, -18, -11, 14, -8, 19, 17, -15],\n [8, 24, 16, -22, 11, -21, 24, -13, 21, -15, 23, -5],\n [18, 25, 14, 23, -23, 16, -9, 26, 4, 8, -23, -18],\n [18, -12, 15, -6, 5, -18, 21, 5, -11, 18, -22, 15],\n [4, -2, -26, -24, -6, 1, -24, 15, 5, 5, 22, 3],\n [23, -14, 7, 21, -23, -9, 5, -13, 5, -21, 16, -10],\n [-19, 8, -3, -24, -10, 9, 24, 13, -10, 3, -2, -5],\n [10, -16, -15, -6, -12, -15, -5, 12, 8, 15, -11, 6],\n [26, 16, 22, -13, -9, 17, -11, 13, -24, 16, -1, -12],\n [9, 0, 21, -10, -13, -25, 0, 20, -3, 13, 18, 8],\n [-23, -1, 9, -23, 7, -14, 13, 14, -26, -26, -18, -16],\n [-11, 2, 9, -12, 12, -25, -17, 22, -16, 3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "539", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[24, 15, 9, 2, 18, 5, 6, 12, -18, -26, -9, 23],\n [21, -5, 21, 10, -13, -5, 6, -21, 0, -21, 17, 23],\n [14, -11, 20, -25, 10, 2, -4, -6, -14, 24, -26, 2],\n [21, -20, 4, 18, -5, -11, 1, 17, 12, -2, -13, 23],\n [-6, -8, -14, -25, 24, 9, -13, 7, -9, -3, 3, 24],\n [-8, 9, -6, -8, -1, 8, 13, -23, -6, -24, -22, 16],\n [2, -8, 24, -10, 7, -7, 1, -18, -24, -17, -6, 14],\n [25, -23, -5, -20, -15, -16, -5, 2, 0, 20, -7, -13],\n [-20, -12, 19, 1, 16, -17, 24, -24, -15, -14, 12, 17],\n [7, -26, 11, -2, -8, -2, -21, 18, -23, -1, -1, -1],\n [-13, 5, 21, 1, -25, 14, 18, -6, 19, -13, 10, -25],\n [-22, 11, -25, -26, 21, -5, 14, -2, 19, 3, -18, 10]]\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 difference between the largest and smallest singular values:\n[[20, -17, -12, 22, -24, -19, -2, 9, 16, 24, 19, 23],\n [-6, 7, 0, -18, -17, 0, -2, -14, 24, -23, -11, -15],\n [-2, 21, 22, -11, 12, -25, -18, 17, -14, -13, -15, 8],\n [-5, -6, 21, 23, -24, -5, -18, 20, 13, 15, 26, -24],\n [4, 10, -21, -13, -8, -9, -20, 9, 2, -24, -14, 9],\n [14, -2, 1, 11, -16, 14, -18, -5, -6, -8, 6, -23],\n [6, 18, -11, 17, -26, -12, -5, 5, 10, -4, 6, 22],\n [13, -5, 13, 20, -15, 21, -9, 5, -24, 9, 20, 19],\n [-26, -2, -7, -10, 22, -5, 23, 6, -1, 0, 7, -4],\n [-11, -13, 25, 25, 23, 14, -13, 18, -1, 19, 24, 22],\n [0, 13, -23, -18, 0, 16, 12, -12, -2, -9, 25, 3],\n [10, -11, 26, -15, -10, -2, -12, -2, -6, -8, -3, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[26, -15, 22, 12, -16, 6, 22, -2, 12, 7, -16, -11],\n [5, -12, 13, -12, -20, 10, 13, -25, -21, 9, 12, 11],\n [1, -5, 10, -22, -9, -16, -19, -7, -16, 0, 2, -2],\n [24, -8, -25, 15, 12, 17, -25, -20, 24, 4, 6, -16],\n [13, 13, 19, -14, -17, 22, 11, -7, -6, -13, -3, 13],\n [-20, -22, -21, 13, 26, 8, -18, 15, -26, 12, -7, -21],\n [5, -14, 12, 13, -6, 10, -15, -21, -12, -6, -6, 1],\n [9, -10, 19, -20, -4, 18, -5, -17, -9, -25, -15, 18],\n [26, 12, 23, -5, 16, -5, 15, -5, -21, 19, 25, 10],\n [-7, -21, -18, 2, 10, -22, 24, -14, 0, -4, 10, 19],\n [7, -2, 10, -4, 1, -1, -15, 25, 12, -24, -18, 20],\n [-12, -19, 1, -1, -11, 7, -7, -26, -3, 2, -23, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[11, -24, 13, -25, 2, 22, 1, -15, 17, -12, 23, 14],\n [4, 26, 10, 5, -5, -24, -10, 2, -15, -13, -19, 14],\n [-25, 26, 7, -3, 21, -7, 16, 25, -17, 13, -20, -26],\n [-17, 24, -22, 13, -6, -18, 2, 4, 18, 19, 0, -21],\n [16, 4, 14, 18, 9, -25, -6, 7, -5, -14, -8, 6],\n [11, 13, 22, -24, 11, -8, -20, -12, 11, -2, -5, -4],\n [23, -17, 9, 10, 23, 15, 15, 15, -20, 25, 19, -2],\n [13, 14, -3, -22, -6, 13, -7, 2, 10, -7, -9, -23],\n [-16, 26, -5, 25, 16, -13, 18, 1, -23, -11, 11, -4],\n [-14, -7, -22, -8, -6, 15, -22, -13, 9, -21, -22, -3],\n [2, 2, -25, -21, 7, -15, -5, -23, 18, 22, -21, -24],\n [-14, -4, 8, -1, 25, -18, -4, -23, 7, 10, -19, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[10, -21, -20, 18, 14, 12, 9, -22, -24, -10, -8, 18],\n [-26, 10, -18, -23, 15, 19, -17, 5, -26, -4, 24, -10],\n [25, 3, 0, -12, 11, -20, 6, -22, 25, 25, 12, 7],\n [26, -24, 5, -25, -11, -10, 26, -15, -22, -23, -11, -9],\n [18, -7, 26, -18, -11, 8, 2, 22, 3, -7, 15, -5],\n [-4, 25, 9, -5, -26, -6, 21, 16, -8, -19, -22, 13],\n [2, -9, 2, -12, 23, 18, 4, -12, 26, 18, -24, 17],\n [17, 15, 6, -3, 11, 24, -3, -14, 0, 6, -8, -2],\n [-21, 6, -2, -4, 22, -10, -6, 16, -7, -15, -14, -9],\n [-5, -3, 6, -24, -10, 12, 5, -10, 21, 17, -2, -19],\n [16, 8, 2, -15, 9, -18, -1, -5, 26, 4, 26, 22],\n [21, 17, 3, -12, 20, 6, -24, 7, -10, 17, -22, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "558", "dataset": "MATH"}
{"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, 24, -12, 12, -19, 15, 11, 1, -6, 20, -17, 1],\n [-6, 22, 1, -5, 11, -8, 25, 25, 11, 19, -3, 1],\n [18, -14, -18, -18, -6, -3, 4, 2, 13, -17, 25, -23],\n [-24, -14, -6, -19, -18, 19, -26, -13, -15, 9, -5, 26],\n [9, 18, -11, -16, -24, 7, -2, -1, -24, -7, 4, 22],\n [-26, -1, -2, -16, -11, -7, 15, 25, 11, -25, 2, -20],\n [22, 13, 18, -2, -23, 16, 7, -2, -19, 5, -9, 13],\n [-16, 10, 12, 9, -17, -21, 18, -11, -2, 7, 4, 20],\n [-19, -10, -13, 3, -9, 19, 9, -6, 26, 4, 6, -4],\n [11, -22, -12, 3, -11, 13, 2, 1, -21, -22, 11, -2],\n [1, -26, -13, -8, 4, 24, -12, -8, 11, 5, 4, 10],\n [-1, 21, 14, -2, 20, 13, -19, -23, 4, 5, 7, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-24, 14, -1, -23, -25, -8, -4, -2, 20, -20, -19, -24],\n [-4, 20, 6, 21, 1, -5, 8, 7, 3, 20, 9, -13],\n [-18, -5, 1, 14, -13, -12, 10, -3, 7, 22, 16, 18],\n [17, -24, -4, -7, 18, -12, 16, -11, -20, 6, -8, -9],\n [14, -9, -24, -24, 9, -11, 16, -4, -4, -12, -18, 13],\n [11, 26, -9, 11, -21, 17, 10, 19, -21, -6, 3, 1],\n [-7, -8, -13, -26, 0, 25, 5, 2, 4, -2, -20, 12],\n [19, 25, -11, 17, -16, -9, 17, 15, -22, -25, -17, -1],\n [-3, -1, -11, -2, 11, -21, 25, -15, -18, 22, 15, -19],\n [4, 14, 5, -20, 5, 15, -2, 6, 24, 1, -16, 4],\n [25, -17, -25, 19, 17, -23, -5, 18, 25, 1, -17, -25],\n [22, 4, 15, -4, -11, -18, 24, 16, -21, -2, -23, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "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, -3, 0, 21, -24, -15, 20, 25, 3, -15, 14, 15],\n [13, 18, -5, -12, 1, -10, 17, 21, -2, 16, 24, 18],\n [-24, 9, 4, -12, 19, 1, 16, 4, 18, -7, 23, 18],\n [-6, 0, -8, 9, -15, 8, 21, 6, 9, 14, -4, -14],\n [3, -17, 14, -7, -21, 4, -8, -24, -17, -17, -6, -25],\n [18, 12, 18, 3, 19, 1, -9, -13, 18, -8, 13, 9],\n [14, -15, -7, 7, 9, -6, -8, 14, 14, 16, 15, 8],\n [-19, -5, 16, 11, -9, -19, -25, -7, -22, 15, 3, -9],\n [17, -4, 26, -25, 15, 17, 24, 10, 15, 5, -26, 12],\n [-26, 22, 17, 4, 12, -19, -24, 20, -15, 22, 7, 22],\n [-2, 9, -20, -12, -6, -2, 21, 11, 10, -11, -26, 20],\n [25, 10, 18, -13, 7, -25, 4, -8, -8, 17, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-10, -25, -16, 22, -13, 14, 2, -8, 1, 24, -26, -22],\n [24, 7, -13, -8, -3, 13, -10, -25, 4, -10, -19, 19],\n [-10, 11, -1, 16, 13, 18, 13, -20, -3, 3, -1, 3],\n [8, -25, 17, -23, -22, 21, -25, 4, 0, -3, 18, -23],\n [1, -22, 0, 17, 20, -22, -22, 21, -18, 20, 0, -23],\n [22, -3, 0, -26, 5, -11, -4, 1, -7, -10, 9, 18],\n [-19, -9, -14, -18, 10, 3, 16, 1, 19, 23, -9, -7],\n [21, 9, -8, -22, 7, -10, 1, 9, 11, 3, -9, -21],\n [25, -1, -12, -26, -10, 4, -25, 9, 8, 0, 26, -24],\n [19, -7, -19, 2, -19, 14, 23, 0, -1, 12, -17, 3],\n [6, 9, -7, -23, -4, 2, 19, 5, 10, 10, 24, -1],\n [26, -22, -3, 16, -25, -12, 19, 19, 13, 25, -19, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[10, -13, -22, -18, -5, 16, 22, 17, 17, 21, 3, 6],\n [23, 11, 10, 23, 18, 11, -20, -24, 16, 13, 5, 9],\n [15, 14, 18, -8, 4, 3, 20, 10, -2, -14, -15, -18],\n [13, -18, 26, 18, 0, 14, 4, -21, 2, 3, 11, -16],\n [15, 19, -21, 12, 14, 4, 8, -15, 21, 18, -21, 18],\n [-1, 10, 5, -23, 13, -24, -25, -7, -8, 12, -15, 9],\n [15, 1, -18, 17, -16, 26, 3, 24, -25, 11, 11, 6],\n [-20, 17, -6, -15, 25, -6, -4, -21, -13, 5, 22, 22],\n [23, 18, -14, 0, -16, 5, -24, 22, -25, 3, -25, 12],\n [2, -5, -2, 15, 19, 26, -8, 22, -11, -10, 23, 0],\n [16, -8, 16, 15, 3, -13, 19, 15, 5, 26, -4, 9],\n [-17, 11, 2, -16, 23, 11, 26, -12, 5, 0, 11, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "552", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-26, 14, -13, -24, 3, 4, -26, 19, -13, 9, 19, 9],\n [16, 25, 14, 16, -12, 11, -2, 17, 18, 23, -13, -3],\n [16, -25, 24, 7, 22, -4, -19, -22, 2, 16, 25, 6],\n [-7, -11, 10, 21, 10, 15, 14, -3, 24, 2, 8, -18],\n [-5, -7, 13, -23, 16, 9, -15, -4, 12, -19, -17, -4],\n [2, 18, 5, -13, -11, 12, 21, -10, -7, 24, -15, -18],\n [-19, 14, 10, -6, 15, 5, 10, 19, -9, 2, -20, 13],\n [10, -21, -7, -18, 26, -18, -19, -10, -3, 13, -4, 6],\n [-5, 23, 20, -5, 0, 21, -25, 4, -14, -25, 19, -20],\n [-16, 20, -1, 22, -6, 22, -12, -11, -18, -6, 26, 25],\n [24, 14, -21, -26, 4, -22, 10, -1, -26, -26, 2, -5],\n [11, 14, -8, 1, -22, -6, 22, -5, -7, -15, -21, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "552", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[18, 13, 8, -16, 25, 6, -2, -13, 2, 26, -14, -12],\n [26, -19, 20, 18, 6, -16, 25, -12, -6, 9, -21, -2],\n [17, -26, 15, 23, 6, 12, 5, -25, -2, 13, 6, 24],\n [11, -16, -8, -2, 1, -17, 4, -11, 21, 15, -9, -5],\n [23, 8, -15, 15, 1, 21, -18, 3, -9, 18, -3, 19],\n [-8, -13, -25, -16, -1, -19, -24, -12, 18, 13, -14, -11],\n [-5, 6, -25, 18, 2, 19, 7, -11, -13, 12, 19, 23],\n [22, -22, 16, -9, 21, -1, -17, -21, -13, -25, 0, -18],\n [-14, -6, 25, 17, -25, -24, -14, -6, 6, -7, 9, -9],\n [-2, 18, 11, -2, 11, -12, 23, -10, 19, 9, 2, 6],\n [5, -19, 16, -14, -10, -6, -13, -2, 22, 25, -3, 6],\n [-19, 1, -8, -16, -17, -26, -22, -11, -7, -7, 1, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[21, -24, 3, -4, 7, 22, 1, -26, 21, 0, 7, 4],\n [5, 25, -20, 16, 11, 7, 19, -23, -8, -5, 2, 7],\n [7, 18, 18, -24, -6, 11, -6, -10, 2, 6, 12, -1],\n [-20, 18, -18, -9, -26, -16, -5, 5, 16, -17, 22, 0],\n [22, -15, 3, -17, -15, 11, -6, 0, -21, 11, 25, -19],\n [10, -21, 7, 22, 13, -5, 2, -18, -6, 5, -19, 16],\n [-17, 22, -4, -7, -14, -5, 14, -12, 4, 18, 5, 18],\n [-14, -2, -6, -23, 15, -12, -6, 15, 26, -19, 4, -17],\n [-6, -10, -22, -14, -6, 26, 24, 17, -15, -2, 26, 1],\n [-25, -6, 14, -5, -25, 3, -26, 19, -14, -24, -7, -22],\n [-25, -1, 26, 2, -9, -18, -5, 1, -15, 10, -9, 7],\n [15, 15, -24, 19, -22, -4, -14, -3, 1, -10, -21, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "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, -15, 8, 21, -22, -25, -16, -23, -5, -26, 18],\n [23, -11, -25, 14, 0, -15, -22, -22, -5, -14, -11, -1],\n [24, -18, 21, 5, -8, 9, 1, -12, -18, -11, -21, -19],\n [6, 5, 19, 9, 15, 21, 9, 7, -25, -14, 16, -17],\n [11, -20, 20, 25, 24, -24, 26, 0, -13, 3, 7, -4],\n [21, -10, -12, 18, 17, -20, 25, 25, -24, -18, -24, 21],\n [25, 8, 13, -19, -1, -12, -22, -14, -12, 12, -15, 8],\n [-19, -17, 7, -19, -5, 23, -15, -5, 0, -9, -8, -22],\n [-11, 22, 14, -17, -8, 17, -26, -5, -10, 8, 12, 25],\n [-18, -22, -18, 24, -16, -13, 19, 13, -3, -7, 6, -23],\n [-11, -2, -26, 24, -3, -24, 5, 7, 22, -2, 16, -24],\n [-20, 15, 8, 2, 13, -2, 1, -3, -22, 0, -17, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-9, 11, -19, 23, 11, 3, -18, 21, 16, -2, 3, -25],\n [-10, 18, -20, -5, -17, -1, -14, 15, 1, 9, -16, -18],\n [-11, -10, -22, -22, 11, 4, -25, 0, 19, 16, -8, 16],\n [-2, 25, 11, -14, 2, -8, 8, -2, 21, -18, 8, 24],\n [-12, -5, -14, 22, 3, -6, -2, -2, 13, -5, 19, 14],\n [-24, -18, -3, 17, 20, 5, -10, 14, -3, -19, -21, -18],\n [-12, -3, 23, -16, 4, 19, 18, 18, -14, 3, -2, 21],\n [-15, -6, -3, -1, 23, -15, 10, 22, -6, -4, -26, 18],\n [-17, 8, 11, 21, 1, -26, 24, -19, 14, -4, -7, 5],\n [-4, -20, -16, -19, 16, -13, -13, 9, 25, 14, 13, 20],\n [0, -7, 11, -2, 21, 21, 2, -13, 1, 3, -12, -6],\n [-15, 23, -16, 12, -21, -24, 14, -12, 7, -23, 7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[17, 12, 14, -21, -5, 10, 5, 1, -1, -23, -17, 0],\n [-7, 9, -22, -10, 23, 5, 8, -4, -14, -26, 4, -8],\n [-4, 7, -23, 21, 21, 22, 26, 17, 7, 3, -17, -21],\n [-15, -15, 22, -9, 9, 8, -2, 22, 14, -5, 3, 17],\n [2, -20, 21, 13, -24, -6, 18, -7, -18, 14, 9, -13],\n [-9, 6, 24, -25, 10, 4, -5, 19, -18, -7, -7, 20],\n [25, -26, 3, -8, 9, -13, -26, -22, -17, -18, 22, -13],\n [12, -9, 15, -2, 9, 4, 19, 8, 0, -5, -16, -17],\n [-19, 14, 1, -4, -21, -13, -3, -18, 19, 13, 11, -2],\n [11, 3, -5, -25, -2, -3, 10, -24, 16, -1, 3, 2],\n [-20, -18, 18, 3, -11, 17, 13, -13, -1, 19, 10, -17],\n [3, -5, 3, 5, -13, -4, -10, 9, 2, -3, 20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, -12, -5, 0, 25, 7, 6, -6, -3, -7, 22, -23],\n [10, 10, 19, 6, 4, 7, -5, 15, 3, -22, 14, 18],\n [-4, 26, -14, -18, -13, -10, 8, -9, -15, 14, -11, 3],\n [-14, -9, -15, 7, 24, 6, -21, -9, -24, -21, 9, 22],\n [23, -5, -20, 3, -25, 5, -12, -5, 22, 11, -19, -19],\n [12, 9, -7, 10, -19, -13, -7, 8, -2, -9, 20, -6],\n [10, 20, 4, -21, 15, 25, 20, -7, 1, 14, 9, 13],\n [-1, -14, 22, -23, 7, 10, 7, -11, -4, -4, -12, -2],\n [2, 9, -12, 10, 8, 19, 12, 20, 10, 14, 1, 18],\n [3, -20, -23, -20, 6, 20, 20, -9, -12, 8, 10, -22],\n [21, -4, -17, -2, -5, 4, -4, 1, 18, -12, 13, 25],\n [-20, 19, 11, 13, -12, 22, -22, -15, -14, -24, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 1, -12, -9, 26, 25, -20, -13, -3, 25, 24, -3],\n [-16, 12, 16, 13, -17, 16, 6, -7, 15, 12, -5, 8],\n [24, 1, 9, 3, -21, -26, -23, -2, 12, -16, 11, 10],\n [-15, 2, 7, -9, -18, 19, -15, -18, -26, -20, 12, 15],\n [7, 5, 1, -1, 9, 13, -13, 18, 4, -11, 12, 15],\n [-16, -16, 11, -15, 15, -18, -5, 11, -18, -24, 12, 8],\n [25, 3, -1, -19, 5, -5, -19, 18, -25, -13, -22, -14],\n [-4, -14, -8, -3, 8, -13, -23, -1, -17, 11, 11, 7],\n [7, -8, -24, 25, 9, -23, -1, -16, -24, 22, -18, 19],\n [-25, -13, -24, -25, -5, 2, 6, 9, -17, 20, 26, 17],\n [11, -6, 4, 8, -24, -8, -5, -7, 9, -8, 19, -23],\n [5, -19, 24, -1, 24, -26, -1, 20, 16, -18, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-8, 21, -11, 1, -24, -9, -14, 0, 25, 13, 12, -3],\n [2, -5, 24, -1, -7, -3, -15, -9, 20, -15, 11, 5],\n [22, -4, -23, -15, -10, -6, 10, 2, -21, 20, 1, -19],\n [4, -7, -11, -14, -12, 25, -14, 20, -25, 26, -7, 1],\n [-9, -20, -6, 14, 12, -18, 17, -17, 4, 15, -14, -22],\n [13, 15, 11, 16, 9, -25, -21, -14, 2, 17, -13, 3],\n [-2, 13, 8, 10, -20, 23, 11, -9, -19, -20, 7, 9],\n [14, 21, 24, -17, 13, 2, -11, -2, 2, -19, -7, 9],\n [25, 0, -14, -1, 15, -2, 1, -18, -1, -15, -1, 20],\n [-5, -26, -15, -3, 3, -13, -4, -25, -24, -21, -8, -6],\n [18, -7, -6, 13, -23, -2, 24, -20, -20, 6, 24, -1],\n [-10, -19, -1, 26, -12, -7, -8, -20, 18, -26, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "513", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-9, -19, -12, 23, -21, 10, -5, -16, -1, -19, -18, -14],\n [-24, -24, -20, -24, -16, 19, 1, 26, 15, 4, 25, -18],\n [0, -15, -19, 17, 14, -5, -9, 3, 22, -16, 26, -25],\n [2, 26, -1, 24, -13, 1, 8, -21, 9, -15, 7, -21],\n [10, 10, -19, 10, 13, 6, 25, 14, 19, 4, 7, -16],\n [9, -23, -10, -11, 3, 12, 17, 22, -22, 13, 25, 10],\n [16, -1, 1, -8, -6, 1, -8, 9, -16, -8, -22, -25],\n [-2, 24, -1, 3, -10, -6, -7, -9, 20, -11, 1, -15],\n [13, -21, -3, 23, 16, -21, -10, 15, -8, 20, 21, 1],\n [2, 22, -20, -8, -19, -19, -22, 16, 7, 23, -6, -23],\n [17, 9, -22, 22, -4, -8, 15, 19, -12, -13, 21, -19],\n [-18, 13, -16, 17, 19, -9, 5, 17, 9, 18, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "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, -6, -16, 17, 23, 7, 24, -22, 1, 25, -17],\n [21, -15, 14, -24, -26, 10, 13, 22, -26, -14, 11, -12],\n [-20, 3, -3, -19, -24, -12, 9, 14, 16, 26, -13, 0],\n [3, 14, 17, 10, 26, -21, -8, 10, -26, -2, -17, 19],\n [-1, -4, -10, 3, 0, -16, -23, -9, -8, 9, 17, 19],\n [23, -1, -26, -7, -16, -2, -8, 5, -26, -26, -24, 19],\n [13, 5, 20, 9, 16, -19, 3, 12, 7, -19, -2, -1],\n [0, -8, -4, 14, -11, -19, 3, -19, -16, -20, -6, 7],\n [-6, -22, 23, 16, -10, -6, -21, 18, -20, -16, -9, 11],\n [-15, -5, -24, -8, 16, -4, 7, -24, -4, 22, -22, 2],\n [7, 17, -22, 2, 18, -3, 12, -6, 5, 16, -22, -9],\n [11, 8, 11, -11, 8, 23, -3, 9, -22, -18, -23, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[0, -5, -16, -22, -17, -24, -12, 19, 10, 13, -10, -7],\n [24, -23, 7, 7, 4, 7, -24, 1, 14, 10, 25, 2],\n [-12, 9, 8, 14, -17, -10, 3, 25, -19, -4, -8, 10],\n [16, 9, -23, -1, 20, 13, 0, -14, 25, 17, 7, 6],\n [19, -1, -7, -19, -11, -22, 7, 20, 0, 9, -23, 15],\n [26, 23, -20, 10, 9, -3, -12, 23, 22, -21, -1, -1],\n [-2, 6, -24, -18, 10, 11, 3, 0, -14, -4, -24, -4],\n [8, -3, 10, -15, -7, -9, -20, 25, -1, -15, 7, 21],\n [5, 3, -25, -19, 6, 19, 15, 3, 26, 18, 15, 18],\n [1, -14, -3, 6, -22, 21, -21, -23, 15, 16, 7, 2],\n [-6, -1, 5, -5, 14, -13, 7, 10, 17, -26, 5, 5],\n [24, -3, 17, -6, -15, -7, 10, -7, -25, -13, -10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510", "dataset": "MATH"}
{"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, -12, 22, 7, 26, -19, 15, -24, -16, 0, -18, -12],\n [5, -16, -24, -1, -20, 1, 12, -23, 3, 11, 24, -13],\n [9, 4, 24, -8, 22, 26, 24, -15, 22, -12, -18, 0],\n [-7, 1, -2, -11, -9, 23, 9, -23, -6, 0, -26, -22],\n [17, 19, -17, 23, -6, -17, -1, -11, 11, -24, -7, 20],\n [-22, -21, -2, -2, -15, -26, 15, -24, -6, -22, -12, -23],\n [-8, -10, -19, 10, -3, -23, -3, -8, -3, 14, 18, -6],\n [-10, -19, 4, -8, -16, 26, 19, 23, -4, 10, 1, -4],\n [-15, -11, -11, -13, -20, -6, -6, 14, 8, 19, -3, -26],\n [-13, -7, 1, -9, -24, 0, -21, -23, -26, -6, 8, 1],\n [-9, 25, 25, 8, 26, -6, -11, -1, 12, -18, -4, -25],\n [-24, 6, -3, -4, -21, -6, 20, -22, -14, 13, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-18, -24, 4, 19, 12, -14, 14, -16, 14, -16, 19, 20],\n [22, -26, 8, 8, -24, -23, -3, 3, 5, 22, -7, 9],\n [-14, 12, -23, 1, 13, 16, 24, -20, -18, -5, -23, 9],\n [6, -21, -24, 8, 6, -20, 14, 8, 20, -24, 16, -9],\n [-24, 25, 12, 0, -18, -10, 14, 15, 18, -22, 19, -23],\n [-13, 2, -16, -5, 15, -22, 26, -15, -6, -12, -3, -14],\n [5, -1, 13, -1, 9, 18, 3, 20, -18, -3, 11, -9],\n [-18, -5, 11, -6, -20, -15, 9, -16, -24, 0, -20, -25],\n [-17, -24, -10, 16, -26, 7, -14, -13, -10, 7, -10, 24],\n [14, -2, 17, 3, 21, 9, -16, -6, -7, 2, -23, 7],\n [15, 14, -10, -15, -23, 14, -13, -23, 7, -9, -14, -17],\n [-13, -18, 16, -7, -26, 17, 2, -10, 22, -19, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, -7, -2, -6, -14, -14, 20, 23, 3, -14, 13, -20],\n [24, 15, -15, -25, -13, 15, -10, -14, -26, 20, -26, 20],\n [-1, 25, 20, 19, -14, 7, 13, -18, 24, -8, -4, 14],\n [1, 3, -20, -13, -25, -15, 16, 22, -25, 1, 1, -15],\n [3, 20, 13, 13, -5, -9, -13, -2, -17, 9, 21, 21],\n [26, 22, -18, -16, 0, -14, -26, 12, -16, -24, -25, 19],\n [15, -3, -7, 22, 13, -12, -21, -7, -5, -25, -12, 21],\n [7, 19, 4, 3, 1, 25, 6, 14, 22, -6, 19, -4],\n [15, -14, 18, -1, -8, 0, 13, -20, -2, 22, 13, 9],\n [-20, -7, -3, 1, 22, -22, 25, 9, 4, 24, 6, 26],\n [-3, -17, 11, 17, 22, -22, 4, -18, 5, 14, -22, 24],\n [0, 1, 16, -15, -22, -19, -10, -19, 7, -4, -9, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[26, -17, 12, 14, 17, 17, -22, 16, -10, 20, -16, 20],\n [21, -8, -6, 17, -24, 13, 16, -26, -3, 9, -21, -17],\n [20, 13, 19, 7, -3, -4, -7, 26, 11, 8, 7, 19],\n [23, 20, 9, -11, -4, 17, 22, -26, 25, -18, -15, 10],\n [-10, -24, 11, 2, 4, 8, 11, 26, -1, -14, 26, -8],\n [5, 20, 0, 12, -14, 25, 7, -8, -8, -24, -24, -1],\n [-21, -14, 19, 11, 0, 14, -3, -17, -11, -4, 20, -15],\n [1, -14, -9, -25, 19, -10, -4, -4, -26, 16, -13, -15],\n [-13, 22, 17, 11, 14, 17, 22, -11, 7, -9, 21, -17],\n [-8, 3, -23, -20, -11, 24, 10, -22, 12, 22, 6, 8],\n [21, 7, 6, 26, 12, -17, -24, 23, 2, 8, 4, 12],\n [-12, -26, -8, 10, 0, -6, -20, 16, 6, -25, -13, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-24, -13, -22, -10, 12, -26, 16, 1, 11, 21, -13, -10],\n [-12, 19, -20, 15, 24, -20, 20, -3, -1, -13, 20, -8],\n [26, -1, -11, 7, -25, -26, 21, 24, 9, 8, 16, -3],\n [22, -22, 2, 14, -26, -18, 9, -11, -12, -17, 10, -11],\n [11, 21, 9, 26, -12, -24, -8, 14, 10, 21, -24, -19],\n [-3, -13, 8, -11, -20, 14, 8, -19, -15, 22, 19, -11],\n [24, -23, 8, 18, 14, 18, 5, -15, -6, -12, 8, -24],\n [-25, -21, -11, -4, 4, 23, 14, 3, -24, -11, -23, 19],\n [9, 1, 23, 23, 23, 1, 26, -24, -1, 12, -14, -20],\n [-14, -23, -11, 1, 20, -14, 15, -17, -22, 9, -8, 3],\n [20, 14, 21, 1, 4, 9, 16, 22, 26, -26, -18, -15],\n [-4, -15, 15, -18, 26, -1, 3, -7, -11, -14, 8, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-23, 24, -2, -14, 1, 18, -15, -3, 1, -26, 7, -24],\n [-5, -6, 0, -6, -5, -14, 17, -11, 19, -3, 19, -10],\n [-22, 11, 15, 0, 14, 5, -1, -20, 9, -20, 16, 0],\n [11, 21, 21, -3, -3, 18, 17, 2, 0, 7, -6, 18],\n [-26, -17, 3, 1, 15, 3, 1, 2, 4, 16, 14, -23],\n [22, -8, -17, 18, 4, 7, 14, 12, 15, 17, 4, 25],\n [-16, 9, 17, 17, 5, -4, 13, 25, 19, 12, -24, 1],\n [-2, 1, -8, 19, -8, 15, 17, 2, 23, -8, -9, 18],\n [22, 26, -3, 11, -11, -9, 14, -14, -23, -14, 8, -23],\n [-8, -3, 6, 6, -18, -24, -24, 3, -9, -25, 5, 16],\n [-18, -25, -7, 0, 9, 14, 19, -8, -11, -1, -13, 20],\n [-9, 1, 20, -8, 3, 14, -6, -6, 21, 3, 22, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "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, 14, 19, 5, 3, -5, -3, -17, -3, -26, 25, 8],\n [-11, -22, 4, 18, 10, -2, 16, 22, -2, -24, 11, 5],\n [21, -7, 3, -25, -22, -8, -7, -5, -16, -9, 0, 4],\n [8, 17, 18, -6, 25, -7, -18, 4, -18, -20, 6, -26],\n [-8, -24, 12, -15, 3, -11, -14, 23, -3, -10, 0, 2],\n [14, -13, -22, 16, 25, 11, -21, -3, 13, 6, -18, 15],\n [22, -24, -4, -6, -5, 18, -19, -7, -13, 3, 25, -19],\n [-8, 18, 11, 9, -21, 25, 7, -17, 4, -16, 16, 8],\n [-16, 13, 5, 22, -1, -5, -26, 21, 2, 25, 12, -5],\n [5, -2, 13, 18, 2, 10, 5, 3, -9, 17, 21, -24],\n [-15, 24, -7, 23, -19, 4, -3, -14, -19, 15, -13, -12],\n [-6, -12, -1, 11, 19, 11, 6, -17, -8, -16, -24, -4]]\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[[-21, 14, 14, 2, -23, -24, -7, 24, 16, 24, 22, -19],\n [-21, -22, -19, -19, 8, -8, 21, -17, 8, -18, -19, -19],\n [-19, -7, -20, 19, -5, -10, 17, -22, 7, -2, 20, 16],\n [-12, 4, 18, -8, 17, 4, 20, -15, -4, 23, -4, 9],\n [-16, -5, 20, 3, -22, 10, -7, -17, -5, 15, 3, 3],\n [-5, 11, 11, 11, -20, 23, 9, -13, -16, -20, 5, -9],\n [25, 7, -25, -20, 16, 4, -9, -7, -20, -5, 25, 10],\n [7, 19, 12, 15, 23, 13, -11, -13, 14, 5, 11, 12],\n [-1, 3, 14, 12, -18, 5, 26, -20, -15, -4, -10, 25],\n [-6, -15, -5, -4, -22, -9, 10, 10, -20, -24, -26, -21],\n [-20, 0, 4, -19, -13, -12, -20, -20, 6, 14, -20, -7],\n [-20, 23, -13, -12, -9, -17, 8, 0, 16, -26, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[21, -24, 22, -24, -16, -23, 3, 12, 5, -11, -10, -16],\n [9, 5, 8, 0, 21, 7, -22, -2, 1, -9, -24, 1],\n [-25, 7, -5, -5, 26, 3, 7, 21, -26, 2, -8, -8],\n [14, 25, 14, 2, 16, 6, 24, -10, 11, -26, 23, 14],\n [6, 9, -5, -9, -10, 5, -7, 24, -4, 1, 19, -1],\n [-20, 14, -7, 14, 20, -16, -20, 11, 0, -18, -23, 22],\n [11, 2, 22, -1, -2, -13, 10, 23, 1, -19, 15, -16],\n [8, 4, 7, 19, 9, -10, 22, -6, -1, 14, 1, 26],\n [-5, 14, -24, 1, 9, -25, 19, -7, 13, 23, 9, -19],\n [12, -2, -12, 3, 20, 7, -23, -5, -2, -18, -4, 12],\n [23, -15, -13, -20, 4, -21, -4, -8, -6, -8, 20, -8],\n [17, 7, 16, -14, 9, -2, 6, -6, 7, 19, -2, -9]]\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 sum of all singular values:\n[[16, -16, -8, 22, 22, 7, -25, 3, 18, 11, -12, -16],\n [-3, -23, -8, 2, -13, 23, -10, -19, -14, -4, 2, 20],\n [-16, -11, 23, 17, -4, -15, 11, -3, 4, 11, 9, -26],\n [-1, -10, 9, -10, 10, 0, -2, 3, 14, -2, 11, 5],\n [-15, 22, -6, 15, 7, -26, -14, 26, -6, -26, -14, 4],\n [-4, -24, -16, 2, 21, -9, -2, 7, -9, 22, -26, 1],\n [-23, 25, -6, -21, -6, 10, 3, -7, 14, 5, 26, 4],\n [9, -2, -22, -19, -10, -12, -7, 18, 20, 2, 9, 23],\n [24, 1, -19, -13, 6, 7, 25, 2, -5, -24, 21, -4],\n [-24, -21, 13, -4, -15, -22, -22, -24, -23, -3, -22, 4],\n [8, 15, -8, -19, 1, 11, -4, -20, 11, -14, 18, -6],\n [10, -21, -17, 0, 25, -1, 15, 1, -11, 23, 1, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-26, 26, -24, 3, -8, 6, -19, -8, 9, 21, 10, -22],\n [7, 11, 0, 12, 20, 15, 15, 24, -3, 21, 4, -5],\n [-4, 14, -3, 13, 5, 24, 6, 1, -10, -1, -9, -12],\n [11, -5, 22, -9, -6, -8, -25, 3, -2, -1, 12, -10],\n [20, -11, 0, 22, -24, 15, 11, 2, -25, 16, 13, -13],\n [-15, 25, -3, 1, 12, -9, -2, 10, -21, 18, 3, 4],\n [7, -8, 1, -19, -16, 26, -11, -1, -26, 4, 0, 21],\n [17, 22, -18, -1, -21, -20, -14, 22, -17, 16, 19, 22],\n [4, 21, 10, -9, -16, -17, 1, -6, 26, -2, -21, 15],\n [-16, 6, -22, 7, 5, 16, 19, -3, -14, 16, -21, 7],\n [24, -2, 14, -4, 23, 19, -14, 1, 17, 17, -14, -20],\n [21, -10, -18, -13, 3, 14, 11, 3, 6, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[25, 0, 6, 24, 20, 22, -7, 1, -19, -5, 8, 4],\n [17, -3, -12, 23, 18, 4, -22, -5, -10, 1, 26, -24],\n [-8, 11, 0, -10, 5, 10, -6, 10, 24, -16, -26, 3],\n [-1, 18, 22, 16, 23, 9, -1, 15, 0, -1, 16, -9],\n [6, 9, 10, 7, -1, -5, -3, -15, -16, -6, -11, 9],\n [-20, 26, 1, -3, 26, -14, -13, 16, 4, -19, -26, 13],\n [24, -10, 14, -14, 20, 0, -14, 13, 0, 5, -15, 16],\n [25, -14, -11, 7, -21, 21, -9, -10, 20, 12, -13, -20],\n [-21, -15, 7, 26, -26, 23, 2, 1, -22, -6, 12, 20],\n [26, 11, 7, -6, -3, 22, -14, 18, 19, -4, 5, -19],\n [20, -16, -14, 26, -7, -26, -25, -16, 19, 3, -22, -20],\n [-3, 4, 21, 3, 16, -12, 9, -17, -26, -20, 17, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "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, 16, 22, 3, -26, -12, 26, -7, -5, -2, 23, 26],\n [9, 24, 10, 19, 18, 0, -8, -8, -11, -6, 24, 6],\n [15, 4, 7, -12, 24, 9, 26, -1, 3, 4, -2, -23],\n [-15, 26, -8, -18, -2, 21, 20, 14, 24, 23, 26, -20],\n [0, 21, 20, 16, -21, 8, 5, -13, -21, 22, 24, -9],\n [4, 25, -11, -24, 4, 11, -10, 25, -22, 26, -11, -10],\n [4, -11, -6, 14, 12, 10, 14, 26, -17, 5, -2, 26],\n [6, 12, 26, 10, 11, 11, 1, -12, -19, -26, -17, 8],\n [21, 6, -11, -13, -22, -11, -6, -16, 23, -20, -19, -10],\n [3, -13, 22, 17, 23, 6, -3, -20, 11, -12, 23, 16],\n [-2, -10, 6, -25, 12, -17, -13, -15, -10, -13, 24, -17],\n [17, 12, 13, 2, 18, -21, 13, 4, 10, -18, 16, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "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, 11, -19, 7, -10, -10, 3, -9, 26, 12, -12],\n [18, -7, -2, -13, 0, 20, 8, 1, -21, 14, 4, -13],\n [-11, 22, 17, 9, -22, 5, -16, -5, 16, 13, 1, 23],\n [-21, 12, -21, 19, -7, 11, -23, -2, -14, 22, -15, -18],\n [25, -24, 5, -16, -22, 8, 22, -3, 14, -21, -9, 11],\n [-21, -5, 15, 16, -13, -15, -2, -7, -9, -3, -12, 4],\n [15, -26, -12, 7, 25, -25, 9, -4, -3, 19, 5, 24],\n [19, -14, 6, 15, -13, -10, -11, 5, -12, 16, 4, -15],\n [6, -24, -16, 26, 16, -22, 20, 0, 25, -11, 8, 13],\n [-11, -11, -5, -23, 5, 0, -12, -8, -1, -12, 18, -17],\n [7, 11, 22, -1, -19, -11, 2, 5, -6, 5, 18, -15],\n [21, 12, -17, -21, 10, -9, 21, 4, 8, -24, -22, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[6, 9, -17, 18, -24, -16, -24, 1, 15, 1, -18, -1],\n [2, -17, 0, 18, 5, -9, 26, -9, -5, -10, 22, -2],\n [-1, -22, -18, 17, 17, -3, 24, -20, -7, 17, 14, -19],\n [-8, 26, 8, 16, 17, -2, -10, 12, -2, 8, 12, 12],\n [19, -25, -11, 26, 15, -13, 2, 12, -25, -17, -25, 0],\n [-14, -25, 15, -13, -10, 24, 17, 22, 11, 9, 7, 2],\n [20, -4, -4, -11, 17, -20, 18, -26, -8, 18, 6, 7],\n [-26, -15, -2, -4, -2, 4, -3, -17, -25, 6, 10, -4],\n [-25, -23, -4, 19, 14, 11, -4, -15, 17, -3, 2, 14],\n [1, -12, -17, 7, 2, 4, -4, -9, -20, 0, -18, -7],\n [26, -6, 1, 23, -24, 18, -17, -10, 8, -6, -18, -10],\n [5, 21, 11, 1, -9, -21, -21, -10, 26, -17, -25, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[16, -2, 11, -26, -11, -1, 14, -15, -18, -14, -20, -26],\n [4, 8, -3, -24, -8, -23, 1, 17, 3, 9, 26, 15],\n [-23, -4, -16, -23, -16, 22, 26, -3, 25, -7, 18, -10],\n [-14, -10, 24, 25, -12, -23, -9, 16, -18, 21, -24, 0],\n [-9, -10, -17, 10, 2, 20, 25, 23, -22, 20, -21, 13],\n [8, -22, 23, -12, 0, 17, 24, 12, 6, -3, -6, -25],\n [-8, 18, 25, -9, -17, 18, 10, -4, 18, 14, -26, -21],\n [-26, -9, 0, 21, 13, 11, 18, -10, -1, -14, -17, 11],\n [-1, 4, -4, 23, -7, -4, 18, 0, -12, 11, -16, -19],\n [-13, -14, -5, 7, -26, 10, 5, -16, -17, 3, -15, 15],\n [14, 7, -2, 9, -23, -6, 3, 11, -15, 12, -2, -8],\n [-25, -5, 3, 24, 9, -24, -4, -23, 1, -13, -21, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "dataset": "MATH"}
{"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, 10, -20, -14, -26, -3, 7, 25, -17, -21, -23, -19],\n [19, 21, -12, 18, -15, 12, 20, -21, 26, -6, 19, 5],\n [5, 0, 20, -16, -5, 9, -4, 10, -4, 0, 7, -7],\n [-12, 15, -23, 2, 13, -16, 22, -20, -16, 15, 6, 3],\n [5, 13, 10, -14, -20, -3, -16, 4, 17, -13, 17, -1],\n [-26, -21, 4, 16, 16, -15, -26, 25, 25, -21, 2, 3],\n [-14, 3, -15, -17, 12, -17, -9, -21, -19, -7, 14, -11],\n [-25, -16, -3, -8, -23, -24, -12, 13, -23, 16, -10, -18],\n [-2, -26, 13, -25, 18, 6, -5, 15, -15, 0, -16, 15],\n [-13, -13, 13, 16, -5, -18, -12, 6, -8, 4, -9, -15],\n [13, 10, 18, 22, -26, 7, -20, -25, -5, -23, 18, 19],\n [-7, -24, -18, -9, -11, 24, 25, -18, -8, -21, 17, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[26, -21, -22, 2, 19, 0, 24, 23, 18, 14, 25, -1],\n [1, 5, -2, 26, -20, 3, 26, 4, -15, -18, 7, -24],\n [10, 23, 1, 19, -5, -1, -8, -6, 10, -17, -11, -3],\n [-2, 25, -1, -26, 26, -23, 10, 16, -13, -3, 0, 16],\n [0, -3, 13, -26, 12, -14, -7, 11, 9, -15, -22, -22],\n [-10, 11, -17, -11, -3, 2, 26, -13, -17, 2, 1, 26],\n [-10, -22, -25, 9, 23, 13, 19, 18, 12, -18, 9, -22],\n [-12, -18, -2, 23, 1, 0, 19, 20, 6, 24, 6, 11],\n [-19, -23, 21, 16, 9, 16, 4, -17, 22, 14, 15, -19],\n [3, -13, 18, 8, 19, 19, -24, 2, -11, -17, -23, 25],\n [23, -23, -25, -16, -12, -16, 26, -4, 11, 23, 3, 23],\n [-26, 18, 6, 18, 26, 10, -4, 22, 21, 26, -9, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-10, -20, -12, 24, 0, -18, -6, 26, 10, 2, 15, 18],\n [6, 26, -21, -2, 8, -10, 17, 0, 16, 13, -2, -15],\n [16, 10, 13, 17, 11, 14, -2, 22, -25, -26, 23, -24],\n [2, -13, 18, 7, -5, 9, -12, 10, -17, -18, 23, 8],\n [19, 15, -10, 20, -9, 22, -2, 8, -11, 24, 18, 22],\n [-2, -11, 14, -3, 26, -15, 8, -18, 21, 10, 5, -8],\n [-5, 18, 7, -8, 23, -15, -9, -22, -1, 25, 0, -7],\n [-19, -11, -25, 18, -26, -22, 4, -4, -6, -15, -23, 10],\n [-16, 15, 13, 26, -18, -1, 12, 0, 2, 19, 16, 23],\n [-2, -9, 3, -19, -25, -5, -6, 12, -1, 2, -22, 19],\n [-13, 8, -21, -4, -10, -3, 13, 2, 25, 3, -3, 8],\n [20, 10, 24, -25, -6, 13, 14, -22, 8, 17, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509", "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, -2, -11, 4, 6, -10, -6, 25, 8, 22, -4, 22],\n [-11, 11, 23, -13, 25, 13, 24, 14, 26, 23, 6, -6],\n [-10, -23, -11, 3, 17, 18, 7, -5, 17, 15, 2, 20],\n [-22, -26, 13, 26, -2, 23, -21, -4, 6, -13, 15, 9],\n [-9, 24, 13, 17, -17, 18, 12, 22, -15, 11, -4, -20],\n [18, 19, -2, -14, 11, -8, 18, -5, 14, -16, 15, -24],\n [-8, 0, -20, 10, 0, 20, 7, -16, 11, -22, 25, -20],\n [9, -22, -22, 0, 2, 0, 5, -2, 15, 23, 7, -12],\n [14, 7, 8, -7, -3, 7, 7, 24, 19, 0, 23, -6],\n [6, 12, 13, 17, 9, -2, -20, 23, 23, -17, -17, 11],\n [-3, 17, -17, 18, -1, 3, 0, 17, -8, -26, 6, -16],\n [23, 7, 11, -11, -26, 14, 1, -12, -11, 19, 5, 12]]\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[[-26, 21, -18, 2, -2, -16, 15, -16, -21, 7, 23, 17],\n [-13, -19, -2, -23, 23, 4, -6, 18, 5, -13, 25, 1],\n [-2, 1, -12, 25, 24, 19, 17, -5, 20, -21, 24, -25],\n [-21, -4, -1, -16, -26, 1, -5, 14, -14, 14, 20, 23],\n [9, -5, -23, 17, 14, -9, 11, -10, -2, -10, 2, 18],\n [17, 19, -19, 2, -12, 14, 6, 22, -17, 10, -16, 8],\n [7, 5, -5, -23, 26, -25, 6, -18, 8, 11, 4, -13],\n [4, 6, 17, 26, -11, -7, 24, 23, -13, 8, 19, 22],\n [18, 6, 2, -19, 26, 7, 24, 20, -13, -13, 23, -12],\n [15, 23, -7, 1, -23, -20, -25, -18, -4, 9, -15, -4],\n [4, 15, -16, -26, -14, 12, 2, -21, 4, -18, -9, -24],\n [5, 18, -24, 18, 3, -21, 23, 0, -25, -7, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "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, 10, 2, -18, -23, 19, 13, -14, -21, 19, -18, -1],\n [22, 12, 14, 20, 15, -13, 21, 7, -23, -6, 4, 20],\n [16, -6, 16, 2, -3, 18, -11, -18, -6, -25, -25, 10],\n [10, -22, 19, -21, 21, 21, -19, 5, 10, -14, -24, -18],\n [-23, 1, 13, -11, -16, -8, 15, -5, 12, -15, 3, 13],\n [15, -22, 10, 18, 5, 7, -15, 16, -25, 20, 25, -20],\n [5, 13, 8, 22, 25, -21, -5, -2, 20, -14, -4, 18],\n [17, 19, -18, 15, 10, 26, 10, 26, 3, -7, 11, 17],\n [22, -11, 23, -5, 11, -17, -7, 26, 14, -25, -24, 15],\n [-19, -18, 1, -6, 24, 6, 7, 25, -23, 21, 26, -2],\n [5, -15, -25, 20, 23, 21, 26, -15, 23, 19, -1, -6],\n [17, 10, 9, -9, -3, 3, -10, -11, 15, -10, 17, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[0, -23, 8, -26, -15, 2, -19, -19, -15, 9, 21, 7],\n [9, -23, -16, -24, -17, -15, 22, -18, -6, 7, -5, -9],\n [17, -21, -2, 23, 18, -12, -26, 13, -9, 25, 17, 4],\n [-7, 17, -2, 6, -17, 2, -8, 1, 0, -8, 16, 4],\n [8, -13, 23, -21, -18, 14, 0, -10, 9, -23, -3, 24],\n [-11, -10, -24, 12, 10, 26, -24, 17, 24, 14, 8, -24],\n [-11, -7, 18, -21, 6, 16, 23, 0, 3, 8, -9, 3],\n [16, -1, -12, 5, 8, -15, -6, -15, 22, -26, -16, -2],\n [20, -18, 12, 16, 0, 2, 23, 0, 1, 12, -9, -12],\n [-11, 20, -4, 3, 9, 8, 1, 19, 26, -24, -11, -12],\n [-8, -17, 26, 22, -23, -5, -9, -5, 15, -11, -24, 17],\n [24, 26, 8, 14, 12, -11, -6, -6, -26, 3, 20, 7]]\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 difference between the largest and smallest singular values:\n[[21, 12, 19, -4, 7, 3, 23, 6, -11, 14, 3, -24],\n [18, -25, -1, -9, -25, 13, -24, -10, -3, -25, -21, 13],\n [-1, 22, -21, -15, -6, -11, -21, 7, -24, 14, -8, 2],\n [5, -17, 0, 2, -14, -7, 1, 0, -14, -2, 2, 25],\n [-12, 18, 18, 3, 11, 5, 23, -20, 8, 6, -15, -4],\n [-22, 16, 17, 4, -11, 6, 26, 23, -26, -5, 1, -22],\n [-23, -26, -12, 10, 12, 22, 25, 11, 18, -3, -4, 20],\n [-20, 4, -20, -14, -23, -9, 13, -8, -11, 25, -9, -11],\n [21, 4, -2, -25, 19, 24, 1, -11, 9, 18, 13, 8],\n [-3, 8, 3, 10, -16, 18, 7, 11, 12, -3, 2, -23],\n [14, 23, 3, -13, -3, 11, 25, 7, 9, -12, 8, 2],\n [9, -23, -12, -16, 22, -12, -6, 8, -4, -17, -23, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"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, -25, 11, -8, -3, -19, -21, -7, -13, 13, -21, -15],\n [14, -20, 18, 3, -11, -19, -13, 21, -7, 1, -21, 3],\n [-23, 9, -24, -17, 11, 0, -9, 18, -16, 9, 13, 8],\n [17, -14, -4, 16, -18, -23, 16, 13, 23, 4, -24, 9],\n [-10, -11, 12, -25, -22, 6, -14, -15, -8, -5, 13, -19],\n [17, -23, -20, 21, -5, -9, -21, 23, -23, 26, 14, 18],\n [24, -15, 21, 10, -25, -24, 18, -6, 12, -14, 21, -13],\n [3, -9, -14, -13, 14, 13, -2, 10, 0, -4, -20, 21],\n [-17, -2, 8, -3, 22, 15, -16, -7, -17, 23, -6, 1],\n [1, 0, 6, -23, 8, -7, -21, -21, -10, -8, 22, -10],\n [22, -24, 19, 7, -23, -4, -9, 7, 2, 17, -12, 18],\n [-16, 12, -18, 20, 8, -17, 13, 11, 2, 19, -21, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -18, 14, 25, 21, 18, -14, -1, 17, 26, -7, -25],\n [-23, -20, -8, 8, -16, -8, 5, -13, 22, -22, -2, -13],\n [12, -15, 22, -7, 26, -9, -26, 16, -23, -15, -1, 5],\n [10, -12, 25, 8, -1, -12, -19, 1, 3, 16, 17, -24],\n [-21, 4, -1, -19, 12, 2, -10, -11, 22, 18, -23, -17],\n [-11, -8, 12, 23, -14, -23, 5, 26, -9, -11, -2, 23],\n [-11, -5, -3, 1, -4, -6, -18, -25, 11, 1, -1, 0],\n [-2, -6, 11, -2, 11, 19, -16, 1, 22, 9, -23, -8],\n [-3, -5, 21, -2, -19, 24, -7, -26, -23, -15, -2, -6],\n [-8, 7, -21, 25, 8, -24, 6, -18, -20, 14, 0, -26],\n [13, -9, 8, -10, 12, -16, 10, 18, -16, -24, -14, 25],\n [1, 11, 20, 7, 1, -25, 19, -25, 10, -11, -19, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-16, 18, -12, -23, -4, -19, -11, -11, -3, 26, -17, 7],\n [-9, 26, -11, 9, 25, 24, -19, -7, -4, 13, -13, -11],\n [11, -9, 13, 24, 3, 9, 9, 12, 13, 14, -26, -10],\n [1, -20, -7, 15, -3, 26, -26, -9, -1, -13, -8, -9],\n [18, -20, -25, -20, 1, 1, 15, -10, 3, -6, 10, -18],\n [9, 25, -5, -12, -13, 0, -9, -17, 21, -5, -4, 25],\n [15, 14, 21, -22, 24, -2, -26, -3, 6, 10, -20, -3],\n [-12, -16, 17, -10, 22, -4, 22, -23, 4, 7, -17, 10],\n [-17, 15, -16, 4, -17, 16, 11, 26, 15, -19, -16, -7],\n [-3, 24, -20, -6, 17, 26, -21, 4, -15, 10, -14, 22],\n [4, -18, 0, 25, 26, -10, 24, 24, -19, 0, 13, -12],\n [12, -21, 5, 21, -19, 8, 4, 15, -1, 15, -3, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-25, 14, -26, -17, 23, -4, 6, 17, 10, -16, -7, -1],\n [19, 20, -25, -2, -23, -8, -14, -8, -14, -15, -25, 10],\n [23, -4, -8, -24, -3, -4, -23, -9, -15, 8, 0, 16],\n [-13, 4, -24, -22, 2, 12, 25, -10, -8, 8, 6, -19],\n [25, 10, 8, -7, -10, 18, -14, -23, 23, 3, -21, -25],\n [-12, 7, 25, -7, -11, 16, 22, 2, 0, -26, -14, 13],\n [5, -24, -13, 1, 19, -1, -6, 19, 24, -16, 0, 17],\n [-26, 6, 19, -9, -25, -23, 23, -23, -10, 21, -11, -18],\n [-1, -17, -20, -18, 21, 0, 5, 22, -4, 0, -2, 2],\n [-3, -11, -11, 1, -7, 26, -8, -17, -1, -25, -24, 12],\n [-25, -2, 18, -23, -12, -9, -20, 0, -9, -20, 2, 14],\n [17, 6, -25, -9, 19, -4, -21, 16, -2, -8, -19, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[10, -1, 2, 1, 26, -20, 9, -12, 6, -22, 2, -10],\n [18, 0, -10, 24, -23, 22, -15, -4, 23, -16, 9, -15],\n [-18, -3, -9, 0, -18, 6, -21, 24, 6, 13, -21, -23],\n [-24, -14, -1, 7, -14, 26, 20, -19, -15, -19, -8, 14],\n [-17, 5, -6, -4, 0, -2, -20, 15, 8, -25, 1, -20],\n [15, 13, -15, 25, -10, -5, -18, 25, -24, -5, 9, 12],\n [-9, -10, 0, 8, 5, -24, -14, -10, -9, 24, -10, 21],\n [-11, -5, -2, -26, 0, -13, 1, 20, 9, 25, 26, 16],\n [23, 5, 2, -10, 1, 14, -6, -3, 19, 8, -7, 25],\n [-5, -23, -11, -6, 17, -6, 13, 14, -16, 10, 17, -5],\n [-7, -25, 16, -16, -6, 6, 22, -10, 9, -13, 10, 4],\n [-23, -21, 23, -6, -14, 11, -12, -22, 11, -3, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -20, 3, 11, -1, -19, -2, 3, -3, 3, -22, -23],\n [24, 15, -18, 6, 24, 2, 4, 17, -8, 18, 20, -25],\n [-7, -15, 23, -6, 4, 9, -7, 17, -7, 18, 9, 19],\n [26, -9, -21, 6, -17, -9, 24, 7, -12, -24, -19, 24],\n [-16, 19, 5, 21, 15, -10, 20, 3, 16, -19, 13, -20],\n [-7, -15, -6, 1, 1, -11, 21, -17, -5, -20, -23, -3],\n [7, 14, 20, -13, 17, 22, -10, 18, -19, 15, -14, -20],\n [-24, -3, 20, -3, -20, 3, -22, 13, -6, 22, -19, -20],\n [12, -25, 16, -15, 1, 17, -8, 1, 8, -15, 1, -1],\n [11, -21, -8, 0, 26, -18, 14, 23, -17, -17, 6, -9],\n [-17, -20, 13, 5, 16, -21, -8, 14, 16, 7, 16, -22],\n [-8, 22, 23, -13, -17, 22, -16, 4, -25, -17, -6, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "539", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[19, 4, -16, 16, -17, -7, -6, 10, 10, -13, -22, -21],\n [-3, -11, -4, 20, 11, 25, -11, 24, 25, -14, 24, 18],\n [-19, 11, 5, -5, -10, -22, -19, 23, 3, -8, -15, -2],\n [17, -14, -23, -17, 21, 1, -22, 1, 17, 4, -11, -4],\n [2, 20, -6, -25, -4, -11, -16, -18, -25, -9, -14, 18],\n [-19, -17, 0, -10, -3, -6, -26, -11, 16, 6, -21, -15],\n [5, 21, -16, -9, -25, 5, 22, 22, -7, -6, 9, 11],\n [0, 20, -16, -9, -10, 7, 18, -1, -21, 16, 3, 25],\n [12, 23, 5, -10, -14, 26, 19, 14, -14, -21, -5, 6],\n [6, -23, -13, 23, 21, 8, 0, -21, -26, 16, 1, 2],\n [5, 1, 0, -17, -9, -23, 11, 24, 14, 15, 25, 5],\n [-22, -5, 21, -5, -25, 14, 16, 7, 23, -25, 19, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[13, -19, 6, 6, -23, -9, -8, -17, 23, 15, 14, 3],\n [-5, 12, 11, -26, 3, -22, 24, 20, -1, 19, 4, 12],\n [14, -15, -10, -9, -25, 22, -3, 1, 25, 12, -17, 20],\n [6, -3, -16, -19, 0, -1, -15, 8, -12, -6, 10, 3],\n [-22, -10, -1, 7, 6, -9, -2, 14, 3, 10, -7, 18],\n [-25, -14, 13, 15, -7, -21, -16, 19, -2, 15, -17, 4],\n [16, -23, -2, 1, -3, 8, 14, -22, 6, -16, -19, -6],\n [5, -22, 7, -18, 11, 16, 5, -17, -15, 8, 12, -9],\n [-4, -15, 4, -16, 7, 0, -6, -17, -14, 18, 20, -2],\n [-14, 14, -21, 8, 1, -7, -7, 14, -23, -7, -22, -5],\n [-3, 17, -10, -22, -1, 9, -19, -18, -10, -19, -22, -17],\n [23, -13, 0, 0, -22, -12, 1, -22, -5, -15, 15, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-26, 8, -11, 3, 16, 14, -17, 7, 25, -16, -7, 16],\n [-20, -6, -16, 10, -4, 17, 4, -9, -3, -5, 10, 20],\n [17, -26, 23, -21, 11, 2, 16, -16, -11, -21, -26, 21],\n [8, -3, 11, -24, 24, 13, -25, 24, -12, -5, 19, 19],\n [-23, -3, -8, 3, -5, 12, 21, 13, 0, -12, 25, 10],\n [-26, -15, -18, -8, -9, 12, -16, -16, 3, -7, 25, -12],\n [-2, 22, -24, 16, -1, 18, 1, -21, 19, 5, -16, -14],\n [-10, 19, 26, 19, 9, 3, -23, -13, 19, 1, -20, -11],\n [-13, 10, 12, 22, 0, 3, -12, 12, 15, -9, -16, -5],\n [19, -23, -24, -3, -13, 25, -24, 4, 26, 8, 4, 25],\n [-15, -17, -7, -9, 17, 9, 24, -8, -10, 13, -16, -22],\n [10, 18, 9, 18, 21, 17, -13, 26, 1, 26, -18, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[2, -2, -19, 21, -8, -25, -21, 3, -25, 24, -8, -14],\n [22, 26, -19, -18, -4, 10, -19, -18, -11, -11, -15, -2],\n [-16, -9, -14, 8, -9, 16, 3, 16, 10, 3, -24, 2],\n [-2, -25, 20, -22, 4, -22, -6, 21, 22, -1, -20, 3],\n [7, 1, -13, -9, 17, -10, -2, -21, -22, 26, -6, 12],\n [23, -7, -16, -22, 11, 12, 8, 8, -2, 3, -25, -7],\n [9, 10, -25, 21, 17, 20, 0, 5, -23, 0, 3, -24],\n [19, 18, 0, 11, 9, -26, 8, -15, 8, -9, 19, 10],\n [-4, 6, -13, 17, -26, 0, -3, -25, -15, -14, 0, -7],\n [20, 21, 24, 10, 7, -21, -19, -6, 12, -6, 18, -21],\n [14, 17, 3, -17, -16, -26, -17, -2, -11, -8, -17, 20],\n [-13, -24, -23, 13, 6, -7, -12, -20, 17, -24, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[2, -1, 0, -2, 13, 16, 24, 3, 17, -7, -20, 2],\n [19, 7, -1, 0, 17, -18, -5, -15, -21, -21, 0, -8],\n [25, -21, 22, -10, 2, -4, -10, -6, -17, 16, -19, -13],\n [4, 24, -9, 20, 3, -9, 25, -2, 22, 10, -2, 3],\n [3, 9, -16, 21, 12, 0, -11, 11, 5, 2, 25, -17],\n [3, -16, -12, 17, -4, 21, -4, 23, -20, -13, -18, 1],\n [-21, 16, 18, -5, -9, 17, 11, -5, -18, -9, -6, -12],\n [-18, 15, -25, -13, -6, 16, 18, 7, 26, -20, -12, 12],\n [-15, -20, -22, 20, 12, -4, 26, 1, 7, -2, -25, 24],\n [-18, 7, 19, 20, 5, -15, -8, 20, 11, -17, -17, 8],\n [14, 10, 5, -20, 24, -17, 16, 11, 0, 5, 24, -20],\n [21, -1, -5, -15, -3, 23, 19, 2, 5, -11, -1, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "531", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-26, -14, 11, -21, 11, -15, -18, -7, 12, 0, -24, -3],\n [-12, 7, 23, 5, -6, -26, 6, -16, -24, -5, -17, 17],\n [11, -3, -20, 22, 22, 9, -26, -26, -1, -10, -16, -24],\n [-17, -25, 5, -11, 21, -1, 13, 12, -17, 9, 3, -18],\n [-22, -20, 9, -26, 0, -15, -11, 21, -19, -2, -14, 14],\n [-17, 13, 6, 8, 10, 12, 1, -11, -19, 6, 26, 8],\n [11, -15, -12, -10, 0, 23, -6, -6, -10, 0, -15, 21],\n [17, 9, 1, -2, -18, 20, 10, -4, -16, 23, -26, -11],\n [23, -14, -7, -11, -11, 8, 23, 5, -4, -2, 16, 1],\n [18, -25, -24, 4, 6, 6, 20, 8, 9, -1, -15, 26],\n [17, 19, -16, -21, -2, 19, 7, 8, -6, -9, -19, 7],\n [25, 21, -13, -8, -7, -23, 11, 5, -1, 1, -15, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, 8, 6, -13, 13, -4, -9, 26, 17, -15, 15, 9],\n [-2, 25, 10, 13, 24, -5, -21, -11, -4, -18, 16, 8],\n [2, -13, -22, -6, 26, -21, -26, 4, 18, 14, 1, -24],\n [11, 25, -4, 13, -23, -21, -15, -15, -20, 1, -1, 21],\n [-20, -24, -14, 25, 14, -16, 12, -4, 20, -26, 7, 4],\n [6, 20, 9, 9, -13, 10, 5, 26, 1, -26, 20, -20],\n [-11, 5, -3, -13, 20, -12, 25, -26, 1, -8, -20, -9],\n [20, -14, 24, -9, -23, 23, -23, 0, -11, -13, -13, -20],\n [18, -13, 15, 18, -21, 16, 11, 0, -16, 4, 24, 22],\n [-24, -26, -11, 17, 0, 19, 23, -24, -19, 23, -11, 20],\n [-25, 2, -11, 2, 4, 15, -16, 24, 5, -3, -8, 5],\n [-17, 22, 5, -4, 6, 3, 3, -20, -11, 16, 26, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-26, 3, 7, 7, 11, 4, -19, 26, -7, 19, 2, 4],\n [-6, -1, 4, -7, -5, 13, -1, -10, -2, 10, 0, -24],\n [-3, -2, 23, -17, 9, 15, -9, 18, -10, -13, -8, -9],\n [-4, -19, 23, -11, -2, 16, 5, 22, 23, -8, -9, 5],\n [19, 22, 13, -12, 22, -6, -16, 2, 5, -21, -8, -11],\n [-15, -12, -16, 12, -17, 24, 10, 22, -3, 24, 9, -26],\n [19, -10, -13, 11, -2, 10, 8, -5, 20, -20, -16, -17],\n [-13, 8, 19, 22, 9, -21, 25, -22, 15, -20, -12, -6],\n [26, -9, -26, -23, -16, -17, 18, -8, 15, 3, 23, 14],\n [14, -7, 0, -15, -13, 7, 15, 23, 11, -25, 22, 5],\n [-9, 23, -6, 19, -16, 3, -8, 21, 13, 23, 3, 8],\n [-23, -6, -22, 9, 0, -20, 4, -7, -2, 11, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[19, 10, -12, -17, 7, 17, 16, -20, 12, 24, -2, 12],\n [19, 17, 1, 15, 0, 10, 12, 11, 25, 1, 7, 2],\n [18, 21, -19, -14, 19, 10, -24, -13, 5, -4, -4, -14],\n [22, 14, 12, 23, -6, 16, 21, 4, 23, -20, 9, -8],\n [-5, -3, -3, -6, 16, -14, -21, 1, 5, -14, 7, 5],\n [-13, 5, 18, -22, 8, -23, -13, -9, -16, -8, -25, 7],\n [-24, 2, -4, 21, -26, 15, -21, -10, -8, 17, 25, 21],\n [-25, -12, -4, -8, 6, -21, 23, -8, 3, -5, -24, -22],\n [3, -24, 12, 12, 1, -26, -5, 18, 18, 20, 24, 12],\n [-10, 15, 24, 1, 23, 3, 13, -19, 0, 14, 18, -2],\n [-14, 7, 12, -20, 25, -5, 6, 19, 11, 4, 18, 6],\n [26, 25, -5, 0, 0, -6, 26, 8, 20, 23, -17, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "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, 13, 10, 14, 6, 24, -19, 10, 23, 14, 6, -8],\n [3, -13, -13, 9, -20, 25, 16, 7, 23, 5, 15, 6],\n [-13, -2, 1, 15, 23, 12, 3, 4, -3, 24, -23, -13],\n [-18, 9, -21, -3, -1, 7, -26, -4, -10, 9, 10, 23],\n [18, -7, -1, -16, -7, -26, 17, -14, 9, 17, 11, -14],\n [-13, -15, 26, 25, 7, 0, -15, 11, 9, -26, -1, 13],\n [13, -6, 5, -2, -15, -2, -1, 9, -11, -13, 19, 7],\n [22, -3, -19, 0, 12, -14, 2, 4, 16, -8, 24, -17],\n [16, 21, 13, 7, 19, 22, 22, 16, -26, -8, -26, -3],\n [-2, -23, -3, 12, -7, 6, 1, 16, 18, 8, -3, 13],\n [17, -25, -4, 6, 25, -13, -12, 5, -4, -23, -7, 4],\n [-20, -26, -22, -13, 3, 11, -4, -20, 17, 12, 23, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-18, 12, 19, 7, 4, 18, -20, 24, -25, -21, 17, 7],\n [-10, -1, -15, -7, 14, 19, 8, 8, 2, 21, 11, 4],\n [13, -14, -1, -5, -19, 13, -20, -22, 25, -26, 18, 13],\n [-16, 25, 5, -20, 24, 2, 3, -6, 12, 21, 17, 16],\n [14, 12, -7, -5, 2, 19, -23, -24, -18, -22, -24, -2],\n [5, 6, -9, 18, 9, 23, 14, 2, 12, 20, 18, -25],\n [-16, 4, -23, 2, 23, -24, -25, 17, 9, -13, 21, 26],\n [-23, 17, 3, -8, -8, 17, 4, -12, 2, -24, -8, -5],\n [20, -7, -20, -23, -26, 14, -20, -5, 10, 3, -18, 0],\n [11, -4, -15, -14, 6, -12, -11, 7, -18, 15, 25, 0],\n [21, -12, 8, 7, 13, 3, 21, -4, -18, 5, 8, 22],\n [5, 18, -11, 5, -2, 3, 10, 10, 8, 18, -19, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[22, 20, 9, -2, -9, 12, -17, -26, -23, -1, -16, -12],\n [5, -12, 1, -4, -24, 24, 5, -7, -13, 8, 13, 15],\n [-18, 20, -3, 14, -23, -15, 24, -3, -26, -13, 4, -17],\n [6, 9, 15, 8, 21, -9, -2, -15, 1, 26, 24, -18],\n [-3, -7, -1, -22, 0, 1, 10, 13, -20, -8, -5, -9],\n [-12, 6, 12, 24, -22, 13, 10, -22, 10, 16, -20, -25],\n [3, 22, -16, 25, 10, 12, 6, -18, -16, -15, -17, 25],\n [-16, 6, -7, -22, 20, -3, 5, 4, 15, 17, -13, -8],\n [15, -3, 5, -15, 23, -6, 24, 9, -2, 24, 26, -13],\n [-19, 2, -2, -4, 9, 21, -15, 23, -15, -9, 9, 21],\n [23, -8, 21, 26, 8, 22, 0, -24, -14, 11, 24, 14],\n [-8, 16, 8, -12, -11, 8, -22, -20, -6, 14, -26, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"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, -8, -3, 19, -12, 8, -3, 9, 22, -13, -5, 12],\n [-19, 21, -11, 19, -10, -22, 14, 8, 26, 10, 25, -9],\n [-6, 15, -26, -10, -19, 2, -7, 22, 23, 10, 12, -22],\n [-17, -21, -20, 8, 0, 15, -6, -3, 2, 0, 11, -25],\n [-2, -25, 11, -9, 15, -20, 22, -23, 17, 13, 14, -17],\n [24, 14, 1, 3, -3, 9, -11, 6, -17, 21, -6, 0],\n [-6, 0, 5, -22, 26, 8, -5, 9, -17, 7, 25, -21],\n [-13, 10, -8, 5, -7, -6, -12, -10, 17, 18, 25, -3],\n [-6, 21, -12, -16, 10, 3, -9, 1, -14, 16, -17, 20],\n [12, -15, 23, 11, 14, 21, 13, -1, 17, -8, -4, 21],\n [9, 0, 25, -11, -20, -14, -15, 0, 6, 4, -16, -10],\n [11, -25, -24, 7, 23, 5, -3, -3, -14, -5, -8, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[3, 12, -6, 21, -4, -11, 15, -20, -7, 21, 15, -13],\n [-1, -5, 14, 9, -1, -15, 22, 4, 13, -23, 13, 0],\n [-18, -15, 2, 1, -11, -19, 20, 22, -14, -13, -12, -18],\n [26, 17, 5, -5, 24, -2, 14, -1, 18, 2, -9, 9],\n [-7, 6, -7, -24, 16, 7, -21, 4, 8, 5, 15, -18],\n [19, 21, 0, -3, 23, -5, 3, 9, -1, 23, -25, 15],\n [17, -20, 0, -11, 22, 19, 2, -6, -1, -9, -26, -25],\n [-13, 11, -12, 9, -3, -2, -18, -12, 10, -21, 16, 18],\n [-15, 0, -20, 1, 25, -15, 15, 8, -25, -1, -7, -2],\n [-6, -26, 1, 26, 11, -14, 3, -17, 18, -5, 2, -22],\n [-19, 26, -16, -1, -8, -8, 3, 9, 15, -18, -20, -9],\n [-18, -21, -21, 18, -5, -10, -12, -18, -21, -4, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509", "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, 10, -24, -11, -25, 25, -24, 14, 24, -13, -13, 3],\n [22, 13, 22, 0, -10, 12, -18, 9, -17, 2, -23, -6],\n [10, -25, -12, 1, -2, -1, -18, 3, -18, -26, -15, 18],\n [25, -14, -13, -17, -10, -10, 4, 19, 22, 24, -1, 8],\n [9, -16, -11, 2, 18, -9, -16, -16, -18, -2, 5, 7],\n [-24, -13, 21, 13, -2, -11, 9, -18, -23, 18, -25, -2],\n [23, -5, -22, 22, -6, -17, -4, 0, 3, -23, -21, -1],\n [-17, 22, -22, 12, 10, 13, -26, 7, 21, -19, -6, 4],\n [20, -4, -16, -11, 0, -20, 22, -3, 5, 8, 4, 20],\n [2, -23, 8, -16, 7, 12, -12, -13, -6, -20, -10, 15],\n [-9, -13, 11, 2, 24, -17, -10, 5, 24, -7, -10, 19],\n [-20, 24, 12, 17, 3, 11, 13, 14, 23, -17, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[26, 21, -10, -26, 12, -1, 3, -18, 17, 6, -1, 15],\n [-17, 15, 5, 12, 20, 15, 21, 21, 25, 6, 0, 16],\n [2, -8, -9, 8, 20, 1, 11, -17, -24, 15, 2, -11],\n [9, -26, -9, -23, -22, -6, -23, 24, -7, -8, 8, 25],\n [18, -3, -7, 23, 1, 11, -3, -7, -3, -21, 11, -2],\n [5, -10, -10, -22, -10, -18, -7, -25, -8, -18, 13, -8],\n [18, -23, -21, 9, -16, -6, 15, 21, -2, 3, -9, -2],\n [24, -6, -4, 3, 17, 19, -9, 25, 6, 18, 8, 19],\n [-5, 23, -3, -4, 24, -26, -12, 21, 1, 15, -7, 9],\n [16, -11, -22, 24, 16, 23, -12, -25, -3, -14, -4, -15],\n [19, 6, 17, 18, -2, 8, 8, -26, 16, -23, 4, 1],\n [-16, 5, -25, 24, 17, -14, -10, 24, -23, 4, 11, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, -15, 17, -9, 3, 19, -16, -3, -6, 22, 21, 8],\n [-23, -1, -19, -3, 16, 18, -15, -22, -11, 5, 2, 6],\n [14, -13, -2, -19, 0, 8, -5, -20, 9, 20, -15, -18],\n [23, 18, 8, 12, -8, 1, 2, -19, 16, 0, -22, 21],\n [2, 8, 6, 5, -6, -17, 15, -11, -16, -8, 25, -14],\n [-12, 15, 9, 5, -8, -12, 11, -5, 22, -14, -7, 22],\n [-12, -20, -5, 16, 23, -7, -8, 0, -19, -9, -17, 23],\n [22, 14, 8, -12, -4, -15, 22, 0, -21, -3, -5, -18],\n [-17, -24, -21, -1, 18, -13, 9, 15, -8, 21, 12, -4],\n [-22, 17, -12, 3, 6, 11, -8, -22, -18, -20, -3, 14],\n [-11, 10, -17, -6, -6, 20, -12, -14, 25, 23, -20, 13],\n [-19, 16, 14, 11, 25, -25, 10, -5, -23, 25, 20, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-26, -8, 3, 23, -25, 26, -14, 1, -13, -24, -11, -2],\n [19, 20, -24, 7, -24, 14, 2, 13, -8, -7, -6, -7],\n [1, 20, 0, 17, 19, 23, -2, -25, 26, 16, -3, 6],\n [-8, -1, 19, 14, -24, 0, -13, -7, 8, -4, -2, -23],\n [-25, -25, -2, 20, -4, -6, 26, 18, -2, 0, 25, -16],\n [-13, -10, -12, 19, 24, 4, 7, 9, 13, 17, -14, -9],\n [-10, 18, 17, 12, 1, -1, 21, -13, 10, -16, 5, -3],\n [26, 26, 4, 13, 14, 23, -19, 12, -19, 20, 4, -8],\n [9, 12, 5, -6, -4, 9, -12, -25, -15, 11, -21, 19],\n [11, -26, 11, 23, -1, 26, 21, -4, -26, -6, -8, 2],\n [23, -1, 7, 24, -10, -9, 5, -23, 3, 4, -9, -22],\n [5, 2, -15, -12, -12, 8, 26, 8, 16, 25, 26, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "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, 11, -5, 11, -16, -24, 26, -13, 17, -2, -13],\n [20, 4, -2, 14, -8, -15, -20, 22, -13, 2, 20, -13],\n [-4, 24, 24, -13, -4, -19, -14, 9, 17, -26, 10, -1],\n [-23, -11, -2, -8, -7, -1, 24, 5, -24, 21, -20, 5],\n [-22, -6, 3, -7, 2, -3, -26, 16, -2, 0, -2, -6],\n [-10, 1, 5, 17, 23, 7, -5, 15, -8, 21, -19, -25],\n [-22, 1, -23, 26, 9, -26, -12, -14, 4, -10, -21, -3],\n [25, -14, -6, -3, -5, 2, -3, 17, -15, -7, 15, 7],\n [-12, 24, 26, -23, 26, -13, -26, 6, 23, 20, 16, 23],\n [2, -17, 9, -13, -5, 23, 6, 1, -20, 9, 9, 23],\n [14, 7, 10, -21, 8, 0, 3, 5, -8, -5, -6, -22],\n [-6, 14, -7, 11, 4, 10, -21, 4, 20, 16, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508", "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, 24, -15, -15, 2, -20, -11, -15, -6, -23, 15, -10],\n [1, 4, 20, -19, 19, 23, -1, 13, 19, 21, 4, -8],\n [-20, 22, -22, -14, -9, -9, 24, 23, -7, 25, 22, -4],\n [9, 22, 24, 13, 25, 6, -20, 13, -22, 5, -18, 3],\n [5, 12, -23, -2, -5, -19, -25, 10, 8, 10, -5, -26],\n [12, 15, 21, 6, 22, -23, 21, -18, -19, 24, -5, 22],\n [15, 22, -6, 21, 14, 1, 10, -25, 19, -10, 4, 18],\n [-14, 18, -9, -3, 4, 6, 26, 4, 0, 9, -6, -22],\n [-16, 7, 7, 21, -24, -21, -7, -23, 10, 26, 12, -20],\n [-10, 11, 9, 7, -21, 12, -25, -9, 15, 0, 12, 14],\n [24, -8, 5, -3, 7, -2, -3, -2, -15, 3, 24, -21],\n [3, 6, -12, 2, 24, -13, -2, 18, -22, -25, 20, -11]]\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[[12, 11, -10, 4, -26, -21, 4, -21, 9, -19, 2, -18],\n [-5, -17, -3, 13, -25, -7, -10, 6, -13, 5, 10, -3],\n [14, -7, 22, -21, 6, 23, 1, -16, 9, -7, -21, -19],\n [-8, -12, -5, 24, -25, 1, 9, 9, 17, -9, -15, -8],\n [-1, -2, 1, -12, -17, 12, 7, -14, -11, 26, 13, 4],\n [-26, 22, 20, -4, -13, 12, 3, 24, 15, -7, -2, -16],\n [-1, 25, -6, -22, -20, -15, -25, 12, -6, 5, -22, 0],\n [4, -15, 9, -6, 26, -8, -24, -10, 3, 9, -18, 7],\n [2, -17, 25, -18, 13, 23, -16, -8, -5, 23, 24, 22],\n [25, -5, 22, 20, -11, -10, 13, -20, 26, 4, -23, 2],\n [-20, 16, 3, -24, -2, 7, 6, 4, -3, 11, 19, -23],\n [21, -17, -2, 10, 16, -26, -10, 19, -20, -13, -26, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"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, 16, -17, -6, -24, -8, 1, -25, 0, 17, 5, -15],\n [-26, 19, 16, 13, 2, -18, -9, 18, 9, -11, 8, 9],\n [-23, 13, 16, 8, -8, -21, 4, 0, -24, 26, 9, 9],\n [-25, 21, 10, -12, 10, -4, 17, 24, 20, -21, 6, -22],\n [-6, 1, -6, -3, 24, 1, -16, -5, 19, 19, 7, 10],\n [14, -10, 24, -12, 2, 7, 14, 16, -5, 0, 11, -12],\n [-6, 25, -23, 20, -9, -20, -11, 8, -15, -20, 14, -17],\n [-26, -15, 0, 1, -9, -26, 23, -4, 12, -10, 18, 15],\n [19, -26, 11, -23, 24, -12, -6, -6, 24, -5, 17, -13],\n [8, -23, 8, 5, 1, -15, 3, -18, -8, -11, 3, -26],\n [19, 18, -4, -15, -22, -7, -24, -25, 16, -7, -25, 21],\n [13, 8, 26, -23, 26, 9, 13, -21, -13, -12, 22, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, 17, -8, -15, 16, -18, -8, 5, 1, 1, 4, 9],\n [-14, 15, 6, 15, -9, 2, 18, 12, -19, 22, -5, -26],\n [21, 4, -7, 9, -4, -10, 18, -17, -18, 19, -10, -24],\n [6, -26, -7, -25, -11, -18, -13, -26, 8, -9, -26, 16],\n [-22, -16, 11, -3, 12, 18, 5, -11, -24, 20, -19, 5],\n [-5, 25, 21, -10, 0, 18, -24, -1, 8, -14, -10, 3],\n [2, -13, 3, 10, 17, 21, 11, -18, 21, 5, -23, -21],\n [24, -26, -2, 13, 11, -24, -6, -13, 3, -25, 21, -5],\n [-14, -2, 21, 16, -16, 21, -17, 22, 17, 10, -2, 17],\n [8, -8, 1, 15, 21, 24, 16, 21, -17, -12, 5, -24],\n [-3, -17, 17, 3, 14, 24, 6, 18, -2, 12, 25, 26],\n [12, -2, 11, -15, -23, 1, -7, -17, 4, -8, -25, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "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, 6, -9, 13, 5, 5, -14, 24, -11, 6, 7],\n [24, -13, 20, -25, -14, 25, 2, 25, 16, 15, 7, -10],\n [-24, 3, -23, 4, -22, -25, -23, 17, 11, 25, 0, 0],\n [-12, 12, 11, -13, -9, 2, -20, 11, -3, 11, -21, -7],\n [15, 9, -17, -5, 6, -4, 19, 23, 14, 15, 24, -23],\n [-6, -14, 15, -14, -15, -3, 8, -8, -18, -14, -5, 13],\n [9, 26, 1, 14, -20, 3, 4, 26, -16, 3, -12, -14],\n [8, 8, -7, 16, -4, 26, 10, -7, -8, 17, -9, -23],\n [-19, 19, 3, 21, -7, -19, -22, 14, 7, 13, -20, 23],\n [26, -5, -18, -16, -15, -19, 5, -10, -1, 24, 6, -1],\n [-5, -24, 4, -13, -9, 7, 13, -10, 14, -15, 12, 6],\n [5, -6, 26, -13, -25, 22, -20, -12, 4, 1, 14, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, 9, -17, 12, 20, 3, 18, 13, 14, 14, -22, -6],\n [-21, -11, -11, -3, 19, -8, -8, 21, 10, 6, -22, -18],\n [-6, -20, 15, -2, 20, -6, 17, -14, 23, -6, -17, -3],\n [0, 6, -1, 9, -10, -6, 18, -25, -12, 17, -25, -20],\n [9, 19, 23, 16, 5, -24, -24, 23, 6, 18, -2, 10],\n [9, 8, -8, 18, 21, -8, 6, -9, 0, 3, 4, 12],\n [-24, -5, 25, -17, 26, -19, 7, 15, 26, -9, -15, 19],\n [5, -25, -10, 25, -15, -20, -12, -25, 0, -1, -2, -15],\n [-10, -26, 4, 13, -22, 1, 1, -19, 25, -13, -21, -9],\n [10, -17, 20, 8, 8, -10, 19, 0, -3, -17, 24, 21],\n [-10, 25, 18, 6, 6, -10, -9, 22, 17, 11, -20, 22],\n [-1, 21, -26, -16, -17, 4, -2, -26, 16, -24, 21, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-20, 16, 22, 24, -13, -4, 21, -10, -13, -18, -6, 18],\n [-25, 25, 5, -19, 9, -1, 10, -12, 7, -6, -4, -18],\n [13, -1, 16, -5, -14, -2, -20, 24, 0, -12, -15, 18],\n [6, -6, -2, 13, 20, -5, -13, -19, -3, -24, -15, 20],\n [-5, -11, -20, -9, 18, -4, -1, 11, -25, -25, -5, 24],\n [11, 15, 1, -10, 24, 21, -9, 24, -25, 8, -12, -12],\n [17, 25, 18, 7, 23, -12, -9, -14, 11, -19, -11, -7],\n [-1, 8, -10, -1, -9, 17, -20, 17, 8, -15, 20, 22],\n [17, 14, -26, -2, -11, -12, -16, 10, 12, -24, 18, 18],\n [24, 15, 12, -7, 26, -4, -12, -9, 25, 12, 8, 2],\n [-7, 15, -12, 5, -15, 21, 24, -15, -2, 26, 7, -19],\n [-3, 18, -26, -2, 7, -13, 9, -21, 18, -18, 21, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-18, -3, 12, -9, 21, 12, -9, 14, 1, 25, -25, 10],\n [14, 9, 21, 26, -3, 8, -21, -10, 3, 24, -19, 15],\n [-17, -11, 11, -1, 4, 25, -19, 8, 7, -17, 13, 17],\n [25, -15, 14, 0, -8, -1, -12, 4, 19, 10, -9, 2],\n [17, 0, 11, -7, -6, 2, 16, -12, -5, -4, -23, -3],\n [-13, 10, -6, 16, 25, 12, -14, -8, -1, 9, 25, 17],\n [19, 6, 13, -11, 26, -8, 10, -13, 17, 17, 3, 4],\n [-7, 17, 16, 20, -20, 15, 10, 20, -25, -5, -14, 19],\n [25, 11, 4, -26, 20, 16, -14, -10, -23, 16, 4, 6],\n [-13, -6, -5, -22, 26, 10, 5, -24, 14, -14, -16, 23],\n [15, 11, -3, -18, -14, -5, -9, -17, 20, -15, 25, 3],\n [20, 19, -8, -8, 26, -17, -26, 25, -20, -16, 26, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, -6, -5, -17, -4, -22, 21, -15, 3, 6, 10, -9],\n [-23, 0, 20, -4, -21, -20, -8, 19, -12, 26, 21, -5],\n [5, -12, -21, -21, -21, -15, -25, -2, -23, -21, 15, 24],\n [10, 11, -13, 20, -8, 24, -20, -9, 17, -19, 1, -6],\n [8, 20, -17, 26, 1, -8, 17, 8, 1, 19, 22, -24],\n [12, 0, -10, -12, 25, 15, 12, -5, -7, 0, 8, 20],\n [25, -22, -25, 14, 23, 18, -7, -20, 9, -19, 0, -21],\n [-3, 9, -22, -7, -7, 26, 14, 13, 7, 12, 23, -17],\n [-24, 22, 7, 8, 10, 18, 18, 11, 19, -4, 10, -6],\n [0, -26, -18, -24, 11, 9, 7, 3, 4, 3, -11, 2],\n [-21, -13, -17, -3, 9, -3, -20, 22, 10, 19, 21, 13],\n [21, 11, -2, 16, 7, -26, 1, 14, 2, 5, -22, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "536", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[19, 25, -1, -14, -15, -5, -18, -21, 9, -17, 10, 5],\n [-23, 25, -23, -14, -11, 16, 24, 23, -1, 6, 26, -23],\n [-1, -18, 14, -16, -22, 26, 11, 25, 5, 2, 11, 13],\n [1, 26, -3, -8, -26, -22, -4, 26, -8, -25, 21, -25],\n [-18, -9, -11, 12, -18, 17, 24, -4, 6, 11, 7, -1],\n [-10, 26, -13, -14, -5, 16, 21, -9, -7, 3, 8, 6],\n [19, -10, 8, -15, -25, 7, -15, -1, 5, -6, -22, 1],\n [-4, 21, 5, -22, 8, -21, -8, 17, 13, -21, -13, -24],\n [-16, 12, 14, -3, 16, 18, -9, 4, -17, -1, 2, -25],\n [3, 12, 20, -17, -15, -7, 14, -8, -21, -4, -8, 4],\n [6, -25, -12, -16, -1, -9, -26, 5, -23, -5, 9, 2],\n [9, 23, 6, 12, -13, 21, 20, 10, 18, -22, 23, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-22, 10, 11, 19, 7, -12, 21, 10, 0, 21, -26, 2],\n [-19, 6, -20, 2, 4, 11, -19, 4, 10, -12, 25, 5],\n [-1, 21, 22, -16, -4, 7, 6, -10, 6, -25, 22, -23],\n [-15, 2, 15, 15, 20, 16, 12, 15, -8, 23, -25, -20],\n [19, -5, -16, 6, -7, -22, -23, -13, -24, 23, -9, 0],\n [-23, -24, 0, 1, -5, 15, 2, -11, 8, -8, 25, 3],\n [-12, -22, 4, 16, 4, -18, -14, 16, -6, 19, 4, -26],\n [14, -14, 7, 9, -11, -17, 11, 14, 7, -2, -26, -15],\n [-5, -5, 21, -25, 18, -19, 6, -22, -17, -24, -16, 3],\n [1, -22, -15, 17, 18, 2, -1, 2, 2, -13, 9, 8],\n [22, -19, -11, 16, -22, -11, 14, -14, -19, -1, -22, -18],\n [11, -25, -20, 3, -10, 17, 4, -26, 1, 3, 20, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, 4, 26, -16, 15, -11, -18, 3, -15, 20, -11, 6],\n [-21, 18, -26, -14, 10, 8, 17, -1, 15, -18, -10, 11],\n [19, 8, -2, 23, -20, 14, 20, 4, 5, 24, 21, -8],\n [24, -10, -21, -2, 6, -8, -12, 8, 22, 5, 11, 9],\n [5, 5, 13, 9, 26, 7, -17, 17, 6, 17, -17, 17],\n [24, 8, -5, 24, -4, -20, -6, -26, -14, -18, 21, 23],\n [20, -7, 20, 20, -17, -1, 23, 20, 17, -26, 18, -10],\n [-10, 12, 16, -15, 14, -12, -26, 5, -16, -22, 24, -9],\n [23, -9, -4, 25, -20, 19, -1, -26, 1, -7, 14, 21],\n [-4, 5, 11, 12, -9, 6, -2, 5, 21, 23, 23, 24],\n [1, -14, -8, -24, 25, 0, -10, 16, 2, 22, 17, 17],\n [25, 21, 6, 1, -7, 18, 7, -11, 12, -25, 23, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-10, 21, -7, -9, 26, 1, 1, 25, -11, 6, -6, -22],\n [20, 18, 10, -9, 25, -22, 21, 16, -16, -5, -4, -1],\n [0, -24, 24, 15, -25, -10, -24, -24, 13, -11, -15, 24],\n [-26, 24, -23, -10, -8, -23, 20, 12, -7, 22, 14, 12],\n [-23, -10, -12, 14, 1, -11, -21, 1, 5, -10, -2, 12],\n [-10, 19, -12, 25, 26, 23, 24, -9, 19, -7, -4, -22],\n [12, -15, -10, 3, -8, 5, -11, -25, -15, 22, 26, -24],\n [-19, 10, 26, -3, 22, 26, -2, -2, -13, 19, 9, -12],\n [5, -25, -6, -23, 2, 22, 2, -4, -24, -6, -11, 17],\n [-7, 8, -22, 21, -1, -20, 25, -11, -10, -25, -15, -14],\n [-22, -11, 1, -19, 1, 19, -19, 2, -9, 25, 17, 16],\n [-11, -1, -5, -12, -14, -5, -6, 23, -3, -26, 2, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "561", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-26, -18, -6, -13, 1, -9, 6, 25, 16, -25, 24, 7],\n [-3, -8, -25, -21, -12, -16, -11, 25, -6, 0, -5, -24],\n [-24, 24, -6, 16, -21, -2, 14, 10, 3, 12, -7, -26],\n [8, 16, -1, -6, -17, 18, 2, -24, 16, 25, 14, 16],\n [14, -14, -18, 19, -11, 22, 20, 1, 1, -16, 17, 3],\n [-16, 2, 23, -15, -19, 26, -17, 8, 25, 9, -14, 25],\n [0, 13, -25, 1, 7, -6, -21, 25, 12, -1, 9, 13],\n [-9, 15, 25, 16, 12, -22, -1, -16, 23, -11, -8, 25],\n [-22, -20, -24, -2, -17, 24, -22, 5, 5, -22, 16, -8],\n [-15, 4, -10, -5, 25, 20, 23, 14, -5, 22, -1, 4],\n [16, -21, -15, 16, 0, -10, -17, 18, -22, -23, 12, -12],\n [-25, 22, 26, -19, -11, -7, -3, 8, -10, -22, -13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "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, -7, -14, -18, 25, 7, -15, 13, -11, -26],\n [-11, -21, -7, -21, 8, 14, 24, -24, -6, -20, -13, 3],\n [-5, -13, -2, -24, -22, -22, 24, 15, -18, 21, 14, 11],\n [10, -23, -7, -6, 23, 21, -3, -20, 19, 22, -19, -16],\n [22, 19, -18, -21, 13, -10, -14, 18, -10, 24, -25, 3],\n [5, 23, 9, -20, -11, -8, -12, -13, 18, 25, -20, 20],\n [6, 7, -3, 8, -6, -3, 10, -11, -10, 2, -9, 21],\n [-16, -24, 15, -9, -11, 14, 26, -26, 16, 16, 0, 4],\n [18, 1, 13, 24, 0, -18, 11, 9, 14, 0, 20, 23],\n [-1, 0, -23, 24, 21, 11, -15, 20, -12, 20, 21, 3],\n [-13, -19, 1, 4, -25, -12, 13, 16, 21, -19, -22, 25],\n [-23, -15, -17, -23, 24, -17, 2, 1, 2, -8, 24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "577", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, 26, 7, 19, -7, -9, 21, 9, -26, -1, -24, 17],\n [-24, -6, -9, 4, 9, 22, 17, 25, 4, -19, -2, 22],\n [19, -7, -16, 13, -26, -6, -10, 25, 1, -9, 2, -17],\n [-18, 7, -7, 4, -24, -26, 6, 23, -19, -9, 3, 6],\n [-5, -10, 15, -18, -5, -17, 6, 21, 12, -24, -10, -18],\n [20, 13, 9, -8, 7, -25, 18, 0, -8, 6, -1, 20],\n [7, 1, -11, -5, 1, -13, -21, -16, 19, -7, 9, 22],\n [-11, -21, -19, 18, 9, 21, 22, -23, 21, 7, -7, -3],\n [18, -24, 1, 3, 2, -6, 15, 0, 23, -2, -24, -26],\n [-4, 16, -22, 4, -2, 8, 16, -26, -12, 12, -3, 7],\n [20, -9, -2, 9, -26, -18, 14, 4, -5, 11, 19, 14],\n [-25, 14, 18, 25, -7, -4, -15, -17, 5, -22, 17, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "536", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -4, 9, -14, 23, -25, -16, 1, -2, 9, -9, 12],\n [-18, -25, 9, 19, -10, 6, 8, 6, 5, -7, 3, -5],\n [26, -2, 18, 19, 17, -16, 23, 7, 1, 8, -23, -18],\n [16, -5, -2, -6, -2, 14, -10, -12, 14, -20, 5, -19],\n [-24, 6, 9, -10, -26, 9, 13, -10, 17, 21, 10, -2],\n [-2, -14, -14, -15, 5, 8, 1, 17, 25, -7, 1, 4],\n [-3, 25, -16, 15, -11, 11, -10, 18, 23, 17, -22, -7],\n [21, 8, 21, 16, -13, -1, 18, 16, 19, 15, -3, 4],\n [-9, 12, 23, -5, -6, 7, -2, 13, 20, 3, -21, 26],\n [18, -2, -22, 2, -5, -24, 20, 3, -3, 14, -10, 22],\n [18, 23, -7, -1, -22, -14, 12, -23, 18, -10, 13, 8],\n [4, -11, 7, 5, 6, -19, 3, -24, -10, 24, -3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "518", "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, -17, -3, 20, -20, 21, 22, -7, -14, 2, -17, -18],\n [-20, 17, 6, -3, -11, 5, -23, -13, 2, -5, -4, -1],\n [-1, 22, 17, 20, -5, 17, -24, 15, 25, -10, -13, 18],\n [3, -14, -1, 13, 5, 19, 7, 24, -4, 7, 17, 25],\n [-15, -4, 1, -8, 21, 7, -19, 7, 15, -11, -20, 0],\n [24, -7, 8, -10, 1, -19, -23, 6, 23, -5, 4, -26],\n [14, -13, -20, -19, -19, -3, -26, 8, 14, -19, -22, 5],\n [-26, -25, 15, 19, -12, 15, -18, -15, -17, -3, 14, 23],\n [-8, 24, -10, -25, -17, -22, 12, -21, -25, -19, -23, 23],\n [4, 9, -19, 4, -10, 19, 13, -13, -19, -2, -13, -4],\n [16, 14, -10, 22, -15, -7, 7, 22, 25, -16, 0, -18],\n [-9, 11, 9, 19, 1, -7, 15, 2, -23, -12, 14, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 13, -3, 10, -11, -5, 20, -10, -26, 4, -2, -15],\n [-7, -8, -22, -12, 14, -2, 8, 17, 24, 20, -24, 25],\n [-9, -5, -11, -12, -22, 15, 15, -14, 23, 1, -17, -11],\n [-25, 23, 9, 24, -2, -22, 1, -10, -25, -12, 11, 2],\n [-4, -9, -13, 5, 17, -21, 1, 25, 25, -9, 8, 11],\n [-23, 24, 22, 4, -16, 19, -16, 2, -8, -10, -23, 17],\n [-23, -15, 22, 20, -20, -6, 6, 10, -15, -20, -12, 10],\n [-18, 6, 11, -11, 4, -12, -25, -14, -22, 21, 6, 5],\n [26, 15, 21, 18, -6, -25, 9, 6, -16, 14, -4, 11],\n [6, 13, -19, 9, 9, 6, 2, 4, 3, -19, -1, -4],\n [23, 25, 24, 16, -1, 25, 15, 11, 12, -25, -1, -9],\n [0, 23, -10, 18, -12, 16, -20, -10, -8, 0, 13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -11, 3, -13, 23, 14, -9, -5, 25, -11, 22, 22],\n [-11, -1, 24, 16, -21, 24, -20, -18, 17, -1, -25, 9],\n [-24, -6, 17, -24, -18, -15, -19, 24, 10, -6, 10, 13],\n [-24, 24, 14, -6, -1, -3, 19, 26, 25, 7, 5, 0],\n [20, 3, -23, -25, -4, 14, -23, 10, -16, 9, 9, -12],\n [10, -24, 21, 3, -4, 6, -26, -26, -24, -18, 5, -14],\n [18, 4, -6, -4, -14, -1, -2, 26, -19, 13, 3, 24],\n [-22, -3, -17, -8, 8, -5, 12, 11, -20, 12, -7, 13],\n [5, -25, -12, -17, -6, -12, 7, 8, 24, -22, -8, -20],\n [26, 19, 17, 15, 15, 9, -9, -21, 25, -23, -22, -13],\n [14, 20, 6, 26, -6, -14, -25, -12, 20, -11, 8, 18],\n [-7, -26, 19, -24, -10, -10, 14, -7, -7, -23, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "576", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, 0, -3, -7, 17, -12, -21, -9, -5, 22, -6, -3],\n [-10, -16, -9, 8, 4, 1, -3, 9, 18, -3, 6, 24],\n [3, 25, 10, -14, -11, 21, 16, -18, 23, 20, -14, -20],\n [8, 17, -1, 23, -18, 8, -3, 6, -6, 26, -5, 12],\n [-8, 17, 19, 18, 5, -22, -15, 13, -21, -9, -20, -8],\n [-12, 15, -18, -7, 21, -7, -23, -17, 15, 13, -26, 8],\n [-3, 17, -20, -5, -4, -26, -3, -7, 5, 4, 6, 9],\n [-9, 10, 6, 6, -22, -9, -18, 15, 4, -20, -12, 19],\n [-23, 19, 12, -19, -3, -19, -22, -4, 16, 7, -12, 24],\n [23, 20, -8, -2, 12, -23, 19, -19, 2, 15, -14, 11],\n [9, 10, 15, 18, 24, 16, 4, -8, 10, -2, 10, -26],\n [-6, 14, 12, 14, -1, 15, 26, -24, 23, 14, -22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 6, -25, -9, 25, -13, 13, 3, 2, 2, -8, 19],\n [-1, 19, 25, 13, -18, 19, 17, -14, 11, 4, -13, 4],\n [-12, 7, 23, -17, -6, 12, -2, 10, 13, -7, 18, -20],\n [-9, 14, 17, -1, -10, 15, -20, 1, -6, 10, -4, 20],\n [21, 21, -17, 19, 25, -10, 11, -26, -16, 6, 4, 17],\n [-3, -7, 20, -22, 15, -1, 22, 15, -20, 0, -9, 11],\n [4, -18, -25, 17, 10, 20, 18, 2, 7, -12, 19, -18],\n [-11, -25, -26, -18, -7, 19, -25, -26, -17, -4, -8, -9],\n [-3, 25, -5, -7, -16, -18, -12, -11, -14, 26, -21, -2],\n [20, -12, -9, 16, 6, -13, 7, -25, -7, 15, -11, -24],\n [19, 3, -4, 12, 24, 24, -4, 24, -24, -14, 24, 19],\n [13, 2, -4, 13, -10, -6, 2, 10, -22, -6, -25, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "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, -4, -20, 16, 7, 11, 14, 22, 24, 17, -21],\n [-11, -25, 5, 16, 20, 11, 1, 14, -18, -2, 23, -1],\n [18, -1, -22, -10, -1, -1, 26, 16, -18, -4, 25, -3],\n [14, -18, -17, 25, -21, -23, -26, -21, 11, 2, 17, -24],\n [18, -3, 15, -18, -10, 16, 11, 15, 23, -13, 9, 18],\n [6, -7, 7, -24, -7, -24, -21, 2, 12, 16, 4, 12],\n [22, -6, 24, 17, -26, 6, 23, -17, 25, -1, -24, -13],\n [-19, 21, 23, 5, 14, 9, 0, 6, -6, -1, -13, 16],\n [9, 1, 1, -6, 21, 14, 2, 19, 11, 7, -26, -7],\n [-1, 24, 0, -4, -20, -5, 20, 10, 8, 20, -23, 2],\n [10, 9, -24, -25, -22, -9, 7, -12, 23, 23, 13, 17],\n [14, 24, -26, -5, -2, -10, 6, 25, -10, 11, -22, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[16, 16, -16, -15, 17, 7, 8, 12, 25, 19, -11, -3],\n [4, -13, 22, 20, 5, 16, -14, 11, -10, 17, 9, 26],\n [15, -9, -8, -20, 3, -15, -16, 2, -24, 7, 7, 4],\n [-5, -25, 0, 20, 9, 5, 8, -10, 7, -1, -17, 12],\n [-18, -2, -7, -12, 13, 22, 0, -16, -11, 3, -5, -3],\n [23, -3, 9, -9, -7, -19, -12, -14, 9, -13, 20, 20],\n [-3, 10, -3, 20, -9, 5, 8, -7, 15, 5, 10, 10],\n [20, 6, -26, 21, 1, 0, -10, 19, -12, -13, 26, 4],\n [7, -24, -15, -1, -3, 7, -19, -15, -18, -1, 19, 11],\n [22, 16, -8, -6, -14, 8, -24, -2, 5, -6, -13, 4],\n [-19, -20, 9, 8, -8, -25, -22, 17, -25, -9, -12, -11],\n [-15, 17, 9, -5, 1, 13, 16, -5, -23, -15, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 15, 0, 14, -11, 5, 9, -10, -9, 0, -20, 14],\n [11, -7, 8, 20, 6, -1, -3, -3, 4, 0, 22, -18],\n [-25, -21, 4, -2, -11, 18, -21, -4, 20, -22, -10, -18],\n [-1, -14, -20, 21, 13, -9, 10, 18, -3, 5, -20, -7],\n [18, 7, -8, 19, -13, 5, -18, 9, 22, -1, -7, 2],\n [-11, 4, -3, 3, -19, -1, -12, 23, -17, 9, 12, -3],\n [22, -19, -26, 26, -17, 20, -4, 11, -17, 6, 4, 11],\n [-14, 8, 17, 20, 5, -5, -20, -21, 14, -11, -15, -18],\n [13, -22, -24, 9, 16, -17, -19, -18, -14, -8, -4, 16],\n [-3, -24, 6, -4, -13, -8, 6, -4, 0, -15, 19, 20],\n [-20, 9, 19, -9, -11, -13, -6, 16, 0, -2, 11, -12],\n [-17, 3, 17, -18, 1, 22, -9, -16, 11, 24, -25, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "497", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -7, 18, 2, -1, 14, -15, 21, 2, -8, 7, 21],\n [0, 3, 10, 4, 1, -2, 22, -21, -20, -21, 8, -2],\n [-6, 20, 21, -10, 14, -1, 14, -10, -20, -2, 7, -1],\n [-21, -17, -10, -13, -24, 21, -11, -22, 21, -4, 0, -22],\n [10, 11, -9, -15, -6, -20, -10, 15, -18, 14, -3, -16],\n [-2, 19, 10, -20, -10, 14, -8, -6, 18, -18, 18, 19],\n [-19, 19, 18, 0, -4, -17, -25, 17, 21, -20, -25, -11],\n [-21, -11, -2, 18, -17, 25, -18, 5, 5, -25, -6, 21],\n [-24, 7, 2, 15, -7, -4, 10, -19, 17, 9, -13, -4],\n [0, -12, 26, 8, -5, 20, 9, -12, 5, 14, -9, 18],\n [4, 14, 9, -2, 18, -17, 13, -13, 21, -1, -8, 3],\n [12, -15, 4, 18, 20, 20, -9, -25, -13, -7, 12, -7]]\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[[7, 7, 10, -24, 8, 6, -8, 4, 25, 17, -5, 0],\n [11, 1, -6, -7, 11, -14, 2, -6, 15, 6, 5, 21],\n [19, 1, 23, -13, 15, 25, -5, 10, 7, -10, 6, 6],\n [11, -1, 12, -20, -2, 21, 24, 3, 14, 6, 23, 12],\n [1, -9, -17, 25, -25, 16, 23, 16, -13, -14, -26, 5],\n [-2, -17, -12, 24, 2, -10, 15, 13, -4, -20, 23, 9],\n [-21, -25, 18, 5, 26, 17, -22, -8, -25, 16, -4, 13],\n [-23, -23, -16, 19, 14, -7, -13, 8, 18, -13, 22, -24],\n [-12, -6, -25, -6, -17, 0, 20, -8, 26, -15, 22, -11],\n [-19, 10, -2, -3, 20, 13, -9, -6, -19, -8, 22, 3],\n [0, 9, 9, -1, -7, 25, 14, -13, 6, -18, -4, 18],\n [3, 26, 23, 15, 1, 4, -1, 9, 20, 9, 25, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"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, 18, -25, 13, -23, 5, 14, 7, -22, -22, -23, 24],\n [14, -15, 8, 10, 7, 18, 1, -20, 26, 13, 25, -16],\n [17, 5, 23, 23, 5, 4, 21, -7, -21, 23, 22, -9],\n [-6, -24, 14, 1, 1, 5, 12, -3, -20, -8, -26, 6],\n [6, -16, -4, 23, 18, 1, 20, -10, -17, -19, 26, -18],\n [-8, 23, -19, -22, -13, 18, 6, 16, 17, 11, -15, -24],\n [13, 2, -5, 7, -21, 8, 12, -11, 4, 22, 17, -12],\n [19, -26, 17, -7, -4, -7, 5, 19, 21, -2, 20, -19],\n [26, 6, 18, 3, -24, -3, -15, 4, -20, 13, -10, 23],\n [-17, -12, -6, -6, 2, 15, 14, -26, -6, -22, -12, 19],\n [-1, -16, 22, -6, 19, -21, -23, 18, -6, -10, 26, 4],\n [17, -4, 5, 17, 9, 7, 25, -21, 11, -5, 6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 26, 17, 9, 1, 21, -8, 16, 16, -14, -14, -19],\n [16, 21, -14, 8, 0, -16, -6, -19, 15, -1, 3, -5],\n [23, 22, 12, 23, -17, -1, 25, 0, -5, -14, 12, -20],\n [25, 16, 15, -15, -14, -15, -15, 11, -24, -19, 22, 4],\n [-14, -19, 10, -3, 1, -23, -11, -9, -23, 16, 13, 6],\n [18, 26, 0, 9, -23, 9, -14, 24, 21, -13, 15, 10],\n [20, -21, 24, -13, 16, -24, -2, 7, -21, 13, -26, 19],\n [21, 22, -19, -10, -14, -8, 14, 8, 23, 6, 18, 18],\n [17, 6, 15, 24, 12, 19, 11, 11, -18, 25, 21, 10],\n [20, -26, 9, 15, 11, -25, -17, 24, -4, -18, -16, 9],\n [15, 11, 8, -14, -8, 8, 25, 3, -9, -15, -15, -6],\n [-15, 1, 2, 12, 14, 17, 24, -23, 4, -3, 15, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[22, -9, 15, -1, 17, -7, -19, 24, 6, -23, 11, -5],\n [9, 21, 4, -19, -18, 20, -9, 8, -3, -10, -26, 12],\n [15, -12, -14, -4, 2, 4, 10, 1, 5, -20, -13, -13],\n [5, -18, -21, 24, -12, 3, 3, -11, -4, 4, -15, -6],\n [-24, -24, 11, -5, -6, 24, 17, -11, -9, -23, -7, 18],\n [-14, 4, -25, 3, 4, 1, -18, -16, 8, 22, 17, 10],\n [19, 24, -10, -1, -23, 6, -10, 15, -19, -1, 16, -7],\n [15, 24, 11, 16, 21, 15, 6, 13, -10, 24, -18, -7],\n [-19, 14, 21, 19, -21, -18, -16, 20, 20, -22, -19, 25],\n [8, 25, -2, 9, 12, 22, 17, -21, -3, -6, 9, -9],\n [21, -26, 2, -10, -22, 23, -21, 18, -19, -2, -8, 21],\n [23, 12, -18, 1, 26, 4, -26, 14, -17, 26, 23, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-26, -14, -13, -4, 12, 1, 2, 13, 6, -25, 16, 6],\n [-3, -15, 13, 1, 8, -17, 20, 17, 7, -22, 14, -9],\n [-21, -16, 19, -26, -4, -23, -20, 14, 22, -10, -16, 0],\n [-15, 20, 7, -19, 25, -4, -1, 7, 5, -21, -26, 23],\n [-23, -2, -19, 13, 19, -7, -13, 6, 25, -24, -12, 0],\n [-8, -26, 8, 25, 6, 24, -10, -14, 25, 21, -15, 12],\n [-1, 0, -3, -10, -16, -5, -19, 15, 21, 5, 2, 15],\n [5, 13, -22, 22, -14, -2, 15, -17, -1, -1, -6, -4],\n [17, -15, 12, 16, 25, -2, -15, 9, 5, -9, 15, -7],\n [-25, 6, 19, -10, 9, 3, -18, 4, 12, -6, -5, -10],\n [-24, 5, 6, -17, -22, -23, 24, 11, 5, 11, 14, -7],\n [-18, -12, 25, -19, 7, 3, -17, -13, 7, -5, -14, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 2, -20, 17, -21, 8, 10, -23, -13, -21, -10, 22],\n [-3, -14, -15, 2, -3, 7, -13, 0, -22, 13, 20, -18],\n [-11, -14, -12, 9, -2, -11, 17, 25, 17, 4, 20, 10],\n [6, -7, -1, 8, 13, -20, 18, 15, 4, -10, 16, -19],\n [-4, 20, 17, -9, 15, -15, 3, 9, -12, -9, -2, -14],\n [-3, -10, -26, 10, 22, 0, -7, -9, -18, -17, -2, 22],\n [-26, 9, -9, 20, -12, 6, -5, -3, -26, -16, 16, -1],\n [-1, -21, 6, -13, -3, 11, 22, 14, -10, -13, -8, -19],\n [-4, 17, -25, -24, 26, -14, -22, -9, -26, 10, -6, 17],\n [-8, 11, 7, -25, -7, 4, -14, -13, 11, -15, -14, -3],\n [13, 4, -13, 23, 3, 0, 9, -21, -21, -12, -3, -14],\n [-20, 18, -6, 11, 11, -13, -24, 16, 18, 8, -15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-7, 0, -22, 18, -16, 22, 15, 17, -21, -22, -5, -26],\n [-7, -3, -7, 20, 21, 2, 15, -3, -19, 7, -5, 12],\n [6, 25, 3, -21, -14, 17, -8, -1, -10, 10, 0, -3],\n [20, -13, -24, -22, -13, -19, 16, -2, -12, 18, 10, 18],\n [-24, 18, -16, -18, -23, 22, -12, 0, 4, 23, -11, 5],\n [7, -21, 17, -22, -3, 22, -8, 3, -15, -22, 1, 12],\n [7, -15, -4, -22, 13, 10, -11, -18, 6, 10, 6, 22],\n [-26, 20, 10, -18, -9, 11, -6, 17, -13, 12, 12, 24],\n [-21, -24, 21, 21, -9, 10, -7, 2, 9, -11, -23, 18],\n [-13, -10, 8, 8, 22, 18, 5, 26, 25, -17, 2, -15],\n [-18, -1, -6, -26, 9, -8, -21, 20, -9, 10, -19, -16],\n [-22, -6, 13, 16, -6, -7, 15, -18, -25, 22, -23, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, -8, -8, -8, 2, 12, 18, 7, -19, -21, 5, 1],\n [-16, 1, 5, 14, -19, -7, -3, 25, 0, 20, 26, -16],\n [20, -4, -5, -22, 21, 7, 4, 20, 10, 20, -1, -4],\n [16, 11, 11, 5, -22, -2, 6, 25, -20, -11, 22, 2],\n [-12, -7, -5, -17, -19, 5, 1, -18, 4, -4, -8, 5],\n [-17, -7, 8, 4, -16, 16, 13, -17, -18, 15, -17, 23],\n [10, 10, -20, -7, -7, -19, -10, 11, -2, -14, 18, -14],\n [21, -25, 10, 15, 15, -16, -7, -18, 18, 18, 2, 7],\n [-22, 4, -1, 10, 17, -7, -19, -21, -9, -19, 26, 25],\n [-2, -25, 1, 15, -2, -7, -21, 10, -11, 8, 9, -26],\n [-13, -13, -3, -8, 11, 17, -9, -18, 25, -14, 24, 18],\n [24, -8, 26, -17, 11, -24, 21, 14, -10, -4, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-22, -8, 2, -12, 15, 9, -15, -13, -12, 24, 4, -22],\n [17, -24, 20, 3, 20, -15, -12, 11, 1, 22, -4, 20],\n [-12, -16, 3, -15, -8, 5, -26, -11, -16, 4, 6, 9],\n [3, 11, -23, -2, 7, -10, 6, 3, -14, -15, 5, -4],\n [2, 7, -8, -15, -23, -2, -1, -9, 3, 7, 6, 4],\n [4, -14, -3, -22, 24, -26, 7, 19, -18, -19, 16, 9],\n [2, 8, -22, 19, -17, 11, -17, -16, 25, -19, -23, 26],\n [-9, -7, 19, -24, 17, -12, -19, 19, -21, 19, 9, -7],\n [5, -21, -11, 22, -25, -9, 18, -1, -7, -11, -6, 18],\n [-13, -9, -19, -22, -3, 14, 20, 2, -18, 25, 15, -9],\n [19, -9, 21, 1, 10, -17, -7, 11, 14, -4, 21, 16],\n [-7, -4, 23, -22, 0, -18, 16, 14, 9, 13, 10, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[9, 21, 18, 8, 9, 2, 6, -1, -19, -18, -5, -22],\n [17, 14, 9, 5, 3, 22, 17, 18, 16, -10, 3, 20],\n [-18, -23, -15, 8, -7, -10, -5, -20, 12, 26, 17, 26],\n [15, -19, -18, 19, -21, -8, -5, 20, -7, -7, 0, 0],\n [-20, -3, -19, -24, -16, 9, -25, -26, -20, -3, -15, -19],\n [-14, -21, 12, -3, 25, -3, 11, 17, -20, -17, 3, 12],\n [-3, 0, 3, -12, 26, -25, -19, -10, 21, -14, -9, -6],\n [9, -15, 16, -25, -7, -4, -6, 4, -11, -14, -23, -25],\n [23, -26, -1, 3, 11, -7, -2, 25, -8, 0, -17, 14],\n [-10, 20, -25, -10, -20, -11, 22, 0, -26, -5, -5, 0],\n [-11, 26, 9, -11, -3, 8, 6, -10, -22, 8, -8, 16],\n [20, 7, 5, -2, -5, 12, 23, 0, 6, -19, 3, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -12, 9, 18, -15, 14, 18, 16, -15, -23, -24, 10],\n [11, 5, -1, -23, -26, -22, -25, 19, -16, -18, -19, 12],\n [-12, -18, 15, 23, 3, 2, 24, -2, -5, 7, -5, 19],\n [3, 26, -17, -22, -22, -25, 3, -5, -14, 12, -2, 26],\n [0, 20, 0, -6, 4, -12, 11, 12, 9, 9, -26, -16],\n [-22, 7, 10, -22, -7, 18, 17, 15, -14, -18, -22, 11],\n [5, 3, 22, 1, 10, 1, 16, -21, 14, 17, 2, -23],\n [-9, -12, -2, -23, -13, 23, -10, 7, 26, -8, 2, -5],\n [-13, 9, -25, 18, -20, 1, -19, 2, -17, -6, 8, -23],\n [26, -6, 11, -2, -7, -20, -20, 5, 5, -5, 22, -2],\n [-21, 24, 0, -9, -15, 1, -8, 16, -10, 8, -12, -22],\n [9, 6, -6, 8, 15, 0, 18, 3, 12, 19, 3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -1, -3, -5, 10, 16, -1, -5, 19, 6, -3, -22],\n [-3, 8, -5, 6, -10, 25, -15, 3, -1, -14, -21, -24],\n [-16, 16, 26, -17, -16, -11, -7, 15, 17, -8, -18, 9],\n [-12, -4, -6, 12, -22, 24, -5, 4, -12, 1, 11, 25],\n [-12, 22, -8, 8, -9, -17, -12, 23, -3, 20, 24, -7],\n [10, -16, -18, -22, -16, 12, 0, -25, 25, -7, -6, 24],\n [23, 3, 21, -26, 8, -1, 5, -18, 22, 13, -6, -11],\n [-15, 9, 10, 0, -20, 3, -3, 23, 3, -7, 19, 13],\n [18, 1, -23, -15, -24, 10, -23, -12, 1, 10, -18, -13],\n [5, 21, -24, 20, -9, 23, -13, -2, 12, -1, 25, -21],\n [-1, 21, 24, 14, 25, -26, 23, -6, -13, 19, -19, -2],\n [22, -9, -12, 15, -7, -11, -20, 2, 4, 2, -10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"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, -13, 4, 23, -9, 20, -2, -16, -1, -22, -11, -19],\n [-14, 5, 0, 22, -1, -18, 20, -20, 23, 19, -19, -25],\n [-9, 9, -3, 7, 15, 11, -16, 25, -17, 2, 22, 13],\n [-21, 21, -17, 3, 1, 2, 24, -2, 9, 0, 7, 25],\n [7, 5, 17, -23, 21, 7, -11, 20, 19, -16, -12, 11],\n [3, 0, -11, -26, -2, 1, 16, -13, 7, 21, -23, -13],\n [-11, -12, 7, -14, -10, 1, 25, -17, 20, -10, -19, -25],\n [-26, -22, 8, -5, 16, -11, 26, -18, 9, -18, -13, -17],\n [-5, -11, 14, -24, 1, 3, 2, -26, 1, -5, 5, 25],\n [-16, -1, 4, -7, -7, 6, -22, 14, -24, 17, 23, 7],\n [4, 15, -20, 3, -9, -11, -14, 6, -20, 3, -16, -21],\n [-6, 5, -22, 15, 2, 8, 20, -15, 10, 19, 17, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-16, -4, 18, -17, 15, -3, 26, 19, 25, -11, -15, 23],\n [5, -3, -23, 15, 6, -9, 20, -10, -6, -26, 19, 17],\n [-2, 4, 16, -7, -1, -8, 3, -2, 9, 22, -9, -23],\n [0, 6, -21, -20, -26, 11, 8, -4, -11, 7, 7, 4],\n [16, 4, 25, -16, -19, 24, -3, -4, 5, 26, -12, 1],\n [-7, -13, -1, 23, 25, 10, -25, 7, 7, 7, -18, 17],\n [26, 25, 23, -24, 3, -8, 4, -11, 16, -3, -12, -5],\n [5, -16, 2, 15, -3, -8, -22, 19, 14, 26, 11, -26],\n [3, -15, 19, -23, -12, -10, 25, -15, -26, -14, 3, -17],\n [9, -21, -18, 23, -25, -21, -16, -1, 1, -14, 11, -15],\n [-8, -9, -8, 1, -15, 5, 25, -14, 25, -4, 9, 3],\n [-5, 11, 18, 15, -24, -18, -12, 3, -1, 3, -22, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 14, -12, 18, 26, 8, -8, 7, -9, -13, -5, -3],\n [-14, -19, 15, -25, 15, 0, 7, 2, -1, -4, 9, -18],\n [-6, 15, 9, -24, -20, -4, 5, -4, -11, -22, -14, -17],\n [-25, -11, 25, -26, -21, -8, 6, 1, -22, -15, 3, -10],\n [-8, 13, 15, -2, 8, -18, 5, 12, 11, -12, 18, 19],\n [10, -1, 4, 3, -25, -20, 3, 6, 21, 12, 20, 11],\n [-7, -8, -18, -5, 5, 3, -21, -10, 10, -12, -20, -13],\n [-7, 3, -9, -5, -2, -3, 4, 22, -9, 7, -9, -13],\n [-23, -20, -20, -26, 13, 25, -3, 5, -17, -18, 12, -24],\n [17, 8, -22, -20, -15, -4, -2, -10, -13, 8, -26, -5],\n [1, -4, -9, 19, 18, 17, 10, -24, -13, 12, -20, -10],\n [-21, 20, -8, -12, 12, -22, -12, 25, 18, -1, 12, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "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, 4, -14, -4, 13, 5, 10, -23, -10, -7, 19, -16],\n [15, 6, 12, -21, 12, 20, 11, -9, -25, 14, 11, -10],\n [-3, 3, 16, -3, -23, -20, -12, 3, 2, 22, 17, 18],\n [26, -14, 13, 12, 2, -1, 9, 8, 22, 21, -8, -25],\n [26, -13, -11, 22, 9, 13, 14, 4, 21, 21, 22, 8],\n [-5, -6, 1, -10, 23, -9, 5, -4, -21, 2, -21, 6],\n [21, 5, -10, -23, 21, 4, -5, 0, -6, -7, 7, -4],\n [17, -11, -21, -11, -20, -13, -24, 6, 22, 25, 9, 12],\n [2, 12, -23, 12, 13, 14, -5, -12, -23, -9, 17, -4],\n [11, -23, -23, -9, -26, 5, -6, 11, -1, 14, 22, -6],\n [16, 2, 26, 14, 16, 5, -23, -14, 24, 8, 0, -26],\n [22, 22, 12, -13, 10, 3, -13, -16, 4, 1, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-21, 12, -8, 14, 7, 1, -15, 12, -17, 25, 20, -2],\n [-4, -1, -8, 11, -7, 18, 25, 17, -9, 21, -16, -2],\n [16, -26, 5, 6, -20, 4, -1, -20, 9, 19, -3, -22],\n [-5, 17, 9, -24, 23, 10, 11, 19, -21, 25, -2, -4],\n [-15, 1, 17, 13, 5, 25, -2, 7, 3, 10, -9, 8],\n [21, 10, 14, -21, -8, -5, 5, 0, -11, -1, 12, -23],\n [-11, 25, 22, -8, 1, -10, 18, -25, -25, -3, 0, -23],\n [21, 9, -7, -15, 1, 2, 25, 19, 6, 22, -9, -15],\n [-17, -3, 20, -10, 16, 5, -2, 25, -20, -7, 2, -8],\n [-16, 6, 23, -12, 4, -14, 21, -8, -21, 1, -5, 1],\n [-11, 23, 6, 23, 14, 18, 21, 24, -1, -4, -26, 2],\n [-19, 15, 12, -24, -14, -7, 16, 25, -22, 18, -15, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, -13, 26, -1, 3, 15, 18, 5, 3, -15, 9, -8],\n [17, -2, 6, 15, -6, -25, 10, -6, -1, 5, 0, -10],\n [-23, 12, -12, 6, -13, -1, 20, -25, -7, -1, -25, 21],\n [-25, 21, -10, -9, 24, 21, -23, -10, 6, -4, 26, -14],\n [-20, 14, 19, -26, 13, 15, 4, 9, -2, 18, 23, 14],\n [13, 3, 11, -6, -8, -11, 6, 20, -21, 15, 10, -19],\n [-26, -14, -1, -11, 22, 12, 20, 19, 1, 22, -4, -20],\n [-3, 19, -19, 18, -26, -23, 16, 14, -8, -5, 9, -26],\n [-8, 24, 2, -8, 16, -21, -2, 12, -4, -26, -12, -2],\n [-23, 18, 17, -26, 13, -6, 16, -17, -25, -10, -14, 0],\n [14, 21, 1, 22, -17, 22, 25, -17, 19, 20, -18, 7],\n [19, 26, 12, -23, 18, -23, -23, 14, -16, -26, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -18, -2, -9, -20, 19, -1, 22, -9, -26, -18, -17],\n [21, -16, 5, -6, 9, 5, -8, -19, 8, -5, -23, 2],\n [4, -19, -15, -22, 3, 8, 10, -23, 16, -6, -11, 26],\n [-9, 4, 11, 5, 21, 6, -8, -7, 21, -17, -1, 19],\n [-9, 18, 18, -12, 9, -9, 4, -12, 11, 2, 15, -12],\n [-26, 10, 14, -4, 19, -16, 11, -11, 3, 2, 14, -24],\n [13, -10, -1, -18, -10, 10, 4, 4, -16, 11, -5, 19],\n [-24, 22, 1, 5, -23, 13, 11, -16, -26, 20, -11, 7],\n [18, 5, 17, 19, 6, -16, 9, -14, -7, -2, -21, 10],\n [-1, -23, 18, -1, -9, -14, -19, 24, 20, 6, 16, -11],\n [15, 12, 4, 13, -4, 25, -11, -17, 9, 4, 17, 5],\n [-6, -11, 2, 23, 21, 18, -11, -12, -19, -12, -6, -6]]\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[[-20, 25, -8, -5, 19, 11, -14, -1, 17, -5, -20, 25],\n [8, -24, 8, 20, -11, 18, -11, -25, 11, -10, 11, -3],\n [-5, 23, -4, 17, -8, 17, -5, -10, -25, -13, 1, -14],\n [11, -10, -18, 13, -13, -25, 15, -6, 8, 3, -10, 12],\n [-2, 17, 12, 8, -21, -24, 9, 21, 20, -26, 7, -26],\n [-1, -9, 9, -21, -16, 17, 13, 3, -13, -17, 4, 9],\n [-12, 3, 21, -13, 20, -4, -10, 0, 17, -14, -13, -1],\n [16, -16, 11, -26, -3, -7, -19, -19, 3, -9, -14, 19],\n [20, 9, -8, -14, 14, 21, -1, -18, 7, 26, 4, 15],\n [-20, -18, 13, -1, 25, 24, 6, 6, 25, 13, -23, 1],\n [-23, 20, 7, 22, 13, 21, -21, 6, -22, -8, -9, -24],\n [7, -25, -26, 8, 24, -23, 8, -19, 17, 2, 9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"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, 22, 3, 23, -20, -14, -5, 18, -25, -19, -6, -7],\n [-16, 7, 17, -22, 26, 21, 3, 6, -15, -22, -26, 8],\n [-2, -23, -18, 22, 17, 24, -24, 3, -7, -17, -7, 13],\n [-24, -16, -12, 25, 1, 17, 8, -20, 6, 15, 22, 11],\n [-8, 17, 2, -25, 17, -8, -18, -21, -10, -25, 12, -21],\n [-13, 22, -1, -9, -21, -15, 11, -5, -13, -14, -18, 23],\n [15, 5, -17, 0, -13, -18, -18, -1, 5, 14, 8, -1],\n [14, 18, 15, -24, 3, 2, -7, -23, -13, 18, 25, 12],\n [-6, -20, -21, 13, -21, -2, -23, 10, -2, -9, 7, -2],\n [-5, 19, -13, 10, -16, 0, -1, 25, 8, -11, 25, 13],\n [-7, -12, -13, 19, -19, -3, 6, -11, 0, 1, 17, -13],\n [-18, 19, -14, 24, -5, 3, 5, -11, 24, -2, 22, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, 1, -24, -4, 6, 12, -2, -2, 12, -6, 4, 22],\n [3, 12, 18, 18, 15, 25, 7, 11, -20, 0, -14, 2],\n [-4, -19, -6, -14, -1, 16, -17, 2, 0, -23, 15, 4],\n [-10, -19, 25, 10, -7, 20, -17, 24, 23, 17, 7, 12],\n [-16, 20, -15, -17, -14, 7, 3, -12, -19, 11, 9, 13],\n [25, -5, -22, 5, -7, -4, 13, 19, 22, 25, -25, -8],\n [-1, 9, -13, -20, -11, -17, 16, -5, -1, -22, -15, -3],\n [-3, -12, -3, -3, 15, -1, 7, -9, 16, 10, -21, 18],\n [-2, -10, -11, 2, -26, 18, 15, 18, -7, -1, -6, 23],\n [23, 0, 9, 8, -11, 2, -20, -20, 7, 21, -22, 26],\n [-19, -19, 16, 2, 25, -17, -26, 11, 1, -20, -10, 21],\n [19, -3, 8, -18, 15, -24, 17, -23, 5, 17, -14, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "539", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-20, -8, 0, 23, 0, -9, 3, 1, 2, -18, 12, 12],\n [-6, 18, 11, -20, 18, -2, -1, 25, -21, 22, -7, -9],\n [-7, 13, -9, 20, -26, 6, 12, 21, -4, 25, -13, 1],\n [-6, 17, 10, -20, -15, 24, 10, 12, 1, -20, 18, 25],\n [-10, 10, -13, 16, 25, 24, -23, -5, 22, -10, 8, 19],\n [26, 5, 11, 4, -2, -17, 22, -25, 0, -15, 26, -11],\n [-11, -24, -2, -9, 12, 15, 13, 5, 23, 22, -24, -19],\n [25, -22, -7, 17, -2, -21, 1, -4, -3, -17, -17, 6],\n [-18, -9, -24, 6, -17, 0, 8, -9, -20, -20, -5, -17],\n [0, 18, -23, -15, -24, 21, 16, -24, -2, -1, 13, -20],\n [19, 7, -17, -24, 1, -16, 24, 5, -19, -7, -22, 14],\n [-14, -16, 7, 17, -24, -12, 6, 16, -17, -24, 19, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "561", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[21, 14, -13, 26, 6, 6, 9, -4, -26, 0, 24, 5],\n [-6, 17, -7, 0, 9, 14, 5, 12, 2, 19, -4, 8],\n [-12, 16, -17, 25, -12, -2, -10, 24, 4, -16, -7, 4],\n [-11, 9, 12, -16, -7, -1, 22, 24, -1, 15, 20, -21],\n [18, 8, -19, -20, 10, 23, 26, -11, -18, -16, -6, 24],\n [19, -20, -15, 24, 13, -6, -22, -21, 16, -1, 2, -24],\n [-16, -4, -2, -15, -26, -23, 25, -26, -21, 7, 0, 18],\n [-11, -16, -13, 11, 21, 22, -17, 26, -14, 18, 7, 6],\n [6, 12, -14, -10, -18, -14, -11, 10, 3, 12, 6, 13],\n [-21, -15, -25, 6, -12, -10, 25, 8, 4, 3, 11, -11],\n [15, 18, 13, -10, -20, -22, 13, 0, -26, -25, -23, -26],\n [2, -6, 15, 8, 7, 12, -25, -2, -21, -19, 8, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "559", "dataset": "MATH"}
{"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, 6, -19, 11, 5, -4, 7, -4, 19, 5, -26],\n [-20, 16, 21, -3, -25, -9, -8, 15, 9, 1, 8, 5],\n [-14, -21, 2, -17, 13, -17, 7, -7, 20, 6, -16, -3],\n [6, -5, 21, -15, 3, 5, 17, -8, 18, 13, -25, 24],\n [-13, 6, 5, 14, -8, -13, -23, -25, -17, 2, -12, 4],\n [6, 2, -16, 21, 18, 13, -18, 20, 2, 10, -6, 4],\n [26, -5, 25, -9, -25, -5, 10, -7, 21, 21, -23, -1],\n [-7, -5, 16, -7, 2, 21, 4, -4, 17, 11, -11, -8],\n [-16, -15, 9, -14, -25, 24, -16, -26, 14, -17, -24, -19],\n [-11, 9, 16, 13, 12, -7, 20, -19, -17, 24, 10, 5],\n [0, 4, -24, 12, -21, -10, -17, -6, 2, 2, -7, -12],\n [-25, 6, -15, -14, 17, 17, 12, 12, 11, 18, -6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "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, 0, 16, -24, -18, 17, 7, -8, 11, -1, -4],\n [-9, 18, 19, 13, 14, 18, 22, 11, 25, -17, 16, -17],\n [-6, 11, 11, 20, -20, -15, 25, 14, 6, -2, 1, -3],\n [21, 4, -9, -4, -20, 23, -19, -12, 11, 1, 0, -6],\n [17, 0, 20, 20, 15, 14, -13, -6, -13, 22, 16, -21],\n [-15, 1, 22, 2, 10, 11, -24, 6, 23, 19, -15, -15],\n [-16, 1, 24, 8, 7, -5, 12, 26, -4, -15, -8, 4],\n [26, -14, -8, 9, -5, 17, 3, -23, -14, -7, 12, -21],\n [17, -15, -11, 18, -10, -19, 6, 17, 25, 12, 26, -15],\n [-1, -8, -14, -17, 7, 4, 0, -24, 17, -22, -22, 10],\n [-20, 13, 24, 21, 15, -14, 7, 9, 7, 26, -24, -17],\n [16, 8, 10, 25, -21, -6, 18, -22, -24, -7, 3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[8, 5, -8, -12, -17, -1, -21, 21, 20, -1, -25, 22],\n [21, 5, -24, -8, 9, -7, 3, 10, 18, -7, 7, 17],\n [-10, 15, -4, 14, -18, 0, -10, 14, 19, -10, 22, -25],\n [-12, -16, 10, 14, -18, -13, -19, 16, -15, -20, -24, -1],\n [-24, 19, -23, 5, 19, -13, -24, -14, -19, 11, -25, 11],\n [25, 19, 4, 12, 0, -10, 8, 19, -3, -26, 2, -1],\n [17, 8, 24, 17, -3, 19, 6, -1, 10, 12, 25, 24],\n [-1, 11, 26, 23, 11, -16, 2, 2, -24, -18, 8, -21],\n [-18, -19, 0, 7, 24, -3, 21, -22, -17, -7, -5, -15],\n [17, 2, 4, -21, 19, -20, 26, 6, 19, -12, -14, -3],\n [3, 6, -7, -8, -8, 11, -3, -22, -5, -5, 1, -10],\n [4, 20, -20, -10, -15, -20, 2, 18, -19, -23, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-11, -5, -16, 14, -16, -22, 15, 11, 21, -15, 13, -2],\n [18, -14, 21, -1, -16, 13, -4, -14, 6, 25, 25, 1],\n [24, -23, 1, 7, 24, 24, -17, 22, 25, -19, -18, -9],\n [-25, -9, 13, -25, -5, -11, 10, 5, -17, 14, 7, 21],\n [-11, 22, 7, 10, 13, 7, 17, -14, 21, 10, -15, -12],\n [3, 4, 2, 7, 5, 17, -4, -17, -19, -6, -16, -15],\n [22, 12, 20, -8, 7, 11, 7, 19, -1, 13, -11, -8],\n [23, 2, 18, 11, 9, -6, -17, 20, -4, 17, 25, 17],\n [-20, 11, -22, -8, 19, 6, -3, 16, -4, -5, 9, 26],\n [19, -6, -9, 11, 0, 10, 22, -2, 12, 3, 16, -13],\n [7, 5, 4, 22, -25, 20, 12, 8, -4, -21, -6, -1],\n [3, 14, 15, 26, 3, 26, -19, 12, 6, -17, -9, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, 14, 23, -16, 17, -19, -26, -19, -22, -26, -24, 0],\n [18, 21, -4, 17, 12, 13, -16, 18, -16, 9, 11, 4],\n [-3, -8, 26, 5, 13, 11, -10, 23, 8, -15, -12, 12],\n [-14, 3, 15, -8, -18, 1, 17, 16, -2, 13, 14, -23],\n [25, 10, -20, 14, -23, -4, 17, 17, -21, 18, -18, -18],\n [-6, -24, -14, 11, -9, 19, 4, 2, -25, 4, 11, 25],\n [-20, 13, -17, -14, -26, 10, -2, 3, -25, 9, -3, -15],\n [-22, -12, 15, 22, 19, -20, -25, -24, -23, 21, -11, 0],\n [-5, -24, 22, -10, -5, 25, -20, 3, -19, -8, -20, -26],\n [-11, 23, 13, 4, 12, 0, -17, 7, 20, -13, -25, 12],\n [-5, -1, 17, -22, 11, -11, -15, 14, 25, 17, 15, -10],\n [-2, -3, -16, -9, 9, -24, -8, -21, -4, 13, -20, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575", "dataset": "MATH"}
{"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, -18, -25, 25, 20, 23, 18, 21, 20, -16, -24],\n [15, 22, 3, -19, 10, -6, -19, 20, -16, 14, 7, 12],\n [-11, -20, -23, 5, 10, 19, -5, -20, -14, -9, 15, 7],\n [-14, 7, 2, 20, -22, 4, -16, 11, 24, 20, -23, -20],\n [-4, 4, -10, -17, -5, 3, 2, -10, 16, -6, -5, 21],\n [12, 13, 21, 21, -5, 0, -4, -23, -1, 12, -10, -24],\n [-10, 16, 13, -8, 12, -9, 1, 26, -12, 24, -1, 8],\n [-11, -12, -22, 19, -3, -25, 9, 25, 18, 21, 4, 3],\n [-15, 10, -6, -15, 13, 10, 8, -5, 18, 9, 26, -19],\n [0, 0, 9, -20, -24, -23, -3, -19, 18, -14, -18, -7],\n [-7, -22, 19, -22, 8, -26, 15, -12, -10, -15, 19, 9],\n [16, -12, -13, 0, 23, -5, -18, 20, -6, -24, 25, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, -25, 20, -13, -20, 2, -23, -23, -3, 15, -6, 24],\n [18, 1, 11, -19, 15, -10, -18, 19, -7, -22, 8, 14],\n [2, -15, 5, 4, 4, -26, 16, -22, 24, 9, -15, -11],\n [-11, -6, 6, -1, -24, -4, -2, -7, 20, 25, 22, 9],\n [8, 16, 6, -22, -23, 25, -19, -16, 16, 23, 0, -17],\n [18, -7, 5, 21, 0, 22, -9, -1, 8, 1, -26, 7],\n [-1, -21, 23, 22, 19, -2, -10, -1, -6, 5, -2, 5],\n [14, -8, -25, 8, -11, -11, 6, 24, 23, -3, 4, 15],\n [-4, -10, 6, 10, 9, -8, -6, 12, 13, -8, -19, -1],\n [14, 24, -9, -13, -9, 10, 1, 6, -21, -20, -22, 0],\n [-19, 11, 6, -15, 10, 10, -12, -10, 10, 24, 15, 2],\n [-24, -16, -1, 13, 18, -21, 8, -3, 24, 12, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "494", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-8, -14, 16, -18, -8, 24, 5, -6, 5, 19, -15, 2],\n [6, -26, 22, -23, -14, -4, 1, 16, 23, -15, -8, 25],\n [6, -9, 7, 3, 16, 20, 20, -21, -23, -15, -4, 1],\n [-16, 1, 13, 7, 21, 7, -6, 9, 1, 7, 14, 2],\n [-1, -14, 25, 7, -8, -19, 2, 16, 13, -11, 1, 3],\n [-4, 2, -7, -10, -1, 20, 12, 6, -13, 4, -11, -6],\n [8, 23, -8, -21, -4, -1, -18, -14, 17, -12, 5, 12],\n [17, -10, 18, 2, 22, 13, -9, 7, 22, -2, -15, 18],\n [-12, 16, -3, -18, 13, -7, -2, 20, -3, 22, -1, -13],\n [-22, 21, 2, -19, -10, 16, -5, -9, 0, -25, -26, 14],\n [-19, -6, -3, -25, 17, 11, 1, 7, -15, 23, -22, 18],\n [9, -19, 3, -17, -6, 19, 25, 7, 7, -23, -16, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[14, 23, -4, 22, 7, 3, -2, -3, -2, 3, 12, 17],\n [-11, -17, 4, -16, -18, 9, 21, -8, 25, -22, -15, -17],\n [-13, -7, -7, 17, 9, 25, -2, 14, 19, -22, 14, 0],\n [-25, -15, 1, 17, -14, -6, 16, -19, 26, -15, 14, 17],\n [-16, -8, -19, 0, -20, -6, 0, -13, 5, 2, -3, 1],\n [-3, -25, 25, 4, -15, -26, -6, 2, 3, 15, -26, -5],\n [15, -19, -14, -13, 15, -26, 5, 11, -15, 25, 20, 18],\n [20, -11, -3, 17, -7, 16, 17, 5, 0, 7, -5, -24],\n [-10, -13, 0, 12, -7, 19, 4, 14, 4, 2, 15, 16],\n [5, 3, 16, 0, -8, 1, 18, -17, -11, 4, -17, -17],\n [1, -15, 6, 1, -9, 25, 1, 1, 16, 12, -13, -19],\n [3, 9, -24, -17, -18, 20, 13, -14, -5, -3, -20, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-21, -17, 24, -16, 2, -11, -7, -6, 2, -13, 14, -11],\n [-18, -21, 11, 2, -9, -3, 24, -10, 9, -6, -8, -4],\n [0, 26, -16, -1, 26, -16, 16, -5, -8, -19, -4, 21],\n [26, -4, 13, -18, -3, -15, -15, 5, -25, -21, -23, -14],\n [9, 14, 12, 11, -9, -12, 21, 6, 15, 3, 9, -2],\n [-23, -9, 18, 6, -7, 15, -6, -26, 7, -18, -26, 20],\n [0, -12, -3, -2, 7, 17, 23, -17, 3, 18, 14, -2],\n [-24, -5, 13, 19, -3, 0, -1, -11, 11, 14, 26, -23],\n [-4, -8, -12, 4, -3, -16, 26, -17, -19, -24, -8, -23],\n [2, 18, 14, -6, 25, 18, -18, 25, 24, 21, -9, -8],\n [-10, 17, 16, -3, 22, -21, 4, 0, 20, 7, 19, 0],\n [0, 8, -15, 2, -21, 10, -20, -21, 26, -8, -13, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -13, 13, -13, 26, 24, 5, -1, -24, -12, -6, 3],\n [21, 20, -13, 20, 12, 10, 14, 21, 1, -25, -5, -20],\n [17, 5, -11, 9, -25, -10, 22, -24, 21, -4, 10, 12],\n [1, 18, 14, -19, 6, -23, 26, -20, -16, 13, -19, -7],\n [16, 12, 1, -16, 23, -5, 9, -21, -20, -17, 13, -23],\n [-18, 11, 22, -8, 19, 6, 11, -5, 12, -26, 22, 26],\n [-6, 22, -20, 19, -20, -5, -14, -4, -5, -1, -9, 26],\n [-20, -25, 26, -8, -13, -2, 6, 21, 12, 21, -7, 17],\n [-22, 22, -6, -14, -13, -11, 18, 23, 23, 14, 1, -26],\n [-25, -19, -14, 11, -8, 24, -25, 4, -17, -22, -4, 3],\n [5, -26, 18, 17, 15, -24, 20, 3, 10, 1, 24, 24],\n [-6, -14, 13, -1, 13, 3, -3, 11, 14, 19, -22, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[19, 15, 22, -11, 25, 22, 21, -17, -9, 11, -10, 14],\n [13, 4, -1, -1, 13, -15, -9, 7, 8, -16, 26, 3],\n [18, 23, -16, 19, 25, -23, 9, -17, 7, 4, 5, 23],\n [1, 16, 10, 5, 5, -10, 7, 8, 12, -6, 5, 7],\n [7, -19, -11, 8, -4, -5, 4, 2, 11, -8, 18, 9],\n [22, -18, 8, -26, 6, -10, -1, -14, -22, -8, 15, -18],\n [-21, -6, 22, -5, 26, 12, 21, 24, -22, -5, 23, -20],\n [-1, -2, -22, 5, -19, -18, 1, -7, -23, -24, 17, 14],\n [15, -16, 21, 2, 16, -5, -19, 19, 7, 4, -23, -12],\n [-9, -16, 0, -8, 23, -18, -2, -5, -4, 10, -17, -10],\n [25, -14, -23, 5, 1, 3, 19, 13, -6, -12, -24, -10],\n [-12, 6, -22, -19, -18, -1, -25, 10, 9, -15, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -25, -11, -25, -6, -17, 15, -10, -15, -20, -18, 19],\n [23, -17, -11, -26, -18, -14, 21, -11, 7, 14, 3, -14],\n [-19, -16, 22, 25, 4, 16, -16, 21, -20, -26, -4, 5],\n [-12, -9, 1, -13, -14, 7, -7, -3, 1, -16, 24, 1],\n [-5, 3, 11, -10, -5, -26, -7, -22, 6, 18, -26, 17],\n [-18, 5, -1, 18, 15, 21, -21, 26, 3, 13, -4, 12],\n [-2, -2, -14, -2, -10, 17, 0, -16, -21, -12, 10, 5],\n [21, -3, -16, 15, 2, -19, 10, -17, -17, -26, 18, 25],\n [-4, -9, -4, -22, 21, 11, 4, 26, 15, 12, -7, 2],\n [21, 6, 12, 5, -2, 17, 0, -4, 20, -25, 23, -23],\n [-2, 18, -4, 14, 9, 14, -4, 6, 1, -19, 6, 2],\n [21, -12, -12, 10, -8, 16, 24, -6, 8, -1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "496", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, 26, -11, -15, 1, -20, 6, -3, -16, -12, -8, -12],\n [-18, -14, 23, 2, -1, -4, -10, -22, -11, 12, 3, -6],\n [-22, -1, 16, 21, 3, -5, 18, -25, 17, -15, 15, 0],\n [-1, 18, 17, -2, -8, 22, 0, 21, -10, -21, -4, -9],\n [16, 17, 22, -25, 18, -8, 24, -23, 6, 7, 5, -9],\n [17, -18, 10, 21, 9, 25, -24, -9, 13, -2, -25, 17],\n [-26, -3, -3, 26, 23, 15, 26, 13, -23, 23, 8, 8],\n [-15, 24, 22, -4, 22, -5, -1, -23, -20, -4, 4, -20],\n [-5, 12, 13, -8, 26, 3, -1, 14, -5, -18, 19, 2],\n [5, 26, -9, 4, 5, -18, 3, 10, 5, -19, -3, -23],\n [25, 19, -10, -6, 21, -18, -22, -22, 3, -21, 11, -19],\n [21, 19, 6, 21, -12, 10, -18, -24, 4, 12, -20, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 8, -12, -20, 8, 21, 4, 11, -19, 21, 11, -11],\n [7, -26, -8, -13, -8, -4, -23, 7, -25, -15, -4, 16],\n [26, -9, 5, 24, -10, 4, 9, -1, -15, 8, -11, -23],\n [1, 11, 6, 10, -17, 4, -13, -22, -17, -2, 14, 18],\n [-10, 24, -7, 6, -18, 23, 4, -22, 19, 2, 24, 20],\n [-23, 4, -23, -9, -9, 13, 7, 21, -13, -1, -4, 6],\n [-10, 15, 5, 21, 8, 24, 16, 3, -12, 23, 25, 24],\n [-20, -21, -18, -14, 13, -9, 8, -26, -3, 23, 9, 23],\n [-11, -9, -24, 19, 15, 10, -19, -9, 2, 10, 0, 17],\n [2, -23, -15, -14, -13, -13, 24, -17, -5, -18, -3, 23],\n [-10, -3, -22, 7, 15, -26, 0, 13, -19, -21, 26, -22],\n [26, -9, -20, 9, 6, 7, 5, 24, -24, -26, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-19, 17, 3, -19, 0, 12, -4, -19, -12, 26, -20, -15],\n [23, 9, 11, 16, 3, -17, -8, -9, 17, 22, -7, -25],\n [3, 24, 17, 16, 20, 16, -16, -5, 15, -8, -24, -23],\n [8, 20, 11, -18, -19, 7, 24, 20, 4, 13, -8, 10],\n [5, 17, 17, 1, 14, -9, -2, -17, -22, -12, -2, -7],\n [24, 26, -17, 22, 11, 14, 1, 22, 23, 19, -21, -16],\n [-8, -11, 5, -25, 12, -1, -6, 11, -12, -14, -20, 25],\n [-24, -12, -7, -24, 0, -12, -24, 1, 20, -26, 26, -7],\n [-16, -2, -23, -8, 1, -17, -6, 9, -11, 6, 18, 24],\n [19, -14, 2, -23, 15, 0, -19, 14, 19, -19, -2, -1],\n [-26, 16, 21, 6, -8, -7, -9, -1, 12, -18, 0, -21],\n [-7, 11, -26, 11, -11, -23, -24, -5, -18, -19, -20, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "557", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-26, -15, -11, -13, 3, 16, 25, -8, -8, -14, 17, -17],\n [20, 2, 1, -14, 18, -12, -10, -4, 16, -17, 9, 22],\n [-13, 5, 7, 4, 12, 5, -11, -1, -10, -5, 9, 8],\n [-4, -2, -22, -21, -1, 11, -21, -8, 16, -8, 19, 20],\n [4, 10, -4, -15, -14, -5, 23, -24, -15, 10, 4, -14],\n [-4, -14, -21, 21, -24, -20, 26, -17, 4, -23, 17, -21],\n [-9, -20, 7, -4, -19, 23, -3, 1, 18, -24, -14, 12],\n [6, 23, 26, -11, -16, 2, -2, -10, 10, -21, 19, -13],\n [-8, 10, 23, 16, -15, -8, -6, 2, 1, -10, 26, 22],\n [-25, -21, -2, -8, -21, -26, 19, 7, -6, -6, 17, 22],\n [0, -4, 9, 9, 5, 12, 18, -10, -13, -5, -10, 2],\n [21, 21, 11, -1, 4, 7, 0, -10, -4, 7, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-7, 5, -15, -23, -18, -16, 22, 3, 18, -1, 5, 1],\n [24, 13, 10, 15, 20, 24, 14, -11, 21, -19, -24, -24],\n [-17, -15, -12, 20, 0, 24, 19, -16, -21, -15, -9, -2],\n [7, -1, -3, -11, 9, 9, -6, 3, 22, -7, 15, 23],\n [-8, -16, -13, 9, -11, -24, -5, 16, -22, 26, -25, -15],\n [18, -25, 10, -8, -3, -22, -1, 1, 8, -8, 4, -8],\n [16, 17, -8, -7, 15, -10, -15, 8, -1, 26, -19, 13],\n [-2, -2, 18, -5, -14, 15, -12, -4, 1, 21, -14, 5],\n [-16, 17, -13, 25, 8, 20, 16, 8, 23, 13, -4, 13],\n [-14, -21, 2, 15, -12, -22, 6, 13, -25, 6, -2, 0],\n [21, -2, -22, 24, 16, 13, -23, -13, -10, 14, 0, 9],\n [7, -17, 24, -5, 14, -5, 1, 21, -7, 22, -25, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "519", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[24, 7, 21, -11, 1, -13, 25, -26, 14, -12, -12, -2],\n [16, -22, -19, -5, 12, 11, 12, 24, 19, 16, 24, -13],\n [-8, -1, 11, 6, 19, -15, 2, -15, 2, 14, 14, 19],\n [-7, 7, 19, 3, 2, 12, 20, 13, 24, -25, -1, -26],\n [1, 24, -19, 4, 12, 23, -8, -14, -11, -4, -16, -3],\n [-17, 24, -22, -15, 9, -1, 1, -11, -25, -1, -23, 2],\n [-11, -5, 16, -21, 1, -16, 15, 20, -6, -1, 12, 26],\n [20, -5, 3, 3, 6, 13, 3, 10, 26, 3, -1, -21],\n [-23, -12, 9, -24, -11, -11, 13, 26, 0, -21, -6, -14],\n [-18, 14, 16, -19, 1, 18, -8, 2, 4, 6, 22, -21],\n [17, -23, 26, -11, 26, -24, -2, -10, -5, -9, 5, -9],\n [-1, 23, -2, 1, 13, -4, -19, -14, 17, 20, -17, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-24, -17, 22, -12, -3, -17, 25, -6, 19, 21, 11, 12],\n [15, 24, 23, 1, 14, -25, 14, -23, 16, 22, -24, 5],\n [20, 7, -11, -23, -9, 1, 15, -21, 16, 15, -26, -11],\n [10, -18, -10, 9, 7, 4, 7, 10, 7, 18, 10, -26],\n [26, -12, 4, 24, -13, 17, 7, 25, -26, 8, -16, -10],\n [-22, -10, -9, -2, 8, 20, -11, 20, 22, 23, -4, 13],\n [-6, 2, 19, 9, -17, -7, 26, -20, 3, 2, 25, -26],\n [-6, -20, 17, -23, 12, -12, 7, -25, 10, -24, 21, -23],\n [20, 22, 16, 9, 0, -23, 9, -8, 7, -11, 25, 18],\n [13, 24, -5, 5, -25, -10, -4, 17, 19, -15, -14, -17],\n [-23, -20, -25, -12, 9, -18, -3, -21, 22, -20, -11, -10],\n [3, -19, -24, -2, 2, -6, 25, -21, -4, 23, -16, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 0, -14, -18, -19, 18, 0, 5, 2, 19, 6, -22],\n [11, -18, 25, -14, 6, 3, -2, -21, 12, -17, 9, 23],\n [21, -8, -16, -10, -25, -20, 14, 4, 4, 19, -10, -12],\n [-20, 3, 12, -13, 4, -18, -18, 22, 26, -25, 17, -5],\n [-11, -25, -12, -21, -4, 1, 16, -10, 9, -8, -22, -4],\n [17, -8, -26, 0, 16, -2, -21, 9, -10, -15, -2, -17],\n [19, 12, -3, -16, -3, -24, 13, -7, -4, -22, 9, -14],\n [9, -21, -25, 2, -22, -12, -19, 7, 26, 10, -1, -18],\n [-19, -13, 21, -2, 7, -24, 5, 9, 20, -22, -12, 1],\n [-9, 18, -16, -17, -23, -7, -22, -26, -14, 19, -5, 21],\n [-14, -12, -18, -24, -25, -15, -3, -9, 9, -2, 25, -12],\n [-26, -19, 22, 10, -20, 8, 11, 18, -11, -10, 11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -9, 9, -15, 1, 21, -16, 16, -21, -1, -11, 11],\n [-18, -9, 6, 23, -8, -18, 19, 17, 15, -18, 17, -22],\n [-4, 24, 15, 7, 11, -5, -22, -26, -1, -9, -1, -12],\n [-25, 26, -12, -16, 18, -7, 20, 15, -10, -22, 6, 24],\n [17, -2, -20, 7, 26, -12, 25, -14, 5, 12, -13, -7],\n [-11, 3, 14, -8, -5, 10, -17, -19, 2, -13, -16, 3],\n [6, 15, 7, 12, 22, 10, 15, 10, -22, 14, 16, 20],\n [-22, -10, -8, 19, 26, -1, -25, -13, 25, 1, -23, -24],\n [-12, -5, 21, 15, 23, -8, 7, -17, 7, -11, 10, 9],\n [22, 18, -5, 5, 17, -10, -18, 25, 6, 6, -25, -13],\n [10, 6, -26, 20, -5, 3, 0, 6, 26, -11, -17, 0],\n [10, -25, 3, 19, 16, -8, -8, 24, 8, -16, 25, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "549", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-11, -10, 2, -7, 9, 20, -3, 16, 21, 25, 26, -23],\n [-22, -8, 21, 24, -3, 21, -26, 8, -25, -17, -21, 13],\n [11, -7, -8, 21, 9, 21, 2, 14, -3, -18, 5, 13],\n [-22, -6, -10, -3, 0, 21, -9, -5, -21, 1, 15, -7],\n [-11, -8, -19, -9, 10, 18, 20, 4, 11, -25, 5, -12],\n [-16, -22, 15, 2, -7, -7, -9, -15, 22, -10, -23, -8],\n [-4, 0, 23, 25, 26, 15, 19, 25, 18, -13, -23, -23],\n [-3, -4, 9, -16, 6, 11, -22, 0, 10, 0, 4, -15],\n [20, -21, -15, -13, -5, -16, 13, 25, 12, 11, -14, -21],\n [-7, -25, -16, -19, 3, 0, -23, -20, 20, -3, 5, -8],\n [15, 8, 15, 24, -24, -9, 10, -5, 6, 11, 12, 7],\n [22, -4, 8, 2, -25, 23, -13, 21, 17, 23, -19, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "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, -24, -20, 7, 21, 5, -18, 8, -8, 19, -12, 4],\n [-11, 24, 20, 19, 10, -20, 8, 2, -25, 21, 7, 8],\n [4, -15, -26, 20, 2, -26, -26, -12, -24, -13, -17, -24],\n [-7, 23, 9, 0, 22, 25, 9, 20, -16, -24, -3, 12],\n [-17, -1, 24, 5, 25, -19, 20, -14, -24, 26, 26, -12],\n [26, -6, 15, 2, 26, 20, 0, 3, -13, 14, -12, 19],\n [20, 19, 15, 17, 25, -13, -2, 0, 20, 17, -25, 24],\n [-10, -12, 0, -17, 16, 19, -18, -24, -3, -26, 11, -21],\n [-22, -23, -24, 18, 3, 9, -4, -20, 24, 5, 16, -17],\n [24, 24, 10, 6, -1, 16, 18, 4, 3, -4, 2, -19],\n [-11, -18, -23, -8, 12, 17, 14, -14, -15, -18, -15, -3],\n [21, -14, 8, 5, 11, -13, -25, -6, 4, 25, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[13, -1, 11, -24, 10, 9, 11, -25, -5, -24, 13, 20],\n [15, 20, -1, 0, 11, 17, -19, -4, -21, -2, -11, -1],\n [-12, 25, 20, 5, 13, -8, -13, 26, 21, 17, 8, -1],\n [25, 10, -14, 20, -19, -13, -1, 20, 3, 24, 13, 15],\n [-14, 9, -16, -25, 3, 24, -3, 26, -9, -4, 26, -21],\n [19, 23, -16, -20, 20, 6, -17, -6, -18, 3, 21, 21],\n [-2, -2, 22, -3, -15, -20, 7, -24, -21, 0, -8, -19],\n [9, 12, 9, -9, -20, -26, -22, 15, -13, -26, -15, -8],\n [-25, -13, -24, 24, 8, -14, 22, -24, -13, 7, 18, -18],\n [-17, -19, 2, 12, 6, -4, -19, 13, 11, -4, 23, 9],\n [16, -7, 21, -15, 9, -18, 6, -21, 5, -26, 25, -3],\n [2, -19, -14, -2, 2, -3, 0, 24, -1, -7, -23, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-20, -9, -17, 4, -1, 20, 18, -1, -2, 25, -9, -3],\n [17, -12, -19, 16, -2, 8, -3, 19, 13, 26, 11, -6],\n [-26, -1, -17, -1, -25, 13, -13, 6, 12, -26, 3, 10],\n [-9, 3, 0, 22, 22, 3, 18, 26, 9, -6, -11, -10],\n [-9, 7, -6, -15, 4, -17, 14, -23, -12, 26, 15, 14],\n [1, -20, -16, 2, 7, 25, 25, 3, 0, -2, 21, 11],\n [13, -4, 2, 23, -16, -23, 9, 4, -17, -11, 26, 3],\n [8, 17, -10, -22, -24, -11, 24, -23, -18, -23, -6, -17],\n [26, 4, -10, -11, 12, 20, 23, -21, 3, -12, 16, 25],\n [4, 3, 10, -11, 17, 26, 9, -25, 1, 21, 13, -10],\n [14, 11, 9, 5, -2, -14, -13, 17, -2, 8, 2, -12],\n [-12, 20, 20, 13, -10, -2, -4, 19, 5, 4, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, 2, -25, -16, -11, 24, -10, -6, -6, -21, 19, 18],\n [-4, 5, 12, 18, 11, 2, 4, -2, -25, -5, 10, 17],\n [-12, -21, 6, -16, 26, -15, -3, -24, 3, -8, 18, 16],\n [-20, -15, 23, 2, 21, -19, -6, -14, 22, 0, -23, 5],\n [-3, 14, -18, -17, -16, 6, 22, -20, -16, 18, 1, 11],\n [3, -19, 0, -5, 15, 5, -13, -1, 17, -16, -20, 18],\n [3, -25, 8, -1, -2, -26, 2, -3, 11, -26, -2, 7],\n [15, 17, -22, 14, -15, -19, 15, -13, -7, 20, 13, -18],\n [-22, -26, -16, -23, 11, -10, -23, 5, -22, -5, -13, -6],\n [-9, -24, 26, -16, 20, 12, 9, 0, 11, -2, 15, 12],\n [8, -12, 26, 21, -6, -24, -3, 17, -22, 10, 6, -3],\n [-21, 20, 26, 18, -20, 23, -8, -6, -21, 13, -24, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538", "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, -13, -25, -2, -23, 14, 21, 6, -25, -4, 17],\n [21, -6, -12, 24, -3, -7, 11, -2, -5, 25, 24, 20],\n [-23, -11, 16, -20, -3, 7, 12, 2, 17, -1, -13, 20],\n [-7, -20, -9, 16, -17, 19, 3, -24, 23, 17, 26, -26],\n [3, 18, -25, -12, -16, 5, -21, -21, 1, -2, -4, -15],\n [21, 21, -17, -10, 25, -25, 18, -10, -18, 20, -20, -14],\n [-17, -5, 1, 23, 15, 23, -13, -8, -26, 0, -23, -3],\n [-13, 10, -4, -22, -7, -5, 19, 13, 17, 22, 8, 9],\n [-22, 6, -3, 7, 10, -2, 24, 10, -2, -5, 18, -22],\n [-19, 26, 14, 20, 0, 8, -26, -7, -20, 18, -24, 15],\n [23, 21, -18, 20, -13, -8, 0, -21, -20, 10, -1, -14],\n [10, 19, 6, 25, 6, 14, -18, -12, -22, 26, 2, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-20, 4, 7, -16, 15, -8, -22, -4, 20, -25, 16, -23],\n [-10, 4, 3, -25, -3, -17, 1, 16, 5, 6, -9, -3],\n [10, 3, -22, -4, 3, -23, 14, 24, -3, -24, -12, 19],\n [-26, -17, 18, -1, -15, -26, -25, -16, -15, 1, 6, 15],\n [-24, 14, 22, -8, -9, 10, 1, 4, -20, 20, 11, -22],\n [-8, -14, 12, 1, -25, -21, -12, 1, 10, -2, 5, 10],\n [9, 3, 18, -3, -9, -26, -24, -20, 6, -6, -13, 20],\n [21, 10, -24, 22, 10, -2, 6, -14, 26, 23, 6, 2],\n [-8, -1, 26, 11, -18, 19, 3, -5, 16, -23, -20, -9],\n [23, -21, 2, -22, -21, 7, 7, -26, -9, 0, -17, 12],\n [-25, -8, 0, -5, -17, 17, 0, -15, -12, 23, -26, 11],\n [14, -3, -21, 2, -21, 11, 21, -12, -19, 2, -25, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "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, -3, 7, 16, -3, 22, 11, 11, -2, 14, 26],\n [6, 17, 16, -10, -20, 0, 9, 14, -8, -12, -21, 9],\n [-22, 26, 18, -22, -25, 16, -9, 5, 20, 22, 2, 22],\n [-7, -8, 25, -11, -16, 1, -5, 0, -10, -19, -19, -4],\n [5, 17, -12, 0, -23, 13, 5, 20, 10, -17, 26, 1],\n [25, 5, 5, 24, -12, -21, -18, 11, 3, 14, 13, -11],\n [-2, -17, 3, -18, 13, 19, -20, 16, 25, 21, 22, 13],\n [-15, -10, -2, 20, -20, -8, -10, 5, -4, 18, 5, -1],\n [-19, -5, 19, -19, 19, -22, -15, 0, -7, -16, 9, 25],\n [-25, -17, 15, -20, -15, -11, 4, 0, 5, 15, 13, 0],\n [-2, 13, -22, -23, 26, 17, 16, -12, -14, 6, -22, -21],\n [18, -2, -2, -17, -15, -24, 2, 2, 16, -3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"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, 22, 10, -22, -16, 13, 16, -5, 25, -12, -18, 23],\n [-21, -1, -21, 5, 16, -7, 8, 16, -24, -9, 8, 25],\n [-17, 9, 3, -1, 3, 4, -23, -3, -26, -1, 22, 2],\n [11, 9, -18, 15, 5, 10, 13, -9, -3, 13, -9, 12],\n [-19, 12, 24, -16, 16, 8, -3, 25, -14, 4, 3, 2],\n [15, -21, -24, 1, -17, 7, -26, -15, 9, 25, 5, -16],\n [-26, 21, -21, 0, -12, -17, -3, -19, -10, -3, -14, -18],\n [-21, 2, -4, -5, -6, -10, 7, -1, 23, -2, 21, 11],\n [-24, -24, -13, 15, -17, -25, -20, -13, 22, -10, -17, 8],\n [22, 18, 0, 21, -24, 20, -2, -20, -14, 12, 16, 19],\n [-2, 16, 2, -8, 12, -5, -25, -5, 8, 7, 26, -22],\n [0, -9, 21, -24, 20, -6, -3, -1, -7, 25, -14, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 21, 16, 3, -13, 20, 26, 10, 11, 3, -12, -8],\n [-16, -7, -2, 11, 16, 3, 13, -4, 17, -10, -26, 15],\n [-13, 12, -9, 14, -11, -17, 17, -18, -13, -25, 15, -6],\n [15, -25, -21, -16, 14, -24, 24, -16, -23, -12, -1, 17],\n [9, -12, 22, 23, -5, 10, -17, -7, 5, -18, 23, 4],\n [17, 13, 4, 1, -16, 9, 14, -23, 23, -13, 19, 2],\n [1, -2, -4, 6, 3, -18, 11, -2, -9, 16, -20, -3],\n [13, -6, 8, 16, -16, -25, -12, -12, -22, 25, 13, -11],\n [17, 19, -6, 18, -18, -20, 0, -10, -25, 13, -1, 18],\n [-19, 23, 18, 13, -11, -7, 5, 5, 8, -12, 15, 23],\n [5, 3, -8, -3, -25, -6, 15, -11, 13, 12, 9, 14],\n [-25, -11, 2, -20, -12, -4, -22, -26, 25, -22, -14, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[25, -14, 5, 2, -9, -25, 0, 23, 15, -24, 26, 3],\n [-17, -18, -24, -5, 11, -16, -21, -22, 3, -13, -25, 6],\n [10, -19, -17, -6, -8, 8, -9, -20, -14, 19, 23, -15],\n [13, -3, -9, 11, -15, -24, -2, 8, -11, 22, 21, 18],\n [-14, -3, -15, -25, -1, 19, -17, -8, -5, -3, -1, -22],\n [-11, 10, 7, 11, 1, -15, 18, 18, -6, 5, -2, -13],\n [24, 20, 26, 8, -18, 3, 15, 2, 12, 4, -13, -10],\n [-2, 19, 15, 10, 0, -9, 2, 22, -9, -23, -7, -26],\n [18, -3, 15, 20, -3, -22, -1, -9, 9, -26, -17, -10],\n [8, -23, 17, 0, -16, -24, 1, -16, -24, 9, -24, -2],\n [-15, -15, 22, 26, 5, 13, -17, 21, -8, 20, 16, -20],\n [-3, 12, 5, -4, 23, -8, 21, -24, -2, -2, -21, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"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, -12, -7, 16, 15, 5, -3, -24, -23, 17, -21, 25],\n [-8, -1, 21, -2, -2, -17, 11, -7, -22, 15, 17, 23],\n [8, -22, 8, -24, 14, 5, 9, 3, 25, 22, 12, 2],\n [-1, 18, -2, -15, -9, -1, -12, -22, 6, 14, -18, 5],\n [-14, 16, 1, -4, -3, 14, 4, -22, 19, 21, -25, 20],\n [3, 22, -22, -17, 20, 25, 9, 9, -20, 2, 5, 0],\n [-26, -7, 7, 24, 9, -1, -4, 6, -26, -24, 23, 8],\n [8, -14, 6, -14, -5, -22, -10, 16, -17, 0, -12, 18],\n [15, -18, -20, -17, 14, -14, -11, 7, -19, 4, 1, -20],\n [7, 6, -23, 11, -1, -25, 5, 12, 15, 14, -25, -1],\n [20, 0, -12, -6, 21, 0, 7, 22, -16, -4, 23, -5],\n [-4, -26, -15, -2, -21, 23, 22, 22, 7, 1, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[20, -26, 5, 2, -7, 19, -14, -15, -19, 12, -19, -9],\n [-6, 1, 4, -12, 12, 6, 11, -4, -11, -3, -6, 19],\n [-19, 15, -10, -12, -13, -7, 5, -16, 11, 5, -23, 2],\n [-22, 16, -15, 16, 23, 12, -4, 6, -11, 23, 17, -16],\n [-19, 6, 21, 7, -6, 11, -10, 22, 7, 24, 14, -24],\n [-3, -5, -17, -22, 14, 4, -3, 19, -16, 24, 21, -13],\n [19, -23, -19, -20, 8, 5, -5, -5, 19, 16, -1, 24],\n [9, 2, -23, 4, -5, 26, -19, -6, -12, 21, -23, 15],\n [-22, 9, -25, 23, -19, 20, -23, -14, -13, -18, 1, 11],\n [-15, 1, -14, -6, 11, 25, -1, -2, -5, 24, 25, 25],\n [-19, 10, 13, 18, -5, -14, 10, -13, -9, 20, 6, -20],\n [-17, 3, 7, 18, -24, 13, -15, 9, 26, 4, -4, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-26, 8, 20, -12, 26, 1, -15, -26, -16, 24, 10, 22],\n [-25, 18, 8, 18, -19, 4, -6, 26, 18, -24, -2, 14],\n [1, 1, -25, -19, -26, -6, -12, -19, 13, -5, 12, -7],\n [-14, -1, 12, -20, -16, 4, 7, -16, -3, -2, 24, 6],\n [2, -6, 22, 6, 18, -21, 10, 26, -25, 15, 3, 1],\n [5, 26, 24, 0, 12, -5, -12, 16, 11, 10, 9, 11],\n [-20, 4, 17, 3, -13, 7, 25, 0, -4, -24, -22, 15],\n [3, -20, 14, -9, 11, -17, 17, 7, 6, 5, 4, 1],\n [-23, -12, -25, -4, -4, 8, 0, -1, 22, 7, -14, 13],\n [25, 24, -17, 12, -1, -23, -9, 8, 20, 25, -10, 0],\n [-19, 26, 20, -14, 19, -5, 9, 16, 3, 8, 24, 18],\n [-23, -14, 20, -21, -9, -19, 14, -7, -6, 5, 5, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[15, -25, 14, 5, -5, -1, 14, 18, -17, 12, 18, -22],\n [-15, 14, 14, 5, 23, 13, -9, -17, -4, -26, 26, 26],\n [15, 10, -9, 3, -8, 18, 11, -10, 1, -5, 19, 11],\n [5, -2, 21, -18, 9, 23, 10, -26, 2, -12, 17, 19],\n [2, -6, -15, -1, 18, 4, 8, -13, -20, -24, 26, 14],\n [-23, -25, 8, 6, 10, 14, 23, -14, 24, 24, -20, 12],\n [20, 0, 22, -24, -10, -2, 3, -13, 2, -22, -20, 24],\n [-8, 6, -6, 24, -6, -10, -4, 0, 4, -12, 13, 13],\n [-26, -7, 14, 7, -26, 5, 21, -5, 2, 18, -16, 6],\n [11, -26, 11, -18, -14, 21, 26, 25, -3, 9, -7, 16],\n [18, -26, 8, 16, -7, 13, -26, 24, 19, 23, -21, 14],\n [-1, 2, 14, -12, 10, -8, -18, 14, -10, 5, 1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[26, 15, 1, -18, 0, -8, -20, -2, 3, -14, -25, -9],\n [26, 13, 26, -19, -7, -18, -14, 25, -6, 1, 17, -20],\n [4, 26, -4, -14, 18, 9, -25, 7, -22, -25, 20, 7],\n [-25, -7, -19, -4, 10, -11, -5, 19, -19, 26, 16, 16],\n [-1, 13, -4, -11, -6, 13, 25, 2, -7, -15, 10, -1],\n [-24, -9, -26, -8, -14, 16, 6, 3, -5, 0, 23, 24],\n [-14, -19, 26, 23, -25, 24, -8, -3, -22, -19, -7, 8],\n [-25, -21, -11, 20, 9, -25, -13, 11, 25, -1, -7, 2],\n [-23, -7, -3, -26, -2, -13, 8, 26, -6, 9, 25, -4],\n [19, -7, -1, 24, 0, 14, -13, 9, -23, -1, 17, 13],\n [-11, 16, 12, -7, 19, -3, -17, -25, 18, -18, -9, 15],\n [19, 3, -24, 2, -20, -2, -3, 16, -21, -12, -12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -6, 18, 5, 5, -15, 17, -18, -7, 22, -12, -14],\n [19, -19, -6, 18, -2, 8, 13, 3, 4, -21, -16, 15],\n [-19, -19, 12, 24, -15, -24, 16, 18, -11, 14, 0, -11],\n [-22, 13, -15, -24, 8, 18, -24, 4, -3, 14, 2, 6],\n [11, 24, -11, 6, -17, 3, 7, 8, -20, -21, -12, 5],\n [-25, 5, 1, -6, -10, -8, -13, 22, 24, 7, 21, -7],\n [-6, 21, -24, -13, -6, 0, -20, 15, 2, -18, 13, -12],\n [17, 1, 11, -12, -12, 3, 5, 13, -15, -7, 0, -25],\n [14, -5, -1, 13, -19, 9, -1, 10, -10, -20, -26, 0],\n [15, -1, 5, -13, -8, -18, 16, 17, -26, -6, -7, 22],\n [6, 6, -9, 14, -10, -14, 22, 16, 22, -18, 19, -26],\n [-4, 13, 7, 9, 23, 18, -13, -6, 16, 16, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, 13, -15, 2, -26, -1, -11, -9, 6, 25, 23],\n [15, 16, -4, 21, -22, -6, -26, 4, -9, -6, -20, -26],\n [-4, 0, -25, 7, -11, 13, -17, -7, 21, 10, -2, -23],\n [5, 18, 1, 13, -14, -22, -10, 20, -20, -17, 0, 8],\n [-4, -11, 25, 0, -12, -21, 15, 12, -3, 24, -4, -22],\n [-20, -5, 2, 26, 4, 8, 7, -8, 7, 3, -8, -9],\n [-26, 14, 26, -11, 13, 1, -16, 21, 25, 5, -1, -17],\n [-4, 21, 18, 12, 6, -13, -18, -13, 9, 14, -25, -16],\n [25, -13, 9, 8, 15, 25, -2, 6, -18, -14, 16, -17],\n [6, 18, -18, 13, -14, -3, 13, -10, 6, -4, 0, 17],\n [17, 16, -1, -3, -16, 2, 21, -22, -3, -18, -17, -16],\n [4, -24, -2, 26, 16, 13, 0, -26, 22, 21, -11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "531", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-12, 7, 26, -16, -18, -3, 10, 8, -5, 13, 11, -20],\n [17, 3, 2, 12, 14, -18, -26, -24, -22, -16, -23, 17],\n [6, 6, 18, -7, 10, -7, 7, -6, 24, -20, -11, 5],\n [9, 23, -16, 21, 2, 15, 7, -17, -24, -5, 5, 17],\n [-7, -25, -19, 23, 14, -2, -16, -3, -1, 8, 13, -22],\n [-12, 15, -13, 10, -9, -15, -24, 13, 19, 6, -23, 13],\n [-1, -6, 18, -11, 21, -4, -3, -18, -8, 0, 13, 4],\n [24, -26, -14, 18, -23, -2, -17, -4, 16, 3, -13, 5],\n [3, -22, 18, -12, -10, 21, 6, -15, -2, 25, -8, 26],\n [-4, 12, -22, 13, -6, 9, -13, -21, -8, -23, -3, -1],\n [15, -8, 5, 15, 18, 8, 13, 15, -25, 6, -17, 18],\n [6, -4, 7, 15, 9, 3, 12, -22, -6, -11, -20, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[25, 14, 16, -3, 22, -1, 5, 16, 0, 14, -8, -19],\n [10, -21, -8, 16, -4, -25, -24, -25, -14, 5, 16, -2],\n [16, -14, 3, -8, -3, 18, 6, -14, 4, 11, -19, 3],\n [-8, 5, 3, 19, 11, -10, 7, -11, 10, 25, -21, -25],\n [-22, 15, -8, -26, 11, -2, -11, 3, 3, -17, 13, 25],\n [-3, -6, 24, 25, 12, -12, -22, 9, 24, 24, 15, -5],\n [-19, 4, 25, -26, -7, 1, 4, 26, -3, 18, -20, -25],\n [-18, -8, 14, 22, -2, -4, 23, -17, -4, 6, 16, -8],\n [24, 7, 10, -24, 18, -20, 16, 22, -26, 9, -26, 14],\n [3, 23, 5, 22, -8, 20, -17, 17, 21, 17, 6, 18],\n [-23, -7, 17, 24, -12, 14, 3, -20, 11, 14, -9, 3],\n [-19, -6, 23, 18, -20, 17, -22, 5, -11, 13, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[12, 1, 6, -25, 14, -12, 12, -20, -7, -14, 5, 2],\n [-23, -8, -17, 9, -15, -5, 0, 8, 13, -10, -21, 18],\n [23, 21, 16, -13, 6, 17, 25, 1, 11, -20, -16, 6],\n [-24, -5, -14, 2, -21, 15, 12, 16, 1, -12, -3, 16],\n [23, -1, -26, -1, 19, 4, -4, 5, 17, -26, -9, -10],\n [19, 17, 1, -26, 24, 9, -22, -22, -25, -16, 8, 3],\n [5, -19, -25, 9, 12, -2, -8, 24, -20, 13, -13, -23],\n [19, 6, 10, 16, 3, 20, -7, -13, 0, -14, -20, -9],\n [11, 25, 12, -18, -4, 4, -25, 13, 11, 14, 12, -22],\n [-4, 22, 5, 26, 12, -11, -16, -13, -24, 26, -19, -12],\n [-18, -11, -1, 26, 5, -9, -19, 12, 25, 26, 5, -17],\n [-15, -15, -17, 7, 3, 17, 4, 11, -2, -3, 6, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "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, -7, 21, -10, 25, -21, 9, 14, -7, -1, 13, 23],\n [-15, -20, 13, 3, -5, 15, 2, -5, -3, -24, 23, 14],\n [-3, -1, -22, -14, 10, -5, 7, 12, -24, 5, -3, -18],\n [-24, -5, -3, 11, -17, 8, -7, 14, 17, -15, 21, 16],\n [-15, -10, -23, 15, 22, -19, -20, -9, -1, 4, 26, -19],\n [7, 19, -11, -7, -17, 23, -22, 21, -16, 24, 11, 12],\n [-5, -16, -9, -9, 4, -7, -4, 13, 26, -17, -10, 14],\n [18, -19, 4, 22, 21, 21, 26, 13, -1, 15, 17, 23],\n [-18, 5, -4, 5, 9, -22, 21, -26, 23, 23, 4, 4],\n [24, -18, 6, 8, -1, -25, 7, -10, -21, 10, 4, 1],\n [-6, -16, 14, 9, 12, 18, 21, 0, -7, 22, -7, -25],\n [10, 0, -9, -14, -9, -16, -13, 17, -23, 12, -14, -8]]\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[[16, 12, -2, -12, 24, -7, -10, -26, 2, 17, -8, 3],\n [-2, 1, 10, 15, -16, -11, -9, 14, -18, 1, 0, 19],\n [25, 11, 17, -4, 16, -5, -23, 5, -3, 11, 23, 1],\n [-21, 6, 4, -17, -15, -20, -3, 1, -16, 5, -7, 1],\n [-26, 0, -11, 9, -21, -17, 12, 17, -8, -17, -1, 7],\n [14, -26, -17, 6, -1, 7, 10, 22, -14, 11, 3, -3],\n [15, 7, 10, -8, -25, 3, -5, 5, 6, 13, -12, -21],\n [9, 17, -11, -6, 7, 13, 11, 8, 6, -19, -15, 12],\n [22, 18, -9, 21, 13, -6, 0, -15, -21, 4, 7, -20],\n [4, -23, 25, 21, -10, 2, -24, -3, -24, 19, 19, 12],\n [0, -26, -12, -13, -23, -23, -2, -16, 6, -16, -15, -12],\n [-1, -3, 20, -1, 0, 9, 0, 11, -25, -4, -18, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[24, 13, 25, 15, 22, 24, -26, -6, -1, -12, 16, -2],\n [12, -11, 8, -4, -15, 21, 25, -8, 7, -19, 24, -4],\n [-16, 16, 7, -22, 10, -2, -3, -3, 15, 7, 20, -9],\n [-15, 15, 12, -12, 20, -15, 2, 2, -7, -12, -24, -11],\n [-8, -20, 22, 9, -5, -12, -18, -10, 6, -25, -20, 4],\n [-13, 10, -23, 18, -17, 18, -5, -3, 17, -9, -16, 23],\n [17, -26, 26, 5, -11, -13, 6, -20, -8, -2, -22, 22],\n [-17, -23, -3, 19, -21, -15, -7, -1, -15, 6, -15, 11],\n [-23, -10, -17, -8, 16, 6, 10, 1, 19, 18, -25, 19],\n [11, 11, -6, -4, 6, -1, 25, 16, 3, -23, -21, 7],\n [-7, 10, -12, 13, 22, -4, 15, -18, 7, 16, 7, 0],\n [-11, -23, 1, -10, 14, -15, -22, 8, 11, 12, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-13, -13, -25, 1, -6, -12, 17, 19, -4, -17, -1, 8],\n [7, -25, 4, 16, 17, 20, 17, 16, 25, 25, 19, -22],\n [-8, 3, 22, 20, 25, -10, 2, -15, -19, -12, 26, 7],\n [1, -6, 26, -10, 26, 15, -9, -3, -3, -15, -26, 9],\n [5, -22, -1, -24, 6, 12, -7, -15, 26, 11, -7, -10],\n [16, -19, 16, -14, -18, -8, -1, 25, -22, 15, 18, -2],\n [-22, -4, 8, 22, 5, 15, 22, -21, -13, 14, 2, 10],\n [-5, -7, -19, 0, 21, -20, 7, 14, 1, 4, -6, -17],\n [24, 9, -14, -1, 7, -8, -21, 21, -12, 19, 18, 22],\n [-9, -7, -26, -5, 9, 21, -9, -17, -7, 13, -21, 22],\n [10, -5, -23, -23, -8, 2, 1, 14, -14, 12, 1, 3],\n [-5, 23, -4, -9, -10, 4, 1, -19, 5, 16, -21, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "537", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 13, 24, 20, 4, 24, -21, -23, -20, 7, 0, -25],\n [-13, 14, 2, 12, -5, -22, 17, -9, 24, -11, 17, -21],\n [-26, -15, -3, -16, 16, 14, 7, 2, 5, -6, 13, 6],\n [6, 1, 17, 9, -26, -15, 19, 6, 17, -22, -25, 9],\n [-3, 16, 23, 24, 23, 25, 20, -6, 3, -12, -18, 5],\n [-19, -4, 0, 15, -19, 2, -16, -6, 24, 17, 12, 3],\n [6, -24, -14, 9, -4, -1, -17, 11, 9, -4, -19, -13],\n [-3, -9, 13, 10, 19, -2, 20, -7, -2, -10, -23, -6],\n [-7, 18, 20, 14, -10, 8, 14, -4, -6, 16, 25, -6],\n [-3, 10, -9, 17, -8, -22, 17, 0, -21, 22, -13, -24],\n [-26, 4, 18, 23, -17, 4, 24, 24, -10, 12, 13, 21],\n [-11, 0, -11, 25, 14, 18, -23, 15, 26, 0, -18, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 1, -9, 17, -1, -17, 22, 17, 7, 19, 11, -16],\n [-13, 19, 11, -26, -10, 22, -10, -17, 3, 15, 19, 6],\n [-25, 23, -7, 5, -24, 9, -22, -7, -24, -24, 9, -21],\n [12, 9, -3, 20, 11, 10, -19, 11, 22, -11, 16, -26],\n [-13, 18, -17, -17, -5, 13, 14, 4, -23, 16, -4, 14],\n [-15, 18, -19, 18, -3, -26, -1, -5, 16, -2, 4, 7],\n [10, -16, -23, -19, 17, 8, -2, 4, 22, -4, 13, 11],\n [-23, 9, -20, -17, -21, 4, -23, -6, 15, -7, -10, 25],\n [-21, -16, -9, -18, -15, 4, 4, 16, 23, 7, -11, 14],\n [21, -15, 22, -14, 9, -14, 17, -25, 22, -12, -14, 7],\n [-1, -21, -6, 17, 6, -12, 8, 1, 15, -21, 10, 13],\n [-21, -16, -13, -6, -7, -22, 18, -18, 3, 15, 16, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[26, 0, -22, -22, 21, 13, -12, 20, -18, 20, -2, -19],\n [-13, 12, 5, 4, -4, 17, -26, 20, 4, -20, -12, 15],\n [-21, -11, -13, 17, -10, -17, 2, 15, -19, -16, -9, 18],\n [-7, -11, 0, -4, -13, -15, 18, 0, -14, -11, 6, -3],\n [-15, -18, -14, 18, -19, 23, -9, 0, 14, 6, -20, -14],\n [-12, 7, 13, -7, 10, 14, -10, 2, -6, -13, 2, 14],\n [20, -5, 25, 6, -14, 15, 4, -15, 5, 19, -21, -16],\n [-4, -20, -7, -23, -6, 17, 3, -2, 4, -25, -7, 19],\n [14, -13, 11, -4, -22, 25, -8, 23, -20, -6, 6, -7],\n [-18, 4, -19, -16, -20, -6, 22, 1, 26, -12, -19, 25],\n [-15, -22, -19, 10, -13, -23, 0, -12, -7, -5, 15, 22],\n [9, 3, 6, 1, 11, 13, -23, -13, -25, 10, 20, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"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, -20, -18, 6, -3, 25, 15, 16, -6, 17, -26, -6],\n [13, -3, 11, 17, 14, -23, -21, -24, 7, -2, 26, 0],\n [-9, -22, -3, 5, -6, 17, 7, 2, -22, 23, 1, -21],\n [-16, 12, 21, -19, 8, -16, -7, 24, 16, -5, 14, -15],\n [21, -22, 7, 15, 7, 3, -4, 9, -2, 21, -21, 15],\n [2, -6, -20, 10, 18, 14, -18, 20, 9, -26, 4, -7],\n [1, 19, -8, -26, 2, -17, 9, -4, -9, 2, 1, 17],\n [-20, 4, 11, 14, -25, -12, -5, 18, -16, -8, -21, -18],\n [17, 2, 16, -24, 23, 18, -14, 20, 24, 20, -12, -22],\n [-22, -25, 23, 11, 23, 3, 1, 12, 5, -7, -7, 2],\n [8, 5, -10, 25, 24, -19, -6, -4, 24, 24, 0, -21],\n [25, -19, 8, -22, 6, -26, -3, 5, 6, 11, -25, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-10, -17, 10, 10, -25, -15, 10, 3, -12, -4, 25, -9],\n [4, 26, 11, 2, -13, 16, 13, -4, -2, 14, 11, 1],\n [8, 3, 0, -19, 21, -8, -26, 18, 17, -7, 3, 2],\n [-19, -13, 11, -24, -24, -13, -6, 8, 17, 17, 22, 16],\n [14, 0, 1, 1, -22, 16, 12, -17, -18, -7, 2, 20],\n [2, 1, -16, -6, 8, -4, 2, -12, -10, -3, 8, -7],\n [9, -16, 3, 12, -7, -5, -3, -13, 9, -14, -26, 23],\n [0, -14, 8, -19, -9, 7, 25, -21, 0, -9, 23, -18],\n [-12, -4, -24, -18, -5, 23, -4, -7, 25, -20, 26, -10],\n [-24, -20, -14, 14, 14, -4, 10, -23, -18, -21, 15, -9],\n [8, -4, 4, -7, -20, -15, 10, 22, 24, -23, -15, 26],\n [-12, -25, 20, -16, 6, -13, 0, -23, 11, 13, -7, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-23, 22, -3, -18, -8, -19, 14, 1, -14, -19, -13, 23],\n [23, -17, -7, -26, -15, 8, -7, -15, 23, -15, 12, 2],\n [-24, -20, -4, -14, -16, -2, 25, -7, 22, 20, 0, -21],\n [-21, 12, 14, -18, -6, -9, -26, 23, 23, -15, -26, 1],\n [-3, -8, -13, -13, -1, -11, -3, 5, -21, 22, 18, 3],\n [-4, -8, -2, -2, 25, -25, -17, 14, 26, 0, 17, -19],\n [14, 16, 6, 16, -8, 3, 7, -13, 9, -7, -4, -12],\n [-25, -3, -3, 4, -11, -23, 7, -12, -8, -8, 21, 17],\n [8, -7, 20, 12, 14, 2, -12, -7, 5, -14, -20, -11],\n [-17, -25, 24, 11, 26, -9, 7, -6, -6, -26, -12, -17],\n [8, -2, 5, 4, -17, -24, -5, 11, -25, -4, 14, 13],\n [26, -3, 5, 6, 22, 0, -14, 10, 12, 2, 14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[19, -8, -26, 8, -11, -19, -20, -6, -16, -1, -12, 18],\n [25, -21, 10, -23, -8, 20, -6, 10, 16, -9, 15, 21],\n [9, 24, 10, -12, 11, -25, 15, 25, 4, -21, -8, 11],\n [-12, 6, 13, -1, 26, 3, -16, 19, -26, -13, -17, -10],\n [-16, 15, -12, -15, -24, -5, 23, -1, 12, 16, 23, 22],\n [-4, -11, -24, 3, -14, -19, -3, -22, -20, 24, 24, 0],\n [-15, 14, 22, -2, 15, 23, 6, -12, 4, -16, 9, -21],\n [18, -1, -19, 12, 10, 10, 21, 3, 11, -11, -12, 11],\n [26, -19, 8, -18, -6, 14, -22, -8, 21, -11, -9, -15],\n [-11, -22, -24, -20, 25, 5, 4, -13, -3, 21, 6, -22],\n [-19, -25, 12, 11, 15, 8, 11, 24, 7, 24, 3, 22],\n [-4, -23, 8, -13, -5, 3, -24, -16, -17, -24, 14, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "558", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[23, -22, -12, 21, 23, -21, -23, -4, 18, -26, 7, -12],\n [-23, 0, -14, 19, 20, 13, 5, -18, 10, -2, -24, 12],\n [13, -11, -10, 0, -17, 26, -26, 24, 23, 2, -9, 25],\n [5, 10, 16, 6, -5, 16, -16, 10, 2, -7, -5, 5],\n [23, -19, -5, -12, 8, -11, 25, 17, 2, 7, -7, 25],\n [-14, 24, -14, 4, -6, 23, 3, 21, -2, 3, -17, -20],\n [7, -23, -5, 2, -23, -26, 21, -4, -4, -21, 24, -22],\n [-4, 11, -20, -22, 6, -1, -6, 7, -1, -17, -25, -7],\n [-13, 26, -20, -17, 4, -19, -26, 2, 4, -19, -11, 19],\n [-8, -1, -17, -9, -25, 10, 2, -25, 25, -24, -3, -18],\n [16, 21, -13, 19, 25, 16, -16, 23, 16, -3, -13, 24],\n [-9, 9, -14, 7, -8, 14, -16, 22, -1, -22, -6, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[21, -15, -26, 22, -13, -1, -20, -11, -12, -23, 3, -4],\n [-5, -12, -10, -25, -19, -21, 12, 1, 21, -22, -6, 23],\n [-7, 16, 7, -20, 3, 3, -12, 0, -18, 0, -25, 9],\n [0, 20, 13, -2, 9, 13, -20, -14, 10, -7, -5, -9],\n [24, -16, -21, -23, -24, 25, -21, -12, -24, -10, 3, -5],\n [-25, -11, -5, 22, -16, 9, 26, -15, 13, 8, 16, 18],\n [14, -12, 17, 15, -6, -23, -20, 2, 14, -21, 12, -10],\n [9, -25, -10, 2, 0, -20, -16, -1, 25, 23, 26, 12],\n [5, 23, -4, 24, 19, 13, -20, -26, -2, 4, -21, 1],\n [4, 9, -11, -12, -5, -9, 23, -19, -17, 10, 12, 22],\n [-21, 16, -17, 12, -20, 15, 18, 8, 1, -2, 1, -18],\n [-22, -11, 2, 16, -4, -9, -1, 20, -22, -19, 13, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[10, 1, -23, -7, 23, -5, -15, -26, -19, 14, 0, -6],\n [18, 6, 11, 6, 19, 10, 18, -22, -12, 3, -24, 1],\n [3, 9, -24, 25, 17, 4, -13, -21, -8, -22, 22, 24],\n [-1, 23, 17, -9, 10, 18, 9, 4, -9, 25, -18, -1],\n [-25, 5, 15, 18, -21, -7, -19, 18, -23, -2, 4, -8],\n [-20, 20, 10, 3, 0, -10, 5, -8, -2, 2, -2, 26],\n [5, 10, -16, -23, 19, 4, 9, -23, -25, 12, 24, 6],\n [17, 0, -1, -8, 17, 14, 12, 6, 11, -17, -26, 23],\n [8, -16, -13, -21, 16, 12, 13, -2, -4, -22, -1, -9],\n [5, 20, -6, -1, 23, 8, -17, 1, 4, -12, 13, 26],\n [-19, 19, -17, 18, -17, 11, -9, 21, 1, 1, 23, -7],\n [-3, -21, 14, 21, 5, -21, -16, 3, -24, -19, 6, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[20, -8, -17, -8, -18, -20, -13, -25, -5, 18, -7, -1],\n [-23, 12, 13, -4, -11, -2, 25, -18, 26, -16, -2, 4],\n [19, 0, 9, 24, 20, -13, -4, -11, -7, 26, -24, -21],\n [2, -23, -26, 23, -19, 21, -7, -11, 20, 4, 5, 7],\n [2, -15, -23, 16, 7, -21, 22, 24, -18, -22, 19, -11],\n [-26, -7, 8, -17, -2, 20, 1, 8, 6, 18, -12, -6],\n [15, 8, 23, 24, 26, 10, -17, -11, -7, 23, -19, 18],\n [4, -19, -14, -3, -15, 18, -10, 20, 14, 25, 9, -15],\n [9, -14, 8, -22, -14, 19, -19, -16, -19, 4, -15, -16],\n [-10, 0, -14, 9, -14, 14, -5, 19, 17, -3, 3, -14],\n [-19, -22, 16, 25, -21, -20, -5, 3, -12, 10, 14, -7],\n [4, 24, -22, 18, -15, 10, 3, 12, -24, -14, -16, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -18, 3, 2, 11, 19, 15, 22, 7, -1, -25, 9],\n [-20, 25, 9, 13, -13, 0, -1, -7, 8, -16, -1, 8],\n [-22, -11, -16, 6, -18, -5, -22, -7, 16, 7, 3, -17],\n [10, 5, -3, -10, 17, -24, 12, 16, 16, -1, -15, 10],\n [15, -15, 19, 6, 0, -13, -20, 15, 17, 11, 21, 15],\n [25, 17, 0, -17, 15, 16, 14, -18, 17, 7, 19, 14],\n [2, -9, 2, 3, -14, -5, -11, 18, 5, 13, -1, 4],\n [17, -8, 15, 7, 20, 22, -21, 8, -16, 10, -5, -14],\n [-11, -1, -5, 15, -14, -4, 5, -4, 16, 5, 21, 11],\n [1, 6, 13, -1, 3, 25, -10, 15, 2, -25, 24, 11],\n [7, 23, 19, 11, -15, 25, -6, 0, 13, -24, 10, 22],\n [-1, 25, -22, 19, -7, 19, 14, -19, 16, 1, 2, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"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, -25, -25, 11, 11, 16, -4, -17, 18, 26, 1, -8],\n [1, 4, -25, 2, 25, -13, 1, -26, 17, 23, -11, 10],\n [-6, 24, -13, 16, -10, -12, 21, 4, 19, 22, 9, -13],\n [9, 0, -24, 9, -21, 0, -5, -5, 9, 5, 0, -20],\n [12, 23, -15, -11, 11, -22, 15, 22, 8, -18, 2, 0],\n [5, -17, -2, 15, 26, 11, -2, -23, 16, 25, 14, 17],\n [-4, -17, -21, -14, 4, -22, -23, -24, 3, -4, 10, -9],\n [8, -22, 14, 1, 11, 20, -9, -19, -15, 3, -5, -21],\n [3, -19, 20, 21, 2, 4, -22, -16, -10, -14, -7, 4],\n [-1, 1, -2, 21, -9, 18, 5, 2, -24, 8, 11, -12],\n [24, -24, -6, -24, 26, 8, 23, -19, 21, -24, -16, 21],\n [-25, 6, -19, -15, -8, -9, 23, -6, -5, 16, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-21, -26, -18, 25, -11, 2, 2, -22, -8, -5, 22, -19],\n [24, -9, 17, 21, -13, -23, 13, 0, -3, 3, -15, 16],\n [-14, 13, 23, 18, -23, -1, -26, 0, -4, 15, 11, -16],\n [12, 15, 17, -6, -5, 1, 11, -21, -2, -23, 7, -1],\n [12, 26, 0, 12, -6, -6, 2, 7, 0, 15, 19, -1],\n [-22, -7, -19, 25, -9, 26, -22, -23, 24, 16, -22, -11],\n [-18, -2, 11, -19, -26, 4, 6, -22, -9, 9, 21, -7],\n [-3, -8, 1, 3, 12, -12, 23, -18, 12, 4, -26, -14],\n [9, -25, 15, 10, 8, 10, -16, -9, -7, -25, -3, -11],\n [-4, 23, 11, 20, 17, 2, 3, -23, 2, 17, 16, 14],\n [0, 6, -9, -21, 5, 4, -15, -4, 2, -24, 6, 12],\n [1, -9, 17, -5, -7, -11, 25, -20, 22, -23, 15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "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, 9, -9, 6, -26, 21, -2, 18, -13, -16, 25, -19],\n [15, -11, 12, 10, 4, 15, -9, -20, -23, 5, 4, -17],\n [3, 23, 23, 8, 18, 4, 4, 19, 19, 6, -22, -17],\n [19, 24, -4, -20, 20, 1, -6, 4, 14, 0, 2, -17],\n [-19, -18, -16, -5, 13, -1, 23, 10, 13, -25, 23, -8],\n [23, 25, -11, -23, 22, 11, 17, -20, -13, -15, -6, 25],\n [7, -6, 9, 13, 15, 22, -20, -6, -17, -6, 22, -11],\n [-2, -14, 23, 0, 10, -19, 3, 4, -20, 3, -9, -4],\n [11, 18, 14, 3, 3, -19, -15, -17, -20, 12, -10, 5],\n [-22, 15, -6, 4, 25, -12, -14, 19, 22, -20, -3, 26],\n [-23, 14, -8, 19, 8, 2, 9, 7, -19, -25, -23, -25],\n [3, 2, -23, -6, -18, -25, -7, 22, 6, -21, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, -22, 10, -18, 5, 10, 7, 12, 20, 13, 2, 4],\n [-24, 16, -2, 15, 9, 17, -14, 12, -8, -11, 15, 3],\n [12, 8, -25, -26, 21, 18, -24, -1, 1, 0, -13, 23],\n [16, 24, -3, 8, 25, 7, -3, -21, 4, 2, 9, 2],\n [-14, -19, -12, 6, -2, -11, -6, 25, 10, 18, -10, 7],\n [-14, 7, 16, -12, 14, -5, 24, -23, 22, 20, 12, -4],\n [-14, -19, -26, 14, 23, -10, -10, -19, -24, 2, -5, 16],\n [-25, -25, 21, -10, -18, 6, 2, 2, 17, -21, 16, -21],\n [25, 10, 18, -26, -11, 24, -16, -5, 7, -26, -14, 22],\n [19, 22, 15, 1, 22, -14, 11, 3, 9, -23, -13, 9],\n [-4, -22, 19, -12, -4, -19, -16, -20, -4, 18, 19, 14],\n [0, 4, 20, 26, 13, -25, 17, 21, 4, -19, -26, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "558", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-10, 3, -3, 4, 24, 25, -14, -12, -1, 5, 18, 8],\n [-11, -18, -8, 13, 13, 19, 24, 18, -24, -1, 10, -19],\n [-21, -22, -6, 0, 17, 11, -19, -5, -4, -2, -20, -13],\n [14, 2, -10, 24, -21, 5, -8, 0, 3, 23, 26, 6],\n [10, 18, -16, 14, -17, 2, -5, -7, -8, -3, 1, -25],\n [13, -9, -9, -25, 20, 22, -4, 20, 25, -12, -2, 18],\n [-9, -6, 20, 5, 23, -8, -9, -3, 20, 15, 3, 2],\n [-6, -6, 21, 14, -25, 18, -26, -5, 13, 11, -8, -8],\n [-25, 2, 23, 23, -4, 20, 21, 0, 18, -4, 1, 1],\n [-22, -9, 3, -3, 10, -11, 2, 3, -2, 11, 12, -26],\n [13, 12, 12, 4, 12, 4, 6, -15, -2, -4, 16, 21],\n [1, 6, 11, -1, -3, -22, 17, -10, 18, 10, -12, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[7, -7, 3, -11, 17, -23, 4, -1, 14, -15, -25, -19],\n [-13, -3, 16, 13, 14, -2, -20, 5, 26, -4, 19, 12],\n [-1, 15, -20, 20, 23, 18, -23, 17, -2, 25, -9, -20],\n [-5, -23, 2, -3, 13, 25, 23, 11, 14, -15, -18, -12],\n [-14, 3, 8, 8, -1, -8, -6, -6, -14, -6, -3, -1],\n [17, 4, 3, -3, 5, 3, -1, 11, -9, 14, 22, -15],\n [-6, -4, 1, -10, -12, -4, 26, 26, 7, 1, -23, 14],\n [-15, -25, -2, -3, 4, -23, 17, 7, -21, 4, 12, 23],\n [-3, -2, -22, -17, -9, 2, -16, 22, 3, 16, -22, -21],\n [-13, -11, -13, 6, 10, -22, 13, -13, 13, -18, 0, 25],\n [-24, -17, 21, -16, 7, -26, -17, 26, -21, -19, 4, -21],\n [4, 7, 13, 26, 2, -24, -5, -15, 11, -8, -20, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, -23, -6, -13, 9, 23, -20, -14, 8, 22, 6, -16],\n [24, 12, -2, 19, 12, -3, -5, 16, 24, 21, 22, 19],\n [-5, -12, -9, 17, 18, 5, 9, -17, -18, 17, -2, -23],\n [11, 19, 9, 15, 10, 12, -20, 15, -1, -7, 18, 20],\n [-6, -22, 3, 21, 11, 9, 11, -4, -4, 21, 24, -21],\n [16, 19, -4, -12, -26, 9, 12, 1, -17, 6, 19, -3],\n [-21, -13, 5, -8, -21, -7, -2, -7, 11, -16, 5, 2],\n [3, 2, -5, -16, 22, -7, 14, -13, 0, 11, -23, -20],\n [3, -17, -20, -22, -23, 20, 9, -12, 12, 11, 9, 24],\n [-25, -12, -7, 7, -14, -2, -13, 14, 21, -18, 22, 8],\n [-5, -22, 17, 10, -13, -10, -22, -14, 20, 4, 22, -17],\n [21, -4, 2, -11, -10, -20, 16, -13, 17, -18, -20, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-11, -17, -22, 24, -20, -5, -3, 13, 15, -5, 8, 19],\n [25, -24, 20, 15, -20, -8, 15, 19, -19, -4, -7, 6],\n [-21, -12, -22, -13, -18, -1, 5, 4, -21, -26, -8, -12],\n [7, -8, 22, -16, -9, -3, 19, 24, -18, -16, 16, -23],\n [-9, 17, -4, 14, 10, -26, -2, -18, 12, -26, 25, -10],\n [-24, -4, -26, -3, -14, -7, -7, -15, -10, -6, 13, -3],\n [3, -4, -4, 20, -10, -25, 15, -3, 6, 18, 17, -12],\n [5, 15, 7, -5, 4, -12, -7, 15, -4, 4, -25, -14],\n [15, 5, 22, -11, -12, -2, -15, 1, 14, -15, -6, -15],\n [24, 22, -11, -17, -17, 25, -25, 0, 25, 3, 6, -11],\n [-17, -12, -1, -12, -21, -10, 18, -26, 23, -4, 7, 8],\n [16, -2, -26, -2, 11, -11, 20, 14, -15, -17, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "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, -20, -21, 18, -16, -3, 13, -2, 10, -24, -23, -23],\n [14, -26, 3, -12, 18, 4, 10, 23, -22, 16, -6, 8],\n [-23, -20, 2, 9, 8, 5, 15, 25, -16, 23, 6, 26],\n [14, -10, -15, -26, -4, -20, -13, 14, 17, 26, 13, -20],\n [-13, 7, -25, -7, -10, -17, 26, -22, 6, 10, 9, 17],\n [19, -16, -6, -23, -2, 14, 8, 8, 8, 12, 6, -14],\n [-23, 17, 13, 24, 11, 15, 18, 3, 0, 8, 1, 14],\n [15, 18, 21, -19, -1, 16, 7, 24, 2, -25, -21, 21],\n [-11, -20, -16, -11, -21, 10, -18, -24, 26, 2, 26, -19],\n [13, -10, 11, 17, -21, 20, -16, -17, -25, 26, 2, -21],\n [24, 22, -18, -25, -23, 14, 13, 3, -23, -26, 16, -16],\n [-20, -9, -19, 3, -12, -17, 19, -25, 15, 24, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[25, 7, 22, -24, -23, -2, -22, -15, 26, -3, -8, 5],\n [-15, 10, 20, 0, -9, -2, 24, -4, -24, -25, -16, 19],\n [26, 10, 3, -14, 13, -21, -15, 12, 16, -19, -18, -23],\n [10, 9, 5, -15, -9, 4, 20, 13, 16, 19, 12, 2],\n [21, 13, 2, 0, -16, 6, 22, 12, -9, 17, -7, 1],\n [-5, 5, -6, 10, 0, 11, -1, -4, 7, -15, -16, 9],\n [5, 12, 10, 16, -11, 15, 4, 14, -21, -14, 9, -16],\n [-16, 21, -7, 2, -8, 3, -21, -10, -9, 9, -9, 16],\n [-15, 15, -24, 20, -9, -11, 12, 16, 1, 15, -18, -7],\n [-9, -2, -6, 18, -1, -4, -17, 26, 17, -14, 26, 10],\n [-15, 9, -24, -13, 8, 7, 13, 2, 3, -20, -25, -9],\n [-1, -10, 19, -15, 23, 5, 22, 2, 21, -17, 9, -25]]\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[[10, -13, -17, 13, -26, 14, -6, -22, -18, -18, -9, -22],\n [-11, 7, -23, -6, 23, 10, 13, 17, -13, 0, 22, -15],\n [0, 7, -23, 16, 17, 24, -25, 15, 15, 5, -25, -5],\n [-8, -1, -7, 9, -9, 25, 23, -13, -7, 18, -3, 20],\n [20, 4, 25, 9, -12, 19, -20, 22, -4, 2, 14, -23],\n [4, -9, 18, 4, 20, 9, -9, -17, -20, 11, 18, 1],\n [-9, 4, -18, 16, -11, 13, -2, 10, 3, 20, -25, -22],\n [15, 3, -8, -13, 0, 3, 18, -13, 4, 9, 12, 23],\n [3, 11, 20, -16, -10, -17, -11, 24, -16, 12, 1, -6],\n [1, -4, 19, -26, 22, -14, -19, -8, -3, 13, 22, 10],\n [-2, 16, -1, 19, 15, 0, 5, 17, -24, 14, 16, -18],\n [-26, -9, -24, -13, 5, -23, 10, -6, 15, 0, -22, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-5, -7, 14, 17, -25, 16, -26, -4, 21, -2, -1, -24],\n [4, 0, -14, 20, 6, -2, -11, 20, 11, -1, 20, 25],\n [-9, -10, 19, -2, -1, -9, 22, -26, 19, -20, 3, 6],\n [-2, -2, 0, 8, 16, -9, 3, -13, 8, 7, -7, -12],\n [-20, -14, 9, 13, 26, 7, -14, -23, -14, 21, 17, -14],\n [-4, 2, 6, -4, -24, 5, -24, -15, -23, 6, 5, -10],\n [25, -18, -22, -6, -24, 26, 12, -24, 10, 17, 8, 6],\n [-24, 21, -9, -24, 2, 10, -22, -18, -15, -11, 0, -18],\n [23, 16, -5, -10, -26, -24, -22, -5, -26, 20, 22, -23],\n [-5, -3, 5, 19, -25, 9, -22, -20, 9, 13, 16, -19],\n [9, 16, -15, 1, -25, 20, -13, -8, -6, 3, 22, 21],\n [10, 25, -6, 1, 6, 15, -20, 15, -11, 10, 24, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "531", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[11, 17, 11, 15, 15, 18, 24, 3, -10, -11, -23, 3],\n [-7, 8, -22, 18, -13, 14, 14, 13, 1, -17, 25, 3],\n [23, 5, -15, 18, -11, -1, 8, 14, -11, -10, 21, -4],\n [15, -5, 23, -6, 7, 19, -22, 11, 25, 4, 6, 20],\n [-24, 26, -8, -9, 1, -12, 23, 6, 1, 19, 22, 25],\n [-19, 13, 22, 3, -26, -20, -13, -6, -21, -10, -13, -20],\n [-12, -19, 21, -17, 2, 14, -8, -25, -19, 3, 16, 9],\n [23, -9, -25, -22, 19, -14, 13, -16, -19, 20, 11, -10],\n [-16, -1, 12, 7, -24, 23, -2, -3, 26, 25, -4, 3],\n [19, 14, 13, 0, 23, 17, 17, -17, -18, -25, -6, -16],\n [-17, -2, 13, -22, -5, -22, -18, -16, 17, -22, -21, 6],\n [-11, 19, -3, -13, -3, 18, -15, -4, 12, -21, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[21, -18, 19, 14, 9, 14, 13, 19, -22, 21, 15, 4],\n [8, 14, -24, -8, -8, -26, -5, -8, -1, -12, -8, -2],\n [12, 4, 3, 6, -11, 13, -15, 1, 3, -21, 15, -13],\n [-22, 9, -4, 5, 4, -13, 5, 22, 0, -26, 22, 25],\n [-18, -11, 8, -17, 22, -11, 3, 6, 24, -12, 12, -19],\n [-23, 17, -25, -20, 11, 7, -2, -20, -2, -25, -1, 9],\n [21, 11, 15, 19, -24, 19, 2, -16, 16, -6, 16, -23],\n [-22, -21, -5, 19, 12, -21, -13, -5, -11, 5, 9, 23],\n [-20, -4, 24, -13, 20, 26, -21, 15, -2, -24, -14, 24],\n [26, 23, -24, 4, -24, -10, 12, -25, -22, -18, 2, 8],\n [13, 9, 8, 23, 3, -12, 2, -2, -16, 10, 21, 24],\n [-23, 16, -15, 5, -22, 15, 15, 24, 10, 10, -2, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, 9, -25, 8, 9, -19, -18, 1, 13, 17, -17, -22],\n [10, 20, 4, 25, 2, -24, -1, 4, -25, -12, -14, 1],\n [17, -13, -15, -12, -6, 2, 18, 8, 20, -7, -9, 11],\n [-12, -15, 7, -22, -10, -14, -14, 9, -11, 13, -24, 25],\n [-25, -2, 26, -24, -16, -16, -17, 1, -16, 22, -20, 2],\n [-26, 25, -12, -20, -23, -24, -7, -24, 2, -7, -17, 8],\n [-1, 3, -1, 10, -7, 24, 26, 15, -18, -16, 6, 3],\n [3, 25, 18, -4, 9, -3, 4, -4, 26, 15, 9, 13],\n [22, 7, -6, -1, -20, -2, -24, 26, 16, -9, -21, 25],\n [19, -14, -25, 21, 13, 20, -14, -26, -25, -23, -14, 3],\n [17, -15, 6, 11, 16, 21, 7, -24, 16, -18, -20, -23],\n [1, 15, 5, -26, -14, 9, -1, -14, -5, -3, -16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-12, 18, 9, 11, 7, 7, 5, 11, -2, -24, 25, 16],\n [20, 2, -6, -18, -6, -6, -20, 20, 5, -5, 15, -16],\n [7, -13, 21, 14, -5, -2, -11, 6, -25, 12, 17, 23],\n [-21, 7, 19, 21, 15, 10, -5, -11, -20, 20, -14, 22],\n [23, 23, -10, -24, -15, -21, -15, -16, 14, -8, 4, 24],\n [-25, 18, 5, -9, -23, -5, -13, -13, 10, 2, 24, 7],\n [21, -21, 16, -15, -3, 18, 2, -17, 19, 9, 7, 24],\n [5, 5, 24, -12, -18, 9, -5, -14, 14, 17, -13, -1],\n [17, -2, -5, 3, -14, 23, 5, 10, -8, 8, 22, 25],\n [2, -20, 8, 12, -21, -13, 1, -26, 19, -6, 0, -5],\n [-16, -18, -17, 16, 23, 22, 19, 22, 12, 4, 5, 4],\n [-19, 13, 24, -22, 4, -20, 18, 20, -13, -2, -6, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 19, 18, 4, 25, -23, 14, 19, 2, 22, -26, 5],\n [-26, -23, -7, 13, 10, -13, 25, -13, -25, -6, 2, -15],\n [-9, 11, 14, 5, 14, -5, 9, 15, -15, -6, -19, 1],\n [26, -5, 25, -11, -15, 22, -10, -6, 24, -20, -7, 9],\n [25, 14, 17, -14, 14, 2, 16, 10, -19, -7, 17, 21],\n [-17, -12, -15, 19, 18, -11, 15, -19, -7, -13, 10, -1],\n [11, 26, 14, 18, 2, -14, 7, -5, 18, -1, 7, 20],\n [-3, -6, 4, -15, 15, -3, -6, -23, -2, -19, 9, 7],\n [23, 23, 19, 0, 1, 2, 2, -17, 17, 5, -19, -10],\n [-15, -1, 25, -24, 15, -16, -13, -20, -1, 10, 6, 17],\n [21, 5, 11, -7, -17, -12, -12, -21, -2, -26, -21, -14],\n [-16, -3, -7, -1, -2, 25, 25, -15, 19, -18, 18, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-18, 6, 13, 7, -3, 26, 18, 18, 6, 6, 2, 11],\n [21, 22, -14, -9, 8, 20, -25, -2, -21, -2, 26, -7],\n [-13, 23, -23, -19, 7, 1, -25, -10, -23, 21, 7, 0],\n [-8, 1, 11, 7, 5, 14, 4, -21, -21, 1, -19, -26],\n [-11, 15, -8, -9, 3, -11, 6, 1, 20, -11, -16, -21],\n [-13, 21, 9, -5, 13, -4, 4, 1, -8, 24, -5, -26],\n [-24, -19, -14, 24, -26, 2, -14, 15, 2, 3, -11, 14],\n [7, 13, -24, 2, 3, 25, 7, -23, 21, -19, 20, 21],\n [-9, -5, -17, 24, -13, 24, 19, 4, 8, 19, -25, -25],\n [8, 7, 2, -21, -23, -26, 8, 21, 20, -1, 2, -16],\n [24, -23, -5, 6, 7, 4, -17, 8, 26, 1, -4, 22],\n [-15, 2, -25, -14, 9, 20, -1, -10, 16, 6, -5, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-17, 12, -1, 3, -5, -16, -5, -3, 2, 24, -17, 7],\n [19, -2, -6, 12, -14, -25, -21, -26, 1, -5, -16, 12],\n [-22, -9, -7, -15, -6, 0, 23, 14, 7, -9, 7, -25],\n [26, -13, 12, -26, 1, 14, 0, 3, -5, -15, -26, 6],\n [14, 21, 22, -26, -22, 21, -22, -20, -7, -1, 22, -21],\n [-1, -24, 12, -13, 22, -13, -7, 17, -18, -21, -25, 11],\n [14, 16, 6, 17, -22, -14, -12, 18, 7, -18, -1, 3],\n [-5, -2, 13, -23, 20, 1, 10, -17, -18, 9, -26, 3],\n [-16, -2, -16, 14, -22, 0, -4, -8, 26, -24, -19, 21],\n [22, 9, -12, -14, 3, 14, -17, 7, 3, -2, -21, 25],\n [10, -10, 9, 13, 5, -5, 6, -5, 9, -9, 1, -14],\n [-9, -4, 8, -9, -17, 24, -25, -13, 5, 3, -8, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[21, 5, -17, -22, -13, 12, 15, 16, -8, -16, 8, 12],\n [19, 11, -5, 25, 18, 19, 3, 25, 3, 20, 23, -16],\n [-5, -17, 16, -8, -12, 8, 8, -26, 20, 18, 20, 26],\n [-9, -1, -9, 14, -9, 16, -9, 5, 11, 0, 22, 2],\n [22, 14, -7, 8, -4, -15, 26, 8, 9, 15, 1, 10],\n [-7, 8, -20, 7, -21, -8, 15, -19, 21, 3, -25, -11],\n [26, 19, -3, -2, -14, -18, 3, -18, 13, -20, -11, 11],\n [5, 2, 16, 24, 13, 24, -12, -16, -18, -11, -2, 5],\n [18, -17, -17, 3, -7, 14, 7, -26, 5, 13, 4, 21],\n [-16, 14, -8, 23, -20, 26, 2, 15, 11, 26, 9, 6],\n [9, -1, 2, 2, 8, -24, 19, -22, 6, -16, -21, -25],\n [-14, -26, 0, 13, 15, -12, 8, 3, -21, 7, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "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, 8, -18, 25, 10, -21, -17, 26, -18, 6, -11, 5],\n [11, 21, -7, -7, -24, -13, -6, -19, 25, 19, -3, 20],\n [-6, 15, 5, -10, 13, 24, -23, 15, -4, 9, 25, -5],\n [-2, -23, -17, -3, 8, 23, -13, -7, 19, 25, -13, 12],\n [-18, 7, -7, -24, -15, 24, 21, 12, -15, 15, -5, 8],\n [13, 4, -20, -18, 24, 10, -5, -18, -11, 25, -6, -18],\n [-15, 0, 25, 20, 23, -18, 0, 1, 8, 16, 11, 5],\n [14, -24, -18, -24, 24, 9, -14, 22, 7, 3, -11, 6],\n [8, -11, 11, 13, -22, -19, 6, 24, 3, -25, 11, 11],\n [-7, 25, -18, -26, -25, 25, -8, -11, 14, -22, 5, -7],\n [16, 25, -13, -14, 0, 8, 7, -11, 1, 16, 8, -12],\n [-24, 0, 0, 24, -23, -6, -5, -22, 14, 12, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-14, 0, 23, -12, -15, -17, 22, 11, 1, 16, 8, 11],\n [-7, -15, -24, -25, 1, -5, 8, 18, 25, -18, -4, -10],\n [-13, 25, 5, 13, 9, 6, -17, -14, 7, -22, -21, 6],\n [-22, -3, 20, -19, -9, -2, -9, 9, -1, -7, -7, 12],\n [13, -3, -7, 18, -23, -5, -2, -6, -9, 18, 19, -18],\n [17, -18, 6, 14, -20, 6, -25, 23, -19, 6, 8, 2],\n [5, -26, 26, 4, 25, 8, 13, 17, 12, -7, 6, -4],\n [-24, 26, -15, -19, 14, 20, -16, -1, -4, 11, -22, 5],\n [-22, 21, -12, 16, 25, -4, 22, 1, -8, -10, -12, -14],\n [-4, -9, -4, -11, -7, -2, 5, -6, -26, 1, 0, 25],\n [0, 18, 9, -15, -12, -7, 17, -8, 24, -1, 20, -6],\n [10, 16, 23, -17, 1, -1, -14, -2, 24, 4, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"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, 13, -4, -24, -16, 0, 10, -15, 6, 1, -21, -21],\n [17, -6, -2, 20, 9, -9, 17, 12, -22, -4, -4, -4],\n [8, 2, -22, -10, 11, 25, -25, -8, 20, -24, 3, 6],\n [-4, -1, 3, -8, 12, -1, 5, 15, 1, -18, 21, 4],\n [-12, 5, -14, -5, 13, -16, 6, -3, 13, 17, 24, -21],\n [-11, 3, 3, -13, -20, -24, 4, -17, 6, 11, 10, -12],\n [23, -23, 10, 15, -23, -17, 25, -5, 4, 9, -15, -18],\n [1, 7, -22, 3, -11, -8, -13, 20, 24, -3, 23, -16],\n [-14, -17, 2, 12, 0, -26, 5, -9, -23, -11, -9, -6],\n [24, 20, -2, -17, -20, 26, -26, 6, 6, -8, -20, 20],\n [18, 14, -13, 11, -20, 19, 16, -24, -16, -19, -1, 11],\n [-24, 2, -15, -9, 16, -20, 3, 15, 21, -11, 20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -23, -23, 11, 23, -26, 15, -24, 1, 19, -16, 10],\n [-25, -18, -10, 5, 24, 4, -6, -10, 25, 15, -10, 16],\n [0, 1, 12, -26, -11, -24, -12, -23, 9, 3, 2, -4],\n [-22, 20, -16, -8, -19, 16, -16, -18, 19, -2, -2, -13],\n [4, -14, -26, 3, -18, 13, 2, 4, -9, -24, 8, -25],\n [-23, 14, -12, 23, -10, -1, 4, 3, -4, 3, -16, 6],\n [11, 19, -22, 8, 24, -26, -23, 21, 11, 10, -20, -17],\n [6, 24, -13, 9, 20, 11, 25, 3, -1, 4, 15, 20],\n [-8, 13, -14, -4, -8, -11, -2, -1, -6, -9, -18, -3],\n [20, 13, -10, 3, -23, 1, 14, 13, -18, 9, -19, -5],\n [-2, 22, -21, -1, 15, -25, 4, -15, -8, 10, 21, 10],\n [-26, -17, 7, -11, 14, -20, -14, -23, 12, 4, -17, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, 1, -22, 1, 20, -16, 7, -12, 24, -22, 21, -6],\n [4, 13, -20, 8, -6, 13, -22, -13, 7, -17, -9, -10],\n [11, 22, 5, -10, -5, -2, 24, -11, 3, 7, -22, 17],\n [6, -22, 13, 15, -24, 11, -14, 25, -19, 3, 23, -22],\n [11, 4, -25, -20, -11, -17, 2, 3, -7, 15, 7, -19],\n [7, 7, 18, 9, -20, -13, -7, 10, 6, 4, 6, -1],\n [-1, 24, 11, -11, -15, -26, 17, -7, 23, -25, 4, -9],\n [15, -17, -21, -25, -11, -22, 11, -5, -5, -5, -26, 9],\n [22, -14, -15, -14, 24, 21, -16, 23, -9, -5, -26, -23],\n [-18, -24, -19, -18, -9, -22, -5, 10, -22, -4, -11, -22],\n [10, 17, 12, -24, -1, -19, -6, 25, -9, -22, -21, 0],\n [-5, -5, 11, 11, 16, 0, 18, 19, 22, 6, 15, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, 3, 7, 18, -10, 24, 8, 9, -21, 18, 2, -4],\n [-13, -18, -12, 11, -2, -7, 16, -5, -20, -9, -10, -13],\n [-1, 13, 5, 2, 13, -20, -18, -15, -24, 5, 6, -12],\n [-18, 22, 17, -10, 1, 18, -14, 20, -6, 23, 20, 23],\n [-22, -20, 11, 10, -8, 14, 5, 16, -24, 12, 8, 0],\n [11, 24, 21, -19, 24, 26, -8, 3, 21, 13, -17, 3],\n [-18, 21, -5, 4, 19, -17, 9, -17, 25, 26, 0, -12],\n [-8, -16, 5, -7, 19, -12, -23, -10, -26, -8, -22, -9],\n [-10, 15, 14, -23, 25, -8, 4, -24, 23, -24, 2, 26],\n [-19, -22, 4, 0, 6, -9, -3, -1, 4, -13, -2, 5],\n [12, 14, -13, 21, 21, 0, -5, 11, -20, 6, 16, 14],\n [6, -3, -1, 23, 15, 4, 0, -14, 4, 5, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "499", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[13, 18, -11, 12, -19, -9, 0, -18, 1, -5, -16, -5],\n [22, -13, -4, -25, -12, 23, -22, 2, 6, 21, 17, 3],\n [19, -10, -26, -13, 20, 17, -10, -18, 8, 4, -15, 18],\n [-25, -12, 7, 10, 26, 14, 3, -13, 18, -23, -19, -4],\n [-20, -10, -5, 11, -1, -19, -5, 13, 18, -5, 13, -22],\n [-18, -7, -5, 7, 8, 9, -8, 1, -20, 14, 11, -24],\n [5, 19, 18, 4, 18, -2, 6, 20, -22, 2, 4, -1],\n [-6, 7, 10, 22, -26, -23, 20, 20, -5, -11, 18, 19],\n [5, 7, -6, 0, 15, 10, -24, 25, 16, 18, 7, -20],\n [2, -24, 18, 11, 14, 25, -25, -15, -12, -11, -24, 0],\n [19, -4, 6, 21, 0, -3, 11, 0, 20, 4, -12, 8],\n [9, -3, -10, 18, 7, -26, -7, -21, -22, 2, -21, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[26, 6, 18, 11, 25, 2, 17, -17, 5, -2, 1, 2],\n [24, 8, 20, 5, 19, 9, -20, -17, 19, 7, 6, -1],\n [21, 21, -14, 3, 5, 6, -21, 9, -25, -20, 3, 19],\n [-1, -2, 6, 15, -21, -19, -18, -16, -3, -21, 13, -11],\n [-10, -3, -20, 13, 13, 0, -17, -18, 24, -17, 22, 3],\n [-18, 19, -1, 7, 8, 0, -7, -3, 0, 14, -8, -9],\n [23, 16, 14, -15, 13, -9, -19, 9, 11, 26, -11, 26],\n [-14, -1, 21, -1, -6, 25, 23, -6, -19, 6, -21, 23],\n [-25, -19, -21, -21, -5, -2, 19, 4, 8, 23, -22, -5],\n [21, -2, -9, -18, -2, 2, 6, 16, -19, 13, -14, -19],\n [21, 26, 23, 14, 17, 0, -24, 6, 4, 1, -6, 25],\n [2, 2, 25, -18, -5, -19, 18, -10, -4, 12, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-13, -2, -11, 22, 21, -9, 5, 19, 11, 25, 26, -12],\n [10, 22, 6, -14, -20, -8, -6, 10, -18, -23, 4, -20],\n [-14, 13, 9, -19, -1, 0, 21, -1, 18, 15, -13, -7],\n [15, 18, 1, -19, 25, -22, 26, 26, 24, -14, -25, 21],\n [-13, 22, -24, -11, -18, 12, -25, -16, -3, 16, 2, -13],\n [21, 13, -5, 20, 21, 7, 9, 6, 12, 16, -9, -5],\n [-2, 10, -22, 5, 25, 22, 9, -18, -13, 5, -18, -4],\n [18, 21, 25, 18, -18, -6, 17, 5, 17, -17, 2, 7],\n [-5, -22, -16, 1, -3, 7, 26, 15, 13, 25, -17, -1],\n [16, 14, -20, 17, -20, 21, 24, 21, -12, 19, 18, -24],\n [18, -1, -20, -25, -17, 3, 20, -24, 11, 2, -2, 19],\n [-23, 20, -22, -21, -8, -9, 25, 11, 9, -15, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "577", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-13, 12, -25, 7, 26, -7, 9, 25, -4, 8, 7, -6],\n [11, 19, -19, 16, 24, 3, 20, -7, 25, -7, -4, -7],\n [19, -4, -23, -17, 13, -22, 5, -9, -2, -10, -22, 8],\n [15, -6, 9, -8, -4, -22, 6, -23, 6, 20, 8, 15],\n [-1, 10, -5, -16, 22, -1, 14, -14, -13, 14, 22, -20],\n [-11, -7, 18, 19, 23, 16, 0, 7, -5, 11, 10, -24],\n [0, -20, 8, 18, -4, -25, -3, -25, 23, 9, -10, -16],\n [-20, -25, -12, 19, 4, 19, -21, 10, 19, 26, 2, -23],\n [19, 10, -15, 0, -2, 18, -15, -10, 23, -15, 4, -18],\n [-8, 2, 26, -2, -12, -18, -14, 20, 17, 15, -24, -17],\n [-9, -17, 9, 1, -24, -7, -9, 22, 10, -7, -17, 7],\n [-5, -6, 6, -11, 15, 8, 9, -26, -15, -14, -19, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[4, -22, 17, 24, 9, 20, -2, 18, -14, 8, 5, -19],\n [-5, -21, 22, -16, -20, -12, -23, 13, 7, 16, 13, -5],\n [3, -8, 10, 23, 11, 3, 5, -8, 25, -2, 10, 18],\n [-4, -15, -18, 10, -10, 23, 8, 24, 20, 22, 14, 3],\n [-23, 14, -23, -3, -24, -18, -16, 5, 16, 25, 13, 2],\n [7, 21, 7, -6, -2, -6, -7, -3, -22, 14, -25, -18],\n [16, -19, 5, -20, 11, -7, 20, -12, 12, 1, 4, -5],\n [13, 22, 24, -3, 7, -18, -25, 18, -2, -15, -23, 24],\n [13, -14, 2, 5, 0, 3, 19, 12, -26, -16, -4, 22],\n [-10, -12, 0, 26, -17, -11, 10, 1, -25, 12, 8, -12],\n [-16, 6, -11, -16, -7, 25, -8, 12, 23, -4, -17, -19],\n [-25, -20, -1, 13, -8, -21, 6, -16, 25, 9, -15, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535", "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, -4, 13, -21, 23, -8, -7, -9, 0, 6, 2, -18],\n [18, 17, 23, 0, 26, 12, -16, 23, 15, -19, -13, 19],\n [-14, -20, -12, 11, 17, 16, -9, 9, 4, -23, -14, 12],\n [3, -8, -23, -26, 13, 5, -15, -15, -7, -16, 26, 26],\n [22, 3, 22, 17, 4, 1, 17, 22, 2, 14, -5, 18],\n [22, 2, -26, -6, 4, 0, 8, -19, 13, -19, -21, -12],\n [-6, 10, -21, 2, -2, -4, 11, 0, 15, -4, -8, 1],\n [7, -20, 24, -14, -23, -16, 23, -6, -6, 16, 18, 15],\n [-1, 4, 22, -23, -24, 12, 21, -6, 11, -9, 6, 24],\n [15, 8, 5, -16, 12, 4, 3, 11, 19, -7, 13, -1],\n [-16, -25, 12, -10, -3, 3, 10, -21, 22, -4, 20, 8],\n [23, 20, -1, -2, 9, -6, 15, 16, -4, -26, -17, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "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, 20, -19, 14, 6, 26, -15, 21, 12, -15, -15, -16],\n [21, -19, 24, -19, 10, 22, -11, 9, -9, 17, -6, -23],\n [23, -20, 7, 7, 18, 9, 10, 3, -1, -15, -16, 2],\n [-24, -16, -18, -1, -19, -6, -19, 15, -21, -9, -21, -6],\n [17, 21, 26, 21, -4, 9, -9, 0, 18, -24, -15, -7],\n [-8, -4, -22, 24, -8, -15, 1, 10, 7, -11, 26, -23],\n [20, 15, -21, -20, 7, -23, -12, -14, -18, 10, -10, 11],\n [-13, 10, 4, -25, 19, -8, -8, -14, -6, 4, 17, 1],\n [-26, 8, -17, -19, -14, -8, -24, -24, 0, -9, 8, 17],\n [7, 3, -19, -6, 19, -8, 16, 21, 19, 13, 3, 0],\n [-7, -13, -15, 22, -4, -15, 26, 17, 17, 12, 15, 3],\n [21, 0, -3, -24, 3, 8, 6, 10, 13, 22, -11, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-9, -9, -13, 5, -15, 15, -25, 26, -1, -4, 8, 6],\n [14, -2, -23, -6, 21, -23, 4, 22, -12, -23, -23, 17],\n [-24, 25, -22, -8, 11, 5, -18, -24, 7, -2, 26, -17],\n [5, -22, 2, -20, -12, -25, -17, -16, 26, 13, -6, -15],\n [-23, 1, 2, -14, 23, -9, 0, -24, 8, 12, -5, -10],\n [1, 11, -11, -22, -5, -10, -16, -5, 17, 17, 9, 14],\n [19, 17, 15, 13, -24, 0, 18, 21, -14, -14, 24, 3],\n [-9, 13, 6, -10, 14, -17, 14, 17, -3, 15, 2, -19],\n [9, -13, 2, -20, -2, 15, 3, 1, -17, 20, 20, 7],\n [-11, -17, 2, -12, 1, 24, -3, 15, -7, 20, 26, 2],\n [-25, 19, 5, 20, 15, 3, -18, -8, -21, -19, 7, -26],\n [-14, -21, 8, 2, -25, -17, 4, -19, 14, 12, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-14, -20, 24, -26, 18, 22, 17, 26, -1, 19, -11, -15],\n [-11, 7, 0, 25, -2, -8, -20, -15, 19, -3, 23, 12],\n [-22, -26, -20, 21, -1, -3, 21, -10, -23, -11, 9, -22],\n [-22, 25, 16, 19, -10, 14, -6, 3, 22, 24, 6, 18],\n [-4, 15, 2, 15, 12, 11, -20, 10, -20, -12, 2, -17],\n [-7, 18, -18, -21, -7, -6, -20, 11, 21, 7, 20, -24],\n [18, -10, 24, 16, -25, 15, -15, -14, 11, 9, -15, 0],\n [-1, 20, 24, 13, -22, 5, 9, 18, 11, 25, -11, -17],\n [10, -12, -16, 25, -18, -9, 6, -18, 14, -12, 9, 9],\n [-26, 1, 6, -26, -21, -16, 21, 0, -22, -17, 1, -11],\n [16, -1, 23, 1, -13, -14, -26, 8, -12, 2, 4, -15],\n [-22, 21, 19, 5, -17, -22, 0, 12, -6, -11, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[11, -20, -9, 24, -8, -10, -13, 14, 21, -17, -2, 14],\n [17, -18, -11, 21, -3, -6, 7, 12, 25, -20, -20, 1],\n [24, 8, -17, 11, 5, 7, -3, 25, 23, 14, 20, 19],\n [14, -25, 15, -23, -26, -5, -16, 21, -16, 18, -13, 0],\n [6, 1, -4, -18, -9, 16, -3, 0, 8, 26, -23, -5],\n [-16, -20, 14, 10, 7, -15, -23, 18, -25, 20, -26, -9],\n [-4, 7, -23, 26, 24, 25, 15, 18, -8, 13, 15, 13],\n [24, 14, -18, -4, -14, -26, -15, -17, 0, -8, 13, 5],\n [-5, -2, -16, -16, -1, -11, 2, 3, -16, -26, -21, -14],\n [0, 16, 8, 26, 6, -13, 16, 19, -5, 15, -6, -25],\n [-22, -12, 23, 21, -7, -1, -3, 8, -3, -1, 14, 23],\n [-5, 0, -8, 10, 9, 2, 13, 12, 16, -15, 17, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "536", "dataset": "MATH"}
{"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, -12, 6, -12, 5, -5, 23, -21, 3, 14, -10],\n [17, -25, -11, 20, -15, 20, 18, -15, 24, 21, 12, -10],\n [15, 14, -21, 14, -1, -26, -11, 19, 13, 20, -11, 19],\n [-11, 12, 2, 23, 22, -1, 3, 6, 16, -7, 10, -14],\n [-19, 5, -9, 18, 14, -16, 11, 16, 20, -13, 13, 23],\n [6, 26, 14, -4, -20, -12, -12, -18, -6, 10, 12, 1],\n [17, -21, -17, -12, -3, -23, 20, 23, 8, -12, 25, 10],\n [-25, 20, 13, 1, -22, -4, -18, -20, -23, -8, -19, 4],\n [-13, 2, -18, 10, -21, 15, 1, 18, -17, 18, -24, -15],\n [9, -16, -18, -21, -15, 19, 26, 14, -19, 14, -14, 16],\n [-18, -7, 13, -17, 14, 0, 26, -23, -17, 22, -8, -17],\n [23, 21, -4, 9, 14, -18, -25, -8, -19, -1, 24, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-16, -24, 3, -9, -10, 24, -18, 3, -11, -19, 14, -1],\n [-22, -22, 19, -3, -13, -22, 9, -2, -10, -21, -20, 19],\n [-12, -21, 5, 15, 13, 0, 13, -22, -11, 25, -16, 12],\n [-2, -25, 1, -20, 11, 24, 23, -26, -9, -15, 26, 22],\n [-19, -7, 8, 15, -11, 23, 6, 13, -2, -8, 8, -11],\n [-11, 21, -2, 5, 17, 1, -18, -9, -4, 3, 5, -3],\n [-16, 25, -1, -16, -7, 17, -9, 7, 9, -23, -6, -1],\n [-13, -1, -14, -1, 14, -12, 0, -4, -5, -17, -22, -23],\n [23, 9, -11, 5, -16, 12, 6, 8, 21, -23, -4, -24],\n [-7, -26, 6, -17, 17, -24, 5, 18, 11, 4, -6, -3],\n [-3, 25, -17, -21, 1, -26, 20, 19, 17, -17, 14, 3],\n [26, -12, -13, -3, -17, -1, -26, -7, 2, 7, -25, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-25, -19, -2, -9, 18, -10, 3, -19, 15, 19, 2, 24],\n [-8, 10, -3, -9, -17, -11, 23, 14, 15, 17, -22, -12],\n [-4, 4, 3, -20, -7, 12, -24, -24, 4, -20, -26, 0],\n [23, -26, -21, -7, 12, 17, -24, -25, 20, 5, -7, 9],\n [0, -7, -8, -6, 16, -7, -22, -7, -15, 21, -17, 26],\n [-5, 11, 1, -15, 12, -17, 21, 8, 21, 17, 13, 10],\n [-10, 25, 0, 25, 19, 2, -1, -18, 24, -15, 16, -1],\n [6, 5, -16, 2, -19, -2, -7, -6, -23, 9, 16, 2],\n [-8, -1, 9, -2, -4, 11, 1, 14, -16, 2, 17, 23],\n [-7, -18, -3, 20, 22, 14, -14, -25, -10, 23, 0, 11],\n [-25, 6, -22, -13, 0, 23, 9, 0, -13, -12, 0, -19],\n [-6, 7, 22, 1, -3, -10, 25, -21, 11, -8, -26, 11]]\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[[-1, -22, -23, -2, 18, 25, 22, 18, -5, 21, -14, -4],\n [6, -2, -17, -9, 0, 22, -1, 22, 15, 25, -25, -17],\n [-7, 11, -24, -17, 1, -8, -10, 17, 26, 17, -4, 1],\n [0, 5, 11, -15, -7, -21, -24, -24, -4, -18, 6, 9],\n [-15, -1, 10, 23, 21, -17, 17, -16, -8, -22, -3, 8],\n [1, 3, -8, -21, 22, 18, 12, -8, 24, 4, 17, -16],\n [-10, -10, 23, -12, -21, 5, 13, -16, -14, -10, 1, 22],\n [-9, 1, 21, -11, 9, 22, 13, -7, 12, 0, 13, 6],\n [-25, -14, -25, 10, -22, -21, 23, 5, 21, -3, -10, -18],\n [26, 13, 13, -25, -18, -21, -8, 6, -8, 6, 26, 18],\n [3, 12, 26, -14, -9, -25, -24, -21, 1, -14, -7, 5],\n [4, -18, -24, 4, -12, -23, 22, -10, 18, 4, 2, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, 13, -24, 23, -26, -19, 14, -10, -19, 16, 6, -1],\n [-25, 20, 22, 2, -12, 3, 23, 17, 19, -15, -25, -6],\n [2, 2, -11, 24, 4, 6, -25, 17, -23, 12, 22, -22],\n [-25, 18, -19, 23, 9, -21, 14, -17, 9, -23, 12, -13],\n [-15, 20, -10, -6, 26, -14, 6, -14, 21, 18, -18, 23],\n [21, -7, 17, 13, -26, -14, -5, 24, -14, 8, -26, 19],\n [26, 6, -22, 3, -22, 16, -2, -1, -8, -15, -19, -17],\n [-9, 14, -16, 3, -22, -3, 18, -14, 9, 22, 0, 5],\n [-13, 14, -25, -23, -16, 15, 10, 21, 11, 10, -14, -18],\n [15, 0, -25, 20, 0, -15, -15, -24, -1, -12, 0, 24],\n [18, 8, -14, -22, 16, -10, -8, -7, -4, -15, 5, 2],\n [-22, 22, 24, 16, -25, -21, -6, 8, -12, -9, 22, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-25, -22, 10, 14, -21, 24, 15, 24, -8, -11, -15, -3],\n [-18, -24, -10, 3, 0, -3, 15, 23, 12, -20, -18, -11],\n [-16, -18, -26, 17, 8, -7, 24, -19, -20, 10, 10, -7],\n [-22, -15, -6, -7, -22, -4, -20, -26, -2, -8, -25, -15],\n [15, -2, 5, 21, 16, -9, 4, 17, -18, -6, 12, -20],\n [-14, -7, -14, 25, 1, 10, -2, 19, 21, 18, -1, 17],\n [6, 13, 13, 0, -12, -24, 2, 4, 13, -9, -3, 12],\n [17, 20, -19, 2, 21, 10, 10, -18, 18, 3, -12, 13],\n [-15, 25, 14, 0, 20, 20, 4, -14, -12, -22, 15, -2],\n [-15, 22, -18, -1, 10, -18, -22, 19, -20, 14, 4, 17],\n [10, -20, -22, 25, -10, -16, 10, 9, 0, -26, -26, -13],\n [26, 1, 14, -26, -19, 18, 14, 20, 16, -1, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[13, 18, 22, -23, 15, -25, 3, 20, -7, 3, -9, 3],\n [19, 8, -26, -24, -4, 18, 13, -5, 22, 21, 21, 17],\n [24, 21, -12, 14, -11, 0, 5, 7, 15, -15, -9, -9],\n [-23, 7, 12, -8, 16, 18, 25, 4, 22, 4, 15, 21],\n [-7, 21, -7, 5, -7, -11, -8, 4, -14, -7, 16, -15],\n [22, 20, -1, 8, 14, -17, -15, -3, -18, -22, 4, 7],\n [18, -16, -18, -5, 13, 20, 1, -11, -17, 7, -12, -9],\n [18, 4, -22, 24, 6, 2, -24, -4, -17, 20, 5, 21],\n [0, 9, -3, -7, -24, -22, -24, 13, -21, -12, -21, -4],\n [3, 12, 13, 21, -6, 18, 10, -5, 25, -25, -13, -9],\n [23, 23, -12, 10, -25, 16, -7, -17, -22, 5, -25, 17],\n [22, -22, -6, -9, 21, 13, -23, 5, 9, -23, -10, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[15, 6, -5, -9, 0, -12, -2, -17, -11, -23, 4, 5],\n [-3, -9, 5, 26, 1, -16, -19, -26, -25, -6, 22, 25],\n [-8, 15, 3, 26, 13, -2, 26, -18, 15, 25, 1, 10],\n [5, 14, -16, 23, -6, -3, -26, -11, 25, -3, -17, 5],\n [1, 23, 6, 11, -5, -26, 8, 18, -15, 19, -2, 1],\n [-10, -11, 5, 18, -23, 20, 14, 22, -16, -7, -1, -20],\n [4, -20, -23, -19, 24, -13, -5, -4, -2, 9, 26, 22],\n [-1, -3, -9, -6, 20, -22, -12, 4, -1, -23, -23, 17],\n [23, -8, -1, 23, 6, -23, 20, 11, -3, 4, 7, 7],\n [-25, 16, -19, 22, -6, -15, 9, -26, 15, 12, -11, 22],\n [-21, 6, 16, -14, 18, -18, 8, 1, 7, 5, -26, 12],\n [-2, 25, -17, -25, -23, -2, -11, 13, 17, -22, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-24, -26, 19, 24, -2, -11, 14, -22, 9, -21, -15, 19],\n [-4, 19, 11, -22, -25, -24, 14, -20, -1, -15, 23, 18],\n [-26, -26, 6, 26, 12, 26, -18, -26, -12, -2, 17, 9],\n [-17, 23, 4, 24, -7, -22, 1, 7, 12, 11, -11, -12],\n [14, 12, 15, -1, 3, -25, -24, -8, -3, -24, 13, -22],\n [5, 25, 4, -15, 16, 9, 9, 4, 6, -20, -1, -1],\n [-7, 7, 6, -8, -10, 16, 10, -21, -5, 11, -10, -7],\n [15, 15, 14, -1, 1, 23, 18, -19, 16, -20, -20, 2],\n [-24, -11, -14, 23, -9, 17, -14, 4, -24, 3, -24, -1],\n [-25, 12, 7, 11, -14, -16, 10, -20, 16, 0, -20, -19],\n [9, 15, 2, -6, -1, -7, 2, -12, -4, -12, 24, -17],\n [-25, 21, 25, 3, 10, 0, -10, -24, -19, 16, 10, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-23, -3, 2, -19, 7, 21, -18, -10, -17, -3, 18, -5],\n [-10, 4, 17, -18, -12, 15, 24, 3, -10, -20, 19, 18],\n [-1, 26, -25, 21, 2, 22, -21, 6, 11, -26, -17, 25],\n [4, -3, -19, 1, 1, 21, 17, 24, 19, -19, 2, -8],\n [2, -12, 4, -22, 22, 1, 19, -12, -19, 9, 5, 12],\n [12, -5, -22, -17, 25, 4, 10, -4, 5, -3, -23, 26],\n [16, 11, -12, -16, -2, -1, 12, 24, 10, 9, 6, 21],\n [17, -7, 23, 25, 7, 18, -15, 9, -23, -14, -24, 26],\n [-10, -20, 18, 20, -13, 5, 21, 22, -1, 4, 21, 4],\n [-11, -26, 19, 7, -1, 3, 14, 24, -22, -3, -17, 11],\n [8, -25, 2, -8, 11, 26, 15, 23, -13, 1, 7, -23],\n [20, -2, 26, -21, 1, 11, -18, 25, -9, 4, -5, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 9, 8, -14, -12, 6, 1, 21, 7, 11, -26, 4],\n [22, -10, -5, 5, 2, -26, 21, 1, 14, -25, -2, -6],\n [10, -1, 13, -26, 5, -18, 19, 22, -22, 13, -10, 26],\n [2, 17, -8, 13, 2, 24, -15, -19, 16, 16, 4, -12],\n [7, -1, 8, 2, 6, 6, 9, -6, 3, -8, 5, 23],\n [-26, 24, 6, -1, 15, 18, 0, 24, 1, -7, -19, -1],\n [4, -22, -16, -6, -19, -1, 19, -15, 16, -14, -17, 25],\n [2, -19, 15, 26, 11, -26, -18, -23, 6, 15, 25, -6],\n [-20, 5, 12, 1, -1, 10, 7, -18, -21, -5, -18, 20],\n [18, -12, -26, 5, 20, -9, -16, 8, 6, -23, 7, 21],\n [-8, 21, -15, 13, 9, 21, 14, -5, 20, -15, 22, 1],\n [-12, -23, -19, 4, -1, -24, 12, -20, -12, -7, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-17, -11, 21, -1, -5, -12, -15, 12, -24, 26, -3, -25],\n [-23, -4, -4, -19, 15, 17, -15, -18, -16, 18, 4, -26],\n [8, 16, -12, -20, 1, 21, -21, -7, -3, 15, 9, 11],\n [-15, -24, 1, -15, -11, 17, -12, 4, 26, -6, -9, 21],\n [-21, -10, -4, 8, -9, -16, -4, -10, -21, -3, 23, 10],\n [-11, 2, 2, 25, 15, 1, -11, -24, 15, -3, -9, 21],\n [-10, 22, -17, 10, -2, 9, 20, 21, -4, 23, -8, -17],\n [-16, 14, -22, -21, -24, 18, 11, -16, 21, 16, 15, 21],\n [-3, 19, 21, -1, 22, -1, -3, 13, -23, 22, -17, 7],\n [17, 2, -1, -8, -6, -8, 13, 11, -8, -9, -13, 8],\n [-9, 1, -8, -2, -12, 21, 22, -24, -4, 23, 18, -15],\n [5, 24, 1, 7, -26, -17, 23, 0, -15, 18, 9, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -23, -6, -7, 23, -10, 25, 19, 7, -13, -17, -7],\n [8, -12, 12, 0, -12, -8, -1, -15, -3, 26, 9, 6],\n [-22, -18, 13, -13, 19, 9, -2, -20, 7, 16, -20, 4],\n [25, 5, -6, 22, -12, 3, -23, 7, -18, -15, 3, -3],\n [24, 2, 24, -5, 8, -7, 10, 14, 24, -18, 26, -5],\n [23, -11, -25, 17, 23, -4, 2, -16, 8, 25, -5, -24],\n [20, -15, -26, 16, -1, 7, 2, 26, 19, 6, 5, -2],\n [23, 23, 20, 9, -25, -12, -14, 15, -12, -21, -6, 15],\n [-1, 8, 18, -9, -21, -13, -9, 16, -7, -12, 26, 18],\n [21, 0, -3, -15, -26, -13, 5, -24, -17, -1, 4, -17],\n [-26, 23, 22, 5, -8, -26, -1, -22, -1, 11, -26, 3],\n [22, -15, 9, 9, -3, 15, -2, -19, -15, 0, -15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"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, -11, 9, 3, 10, 5, -12, -6, 13, 2, 3, -2],\n [-7, -17, 4, -26, -17, -9, 22, 9, -14, 5, -5, -21],\n [6, -26, -24, -22, 23, 0, -15, 6, 14, 0, 22, -14],\n [19, -16, -16, 9, 14, 23, 24, -23, 17, -9, -9, 1],\n [-21, 16, -22, 21, -16, -22, -18, -4, -16, -12, -2, -10],\n [23, 26, -1, -13, 12, 21, -18, 0, 8, 0, 26, -11],\n [-5, 3, -1, 12, 12, 25, 6, 13, -26, -15, -10, -2],\n [2, 15, 1, -8, 14, -17, -16, -17, 3, 22, -20, -22],\n [1, -7, 5, -15, -22, 3, 6, -17, 12, 0, -15, -25],\n [3, 14, -22, 10, -13, 24, -1, 23, -19, 4, -24, 1],\n [-13, -16, 2, 13, -15, 16, -18, 9, -8, -20, -10, 21],\n [24, -4, -15, -20, -2, -13, 4, -2, -16, -16, -20, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-24, -12, -24, 26, 14, -10, 22, 17, -20, -16, 19, -7],\n [-26, 5, 11, -6, 4, -10, -2, 14, 6, -15, 25, 1],\n [22, -1, 9, -19, 5, 24, 24, -1, -22, 16, 11, -14],\n [-8, -21, 18, -21, -11, 2, -9, 5, 2, 16, 25, -10],\n [15, 21, -22, 5, 2, 2, 15, -24, 24, -23, 17, -2],\n [-5, 15, -16, -19, 0, 17, 19, 26, -5, -24, 0, -16],\n [0, -20, 0, 20, -16, -2, 12, 24, -11, -6, -1, 0],\n [24, 18, 26, -10, 4, -13, -4, -25, -1, -1, -5, 15],\n [1, -21, 21, 12, -8, -6, 15, -7, 4, 0, -12, 17],\n [4, -18, 23, -10, -8, 5, -17, 13, 25, -22, -14, 26],\n [0, -25, -26, -19, -17, 1, -22, 23, -25, 14, 21, 25],\n [26, -10, 21, 6, -2, -22, 1, 24, -9, -4, 25, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-9, -16, 16, 16, -17, -17, 9, -18, 15, -14, -4, -26],\n [-11, -8, -15, -22, -22, -20, 17, -13, 6, -21, -9, -21],\n [24, 3, -15, 23, 8, -16, -23, -14, -26, 25, 11, 26],\n [2, -13, -6, 14, 4, 14, -20, -12, 15, -18, 2, -3],\n [-12, -6, 14, -3, -20, -3, -4, -2, -19, 7, 8, -5],\n [7, 1, -26, 17, 10, 3, 23, -2, 24, -25, 1, 21],\n [1, -4, 11, -3, 8, -19, 9, -9, -7, -23, -19, -1],\n [12, -7, -9, 6, -9, 7, -8, 15, 26, 6, -6, -20],\n [-13, 6, -23, 16, -25, 13, 23, 4, 22, 19, 3, 23],\n [-17, 25, -6, 23, 25, -4, 10, -19, -17, -2, 6, -10],\n [24, -3, 22, 15, 23, 3, -26, -10, 1, -14, -17, -26],\n [-7, -20, 5, -6, -1, 18, 26, -20, 11, 18, 13, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541", "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, 18, 0, 7, -15, -15, -12, -7, -17, 19, -1, -10],\n [-17, -16, -10, -16, -12, -23, -2, 9, 26, 20, 4, 19],\n [2, 4, -18, 21, -26, -24, -23, -8, 14, -5, 24, -19],\n [-2, -23, 18, 26, 24, -13, -22, 23, 23, 2, -6, -12],\n [-4, -10, -24, 6, 23, 0, -11, -21, 14, -17, 2, -10],\n [12, 19, -13, -15, 11, 2, -13, -19, 22, 13, 13, -10],\n [16, 12, -4, -20, -15, -11, -14, 20, -8, -24, 16, -19],\n [13, -15, 4, 8, -7, 1, -25, 0, -24, 21, -6, 24],\n [25, -20, 24, 6, 18, 19, 6, 9, -10, -21, 25, -6],\n [11, 7, 22, 21, -15, -15, -9, 21, -21, -14, 4, -2],\n [21, -3, 15, -16, 6, -6, 12, -3, 22, 17, 25, -7],\n [20, -18, 4, 1, 11, -22, 10, 14, 7, -17, 5, 10]]\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[[-10, 26, 9, 9, -14, -7, 24, 11, -8, -5, -11, -21],\n [-16, -17, 4, -9, 5, 14, 15, 20, -3, 19, -11, 2],\n [12, -2, 13, -2, 13, 18, -8, -17, -26, 0, -5, 1],\n [21, 8, -24, 11, -1, 17, -22, 21, 22, -17, -20, 3],\n [-2, 15, 7, 20, -6, 2, -10, 9, 13, 24, -6, 7],\n [26, -11, 19, 17, -18, 17, -24, -4, -14, 11, 7, 3],\n [12, -1, 5, -7, 19, 11, -18, 12, 24, -11, 18, 11],\n [-23, -15, -1, 26, -17, -11, -26, -15, 25, 24, -5, 2],\n [-8, 3, 1, -6, -9, 14, -3, -1, 9, 16, -11, 25],\n [5, -25, -18, -9, 22, 22, 19, 18, -8, 11, -15, -14],\n [8, 21, 26, -17, -5, -17, 23, 8, 18, -11, 9, -16],\n [-10, -2, -26, -15, -24, 24, -18, -8, -8, 23, -7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, -5, -26, 26, 17, 16, -17, -16, -19, -10, -21, -20],\n [4, 10, -23, -20, -11, -2, 9, 8, -13, 9, 26, -18],\n [-16, -26, -18, -2, 13, -12, -3, -19, 25, 2, -20, 19],\n [-9, -24, 20, -3, -7, 4, -1, 11, 20, 19, 16, -19],\n [5, -19, -22, -11, 0, 12, -26, -22, -24, 18, 25, -10],\n [6, -8, -23, -14, 24, 23, 16, -1, 14, 4, 8, -11],\n [-3, 26, 3, -10, -14, 11, -20, -18, -6, 3, 10, 10],\n [-5, 20, 4, -23, -17, 3, 3, 14, -20, -12, -8, -17],\n [12, 0, -24, 8, 25, -9, -3, -14, 17, -10, -10, -16],\n [-10, 25, 22, -8, -20, -8, 7, 2, 3, 15, 2, 11],\n [21, -19, -23, 1, 25, -16, -9, -6, 20, 21, 13, 5],\n [-10, 7, -10, -12, -7, 12, -16, -8, 5, -3, -21, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, 21, -14, -1, -19, -1, 22, -13, 14, -21, -11, 8],\n [7, 13, 0, 9, -15, -26, 2, -10, -9, 22, -11, 8],\n [-18, 17, 12, 11, 16, -21, -1, -10, -3, -17, 5, -24],\n [-8, 8, 0, -2, -6, -25, -7, -4, 6, 23, -19, 24],\n [10, 15, 3, 4, 14, -9, 4, -1, -3, 24, -22, 26],\n [-16, 25, -3, -26, -15, 11, -4, 25, 17, -2, -15, -24],\n [-3, -1, -12, 4, 16, 15, -6, -6, -6, 21, -2, -15],\n [21, 10, -9, -17, -21, 2, 2, 2, 19, 19, -18, 5],\n [21, -14, 19, 26, -16, 7, 25, 25, 2, 24, -15, 22],\n [4, 14, -5, -1, 16, -15, 8, 22, 11, -23, 18, 22],\n [-17, 25, -9, 19, 21, -8, -12, -4, -4, -6, -1, 18],\n [7, 14, -14, -2, 17, 6, 1, -14, 0, -19, 9, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-21, -14, -7, -22, 18, 0, 22, 24, -8, -26, -23, -25],\n [17, -1, 6, 17, 18, 11, -20, 2, 25, -22, -18, -14],\n [19, 13, 21, 19, 2, -9, 3, -17, -8, 21, -18, -6],\n [-26, 14, -1, -13, 12, 2, 16, 25, -20, -3, 0, 15],\n [24, -25, -25, -11, -15, 13, -1, -17, -12, 21, -2, -23],\n [-1, -4, 10, 22, 15, -23, -26, -26, 12, -24, 21, 21],\n [-12, 16, -9, -6, 25, -19, -2, 5, -21, 23, 13, -7],\n [22, 2, -22, 8, -8, 12, -15, 6, 8, 15, 11, 21],\n [19, -19, 11, 4, -16, -23, 13, -22, 15, -5, 17, -10],\n [-7, 16, 25, -15, 26, 17, -10, 25, 0, -4, -22, 22],\n [1, 10, 3, 18, 2, -13, -19, 19, 0, -21, -20, -1],\n [15, 3, -10, -21, -24, -8, -8, -3, 1, 8, 8, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[11, -21, 2, -4, 18, 24, 10, 5, -26, 22, 7, 17],\n [1, 23, -20, 10, 2, -8, 21, 17, -8, 24, -7, 26],\n [-12, -3, 14, 26, -19, 24, -20, -8, 1, -15, -1, 8],\n [-23, 7, -20, 0, -24, 6, -15, -8, 25, -10, -9, -24],\n [-14, 5, -22, -2, -5, 24, 24, -19, 25, -11, 5, -22],\n [9, -2, -11, -3, -13, -14, -4, 25, -2, 0, -19, -9],\n [10, -21, -21, -2, -7, -4, 26, -10, 5, -11, 10, -7],\n [-24, -26, 10, 8, -11, 21, -23, -24, 17, -10, 17, 15],\n [7, 15, 7, -10, -3, 10, -25, -13, -17, -12, 10, 19],\n [26, -9, 18, -14, 8, 9, 10, -17, 2, 7, -3, 26],\n [0, -18, -18, -17, -15, -12, -24, 1, -18, 12, 3, -4],\n [3, -11, 9, 3, 19, 10, -11, 1, -7, -13, 18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, 10, -8, -10, -26, 2, 2, -3, -8, 16, -17, 9],\n [-10, -10, 5, -11, 24, 25, 19, -4, -11, 5, -25, 13],\n [-21, -17, 7, 3, 24, 9, -21, 18, 6, -22, 1, -20],\n [19, -8, 16, 23, 23, -1, 26, 11, 11, 12, -10, -8],\n [0, 10, -20, 11, -10, 2, 24, 17, 12, 17, -10, -12],\n [-11, 6, -16, 6, 5, 18, 1, -7, 22, 2, -11, 3],\n [-10, -13, -3, 10, -14, -9, -20, 22, -16, -10, -8, -21],\n [25, -9, 26, -17, -26, -26, 20, 11, 0, -2, -1, 12],\n [-17, 9, 19, -19, 6, 2, 26, 7, 0, 24, 15, -23],\n [22, 21, -22, 15, -16, -26, -14, -7, 7, 6, -13, 26],\n [-15, -16, -26, 19, -19, -9, -22, 4, -24, -5, -21, -3],\n [0, -6, 10, 26, 7, 8, 9, -1, -26, 21, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "521", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 13, 7, 0, -24, 19, 12, -14, 12, -11, -24, -1],\n [-22, -24, 1, 20, 25, 16, 3, -4, -9, -22, -5, 18],\n [-26, 0, -13, 14, -18, -23, 26, -2, 4, 5, -25, 21],\n [10, 25, 23, -25, -13, -12, -2, -17, 1, 21, -19, 26],\n [-13, -7, 15, -14, -8, 7, -1, 10, 19, -3, 26, -6],\n [-3, -19, 6, -22, -2, 16, 13, -10, -2, 15, 19, 6],\n [-22, -12, 15, -12, -26, 16, -9, -21, 7, -25, -10, -22],\n [-7, -13, -15, -23, 14, 23, -17, 12, 3, 10, 20, -1],\n [18, 19, -23, -21, -12, 18, 18, -9, -10, 6, 9, 16],\n [-2, 24, 1, -14, 5, 21, -8, 4, -12, 17, -4, 13],\n [0, -26, -5, -19, -22, -3, 6, -15, -23, -12, -18, 15],\n [26, -14, -17, 15, -13, 24, 24, -26, 0, -5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 3, 13, -10, -4, -17, 6, -19, -22, 7, 24, 0],\n [4, -2, -25, -7, 16, -24, 14, 13, 11, 19, 13, -12],\n [0, -3, 8, -4, -19, -5, -11, -21, 12, 18, 25, 2],\n [-1, -18, -8, -20, 21, -2, -3, 12, 20, 10, 7, 2],\n [7, -7, -22, 17, 9, 3, 23, -7, -16, -6, -7, -21],\n [18, -1, -4, -22, -2, 2, -23, 0, -17, 7, 0, -19],\n [25, 25, 8, 1, -18, 25, 7, 3, -10, 6, 2, 22],\n [10, -14, 2, 13, 12, -13, -19, 5, -16, 8, -22, 23],\n [10, 18, -22, -25, -1, 3, -14, 11, 22, 13, 0, -10],\n [24, -12, 6, 3, 5, 23, -20, 12, -11, -16, 10, 26],\n [-13, -4, 4, 1, 15, -22, -3, 24, -9, -23, -4, -18],\n [24, -16, 8, -16, -20, -10, -9, -1, 20, 22, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "511", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-17, 3, -12, 21, 20, -1, 14, 1, 26, -8, -26, 7],\n [11, -3, 14, -3, -9, -26, -17, -23, -13, -6, -1, 11],\n [25, -22, -12, -3, -17, 8, -10, 5, -18, 4, 14, -12],\n [23, -24, 13, 8, 24, -14, -5, 21, -20, -7, 10, -1],\n [-8, 3, 7, 8, 1, 8, 7, 21, 22, -11, 21, 24],\n [5, -10, -3, -22, -15, -5, -15, 2, 12, 12, 9, -21],\n [21, -19, -21, 3, -8, 3, -2, -17, 21, -25, 19, 16],\n [-3, 1, 7, -24, -1, -5, 5, 16, 9, -13, 10, -24],\n [1, -1, 13, -17, 17, -1, 13, -4, -20, 7, -15, -5],\n [25, -16, -18, -22, -21, -20, 19, -9, -12, -26, 21, -12],\n [-18, -20, 17, -18, 17, -16, -24, -14, -22, 5, -5, 26],\n [23, 16, -1, -24, 14, -19, -3, 13, -14, -16, 11, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[16, -13, 19, 24, -22, 20, -14, -3, -11, 2, -8, -10],\n [4, 21, 2, 5, 19, -10, -20, 11, -22, -3, 6, 21],\n [-4, -13, 7, -23, -26, -25, 2, -18, 1, 6, -4, -7],\n [4, 21, 19, 18, -1, 4, 5, 24, 20, 23, 8, -12],\n [-12, 10, 18, -2, -7, 21, -5, -7, -12, 3, -13, 14],\n [-6, 23, -10, -22, -12, 16, 0, 17, 12, -7, 26, 14],\n [8, -10, -18, 16, 19, 15, -23, -11, -11, 2, 17, 5],\n [5, 11, 12, 13, 11, 12, 14, -11, 18, -12, -9, -23],\n [10, 13, -23, -10, -10, 7, 21, -8, -5, 12, 16, -26],\n [26, -9, 12, 1, -14, 8, -18, -10, 7, -12, -18, 12],\n [-8, -16, -3, -6, -9, -1, 22, -23, -25, -10, 25, -26],\n [-14, -17, -10, -6, 22, 16, -18, 4, 8, -17, 22, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"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, -12, 18, -25, 11, -24, -1, 6, 22, -3, 6, 3],\n [16, -23, 16, 18, -5, 22, -7, 2, -6, 18, -10, -25],\n [7, -5, 23, -21, -2, -25, 16, -10, -18, -7, 10, 25],\n [-12, -1, -2, 4, 3, 22, -17, 11, 18, -6, 21, -3],\n [7, 1, 25, 10, -3, 2, -10, 12, -3, -10, 10, -21],\n [15, 10, 19, 4, -7, 19, -25, 14, -9, 23, -5, 14],\n [10, -1, 23, -15, -21, -10, -13, -17, -1, 24, -24, 15],\n [19, -12, -11, 11, -13, 9, -14, 0, -19, -4, 14, 26],\n [-16, -22, -22, -2, -9, 21, 24, -3, -18, 16, -16, -13],\n [15, -18, -22, 0, -16, 1, -18, -14, -8, -19, -23, 17],\n [-2, -20, 0, 13, 24, -4, 13, 24, 2, 9, -17, 5],\n [20, -4, 13, 20, 21, -3, -6, 12, 13, 2, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "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, 7, -1, 25, -12, -21, -2, -9, -20, -25, 7, -26],\n [19, -25, 15, 9, -23, 1, -4, 12, -7, 10, 17, -15],\n [5, 11, 4, -9, 2, 7, 24, 2, 0, 4, 21, 7],\n [-10, -7, 4, 4, 12, -6, -20, 5, -15, -4, 16, 22],\n [16, 13, -21, 5, 11, -12, -1, -7, -15, 14, 18, 20],\n [20, -1, 3, 2, 3, -14, 14, 16, -5, 16, 14, -10],\n [-4, -2, 26, -21, 10, -1, -6, 8, -21, -5, -10, -16],\n [-23, 17, -17, -10, 11, -9, 26, -8, -5, -12, 17, -8],\n [-2, 10, -9, -15, 5, -1, -1, 20, 15, 1, -2, 3],\n [24, 14, 11, -13, -26, 6, -16, 8, -6, -5, -22, 13],\n [-9, 10, 17, 2, -9, 26, -15, -6, 13, 3, 14, -12],\n [8, 20, 1, -23, 1, 3, 21, 24, 23, 0, -11, 5]]\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[[-15, 17, 9, -12, -8, -9, -1, -16, 3, 1, -4, -12],\n [21, -16, 16, -6, 18, 12, 4, -12, -10, -2, -3, 18],\n [9, 6, 17, -23, -26, 11, -16, -6, -2, 23, 1, 23],\n [25, -21, 19, -21, -5, -12, 6, -10, -15, 4, 8, 7],\n [5, -4, 11, -22, 13, -25, 4, -15, 12, 19, 15, -7],\n [-13, -16, 4, 24, 6, -1, -25, 4, 8, 0, -22, -16],\n [24, 12, 1, -11, 25, 13, -1, -3, -23, -15, -9, -13],\n [-10, 17, 14, -11, 26, 15, -7, 25, 16, 1, 14, -26],\n [-11, -23, 5, 2, -19, -25, 19, -3, 14, 19, -13, 26],\n [17, 16, -26, 6, -16, -7, -12, 1, -6, -4, -18, -7],\n [26, -10, 15, -12, 17, -22, 19, 15, 25, 6, 3, -11],\n [9, 10, 14, 22, 11, -3, -2, 0, -22, 23, 22, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[16, 8, -21, -18, 18, 0, -26, 3, -12, 5, -7, -23],\n [7, 21, 11, -7, 20, 24, 1, 12, -2, -16, 23, -19],\n [7, 0, 17, -5, -19, 6, 12, -18, -5, -18, 4, 7],\n [-23, 19, -13, -19, 26, 14, 8, -5, 24, -21, 6, 26],\n [-9, -19, -20, 5, -20, -17, 9, 23, 24, 4, 4, -17],\n [-7, 24, 8, 2, 3, 22, 4, 6, 13, 22, -23, 7],\n [-10, 7, 5, 6, 10, 4, -1, 4, 4, 1, 11, 17],\n [-17, -19, 19, 9, -8, 1, -22, -3, 26, -20, -7, -25],\n [16, -17, -9, 7, -13, -17, 11, 5, 26, -24, 21, -19],\n [-18, -16, -11, 7, -3, 4, -22, 6, 3, 3, -12, 12],\n [-11, -1, -15, -8, 20, 8, -7, -6, 26, 10, -12, 22],\n [-11, -11, -4, 17, -23, 2, 10, -3, -19, 17, -22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[2, 24, -17, 23, 17, -18, -5, -17, -7, -7, 24, 0],\n [26, 11, -17, -8, 14, 3, -11, 13, -15, -22, 16, 24],\n [-24, -3, -1, 4, 20, 25, -24, -26, -16, 18, -22, -20],\n [6, -14, 15, 4, 25, 23, -14, -26, 22, 17, 11, 12],\n [6, 15, 8, 12, 15, 15, -18, -21, 14, -18, 0, 15],\n [2, -23, -2, -11, 7, -16, -18, 8, 0, 12, 18, 18],\n [24, 1, 16, -22, -11, 1, -25, 15, -17, -8, -7, 11],\n [21, 18, 24, 8, 14, -17, 21, 23, 9, 26, -11, 23],\n [-1, 4, 15, -26, -4, 15, 22, 0, -8, -11, 11, -19],\n [-11, -15, -18, 21, -20, 13, 25, 10, -4, 14, -19, -4],\n [-7, 21, -16, -26, 22, 17, -22, -13, -20, -3, 12, -23],\n [20, 0, -20, -3, -18, -26, 7, 13, 4, 12, -4, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[12, -7, 21, -1, 7, 5, 6, 13, -22, -17, 9, 3],\n [-18, 19, 5, -6, 15, 23, -1, -4, -18, -22, -19, 17],\n [25, 24, 19, 16, -16, 9, -9, 4, 14, -19, 9, 24],\n [-8, -5, -25, -16, -24, 6, -17, 26, 18, -24, 12, 10],\n [7, 23, 1, -13, 25, 1, 3, 3, 0, -25, 10, -14],\n [12, 15, 1, -7, 12, 23, -9, 7, 21, 18, -10, 11],\n [-4, 4, -18, 8, -2, 12, 3, -22, 1, 26, -20, 15],\n [15, 15, 11, -8, -2, -9, 26, 20, -1, 18, -7, -25],\n [3, -5, 15, 7, 8, -22, -12, 12, -12, 1, -15, -24],\n [-17, 9, -20, 16, -10, -7, 20, 22, 19, 26, 1, -15],\n [-9, 18, 24, 10, -15, -19, 13, 14, 24, -8, 9, -21],\n [1, 17, -26, 23, -8, 22, -24, 9, 0, 19, -21, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[10, 0, -21, 18, 14, -10, 20, 3, -12, -8, 3, 13],\n [-18, 7, 19, -1, 19, 10, 8, 15, -25, -14, 16, 16],\n [-18, -6, 14, 17, -26, -7, 22, -22, -15, 16, -6, 21],\n [12, -4, -19, -5, -1, -8, -12, 10, 14, -6, 24, -14],\n [-20, -2, 6, -24, 12, 5, 14, 9, 26, 13, 25, 23],\n [-4, -25, 5, 19, -21, -20, -6, 6, -11, -24, -1, -2],\n [-12, -5, 16, 10, 22, 21, -7, 26, 23, 2, 10, -8],\n [13, 4, -13, 16, -12, -26, 25, -15, -16, 20, -18, 17],\n [6, 0, 7, 22, -26, -17, -14, 2, 20, -22, -16, 26],\n [0, 12, 9, 25, 0, 16, 12, 19, -2, 12, -3, 15],\n [21, 4, -20, -2, -5, -16, -2, -8, -23, -2, 7, 1],\n [-11, -25, -1, -19, 16, -1, 11, -6, 23, -10, 3, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[16, 11, 17, -15, 4, 17, 10, 11, 20, -20, -20, 8],\n [0, -1, 13, 16, -8, -5, -26, 7, 23, 5, 26, 2],\n [-5, 24, -7, 1, 18, 23, 24, 1, -19, 20, -6, -9],\n [15, -12, -17, 0, -9, -7, 11, 6, 19, 25, 3, -24],\n [-26, -17, 22, -26, 21, 6, 2, 8, 10, 24, 4, 19],\n [19, 23, -20, -7, 16, -5, 15, -15, -17, 11, 4, 13],\n [12, 18, -6, -4, 4, 17, 17, 3, -5, 18, -6, 14],\n [-7, 1, 12, -11, -8, -3, 16, 4, -22, -10, -26, 10],\n [3, 5, 5, -25, 7, 17, 2, -22, 3, 16, 18, -9],\n [-13, 10, -16, -23, -5, 22, 19, -24, 26, -3, 7, -19],\n [-3, -11, -21, -6, 5, 12, -5, 20, -18, -9, -15, -21],\n [0, 17, 12, 20, -26, -12, -13, -14, -6, 19, 20, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"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, 23, -21, -7, -23, 13, -8, 16, 13, -17, -22, -25],\n [4, 17, 26, -7, -21, 16, -8, -9, 3, -20, -10, 26],\n [26, -23, -24, -2, 3, 9, -13, 14, -4, 23, 23, -11],\n [1, -15, -19, 3, 14, 23, 11, 19, -21, 12, -22, -24],\n [-17, 3, -11, -16, -24, -12, 17, -26, -14, 21, 12, 12],\n [11, -24, 3, 17, 14, -1, -16, -21, -15, -11, -5, -5],\n [11, -15, 9, 23, -10, 13, 5, 18, 10, -24, -2, -8],\n [10, 23, 11, 14, 22, 16, 20, -8, -11, -1, 6, -12],\n [26, 10, -7, -22, 21, 13, -3, -21, -15, -23, 21, 16],\n [-14, 25, 20, -6, -22, -14, -25, 17, -21, 2, -4, 8],\n [-17, -7, -2, 9, -17, 0, -20, 23, -6, -5, 19, -9],\n [-26, -2, 26, -6, 22, 3, 5, 8, 20, -13, 12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 2, 13, 5, -16, 1, -22, 8, -2, 25, 14, 24],\n [-20, 6, 15, 0, 17, 20, -6, 0, -2, -5, -16, -21],\n [-24, 3, 1, 14, -10, -4, 24, 7, -6, -22, 23, 17],\n [-12, 19, -25, -3, -17, -7, 8, 14, 20, -6, 3, 2],\n [8, 24, 11, -1, -7, 9, 16, 13, -9, -5, -14, -12],\n [-11, -2, -24, -22, 0, 12, 6, 13, 11, -23, 16, 11],\n [23, 25, 25, 26, -25, -8, 24, -9, -16, 8, -16, 6],\n [-25, -26, 6, -14, 0, -26, 15, 2, 18, 13, -5, 12],\n [-7, 17, 13, 18, -25, 14, 25, -10, 23, 21, 14, -22],\n [25, 21, -1, -14, 7, 3, 17, 14, -25, -15, -5, 11],\n [-14, 21, 25, -2, 13, 12, 20, 10, -6, -9, 26, -8],\n [-14, -2, -11, 18, 2, 19, -11, -5, 17, -15, 16, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 1, -4, 12, 3, 9, 11, -13, 4, 19, -15, 20],\n [-16, -23, -2, 16, -2, 17, -7, -19, -3, -9, 11, -18],\n [-3, 22, -22, 21, 18, -14, -6, -18, -25, 26, 21, -26],\n [-19, -3, 7, -17, 18, -26, 8, 14, -1, -23, 4, -22],\n [-4, 7, -12, -24, -8, 16, 12, 12, 0, -5, 22, -12],\n [13, 15, -12, 5, 4, 25, 12, -10, 25, 26, -14, 11],\n [10, -11, 1, 7, 5, -3, 10, -22, 17, -4, 23, -6],\n [-26, -14, 25, 17, -19, -26, -12, -17, -26, -13, 18, 25],\n [15, 10, 14, 19, -6, -26, 20, 0, 24, 25, 4, -20],\n [-9, 9, -3, 26, 11, 8, -23, -25, 8, -9, -25, 0],\n [13, -20, 14, 4, 14, 7, -20, 18, 2, -19, 6, -24],\n [13, 5, -8, -23, -17, -9, -8, 26, -15, -16, 5, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "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, 1, -1, -19, -17, -5, 7, 18, 24, -5, -5, -21],\n [4, 9, -16, -9, 7, -24, 22, 14, 24, 23, 11, 9],\n [-10, 3, 3, 24, 26, 16, 23, 4, 5, 21, -8, -18],\n [22, -11, 11, -8, 3, 9, -16, 25, -12, -3, 14, -6],\n [16, -17, 15, 24, -2, 5, 6, 22, 24, 23, -3, -6],\n [-1, -10, -8, -24, -14, -25, 14, 18, 5, 6, 5, 15],\n [26, -2, -24, 15, 24, -20, 22, -2, -4, 1, -15, -19],\n [23, 8, -2, 3, 5, 9, 5, 26, -2, -1, -19, -22],\n [16, -25, -8, -24, -15, 12, 5, -21, -19, -22, -14, 4],\n [-14, -26, 19, -23, -7, 2, 5, 6, -13, -8, 24, -24],\n [25, -16, -18, 24, 1, -25, -14, 8, 4, 16, -13, -12],\n [-22, 12, 7, 11, 16, -25, 18, 6, 0, -24, 25, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[24, 1, 3, 14, 23, -4, 6, 25, -13, -13, 23, -14],\n [-23, 23, -8, -3, 9, -21, -15, -18, -14, -3, 19, -12],\n [19, 23, 3, 5, 5, 7, 8, -9, -8, 23, -12, -5],\n [-2, -3, -21, 9, -17, -15, -22, -7, 10, 21, -9, 20],\n [13, 6, 14, -15, 6, -22, -18, 6, 3, 19, -10, 8],\n [-11, 13, -8, 20, -25, -21, 15, 26, 18, 20, -16, -18],\n [0, -13, 8, -7, 5, 21, -19, -16, -25, -22, 3, 17],\n [14, -16, -11, -2, 15, -2, -16, -26, 6, -26, 25, 20],\n [-18, 0, 11, -8, 13, -10, -15, -25, -19, 6, -14, 16],\n [-6, -8, 7, 3, -7, -9, -6, 9, -20, -22, -18, 18],\n [-9, 20, 23, -26, 9, 18, -13, -19, 26, 10, -7, 4],\n [-20, 14, 11, 17, 16, -12, 22, 8, -10, 0, -6, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[17, 18, -1, 17, -22, 6, 22, -22, 1, -6, -19, -25],\n [10, -13, 7, 26, 17, 19, 10, -6, 0, 23, -9, 21],\n [-22, 7, -9, 8, -1, 2, 14, 1, -21, -1, -9, 3],\n [6, 5, 23, -1, -5, 7, 22, -15, -5, -6, -3, -2],\n [-25, -26, -17, 7, -22, -10, -26, -13, -6, -21, -16, 12],\n [-7, -7, -6, -3, 14, -1, -24, 11, 14, 11, 1, -17],\n [-3, 13, 25, 21, -20, -4, -4, -3, 4, 23, 23, 20],\n [-5, 0, 11, -22, -9, -19, 8, 21, 22, -10, -15, 12],\n [-5, 26, -21, 3, -25, -22, -25, 8, -22, 4, -10, 0],\n [4, 24, -17, -15, -9, 24, -14, -19, 8, 17, -23, 19],\n [-20, -6, 18, 17, -12, 7, -5, -26, -21, -26, -8, 0],\n [-17, -13, 7, 14, 5, -24, 24, 19, -11, 12, 6, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "549", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[8, -10, -4, -1, 19, 21, -20, 14, -20, -12, 3, -7],\n [-24, -5, 21, 23, -20, 4, 22, 23, -24, 16, 19, -10],\n [24, -5, 25, 10, -24, 21, 3, -3, 6, 16, -17, -20],\n [-11, 5, -25, -19, -12, 21, -24, -7, 7, 20, 19, 26],\n [14, -23, -4, -19, -17, 22, 11, -22, -17, -1, 22, -11],\n [-4, -10, 1, -9, 25, 14, -16, 7, 19, -12, -26, 6],\n [-18, 17, -10, -12, -23, 10, 19, -21, -21, -8, -4, 3],\n [-26, -18, -5, -26, 9, -2, -11, -1, 1, -22, 21, -5],\n [-13, -18, -13, -11, 3, 5, -21, -10, -26, -9, -16, -16],\n [1, -15, 7, -11, -17, 26, 19, 12, -19, -1, 15, 15],\n [15, -13, 24, -18, 22, -8, 7, 20, 11, 2, 2, 1],\n [21, 22, -3, 1, 15, 17, -15, -8, -21, -25, 26, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, 4, 10, 2, 13, -15, 6, 20, 18, -2, 15, -9],\n [3, -9, -20, -12, 3, -22, -22, 6, -21, 21, 13, -23],\n [-14, 24, 15, -1, 22, -7, 5, 5, 23, 10, 17, -26],\n [-2, -2, 26, -26, -24, 12, -6, 16, -2, 25, -6, 20],\n [-24, 13, 2, 8, -5, -4, -14, 7, -4, 8, -8, -12],\n [26, -12, 25, -1, 12, -24, -10, 3, 1, 7, -11, 16],\n [14, -16, -3, -4, -2, 10, -14, -8, 18, 7, -25, -19],\n [-22, -16, -25, 11, 5, -3, -15, 11, -11, 24, -3, 23],\n [14, -10, 5, -7, 22, 8, 3, 20, 15, -5, 4, 24],\n [10, -3, -3, -14, -2, 4, 9, -13, 26, -7, 12, 1],\n [-2, 11, 16, -16, -9, 12, -8, -24, 14, 19, 22, 0],\n [-4, 8, 11, 16, -14, -1, -13, 8, 14, -21, 16, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "516", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[25, 13, 26, 20, -12, -19, 18, 20, -11, 2, 7, 2],\n [8, 21, -17, 25, -26, -22, -24, 12, 23, -13, 19, 0],\n [19, 2, -26, -9, -24, -1, -6, -3, 18, 25, 20, -7],\n [2, -9, -24, 24, 20, 23, 6, -9, 10, -6, 17, -8],\n [-4, -7, -3, -8, -1, 6, 5, 8, -2, 6, -3, 22],\n [-18, 10, 10, -16, -6, -10, -11, -22, 17, 19, -17, -14],\n [20, -21, 10, -11, -21, 2, -2, -4, -16, 2, -6, -1],\n [14, 26, 10, -16, 11, -3, -10, -18, -19, 3, -20, 10],\n [22, -4, -18, -8, 17, -19, 21, 19, -13, 24, 1, 8],\n [-20, -21, 3, 10, -11, 16, -26, 15, -10, 26, -20, 8],\n [-22, 0, 3, 17, 15, 8, -11, -21, -11, -19, -7, 4],\n [-7, -18, 3, -14, -1, -25, 14, 18, 19, -3, -14, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "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, -9, -11, -25, -26, -17, -2, -13, -10, -9, -20, -6],\n [2, 0, 22, -23, -15, -5, 13, 7, -1, 1, -8, 4],\n [-13, -4, -10, -4, -10, -19, 11, -17, 3, -20, -25, 20],\n [-5, -22, -24, -18, -22, -7, 2, -21, -23, 9, -6, -10],\n [-12, 0, 12, -8, 16, -24, 1, 20, -5, 24, 22, -21],\n [4, -22, -14, 22, 7, 23, -17, 13, 13, 23, 17, 1],\n [-6, 10, 9, 1, -14, 9, -26, 16, -18, 22, -7, 16],\n [15, -10, -24, 24, 5, 8, -21, 25, -21, -2, 1, 12],\n [-26, 13, -11, -7, -3, -12, 24, -17, -15, 10, 8, 0],\n [-14, 3, 24, -24, 25, 8, 21, -15, 23, 2, 3, -5],\n [-10, 26, 0, -5, 22, 22, -20, 19, -16, -11, 9, 24],\n [-5, 13, 10, -24, 8, 22, 11, 15, 14, 11, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, -16, -12, -13, 18, -10, -6, 1, 16, 11, -5, 7],\n [-26, -4, 5, -23, 14, 16, -21, -11, -17, 8, -3, -17],\n [-15, 6, 0, -2, -17, -2, 5, 15, -1, -23, -18, 0],\n [-18, 17, -1, -16, 26, 11, 5, 3, 12, -18, -16, -4],\n [-10, 5, -16, -5, 23, 5, -18, -10, 26, -2, -11, 19],\n [6, -25, 16, 12, 15, -15, 16, 7, -2, -13, -18, 3],\n [-15, -17, -3, 7, -15, -1, 5, 8, -14, -8, -14, -5],\n [21, -4, -26, -19, 18, 12, 26, 26, 7, -14, 17, 22],\n [14, -17, -24, 1, 0, -6, -16, -3, -15, -20, 15, 5],\n [-17, 1, -1, 2, 0, 25, -17, -23, 15, -5, -17, -23],\n [-20, 23, -4, -24, -3, 20, 10, 3, 14, 25, -15, -6],\n [21, 16, -10, -24, -12, 9, 5, -18, 13, 23, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -22, 14, 21, -23, 21, -22, -20, -16, 12, -21, 2],\n [24, -10, 1, 11, -8, 22, 17, -15, 18, 11, -8, 6],\n [18, -22, -26, 8, 8, 20, 20, 4, 9, 13, 8, 13],\n [-15, -9, 1, -14, 3, 13, -10, -18, 12, -5, -12, 2],\n [-11, -7, -2, 13, -3, -11, 24, -11, -2, 19, 21, -26],\n [23, 23, 6, 22, 25, -20, 11, 18, 1, 12, 1, 5],\n [-3, -19, 17, 5, 1, 21, -24, -20, -21, 2, 18, -13],\n [18, 13, -8, 19, -2, 10, -9, -23, -26, 6, 1, 14],\n [-8, 6, -12, 18, -4, 2, 12, -13, 3, -25, -14, 13],\n [1, 4, -15, -14, -24, 2, 24, 3, -15, -6, -25, 25],\n [23, -11, 5, 1, -18, -10, 23, -8, -20, 9, 13, -26],\n [15, 9, 22, 12, -26, 21, -3, -17, -16, 11, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-26, 14, -16, -21, 24, 18, -10, -13, 5, -7, 26, -23],\n [12, 20, -5, 2, 15, 10, -14, -12, 8, -2, 24, -24],\n [24, -15, -13, 13, 5, 23, -23, 2, 4, 5, -3, -16],\n [3, 22, -8, 9, -21, -25, 12, -8, 19, 21, 13, -9],\n [14, 9, 19, 25, 26, 23, -7, 10, -26, -4, 11, -7],\n [-23, 24, 22, 11, -22, -21, -1, -26, 23, -12, -11, -4],\n [14, -5, -22, 16, -22, -21, -25, -17, 9, 19, 8, 18],\n [-4, 20, -11, 10, 15, 8, 21, 13, -11, -22, -16, 24],\n [2, 21, 19, -16, 19, -11, -2, 23, -24, -24, -26, -15],\n [-20, 16, 18, 19, 5, -5, -15, -21, 11, 12, 11, 14],\n [-6, 1, 5, 0, 22, 22, -12, 6, 5, 19, 7, 25],\n [-20, -14, 26, 12, 23, -21, 24, -18, 15, -23, 26, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "590", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, -6, -15, -14, 23, -14, 25, 0, 1, -9, 10, -11],\n [26, -6, -17, -13, 1, 2, 20, -16, 3, 13, 0, 22],\n [-24, -26, 5, 12, -6, -25, -17, 4, -9, -20, -22, 2],\n [-23, 19, -24, -14, -24, -19, 23, 24, -23, 15, 8, -15],\n [-3, 11, -8, 9, 8, -9, 13, 7, -2, -20, -16, 11],\n [-8, 8, 18, -7, 0, 4, -2, -25, 2, 10, 4, 20],\n [15, -21, 19, -6, 6, -18, -17, -5, 4, 26, -16, -8],\n [14, -15, 25, 11, -11, -14, 11, -14, -12, -9, -11, 14],\n [23, 15, 17, -22, 0, -25, 14, 23, 0, -26, -13, 8],\n [-4, 16, -5, 0, 23, -2, 7, 22, 0, 8, -6, 12],\n [-24, -2, 20, -23, -12, -24, -16, 1, -24, 25, -9, 19],\n [26, -18, -12, 13, -19, 13, -13, 11, -14, 12, 20, -17]]\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[[17, 3, -22, -5, 8, -22, -15, 8, -6, -1, -26, 22],\n [-17, 11, -3, 25, 4, 18, 20, -4, -6, -25, 26, 4],\n [-25, 3, -2, 22, -8, -26, 10, 1, -7, 21, -22, 3],\n [-4, 15, 0, 26, 15, -26, -18, 23, -20, 24, -1, -11],\n [26, -21, 15, 10, 18, -15, -3, -10, -25, 4, 10, 15],\n [2, -26, 17, -13, 13, 22, -16, 5, -7, -25, 4, -22],\n [5, 23, -18, 14, -17, 26, 26, 9, 22, -1, 17, -24],\n [9, -4, 3, 12, -4, -4, 16, 9, -2, -7, 11, 6],\n [6, 11, -26, 20, 6, 11, -3, -18, 4, 11, 22, 1],\n [-4, 3, -9, -1, 25, 6, -11, 2, -11, 6, 12, 19],\n [20, 11, -4, -1, 22, -10, 11, 18, -3, 16, -8, 15],\n [0, -25, 25, -19, -12, 14, -14, 0, -5, 20, 20, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-22, 2, -12, 3, 19, -21, -21, -4, 25, -22, -5, 14],\n [-7, -7, 12, 3, 21, -10, -4, 13, 23, 25, -14, 19],\n [9, 15, -17, 11, 12, 12, -23, -8, 25, 14, 1, 0],\n [-4, -8, -11, 8, -22, -3, -22, 2, -21, 14, 14, 17],\n [21, 21, 10, 2, 6, 0, 8, 11, 13, 21, -21, 19],\n [-17, 9, 17, -20, -20, 2, -11, -26, 21, 8, 20, 2],\n [11, -14, 25, 13, -15, -4, 19, -11, -13, -11, -21, 9],\n [25, -3, 24, 0, -2, 13, 9, 2, 4, -24, -14, -23],\n [-16, 21, -12, -25, -12, -21, 20, -14, 8, 24, 17, 17],\n [22, 13, -14, -15, -11, 26, 16, 25, 14, 24, -7, 13],\n [-14, 7, -8, 18, 0, 2, -8, 16, 0, -25, 13, 12],\n [-26, -13, -19, 0, 6, 4, 3, -2, 22, 26, 9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-26, 4, 8, -6, 7, -10, -18, 2, -19, -8, 20, -21],\n [-3, -21, 13, -24, 4, 4, -15, 25, -19, 16, -1, -1],\n [-12, -14, -5, -14, 19, -18, -3, -24, -4, -15, 14, 17],\n [-16, -8, -18, 10, -17, -18, 6, -14, -7, 17, -16, 14],\n [2, 20, -14, 17, -13, -18, 15, 11, -8, 15, 20, 26],\n [-19, -9, 7, 9, -18, -11, -22, 24, -12, -3, 20, 17],\n [21, 16, 12, -2, -11, 15, -5, 23, -11, 6, -22, -20],\n [-9, -21, 22, -15, 17, 6, 7, -6, -9, -13, 15, 3],\n [19, -24, 26, -14, 24, 10, -8, 10, -14, -12, -1, -21],\n [0, -15, 21, -2, 23, 20, -11, 19, -11, -24, 7, -3],\n [15, 19, -4, 3, 22, -6, 26, -10, -9, -24, 26, 20],\n [-15, -11, 11, -13, 0, -9, -7, 8, -10, -7, -21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "496", "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, 11, -15, -10, -6, 26, -21, 20, 10, -2, -12, -16],\n [-18, -23, -24, -14, 5, -21, -26, 15, -22, -25, -5, 5],\n [24, 21, 14, 23, 22, -20, -6, -10, 26, -7, -26, 5],\n [13, 5, -7, -17, -21, 14, 6, -17, -2, -3, 4, 2],\n [-15, 16, 10, 24, 15, 23, -18, 2, -24, -23, -6, -21],\n [-25, 10, -7, 18, 6, -13, -7, 16, -25, 20, -20, 10],\n [-15, 22, -11, -10, 4, -20, -1, -26, -25, 4, -7, 10],\n [6, -14, -26, 24, 6, -24, 10, -8, 17, 13, 5, -22],\n [20, 16, 20, 10, -21, 9, 10, -14, -15, -21, 3, 10],\n [1, -17, 1, -21, -18, -3, 25, -9, -23, 18, -4, 0],\n [-23, -14, -16, -16, -8, 6, -13, -14, -20, 6, 5, 18],\n [10, -19, 19, 7, -8, 9, 7, 9, -21, 23, -26, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -12, -18, 2, -25, 3, 19, -23, -8, -7, -22, -18],\n [-7, 25, 22, -11, 22, -7, -7, -1, 12, 6, -15, -6],\n [-4, -7, -4, 22, 20, -21, 18, -15, 8, -19, 0, -11],\n [20, 26, 5, 2, -20, -11, 26, 2, -2, 16, 9, 21],\n [-23, 0, -4, -4, 3, 16, -3, 21, -11, -20, -4, 11],\n [4, 15, -8, 25, 20, -23, -21, -8, 0, 25, 2, -15],\n [11, -14, 1, -22, 19, 19, -10, 0, -1, -23, -19, -1],\n [6, -15, -14, -6, 25, 10, -2, 12, -24, -8, -20, -10],\n [-14, -3, 24, 18, -19, -19, 18, -25, 3, -24, 18, -1],\n [-10, 11, -24, 6, 3, -12, -19, 3, -4, -15, 12, 21],\n [-19, -18, -19, 11, 6, 21, 6, 18, -16, -4, 16, 24],\n [24, 16, -2, -12, -17, -7, -11, 8, 7, -6, 19, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[13, -26, -2, 19, -13, -8, -19, 14, -12, 17, -9, -26],\n [20, 6, -26, 26, 7, -23, -10, -25, 12, -17, 15, 18],\n [10, -1, 0, 12, -2, 2, 19, -9, -5, 24, -1, -1],\n [25, -6, -6, 15, -19, 26, -25, 19, 7, -15, 22, -9],\n [-10, -12, -24, -6, -8, 5, -16, -9, 26, 2, -24, 23],\n [-23, 1, -18, 11, -20, -26, 8, 20, 7, -18, -1, -19],\n [-8, -1, 19, -17, 16, 3, 13, 9, 4, -19, 15, 20],\n [-14, 10, 3, -12, 8, -24, 2, -3, 18, -4, -18, -25],\n [-12, 5, -9, 2, 13, -24, 6, -20, 3, 0, 11, 2],\n [4, -26, 14, 16, 0, 0, 2, -22, -24, 2, 14, 12],\n [25, -14, 6, -7, -24, -21, 16, -10, 20, -23, 6, 6],\n [-21, 14, -13, 19, -20, -21, 24, -24, 10, -5, 11, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "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, -14, -14, -26, 24, 26, 14, 9, 5, -22, 22, -20],\n [23, 18, 5, 1, 6, 19, -13, -14, 2, 23, 13, -26],\n [20, 22, 22, 0, 3, 7, 19, -26, 7, -20, -26, 15],\n [-9, 8, 23, -8, -14, -4, -25, -24, -5, 9, 22, -19],\n [-4, -19, -2, 8, 20, -16, 14, 16, -21, 15, 15, 23],\n [18, -10, 9, -9, 6, -9, -20, 2, -22, -11, 4, -22],\n [-17, 2, 2, -11, -23, -26, -19, 1, -26, 1, -24, 23],\n [-25, -2, 10, -16, 19, -9, 15, 12, 13, -7, -10, -20],\n [21, -10, -23, 9, 3, -26, 8, -15, -10, -11, 1, 5],\n [19, 8, -8, 2, 2, 24, -11, -23, -6, 22, 24, 17],\n [-26, -8, 24, 25, 17, -1, -15, -10, 10, 1, 9, 2],\n [-22, 11, -24, -12, -24, -14, -22, -6, 14, -4, 20, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[7, 14, -1, 20, 4, 8, -20, 13, 18, 5, 26, -5],\n [20, -21, -6, 18, 12, 22, 20, 10, 0, -17, -5, 17],\n [24, -9, -23, 18, 8, 11, 11, 9, -23, 18, -17, 5],\n [-17, 16, 18, -17, -16, 23, 12, -18, -14, 15, -9, 20],\n [10, 20, -16, 1, -21, 6, -13, 20, 2, 12, -12, 21],\n [-22, -5, 25, 4, -8, 24, -9, -21, -18, 3, 4, 8],\n [-10, 15, -11, 6, -23, 4, 6, 23, 25, 9, -16, -23],\n [24, 9, -22, -6, -14, -23, 15, 23, 8, -1, -1, -8],\n [10, -16, -25, 4, -9, -16, 17, -11, -25, 5, 21, 21],\n [-5, 9, -19, 9, 16, -2, 13, 17, 4, -23, 12, 18],\n [16, -17, 0, 14, 11, -10, 18, 11, -2, -10, -14, -6],\n [-12, 21, 26, -3, -20, 26, 18, 11, 13, -5, 15, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "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, 6, -15, -19, 13, -5, 12, 12, 20, 17, -11, 21],\n [7, 19, -11, -13, -21, 23, -17, -3, 0, 20, 23, -18],\n [21, -11, -25, 4, 20, -8, -16, -5, 2, 4, -19, -17],\n [-21, 4, 24, 8, 23, 13, 2, -6, 14, -22, -22, -3],\n [-12, 1, 7, -14, 17, 5, -5, 2, -24, -22, 23, -16],\n [21, 14, 26, 26, -1, -18, 17, -16, -26, 11, 18, 1],\n [-4, 4, -25, -9, -11, 15, -10, 21, -10, 20, 8, 4],\n [8, -3, 14, 10, 22, 3, -9, 0, -11, -7, 14, 20],\n [1, -6, 14, 18, 6, 21, -18, -3, -14, 3, 19, 16],\n [6, 19, 26, -3, -7, 23, -26, -4, 6, -10, -25, 4],\n [4, -11, 10, 10, -20, 26, 9, -26, 3, -9, 15, 12],\n [-1, -16, -26, 11, -22, -5, -14, -10, 23, -20, 11, -20]]\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[[-15, 11, -4, 21, -19, -12, 3, -18, 18, -6, 17, -13],\n [-19, 20, 9, -18, -1, -7, 11, -21, 7, -4, 12, 6],\n [-6, 14, -1, -22, -18, 18, 6, -2, 25, 20, -10, 13],\n [20, -8, -16, -19, -21, -21, -19, -3, -8, 25, 14, 0],\n [-7, -3, 11, -22, -11, 12, 6, -17, 24, -22, 25, -8],\n [24, 14, -6, -24, 26, 1, 14, -8, -11, 26, -25, -19],\n [19, 11, -15, -3, -26, -9, -4, 12, 0, 17, 17, -21],\n [1, -4, 25, 7, -2, -16, 21, -26, 11, -17, -18, -1],\n [-17, -9, 23, -18, 18, -1, 15, -18, 9, -12, -3, 13],\n [-25, -23, 11, 4, -7, 12, 18, -1, -22, -23, -5, -21],\n [10, 4, -22, -20, -22, -23, 0, -18, 10, -25, 22, -8],\n [12, -10, -10, 21, 13, 24, 23, -3, -14, 1, 19, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, 15, -13, -4, -4, -17, 11, 22, -10, 0, -16, -8],\n [18, 17, 17, 0, 9, -11, -4, 6, 25, -5, -13, -14],\n [-5, -20, 11, -26, 24, 6, -5, -4, -12, 17, -12, 4],\n [1, -24, 15, -2, 6, 6, -4, 1, 26, -11, 10, -22],\n [16, -16, -15, -6, -9, -13, 6, -6, -1, -2, 13, -2],\n [8, 23, 26, -7, -25, 14, 24, -15, 5, 16, 6, 21],\n [4, 6, -7, 14, 10, 10, 13, -13, 9, -15, -1, 7],\n [-21, 19, -14, -5, 8, -8, 10, -4, 23, 5, 17, -16],\n [-23, -15, 24, 12, 3, -17, 24, -3, -4, -26, 21, -23],\n [1, 17, 18, 26, -24, 21, -25, 14, -21, 15, -10, 10],\n [17, -4, 13, -6, 17, 4, -15, 2, 15, -14, -1, 6],\n [7, -7, 20, -17, -26, 25, 2, -5, 23, -26, 17, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-18, -4, -7, 7, -11, -5, 19, -4, -26, -13, 25, 22],\n [-4, 11, 13, 23, -19, 5, 13, -25, 21, -14, 0, 19],\n [-20, -24, -6, -19, -26, -10, -1, 2, -19, 11, 24, 16],\n [-19, -19, -2, 15, 15, 18, 0, -5, -24, 22, 26, 20],\n [11, 22, -3, 6, 8, 13, 2, -19, -16, -11, 6, -16],\n [2, 22, 18, -3, -25, -22, -3, 26, 17, 20, -20, 4],\n [3, -21, -22, -12, 0, 8, -18, -4, -10, 26, -4, 19],\n [12, 20, 2, 12, 18, 19, -16, 23, -14, -15, -25, 15],\n [-16, 21, 22, -13, -5, -6, 18, 22, 10, 9, -2, 16],\n [22, -24, -25, 0, 6, -9, 21, -16, -20, 10, 23, 9],\n [0, -5, 4, 13, -21, 26, 26, 6, -20, -21, -26, 12],\n [19, 11, 15, 23, 21, 17, 2, -16, 1, 13, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "565", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, -15, 1, 4, 3, 12, -11, 3, -23, 6, 6, 1],\n [-6, -12, -1, -13, -12, -25, -11, 10, -16, -16, 6, -25],\n [6, -24, -7, 6, -1, 22, 7, -13, 25, 2, -25, 23],\n [-19, 0, -19, -20, -16, 25, 12, 3, 12, 22, 20, -6],\n [-6, -20, -7, 22, 24, -13, -7, -22, 4, -15, -15, -25],\n [-1, -23, 3, 7, 10, -7, -25, 18, 8, -12, 24, 21],\n [-13, 9, 22, 26, 3, 17, 0, -25, -6, 25, -13, 0],\n [-6, -4, 8, 21, -19, -15, 1, 14, 6, 6, -18, -12],\n [-17, 22, -25, -24, -4, -17, -8, 14, -9, 8, 14, 16],\n [-18, 4, 3, 10, 25, 23, -15, -10, 0, -6, 22, 21],\n [0, -13, 14, -14, -24, -3, 5, 10, -19, 8, -4, -11],\n [9, -18, 12, -9, 22, 4, 11, 15, 10, 20, 7, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[14, -21, 9, -13, 14, -3, 6, 24, 15, 23, -8, 2],\n [26, -21, -24, -9, -6, 2, 25, 26, 15, 25, 9, 4],\n [-19, 5, -11, -5, -25, 24, -12, 13, -10, -14, 8, -2],\n [-17, 18, -16, 6, -13, 7, -5, 17, -23, 17, -1, -26],\n [-17, 9, -25, 2, -2, -4, 3, -2, -14, 13, 7, 8],\n [-12, 12, 15, -7, 16, -5, -2, -13, -8, 19, -5, -4],\n [-26, 12, 3, -22, 3, -20, -14, 4, -20, 2, 24, -2],\n [-14, 21, 26, -12, 24, 3, -20, -22, -13, 3, -4, -11],\n [-3, 16, -6, 16, 3, -15, 26, 18, 13, 3, 11, -5],\n [-25, -4, 15, -4, -5, 3, 0, 7, -16, 2, 10, -21],\n [-11, -7, -17, 19, 11, 10, -17, 17, -2, -5, 5, -10],\n [-1, -11, -17, -10, -25, -25, 2, 19, -23, 3, -15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-13, -3, -3, -9, -2, -2, 14, -2, 1, 3, -2, -3],\n [13, 12, -14, -25, 7, -11, 21, -3, 23, -25, 2, 12],\n [12, -10, -4, -15, -14, -22, -12, 26, -25, -21, 9, -4],\n [-14, -25, -22, 13, -11, 12, 8, 14, 18, 7, -8, 16],\n [-1, 15, 16, -10, 22, 8, -15, 8, 10, -21, 25, -17],\n [16, -4, -8, 25, 16, 26, -19, -18, -24, 6, -25, 7],\n [8, -9, 0, 22, 17, 0, 11, 12, -10, -18, 5, -4],\n [17, -13, -16, -23, 24, 11, 24, 21, -11, 9, -2, -22],\n [-17, -22, 14, -9, -4, 11, -13, 25, -4, 21, 8, 6],\n [11, -26, -21, -6, 0, -22, 0, 17, -21, 13, -2, 24],\n [-22, -12, 19, 21, 11, -10, -10, 21, 6, -9, 9, -24],\n [-2, 8, 18, -7, 9, 16, 4, -6, 10, 7, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-26, 4, -4, 16, 11, 22, -16, 12, 21, -7, 10, -20],\n [8, -25, 6, 13, -3, 12, -17, 19, -18, 16, 6, 24],\n [-6, -13, 23, -4, -15, -5, 1, 0, -17, -9, -3, -24],\n [-23, 3, -6, -5, 1, -18, 17, 14, 14, -11, 10, -22],\n [-13, 25, -13, 20, -11, 12, 16, -23, 10, -13, 14, -4],\n [-18, -3, -16, 1, -8, -8, -15, 20, 7, -15, -24, 3],\n [20, 19, 24, 8, -12, 16, -5, -18, 1, 2, 12, 12],\n [12, -10, -23, -23, -20, -25, 10, -17, -9, 1, 19, 8],\n [8, 24, 3, -6, -2, -14, -20, -21, -7, 18, -22, 11],\n [17, 13, -2, -9, -3, -12, -19, -14, 12, 21, 25, -2],\n [-4, -22, 25, -5, 20, -5, -2, 20, -26, -23, 25, 26],\n [5, 26, -1, 9, -12, 8, 11, 0, -13, 7, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 21, 8, 25, -21, 8, -1, -12, -22, -1, 6, -2],\n [-10, 25, 17, -7, 15, -25, -19, -8, 2, 21, -8, -18],\n [-19, 22, -12, 7, -23, 0, 11, 20, -14, 5, 8, 25],\n [21, 19, 9, -17, -4, -4, -23, 17, -22, -23, 3, 14],\n [25, 6, 21, 13, -14, -9, 5, 6, -20, -13, 13, 21],\n [-13, -17, 14, 25, 12, 10, 19, -9, -8, 13, 15, 16],\n [10, 20, -24, -20, -20, 26, 25, 11, -21, -17, 25, 17],\n [9, 10, 21, 0, 18, -26, -26, 21, -6, 10, 1, 22],\n [12, 9, -25, -25, -23, -25, -26, 22, 13, -9, 14, 7],\n [0, 9, 12, -1, -16, 13, -24, 22, 1, 9, -11, 8],\n [25, -5, -11, 6, -14, 22, 1, 17, -11, -25, -1, 15],\n [1, -24, 17, -6, 5, -21, -22, -3, -26, -4, -11, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "546", "dataset": "MATH"}
{"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, -2, 19, -16, -15, 18, -19, -17, 8, 11, -6, 24],\n [-9, -9, -1, -7, -2, 4, -9, -11, 26, 18, 16, -9],\n [21, -13, -20, 11, 22, 2, -4, 20, 15, 22, 7, -10],\n [18, -9, -8, -25, 2, -25, -9, 12, 15, 9, 9, -6],\n [6, -25, -17, -12, -15, -24, -23, -18, 19, 15, -17, 4],\n [10, -16, 0, 19, -21, 16, 3, 16, 8, 18, -9, 23],\n [-21, -14, 11, -15, -20, -13, -18, 8, 20, -20, 12, -6],\n [-8, 0, -25, 25, -13, 10, 6, 17, -15, 24, -6, 3],\n [-5, -25, 2, -3, 5, 18, -15, -20, 26, -25, 13, -8],\n [24, -9, 7, -25, 18, 11, 13, -8, -21, 24, 14, 20],\n [-10, -4, 13, -18, 10, 11, -6, -6, 0, -16, 12, 3],\n [1, -7, 20, 18, 20, 19, 11, -23, -9, 23, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "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, 26, -26, 8, -22, 25, -21, 9, -22, 17, 5, 12],\n [18, 4, 13, 18, 17, 15, -17, 4, -19, 0, 2, -13],\n [-4, -23, 25, 7, 14, 11, 0, -8, 4, -24, 2, -14],\n [0, 16, 5, 19, 22, 23, 10, -24, 12, -21, -24, 25],\n [-14, -16, 0, 26, -25, 13, 17, -15, 20, 13, -15, -4],\n [4, -17, 26, 8, -21, -2, 4, 3, -12, 19, -24, -9],\n [26, -10, -13, 19, -11, 24, 0, 16, 10, 6, -7, -2],\n [23, -13, 10, -22, 10, -17, -17, -18, -13, 6, 2, -3],\n [-21, -1, 12, 17, 20, 21, -24, 21, 13, 19, 5, -1],\n [-24, -15, -13, -8, -23, -15, 8, -4, 21, -24, -24, 12],\n [15, -11, -14, -8, 1, 11, 26, -18, 19, -10, -20, -19],\n [10, 25, -15, 1, -25, 21, 1, -2, 0, 8, -12, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[21, 8, 20, 6, 17, 15, -4, 0, 11, -19, 25, 11],\n [24, -23, 21, -22, -11, -9, 18, 18, -9, -19, 2, -6],\n [12, 0, 20, -25, -23, 21, -15, -11, -2, -4, -10, 25],\n [15, 20, 24, 19, -26, -6, 9, -25, -4, 13, -25, 16],\n [-17, 16, -18, 2, -1, 9, 2, -23, -6, 6, 4, 1],\n [9, 6, -23, -23, 6, -13, 21, -18, -3, -2, -20, 19],\n [1, -22, 19, -14, -25, -7, -15, 26, 0, -20, 7, -6],\n [-9, -17, 11, 12, 17, -6, -11, 24, -7, 23, 19, 20],\n [13, -3, 20, -6, 17, 4, 23, -17, -7, -13, -8, 3],\n [-11, -5, -7, -21, 18, 16, 6, 14, -8, -22, -20, 7],\n [-7, -12, 11, -26, -22, 7, -6, -13, -10, -15, 0, -21],\n [12, 21, -2, 0, 18, -25, -5, 5, -10, 10, -25, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[25, -1, 6, -26, 13, 16, 17, 9, 12, -2, -14, 12],\n [9, -15, -6, -4, -9, -14, -8, 8, 19, 21, 7, 25],\n [-26, 19, -5, 1, -23, 10, -20, -16, -15, 13, 26, 12],\n [8, 7, -9, -17, 24, -12, -1, 22, 24, -24, -14, 7],\n [20, -10, -26, -13, -26, -3, -16, -24, -14, -5, 14, 20],\n [14, 3, -2, -20, -2, 12, -2, -25, 7, -5, 26, -26],\n [-9, -11, -17, 4, 21, -14, 7, 7, 15, -15, 10, 13],\n [-10, 14, -12, -14, 19, -19, -10, -16, 13, 19, -26, 5],\n [17, 25, -17, 17, 24, -12, -24, -18, -19, -17, -19, -11],\n [-16, -4, -5, 13, -9, 12, -24, -19, -22, 0, -22, -8],\n [-10, 19, -9, -25, 23, -20, 22, 23, -11, -20, -9, 17],\n [-1, 2, -11, 19, 12, 3, -2, -19, -13, -5, 25, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, 8, 13, 24, -15, 16, -6, -16, -24, -18, 16, -8],\n [15, -4, -11, -23, 5, -26, -23, -1, 0, 13, -11, 3],\n [11, 6, -11, 6, -7, 4, 21, 0, 5, -5, 9, 0],\n [-2, -25, 19, 11, -4, 25, -15, 10, 19, 10, 23, 21],\n [-6, 21, 15, -16, -6, 10, -23, -1, -7, -20, 11, 20],\n [0, 20, -10, 5, -17, 23, -16, -9, -25, 8, -21, -24],\n [-20, 8, 20, -14, 11, -25, -25, 24, -19, -18, 7, 12],\n [4, 2, 22, 20, 9, -5, -4, -14, 8, 17, -24, 26],\n [24, -18, 21, -9, -1, 2, 21, -15, 12, -4, -8, -3],\n [17, 16, 17, 3, 4, -8, -6, 22, 20, -17, -23, -9],\n [18, 10, -7, 25, 9, 21, 5, 26, 25, 0, 14, -3],\n [2, 26, -3, 2, 12, -9, -17, 20, -18, 23, -16, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-25, -1, -18, -10, 8, 19, -24, -21, 16, -4, 8, -12],\n [-19, 5, 7, -16, 19, -24, 2, -17, -9, -9, -15, 0],\n [24, -8, 14, 6, -2, 17, -25, -25, -22, -5, 6, 17],\n [-22, 1, -13, 13, 16, 23, -17, 14, -12, -17, -23, 16],\n [22, -9, -10, 4, 6, -2, -15, 20, -6, -10, -7, 2],\n [-24, -20, 6, -1, -7, 16, 10, 5, 8, -6, 25, 26],\n [14, -19, -25, 24, 21, -11, 0, 9, -17, 1, -10, -2],\n [-12, -9, 1, -25, 13, 15, 4, 4, -2, -26, -9, -11],\n [15, 10, 14, 15, 10, -20, -21, -13, -5, 23, 4, 18],\n [-17, 19, 13, 19, 9, 14, 11, 7, -24, -4, 16, -10],\n [2, -26, -24, -13, -16, 3, -6, -11, 19, 24, -18, -25],\n [-1, 15, -24, -12, -15, -8, 14, -13, -12, -4, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-24, 16, -26, -23, -6, -2, -7, -17, -9, 6, 26, 8],\n [-2, -24, 24, 23, -14, 8, -2, -9, 24, 3, 13, 19],\n [3, -3, -1, -26, 6, -19, -15, -19, -16, -13, -9, 17],\n [13, -26, -6, -17, 10, 2, 19, 13, -3, 17, 9, -9],\n [-12, 5, 11, 16, 18, -7, 7, -18, 14, 7, 8, 0],\n [15, -9, -6, -9, 0, 4, 1, 6, -12, 18, 20, 9],\n [-8, 8, 5, 18, 12, -15, 2, 7, -11, -5, -19, -15],\n [7, -11, 20, -18, 0, 20, 8, -16, -8, 4, -12, 26],\n [0, 6, -20, -4, 9, -5, -26, 0, 25, -16, 24, -15],\n [-6, -19, -14, 10, 6, 23, -25, -18, -14, -1, 18, 20],\n [25, -18, -12, -20, 16, 10, -18, -13, 3, 24, 20, 21],\n [-7, 20, -4, -12, 4, -23, -2, 24, -8, 10, 7, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, 4, 13, 17, 8, 0, -6, -19, -9, -4, 14, 9],\n [2, -11, 23, -17, -10, -5, 13, -25, 15, 3, 17, 12],\n [12, 18, -8, -17, -7, -3, -21, 18, -9, -11, 12, 13],\n [13, -11, 13, -12, 13, -21, 6, 21, -14, -23, 5, 23],\n [2, -20, 6, -22, 13, -23, -20, -11, 10, 22, -16, 23],\n [-22, 2, -2, -24, 5, 3, -7, 3, -24, 17, -12, 14],\n [-13, 13, 23, -17, -10, -12, 2, 26, 7, 8, -18, 24],\n [-10, -25, -1, 11, 16, 1, 3, 16, -18, 1, -11, -3],\n [-5, -7, 25, -13, 25, 16, 5, -17, -25, -20, -26, 10],\n [-12, -16, -7, 23, 14, 6, 25, 11, -7, -17, 5, 9],\n [23, -15, -2, -18, 22, -10, -13, -3, 14, 24, 18, -24],\n [23, 14, -11, -9, 12, 23, -13, -17, -17, -21, -24, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -25, 12, -15, -26, 25, 10, -14, 5, -2, 24, 11],\n [-22, 10, -9, -17, 26, -8, 7, 3, 5, -16, -5, 3],\n [-26, -21, -13, -24, 12, -12, 4, -8, -5, -20, 0, 8],\n [16, -22, 19, 8, 9, 10, -4, 9, -23, -25, 10, 8],\n [19, -23, 21, -23, -21, 24, -10, -23, -5, -6, -15, -20],\n [21, 1, 19, -14, 16, 16, 6, 13, -14, -23, -2, 24],\n [-7, 11, 8, -18, 24, 3, 12, -4, -16, -12, 20, 26],\n [-5, -10, 20, -15, 24, 8, 7, -26, 5, -23, -3, -20],\n [-15, -5, 22, 8, -6, 2, 22, -10, 1, 15, 20, 14],\n [-10, -23, 14, -21, -12, 17, -3, -19, 14, 0, 4, -18],\n [-9, 26, -25, -5, -7, 15, -23, 11, 17, -14, 22, -7],\n [25, -21, -12, -19, 3, 9, 9, -24, 0, 3, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[13, 11, -7, 18, -11, -6, -9, 14, 4, -25, -3, -21],\n [19, -10, -1, 20, 25, 10, -25, -1, 17, 10, -26, -25],\n [6, -16, 3, 7, 0, 16, 7, -20, 12, 12, -25, 3],\n [21, -24, -25, 3, 10, 2, 8, 11, -5, 10, -9, 13],\n [18, 7, 18, 22, 11, 3, -25, -7, 17, -11, -23, 21],\n [-14, -13, -18, 17, -13, -16, -17, 3, -20, -21, -10, -14],\n [20, -23, -1, 5, -24, -16, -7, 25, 2, -25, 16, -23],\n [5, 22, 22, -6, -10, 18, -14, 5, 24, -24, 15, 21],\n [25, 4, 4, -26, 1, -4, 25, -22, -26, -11, -16, 9],\n [10, -11, -15, 3, 17, -23, 22, 14, 11, -19, -19, -6],\n [13, -19, 2, -12, -13, 11, -17, 0, 13, 26, 0, 15],\n [13, 8, 9, -16, -14, 8, 26, -6, 10, 17, -15, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "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, 17, -9, -17, 12, -24, -22, -15, -13, 18, 14],\n [5, 15, 6, -21, 3, -21, 4, -25, -1, 21, 5, -22],\n [19, 21, 14, 16, -11, 25, -15, -12, -6, 10, -6, -2],\n [-10, -19, 3, 6, -25, 6, 25, 1, -1, 14, -26, 8],\n [21, 16, 12, -7, -14, 4, 11, -4, -15, -21, -3, 7],\n [6, -20, 24, -13, 9, -11, 19, -4, -9, 2, -20, -23],\n [-2, 6, 24, -3, -4, 23, -6, 12, -6, 21, 0, -10],\n [26, -1, -8, 6, 21, 25, -20, 4, 12, -12, -25, 18],\n [-25, -10, 7, 20, 19, -2, 21, -16, 17, -18, -20, -16],\n [24, -23, 10, -1, 26, 7, -11, 14, 20, 3, 19, -11],\n [-21, 6, 23, -12, -7, -15, -3, 13, 5, 14, 6, 21],\n [19, -15, -12, -19, -23, 0, 10, 26, -13, 12, -12, -8]]\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[[26, -13, -20, -21, 7, -3, -2, 14, -2, 23, 20, -12],\n [15, -24, 9, -25, -5, 1, 5, 12, -2, -26, 17, -4],\n [-22, 21, 8, -16, -12, -22, 11, -23, 17, -17, -18, 6],\n [15, -21, 19, 0, 16, 1, 19, 16, 7, 2, 5, -5],\n [-12, 0, -17, -2, -16, -19, -6, -19, 10, -3, 19, 21],\n [-4, 26, -3, -14, 12, -22, -12, -3, -16, -10, -19, 15],\n [-3, 11, 0, 15, 24, -20, 25, -3, 0, 10, 18, -24],\n [-5, 21, 11, -5, 13, 21, 22, 2, -17, -10, 15, -20],\n [16, 8, 13, -24, -14, -21, -10, -25, 12, 11, 6, 15],\n [-4, 25, 6, -2, -13, 8, 3, -18, 3, -20, -19, -20],\n [15, 0, -2, 20, 24, -3, 1, 7, 25, -17, 9, -12],\n [11, -24, -15, 6, -1, 14, 14, -21, -24, 0, 14, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[22, 22, 23, -16, 25, 24, -10, 19, 21, 25, -11, 16],\n [-26, 21, -21, -12, 6, -20, -19, 26, 15, 3, -20, 13],\n [18, -13, -24, -1, 17, 7, 3, 3, 2, 10, 17, -2],\n [-23, -26, -19, 26, 25, -25, -10, 14, 25, 16, 22, -4],\n [-6, 2, -22, 5, -6, -18, -20, -9, -12, -2, 21, -11],\n [-7, 18, 10, 7, 24, -22, 6, -26, 21, 22, -20, 15],\n [-23, -23, 18, -14, 8, 16, -9, 25, 16, 23, 19, -16],\n [-14, 16, 4, 12, 15, -21, 11, 23, -16, -6, -1, -12],\n [-3, -9, -19, 14, 8, 1, 2, 20, 25, 19, -25, -9],\n [-26, -25, 18, 18, -13, 1, 17, -6, -7, 7, 7, 19],\n [12, -23, 16, 1, 12, -26, 18, -19, -11, 24, 21, 18],\n [4, -20, 24, -22, -25, 14, 21, 26, -23, -17, 8, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "605", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[12, -24, 16, 18, -1, -10, 15, -19, 3, -19, 2, 24],\n [24, -9, -3, -18, -7, 25, 17, -14, 10, -8, -22, 9],\n [-3, 26, 25, 7, 20, -19, 19, -23, 17, 11, -19, -18],\n [14, 21, 14, 4, 4, 24, 13, -20, -2, -14, -22, 25],\n [-9, -20, 11, 15, -12, 22, 18, 6, 25, 4, 26, -18],\n [-8, -21, 9, 5, 1, 23, 11, -17, 8, 19, -3, 7],\n [24, -18, 0, 7, -12, 0, 0, 5, 18, 0, -1, 17],\n [-10, -11, 8, -1, 11, 3, 15, 10, -13, -9, 1, 13],\n [-11, -25, -7, 3, -18, 24, -26, 0, -18, -7, 0, 12],\n [8, 6, -14, -13, 26, -26, 23, -20, 20, 6, 12, 25],\n [25, 7, 19, 26, 1, -20, 19, 25, -3, -12, -3, 0],\n [12, -24, -17, -15, 14, 2, -19, -17, -10, -18, 15, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-23, -6, -20, 21, -19, 19, -7, -20, 19, -21, -18, -13],\n [21, 9, 25, 2, -24, 18, 4, -3, -3, 21, 9, 8],\n [-2, 12, -6, -12, 7, -18, -24, -17, 23, -12, -11, -14],\n [17, 17, -26, 20, 6, -19, -11, 21, 8, 24, -13, 14],\n [0, 17, 21, -26, 12, 23, 16, 3, 8, -17, 4, -15],\n [13, 8, 7, 12, 5, -15, 18, 1, -8, -3, -7, -5],\n [-16, 1, 18, 13, -7, -22, 24, 25, 13, -20, -5, 10],\n [14, 2, -15, 2, 9, 8, 16, -5, -9, -5, -8, 7],\n [-18, -17, -8, 11, -18, 24, 1, 3, -2, -9, 25, -1],\n [-8, 0, 9, -23, 22, -1, 18, -24, 26, 26, 9, -20],\n [-17, 18, -23, -20, -5, 3, -5, 26, 2, -16, -11, 17],\n [-21, 10, -14, 6, 20, 24, -19, -16, 6, 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[[13, 0, 19, 12, -9, 18, 5, 18, 14, -3, -5, 23],\n [-24, -24, -13, 5, -18, -11, -2, -22, -14, 4, -6, 13],\n [24, -18, -6, -18, -17, 14, 17, -15, -16, -7, 23, 12],\n [6, -20, -26, -13, 18, -6, 18, 22, -19, -10, 18, 22],\n [-12, -25, -14, 25, 2, 1, -19, 8, -3, -20, 1, -5],\n [-1, -10, 11, -21, -16, 11, -25, 5, -1, 4, 5, 8],\n [-25, -24, 6, -20, -6, 21, -2, -11, -4, -10, 6, -9],\n [12, -4, -18, -24, 21, 8, -3, -21, -8, -13, -24, -21],\n [-10, 9, -5, 26, -23, -17, 5, 20, 22, 25, 22, 16],\n [-23, -14, -8, 19, 16, 11, 21, -1, 3, 16, 4, 24],\n [11, -15, -8, -4, 23, 19, 14, -17, -12, 23, -10, 25],\n [-14, -3, -11, 12, 11, 3, 18, 17, -12, -23, 17, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-17, 13, 19, 19, 5, -6, 2, 3, -20, 15, 2, -17],\n [23, -5, -10, -9, 19, -22, 12, -10, 7, -23, 14, -19],\n [-1, -2, 9, 16, 12, -16, -24, 17, 13, 1, 12, -2],\n [-5, -14, -23, 1, -8, -24, 0, -16, -21, 21, 4, 2],\n [-19, -16, -18, 4, -26, -20, -17, -18, -14, 0, -9, -11],\n [-23, 3, 11, -7, 14, -15, 1, 17, -26, -18, 15, 22],\n [6, 26, -26, 15, -18, -5, -18, -22, -25, -13, -15, 2],\n [-11, 21, -18, 24, 5, 26, -3, 26, -7, -7, 26, 24],\n [15, 16, 25, -22, -7, -11, -8, -15, -10, 7, 0, 14],\n [-1, 23, 7, -6, 15, 14, -24, 14, 9, 2, 18, -8],\n [-6, -15, 17, -4, 20, 1, -15, -25, 3, -15, 12, 12],\n [-9, -3, -15, -9, -21, -19, 22, -12, 17, -20, 2, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -14, 5, -15, 21, -2, -8, 15, -11, -15, 8, 9],\n [-3, 6, 9, -23, 8, 23, 23, -19, -19, -20, 13, -2],\n [21, 8, -12, -9, -16, 3, 2, -4, 7, -8, -11, -21],\n [14, -12, -18, 2, 15, -25, 20, 6, 11, -4, -14, -7],\n [-20, -10, 24, -6, 1, 3, -4, -6, 22, -26, -10, 5],\n [-3, -20, 8, 9, -13, -15, 12, -4, -13, -2, -5, 18],\n [22, 10, 2, -19, -16, 3, -5, -12, -6, 20, -2, -14],\n [-20, 22, -9, -15, 20, -1, -22, 24, -19, 9, -22, -5],\n [-4, -19, 24, -8, 7, -21, 23, 22, -10, -10, -12, 12],\n [10, 4, -5, -2, -8, -20, -25, -12, -5, 19, 11, 26],\n [-20, 14, -4, -25, 25, 6, -9, 17, -20, -3, -16, -15],\n [-9, 10, -26, 26, -26, 0, -18, -26, 1, -15, 22, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[22, -20, 8, 14, -4, 8, -11, 21, 15, -19, 21, -11],\n [-21, 9, 4, 20, 1, 8, -10, 20, 3, 25, -18, -4],\n [18, -26, -15, -10, 19, 6, -5, -17, -1, -13, -2, 20],\n [-16, -8, 16, 24, 1, 0, -16, -5, -2, 3, -8, 12],\n [-20, -21, -18, -9, 4, -21, 19, 26, -5, -18, 4, -5],\n [26, -6, 8, 2, -6, 26, 8, -4, 13, 17, -4, -9],\n [-4, -26, 24, 17, -7, -11, -18, -2, 11, -2, 11, -20],\n [19, -11, 8, 4, -26, -7, 22, 0, -26, 10, -3, 22],\n [-22, -16, 8, 2, -4, -17, 3, 4, -3, -13, 24, -16],\n [-26, 17, -1, -7, -25, 6, 20, 18, 18, 18, -10, -21],\n [-15, -12, -24, -5, 11, -6, 8, 17, 16, 0, -21, -16],\n [-10, 9, 4, 16, -14, 21, 2, 11, -7, 11, 22, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[12, -26, 17, 23, -14, 0, -24, -7, 1, -21, 19, 19],\n [-18, 18, 6, -23, -14, 25, 11, -26, 19, -2, -26, 5],\n [15, 22, -8, -10, 25, 12, 14, -15, -7, -5, 18, 4],\n [7, -4, 17, -8, 22, -25, -25, 11, 12, 10, -15, 1],\n [-16, 15, 22, 2, -6, 2, 2, 13, 15, -15, -25, 13],\n [11, 6, 18, 19, -17, 14, -16, -11, -19, 20, 26, 19],\n [-23, 17, 1, -10, -9, 26, -22, -19, 26, -22, 8, -4],\n [-5, 21, 26, -25, 9, -24, 1, 17, -4, -18, -8, -4],\n [-14, 19, -18, -22, 13, 3, -4, 6, -6, 21, -14, 15],\n [14, 21, 14, -15, -5, -23, -18, 4, 23, 21, -25, 19],\n [9, -16, 2, 9, 7, 20, 23, -18, -15, -6, -22, -20],\n [17, 10, 24, -24, -12, -8, 22, -24, -7, -12, 11, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-13, -23, 8, -19, -6, 8, -23, 9, -13, 17, -24, -7],\n [-19, 24, -13, -26, -7, -13, 24, 1, 12, 18, -18, -4],\n [-11, 21, 0, 13, -19, 1, -9, 7, -25, -3, -17, 22],\n [13, -19, -22, -24, 6, 3, 25, 12, -20, 18, -6, 11],\n [-14, -2, -25, -25, -25, -12, -12, -9, -22, -1, 3, -13],\n [-22, 13, -6, 16, -19, -21, -1, -23, 25, 3, 8, 0],\n [0, 17, 16, -22, 13, -16, 16, 25, 8, -16, 11, 11],\n [23, -22, 10, 24, 10, -1, 6, 6, -4, -20, 5, -18],\n [-11, -18, 17, 16, 1, -4, -15, 15, -18, 18, -15, -18],\n [-8, 9, 6, -14, -25, 13, 17, -2, -14, -14, 6, 0],\n [13, 10, -8, -5, 25, -10, 24, -25, -15, 6, 1, -1],\n [-2, 1, 4, 17, 4, 0, 24, 17, -26, 8, 6, -26]]\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[[-18, 6, 17, 26, 10, 20, -12, -12, 22, 2, 14, -6],\n [19, -9, -11, 2, 14, 0, -12, 25, 26, 20, -18, 1],\n [-25, -6, -16, 5, -5, 8, 15, 14, -11, 4, -17, 13],\n [9, -6, -19, 20, 15, 17, 20, 6, 13, -5, 3, -4],\n [25, -12, 20, 16, -1, -11, -17, 9, 1, 15, -1, 4],\n [-9, -10, 21, 25, 5, 12, 24, 24, -22, 15, 2, 9],\n [12, 23, -16, 6, -23, 21, 6, -26, -6, -10, 7, 2],\n [-24, 22, -3, 7, -25, 4, 13, -20, 24, 2, 26, 24],\n [-16, 16, 26, -2, -8, -16, 18, 8, 6, -22, 8, -24],\n [4, -15, -23, 5, 23, 23, -3, 24, 9, -25, -22, -15],\n [-2, 14, -3, -2, 17, 18, 18, -9, 24, -7, 6, 2],\n [2, -5, -15, 7, -23, -22, 25, -17, -5, -2, -26, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550", "dataset": "MATH"}
{"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, 13, 4, 26, -10, -15, -22, 11, 21, 12, 24, -18],\n [24, -10, 2, 24, 15, -10, 19, -13, -7, 20, 0, 24],\n [12, 21, -7, -4, -18, 26, 24, 22, -8, 5, 25, -15],\n [-25, 9, -6, 13, 16, -16, 1, -15, -22, 23, -12, 5],\n [-10, 14, 9, -13, 14, -18, -10, 17, -20, 5, 17, 17],\n [-21, -11, -25, -17, -23, -22, 10, 12, -1, 3, -25, 24],\n [-9, -20, 19, 20, -4, -7, -12, 25, 1, 19, -24, -24],\n [-15, 7, 9, -19, -18, 8, -3, -3, 8, -16, -21, -2],\n [-26, -18, -15, -14, 2, 19, 5, 4, -1, 13, -3, -12],\n [15, 24, -21, 2, 4, -11, -17, 18, 13, -23, 2, -19],\n [13, -16, -26, 16, 10, -4, 3, -12, 2, -3, -18, 16],\n [-16, -12, 17, 19, 11, 21, -1, 18, 10, -3, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, 2, 5, -15, 14, -10, -2, 26, -13, -2, 0, -14],\n [10, -17, -18, -14, -20, -13, 9, 13, -22, -14, -7, 1],\n [24, 25, -12, 12, -6, -10, -21, 19, 19, -2, -17, -13],\n [-8, 25, -16, 5, -17, 20, 7, 24, 17, 26, 2, 2],\n [-5, 23, -13, -25, -15, -5, -26, 23, -15, -15, -23, -10],\n [26, 21, -8, -26, 25, -10, 7, 16, -20, 6, -21, 25],\n [-21, 5, 1, 10, 2, 16, 3, -5, -22, 2, -25, -17],\n [19, -7, 25, 26, -9, 18, 8, 26, 9, 24, -9, -15],\n [23, 19, -2, 9, 15, 14, 26, -7, 21, -16, -7, 6],\n [-17, -2, -17, -3, 14, 6, 7, -12, 13, -3, -12, 22],\n [-17, -22, -5, 10, 4, -4, -16, -17, 8, -5, 14, -5],\n [10, 0, -26, -22, -16, 6, -11, 13, 3, 1, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-26, -19, -23, 24, 9, -9, -8, 9, -18, -1, -25, -24],\n [1, 18, -7, -8, -8, 14, 10, -12, 14, -21, 15, -26],\n [-14, 22, 19, -24, 18, -19, -4, 1, 6, 7, 7, -2],\n [14, -26, 16, -20, 26, 11, 1, -10, 11, 21, 3, -26],\n [1, 9, -9, -25, 6, -20, 21, 18, 23, 12, -9, -20],\n [-23, -10, -8, -22, 12, 11, 10, -14, -15, 10, -23, -2],\n [4, 13, -12, 1, -16, 2, -22, 16, 15, -25, -7, -5],\n [13, 0, -6, -7, 5, 9, 21, 19, -24, -19, 3, -23],\n [-20, -3, -18, 7, 8, -18, 12, 25, -12, 22, -15, -23],\n [-10, -18, 4, 3, 26, 11, -9, -6, -10, 8, -10, -10],\n [-2, -14, -3, -12, -6, -15, -13, 20, 19, 1, -2, 1],\n [4, 9, -11, 13, 2, -16, -1, 0, 3, 26, 10, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[25, -17, 5, -22, -18, -1, 8, -22, -11, -14, 3, -16],\n [3, 22, -6, -23, -10, 6, 4, -21, 6, 25, 12, 16],\n [15, 23, 0, -2, 15, -8, -25, -26, -13, 17, -12, 24],\n [-5, -10, 23, 14, 5, 6, -26, 14, -8, 11, 24, 23],\n [8, -23, -16, 22, -24, -25, 9, -4, -16, 8, 2, -20],\n [-8, -21, -2, -11, -4, 26, -16, 6, -19, 9, 23, -2],\n [8, -14, -21, 8, 19, 12, 23, -23, 18, 16, 15, -11],\n [-16, -3, -13, 13, -19, 3, 4, -21, -3, -26, 11, 19],\n [-6, -21, -12, 5, -9, 20, 5, -15, -16, 7, -25, 17],\n [-5, -6, -21, -21, -15, -23, -20, -15, 3, -18, -20, 21],\n [20, -5, 0, 8, 11, -3, -13, 13, 9, -14, 10, 25],\n [23, -16, 5, -22, -10, -25, 5, -4, -22, 13, 11, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "585", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -25, 13, -20, 13, 23, -5, -20, 20, -18, 19, 18],\n [8, 11, -3, 9, 26, -9, 16, -1, 12, -12, -5, -2],\n [16, 24, -2, 14, -2, 11, -2, -20, 13, 17, -3, -8],\n [-5, 19, -4, -7, -7, -20, 7, -16, 16, -19, 11, -16],\n [16, -2, 4, 10, -1, -17, 6, -20, 9, 18, -7, -12],\n [-11, 8, -6, 8, 13, 21, 7, 12, -26, -18, 14, 3],\n [-6, -9, -5, 17, -1, -15, 4, 10, 16, 9, 21, 17],\n [-25, 10, 13, -11, 23, -4, 8, -21, 9, -5, -16, 7],\n [-6, -14, 18, -9, 18, 17, 3, 14, -3, -26, 10, 1],\n [-23, -23, -13, -16, -4, 19, -15, 21, 20, 15, -23, -26],\n [24, 13, -17, -20, -25, -4, 7, 24, -15, 24, -15, 18],\n [-11, -19, 15, -21, -12, 22, -16, 24, 3, -17, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-18, -18, 23, -21, -11, -15, -25, -10, -1, -18, -22, 1],\n [3, -10, 20, 12, -8, -21, -23, 17, 24, 11, -13, -11],\n [10, 5, 4, -22, -10, -23, 16, -3, -21, 3, 17, -16],\n [0, -18, -3, -7, -14, 1, 20, 4, 5, 8, 10, -8],\n [20, -20, -24, 13, 3, 4, 18, 21, 13, -18, 7, -5],\n [0, 25, 0, 6, 25, 18, 18, 16, 15, 25, -21, 21],\n [0, 5, 11, -5, 25, 26, -14, 5, 0, 17, 13, 3],\n [8, -14, -26, 15, 0, -5, 20, 16, 21, -3, 26, -4],\n [26, 8, -18, 0, -20, -3, -11, -4, -20, 13, -5, 2],\n [-7, 10, -21, 4, 0, 14, 10, -18, -2, 15, 11, 6],\n [-14, 10, 0, -8, -11, 20, -13, 19, -23, 12, -5, 20],\n [10, -26, 24, -6, 23, 3, 0, 19, 7, 2, -23, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -15, 6, 19, -3, 11, -26, 7, -10, 13, 23, -5],\n [22, 21, 0, -12, -12, -4, -15, 0, 22, 23, 13, -18],\n [20, 18, 2, 10, -6, -26, 26, -15, -26, 0, -3, -3],\n [22, 7, 12, 8, 23, 19, -17, -3, 0, -20, -13, 8],\n [16, -12, 24, 17, 5, 10, -18, 12, 20, 6, 6, 11],\n [5, -6, -22, 16, -16, 2, 19, -19, 0, 19, 14, 16],\n [16, 25, 26, 21, -15, -20, 8, 17, -21, -8, 9, 15],\n [13, 15, -11, -16, 9, 1, 18, 25, -4, 8, 8, -10],\n [12, 16, -23, 21, -20, 21, -9, 26, 17, -4, 1, 14],\n [15, 9, 11, -8, 23, 17, 23, -6, 8, 23, -25, 24],\n [-10, -16, -14, 14, 1, -10, 18, 26, -3, 18, 7, 22],\n [10, -13, 22, -21, 14, 17, -5, -7, -4, 17, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[12, 23, -4, -7, 10, 16, 19, 12, 16, 7, -10, -12],\n [-6, -26, 18, 11, 7, 2, -25, -7, 15, 23, 17, 24],\n [-14, -19, -4, 21, -16, -4, 25, 9, 1, -10, -19, -26],\n [2, 25, -24, -14, 6, -4, -4, 7, -1, -22, -19, -10],\n [-2, -4, 1, 7, -19, 16, -8, -14, -1, 12, 24, -21],\n [-14, 22, 25, -4, 9, 16, -10, -26, 16, 24, -14, 1],\n [-13, 21, -13, -20, 10, 14, 16, -9, 14, -18, 11, -7],\n [-6, 11, 9, -2, 16, -25, 17, 3, -19, -2, 3, 3],\n [-14, 4, 5, 9, 14, 2, 21, 7, -8, -1, -22, -7],\n [-13, 16, 2, -24, -7, -2, 14, -22, 2, 23, 14, 14],\n [-25, -21, 9, -26, 4, 0, 18, 10, 19, 19, -8, -26],\n [4, -9, -20, 22, 5, 8, 5, -26, 6, -15, 18, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-23, -12, 5, -3, -4, -2, 22, -1, -6, -21, -5, 18],\n [12, 10, -16, 10, 3, 4, 6, 18, -15, 0, -13, 26],\n [-26, 18, 23, 22, -19, -19, 13, 2, -1, -1, 22, -7],\n [17, 16, 22, 25, -20, 5, 15, 22, -9, -5, 2, 5],\n [22, -7, 4, 16, 14, -19, 16, 9, 24, -19, -18, -13],\n [19, 6, -12, 3, 3, 13, 4, -22, -8, 21, 15, -16],\n [10, -17, 21, 9, 6, -3, -12, 2, 12, 0, -7, 9],\n [-13, 10, 22, 9, 10, -3, 22, 16, 9, 2, -12, 12],\n [-22, 19, 6, 12, 18, 18, -26, 20, 7, 13, -19, -3],\n [19, -4, 9, -14, 10, 19, -9, -17, -23, -20, 9, -5],\n [16, 16, -15, -3, 20, 10, -19, -7, 16, -9, -2, 23],\n [-4, 11, -9, 24, 19, -16, 12, -13, 21, -5, 18, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-12, -22, 22, -22, 23, 15, -8, 7, 26, -11, -6, 18],\n [5, 26, -8, -3, 8, -9, -13, -5, 12, 3, -15, 22],\n [-15, 3, -24, 13, 5, 0, 1, -9, 26, 26, -2, -12],\n [24, 18, 21, 0, -12, 3, -16, 18, 26, -13, 18, 1],\n [-19, -16, -13, 24, 20, -5, -2, -17, 9, 12, -3, -21],\n [6, -5, -7, -16, 24, 8, 8, -26, 15, -1, -13, 22],\n [-25, 19, -22, 12, -12, -6, 2, 24, -6, 11, 25, 9],\n [-13, 6, -4, -19, -7, 11, 20, 11, 20, -26, 15, -23],\n [-13, -5, -15, -2, 25, 21, 25, -20, -20, 12, -21, -8],\n [20, -4, -17, 17, -19, 9, -20, -24, -19, -14, 4, -14],\n [-1, 21, 21, -25, -24, -12, 22, -25, -10, 11, -16, -22],\n [-21, -24, -4, 5, -23, 20, 2, -10, 4, 8, 21, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 21, 4, 26, -26, 26, -16, -26, -20, 14, -14, -7],\n [-21, 3, 22, 25, -21, 7, 8, -7, 11, 3, 24, 6],\n [-3, 4, -11, 13, -11, 0, 9, -5, -12, 19, -26, 1],\n [6, 9, -12, 4, -21, -23, -7, -23, -17, -20, 0, -21],\n [4, 9, 0, -14, -16, 26, -18, -19, -17, -25, -3, 8],\n [7, 23, -16, 25, -26, -22, 0, -20, 23, 10, 25, 11],\n [-26, 5, -10, -9, -23, 22, -14, -22, -5, -1, -23, -4],\n [-22, -18, -14, -18, -23, -1, -13, -25, 4, 23, 24, -1],\n [-25, 14, 19, 17, 25, 10, -25, 13, 1, -4, -20, 12],\n [13, 25, -5, 9, -26, 7, -23, 14, 8, 26, 4, 6],\n [-22, 16, 16, -16, 5, 20, -26, 16, -21, 1, -10, 23],\n [-16, 14, 0, -15, -14, 4, 8, -2, 3, 9, -6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, 1, 0, -15, -17, -1, 2, 18, -21, -2, -19, -16],\n [-10, 11, 20, -14, 14, -12, -8, -8, -17, 1, 10, -2],\n [-12, 8, -11, 10, 0, -22, -3, -25, 13, 22, 26, 8],\n [26, 6, 15, 5, 5, -11, 18, 11, 18, 17, -4, -1],\n [-22, -20, 7, 23, -17, -5, -6, -8, 25, 15, 12, 18],\n [-2, -14, 16, -8, -20, 4, -25, 17, 18, -23, -26, 25],\n [20, 23, -4, 20, -10, -5, 8, -19, -20, -26, -2, 24],\n [-3, 23, 6, -16, 5, 2, -26, 20, -19, 18, 2, 4],\n [8, -20, 4, 18, 23, 5, 3, -15, 8, -17, -1, -22],\n [-4, -18, 6, 10, 3, 6, -25, 15, -23, -1, 3, 8],\n [-17, 4, -12, -6, -21, -26, -17, -25, -18, -10, -11, -25],\n [-11, 8, 1, 24, -14, -21, -2, 12, -1, 17, 19, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-25, -5, 15, 1, -10, -4, -12, 11, 7, 3, -26, 14],\n [-11, -2, 21, 19, -4, 6, 7, -18, -11, 10, 23, 21],\n [-22, 22, 15, -15, -22, -4, -19, 16, 8, -11, -7, 1],\n [3, -16, 23, -10, -17, -3, 4, -16, 20, -19, 4, 10],\n [10, 6, -18, 19, -24, 22, -14, 25, 1, 25, -3, -17],\n [15, 10, -12, 15, 1, 10, -26, -14, -23, 13, 3, 25],\n [-24, -7, 8, 0, 21, -15, 18, 24, 14, -11, 5, 24],\n [6, -11, 2, 0, 4, 24, -3, 4, -18, 18, 9, -21],\n [3, -1, 13, -20, -19, -16, -24, -23, 6, -7, -22, 7],\n [-13, -14, 22, 18, 26, -3, 3, 13, -16, -18, -14, -14],\n [5, -20, -16, 22, 15, -26, 1, -19, -12, -22, -5, -7],\n [-23, 18, -2, -11, 13, 19, 0, 2, -15, 25, -20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "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, 20, 15, 6, 11, 13, 16, -21, -19, -5, 23, -13],\n [-18, -14, 23, 5, -13, 8, -2, 4, 22, 16, 18, 25],\n [-7, 15, 10, -20, 26, -17, -21, -2, 23, -21, 18, -10],\n [-5, -4, 2, -20, 8, 12, 25, -7, -1, 2, 2, -20],\n [7, -22, -14, -21, 5, 9, 6, 16, 6, -8, 14, -9],\n [-13, -6, 12, 7, 4, -10, -20, -6, -20, -26, -5, -5],\n [-4, 1, 13, 19, 3, 18, -17, -15, 18, -11, -6, -14],\n [20, -23, 10, 3, -1, -13, 10, -2, 12, 0, -13, -25],\n [-25, 6, -25, 7, 26, -2, 18, 10, 0, -1, 25, 20],\n [-5, 25, 20, -20, -14, 21, 24, 1, 18, 1, -3, 8],\n [6, 10, -18, 23, -24, 25, -25, -5, -6, 10, -3, -13],\n [6, -10, -6, -14, 17, 24, 17, 13, -16, -25, 10, 1]]\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[[-24, -12, 19, -3, -19, -21, 5, 14, 24, 8, -14, 1],\n [15, -23, 4, -26, 3, -19, 13, 19, 26, -13, 17, 1],\n [7, 12, -23, -3, 0, 15, -16, -4, 15, 5, 23, 26],\n [-23, -8, -20, 6, -13, -14, -21, -8, -18, 8, 22, 24],\n [21, -1, -23, 21, 1, 0, 24, 17, -20, 25, -18, 7],\n [-19, -17, -26, 23, -19, 18, 12, 19, 12, -10, -9, 7],\n [8, 24, -24, -15, -23, 9, -18, 8, -24, -2, 25, -1],\n [10, 21, 0, 1, -8, -3, 10, 13, 17, 11, -2, 7],\n [-12, -11, -23, -1, 20, 12, 20, -1, 21, 1, 22, 10],\n [11, 9, -17, 6, -19, 11, 15, 9, -6, 18, 23, -7],\n [7, 11, 16, 1, 5, -15, -18, 16, -12, -14, -25, -7],\n [-13, 15, -12, 2, -6, -17, 26, 26, 14, 11, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[17, -10, 17, -23, -13, 13, 5, -9, 7, 5, -13, 9],\n [7, -21, 13, 8, -12, 24, -7, 1, 10, 24, 11, -6],\n [-3, -17, 9, -18, -5, 15, 10, -11, 16, -3, -23, 17],\n [-4, 15, -5, -25, 1, 26, -8, -7, 1, 15, -3, 0],\n [17, -25, -20, -26, -16, 24, 4, 3, -14, -3, -9, -14],\n [-10, 19, 21, 3, -8, -15, -1, -9, -15, 17, 23, 15],\n [-25, -7, -21, -26, -1, -20, 5, 6, -17, 18, 14, -12],\n [4, -3, 2, -9, -20, 7, -13, -7, 2, 10, 15, 4],\n [-8, -4, -20, -21, 8, 2, -14, 12, -2, 7, -8, -23],\n [-3, 6, 16, -25, -25, -13, 23, -16, 7, 11, 1, 12],\n [-5, 15, 6, 11, 25, 4, -13, 11, -18, -3, 2, -22],\n [15, 12, 0, -19, 2, 26, -15, -19, 15, 14, -6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[20, -18, -13, -26, 4, -11, 12, 0, -16, -25, 4, 23],\n [-3, 12, -24, 21, -23, 3, -24, -23, -14, 26, -13, -17],\n [-13, -10, -5, 19, 10, -6, -2, -24, -8, 5, -12, 14],\n [-3, -18, -17, 21, 5, 13, -20, 19, 23, 0, -12, 17],\n [-6, -17, -4, -22, 22, -21, -5, 1, -8, 22, -13, 21],\n [-20, -12, 5, -5, 19, -6, -8, -14, -5, -17, 19, 19],\n [17, -3, -19, -19, 22, 22, 12, 23, -8, 15, -9, 6],\n [21, 10, 2, 5, -19, 5, -15, -5, -7, 18, -1, -10],\n [15, 7, 4, -9, -24, -9, -7, 25, -6, 8, 15, 16],\n [3, 9, -23, -12, 21, -20, 5, 6, -14, -10, 26, 13],\n [11, -21, 23, -23, -12, -19, 7, 24, 3, -4, -18, -3],\n [17, -19, 23, -21, -2, -14, 7, -2, -9, -18, 6, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-13, -21, -9, 16, 12, -1, 9, 9, -16, -9, -12, 3],\n [14, -2, -11, -15, -13, 20, -14, 12, 3, 9, 19, -11],\n [-26, 14, 2, 0, -14, -10, 1, -7, 24, 26, -22, -3],\n [-18, 6, 7, 19, 0, 10, 6, 21, 11, 2, 11, 8],\n [-7, -8, -22, -2, 2, -1, 19, 24, -25, -12, 18, -21],\n [-26, -18, 16, -11, -13, -17, -8, 24, -19, 21, -15, -21],\n [8, -21, -21, 8, 17, -16, 11, 0, -1, 1, -19, -2],\n [-8, -11, 23, -1, 17, -12, 12, -15, -3, -14, -10, -14],\n [-10, 16, -26, -16, -7, 4, 17, 8, 12, -21, 8, 1],\n [24, 26, 25, 14, 17, -26, -11, 22, 18, -15, 1, 26],\n [-12, -19, -23, 4, 19, 3, 8, -21, 11, -6, 3, -11],\n [-19, 0, 6, 16, -15, 16, 18, 15, 25, -4, 19, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, 24, 24, -26, -20, 9, -2, -6, 10, -15, 5, 22],\n [11, -11, -26, 17, -1, -13, -21, 14, 24, -7, -24, 26],\n [16, -15, 6, 22, 23, 18, -26, -8, -25, -4, 18, -19],\n [7, -23, -19, 0, -1, 6, 16, 13, 18, 21, 13, 23],\n [-24, -18, -17, 2, -6, 26, 15, 23, -9, -10, -6, -24],\n [0, 5, 15, 2, 20, 2, -1, -18, 0, -15, -11, 20],\n [-25, 24, 12, 0, -18, 19, -25, 15, -20, -19, 11, -21],\n [-8, -12, 18, 1, 3, 0, -17, 18, 4, -26, 23, 5],\n [-11, -21, -25, 15, -25, -24, -8, -23, 14, 16, -9, -9],\n [20, 19, 18, 19, -6, -6, 12, 3, 14, -10, -22, -22],\n [26, -18, -16, 11, 21, 13, -13, 11, -21, -13, -19, 3],\n [-26, -2, -14, 0, -2, -23, 20, 4, 22, -9, -10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "585", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-15, -24, -12, -21, -22, 4, -19, -17, -24, -15, 1, -15],\n [15, 3, -8, -6, -10, -13, 12, 24, -16, 2, 23, -20],\n [22, -26, 14, -20, -13, -11, 8, -11, -6, -14, -9, 2],\n [-6, -18, 4, 10, 18, -10, 4, -3, 20, 20, -21, 5],\n [4, -9, 21, -18, -24, 10, -20, -1, -14, 7, 16, 2],\n [6, -22, 9, -12, -17, -23, 12, 10, 20, 10, 18, 11],\n [5, -3, -7, 21, 14, 11, 13, -23, 14, -16, -16, -11],\n [14, -26, 6, -20, -24, -20, -26, 6, -20, -23, -9, 26],\n [10, -13, 25, -12, -2, -9, -23, -25, 16, -1, -7, -12],\n [-21, 10, 16, 15, -14, -11, 15, 11, -25, -26, -22, 3],\n [4, 16, 5, -24, -24, 15, -22, 8, -5, 5, -4, 11],\n [15, -19, -23, -21, 0, 18, -8, 15, 17, 17, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[17, -21, -24, 5, 21, -11, 6, -25, 16, -1, 8, 1],\n [16, 22, -16, 19, -3, -11, -2, -4, 12, 8, -2, 14],\n [26, 12, 18, 6, -5, -17, -26, 19, 11, -5, 5, -4],\n [3, -4, 16, 20, -15, -8, -20, 0, -1, -9, 1, -16],\n [-25, -10, 19, 2, 5, 23, -12, -9, 1, 0, 14, 24],\n [20, 6, 17, 23, -17, -3, 7, 16, 0, -7, 14, -2],\n [22, -1, 16, 26, -6, 23, -14, 22, 6, -17, 1, 6],\n [-16, -13, -7, 9, 14, -7, -19, -12, 6, -8, 21, -15],\n [-10, 6, 24, -7, 19, 4, 11, 24, -8, -8, 17, -14],\n [11, 22, -26, -16, 0, 10, 12, -26, -12, -9, 16, -2],\n [-26, -8, 7, -17, -15, 12, 18, -25, 5, 24, -1, -7],\n [-21, -20, -25, -10, -1, 4, 7, -9, 14, 16, -13, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "507", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -26, -7, -25, 16, 19, 10, -26, -17, 23, 24, -22],\n [14, 18, -14, -23, -3, 21, 0, 9, 16, 9, -25, 5],\n [-10, -15, -15, -6, -19, -5, -17, -7, 1, 24, -2, 22],\n [1, -23, 18, -1, -14, -8, 7, 18, -11, 18, -23, -7],\n [14, -1, 17, 11, 3, -21, 11, -14, 9, -10, 0, 8],\n [13, 6, 26, -9, -7, 24, 6, 4, 10, -8, 6, -10],\n [6, 9, -22, 13, 20, 18, 0, -20, -13, -23, 23, -9],\n [7, 22, -11, 0, 11, -7, 19, -8, -26, 17, -4, 21],\n [-18, 1, -7, -11, -14, 6, -24, -12, -11, 3, -2, -13],\n [-26, 6, 10, 2, 10, -19, -26, -3, 23, -26, 19, 16],\n [-17, -9, -6, -17, -5, 24, 18, -18, -18, 13, 18, 12],\n [-6, 4, -25, 24, 26, -3, 6, -16, -26, 22, 24, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-18, -6, 20, -5, 2, 13, -24, 22, -2, -9, -16, 3],\n [-2, -16, 7, -3, 21, 5, -24, 18, -2, 18, -7, -7],\n [24, -10, -7, -9, -13, 7, -11, 5, -19, 15, -11, 12],\n [11, -23, 8, 1, 16, 15, -13, -22, -25, 18, 23, -3],\n [-24, -4, -16, 11, 8, -26, -21, -21, 13, -1, 8, -14],\n [-2, -5, -10, -13, -24, -23, 8, 20, 1, 16, -25, 18],\n [21, 11, 20, -23, 20, 22, -15, 7, 10, 17, 14, 3],\n [-6, 1, 15, 23, -22, 6, 7, 5, 0, -24, 13, 17],\n [15, 24, 17, -23, 9, 9, 14, 25, -24, 23, -26, 12],\n [13, 12, 0, 17, -24, 9, 10, 3, -26, -17, -24, 11],\n [-24, 10, 25, 7, 25, -7, -16, -8, 0, -3, -21, -26],\n [-8, 25, -17, 17, 5, 21, 10, 9, -25, 10, -13, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-14, 23, -10, 0, 2, -14, 22, -2, -3, 21, 9, -4],\n [-1, 21, 9, -21, -11, -17, 12, 0, -25, -17, 21, -19],\n [-18, -14, 25, -19, 0, 19, 15, -6, 14, 7, 2, 3],\n [17, -11, -26, 18, 20, 2, 15, 3, -5, -12, -7, 11],\n [-4, 4, -10, 8, -25, 20, 26, 4, -1, 4, -19, -11],\n [-15, 26, -8, 17, -14, -26, -14, -23, 24, 18, 21, 4],\n [-19, 0, -19, 24, -3, -5, 13, 2, -18, -10, -26, 17],\n [5, -7, -26, -2, 14, 0, -4, -9, 25, 4, 1, 25],\n [15, -6, -15, 10, -3, 24, 12, 22, 6, 24, -10, 6],\n [-11, 24, 0, 14, 26, 1, 9, -20, 7, 19, -26, -23],\n [-1, -7, 24, -14, 8, -17, -19, -9, -10, -22, 3, 4],\n [12, 25, -3, -10, 26, 7, 16, 8, -12, -16, 7, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-12, 9, 10, -4, 12, -1, 7, -16, -15, -19, 19, -19],\n [14, -22, 18, -17, -24, 16, 10, -5, -2, -23, 10, -19],\n [3, -18, -12, -26, 24, 17, -14, -23, -11, 17, 20, -26],\n [-13, 0, -1, 20, 5, 13, -25, -11, 1, 22, -1, -16],\n [-4, 3, 25, 4, -25, -7, 2, -17, -9, 4, -23, 0],\n [-9, 17, 4, -20, -8, 12, -25, -13, 9, 16, 19, 1],\n [11, -24, 2, 0, 21, 25, 21, -24, 21, 3, -9, -19],\n [-17, -5, -3, -24, -13, 20, -3, 0, 7, 4, 21, 0],\n [18, 2, 2, 20, 19, 23, 21, -15, -13, 0, 20, -25],\n [10, 18, -9, -14, -18, 2, -17, -7, 10, 2, -21, 14],\n [-1, -5, 16, 20, 11, -1, -10, -26, 4, -18, -1, 23],\n [26, -21, 19, -25, 15, 0, -26, 3, -9, 7, -6, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[20, 5, 16, 7, 20, 26, -13, -22, 9, 5, -18, 18],\n [8, -2, -16, 19, 14, -14, 3, 7, 5, 3, -9, 12],\n [-24, -20, 12, 7, -19, 16, 21, 5, 13, -13, -22, -20],\n [-17, -7, -6, 1, 2, -21, 11, 15, 14, -24, 10, -10],\n [6, -17, 10, 6, 1, -4, 15, 19, 21, 23, 24, 19],\n [-17, -19, -11, 16, 5, 22, 18, -2, 10, -12, -11, 15],\n [-10, 0, 20, -1, -19, 14, 14, -16, 0, -18, -16, -20],\n [1, 3, 9, 24, -18, 8, 24, -14, 21, -23, -17, -1],\n [-24, 23, 26, 16, -10, 22, 0, -5, 17, 9, -19, 6],\n [-1, 4, 26, -16, 2, 2, 11, 10, -12, 24, -12, -20],\n [22, 26, 2, 6, 19, 24, -11, 7, -6, -20, 17, 2],\n [-18, 22, -20, -13, 3, -3, 24, 7, -19, -26, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "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, -12, -12, 24, 7, -22, -5, -15, 18, 4, 2, -5],\n [21, -19, 10, 1, -6, -16, -16, -4, 15, -14, 16, 0],\n [-4, 24, 6, 26, -1, 16, 9, 6, 26, 11, -11, -17],\n [16, 21, 14, 17, 25, -10, 25, 16, -4, -26, 2, -2],\n [-21, -17, 13, -13, -4, -8, 26, 4, 12, 12, 11, -8],\n [16, -26, 11, -14, 23, 7, -10, 5, 22, 7, 6, 17],\n [1, 17, 2, 10, -3, 21, -11, -14, -1, -20, 17, -13],\n [25, 5, 14, -16, 5, -16, -7, 25, 7, 20, 23, -5],\n [-4, 2, -15, 12, 4, 2, 4, -15, 8, 15, 14, 0],\n [-12, 3, -20, 9, 19, -3, -9, -3, 5, -15, 1, -16],\n [-24, 10, -24, 2, 5, 11, 4, -26, 10, -6, 19, 14],\n [15, -7, -16, -17, -24, 21, -13, 18, 18, 4, 8, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-18, -21, 2, 25, 19, 26, 25, -5, 22, 19, -24, -25],\n [1, 10, -22, -18, 5, -10, -16, 11, 8, 20, -9, 9],\n [-8, -2, 19, 13, 4, -4, 24, -13, 0, 8, -14, 9],\n [-3, 6, 22, -20, -18, 23, -6, 5, -25, 17, -2, -26],\n [-16, -11, -4, -12, 0, -11, 19, 6, 12, -19, 21, -26],\n [-8, -1, 10, 26, 20, -24, -3, -5, -26, 12, -18, 6],\n [-4, 7, 22, 22, 8, 22, -17, 5, -25, -20, -3, -24],\n [-15, 12, 15, 9, 0, -26, 19, 9, 5, 0, 17, 4],\n [6, 19, 5, -23, 26, -2, 12, 2, -18, -13, 23, -22],\n [25, -10, 5, -21, -22, 2, 1, -17, -4, 22, 26, -8],\n [-23, 19, 5, -7, 19, 1, 9, -4, -24, -3, -25, -9],\n [22, 5, 21, 19, 21, 21, 3, 11, 0, 11, 11, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-26, 25, -26, 23, 13, -19, -10, -26, -13, 16, 17, -14],\n [3, -14, -24, -5, 8, -13, 13, 18, -5, 6, -15, -3],\n [-22, -18, -25, 4, 19, 2, 2, 9, 3, -5, -6, 14],\n [22, -15, -20, -2, -19, 6, -11, 13, 18, 24, 18, -17],\n [-15, -5, -20, 18, -6, 13, 11, -5, -18, -7, -14, 24],\n [-3, 3, 14, 25, 23, -9, -2, 26, -7, -16, 13, 7],\n [-4, -1, -4, 22, 15, 20, 6, -2, 7, -1, 12, -22],\n [2, 3, 18, 0, 10, 26, -2, 16, -17, 17, 7, -15],\n [2, 12, -8, -8, 2, -25, -1, 18, 10, 21, 24, 7],\n [3, -15, -7, 6, -18, -25, 1, 7, -6, -8, -13, -10],\n [-22, -6, -5, 13, -7, 1, 5, 18, -8, 1, -4, 6],\n [-9, 8, 19, 10, 15, 9, 17, -8, -1, 9, 16, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "502", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-20, -4, -22, 26, -4, 9, 5, -12, 0, -10, -7, -11],\n [21, 15, 1, 4, -11, -13, 20, -17, -25, 6, 14, -5],\n [-25, -20, 25, 14, 18, 17, 3, 11, 12, -8, 20, 11],\n [-10, 10, -17, -12, -22, 23, 11, 16, 8, -23, 8, -26],\n [-10, -6, 19, -5, -22, 19, 9, 11, -18, -7, 19, 15],\n [18, -13, -7, -1, -23, 24, 12, -7, 15, 25, -16, -20],\n [17, 4, 23, -19, -4, 21, -12, -26, 20, -17, 14, -3],\n [-12, 22, 21, -6, -5, -3, -17, -4, -11, -22, 6, 9],\n [-2, 13, -1, -25, 7, 4, 13, 17, 18, -8, 10, -9],\n [23, -24, -20, -4, 10, -26, 23, -20, -5, -24, -8, 3],\n [-18, 8, 8, -14, -1, 18, 24, 1, -2, 12, -24, -16],\n [3, 26, 6, 7, 14, -24, -22, 4, -23, -19, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[11, -3, 4, 22, 25, 22, 19, -2, 11, 5, 22, -1],\n [9, 0, -4, -7, 19, 0, 26, -10, -13, -24, 13, 0],\n [18, -13, 1, 17, -2, 13, -16, 25, -15, 6, -7, 7],\n [-4, -8, 9, 17, -26, -17, -26, -22, -5, 16, -25, -18],\n [17, -20, 21, -6, -20, -18, 13, -18, 24, 22, -15, 17],\n [9, -18, -17, 22, -17, 17, -10, 11, -23, -11, 22, 21],\n [9, 0, -21, 13, -18, 5, 11, 3, -13, 18, 23, 2],\n [1, -5, 4, -10, -10, 22, -12, 20, 5, 1, -16, 12],\n [-10, -15, 24, 24, 12, 25, -18, -2, -1, -23, -8, -14],\n [2, 20, -18, 15, 13, -20, -20, -6, -18, 23, 18, 0],\n [21, -6, -22, -22, -19, -12, -14, 6, 17, 20, 5, 9],\n [22, 26, -4, 7, -9, -15, -4, -25, 17, 0, 23, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[21, -5, -22, -10, 16, -20, -9, -25, 4, 1, -24, -18],\n [6, 1, 1, -9, -12, -16, -2, -22, 14, 19, 0, -15],\n [-17, -18, 26, -25, -18, 20, 24, -11, -26, -6, 23, 10],\n [12, -26, 22, 20, 13, -13, 13, 21, 17, 5, -3, 12],\n [10, 6, 3, -1, 16, 17, -13, -15, 17, -24, -20, -6],\n [0, -17, -17, 9, -10, 15, 7, -9, -1, -25, -18, 18],\n [-22, -1, 25, 14, -12, -2, -1, 1, -4, -6, -5, -8],\n [23, -17, 15, 9, 4, 4, 8, 25, -16, -10, 6, -5],\n [16, -1, 9, 21, -25, 5, -24, 11, 23, -4, 23, -26],\n [-22, 17, 10, -26, -9, 25, -22, -9, 8, 5, -1, 6],\n [15, -3, 0, -8, -9, -12, 0, -16, -3, -24, 12, -20],\n [-15, 6, -5, 8, -13, -1, -8, -6, 14, 18, 4, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, -10, 5, 24, -23, -17, 3, 10, 24, -18, -1, -5],\n [-6, 21, -4, -15, 4, -10, 13, 18, -6, 20, 14, 6],\n [-12, 5, 8, -12, 2, -16, 2, 14, 24, -5, -1, -9],\n [-2, -6, -3, 23, 1, 26, -24, -14, 11, -21, -16, -4],\n [-18, 22, -10, -18, -8, 8, 5, 1, 1, 19, -12, -8],\n [6, -4, 1, -23, 20, 20, 4, 8, -22, 6, 21, 5],\n [21, 21, -12, 10, 7, 13, 20, -18, 14, 8, 20, -3],\n [-9, -10, -26, -16, 6, -21, 2, 17, -7, -9, -13, 18],\n [16, -7, -9, 26, 0, -9, -10, -2, -22, -21, 13, 9],\n [6, -12, 12, -11, 11, 12, -3, -6, 11, -14, 2, 7],\n [-22, -24, -6, -18, -24, 17, 3, -24, 22, 20, 22, 12],\n [14, 23, 7, -10, 26, -13, 22, -16, -26, -26, 25, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-25, -15, 18, 15, -25, -4, 7, -10, 14, -13, -16, -7],\n [17, -20, -26, 21, -12, 18, 11, 7, -18, -26, -18, 15],\n [-25, -5, -2, 24, -13, 8, -11, -8, 14, 4, -25, 5],\n [9, -16, -19, 21, -22, 7, 5, 20, -21, -19, 7, -23],\n [9, 17, -2, -1, 6, -18, 20, -19, -10, -12, 15, -14],\n [16, 21, 20, 23, 17, -24, 26, -15, 2, -26, 5, 10],\n [-7, -19, 10, 4, 4, -2, 23, 13, 18, 22, -19, 3],\n [3, 0, 8, 23, 17, -14, -6, -18, -3, 21, 6, -26],\n [-19, -24, -13, -13, 22, 6, -23, 11, -2, 20, 26, -14],\n [14, 26, 12, -2, 11, -18, 11, 16, 11, 8, 26, 2],\n [23, -13, 11, 7, -2, 15, 1, 24, 3, 12, 10, 20],\n [15, -25, -6, 7, -8, 13, 11, 4, -1, -15, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[21, 4, 21, -12, -17, 9, 13, -1, -18, 26, -10, -21],\n [-5, -11, -5, 26, 12, 25, -23, -23, -18, -13, 15, 24],\n [-1, -24, 5, -16, 24, -24, -14, 17, -14, -3, -7, -17],\n [-4, 25, 15, 6, 8, -13, 26, -11, 3, -8, 6, 14],\n [-25, 23, 11, 22, -19, -7, -24, -6, -26, -6, 23, -19],\n [-25, -4, 14, 26, -16, -11, -18, 22, 5, 20, 12, 9],\n [-4, 20, 22, 3, -17, 4, 17, -1, 21, 12, 15, 3],\n [-25, 2, 5, 17, 24, 11, -6, 0, 25, -3, 7, -4],\n [25, -13, 12, -22, 26, -18, 18, 20, 10, -19, -20, 3],\n [-15, -7, 2, -15, -7, -5, 19, -4, 21, 18, -1, 18],\n [20, 16, 1, 13, -18, -22, -25, 15, 1, -14, -12, 26],\n [-13, 16, 19, 12, -13, -24, -17, 26, 11, -21, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "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, 16, -7, 22, 17, -24, -23, -16, 14, 4, 2, 11],\n [-7, -3, -4, -5, -5, 14, -7, 19, 11, 21, 23, 14],\n [-20, -3, 23, 17, 10, 19, -2, -13, 2, -24, 12, 2],\n [-11, -6, -5, -6, -5, -18, -4, 22, -18, 23, 19, 5],\n [9, 20, 9, -22, -1, -23, -3, 14, 16, -13, 0, -15],\n [-9, 17, -18, -25, 24, 11, 5, -14, 20, -3, -25, 21],\n [11, 19, -8, 20, -9, 17, -25, -1, 25, -3, 21, 0],\n [26, 25, 2, 20, -19, 26, 4, 7, -13, -23, 16, 22],\n [2, 12, 6, -6, 14, 22, -26, 0, -25, 24, 16, -17],\n [-17, 3, -26, 4, 8, 21, 2, -14, -18, 13, 16, 14],\n [-16, -3, -2, -14, -13, 14, -24, -21, 19, -14, -26, 2],\n [-13, -15, -1, -4, -24, -13, 7, -4, -17, -23, 12, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-17, -3, 7, -3, -2, 25, -12, -15, -26, 15, -18, -13],\n [14, 4, -3, 26, 25, -17, 15, 16, -9, -24, -15, 8],\n [17, -4, -5, -16, 19, 22, -4, -15, 2, -2, -3, 26],\n [-23, 10, 2, -24, 4, -2, 20, 10, -4, 22, -5, 2],\n [9, 24, -14, -24, 19, -5, 22, 26, 9, -17, -18, -8],\n [-19, 6, -7, 3, 8, 4, -8, 23, 19, -13, -17, -24],\n [7, 24, 1, -8, 12, -1, -23, -15, -1, -20, -24, -1],\n [-25, -15, 5, 24, 11, -16, 5, 18, -12, -21, -1, -19],\n [-19, 11, -19, -10, 12, -8, -24, 14, 22, -18, 26, 19],\n [6, 5, 5, -21, 22, 22, 26, 2, 10, -10, 23, -8],\n [4, -8, -4, 23, 20, 8, -13, -26, 22, 6, 22, 9],\n [-26, -7, -5, 8, -24, -15, 16, 10, -14, -15, -25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-26, 14, 8, -3, 25, 11, -1, -16, 25, 25, 16, -12],\n [-21, 13, -18, 23, -21, -10, -4, 4, -11, 24, -5, -11],\n [18, -15, -18, -21, -23, 11, -10, -17, 13, 8, 20, -6],\n [26, -8, 0, -16, -21, 14, 16, 1, -24, 14, 18, -3],\n [10, -14, -12, -18, 12, 8, 18, -9, 16, 26, -24, 1],\n [-11, 15, 14, 20, 16, -4, 5, -17, 11, 11, -14, -12],\n [1, -14, 8, -25, -26, 14, 5, 3, -5, -23, 26, 19],\n [-3, -13, -10, -13, 13, 12, 14, 25, 0, -6, 13, 8],\n [-1, 4, 6, 22, -16, -11, -21, 7, 14, 5, -6, 2],\n [-16, -22, 0, 1, 4, 23, -16, -14, 16, -21, 0, 3],\n [26, 21, -8, -13, -18, 18, 1, 1, 19, -2, -1, -23],\n [-24, 7, -6, -10, 11, 7, 17, -15, -2, -6, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-21, -7, 26, -7, 5, 4, -7, 24, 3, -24, -7, -19],\n [-6, 21, -4, -26, -25, -17, 10, 3, 24, 17, -3, 5],\n [23, 3, 11, -13, -24, -2, 18, -20, -10, 14, 0, 11],\n [11, -4, 5, -25, -16, 7, 25, 20, 7, -20, -17, -2],\n [-25, 22, 3, -10, 2, -9, 19, 8, -10, 20, -5, 24],\n [-2, -7, -11, -2, -12, 10, -12, -12, -9, 10, -26, 6],\n [-24, 22, -5, -6, 19, 14, 0, -23, 24, 8, -26, -23],\n [-3, 19, 2, -5, -4, -6, -13, -19, -11, 8, -3, -1],\n [-20, -2, 11, 18, -1, -1, 3, -25, 16, 26, -18, 12],\n [17, -16, -12, -15, 8, 23, 13, 20, -11, 22, 5, -9],\n [26, 18, -6, -11, -20, -22, 17, 14, 6, 4, -6, -24],\n [-17, -16, -5, -10, 23, -2, 14, 1, 23, -7, 3, 4]]\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[[-14, -17, 24, 6, 14, -7, 21, -13, -19, -19, 11, 1],\n [-17, 13, -13, 24, -13, -21, 7, -10, -6, 12, 1, 11],\n [-12, 9, 9, -18, 17, 8, 18, -9, -10, -9, -23, 21],\n [-7, -14, -16, 24, 16, 6, 1, -19, 16, -7, -9, -20],\n [17, 6, 24, -16, 26, 3, 8, 18, -7, 10, -17, 3],\n [-9, -2, 5, 12, 7, 17, 12, 4, 1, -1, 17, -23],\n [16, -7, -19, -25, 23, 23, 0, 7, 9, -6, -19, -4],\n [16, -19, -22, 13, -26, -6, 17, 16, -17, -25, -6, -14],\n [17, 23, 1, 3, -9, 15, -25, -8, -6, -1, 19, -2],\n [-8, -2, 14, -7, -21, -9, 22, -9, -7, 12, 7, -17],\n [6, 24, -8, -25, 20, 22, -24, 3, 12, -8, -6, 17],\n [-13, 4, -6, -10, 26, 24, -3, 10, 13, 14, 7, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "507", "dataset": "MATH"}
{"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, -11, 22, 15, -15, 14, -3, -14, 7, 0, 11, -6],\n [26, -24, 22, -13, 16, 11, 10, 14, 15, 17, 3, 18],\n [-17, -26, 12, 1, 18, -8, 3, -7, 25, -7, -4, 4],\n [5, 20, 25, -1, -13, -21, 6, -19, -23, -14, 8, 2],\n [-2, 7, -16, 11, 2, 18, -5, 7, 19, -16, 1, -19],\n [-3, -17, -12, 18, 12, 12, -6, 9, 9, 23, 21, -7],\n [-14, -25, 20, 0, -20, 14, -1, 3, -8, 13, -6, -1],\n [-17, 9, 17, 0, -19, -1, -26, -4, -18, 4, -20, -18],\n [-20, 1, 7, 26, 25, -11, -17, -3, -17, 19, 2, -2],\n [14, 3, 24, -8, 26, 4, 3, 7, 1, 25, -8, -16],\n [1, -21, -10, 10, 0, 16, 9, -26, -11, -23, 20, -4],\n [5, -24, 17, -6, -3, -12, -16, -24, -8, 16, -19, 24]]\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 sum of all singular values:\n[[7, 7, 17, 13, 11, -1, -24, 5, 16, 21, 16, -17],\n [-17, 22, -16, -13, 4, -18, 21, -21, 22, 8, 7, 16],\n [-9, -4, 3, -24, -12, 10, 16, -24, -12, -24, 2, 4],\n [-20, -20, -16, 21, 1, 9, 16, 19, 13, -2, -10, 23],\n [11, -6, 25, -7, -17, -21, -15, -10, 18, 6, 9, 21],\n [-8, -22, 18, 15, 2, 10, 21, 3, -26, -15, -12, -22],\n [11, -16, -7, 2, -13, -1, 7, -17, 0, 17, 14, 14],\n [-2, -17, 12, 5, 7, -4, 6, 5, -5, -5, 26, -4],\n [-8, -4, -5, 3, -8, -5, -26, 7, -1, -23, 21, 18],\n [-15, 1, 10, -24, 1, 2, -7, -25, 10, -26, 19, 20],\n [9, 17, 15, -9, -18, 10, -2, 14, -8, -2, 25, 22],\n [-12, 19, 23, -1, 19, -7, -24, -2, -6, 7, 25, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[11, -3, 14, -2, -26, 2, 5, 20, -26, 8, -11, 5],\n [20, -12, -22, -17, -5, 16, -19, -12, -7, -2, -15, -1],\n [-23, -1, -17, 21, -12, -22, 5, 5, -5, -5, -15, -16],\n [-3, 16, 18, 14, -11, -11, -26, 24, -4, 1, 5, 24],\n [26, 9, 10, -24, 24, -14, 1, 1, 18, -3, 24, -14],\n [-3, -22, -10, 23, -15, 22, -9, 6, 4, 7, 3, 18],\n [5, -17, 4, 8, -12, 0, 0, -26, -15, -23, -4, 7],\n [25, -4, 24, -8, -7, -7, 2, -14, 1, -3, -5, -5],\n [13, -16, -19, 5, -3, -15, 22, 13, -6, -24, 12, 18],\n [-9, 15, -21, 9, 18, -12, 22, 18, -12, 11, 24, 17],\n [25, 25, -3, -20, -18, -16, -11, -20, -2, -13, -26, -7],\n [1, 22, 11, 7, -18, 21, -7, 16, 25, 11, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"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, -14, 17, 20, -2, -5, 11, 25, -7, 5, -11, 26],\n [-7, 14, -5, 15, 11, 18, 10, -12, -15, -18, 10, 17],\n [-12, 17, -5, -15, 0, -8, 20, -2, -17, 8, 17, -15],\n [23, -19, -16, 12, -8, -4, -3, -12, -7, -2, -13, -17],\n [21, 23, 2, 20, 22, 22, -15, 6, -4, -13, -4, 22],\n [26, 10, -5, 2, 9, -25, -7, -22, 0, -24, -9, -14],\n [-5, -14, -15, 5, 9, -20, -21, 13, 10, -21, -2, 0],\n [-22, -8, -18, 23, 13, -26, 19, -18, 12, -17, 22, 16],\n [22, -13, 19, 13, -2, 23, -8, 23, -10, -9, 19, 13],\n [23, -18, -26, -21, 11, 11, 12, -10, -18, -16, 26, -9],\n [18, 19, 10, -20, 8, 17, -20, 12, -16, -17, 7, -3],\n [-15, -18, -5, 11, 19, 5, -19, 21, -6, -11, 6, 15]]\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[[-2, 24, 12, -21, -23, -4, -18, 9, -16, 8, -15, 8],\n [-20, 2, -6, -24, -3, 3, 0, 2, 3, 9, -4, 10],\n [-1, 23, 9, 1, 10, 24, -23, 2, 17, -13, 17, 18],\n [10, 6, 24, 4, -13, -2, -18, -2, 14, 19, -2, 3],\n [-7, -4, -26, -12, -6, 3, -16, 23, -1, 25, 3, -18],\n [-22, 20, 20, 7, 6, 7, -26, 24, -12, 4, -15, -20],\n [18, 6, 15, 5, 24, -22, 11, -22, -10, -20, -2, -2],\n [-24, 25, 9, 1, -4, -19, 4, -6, 18, 8, 14, 14],\n [15, 23, 2, -24, 17, -2, -25, 17, 14, 7, -12, 12],\n [12, 13, 20, -15, 25, 25, -3, -21, -21, 21, 10, -1],\n [-24, 5, 19, -9, 1, 6, -10, 5, -15, 10, -6, -25],\n [-1, 12, -10, 25, 9, 7, -8, 5, 23, -5, 23, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[12, -9, 24, -3, -26, 14, -25, 13, -3, 13, 25, -25],\n [0, -25, -4, 6, 7, 5, -24, 0, -15, -19, -7, 25],\n [-10, 18, 6, -16, -18, 7, 17, 16, -20, -11, 0, -12],\n [-3, 10, 22, 13, -8, 26, -4, 12, 4, 3, -20, 18],\n [23, 23, -24, 11, 21, 3, -17, 7, -14, 12, -14, -2],\n [14, 7, 13, 13, 13, 7, -12, -24, 25, 19, -5, 7],\n [-22, 14, -5, 2, -19, 7, -23, 25, -2, 23, -4, -2],\n [7, 17, -21, 7, -6, 17, 3, -24, -12, -6, -8, -8],\n [22, 19, 7, -13, -23, 4, 19, -16, 17, 18, -16, 22],\n [-23, -11, 11, -21, -9, 26, -2, -3, 25, 12, 20, -18],\n [10, 7, 7, 13, 13, 10, 1, 23, 21, -16, -13, -1],\n [-19, 1, -7, -2, -17, -16, -1, -4, -8, -9, 23, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, 13, -12, -11, -7, -8, -16, -20, -8, -3, 4, 25],\n [21, -19, 23, -3, -19, -14, -17, -8, 23, -4, 15, 6],\n [3, 3, 2, 10, 8, -18, -19, 21, -2, 15, 24, 19],\n [10, 11, -19, -1, -16, 13, -4, 5, 18, -26, 22, 21],\n [-18, 13, 1, 6, 5, -19, 10, -9, -20, -9, 21, -15],\n [-23, -14, -16, -11, 17, -13, -11, 25, 26, -5, -9, 13],\n [-2, 8, -20, -7, 0, 2, -17, -16, -7, 6, 16, 10],\n [-14, -11, -16, -22, 11, -24, -25, 26, 11, -17, -21, -6],\n [4, 7, 22, 5, 2, -26, 6, 11, -10, 7, 22, -11],\n [-20, 9, -14, -7, -23, -22, -11, -18, 16, -15, -13, -12],\n [-22, 15, -9, -19, -19, -2, -23, 24, -1, -16, -21, 6],\n [-5, 2, -22, -26, -5, 8, 4, -24, -24, -20, -26, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 25, 10, 3, 5, 5, -6, 21, -11, -23, -10, -14],\n [8, 13, 7, -16, 9, -2, 13, 3, -14, -3, 9, 7],\n [-19, -9, -20, 22, 19, -5, -20, -14, -25, 17, -25, 2],\n [0, 13, -9, -25, 26, -23, 22, 19, -19, 9, 21, -18],\n [-9, 23, -5, 18, -16, 0, 5, -25, -25, 3, -5, -5],\n [-3, 0, -16, -14, 0, -12, 21, 21, 22, -10, 12, -18],\n [-4, -23, -12, 16, 4, -21, -1, -26, -5, 3, -5, 6],\n [-22, 9, 19, -17, -26, 26, -15, 22, -24, -17, -26, -8],\n [-9, 18, 25, 4, 22, -5, -23, 14, -17, -17, -12, -22],\n [23, 16, 18, -10, -9, 21, 23, -22, -19, 19, 0, -2],\n [25, -1, 18, -4, 14, -4, 2, 6, -9, -20, 5, 14],\n [-20, -19, 23, -6, 15, -10, 24, 6, 3, -25, 19, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, 22, -2, 22, -19, 6, 2, -10, 13, 18, -25],\n [22, 12, 21, 22, 4, -23, 15, -1, -18, 4, -17, 24],\n [-21, 17, -1, -16, -12, -7, -13, 17, 24, -6, 17, 0],\n [3, -20, 10, -12, -11, 16, -7, 22, 11, -7, -5, -21],\n [17, 25, 13, -7, -22, 26, -16, -25, 3, -19, 13, -19],\n [-10, 12, 8, 3, -26, -22, -11, 9, -12, 22, -10, -14],\n [-3, 16, 21, -23, 20, 17, 19, -14, -18, -1, 20, -11],\n [15, 10, 16, -21, -16, -25, 3, -8, -4, 20, -15, 12],\n [-21, 16, 9, 19, 15, -12, 9, -14, -19, -2, -3, 4],\n [13, -14, 2, 5, 16, 10, -9, -1, -9, 7, 4, -12],\n [10, -7, 1, -23, -19, -9, 5, 26, -4, -12, 17, -20],\n [21, 4, 5, 13, -13, -8, 23, 13, -11, -18, -26, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "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, 12, 5, -19, -14, -24, -25, 18, 1, -23, -4, 7],\n [-20, 3, -18, -8, -18, -4, -16, -14, 2, 4, -19, 19],\n [-8, -22, 21, 0, 12, -13, -5, -5, -22, 25, -11, 12],\n [-1, 26, -11, -15, -11, 22, 13, -15, 5, -22, 9, 1],\n [24, 17, -23, 12, 12, 2, -8, -2, 8, -3, -8, -4],\n [4, -8, 5, -14, 19, -9, -20, 18, -3, 19, -10, -12],\n [-18, 7, 8, -19, 23, -16, -3, 15, 3, -6, 16, 8],\n [-15, -18, -15, 1, 2, 19, 18, 13, 8, 2, 24, -21],\n [-11, 19, 1, -26, 2, 25, 13, -21, 0, 10, -5, -20],\n [-26, -14, 21, 24, 17, -13, -12, -15, 22, 14, -23, 23],\n [17, 16, -6, -25, 25, -6, -13, 17, -25, -16, 10, -13],\n [20, -7, 8, 0, 22, -21, -20, 18, -26, -14, 11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[11, 9, 11, -26, -26, -8, 24, 3, -14, -20, 16, -7],\n [17, -18, -14, 12, -7, -2, -22, 21, 25, 23, -2, -15],\n [-1, -5, -26, -19, 9, 22, -24, -5, 23, 13, -6, -6],\n [4, -26, 14, 0, -25, 2, 15, 19, -26, 15, -19, 8],\n [18, 8, -20, -4, -4, 16, 19, 12, -8, -12, -19, 6],\n [8, 13, -14, 23, 4, -20, -7, 11, -19, 9, -13, 3],\n [24, -18, -14, -15, -25, 11, -6, 2, -7, 23, -18, -12],\n [26, 6, 26, -20, -24, -4, -5, 12, -14, -18, 7, -15],\n [7, 18, 6, 23, 8, 1, 12, -24, 20, -15, 16, -14],\n [-24, -9, 20, -1, -17, 25, -23, 10, -15, 26, 24, -11],\n [-10, 13, 4, -1, -25, 2, 3, 21, 20, -16, 10, 7],\n [-20, 12, 2, 6, 22, 0, -11, -10, -16, -13, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 25, -2, 13, 17, 16, -15, 20, 26, -23, 15, 21],\n [14, 22, 0, 18, -19, -19, 2, -24, -6, 4, -14, 4],\n [-10, 21, 5, -3, -25, 15, -24, -1, -25, 6, 7, -1],\n [7, 11, -13, 4, -7, -17, -7, 6, 18, 21, -25, 19],\n [24, -15, -11, -18, -16, -6, -15, -23, -1, -8, 15, 20],\n [-10, 17, -26, 21, -19, 3, 24, 14, -3, 16, -10, 3],\n [14, 25, 16, -18, -25, -1, 5, 0, 14, -16, -26, 25],\n [10, -9, -19, 0, -9, -18, -25, -10, -16, 19, -21, -22],\n [-15, 17, 15, 8, 24, -3, 3, 25, -10, 20, 9, -21],\n [5, 7, 17, -11, -20, 5, -10, 5, -13, -1, -18, -14],\n [23, -2, -15, 18, -11, 22, 3, 25, -6, -3, 16, -22],\n [20, 6, 22, 4, 23, -18, 22, 8, -19, -16, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "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, 0, -13, -5, 22, -20, -16, -10, -14, 24, -10, -16],\n [-23, -11, 4, -6, 6, -14, 22, 2, -12, -17, 6, -12],\n [16, -14, 8, -6, 3, 21, 19, 16, 15, 18, -20, 22],\n [-3, -11, -22, -21, -25, -24, 26, -17, -3, 21, 6, -7],\n [26, -5, 5, 3, -24, -23, 24, -23, 12, 4, -18, 3],\n [26, 2, -2, 25, 12, 8, -2, 10, 9, -16, -1, 15],\n [19, -2, -6, 22, -25, -17, 12, 8, 6, 14, 4, -23],\n [-24, -22, -10, 22, -14, -26, 18, 12, 17, -4, 14, 26],\n [23, -2, 25, 26, 4, -14, -26, 7, 2, 4, -19, -25],\n [-15, 6, 3, 14, 0, -2, 11, 23, 6, 11, 25, -11],\n [5, -3, -25, -25, -7, 0, -5, 12, 21, -8, -20, -24],\n [23, 7, 14, -4, -22, 16, -24, -3, 0, 7, 24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -15, 5, 20, 22, -5, 7, -4, -26, -23, -10, -1],\n [4, 12, 10, 13, 6, 1, -17, 9, 19, -18, -1, 22],\n [19, 24, 7, -13, 14, -1, 10, 4, 20, 11, 21, 16],\n [1, 14, 17, 13, -10, -15, 0, -26, 13, 6, -14, -22],\n [25, 10, 13, 16, 1, -3, -7, 13, 15, 10, -7, -4],\n [-24, -22, -12, 19, 26, -22, 7, 12, 12, 19, -4, 20],\n [-10, -18, -23, 3, 21, -13, 3, 4, -26, 0, -25, 18],\n [13, 14, -17, -3, -7, 15, -11, 14, 11, 17, 22, 15],\n [16, 14, -9, 8, 3, 10, -22, 10, -16, -23, 10, 24],\n [-16, -15, 22, 20, 1, -1, 7, -26, -21, 6, 20, -3],\n [7, -19, -11, -11, -11, 25, 24, 7, -7, -13, -1, -25],\n [-8, -25, 23, -1, -2, 22, -8, 19, 22, 21, 24, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -15, -6, 9, 13, 1, 6, 19, -18, -9, -3, 5],\n [-4, -15, 7, -1, -21, -22, -4, 23, 19, -12, 5, -14],\n [14, 1, 24, 6, -19, -11, 12, 5, -11, 18, -14, -7],\n [-8, -16, 0, -11, -18, -14, -8, 3, 15, 12, -10, 3],\n [2, 15, -25, 23, 21, -24, -7, -26, -22, 6, 12, -4],\n [-9, -23, 14, 6, -1, -5, 3, -1, -26, -21, -10, 4],\n [21, 24, -23, -17, 21, 26, 12, 7, -5, 25, -5, -20],\n [12, 10, -12, -8, -17, 10, 10, 23, -23, 19, 23, 14],\n [-2, 1, 22, 17, -9, 21, 8, -8, 15, 26, -7, 12],\n [6, -26, 20, -26, 14, 19, 18, -8, 21, 22, -18, -13],\n [-24, 3, 14, 25, -26, -22, -4, -21, -7, 19, 15, -19],\n [4, -12, -1, 6, 21, 25, 12, 5, -26, -22, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[15, 26, -22, -19, -21, -17, 19, 13, 11, 14, 20, -11],\n [1, -26, 19, 25, -9, 12, 17, 15, 20, 12, 10, -16],\n [-24, 2, -23, 4, -16, 3, -12, -12, 5, 2, 22, 16],\n [1, -6, 11, 12, -16, 5, 0, -3, 10, -26, 5, 26],\n [-26, 18, 7, -9, 2, -21, 4, -13, -16, -22, -5, 24],\n [-14, -15, 14, -23, 11, -23, 3, -26, 22, 4, 22, 15],\n [23, -4, -13, 8, -10, 5, 9, -4, 7, 20, 11, 14],\n [12, -5, 15, -25, -7, -13, 11, 10, 10, 25, -15, 1],\n [-19, 2, -6, 12, 21, -9, 21, -8, -17, -18, -4, 3],\n [-5, 2, -21, 23, 8, -13, -22, 19, -9, 8, 3, -20],\n [7, 11, 15, 26, -8, 18, -16, 14, -10, -16, 18, 1],\n [-24, -17, -3, 6, -1, -22, -3, 17, -1, -20, -15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[17, 9, -10, -11, 4, -9, 5, -25, 22, -17, 21, 12],\n [-13, 25, 20, -17, 1, -3, 13, 7, 22, 14, -18, 20],\n [2, 18, 14, 9, -18, 14, 20, -16, -6, -14, 22, -3],\n [-26, 8, 8, -6, 20, -22, -6, -23, 6, 9, -19, 2],\n [26, -20, -26, -22, -14, -1, -15, -19, 26, 22, 7, -5],\n [23, -18, -18, 18, -9, -10, -20, 12, 24, 7, -11, 1],\n [-2, -5, 7, -12, -11, -11, 11, -5, 2, 5, 16, -3],\n [14, 23, -4, 11, -4, -2, -1, 9, 23, 7, -14, 6],\n [14, 19, -23, 26, 9, -7, 2, -12, -12, -14, -13, -5],\n [-26, -26, 4, 6, 20, -26, 11, -3, 12, -5, -4, -25],\n [-5, -18, -23, 23, -2, -12, -3, 13, -20, -19, 0, 0],\n [18, 8, 11, 3, 12, 2, -22, -9, -12, -1, -25, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -2, 5, -5, 25, -17, 9, -15, -6, -12, -16, 19],\n [-20, -3, 3, -13, 13, 19, -21, 23, 19, -19, 9, -15],\n [-22, -14, -8, -5, -15, 5, 23, 11, 11, -10, -1, -11],\n [-15, 10, 19, -11, -22, -19, -20, 0, -1, -14, 8, 19],\n [-10, -20, -18, 15, -17, 18, 15, 11, 26, -13, 10, -14],\n [-19, 14, 25, -17, 6, 10, -7, -23, -26, 24, -8, -3],\n [20, -16, -5, 10, -24, -10, 21, 13, -7, 8, 17, 13],\n [-12, -16, -14, -1, -4, 13, -14, 21, 23, -11, 18, -13],\n [13, 25, 7, 25, 13, 2, 1, 0, 11, -14, -24, 12],\n [11, -22, -11, 4, -5, -24, -22, -24, -12, 7, -12, 0],\n [-14, 7, -9, -17, 5, -23, -25, 3, 25, 4, 19, -24],\n [17, -22, 7, -13, 10, -20, -12, -8, -8, -10, 21, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "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, -6, 16, -26, -9, -3, 3, -20, 0, 25, 0, -24],\n [25, 26, -11, -23, 18, -26, 6, 17, 18, -1, 12, -24],\n [-23, 6, 23, -22, 2, 25, -16, -24, -9, 3, -10, 19],\n [3, 3, 6, -10, 12, -11, 6, 20, -25, -25, -3, -22],\n [9, -24, 13, 5, -13, 11, 16, -22, 10, 19, -1, -10],\n [-8, -16, -20, -14, 24, -2, 23, 21, -15, 4, 1, -12],\n [6, -16, 12, 5, -11, -18, 25, 14, -15, -8, -13, -15],\n [-3, -18, -6, -15, 18, 10, -22, -18, 24, -7, -21, 13],\n [23, -14, -11, -7, -22, 16, -10, -17, 3, -20, -16, -19],\n [24, 10, 4, 21, -26, -2, 1, -4, 24, 2, -5, -17],\n [19, -10, -14, -11, 24, -15, 21, 22, -12, 12, -8, -6],\n [5, -22, 20, -12, 5, -26, -12, 8, -7, 4, -7, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 13, 25, -17, -13, 8, 2, -18, 25, -17, 26, -25],\n [-4, -9, -26, -16, 10, 9, 6, 9, -3, -2, -4, -5],\n [6, 20, -8, 7, -4, 19, -1, -5, -24, -23, 6, -16],\n [-7, 23, 5, 26, 21, -12, -2, -10, -5, 7, 6, -2],\n [-13, 19, 23, 3, -5, -5, -8, 11, -23, -19, 18, 25],\n [12, -17, 23, 1, -6, -26, 10, 7, -16, -11, 12, -13],\n [-26, 4, 17, 16, 22, -15, 0, -10, 23, -11, -26, 3],\n [10, -4, 0, 10, -11, -3, 1, 3, -1, -3, 4, -2],\n [24, -25, -20, 21, -4, 2, 8, 3, 2, 4, 23, 15],\n [-25, 24, -12, -11, -19, 1, 13, -10, 26, -13, -6, 23],\n [0, -6, 5, -11, 1, 11, 2, 22, 24, 9, -3, -6],\n [12, 23, -19, 1, -9, -8, -8, 11, 17, -1, -21, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "519", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[22, -1, 1, 17, 5, 7, 18, 10, -2, -5, 4, -21],\n [4, -26, 13, -18, -15, -6, 15, -24, 15, 19, -22, 10],\n [-14, 2, 1, 22, -2, -17, 7, -12, 3, -14, 10, 22],\n [-22, -13, -17, 20, 7, 4, 24, -22, -21, -14, 13, -14],\n [19, 21, 6, 10, -4, -6, -19, 7, 26, 4, 4, -7],\n [8, -25, -3, -16, -23, -1, -13, 19, 15, -7, 9, -2],\n [12, -17, 8, -22, -23, 22, -7, -4, 16, -22, 2, 17],\n [2, 19, 5, -5, 18, 16, 17, -20, 6, -5, 14, 1],\n [-6, 24, 9, -23, 16, -21, -8, 24, 26, -16, 23, -10],\n [19, -9, 19, -14, 14, 24, -16, 24, 0, 22, -11, 23],\n [-12, -13, -12, -9, -15, -1, 15, 13, -9, -1, 19, -9],\n [-26, -11, 10, -6, -19, 25, -25, -8, 2, 3, -24, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[8, -9, -1, -2, -19, -9, -3, -22, -1, -17, -16, -23],\n [-17, 10, -15, -17, -15, -22, 16, 0, 6, 5, -22, -4],\n [-3, 19, -25, 3, -17, -26, -14, 9, -24, 17, 17, -11],\n [-13, 13, 18, 21, 20, 19, -22, -2, 11, 2, -10, -18],\n [-9, -15, 18, 22, 12, 1, 26, 5, -7, 13, -26, -15],\n [-5, 24, -19, -15, 11, 26, -3, 11, 12, 14, 1, -15],\n [4, 11, 11, 1, -18, -5, -20, -23, 2, 26, 18, -17],\n [15, -6, -23, -3, -6, -9, -1, -19, -4, 20, -18, -2],\n [9, 5, -20, 6, 4, -10, 8, -5, 2, 26, 24, -9],\n [20, -17, -12, -20, 11, -13, -1, -9, -9, -21, 18, 16],\n [-2, 14, -15, 24, 3, -8, -6, -11, 8, -20, 15, -8],\n [11, -1, 14, -9, -15, -22, -1, -22, 11, -9, -21, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-16, -11, -1, 12, 22, -9, 9, 10, -1, 6, -26, 0],\n [10, -5, -8, -14, 10, 23, -24, 0, 8, -18, -7, -1],\n [19, 8, -6, 5, -5, -13, 2, 4, -10, -4, 9, -2],\n [-9, -11, -25, -1, 7, -15, 21, -17, 2, -25, -11, 9],\n [15, 22, 9, -5, -21, 8, 14, 10, 4, 14, 18, -25],\n [8, 1, -20, -6, 17, -2, -9, 14, 18, 16, -14, -19],\n [26, 20, -13, -10, -14, -16, -17, -10, 2, 17, -25, -26],\n [20, 0, -8, -9, 8, -18, -2, -5, -14, 16, 2, 24],\n [-5, -11, -8, -19, -15, 26, -25, -22, -13, -11, 24, 7],\n [15, -17, -19, 17, -2, 24, 0, -17, 9, 12, -20, -12],\n [23, -14, 6, 8, -25, 13, -16, -6, -13, -2, -4, 17],\n [-26, -21, 9, 22, -9, 22, 15, 10, -22, 25, -26, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-26, 21, -13, 1, 4, -4, 15, 4, -20, -7, -7, 4],\n [-18, -16, -21, 16, 19, -9, 2, -26, 17, 6, -24, 11],\n [18, 10, 14, -11, 11, 8, -1, 9, -6, 9, -8, -18],\n [0, 4, -12, 5, 2, -18, 17, 10, -10, 22, -13, 12],\n [24, 13, -21, 11, 5, -21, 24, 24, 26, 5, 22, 7],\n [7, -15, -18, -22, -10, 1, 23, -5, -21, 23, 5, -8],\n [25, 21, 18, -10, -17, -12, 23, 12, 11, 21, -6, 13],\n [-24, 3, -12, 0, 4, -11, 1, 18, 13, 10, 16, -18],\n [-18, -15, 1, -20, 8, 9, 20, 11, -26, 7, -5, 3],\n [-7, 24, -19, 18, -20, -25, 3, -15, 9, 15, 11, 0],\n [7, 11, -16, -7, 3, 16, 5, -1, -4, 14, -3, -25],\n [14, 5, 26, 21, -12, -21, -11, -16, 18, 19, -18, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-20, 25, 25, 3, -5, -23, -22, -5, -23, 13, -23, 16],\n [18, -12, -11, 15, -7, -17, 6, 4, 11, 17, -26, -2],\n [10, -9, -2, -12, -23, 8, -23, 15, -7, -15, 3, 14],\n [-5, 9, 7, 0, -2, 12, -15, -15, -6, 23, 6, -20],\n [-8, -3, 18, -7, -22, 3, 24, -20, -7, 20, -10, 26],\n [7, -20, -16, -9, 3, -7, -25, -20, 0, -12, -8, 7],\n [-25, 1, -25, -16, -21, -4, 19, -17, 6, -8, -16, -3],\n [1, 18, -15, 1, -22, -8, -19, 17, 10, 1, 17, 16],\n [-22, -19, 21, -3, -7, 8, -21, -22, -17, 26, 1, -15],\n [26, -12, -24, -4, 26, 25, 9, -20, -26, -19, 0, 22],\n [-5, 25, 4, 16, 12, -16, 16, -6, 26, -12, 1, 11],\n [-4, 0, -8, 18, -11, -15, 24, -4, 24, -20, 23, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[19, 3, -11, 23, 5, 14, -6, -23, -20, 0, 16, -21],\n [-7, 17, 17, -15, -13, 15, 7, 25, 17, -10, 13, -7],\n [-25, -6, -15, -14, -26, -9, -13, 4, -3, -15, 25, -2],\n [9, -13, -9, -3, -1, 3, -23, 13, 2, -9, -23, 6],\n [11, 18, -25, 24, -15, -5, -1, -13, -18, -17, -20, 14],\n [20, -7, -12, 16, 23, 7, 25, 24, -3, -25, -7, -14],\n [-2, 9, -24, 20, -15, 6, 1, -16, -10, 13, -13, 4],\n [-22, 20, -25, 12, -14, -7, -16, -13, 15, -23, 25, 20],\n [-24, -16, 25, 23, -2, -4, -10, 26, 4, -13, 20, -9],\n [-24, 18, 8, 12, -8, -4, 4, -3, 23, -10, 0, -18],\n [5, -13, -5, 13, -13, 10, 25, -13, 1, 17, 13, 6],\n [21, -5, 13, 10, 8, 18, 1, 10, -24, -5, 19, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[26, 12, -4, -21, -13, -5, 9, -7, 24, 15, -4, -14],\n [17, 19, 18, 24, -18, 21, 14, -21, 19, 1, -20, -8],\n [4, 8, 2, 20, 17, 6, 16, -5, -24, 22, -14, 13],\n [-14, 13, 13, -14, -15, -22, -14, -15, 24, -17, -12, -25],\n [11, -11, 6, 7, -2, 20, -1, 21, 13, -13, 15, -12],\n [8, 11, 4, 7, -18, -20, 24, 11, -26, -4, -13, -2],\n [26, -19, 13, -21, -12, 24, -7, -10, 5, -21, 12, 1],\n [-17, -18, 10, 7, -14, -16, -16, 3, 1, -4, -12, 19],\n [26, -16, -14, 1, 23, -20, 4, 22, 16, -5, 11, -13],\n [-21, 19, 4, 24, -24, -10, -7, -20, -10, 15, 23, -1],\n [23, 26, 0, -14, 13, -22, -26, -10, 10, -11, -9, 1],\n [-24, -9, 14, 26, 3, 5, -13, -10, -8, 20, -19, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 2, 20, 22, -16, -15, -13, -20, -24, 5, -16, -25],\n [-10, 15, -4, 6, -5, 18, -13, 22, 15, -7, 20, 26],\n [-10, 18, -19, -20, 22, 10, 9, 22, -23, 3, 25, 25],\n [-6, 16, 15, 0, -24, 4, -11, -14, -20, -16, 24, 26],\n [7, 15, -16, 5, 18, 25, 6, 2, 23, 4, 0, 12],\n [12, -25, -19, 16, 22, 20, -15, -7, 13, -22, 13, -14],\n [19, 19, -26, 6, -18, 12, 14, 7, -19, 6, 9, -15],\n [9, -8, 12, -6, 6, 16, -23, -23, 17, 22, -16, -1],\n [-22, 3, -25, -3, 14, -11, -9, -15, -1, -15, -1, -23],\n [23, 0, 26, -4, -6, 21, 10, 7, 18, -16, -24, -21],\n [-13, -21, -14, 2, 6, -10, -16, -25, 7, 4, -11, 17],\n [14, 10, -5, 19, 8, -20, 23, 26, -12, -23, -3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "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, 23, -11, -26, 7, 7, -11, 5, 13, 6, -12, -10],\n [-10, 8, 26, 2, -15, 10, -14, -6, 12, -26, 22, -14],\n [16, 22, -3, -3, -14, 9, -22, -13, -11, -21, -25, 18],\n [23, -23, -11, 9, 21, -6, -10, -24, -3, -21, -8, 7],\n [-5, 19, -24, 12, -4, -16, 5, 20, 3, 23, 9, -24],\n [21, 13, 13, 9, -11, 5, 9, 11, -5, 11, 23, -15],\n [13, -13, -20, -25, 13, -16, 22, -17, 12, -21, -18, -8],\n [-2, -22, -22, -24, -23, -15, -1, -21, 26, -17, 0, 13],\n [-4, 22, 11, 3, 10, 15, -2, 17, -13, -24, 25, -23],\n [9, -2, -19, -2, 9, 3, 24, -12, 18, 10, 20, 23],\n [-22, -9, 5, 15, 23, -20, 15, -23, 14, 18, 4, -11],\n [18, -24, 20, 22, -24, -24, 2, -8, -23, 8, 26, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[24, -1, 11, 22, -23, 22, 7, 24, -6, 14, -2, -24],\n [18, -9, -2, 5, -7, -12, -25, 26, 3, -15, 12, 16],\n [20, -20, -5, -19, -4, -4, -15, -21, -13, 1, -22, -23],\n [-2, 0, -23, 2, 14, 20, 23, 0, -20, 5, -7, 21],\n [16, 9, 3, 2, 1, 13, -24, 0, -6, 10, 8, -7],\n [-18, 8, -17, 22, 26, -6, 16, 14, 16, -3, 12, -26],\n [19, 16, 4, 19, -4, -9, 0, 14, 17, 19, -15, 8],\n [14, -11, -6, 0, 9, 26, -14, 23, -19, -19, -11, -4],\n [18, 7, -3, -6, -14, 23, 24, -23, 2, -23, -6, 7],\n [-18, -2, 14, -6, -23, -11, -2, 13, -20, 18, -22, 13],\n [-6, 7, 21, -5, 0, 23, -17, 14, -12, -24, 20, -14],\n [-1, -26, 20, -18, 12, -1, -9, -19, -12, 19, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[19, -23, -6, -11, 19, -2, -4, -10, 5, 21, -25, -26],\n [20, -18, 18, -1, 22, 8, -21, 14, -18, -7, 22, -1],\n [14, 7, 20, -17, 15, 3, -23, 12, 7, -18, -22, 15],\n [-18, -2, 13, -24, -2, 24, -9, 19, -16, -4, 7, 26],\n [7, 20, -3, 23, 21, -25, -14, -7, -20, -18, 24, 7],\n [-26, 26, -19, 24, 26, 14, -26, -2, 22, 2, 25, -10],\n [-20, 8, -11, -6, -25, -1, -22, -22, -18, 20, 26, 21],\n [-9, -8, -21, 0, 22, 4, -6, -13, -11, -25, -9, -9],\n [8, -13, -9, -8, -2, 8, -20, -24, 11, -15, -11, -7],\n [-22, 4, -3, 16, 18, 17, -3, -11, 20, 12, 1, -22],\n [-14, -12, 14, 22, -23, -13, 0, -17, -4, 10, 1, 17],\n [-14, 9, 5, 18, 10, -26, -23, -26, -9, -14, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-12, 14, 14, -17, 26, 8, -23, -22, 17, 11, 11, -3],\n [-3, 13, -8, -7, 25, 1, 16, -16, -4, -12, -6, 9],\n [-14, 5, -17, 19, 10, 5, 22, -7, 12, 20, 24, -11],\n [12, -22, -10, 9, 21, -1, 24, -23, 11, 19, -1, -7],\n [-14, 19, -20, -3, -24, -24, 23, -11, 4, 6, -13, 23],\n [25, 21, -2, 24, -25, 14, -14, -9, -7, -25, -20, -14],\n [-19, -24, -13, -4, -19, 6, 0, -16, 6, -16, 11, 16],\n [-9, 1, 14, -1, 3, 18, -17, 15, -24, 5, 9, -17],\n [-6, 24, 23, -20, 26, -2, 7, -2, -18, -19, 26, 8],\n [17, 1, -17, -13, 2, -26, -8, -13, -7, 11, 21, 9],\n [14, -19, 11, 15, -3, -20, 16, -22, -13, -18, -7, 25],\n [-1, -2, 25, -7, -21, -20, 9, 22, 9, -7, 19, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-19, 0, -22, 4, 19, 14, -6, 25, -24, -1, -10, 3],\n [-4, -2, 23, -23, 14, -16, 14, 11, -9, 6, 9, 11],\n [-9, 22, -11, -5, -6, 23, 17, 4, 4, 0, 25, 14],\n [23, 10, -24, 4, 7, -1, -3, -17, 2, 11, -14, 10],\n [12, 24, -21, -13, 3, 12, 22, -23, 18, 1, 12, -17],\n [-1, 7, 2, -19, 12, -9, -18, -5, -9, 10, 20, 6],\n [21, 18, 21, -25, -1, -10, -23, -18, 25, -17, 22, -22],\n [11, 22, 13, 22, -5, 14, -8, 10, 6, 22, 23, -21],\n [-4, -13, 4, 26, 6, -10, -26, -15, -24, 18, 9, -3],\n [14, 21, -13, 10, 1, 0, -7, -12, 15, -2, 17, -21],\n [24, 19, -13, 12, 15, 3, 20, 20, 23, 1, 4, -18],\n [21, -25, 26, 20, 18, -26, -25, 21, 1, 9, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, 11, -2, 21, -11, 11, 20, 12, -20, 17, 6],\n [7, -10, 22, 13, -23, -14, -1, -14, 5, 16, -15, -13],\n [-6, 6, 14, -24, -20, -12, -20, 16, 21, -1, -1, -15],\n [25, 13, 18, -25, 13, -12, 17, 4, 10, 7, -15, -21],\n [13, 5, 9, -17, -11, -2, 3, 13, 2, 21, -4, 12],\n [17, -20, 22, 20, -13, 10, -25, 10, -22, 11, 19, -5],\n [-21, 18, -20, 23, 9, -22, -1, 1, 20, -4, -25, 13],\n [23, -6, -25, -25, -9, 12, 0, 19, -22, -18, -13, -23],\n [-26, 13, -5, -12, -2, 24, 5, 4, 15, -4, -10, 7],\n [-22, 20, 15, 3, 23, 18, 26, 3, -13, -2, -24, 11],\n [-7, -4, -4, -6, 17, -22, 25, -18, 12, -5, -8, -22],\n [-23, -6, -9, -22, 12, -14, -1, -11, -16, -24, -23, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, 3, 24, 18, -15, 22, -14, -6, 16, 15, -6, 0],\n [-22, -10, -6, -26, -11, 13, -5, -4, -7, 22, -19, 19],\n [22, 14, 11, 26, 3, -25, 5, -8, -14, 15, -3, -17],\n [20, -22, 0, 25, -2, -20, 18, 0, 25, -6, 16, 1],\n [-6, 7, -6, 20, 0, -12, 24, -22, -10, -19, 21, 20],\n [-3, -9, 23, 20, 15, -22, -11, -6, -15, -10, 17, 6],\n [-16, 13, 10, 13, -16, 1, 16, 3, 19, -13, 24, 16],\n [-6, 5, 0, 7, -19, 16, 6, 10, -6, 20, 24, 2],\n [-11, -23, 17, -2, -22, -8, 16, 12, -21, 3, 1, -14],\n [20, -24, 8, -23, -17, 24, -21, -26, -26, -20, -11, -3],\n [-23, -11, -20, 23, -2, -12, -18, -16, -20, 26, 12, -4],\n [-24, -20, -24, -15, -24, -20, -4, 11, -12, -4, 15, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[14, 22, 26, 2, -8, -3, -4, 1, -10, -18, 26, -10],\n [-26, 13, 24, -18, 13, -21, -12, 20, -21, 26, 20, -9],\n [-3, 11, 23, 23, 3, -8, 1, -4, -3, 25, 0, -14],\n [-16, -12, 3, -21, -2, 4, -16, -23, -12, 21, -3, -13],\n [-3, -4, -22, 20, -1, 3, 15, 11, 21, 21, 24, -24],\n [25, -9, -5, 24, 1, 3, -25, -18, -26, 9, -6, 1],\n [9, 5, -21, -4, -21, -5, 4, -8, -19, -19, -7, -3],\n [-14, 14, 26, 24, -20, 25, -19, 0, 16, -24, -10, -22],\n [11, 20, -18, 24, -21, -19, 17, -1, 21, -7, -1, -24],\n [21, -2, -12, -16, 5, 5, -21, -25, -4, 2, -20, 3],\n [-11, -26, -14, 9, -26, -5, 10, 2, -11, 24, 17, -18],\n [-2, 11, -5, 14, -25, -26, -17, 8, -3, 23, -3, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "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, 19, -17, 11, -7, 25, -15, -4, -4, -18, -23, 2],\n [0, 2, -23, -25, -20, 16, 21, 15, 20, 7, -15, 0],\n [-5, -12, 16, -17, 8, 13, 26, -7, 5, -7, -22, 2],\n [0, -1, -16, 2, 17, -7, 16, -21, -19, 18, 20, -25],\n [0, 11, -7, 3, 2, -25, -12, 6, -16, 13, -3, 14],\n [-12, -22, -18, -23, 0, 15, -23, 10, 24, 26, -14, -6],\n [-16, -15, -13, 18, 9, -14, -22, -6, -18, 6, 17, -10],\n [0, -26, 24, -22, -15, -2, -2, -15, -16, 3, 21, 0],\n [-10, 3, -24, -16, 22, 6, 20, -18, -9, -26, -21, 7],\n [-22, -24, -1, 10, 13, -21, -16, -16, 16, 13, 11, -11],\n [-7, -7, -1, 8, 13, 18, 15, -2, 3, 13, -2, -17],\n [18, 8, 0, -23, -11, 2, 8, -6, 14, 4, -8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[11, 5, -23, -13, -26, 13, -8, 21, 5, -19, -22, -19],\n [22, -21, 8, 26, 25, -16, -14, -2, 24, 2, -7, 8],\n [-1, 24, -7, 12, 16, 14, 20, 17, 17, -21, -10, 23],\n [0, 14, 16, -8, 15, 5, 16, -4, 11, 14, 4, -11],\n [-24, -11, 23, 24, -11, -23, -22, 1, -4, 15, -8, -2],\n [-8, -24, -19, -1, 4, -8, -10, -26, 26, -14, 16, -15],\n [5, -3, 7, -3, 15, -18, 21, -23, 21, -2, 9, -3],\n [-4, 12, -12, -2, 16, -17, -17, -21, 25, -22, 2, -7],\n [-26, -5, 20, -4, -1, -13, 9, -15, -12, 22, -11, -12],\n [-19, 17, 23, -13, -25, -15, -3, -25, -9, -23, 1, -2],\n [14, 13, -20, 18, -15, 17, 18, -8, -23, -25, -3, 18],\n [-16, -3, 12, -18, -20, 2, 8, -3, -24, -26, 6, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547", "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, 7, 16, -17, -12, -16, 13, 6, 5, 11, -7, 5],\n [-19, 24, 26, -10, 19, 9, -25, 21, 25, 7, -16, -13],\n [-9, -17, -4, -3, 17, -16, 14, 1, 0, 21, -19, 10],\n [20, 20, 22, -25, 18, 16, -26, 14, -23, 21, 21, -24],\n [-1, 23, -20, -5, -17, -17, 12, -26, 22, 25, 10, -16],\n [7, -17, -13, 11, -25, 12, -17, 5, 2, 23, -26, 17],\n [-23, 6, 19, -3, 14, -5, -17, 17, -1, -13, -15, -7],\n [7, 8, 18, -5, 11, -10, 1, -4, -11, -4, 10, 23],\n [9, -4, 4, -12, -14, -13, -5, -18, -19, -13, 26, -20],\n [-24, 9, -4, -10, 14, -2, -4, -16, 5, 26, -26, 0],\n [17, 1, 12, -1, -18, 3, -24, 16, 4, 26, -17, 24],\n [5, -26, 19, -19, 12, -17, -3, 17, -8, 26, -20, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -8, 12, 2, -11, 12, 17, -24, -22, -21, -10, -10],\n [9, 15, 5, 13, -13, 5, 16, 11, -14, 20, -4, -15],\n [-5, 3, 26, -5, -17, -15, 9, 1, -4, -3, 1, -19],\n [-7, -24, -20, -4, 8, 6, 24, 19, 8, -5, 7, 9],\n [10, 11, -1, 14, -17, 10, 23, -20, 15, -16, -10, -19],\n [-20, 19, 16, -19, 6, -21, 19, -22, -11, 18, 21, -13],\n [7, 23, 7, -2, -5, -24, 14, -9, -7, -14, 15, 7],\n [-6, 2, 24, -18, 13, -5, 4, 18, 4, -21, 14, 19],\n [-25, -20, -15, 16, 24, -8, 20, -7, -14, 20, -6, 10],\n [-1, 6, 21, -5, -16, -12, 18, 20, -9, 4, 20, 7],\n [2, 14, -10, -9, 5, -17, -18, 25, 25, 0, -1, -6],\n [2, -7, -18, -23, -12, 25, -4, 15, 15, -11, -26, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -23, 1, 13, 22, 8, 8, 17, 13, -6, 10, 0],\n [20, 13, -14, -21, 4, -4, 15, 6, -18, -22, 17, 18],\n [11, 21, 17, -23, 5, -24, 7, 15, -15, 9, 20, 19],\n [5, 4, -14, 22, -5, 0, -22, 15, 15, -1, 22, -8],\n [-4, 17, 1, -25, -24, 20, -14, 9, -6, 19, 18, 12],\n [-13, 11, 1, -22, 18, 11, -10, 13, 12, 19, 8, -9],\n [-6, -2, 4, -12, 20, -8, 24, -14, 5, 4, -13, -2],\n [-8, -4, -8, -10, 17, -11, 5, 4, 24, 26, 18, -17],\n [-19, 22, 18, -25, -2, 0, 17, -3, 23, 24, -3, 21],\n [-7, 5, 7, 2, 25, 11, -13, -3, 8, 26, -8, -19],\n [-19, -21, 15, -16, 22, 16, 24, -14, 0, -3, 1, -24],\n [-21, -25, 6, -11, 0, 14, -6, -26, -9, 22, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-9, -13, 22, -1, -21, -16, -25, -2, -24, 13, 3, -18],\n [3, 15, -6, -5, 18, -15, 15, 26, 3, 19, -21, 0],\n [7, -12, 3, -12, 9, 16, 2, -20, -12, 25, 24, 2],\n [-13, -17, -3, 11, -25, -20, 26, 8, 1, 13, 23, -1],\n [5, -12, 16, -5, -4, -17, -2, 26, 0, 22, -1, -9],\n [-26, -25, 5, 10, 4, 15, -15, -14, 21, 2, -24, -23],\n [-11, -17, -13, 26, 24, 10, -8, 16, 22, 3, 12, -23],\n [20, 9, 21, 5, 0, -4, -8, 7, -16, -8, -4, 19],\n [17, 24, 15, 13, 22, -19, -18, -13, 20, 21, 13, 8],\n [7, -26, 5, -19, -4, 5, 11, 16, 8, 19, -5, 10],\n [0, -6, 25, 2, -14, 26, 10, 10, 15, 18, 15, 13],\n [7, 7, 24, -17, -12, 0, -11, 15, 15, -1, 25, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[24, -23, 7, 14, -16, -24, 12, -2, -2, 11, -26, -15],\n [-9, 14, 10, -14, -9, -12, 20, -21, 12, -14, -15, -17],\n [-1, 0, -5, 6, 16, -11, -26, 23, 16, 14, 19, 16],\n [-26, -16, 14, -5, 2, 7, 15, -24, 4, -14, -16, 23],\n [19, 10, -19, -17, 11, -12, -19, 3, 9, 3, 4, 14],\n [-22, -8, 22, 7, -14, 22, -2, -13, -16, 3, -20, -25],\n [8, 16, -24, 6, 24, 19, 5, -10, 24, 24, 1, -6],\n [24, -8, 6, -16, 6, -4, -20, -19, 3, -20, 20, 21],\n [-5, 0, 13, 15, 9, 18, 9, -8, 0, -21, -11, -3],\n [-3, 3, 12, 18, 8, 26, 23, 22, 8, -7, 9, -16],\n [23, -8, 13, 18, -2, 23, -5, -26, -7, 22, 8, -4],\n [-3, 12, -4, 11, 20, -20, 12, 17, -18, 2, 14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[15, -17, -12, 21, -19, 18, 14, 19, -5, -7, -9, 7],\n [-4, 1, 14, -17, 25, 16, -4, -17, 24, -26, 2, 19],\n [14, -22, 17, 2, 25, 23, 22, -7, -19, -2, -26, 9],\n [17, -11, -22, 23, 23, 24, -14, -26, -19, -26, -7, 12],\n [24, -2, 2, -24, 26, 2, -9, 26, -9, -3, 26, -21],\n [1, 25, -13, -1, -20, -16, -6, -22, 4, 18, 18, 0],\n [6, 7, 23, 9, 19, -22, -1, 21, 25, 8, -7, -13],\n [-22, -15, -14, 21, 0, 0, -11, 24, -23, -14, -9, 18],\n [-15, -8, -10, 15, -20, -6, 19, 12, 26, -26, -13, -24],\n [5, -18, -16, -4, 3, 20, -22, 3, 24, -1, -23, 25],\n [0, 2, 18, 11, -20, -11, -19, -2, -3, 14, 14, 24],\n [24, -6, 16, -11, 14, 20, -16, -19, 8, 19, -21, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "582", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-16, 1, 15, 25, -16, -21, 13, 3, -13, -14, 8, -21],\n [22, 6, -16, -26, 0, 3, 19, -1, 1, 14, 5, -17],\n [-15, 26, 9, 23, 16, -5, -11, -9, -20, 25, 9, -25],\n [-18, 17, 3, 1, 2, -8, 1, 14, -2, 2, -4, -17],\n [14, -22, 26, 6, 21, 14, -22, -23, 10, -23, -2, 5],\n [-13, 0, -1, -19, 3, -14, 5, 26, 16, 26, 26, 2],\n [-4, 1, -13, -17, -20, 24, 22, -1, 9, 25, 0, 1],\n [19, 3, 17, 16, -3, -26, 14, 0, -26, -17, 16, -22],\n [-18, -24, 2, -25, -9, -13, 2, -22, 19, -22, -25, 12],\n [-4, 4, 23, -11, -5, 0, 2, -22, 25, -15, -14, -19],\n [19, -3, 1, 10, 0, 9, -18, -12, 19, -22, 1, -12],\n [9, -9, -5, -22, -5, -10, -5, -6, 19, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-10, -8, -14, 18, 18, 7, 20, 6, 20, -11, 16, 3],\n [-24, 0, -7, 5, -6, 19, 26, -22, 22, -25, -5, -20],\n [15, -17, 25, 13, -26, -11, 14, 1, 21, -7, -1, -12],\n [14, 3, -15, -25, -17, 0, -6, -11, 10, 18, -5, 12],\n [14, -5, 22, -10, -10, -1, 10, 11, 11, 14, 15, 22],\n [-24, 25, -18, -26, -8, -13, 13, 23, 11, -25, -20, 11],\n [16, 1, -17, -2, -5, -16, 13, 18, 11, -17, -9, 20],\n [-22, -16, 0, 26, 0, 9, -14, 20, 1, -25, -20, 5],\n [-21, -8, -12, -4, -3, 19, 21, 25, 1, -3, 26, -5],\n [15, -21, 20, -23, 7, 24, 12, 0, 16, -5, 20, -11],\n [5, -22, 14, 6, 18, 8, -22, -4, 19, 10, 5, 25],\n [-13, 26, 6, 16, -22, 8, 15, 14, 20, 11, -5, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "557", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[13, 7, -23, -25, -18, 3, 10, -8, 24, -18, -22, -11],\n [-1, -20, -25, -13, 4, -5, 6, 13, 22, 4, -8, -21],\n [19, 13, 16, 19, -17, 22, -15, -1, -23, 24, 22, -22],\n [3, -3, 19, 12, 8, -22, -22, -19, 8, -26, -25, -20],\n [-12, -13, -14, 17, 2, 23, -25, -20, -17, -7, -2, -1],\n [15, -21, -23, -19, -14, 10, -19, 13, 2, 0, -18, -13],\n [-16, -2, -4, -17, -20, -14, -5, 14, 13, 22, 19, -9],\n [-18, -5, 26, 20, 21, 25, -18, 15, -13, -15, 13, -10],\n [-10, 24, -3, 23, -14, 22, 9, -9, 26, 3, 15, 15],\n [10, -26, -13, -17, -22, -5, 14, 2, 22, 24, 5, 4],\n [10, 6, 3, 12, 6, -17, 8, 22, 1, 15, -18, 14],\n [-16, 18, 0, 5, 14, -6, -15, -20, -5, 5, -24, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "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, -5, 15, 11, 26, 1, 25, -22, 3, 5, 18, -7],\n [-7, 14, -18, -20, -20, -1, 6, 23, 4, 17, -13, 20],\n [8, 3, 8, -8, -18, -9, -26, -10, -5, -15, -9, -25],\n [-3, 12, -23, -4, -23, -6, 0, -16, -3, 0, 9, 0],\n [1, 20, 7, -25, 14, -1, 18, -12, -3, -8, -20, -10],\n [21, -23, 9, 13, 3, 25, 16, 14, -13, 15, 21, 19],\n [26, -7, 2, 15, 26, -1, -8, -19, 11, -7, -26, -11],\n [-26, 8, -19, -19, -25, 1, 4, 17, -11, -16, 22, -13],\n [10, 6, -19, 14, 7, -14, 16, -11, 9, 12, -6, -10],\n [12, 26, 7, -9, 14, 14, 16, 9, 9, -22, 1, 22],\n [-22, -23, -24, 6, 25, -24, -19, -4, -21, 0, -5, 7],\n [-26, 25, 9, 0, -18, 17, 24, -2, -13, -9, 22, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[22, 0, -18, -15, 24, 20, -9, 22, -13, -17, -7, -5],\n [7, 21, 11, -22, 3, -26, -1, -20, -20, 18, -22, -7],\n [23, 1, -4, -19, 20, -11, 14, 21, -21, -16, -14, -25],\n [22, -25, -14, -8, 6, 10, -2, 21, 11, 19, 13, -9],\n [2, 10, -16, 18, 14, 20, 18, -4, -4, 8, -24, 20],\n [-9, 25, -18, 21, -7, -3, -10, 18, -15, 6, -21, 3],\n [-21, 21, -4, 19, -20, -1, -24, -2, -24, -12, 12, -23],\n [11, 18, -6, 3, -20, -14, 23, 16, -20, -4, 17, -20],\n [-17, -13, -22, -8, 10, 6, 26, -13, -24, -20, 3, 0],\n [9, 11, -16, 16, 9, -11, -10, -8, 8, 11, 21, 18],\n [-25, 12, 0, 24, -26, -25, 26, 22, 25, -12, -26, -21],\n [3, 17, 0, -10, 13, -3, 23, 24, -5, -12, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -11, 20, -13, -23, 25, -3, -14, -22, 13, 6, 18],\n [10, -19, 12, -8, -17, 15, 12, -8, 4, -13, -2, -19],\n [-23, 20, -22, 9, 17, -21, 3, 13, 11, 10, 14, -8],\n [15, 16, -9, -6, 10, 16, -10, 4, -6, -16, -11, -18],\n [24, -4, 12, -4, 25, -24, 22, -21, -7, -12, 19, 3],\n [5, -21, 4, -11, 2, -5, 13, 1, -12, -6, -19, -26],\n [3, -25, -3, 22, -22, -15, -22, 7, -13, -15, 0, -25],\n [22, 9, 18, 11, -24, 9, -19, -25, 14, 15, 2, 18],\n [-2, 22, -23, -17, 17, -10, -26, -24, 11, 3, -22, 17],\n [-16, 26, -18, 20, -13, -8, -14, -6, 12, 16, -25, 3],\n [-4, 0, -26, -20, -25, -4, 4, 24, 2, -13, 16, -22],\n [-16, 19, 14, 6, 2, -21, -20, 18, -17, -7, -18, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "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, 19, -21, -26, -16, 16, -10, 12, -18, -11, 26, 0],\n [14, -22, 11, -19, -18, -14, -24, 0, 23, 10, -7, 6],\n [-14, 25, -3, 23, 15, -3, -7, 0, -9, 1, 9, 6],\n [5, -20, -12, -13, 8, 25, 24, 13, 4, 24, 23, 4],\n [-1, -2, 19, -21, 24, 0, 5, -15, 20, 3, -3, -3],\n [-5, -23, -8, -2, -22, -23, 2, -18, 24, 11, 13, 26],\n [7, -19, -16, 7, 19, 5, 5, 22, -22, 5, -22, 5],\n [-26, -21, 12, -2, 0, 19, -13, 21, -18, 1, 23, -3],\n [-18, 9, 12, 10, 22, 15, 7, -24, -6, 12, 10, 15],\n [9, -25, -10, 24, 14, 2, -2, -6, -8, 2, -24, 12],\n [-15, 17, 24, -1, 12, 4, -19, 8, -22, 0, -1, 0],\n [-14, -4, -26, 23, 1, -12, -14, 13, -22, 12, -1, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-20, 8, 22, -5, 26, -18, -26, -12, 26, 3, -24, -21],\n [4, -22, -23, -2, -16, 16, -13, -2, 22, 25, 0, 2],\n [25, 14, -26, 19, -22, -6, 13, 10, 7, -25, 18, 24],\n [-9, -12, 19, 6, 25, -16, 24, 2, 2, -19, -26, 3],\n [16, 26, -17, -21, 18, -26, -18, 23, 25, 16, -11, -24],\n [15, -25, -19, 3, -9, -24, -21, 18, 24, 19, -14, -12],\n [-5, -8, 23, 17, -19, -13, -4, -2, 6, -26, -26, -10],\n [26, -9, 25, -2, -12, 24, 0, 3, -18, -2, 7, 13],\n [13, 20, -16, -12, 24, 2, 3, -16, -26, -10, -16, 2],\n [19, -15, 3, 17, 0, 9, -12, -18, 4, -2, -12, 7],\n [-11, -4, 6, 2, 5, 5, -11, -12, -6, 1, -13, -6],\n [-3, 8, 11, 16, -20, 4, -5, -2, 19, 15, -23, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "549", "dataset": "MATH"}
{"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, -1, 2, 20, -21, -8, 23, -2, -17, 9, 21, 24],\n [16, -17, -11, -12, 22, 7, 19, 13, -12, -26, -21, 25],\n [-8, 16, -21, 24, -23, -17, 16, 13, -18, -26, 24, -10],\n [14, 1, 22, -15, 19, 14, 12, -11, -13, -21, 20, 3],\n [18, -1, -7, -22, -12, 4, -9, -14, 16, -16, 17, 24],\n [-15, 26, -8, -8, -26, -13, -10, -25, 12, 11, -6, -7],\n [25, -4, 3, -26, -21, -12, -10, 9, -1, -25, 21, 26],\n [18, -16, 16, 21, -17, -23, -8, -1, 12, -9, 17, -5],\n [15, 2, -12, 17, 6, 15, -16, -7, 0, 24, -12, -24],\n [-11, 1, 25, 26, 21, 15, -12, 13, -1, 7, 9, 0],\n [-13, 23, -24, -24, -4, -22, -25, 11, 9, -25, 24, -12],\n [-25, 9, 1, -13, -15, 3, 8, -19, 5, -7, 15, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-12, -13, -1, -2, -8, -7, 24, -1, 5, -4, -13, -5],\n [3, 1, 11, 13, 3, 24, -24, 8, -23, 12, 7, 18],\n [-16, -14, -25, 9, 26, 3, -11, 5, -12, -4, 20, 8],\n [18, -10, -9, 5, -11, -26, -13, -25, -21, -1, 17, -19],\n [-3, 12, 23, 16, 4, -6, -7, -25, 16, 13, -7, 22],\n [-5, -14, -7, 17, 4, -4, -1, 16, 26, 3, 18, -18],\n [12, 15, 26, 5, 17, 13, -15, -15, 0, 19, -1, 16],\n [-13, -13, -16, 7, -19, 12, -12, -23, -26, 8, 26, -21],\n [24, -25, 20, -8, 4, 26, -8, -4, -18, -8, -14, -19],\n [1, 0, 26, 11, 15, -18, -12, 19, 7, -2, -26, -16],\n [-12, -1, 20, 11, 6, 22, 8, 19, 0, 25, -15, -7],\n [-15, 10, -21, -7, -4, -12, 1, 7, -19, -7, -21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "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, -9, -13, -7, 15, 18, 22, -26, -4, 13, -11, 18],\n [12, -8, -19, -3, 26, 17, -11, -14, 23, 3, -14, -6],\n [-8, 0, 11, 17, 11, 24, -4, -11, 19, -3, 17, 23],\n [-11, 22, -11, -16, -1, -11, 14, -12, -9, 13, -9, 8],\n [-22, -25, 3, 4, -2, 16, 4, -8, 7, -9, 12, 21],\n [6, 18, -24, -9, 9, 25, -1, 1, 5, 22, 10, -20],\n [1, 5, 14, 9, -5, -18, -10, -17, 0, -10, 5, 17],\n [15, -16, 18, -2, -10, 0, -12, -22, 16, -14, -21, 15],\n [-7, -24, 1, -24, 6, -25, 10, 2, -13, -20, 17, -23],\n [23, -6, -2, -18, -15, -15, -22, 2, 0, 12, 22, -7],\n [2, -8, 9, 6, -19, 3, 7, 4, -26, 8, -8, 19],\n [-9, 19, -10, 15, 4, -7, 2, 12, 16, -6, -18, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[6, -9, 22, 26, 24, -17, -26, 1, 6, 12, -9, 16],\n [18, -18, 1, -4, -1, 22, 16, 6, -7, -11, -8, 5],\n [-16, 19, 17, 13, 20, -1, -26, 11, -15, -18, 23, -19],\n [4, -7, -8, 5, -22, 4, -5, -7, -15, -8, 10, -25],\n [-23, 3, -4, -6, -22, -20, -15, 14, -16, 19, -13, 12],\n [-24, -4, -24, 9, 12, -3, 14, 6, 5, 3, 9, -24],\n [-21, 5, -21, 16, -23, -23, -14, 22, 16, -24, 8, 17],\n [20, -11, -3, 13, -3, 19, -3, 11, -22, 25, -8, -20],\n [3, -2, -26, -25, -19, -23, 20, 5, 19, 11, 22, -21],\n [17, 22, 13, 6, 10, -17, -3, 9, -24, 20, 10, 0],\n [-3, -11, 20, 5, 26, -11, -18, -11, 23, -11, -23, 22],\n [-16, -3, 20, 4, 23, -3, -3, -3, 9, 5, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "537", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, 12, -15, -10, 14, 15, -25, 12, 23, -21, 24, 4],\n [22, -2, 1, 18, -1, -23, 2, -12, 7, 6, -11, 13],\n [12, -22, 25, 7, -5, 10, -17, 4, -13, 7, 26, -8],\n [10, -6, 10, -3, 5, 3, 10, 11, -10, 19, 9, 4],\n [23, 23, 16, -10, -13, -21, 3, -8, 23, 0, 13, 10],\n [4, -11, -14, -12, -1, 2, -26, 6, 7, 24, 7, 21],\n [7, -6, -20, -26, -26, -9, 5, 4, -9, -11, -26, 17],\n [-16, 3, 14, 1, -1, -4, -17, -16, 18, 17, -21, 2],\n [-5, -13, -21, 17, 23, -7, -16, -25, 17, -2, -12, 11],\n [-22, -12, -1, -16, 20, 24, 6, 10, 9, 14, 11, -16],\n [8, -18, -16, 14, 6, 18, 6, 0, -9, -16, 20, 3],\n [-11, -3, -26, -16, -21, -15, -1, -8, -26, 26, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "511", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-15, -3, 5, 6, 12, -17, -5, 21, 20, 14, -13, -23],\n [2, -21, 20, 13, 15, 12, 22, -2, 18, -19, -16, -26],\n [-21, 11, 1, 5, -18, 7, 22, -25, -5, 12, -4, 24],\n [25, -24, 16, 18, -11, 14, 3, -8, 17, -1, -11, -5],\n [-21, 10, -22, 16, -13, -3, -13, -18, 13, -16, -17, 4],\n [24, -2, 26, -7, 4, -11, 10, -21, 16, -16, 21, 13],\n [-8, -26, 0, -6, 14, -13, -7, 8, 10, 4, -25, -9],\n [-6, -2, -14, 9, -10, 19, -15, 15, -5, -3, -12, -20],\n [-24, -7, 16, -1, 18, 1, 26, 8, 18, 13, -18, -20],\n [13, -13, -9, -17, 8, 21, -12, 18, -23, 21, 23, -8],\n [21, 1, 17, -4, -5, -5, 7, 13, -16, 17, 11, 21],\n [4, 0, -22, 15, 2, -22, -9, 2, -25, -13, -4, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "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, -19, -23, 10, 5, 22, 11, 2, 2, -26, -24],\n [15, 18, -8, -13, 5, -4, 16, -1, -9, 16, -12, -2],\n [9, 16, 11, -5, -9, -15, 0, 21, -7, -11, 23, 19],\n [22, -12, -17, 12, -22, 16, 26, 8, -10, 24, 14, 3],\n [-23, 20, 26, -5, 4, 2, 14, 26, -11, -2, -10, -9],\n [10, 10, 2, 14, 0, 4, -4, 15, -2, -5, -14, -10],\n [18, 12, 25, -24, -26, 15, 20, 18, -10, 2, -9, 15],\n [25, -18, -1, -3, 6, -15, 16, 16, -12, 25, -13, -18],\n [4, 7, -25, 21, 11, 18, 11, -26, 18, 7, -4, -26],\n [6, -16, 21, -18, -20, 19, 10, 24, -3, 22, -19, 9],\n [-25, 25, 18, 25, -21, 23, 10, -15, -8, 25, 2, -8],\n [4, 20, 12, 2, 24, -6, 8, 6, -6, -17, -23, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-15, -17, -24, -19, -22, 21, 9, 21, -5, 8, -4, -23],\n [-11, 10, -5, -6, 23, 0, 25, 13, -19, -20, 15, 7],\n [3, 25, -2, 11, -12, 19, 1, 13, -18, -22, 10, 14],\n [-5, 12, 13, -12, 8, 26, 0, -10, -8, -9, -17, -25],\n [-25, 22, 20, 0, -11, 5, 11, 25, -1, 5, 7, 20],\n [26, 23, -19, 9, 3, -22, 5, -19, -5, 22, 11, 20],\n [-26, -16, 11, -21, -7, -7, -9, -9, -20, 5, -1, -3],\n [21, 24, -15, -1, 3, -9, -23, 7, -4, 2, -18, 12],\n [-15, 10, -15, -11, -8, -15, -26, -26, -8, 25, 17, 10],\n [14, 17, -25, -14, -23, -8, 13, 18, 6, -10, -10, -23],\n [-19, 3, 25, 10, 21, 5, -25, -2, -1, 14, -14, -8],\n [-3, -18, 8, 5, -26, 4, -9, -12, -3, -26, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[23, 24, -7, 3, 24, 25, -14, -22, 10, -16, 15, -21],\n [11, -2, 18, 11, 12, 13, 15, 16, 2, 10, 13, 6],\n [-20, -9, 17, 24, 13, 8, -17, -4, -13, -8, 24, 3],\n [-18, -22, 12, 18, 23, 18, 5, 12, 13, 1, 9, 22],\n [-17, -23, 10, 1, 10, 23, -3, 7, 16, 0, -26, -6],\n [-20, 17, 13, 17, -12, -13, 3, 25, -26, 26, -24, 6],\n [-16, -4, 14, -2, -23, 13, 22, 5, 19, -7, -11, -7],\n [7, -3, -19, 20, -23, 3, 26, 20, 26, -26, 0, 4],\n [-14, -5, -20, -11, 0, 9, -24, 17, -9, -13, -26, 12],\n [-8, -24, -5, 20, 24, 14, 23, -26, -20, 2, 20, -20],\n [-18, 26, 21, 24, 5, 17, 23, 5, -11, -22, 7, 21],\n [5, 11, 13, -8, 6, 2, -6, 10, 24, -20, 15, -11]]\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 largest singular value:\n[[-14, 12, 10, -9, -17, -4, -4, 13, 9, 6, 18, 15],\n [-15, -7, 7, -21, -17, -17, -24, 11, 1, -12, 17, -18],\n [-23, 11, 23, 3, 11, 6, -15, 8, -15, 8, 15, 11],\n [26, -10, 6, 7, -8, -7, -1, 11, 15, 4, -17, 23],\n [-19, 25, -20, 15, 6, 20, 15, -5, 8, -18, 18, 11],\n [-8, 5, 7, 17, 16, -14, -5, 8, 22, 14, -12, -12],\n [9, 5, -13, 3, 19, -13, 1, 23, 8, 11, 13, 24],\n [7, -22, -3, -18, -16, 21, -7, 7, 12, -22, 6, 1],\n [26, 9, 14, 3, 20, 0, 23, 15, -16, -10, 23, 17],\n [5, -4, 18, -9, -5, 1, 22, 15, -12, -7, 5, -4],\n [-19, 26, 16, -9, 9, 24, -4, -5, 7, -7, 8, -11],\n [-26, 22, 17, 24, 15, 25, -14, 4, 19, 21, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, -3, 23, -24, 19, 22, -3, 19, 26, -19, 17],\n [-13, -25, -21, -15, 9, -1, 2, -23, 3, 21, 25, -11],\n [-19, 5, 8, 13, -3, 4, 18, 12, 7, -22, -13, 10],\n [9, -10, -7, -26, -11, 16, -4, -16, 22, -23, 21, 17],\n [-4, 4, 4, -22, 0, 2, -14, 18, 8, -18, 23, -9],\n [-12, -3, 4, 26, 20, -20, -18, -11, 7, 5, -4, -7],\n [18, 9, 19, -18, -13, 16, -7, -14, -10, -5, -22, 9],\n [5, 2, 18, -15, 8, -23, -10, -6, -9, 20, 12, -18],\n [-13, 15, 15, 24, -3, -14, 8, -11, 16, -23, -24, 7],\n [-12, 4, -26, -26, 6, -1, 26, 15, -26, -11, 10, 25],\n [23, 8, -19, 20, 8, 24, -25, 17, 26, -9, -17, -17],\n [18, -15, 12, -3, 21, -5, 14, -22, -5, -23, 14, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[3, 19, 6, -5, -21, 11, 19, 21, 11, 25, -16, 19],\n [14, -20, -3, -19, -15, -17, -16, -7, 11, 17, -4, -5],\n [18, -5, 12, 14, -24, 8, -11, -9, -14, -5, -18, -21],\n [20, -18, -9, 25, 18, 6, 11, 24, -5, 6, 17, 2],\n [-11, -23, 9, -17, 5, 5, -13, -7, -9, -24, -21, -9],\n [5, -18, -1, 18, 24, 15, 21, -8, -21, -25, 1, 21],\n [-7, -13, 6, -23, 26, 1, 10, 15, 3, -9, -18, -20],\n [9, 26, -12, 0, 22, -22, 16, 11, -22, -5, -4, -14],\n [-21, 20, 18, 18, 15, 7, -25, -18, -5, -1, -7, -17],\n [-6, -16, 26, 13, -6, -9, -25, 26, 9, 2, 23, -5],\n [-11, -3, -25, 4, -1, -20, 9, 10, -9, 0, 3, -17],\n [14, 4, -11, -8, 22, 9, 6, -21, -11, 18, -23, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "dataset": "MATH"}
{"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, -2, -4, -23, -22, -1, 0, -23, -6, -2, -16, 4],\n [-10, -20, 14, 0, 22, 24, -14, 4, -23, -18, 16, 18],\n [3, -3, 21, 15, -23, -24, 26, 12, 2, -6, -15, -9],\n [-22, -4, -10, 10, 25, 4, -15, 21, 21, -5, 12, 25],\n [18, -22, 24, -7, -11, -17, -15, -21, -4, -2, -6, -8],\n [26, 7, 13, -7, 14, -24, -20, -24, 16, 17, 18, -23],\n [7, -21, -6, 17, 15, 25, -23, 22, -15, 24, -6, 20],\n [7, -20, 24, 13, 23, 19, 13, -6, -2, -21, 0, 8],\n [17, -26, -10, -22, 17, 5, -9, 18, 14, 8, 9, 15],\n [-17, -25, -9, 8, 16, -5, -22, 20, -3, 5, 22, 7],\n [10, 22, -16, -17, -4, 24, 11, -17, 16, -20, 21, 26],\n [-14, -4, -16, 8, -19, -4, 9, -20, -17, -15, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -1, -22, 24, 20, -20, 9, -20, 12, 15, 9, 23],\n [-21, -6, -26, -25, -24, 12, 7, -13, -2, 10, 10, -11],\n [-12, 21, -3, 14, -19, -25, 15, -1, -9, -9, -8, 10],\n [6, 5, -2, 0, -6, -4, -16, -6, 16, 4, 8, 8],\n [-11, 25, 20, 4, -14, 15, -8, -17, 21, 11, -22, 20],\n [22, -23, 13, -15, 18, 14, -1, 20, 16, -12, 5, 2],\n [3, 2, 0, -12, 9, 1, -11, -17, 7, -15, -2, -19],\n [26, 22, 5, -3, -22, -8, -16, -10, 1, -3, 11, -15],\n [4, -20, 21, -24, -15, -1, 13, -24, 20, 26, 11, 2],\n [13, 17, 18, -6, 22, 22, 2, 2, 19, -1, -11, -16],\n [11, -1, 3, 15, 12, -4, -18, 1, -5, 15, 1, -15],\n [-8, 17, -8, 20, -7, 11, 20, -7, 21, -25, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "517", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-6, 4, -22, -19, 16, -12, 10, -13, 1, -17, -21, 19],\n [-7, -23, 19, -24, 4, 23, -7, 16, -2, -2, -15, 21],\n [-7, 14, 26, 16, 1, 4, -18, -18, 12, -18, 6, 9],\n [11, -5, 16, 22, -26, -13, -10, -3, 22, -18, -17, -9],\n [-18, -14, 16, 7, -23, 16, 4, 4, 0, 14, -2, -3],\n [-15, -6, -10, -25, 1, -13, 25, -18, -23, -22, 22, -14],\n [-6, -13, -9, -18, -1, 15, 17, 0, 14, -6, 3, 17],\n [-17, 5, -21, -1, -3, 14, 25, 19, -13, 18, -1, 9],\n [-20, 10, 9, 23, -25, 2, -7, 15, 13, 25, -18, 4],\n [-6, 8, 2, -9, 25, 3, -14, -16, -2, -1, -7, -2],\n [-17, 26, -14, 5, 8, -2, -3, 2, 8, 25, 25, 22],\n [-6, -15, 18, 21, 24, -20, -20, -6, 26, -10, 20, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, 22, 6, -19, -9, -11, 4, 21, 14, -10, 2, 14],\n [-10, -1, -17, -12, 4, 13, 22, -19, 22, 18, 13, -25],\n [26, -12, -3, 1, -21, 13, -24, -11, -25, -17, -24, -16],\n [20, -2, -25, -18, -8, 22, 3, -26, -4, 13, -26, -16],\n [-11, 2, 12, 20, -20, 11, -23, 9, -17, -3, 3, 24],\n [-17, 17, 25, 14, -20, 6, -7, -21, -5, -11, -11, 7],\n [-4, -24, -5, 1, -8, 11, 15, 13, -6, 6, -24, 6],\n [-19, 12, -16, 15, 1, 1, 2, -7, 16, 4, 25, -10],\n [-13, 9, 6, -6, 10, 7, 15, -9, -18, -9, -22, -15],\n [21, -25, -25, -6, -11, 9, 8, -7, 7, 7, -7, -15],\n [18, 24, -4, 6, -20, 24, 18, -23, 21, 23, -12, -16],\n [-22, -13, 16, 23, 13, -18, 17, 5, -6, -2, -9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "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, 4, 4, 14, 13, -9, -5, -10, 18, -4, 11, 1],\n [-20, 7, -25, 17, -25, -5, -26, 7, 10, -16, 0, -13],\n [-19, -10, -14, 13, 20, -20, -12, 14, 19, -12, 16, 9],\n [-13, 3, 20, 9, -13, -23, -18, 6, -19, -12, 11, 2],\n [-26, 11, 25, 0, -13, -19, -20, -3, -11, -26, 15, -15],\n [14, -17, 15, 8, 7, -18, 22, -5, 10, -15, 9, 15],\n [5, -10, -25, 4, -7, 11, -22, -19, -11, 5, -24, -18],\n [9, 6, -21, 5, -9, -23, 17, 19, 1, 8, 24, 7],\n [7, 22, 10, 6, -11, 11, 10, 17, -10, -4, -16, 24],\n [7, -2, 21, -8, -19, -23, -21, -3, -7, -24, 14, -4],\n [-8, -26, -24, -4, -26, 20, -22, 1, 21, -22, -8, 17],\n [-14, 3, -19, -10, -2, -15, 19, 2, 16, -26, -25, 21]]\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[[7, 6, -26, -17, -9, -5, 26, 26, 4, -25, -4, -24],\n [19, 17, -3, -2, 14, -14, -17, -21, -22, 23, 12, -11],\n [16, -6, 15, 13, -22, 6, -24, -12, -17, -26, -17, -11],\n [4, 17, 1, 10, 0, -16, -6, 10, 11, 7, -5, -17],\n [-23, 17, -22, -4, -11, -8, -12, 24, -2, -15, 6, 15],\n [-19, 26, -24, 17, 12, 25, 11, -22, 19, 12, 20, 21],\n [5, -4, -8, 0, -6, 7, -25, 26, 26, -18, 4, 5],\n [-17, 9, -2, -26, -5, -22, 24, 6, 26, -10, -5, -8],\n [8, 8, 17, -8, 0, -16, 15, 1, -17, 8, -9, -22],\n [-21, -5, 3, -9, 18, -26, -23, 15, 21, 21, -3, -10],\n [16, -6, -19, 19, -9, 6, 3, -18, 25, -16, -23, -25],\n [0, -9, 10, 7, -16, -25, 4, 17, -2, 15, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, -20, -13, 18, -26, 25, 6, 7, -11, 4, -25, -15],\n [-8, -12, -11, -11, 1, -16, -21, 0, -10, 12, -16, -14],\n [21, -14, -19, -2, 14, 10, -13, -6, 16, 17, -7, -7],\n [15, 0, 6, 4, -11, -20, -11, 19, -23, -24, 3, -8],\n [0, 2, 22, 17, -10, -26, -6, 6, -2, -16, 8, 9],\n [12, 23, 1, -7, 12, 16, -2, 19, -19, 5, -7, 21],\n [23, 17, 14, -7, -18, 26, -14, 11, -5, 3, 10, 15],\n [-4, -16, -13, -11, 12, 1, 23, 13, 0, 19, -17, 19],\n [-7, 0, -5, 18, 5, 5, 22, 11, 20, 13, -22, 13],\n [-18, -20, -9, 19, 13, -26, 22, -21, -13, -3, -10, -10],\n [17, -6, 21, 8, 22, 7, -14, -13, -23, -3, -21, -7],\n [5, -4, 14, -13, -5, -10, 13, 24, 26, -25, 22, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[8, 9, 23, -13, -7, 1, -14, 22, 17, -20, -24, -22],\n [26, 25, 6, 19, -18, 26, 0, -12, 7, -9, -23, 7],\n [18, -6, -9, 25, 9, 8, -20, 7, 19, 10, -25, 14],\n [-11, 1, 3, 4, -19, 11, 8, -20, -9, 21, 9, -6],\n [-23, 5, -11, -9, 7, -5, 0, -15, 14, 5, -20, 13],\n [11, 17, 13, -17, 9, -17, -20, 24, -24, -15, 5, 24],\n [3, -17, -6, 11, -7, -12, -6, 4, -8, 16, -19, 15],\n [-5, 19, 25, 19, 20, -15, -10, 15, -15, 4, 24, -19],\n [21, -9, 25, 0, 15, 26, 16, -21, 1, 2, -9, 18],\n [16, 19, 19, -4, 9, -17, 25, 0, -9, 14, 26, -14],\n [-4, 24, 13, 16, -4, 13, 23, 22, 2, -17, 3, -5],\n [4, 15, -4, -23, 13, -25, -13, 13, -1, -5, 19, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "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, -19, 15, 9, -16, 19, -11, 15, -12, 13, 20, -8],\n [-19, -10, -9, -25, 10, 21, -3, -10, -12, 24, -3, -4],\n [0, -5, 20, -14, 22, 25, -15, 8, 1, -17, -17, 18],\n [-3, 1, 12, 10, -18, 9, 8, 16, 22, -25, 26, 14],\n [11, -4, -15, 24, -6, 2, 9, 16, 10, 25, 0, -21],\n [-7, 21, 16, 14, -5, -4, 7, -23, 5, -11, -23, 1],\n [1, 14, -5, -19, -1, 12, 3, 23, 26, -18, -1, 15],\n [-16, -2, 7, 0, 24, -17, -12, 23, -22, -15, -19, -21],\n [-3, -26, -2, 18, 20, -16, -4, 9, 13, -20, 0, 18],\n [-6, -22, 6, -11, -16, 5, 23, -3, -18, 9, -20, 1],\n [-4, 12, -14, 24, -20, -6, 12, -14, 9, -15, -19, 21],\n [16, 9, 26, 20, 17, -4, 7, -4, 11, 2, 23, -3]]\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[[-5, -15, -11, -26, 24, 3, 9, 15, 15, -3, 12, 11],\n [5, 5, -15, -17, -15, -14, -12, 3, 26, -14, 24, 21],\n [16, -26, -9, 12, -15, 23, 17, -18, 22, -23, 0, 1],\n [-3, -23, 1, 25, -7, 2, 6, 3, -24, -8, -6, 13],\n [-6, -7, 6, 11, -18, 23, 4, 5, 14, -4, -4, 25],\n [15, -11, -6, -15, -21, -13, -5, 4, 13, 20, 15, 1],\n [-22, -1, 25, 0, 2, -11, -1, -19, -16, -24, -25, -26],\n [-26, -7, 15, 4, 23, -11, 24, 21, -24, 12, -21, 16],\n [10, 14, 9, -15, -17, 8, 12, -25, 4, 13, 18, -12],\n [6, -25, 0, 23, -3, 0, 24, 4, -20, -1, -5, -25],\n [-11, -2, -11, -4, 9, 22, -13, 13, -18, 13, 4, 23],\n [-20, 18, -26, -6, 2, -19, -18, -8, 20, 8, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "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, 16, -13, -15, -22, 7, -20, -22, 8, -2, 3, 15],\n [-16, -19, 11, 1, -15, 18, 7, 4, -6, -11, -3, -5],\n [-14, -18, 18, 20, -19, -4, 22, -17, 14, -10, 2, 22],\n [24, 24, -25, -16, -19, -6, 22, 6, 23, -20, 14, -2],\n [-18, 15, 21, 16, 11, 0, 17, 26, -17, 21, -1, 0],\n [-5, 19, 22, -7, -1, 10, 9, 2, -14, -20, -16, 16],\n [26, 17, -24, 17, 8, -26, 15, -26, 6, -1, 16, 21],\n [-24, -3, 8, 13, 18, -11, 20, 15, 22, 8, -13, 6],\n [-18, -8, 3, -17, 26, -16, -1, -1, -13, -11, 12, 3],\n [-18, -14, 12, -26, 12, -25, -4, 7, -26, 14, 15, 15],\n [-22, 12, 5, -17, -5, -3, 8, 4, 17, 25, 21, 23],\n [21, -6, -17, 0, 6, -11, -22, -3, 17, 21, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"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, -11, 2, -12, -5, 16, -21, 24, 20, 0, 2, 18],\n [1, -8, 6, -17, -16, 17, 3, -13, -11, -20, 26, -23],\n [-11, 24, 8, -18, 22, 9, -18, 5, 19, -1, 17, -8],\n [26, 16, -23, 4, -14, 19, -17, 21, -7, 25, -21, 17],\n [21, -19, 8, -12, 2, 23, -19, -18, 2, -4, 25, -15],\n [1, 20, 17, -12, 23, 8, 2, -9, 13, -9, -17, -20],\n [-25, -9, 15, 24, 8, 11, -17, -7, -17, -14, 26, -3],\n [15, 24, 19, -16, -7, -11, 8, -14, 19, -18, 4, 9],\n [-13, 16, -15, -4, 22, 5, 21, -26, -11, 23, -16, 2],\n [-25, -11, -11, 0, 9, 6, -1, -16, -20, 11, 11, -2],\n [25, 23, -19, 1, -21, 13, 2, -24, 9, -21, 22, -26],\n [-12, 2, -12, -15, -21, 25, 10, -20, 13, 15, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "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, -23, 26, -17, -14, -20, 8, -22, -9, -20, 11, -19],\n [12, 25, 26, 16, 15, -1, -21, -9, 11, -17, -18, 13],\n [-15, 2, -6, -6, 0, 15, -15, 2, -1, 23, -1, 24],\n [1, -13, 18, -2, 12, -19, -12, 0, 14, 8, -22, -23],\n [25, -6, 26, -7, -21, 2, 13, -24, 9, -10, 22, 10],\n [22, -2, 17, 8, -6, -25, -16, 11, -10, 4, -8, 2],\n [-14, -6, 10, -22, 24, 1, -12, 0, -23, 11, -24, 2],\n [-16, 24, 9, 0, 12, 8, -22, -11, -6, -2, 3, 24],\n [23, -24, 10, -20, 12, -24, 14, -19, -6, -9, -17, -7],\n [13, 13, 22, 2, 22, 3, 9, 5, -21, -8, 4, 6],\n [-23, -16, -21, -15, 10, 19, 4, -10, -23, -12, 11, 18],\n [-15, -17, -21, -5, 14, 4, -11, -19, 12, 19, 9, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[2, -24, 24, -17, 19, 5, -6, -21, 17, 5, 17, 1],\n [-23, 3, 15, 17, -10, 1, 12, -17, -26, 24, 4, 5],\n [-7, 2, 10, -2, 11, -26, -12, 7, -4, 2, 23, -14],\n [-25, 13, -22, -5, -12, -14, 3, -2, -6, -10, 9, 12],\n [7, 14, 7, 22, 26, 23, 11, 23, 11, -1, -25, 7],\n [11, 14, 9, 15, 25, 7, 18, -23, -16, 15, -14, 12],\n [9, -22, 12, -16, 0, -24, 18, 1, 8, 10, -13, 2],\n [25, 10, -10, -13, 4, 21, 25, 11, -22, -9, -9, -12],\n [24, -23, 11, 26, 26, 14, -18, -8, -2, 22, -7, -13],\n [-19, -18, -6, 7, 13, 14, -14, -1, 15, 18, 10, 3],\n [20, -7, -20, 17, -7, -11, -25, -17, 14, 25, 8, 16],\n [1, -17, -14, -5, 7, -11, -19, -7, -17, 2, 22, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[25, 26, 15, 3, -3, -25, 7, 15, -6, 7, 5, 3],\n [-13, -8, 3, 14, 0, -11, -2, -2, -3, -24, -3, -16],\n [5, -4, -15, 12, -6, 10, 25, 7, -6, -1, 9, 22],\n [23, 7, -18, -9, 17, 15, 12, 3, -24, 23, -25, -24],\n [-12, 14, -24, 11, 16, 7, -10, -24, -20, 4, -17, 24],\n [8, 1, -7, -26, 15, -14, -19, -3, -5, 0, 20, 6],\n [-1, 17, -24, 3, 11, -17, -21, -10, -20, -13, 7, 19],\n [-21, 6, -9, -21, -9, 3, -23, -2, 19, -24, 19, -22],\n [19, 24, 13, -22, -17, 18, 11, -7, 15, -14, 25, 15],\n [-26, 3, 9, 18, 11, -19, -18, 14, 19, 6, 10, 22],\n [-21, -10, -4, 10, -25, -9, 11, 1, -13, -5, -26, 16],\n [15, 20, 14, 12, 17, -19, 0, -17, 7, 19, 14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[21, 10, -19, 3, -7, -26, 22, -20, -16, 12, -20, 26],\n [9, -7, 6, 20, 7, -4, -3, -18, -4, 19, 21, -10],\n [12, 7, -21, -24, 26, 11, 11, -19, 13, -18, -12, 3],\n [22, -23, 2, 6, -21, 2, -8, 10, 0, -16, 15, -18],\n [-11, 24, -9, -14, -20, -10, -18, 5, -1, 15, 25, -5],\n [18, 1, -11, 9, -2, 1, 2, 15, -26, 4, 3, 13],\n [-2, 25, 26, -9, 10, 16, 24, -18, -12, 2, 10, -22],\n [17, -18, 10, -17, -2, 11, -17, 11, -7, 15, -18, -24],\n [16, -16, -23, 22, 1, 14, 11, -16, 24, 5, -9, 13],\n [19, -8, -11, -24, -14, 22, 24, 10, 26, 21, 3, -13],\n [24, 25, 9, -21, 5, 14, 13, 5, -15, 16, 12, -2],\n [-2, -19, 15, 8, -21, 16, -23, 17, 8, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -17, -20, -1, 1, -25, 17, -13, -20, -10, -12, -5],\n [5, -1, -4, -1, 23, -3, -5, 0, -6, 10, 16, -19],\n [-13, -25, 25, -20, 0, -19, -23, -17, 19, 20, -17, -11],\n [-24, -4, -25, -26, -16, 21, 17, 10, -7, -6, 3, -2],\n [20, -10, 13, 24, -4, -8, 17, -6, -20, -21, -25, -24],\n [14, -16, -5, 23, 21, 26, 15, 21, -18, -7, -25, 23],\n [-11, -1, 25, -4, -13, -6, -4, -15, -23, -10, 4, 1],\n [25, 26, 25, 12, 9, 20, -13, 25, 4, 6, -18, -5],\n [9, 3, 25, -18, -18, -15, 1, -11, 10, 22, -21, -18],\n [16, 7, 4, -20, 5, 22, 16, -3, 3, 15, -1, 6],\n [-1, -8, -26, 25, -7, 11, 21, -15, 16, -5, 23, -20],\n [-5, 0, -13, -14, -7, -19, 19, -9, -23, -4, -4, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[14, -25, 19, 17, -5, 24, 23, 17, -26, -17, 7, 4],\n [-13, 25, 21, -8, 19, 2, 19, 9, 3, -16, 3, -5],\n [26, -25, 12, -2, 18, -19, 5, 17, -20, -5, 2, -25],\n [11, 16, 22, -12, -7, -1, -16, -4, 14, 22, 25, 15],\n [-23, -23, 21, -26, -4, -3, 0, -20, 7, -23, -25, -4],\n [21, 9, -5, -17, 15, 8, 14, 0, -3, -20, 24, -6],\n [-19, 23, 9, -22, -11, -9, 11, -4, 17, 25, 10, 24],\n [-6, 18, -5, -14, 9, -16, -21, -18, -7, 12, -3, -15],\n [15, 8, 12, -2, 0, 15, -26, -15, -26, -14, 12, 23],\n [13, -21, 2, 20, 23, -23, -4, 17, -19, 10, -25, 23],\n [-23, 24, -4, -6, 26, -1, 13, 3, 6, -5, -15, -21],\n [-7, -20, 3, 16, 14, -19, -10, 16, 1, 5, 21, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, -23, -24, 17, 23, 9, 21, -20, -17, 6, -13, -9],\n [6, -1, 12, 23, -10, 16, 1, -25, 13, 10, 5, 0],\n [4, -23, 8, 5, -16, 26, -4, 20, -4, 12, 8, -10],\n [25, 22, -7, 16, 23, 5, 11, 19, -22, -12, 5, 7],\n [-1, 24, -12, -18, -22, 7, 6, -6, -24, 3, -22, -3],\n [25, -11, -21, 13, 8, -1, 17, -26, -7, 19, -16, -7],\n [12, -23, 11, 19, 15, 3, 9, 18, -5, 13, -9, -22],\n [17, 3, -22, 12, 24, -13, -16, 25, -6, -16, 5, 2],\n [-24, -14, -21, 21, 1, 4, -4, 11, 11, 26, -21, -5],\n [18, 13, 22, 7, 11, 11, -20, -26, 5, -5, 13, -24],\n [-23, -10, 8, -4, 2, -25, 19, -21, 23, -3, -25, -15],\n [-22, 15, -12, -14, -17, -5, 2, 22, 18, -20, -5, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "549", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-25, -5, -3, -1, -5, -22, -17, -8, 14, -5, 0, -25],\n [-6, -2, -5, -18, 4, 18, -26, -12, 3, -14, -13, 16],\n [7, -2, 6, 16, -6, 5, -11, -22, 0, -1, -8, -5],\n [-17, 25, -12, 7, 3, 8, -13, -4, 22, -20, 19, -1],\n [2, -17, 21, 3, 19, 19, -4, -17, 20, -1, -9, -26],\n [-24, 14, -17, 2, -22, -22, -12, -1, -1, 9, -23, -1],\n [23, 2, 12, 25, -5, -26, 1, 19, 12, -8, 14, 26],\n [-15, 15, -21, 8, -16, -26, -26, -20, 16, 15, 2, 7],\n [-20, 4, -26, 10, -1, 23, 2, 8, 10, -17, -22, 3],\n [23, 19, -23, -20, 24, -7, 1, -20, -16, 22, -13, -19],\n [-3, 24, 4, -25, -19, 0, 16, -3, 24, -21, -16, 22],\n [-11, 25, 2, 14, 3, 18, -20, -11, 9, 4, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-13, -12, -19, -15, 16, -3, 11, -14, -9, 8, 2, -7],\n [7, -24, 13, 8, 15, 4, -20, -18, 26, 23, 21, -10],\n [25, -20, 24, -22, -3, -12, -25, -12, -6, 10, -13, 24],\n [-25, -2, 0, 25, 26, 24, 11, 26, -8, 15, 21, 3],\n [22, -17, 4, -14, -14, 0, 19, -8, -8, 10, 14, -12],\n [1, 17, 9, 1, 23, 6, 17, -5, -18, 9, -21, -25],\n [16, 16, -1, -22, -4, -21, -26, 8, 26, 14, 6, -1],\n [-2, -14, -10, -11, 17, 3, -25, -23, -14, 11, -10, -4],\n [2, 21, -18, -12, -25, 2, 7, -10, -13, -12, -1, 7],\n [-24, -9, 10, 9, 12, -20, -4, 10, -1, 25, -12, -3],\n [-7, 10, -3, -13, 5, 8, -4, 6, -25, -14, 3, 7],\n [-16, 10, -15, -9, -7, 22, -14, -21, -17, 6, 23, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-23, 14, 10, 15, -15, 25, -22, -2, -2, 6, 25, -12],\n [-7, 12, -15, -13, -5, -3, -15, -7, 21, 1, -16, -5],\n [23, 6, -13, -14, -2, 13, -11, 3, -26, 1, 4, 9],\n [21, 18, 23, -25, 15, 10, 16, -25, 6, 22, 9, 3],\n [25, 7, -9, 9, -3, -26, 19, -3, -6, 2, -14, -17],\n [-14, -16, 11, -21, 24, -17, 23, -14, 21, 23, 8, 20],\n [-5, -10, -24, 3, 7, 0, 18, -23, 6, 16, 4, -8],\n [-16, 25, 10, -12, -7, 10, 22, -19, -25, 11, 23, 0],\n [23, -13, -3, 8, 1, 7, -10, 6, -4, -19, 6, -8],\n [-15, -23, 4, 17, -6, -15, -20, -9, 12, -16, 6, -5],\n [-19, 12, 4, 26, 0, 24, 1, -4, 14, 0, -17, -4],\n [6, -1, -14, 4, 0, -14, 21, 20, 7, 20, -20, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, -22, 11, -21, -1, -8, -12, -18, -14, 8, 20, 7],\n [7, 2, 12, 0, 19, 18, -15, 12, -25, 20, 9, 26],\n [-9, -21, 3, -6, -5, -16, 12, 13, 15, -20, -20, 4],\n [-21, -1, 9, -18, 9, -24, 17, 4, 26, 3, 4, 16],\n [16, 13, 3, -18, -21, -2, 3, -1, -24, -5, 15, 18],\n [-18, 23, 8, -20, 10, 21, -18, 0, 1, 18, 17, 6],\n [23, -21, -10, -4, -2, -8, 25, 2, 4, -21, 10, 7],\n [-3, -17, -16, -3, -25, 23, 2, -11, -4, 8, 16, -5],\n [8, -21, -4, -4, 3, 10, 15, -7, -16, -3, -9, 0],\n [26, -20, 21, -6, -12, -19, 1, -6, -19, 1, 7, 20],\n [-12, 17, 16, 10, 26, 0, 14, -1, -15, 7, 4, -24],\n [-1, -21, -7, 24, 13, -10, 14, -26, -14, -9, 25, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[25, -15, 17, -15, -1, 15, 13, 1, 17, -2, -6, 21],\n [23, 22, -16, -18, 26, 8, 9, 22, 2, 13, -10, 10],\n [21, 22, -19, 26, 17, 20, -22, -4, -17, 20, 14, 20],\n [-12, -11, 0, 5, 13, 24, 18, 19, 8, 10, -3, 4],\n [24, 8, -11, 13, 9, -15, -11, 22, -22, 20, -22, -7],\n [21, 11, 9, 5, 13, -16, -16, 16, 22, 1, -15, 19],\n [4, 13, 3, -7, 0, -2, 23, 7, 8, 16, 25, -22],\n [13, 12, -19, -8, 16, -9, -11, -8, -12, 2, -12, 2],\n [-10, -12, 13, -16, -24, -14, 11, -18, -7, 21, -1, -15],\n [22, 4, -25, 6, -11, -22, 26, -10, 22, 13, 5, -12],\n [-15, -10, -17, -1, 17, 1, 1, -4, -7, -10, 25, 17],\n [-19, 23, -12, 14, -4, 26, -13, 13, 19, 0, 16, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "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, 16, -2, -1, 17, -16, 11, -18, 16, 6, 24, -11],\n [22, -7, -20, 6, -14, 20, 8, -23, 4, 3, -24, 14],\n [0, 5, 20, 11, -21, -19, -3, -12, -2, 0, 17, -14],\n [-7, -22, 11, -20, -22, 1, 10, 2, 15, 10, -20, 19],\n [-1, 20, -8, -17, 15, -7, 19, 4, 9, 19, -21, -12],\n [-3, 3, -18, -26, 23, 20, -12, -21, -12, -20, 19, 0],\n [-17, 5, -6, 17, 10, 11, 9, -13, 15, 12, 14, 21],\n [-13, -25, -3, -17, 15, -21, -24, 7, -1, -17, 11, -6],\n [25, -2, -25, 9, -26, 17, 15, 9, 17, -3, -17, 24],\n [8, -5, 19, 20, 7, 5, -11, 3, 9, 4, 3, -22],\n [-3, 19, 9, 0, -13, 10, -14, -7, 1, 24, -21, -18],\n [-5, -4, -19, -26, -20, -15, 12, -10, 23, -11, -23, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, -18, 0, -15, 7, -4, 8, 13, -18, 16, -14, 25],\n [23, 19, 16, -25, 20, -25, 2, 18, -5, 16, -6, 20],\n [-21, 20, 1, -11, -26, -4, -19, 25, -19, 15, -26, -16],\n [-19, 20, 24, 4, 19, 9, -19, -3, 0, 2, 17, -9],\n [-18, 9, 11, -13, -14, 13, 25, -3, 12, -13, -19, -15],\n [25, 4, 7, 9, -6, -23, -16, 15, 10, 14, -20, -15],\n [-22, -24, 5, 13, 25, 8, 9, -15, 3, 6, 13, 14],\n [-24, -1, 11, 25, 14, 7, -24, -13, 18, 19, -13, -10],\n [-12, -15, 12, 14, 17, 3, 22, 24, -20, 21, 8, 24],\n [24, 25, 4, 25, 13, 10, -13, 24, 1, 26, -15, 14],\n [-21, -23, 6, -22, -18, 12, -9, 5, 4, 7, 13, 0],\n [10, 10, 12, 17, -14, -23, -18, -19, 19, -21, 6, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[21, -10, 10, -14, -5, 23, -8, 1, 26, 16, -2, 17],\n [-19, 18, 5, 20, -16, 11, -9, 21, 0, 11, 10, 19],\n [15, 9, 14, 7, -12, -14, 0, -8, 9, -14, -20, 18],\n [-26, 14, -6, -11, 22, 2, -3, -8, 0, 21, 20, -26],\n [0, -13, -16, -4, 20, -7, 26, -1, -9, 9, 3, 26],\n [-23, -8, -22, -25, -17, 22, 16, 16, -16, 24, -5, 16],\n [-19, -24, 14, 26, 13, -9, 23, -5, -16, -25, -5, 14],\n [24, -12, -19, -8, -18, -22, -19, 6, 22, -12, -12, 14],\n [-20, -6, 19, -1, -26, 24, -1, -1, 1, -18, -1, 24],\n [-14, -22, 19, -9, 26, -4, 1, 10, -22, 0, -7, 9],\n [10, 7, -13, 20, -21, 0, -25, -18, -16, -22, -16, -24],\n [-1, -13, -18, -8, -10, 22, 19, -3, -13, -17, -20, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"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, 4, 11, 15, 10, 26, 2, -21, -19, -2, -22, -17],\n [-4, -26, -14, 10, -1, -8, -1, 21, 23, 24, 15, -25],\n [14, -8, -15, 17, 8, 5, 26, -14, 9, -26, 6, 26],\n [-23, -25, -19, -11, -5, -17, -18, -20, 13, -10, 3, -16],\n [16, -12, -20, -24, -4, 0, 3, 21, -11, -13, 25, -5],\n [23, -7, -17, 2, -23, 4, -13, -22, 11, -23, -16, -2],\n [-15, 25, 4, -16, 12, 5, -16, -20, -25, -26, -2, -18],\n [19, 25, 9, 2, -17, 0, -8, -8, 26, 26, -7, 2],\n [26, -24, -5, -5, 2, -4, 13, -1, 20, 26, -5, 11],\n [-18, -6, 9, 23, 21, 9, 5, 5, 7, -4, -1, -11],\n [11, 22, -24, 18, -25, 9, -18, 1, -3, 22, 18, 1],\n [-20, -1, 19, -26, 14, 18, 14, 8, -9, -5, -14, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[20, 24, 2, -6, 15, -18, 2, -15, -19, -17, 7, 20],\n [-7, -11, 15, 18, -16, 21, -13, 4, 13, 24, 7, -23],\n [23, 21, -20, 15, 11, -26, 23, 19, -3, 15, 1, -3],\n [-14, 11, -17, -1, -25, 6, 1, 0, -21, 24, -10, 6],\n [-12, 19, -24, -17, 2, -20, 23, 9, 25, 17, -5, 4],\n [12, -13, -25, 22, -21, -8, 0, -21, -25, -14, 20, -17],\n [13, -22, -13, 4, -2, -21, -15, -24, 20, 23, -4, -26],\n [-12, 22, 13, -14, 11, -13, -8, -18, 1, 6, 26, 6],\n [18, 12, 6, -23, -9, -1, -2, 8, 12, -9, 6, -9],\n [2, 14, -19, 22, -25, -23, -12, -19, 3, 20, 12, -3],\n [14, 25, -15, 9, -13, 16, 5, 24, -13, 1, 16, -7],\n [-14, 19, 18, -10, 3, 21, 13, -10, 5, 17, -8, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "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, -26, 22, -8, 18, -15, 17, 1, 18, 11, 4],\n [-14, 26, 16, 25, 26, 26, -16, -15, -4, 20, 2, -18],\n [-13, 5, -24, -20, -21, 8, 0, 1, -4, -17, -10, -12],\n [-13, -16, 2, -9, -1, 20, 24, -2, 13, 16, -26, -24],\n [-8, -16, 1, 24, -9, 26, 19, -13, -14, -8, 17, 24],\n [5, 16, 6, -21, 3, -17, 3, -18, -21, 18, -21, -7],\n [-10, -25, -25, -17, -26, 7, 20, 26, 9, 13, 24, -7],\n [5, -10, 12, -5, -22, -26, 4, -9, -22, -2, -20, -13],\n [-20, 3, -10, -14, -3, 9, -15, -9, -4, -5, -2, 17],\n [-2, 9, -6, 21, 19, 2, 26, -19, 22, -22, -25, 25],\n [-4, -25, -5, -6, 17, 22, -10, 13, 4, -2, -20, -2],\n [-9, 5, -19, 20, -13, 21, -21, -4, -12, -5, 9, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[18, 17, -18, -22, -15, 2, -26, 6, -6, -6, 0, -25],\n [-19, -15, -5, 22, -18, 17, 11, 2, -24, -5, -23, 2],\n [14, -14, -3, -25, -24, -12, -3, 23, -1, -19, 13, 26],\n [20, -22, -19, 19, 12, 19, 5, 4, -19, -10, -4, 12],\n [23, -14, 17, -12, 18, 1, 21, 3, -12, 11, -19, 19],\n [-12, 11, 12, 24, 7, 9, -7, 17, -14, 17, 18, 20],\n [-6, 20, -4, 19, -24, -5, 2, 13, 3, -3, -2, -15],\n [23, -7, 6, 12, -5, 19, -8, 5, 26, 24, -1, 17],\n [-20, -19, -16, 13, -11, -18, 14, -23, -16, -17, 26, 2],\n [14, -22, -24, -14, -11, 14, -19, 1, -3, 11, -25, -21],\n [-8, -9, 11, -3, 12, -7, -3, -25, 9, -11, 8, -20],\n [3, 8, 12, 16, -11, -11, -3, -13, -11, 5, 25, -20]]\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[[-2, -4, -25, -18, 10, 15, 5, 16, -5, -9, 15, 19],\n [-4, -18, 0, 7, -18, -6, -10, -22, -13, -9, -3, 24],\n [-18, 4, -6, 8, -1, -10, -23, -20, -24, 14, 4, -6],\n [-13, 17, 0, 11, -4, -17, 19, -6, 23, -24, 21, -16],\n [-14, -18, 19, -12, 24, -25, -3, -14, -3, -4, 23, 7],\n [-24, -13, -1, -26, 2, -15, -22, 24, 25, 14, -20, 8],\n [-20, 20, -2, 5, 1, 16, -1, -17, 6, -18, 8, -21],\n [-9, -23, -8, -21, 6, -23, 6, 22, -23, -6, 1, -20],\n [-19, 8, -15, -8, 15, 25, 11, -9, 1, 11, 5, 3],\n [5, -5, 23, -22, 16, -20, -18, -24, -8, 17, -9, 3],\n [20, 25, 10, -19, 2, 17, -10, -8, -13, -11, -12, 9],\n [-9, 13, 10, 4, 22, 13, -14, -18, 19, 22, 11, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -3, 9, 0, 25, 16, -17, -14, 25, -5, 18, -21],\n [23, -6, 0, 17, 7, -21, -20, 8, 3, -16, 3, -6],\n [14, 19, -16, -21, -8, 20, -2, 5, 0, 19, -15, -14],\n [-22, -15, 22, -1, 24, 8, -9, -9, 14, -24, -1, 16],\n [25, 21, -12, 11, -1, 14, -26, -13, 24, 8, -18, 0],\n [14, 5, -22, 5, 4, -21, 26, 4, 4, 17, 12, -20],\n [25, -17, 21, 22, 4, 18, -22, 5, -13, 14, -13, -19],\n [-7, 15, 14, 12, -17, -17, -19, -10, 25, 11, 25, 24],\n [-14, 10, 9, -6, 17, 20, -25, 3, 20, -8, 13, -12],\n [-3, 15, -14, -3, 24, -26, 16, -9, 24, -9, 24, 12],\n [10, 19, -16, 1, -16, 26, 5, 7, 14, -26, -12, -3],\n [13, -25, -21, -25, -10, -20, -24, -3, 24, -15, -9, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[17, -1, -26, -26, 15, -24, 15, -23, -3, -15, -13, 13],\n [-3, 3, 12, 6, 22, -6, -12, 20, 5, 10, 26, 4],\n [-26, 24, 6, 7, 16, 17, -16, 13, 25, 9, 26, 7],\n [-18, 4, 2, -14, -17, -18, 18, -24, 22, -9, 0, 5],\n [-19, -14, -9, -1, -11, -6, 19, -2, 18, -23, 6, 3],\n [4, 6, -21, -12, -12, 12, 4, -18, 5, 18, 11, 15],\n [-6, 26, -15, 8, -12, 25, 16, 1, 5, 24, -1, -17],\n [14, -4, -26, -11, -6, 20, -10, -7, -1, -10, -2, -2],\n [-23, 1, -26, -13, -5, -13, -12, -22, -12, 25, 17, 20],\n [7, 2, -5, -11, -20, -26, 24, -20, 15, -5, 23, -19],\n [11, -26, -4, 5, -2, 18, -19, -3, 9, -22, 20, 10],\n [-3, 16, 15, 14, -19, -25, 5, -4, 5, 21, -24, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-9, 15, 23, 8, 1, -7, -5, -26, 15, -19, -19, -7],\n [-10, -12, 16, 21, -5, -11, 6, -3, -7, 3, 6, -2],\n [19, 19, 9, -19, 3, -11, 13, -12, 0, 23, 18, -17],\n [-3, 4, 11, -8, -26, -25, 12, -15, 3, 13, -14, -2],\n [6, -2, -9, -19, 5, -15, -8, -6, 17, -25, 26, 20],\n [-16, 24, -2, -26, 8, 6, 14, 0, -6, -13, 21, -24],\n [14, 2, -10, 22, -23, 17, 19, -5, -13, -13, 21, -18],\n [-25, 10, -22, -9, 16, 5, 14, -18, 17, -23, -24, 10],\n [-6, 12, 19, 3, 10, -3, -26, -11, 1, 3, -8, -4],\n [7, 23, 10, -4, 16, -11, 14, 5, -11, 8, 0, -24],\n [-7, 0, -25, -14, -21, -13, -3, 0, -18, 23, -4, 8],\n [17, 24, 10, -13, -1, -19, 26, 18, 4, -19, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "517", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-11, 26, 4, 4, 8, 10, -13, 20, 12, -2, -26, 2],\n [1, 2, -17, -19, 13, 3, 3, 14, -21, -12, -3, -14],\n [-18, 23, -7, 9, 25, 22, -14, 0, -9, -19, 15, 22],\n [-19, 24, 25, -3, 17, 13, 0, 24, -7, 8, -19, -3],\n [13, -15, 20, 6, -13, -6, 6, 14, 18, -26, -21, -13],\n [1, -2, 12, -4, 16, 12, -10, 4, 25, 1, -20, -9],\n [-11, -21, -25, -7, -4, -25, -2, 20, -21, 16, 13, 2],\n [-18, -18, -13, 18, -12, 19, -11, 21, 24, 18, 17, -18],\n [1, -23, 13, -15, -5, -26, 17, 13, -23, 15, 6, -7],\n [8, 20, -25, -17, -19, -13, 0, -14, -14, 2, -19, -3],\n [-22, 1, -25, -6, 11, 0, -19, -15, -17, 23, -20, 14],\n [-17, 2, -2, -1, 25, -1, -21, -5, 12, -15, -20, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-14, -9, -22, 4, -10, -12, 7, -5, -22, -11, 6, 14],\n [-23, 6, 1, -16, -22, 15, 14, -20, 24, -3, 17, 23],\n [-23, -15, -23, -2, -24, -10, -1, 23, -18, 19, -14, -22],\n [20, 26, -22, -15, 1, -17, -26, 8, 1, 24, -25, -4],\n [-22, 6, 4, -12, -26, 25, 2, -3, -18, 8, -11, -19],\n [-19, -4, 20, 17, -10, 0, 2, -16, -4, -23, -10, -16],\n [-19, 24, -1, 25, 22, -19, -19, -20, 24, 7, 5, -14],\n [9, -9, -14, 3, -26, 26, 8, -24, 3, 21, -2, 6],\n [-11, 22, -24, 20, 2, -13, 16, 18, -22, 17, -10, 26],\n [2, -6, -21, -3, 22, 1, -10, 15, -5, -3, 13, -9],\n [1, -17, -26, 10, -1, 23, -1, 6, -18, -9, -22, -5],\n [-17, -13, -15, 5, 12, 18, 9, 24, 23, 20, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-11, -23, 24, -24, -1, 10, 7, 15, -18, 17, -13, 20],\n [6, 21, 11, -22, 24, 20, 1, 6, -10, -6, -20, 13],\n [8, -20, -19, 24, 17, 15, 4, -22, -22, -3, -5, 17],\n [-14, -5, -1, -26, -10, -8, -25, 23, 25, -16, 3, 19],\n [-4, -12, -4, -15, 0, -21, 3, -22, 19, 11, 8, -21],\n [-13, 25, 23, -10, -18, 13, 4, 9, -17, 0, 22, 25],\n [-22, -10, 4, -13, -4, 17, 2, 12, -12, 20, -15, 6],\n [13, 3, -5, 3, 5, -7, 11, -7, -25, 4, 23, 1],\n [-24, -7, 8, -8, -21, -16, 18, -21, -9, 20, -13, -13],\n [-26, -10, -13, 4, 18, -17, 11, 6, -22, -11, -7, 21],\n [-5, 13, -10, 23, 23, -18, 11, 15, -18, -12, 25, 19],\n [-13, -18, -18, 6, 26, 4, -17, -17, 12, -22, -9, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 22, -9, 25, -15, -2, 0, 14, 26, -18, 22, -14],\n [22, -5, -25, 12, 21, -12, -4, -14, 18, 20, -7, -14],\n [0, 15, -10, 4, -1, -5, 14, 5, -5, 1, 15, 20],\n [-26, -23, -11, 16, -4, 11, 14, 21, 9, -13, 16, 16],\n [-24, -26, 17, -11, -19, -26, -6, -25, -15, -13, -5, -7],\n [-10, -20, -6, 7, -5, -5, -6, -14, 18, -21, -2, 17],\n [4, -2, 5, 2, 21, 8, -15, -11, -18, -14, -15, -1],\n [-12, -23, 22, -17, 21, 17, 11, 21, -15, -5, 11, 3],\n [-12, 9, -22, 22, -23, -1, 16, -8, -13, 0, 11, -1],\n [15, -4, 15, 23, 22, -25, -14, -15, 10, 13, 9, -24],\n [-23, 4, 14, 1, 13, -16, 20, 16, -11, 11, 2, -12],\n [-6, -13, -11, 0, 1, -13, 9, -17, 20, -18, 1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-8, -14, 24, 10, 12, 25, -24, -20, 1, -13, 10, 21],\n [25, -5, 4, -26, 20, -15, -3, 3, 19, 21, 0, -11],\n [-6, -23, -25, -6, -20, 10, -20, -25, -15, -26, -24, -26],\n [8, -11, 24, -19, -6, 24, -22, 4, -1, -26, -4, -14],\n [5, -22, -7, 24, 1, -20, -14, 5, 19, -9, 19, 18],\n [-19, 2, -7, -1, -9, 19, -25, 16, 20, 15, 22, -3],\n [16, -19, -5, 7, 5, 8, -2, -20, -13, 17, 2, 10],\n [10, -20, 6, -10, -8, -2, -19, -15, -24, 4, 17, -19],\n [-23, 5, -20, -13, 7, -22, -15, 10, 0, -6, -14, -2],\n [7, 15, 17, 21, -10, -6, -12, -1, 6, 8, -1, -15],\n [-5, -17, -18, 9, 7, -6, 6, -17, 18, -20, 1, -9],\n [-12, 13, 3, -2, 23, 23, 18, 3, -11, -17, -2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[13, -26, -18, -7, 11, -9, 2, 10, 22, -15, 10, 5],\n [-15, 10, 12, -15, 6, 16, 5, 6, -3, 4, 20, 3],\n [-1, -25, 25, -10, -26, 25, 4, 2, -16, 18, -23, 9],\n [-19, 9, 20, -6, -16, -15, -1, 0, 7, -17, -18, 12],\n [-14, -15, -10, -23, 12, 1, 14, -7, -20, -19, 8, 2],\n [20, -12, 4, -15, -6, 21, -11, 12, 5, -21, -3, 5],\n [-9, 17, -17, 2, -18, -14, 24, 0, 10, -19, 26, -25],\n [15, -23, -17, -13, -2, 14, -13, -17, -19, -21, -22, -6],\n [22, -4, 10, -8, 26, 22, -7, -17, -9, -7, 21, -16],\n [-12, 5, -16, 25, 2, 13, 12, -26, 20, 0, 8, -19],\n [-15, 1, 21, -8, 2, 15, 15, -9, 7, 24, -8, -3],\n [7, 5, -25, 5, -19, 18, 26, -18, -4, 2, -20, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"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, 5, 13, -24, -17, 13, 26, 2, 18, -8, -2, -7],\n [20, 11, 19, -17, 24, -16, -13, 24, 4, -22, 16, 1],\n [-8, 6, -25, 2, -9, 19, -17, 11, -12, -5, 0, 0],\n [-5, -6, 4, 7, -21, -14, 13, -12, 0, 4, 21, 15],\n [-4, 19, 8, -19, 6, 1, -20, 9, 16, -14, 15, 4],\n [-14, 8, 23, -20, -5, 13, 25, 7, -18, 5, 8, -24],\n [-6, -14, 6, 9, -17, 9, -9, 4, 18, 13, -26, 4],\n [-1, -11, 11, -15, 21, 16, 16, 24, 2, -15, -22, 15],\n [-25, -15, -13, 20, 3, 8, 20, -10, -24, -18, -20, -7],\n [-15, -20, 2, 2, -9, -25, 21, -16, -1, 0, -8, 11],\n [-7, -3, 12, -14, -21, 13, 10, -26, 25, -25, 11, 14],\n [3, -3, 14, 11, 0, 3, -18, 10, -11, 8, 1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-15, 24, -18, 2, 24, 24, -6, -10, 6, 7, -1, -9],\n [7, 11, -2, 25, 24, 7, 23, 21, 18, -12, -25, -4],\n [18, -21, 12, -8, 7, 10, 19, -4, -12, -25, 11, -2],\n [17, -19, -16, 2, -22, 10, -7, -15, -11, -6, 10, 23],\n [-6, 1, 7, 26, -19, 19, 4, -6, -24, 20, -6, 2],\n [5, 22, -1, -14, -12, -25, 22, 6, 4, -26, -12, 12],\n [26, -12, -7, 25, -20, 9, 16, -15, -14, -22, 16, -21],\n [-22, 18, 12, 16, 20, -21, -21, -16, 0, -11, 18, -24],\n [-5, 5, -2, -9, -8, 21, 3, 8, 24, 19, 0, -9],\n [-14, 17, 4, 26, -24, 4, -3, 10, -5, 6, 18, -12],\n [11, 15, -13, 21, -12, 2, -1, -5, -23, 6, -22, 1],\n [22, 8, 15, 5, 2, 19, -3, 3, -18, 21, -9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-5, 10, -4, 2, -14, 5, 17, -17, 16, 21, -21, -6],\n [8, -24, -6, -7, 23, 16, 7, -24, 18, 18, 13, 10],\n [26, -22, 23, -16, 21, -10, -23, -19, 14, 20, -5, 5],\n [0, -21, 4, -23, 20, 12, 3, 16, 26, 6, 4, 1],\n [-2, 22, -10, 4, 23, 9, 19, 16, -10, -17, 24, 21],\n [-5, 4, 3, 24, -7, -13, -12, 16, -8, 26, 13, 4],\n [10, -4, 17, -13, -5, 3, 21, -19, 17, 4, -11, 12],\n [-3, -6, -19, -9, 11, -21, -13, 3, -13, -20, -23, -8],\n [-2, -2, -8, 3, 16, 3, -12, 21, 2, 8, 6, 12],\n [13, -4, -4, 16, 10, 15, 25, 3, -11, 6, 0, -17],\n [-7, -23, -7, -12, 11, -12, 20, -10, -7, 22, -10, 26],\n [-15, -16, 3, -1, 21, -2, 18, -10, 14, -26, 23, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-24, 26, 16, -16, 20, 1, 1, 3, 8, -20, 6, 21],\n [0, 2, 0, 15, 4, 20, -22, 7, 10, -6, -1, 16],\n [-22, 6, 15, -25, -4, 24, 16, 2, -9, 8, -17, 12],\n [6, 5, 15, 10, -4, -26, -10, 19, 9, 0, 21, 12],\n [-26, 11, -13, -23, 5, -6, 20, 16, 23, -25, -2, 11],\n [21, -13, -14, 17, -8, -15, 4, 7, 14, -4, -18, -11],\n [-3, -19, 10, 4, 5, 26, 15, -4, 11, 9, 5, -4],\n [-4, 6, 14, -1, 13, -24, -26, -14, 0, 23, 0, 17],\n [-5, -16, -12, 3, -9, 17, -3, 5, -5, -22, -22, -5],\n [21, 22, 24, 12, -5, -20, 23, -6, 8, -17, 23, -15],\n [10, -4, 11, -14, -24, -21, 3, 14, -24, -25, 3, 1],\n [26, 22, 22, 16, 13, 7, 4, -10, -18, -7, -14, 0]]\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 difference between the largest and smallest singular values:\n[[9, -23, 0, -19, -18, -6, 8, 1, 0, -20, 23, 18],\n [7, -13, 2, 19, 2, -6, 22, -25, 24, -17, -3, 0],\n [24, 24, 5, 18, -4, 21, 25, 17, 9, -6, -5, -4],\n [-15, -14, 7, -2, -25, 14, -6, 4, -9, -11, -13, 6],\n [19, -20, 11, -7, -23, -16, -21, 12, 23, -20, 18, 3],\n [15, -4, 1, 11, 8, -26, -3, 21, 1, 7, -10, -3],\n [4, -7, 2, 1, -13, 15, -1, 14, 17, -16, -11, 9],\n [2, 0, 2, 1, 5, 0, -16, 18, -19, 22, 26, 16],\n [-23, 25, -15, 5, -15, 24, -2, -3, -7, 23, 15, -20],\n [5, 24, -21, -8, 25, -9, -15, 16, 20, 10, -17, -4],\n [-9, -6, 20, -14, -25, -25, -9, 8, 21, 7, 14, -17],\n [10, 5, -2, -3, -6, 18, 12, 7, -1, 15, 12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, 5, 14, 5, -19, -9, -26, -3, 20, -10, -9, -7],\n [-1, 23, 3, 10, 0, 12, -4, -1, -22, -13, 8, 26],\n [5, 18, -23, -5, 22, 6, -14, -19, 11, 19, -18, 17],\n [1, -26, -12, -20, -10, -15, 2, -13, -14, 26, 5, 15],\n [26, -2, 0, -3, -14, 2, 3, 0, -20, -14, -20, 8],\n [-21, -5, -13, -6, -9, 21, 2, -1, 12, 10, 23, 18],\n [9, 1, -16, -10, -15, 1, -3, 4, 10, 22, 2, -22],\n [8, -14, 24, 18, -18, 4, -4, -11, -7, 26, 20, -19],\n [21, -10, 23, -8, 16, 10, 18, 0, -12, -3, -22, 26],\n [20, 11, -18, -2, -12, 17, 0, 18, 26, -21, 12, -11],\n [24, 2, 6, -9, 9, 14, -26, -14, -21, -7, 11, 7],\n [-9, -20, 10, -11, -13, -13, -23, -13, -26, 6, -19, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[6, 3, -7, -21, -26, -18, 5, 6, -9, 10, -8, 6],\n [-22, -15, -26, -21, -10, -19, -22, 8, 1, -12, 1, -3],\n [-1, -19, 8, -11, -20, -10, 24, 8, 4, -20, 24, -24],\n [-9, 26, 0, -10, 5, -16, -15, 19, 9, -15, -15, -7],\n [15, -24, 4, -22, -7, 13, 16, 20, 15, -26, -16, 18],\n [14, 9, 4, -3, -12, -25, 2, 14, -5, 14, -16, 4],\n [-7, 16, 12, -12, 8, -10, -23, 25, 4, 2, 3, -22],\n [2, -7, -18, 26, 10, -13, 17, -9, 22, -10, -10, -21],\n [-6, 19, 15, -17, 17, 1, 10, 18, -6, -26, 14, -23],\n [10, 18, 25, 21, -21, -2, -26, 9, 15, 8, -24, 17],\n [13, -3, -4, -1, -22, 7, 26, 25, -13, -3, 11, 6],\n [26, -10, 6, 17, 17, -12, 8, -13, -26, 19, -13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[18, 10, -15, 26, 8, 5, -25, 6, -9, 20, -11, -2],\n [-1, -22, -11, 17, -11, -16, -19, -24, 26, -11, -20, 1],\n [-25, 24, 8, 4, -16, 14, -16, -26, 3, 3, 6, -15],\n [-17, 17, 19, 16, -23, 15, 22, 6, 11, 4, 4, -22],\n [-6, -9, -9, -23, 23, -7, 26, -7, 21, 1, 20, -14],\n [8, -9, 6, 10, 9, -18, -1, -26, -2, -3, 3, 15],\n [-15, 17, -12, -7, 0, 2, -25, -12, 8, -17, -1, 7],\n [-19, -26, -12, -23, -24, 18, 15, -25, -8, -8, 19, 14],\n [-8, -7, 22, 10, -25, -2, 12, -5, 7, -5, -15, 19],\n [12, 19, -15, 21, 19, 26, 4, 26, 5, 9, -13, -1],\n [1, -26, -17, -4, 8, -12, 26, 18, -19, -25, -7, 14],\n [16, 2, -25, 13, 14, 17, 24, -12, 26, -23, 15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "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, 13, 16, 10, -6, -12, 6, 26, 22, -15, 3, -23],\n [12, -16, 17, 0, 21, -9, -13, -12, 22, 7, -4, 8],\n [-22, -26, -1, -17, -12, 5, 15, -3, 9, 18, -11, -17],\n [7, 13, -13, -22, -9, -19, 4, 17, -9, -14, 10, -16],\n [-24, -11, -19, -10, 11, -14, 22, 8, 18, 13, -19, -8],\n [15, -12, -20, 23, -26, -14, 22, -8, -25, -5, -19, 16],\n [-2, -1, -15, -24, -6, -22, -15, 0, -26, 16, -24, 25],\n [26, -17, -14, -8, 4, -14, 25, 3, -13, 5, 15, 22],\n [11, 10, -13, 19, 10, 1, -7, -2, -16, 0, 2, -22],\n [-4, 24, 20, 22, -10, -24, 24, -22, -19, 6, -13, 15],\n [4, -19, -26, -22, 24, 12, -22, 7, 20, -26, -17, 11],\n [11, -13, -19, -2, 2, 23, 10, -6, 4, 19, 15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"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, -6, 26, -24, 5, -21, -20, 24, -12, 7, 19, 19],\n [-15, -9, -2, 11, -25, -6, -4, 6, 0, 16, 2, 20],\n [11, -10, -19, -6, -4, 25, -9, 17, -19, 25, -3, -18],\n [2, -16, 18, 9, -19, -23, 19, -3, 22, -25, -15, -15],\n [-1, -8, 23, -1, -3, 15, -2, 14, -11, -26, 5, 21],\n [-3, 13, 24, 7, 23, -7, -4, 1, 25, -9, 5, 26],\n [19, 12, 12, 1, 10, 25, -1, 0, 17, 0, 18, -10],\n [-12, 21, -14, -5, 16, 8, -4, -26, 11, -19, 26, -22],\n [12, 8, 14, -13, -25, -24, -8, -17, -25, 18, -13, -8],\n [18, -20, -24, -26, 25, -4, -14, 11, 17, -17, 8, 4],\n [6, -3, -14, 7, 26, -8, -7, -24, -8, 20, 4, -8],\n [15, 0, -16, 20, 13, -16, -10, 7, 23, -18, 12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-4, -19, -14, 7, 15, -10, 21, 17, 11, -12, 4, 20],\n [21, -24, 18, 23, 8, 9, -22, -1, -1, 25, -3, -21],\n [-20, 25, 1, 18, -13, 12, -6, -16, -15, 23, 23, 7],\n [8, 25, -20, 26, -4, -26, -7, 5, 7, 23, -7, -13],\n [-22, -3, -6, -15, -25, -17, -14, 4, 19, -3, -1, 6],\n [14, -3, -26, -18, 4, -3, 16, -1, 12, 26, -5, 6],\n [5, 6, -18, -12, -5, -11, 8, -2, 8, -2, 19, 10],\n [22, 26, -17, -11, -9, 18, 23, 2, -10, -23, -23, 26],\n [-12, -23, -14, 23, 26, -21, -22, 6, -21, 7, -22, 21],\n [9, -14, 1, -20, -18, -1, 6, -4, 10, -1, 25, -16],\n [22, -14, 25, 0, -25, -11, 24, 2, -7, 5, -4, -18],\n [5, -23, 23, 15, 20, 18, 21, -17, -23, 21, -16, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570", "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, -15, 13, -6, 18, 7, 7, 9, 23, -24, 12, -21],\n [-26, 14, -15, 12, -26, -7, 9, 11, 21, 20, -24, 23],\n [24, 18, -7, 19, 19, -19, -16, 17, -26, 3, 14, 25],\n [-13, -7, 19, 3, 18, -15, -15, 25, 12, -25, -4, -16],\n [21, -14, -9, -8, 0, -16, 26, 3, -26, -14, -19, -5],\n [-7, -13, -13, -11, -8, 12, 2, 11, -18, 23, -21, -1],\n [22, 9, -7, 14, -2, -19, 20, 13, 0, -6, -16, -8],\n [-14, 20, -22, -1, -20, -14, 21, -3, 21, -3, 7, 12],\n [-23, -7, -14, 26, 3, 10, -4, 17, -14, 14, 21, 11],\n [18, -13, 9, 14, -22, -16, -11, -15, -10, 4, -19, -15],\n [-19, -14, -4, -22, -19, -24, 16, -22, 21, 15, 15, -2],\n [5, -11, -16, -3, 14, -3, 12, 19, 19, -5, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-26, -15, -4, -19, 6, -15, -10, 3, 12, 16, -14, -6],\n [-18, 1, -20, -9, 23, 15, 6, 19, -4, 26, -26, 12],\n [-8, -8, -23, -20, 2, 21, 12, -16, 2, -19, 18, -18],\n [-22, 4, -17, 16, -3, -10, 20, -16, 7, -3, -19, 17],\n [12, -3, -25, -19, 4, 20, 17, 8, -23, -15, 12, -11],\n [-5, -10, -2, 24, -12, -7, 4, 23, -22, 3, 0, 19],\n [-13, 19, -10, 3, 19, -23, 15, -23, -24, -20, 25, 12],\n [8, -14, 9, 24, 9, 20, 1, 25, 5, 17, -13, 9],\n [8, 11, 20, -22, -21, -15, 12, 25, 16, 22, -15, -19],\n [18, -9, 24, -9, -17, -21, -22, 18, -4, -2, -20, 16],\n [18, -22, 4, -8, 24, 9, 17, 23, 8, 16, -18, -3],\n [-9, 17, -18, 26, 11, 7, 6, -23, -7, -4, 23, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "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, 16, -26, 12, 16, 5, 21, 24, 1, -3, -14, 6],\n [-15, 6, -13, -14, 21, 10, 0, -23, -23, 13, 20, -11],\n [12, 13, -9, -11, 20, 4, -1, -4, 25, 21, 21, -25],\n [11, -16, -22, 20, -13, -11, 21, 14, 24, 10, -6, -19],\n [-13, -18, -15, -12, -2, -6, 19, 7, -1, -23, -2, 13],\n [5, 2, -5, 7, -8, 23, -21, -7, -11, 6, -18, -5],\n [7, 20, -8, 14, 14, 10, -23, -22, -15, 6, 24, -18],\n [17, 2, 3, 2, 18, 25, -10, 8, -14, 19, 9, -23],\n [-26, 11, 16, 0, 1, -2, -3, -25, -4, 24, -5, -9],\n [25, -11, 5, -24, -26, 7, 18, -1, 19, 13, 19, -21],\n [17, 9, -18, -20, 4, 6, -23, -21, -16, 13, -14, -18],\n [24, -9, -1, -4, -4, 24, -22, -17, 20, 13, -8, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-12, -8, -23, 8, 10, -15, 4, -11, 13, -6, -7, 23],\n [-5, 17, -22, -19, -19, 6, 0, 3, 1, 13, 24, -9],\n [25, -17, 13, -14, 10, 16, 13, 24, -4, -8, -4, 14],\n [-11, -15, 9, -23, -15, 0, -13, -11, 26, 2, -15, 26],\n [-12, -26, 1, -19, 5, -2, 8, -15, -21, 4, -18, 25],\n [-2, -7, 11, -12, 9, -1, 10, 22, 14, -16, 0, 12],\n [-6, 26, -21, -16, 19, 4, -16, 24, 18, -19, -8, 5],\n [-1, 19, 10, 16, 26, 7, 20, -11, 6, 8, -17, 9],\n [-4, 21, 14, -23, -8, -8, 15, 15, -13, 6, 21, 25],\n [10, 19, -9, -19, -17, 4, 8, -2, -2, 13, 20, 19],\n [-24, -12, 5, -6, 6, 12, 0, -13, 9, 19, 14, -17],\n [-3, -17, 4, 12, 20, 1, -23, 23, 21, -8, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -21, 24, -17, 18, -11, -25, -19, 14, 12, -22, 3],\n [-19, 2, -24, -14, 25, 0, 24, -15, 24, 13, 24, -21],\n [12, 22, -12, 19, 20, -19, 13, 25, -3, 5, 4, 11],\n [-24, 21, 8, -14, 20, 15, 14, -12, -1, -15, -2, 1],\n [-8, -18, 8, 18, 9, 5, -24, -22, 25, 14, -9, 15],\n [24, -12, -2, -9, -20, -5, -3, 8, -5, 0, -25, -16],\n [20, -1, -20, -8, 10, -8, -17, 20, 4, -26, -10, -17],\n [9, -6, -10, 15, 17, 16, -24, 24, 23, -5, 3, 23],\n [9, -22, -24, -26, -10, 22, 25, -5, 0, 6, -6, -26],\n [-23, 14, -21, 1, -15, 18, 25, -4, 16, -15, 15, 21],\n [22, 18, 6, -6, 14, 13, 0, 23, 5, -26, 5, -24],\n [6, -26, -3, -8, -9, 5, 17, -21, -10, -15, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[12, -25, -7, -7, 20, 12, 24, 5, -24, -1, 14, -15],\n [23, -24, 1, -18, -1, -21, -22, -18, 19, 7, 1, -1],\n [8, -26, -23, -14, 13, 26, -6, -9, -7, -23, 5, 0],\n [-2, -20, 18, 3, -4, 2, -6, 6, -9, 0, -13, 13],\n [4, 15, -19, -24, 8, 11, -16, 9, 25, 21, 16, 25],\n [7, -4, -22, 3, 10, -11, -13, -20, 26, 6, -25, 19],\n [-22, 18, 18, 12, -12, 15, -25, -3, 2, 2, -6, -2],\n [-5, -8, -14, 11, 6, 6, -15, 19, -4, 2, 2, 16],\n [-26, -3, -22, 8, 18, -22, -14, 5, 15, 0, -3, -24],\n [-26, 2, 18, -5, -22, 16, -6, -15, 1, -16, -12, 11],\n [8, 21, 18, -11, 10, -12, 5, -11, 6, 13, -7, 10],\n [12, 5, -17, -11, -22, -7, 0, 16, 23, -7, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[17, 23, -12, 11, 0, 15, -10, -17, 9, 13, -22, 24],\n [23, 21, 0, 1, -23, -20, -19, -12, 14, 2, 12, -18],\n [-7, -26, -20, 7, 20, -17, 14, 21, -21, -2, -15, 13],\n [14, 12, -13, -16, -15, -8, 15, 1, 26, -8, 2, 18],\n [8, -4, -11, 10, -6, 13, -26, 19, 25, 10, -2, -11],\n [6, -2, -5, -24, -24, -16, 16, 25, -22, 17, -2, 11],\n [26, -11, 5, 2, -21, -5, -18, -17, -13, 20, 12, -7],\n [-22, -20, 13, -13, -12, -10, -7, -11, 14, -6, -16, -23],\n [-2, -25, -25, 0, 4, 20, -19, 21, -19, -22, -5, 16],\n [-22, 13, 21, -21, 11, -20, -9, -2, -24, -2, -6, 4],\n [19, 22, 15, -11, 25, -5, 24, 2, -15, 19, 16, -26],\n [-1, -17, -2, -2, 16, -23, -9, 16, -19, -20, -10, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[15, 17, -6, -25, -14, 5, -14, 2, -22, -1, 11, 5],\n [21, -9, -10, -7, -12, -12, 20, -23, -18, 17, 19, 6],\n [-17, 20, 16, -26, 13, 26, -18, -5, -1, 8, 6, -17],\n [11, -8, -23, -8, -20, -15, 0, 5, 0, -6, -22, -8],\n [24, 25, 26, -20, -13, -18, 10, 23, -18, -22, 21, -18],\n [25, 16, 3, -13, -24, 25, -3, 1, 12, -16, -10, -9],\n [24, -10, -2, 14, -13, -6, -16, 20, 0, -23, 24, 14],\n [7, 13, -20, -9, -8, -9, -12, -16, -15, 8, 9, 26],\n [23, -15, -11, 1, 17, 12, 17, 9, 3, -11, -11, 22],\n [-7, -18, 19, -22, 4, -9, 17, -5, 12, -25, 23, -24],\n [20, 1, -16, -17, -7, 4, 26, 24, 18, 21, 25, -5],\n [-9, -15, -12, 7, 18, 1, 17, -12, 8, -10, 11, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "565", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-1, 2, 25, -2, -23, 0, 15, -5, -3, 26, -8, 14],\n [0, -8, 20, 14, -14, 4, -25, 0, -19, -15, 2, 2],\n [-5, 3, -18, -22, 9, -14, 20, -25, 6, -23, -17, 6],\n [-25, -15, -11, 8, -18, -24, 1, 25, -11, 13, -8, -16],\n [11, 19, 4, -26, 17, 3, -6, -12, -11, -23, -3, 13],\n [-4, -10, 8, -1, 8, -12, -12, 0, -19, 26, -12, 26],\n [-19, 24, -23, -26, -2, 8, -19, 22, -10, 1, -21, 16],\n [-21, -26, -24, 25, -18, -12, 13, -7, -11, -17, -13, -11],\n [-12, 14, -1, -17, 13, -15, 10, -13, -2, 3, 26, 3],\n [8, -12, 4, 11, 24, -9, -20, -24, -22, -2, -11, -12],\n [-7, 14, -5, 8, 0, -15, 6, -3, -1, 25, 11, 7],\n [-14, 1, -7, -19, 23, -11, 7, 5, 21, 3, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "517", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[21, -18, 4, -8, 16, 7, -11, -3, -11, -12, 4, 25],\n [-20, 17, -12, -25, 12, 25, -5, -3, -2, -15, 25, 24],\n [-13, 7, 19, -7, -13, -9, 8, -10, 21, 18, -4, -5],\n [22, 4, 2, -2, 5, 4, -21, 10, -10, 20, 4, -6],\n [-25, -20, 0, -5, -23, 0, 24, 18, 5, -6, 8, -18],\n [1, -17, 23, -4, -3, 21, -23, -10, 21, -3, -26, 10],\n [-25, 13, 21, 26, -21, -13, 9, -6, -2, -19, 25, 0],\n [-13, -23, 19, -19, 0, -8, 3, 1, 0, 10, 17, -24],\n [22, 1, -8, 11, 0, -4, -8, -14, 3, 14, 23, 19],\n [-19, 2, 16, 23, 23, 20, -21, -10, 2, 13, 25, 21],\n [-25, 6, 18, 12, 24, 8, 4, -15, 4, -1, 17, 5],\n [22, 22, 23, -24, -7, 26, 20, -25, 12, 18, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[24, -21, 15, -19, -1, -17, 11, 17, -26, -25, 16, 8],\n [-26, -23, -24, -3, -10, 0, -2, -7, 12, 17, 24, 3],\n [-21, -20, 0, -22, -1, 9, -16, 15, -4, -24, 23, -12],\n [17, 26, -2, -11, 5, -1, -22, -17, -16, 6, 1, -11],\n [17, -25, 2, 17, -25, -5, -16, 8, 5, 10, 20, -22],\n [0, 24, -15, -19, -24, 5, -5, 1, -1, 18, -6, -16],\n [0, 16, -20, 11, 16, -18, 20, 21, 7, 16, -1, -21],\n [-15, 10, 23, 17, 13, -26, 8, -23, 13, 23, -19, -25],\n [-15, 24, -19, 14, 4, -6, 4, 5, -7, 20, -8, 20],\n [3, 24, -18, -7, -9, 21, -14, 3, 20, 2, 25, 24],\n [3, 20, -22, -23, 23, 19, 4, 15, 6, 22, -26, -8],\n [-12, -25, -23, -24, -4, 13, 16, 26, -21, 3, -4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[22, -12, 18, 20, 23, -10, -18, -25, 23, 26, 14, 2],\n [24, 15, 19, 4, 5, -26, 3, 1, -1, -9, -26, 14],\n [25, 21, -8, 8, 6, -19, 25, 22, 0, 10, 15, -19],\n [17, 21, 5, -8, 3, 9, -17, 9, -11, -24, -5, 24],\n [-5, -6, 3, 0, -25, -19, 16, -4, 12, 11, 14, 9],\n [-13, 26, 4, 20, 24, -8, 3, -11, -15, -3, 15, 11],\n [5, 23, -8, 13, 20, -22, 18, 19, 20, -25, 24, 5],\n [0, -25, 10, 10, -5, 7, 0, -10, 12, -4, -17, -5],\n [-12, 23, 13, 9, 16, 12, -11, 1, 8, 5, 25, 20],\n [-3, -6, 14, -8, 5, 19, 7, 25, -9, -16, -16, -9],\n [-26, 13, -26, -3, 14, -5, -20, -10, 22, -15, -26, -24],\n [20, 3, -4, -19, 17, -10, -21, -15, -6, -16, -25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "546", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[21, -7, 4, 9, -3, -5, -18, 22, -10, 7, 26, -16],\n [-21, 24, 22, -4, 21, 22, 20, 18, 22, 13, -1, -18],\n [-19, 22, 25, 19, -1, 25, -15, 6, 18, -20, -11, -1],\n [-2, 8, 16, 2, 23, 15, 1, -11, -8, 13, -21, 0],\n [-24, 7, -10, 5, -3, 8, 8, 5, 26, -12, 10, -2],\n [-6, -13, -4, -20, -22, -13, -8, 16, -20, -19, -23, -21],\n [10, -17, 23, 22, -13, -14, 11, 21, 15, -20, -6, 6],\n [-16, -21, 9, -16, 7, 3, -18, -20, 19, 10, -9, 22],\n [2, -6, -13, -11, -1, 26, 4, 24, -16, 5, -1, 6],\n [10, -16, -7, -14, 7, 6, 16, -23, -19, 23, -16, -25],\n [-5, -23, 15, -2, 25, 17, 23, -12, -15, 6, 5, -21],\n [16, -26, 11, 13, 11, -7, 17, 23, -22, 10, 13, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "559", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-25, -13, -10, 23, -9, -10, 13, 4, 15, 4, 9, -8],\n [5, -10, -3, 18, 13, -23, -22, 25, 26, 20, 25, 14],\n [-26, -1, 15, -24, -4, -14, -5, 4, -19, 3, 19, -15],\n [-5, 16, -12, 3, -3, 22, -2, 26, -25, -26, -7, 18],\n [17, -1, -19, -8, 4, -12, 15, 25, -25, -25, 23, 2],\n [6, -17, 21, 19, -6, -6, 16, -14, 24, -11, -8, -3],\n [-4, -23, 4, -19, 15, -2, -4, -16, 1, 18, -4, 18],\n [26, 18, 16, 21, 20, 9, 7, 21, -16, 22, -19, 7],\n [-19, 25, -10, -5, -19, -26, -13, -22, 0, 21, 22, -4],\n [-15, 25, 3, -19, 13, -25, -22, -14, -10, 8, -12, -15],\n [8, 15, 21, 24, -24, -17, -25, -12, -20, -7, -19, 20],\n [-1, -19, 3, 18, -7, 4, 2, 26, 3, 4, -23, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "590", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[17, 3, -5, 5, -15, 3, -22, -25, -21, 16, 16, 8],\n [-17, -11, 21, -5, 24, -13, 13, -11, 21, 12, -26, -11],\n [-7, 5, -25, -5, -22, -25, 22, 12, 17, 14, 5, -16],\n [-1, 24, 4, -12, -15, -1, 20, 22, -16, 22, -5, 1],\n [-5, -6, 17, -17, 26, 11, -2, 12, -13, 21, 8, -18],\n [11, 10, -23, -12, 2, -17, 6, -20, 26, -10, -23, -17],\n [-26, 15, -7, -20, -18, 5, 1, 1, -25, -23, -10, -21],\n [-19, 19, -15, -8, 2, 5, 1, -22, 16, 22, -15, -22],\n [6, 26, 4, -2, -20, 12, -2, 2, -16, -6, -4, -21],\n [11, -4, -17, 8, -22, -9, -6, -12, -15, 13, -20, 1],\n [8, -20, -9, 21, -7, -1, 7, 12, 10, -13, -12, -11],\n [-4, 7, -7, -8, -17, 23, 7, 13, 11, 24, -19, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-6, -26, 18, 22, 15, -9, 22, -4, -11, 20, 15, -2],\n [-22, -16, 16, 19, -21, 20, -13, 17, -1, 0, -13, 16],\n [2, -9, -9, -13, -20, 1, -22, 22, 13, 22, -12, 22],\n [7, -22, 25, -23, -10, -26, -17, 7, 23, 6, 15, 0],\n [-3, 24, 26, 16, 1, -8, -25, -26, 18, -2, -24, -20],\n [-2, -12, 25, -23, -25, -21, 8, 7, -6, -5, 25, 14],\n [2, 22, -13, 19, 15, 22, -20, -22, -12, 25, 21, -13],\n [10, 8, 22, 1, 10, -1, -21, 21, 20, -19, -17, 19],\n [-5, -17, -8, 5, -13, -3, -9, 0, -9, -23, 2, 4],\n [-24, -10, -24, -20, 4, 0, 11, -24, -14, -9, -5, 18],\n [-15, 12, 23, -8, 19, 3, 26, 17, 4, -10, 1, 14],\n [-23, -22, 8, -20, -11, -1, -7, -23, 5, -18, -24, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[24, 5, 18, 23, 26, -25, 1, -22, -13, 18, -17, 17],\n [5, 11, 20, 1, -26, -24, 12, -2, 3, 9, 11, 3],\n [-12, 4, 16, -2, -4, 19, -1, 23, -5, -11, -10, 0],\n [-10, -10, -7, -25, 9, -4, 1, -1, 16, 23, 18, 24],\n [-15, -10, 14, 1, -16, 11, 18, -16, -12, -1, 2, -1],\n [-4, -16, -23, 25, -17, 15, 13, 6, -23, 9, -19, -5],\n [-6, 3, 3, -11, 19, -25, -4, 7, 3, 1, -22, 8],\n [-18, 11, 19, -8, 14, -20, 26, -1, -13, 5, 12, 3],\n [-17, -25, 11, -22, -21, 1, -12, 2, 3, 17, 17, 4],\n [4, 8, -1, -18, 26, 21, 26, -20, -14, -7, 24, 1],\n [20, 3, 24, 14, 0, 22, 3, 14, -3, 3, -26, -3],\n [-7, -19, -10, 4, -23, 7, 6, 2, 25, -8, -13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-26, -5, 19, -23, 25, 8, 23, 25, 12, 6, -11, 18],\n [8, -15, 9, 24, 19, -20, -23, -15, -20, 19, -12, -21],\n [-10, -10, 17, -23, -20, 9, -20, 11, 9, 15, 6, -4],\n [1, 1, 6, -5, 12, -5, -23, -3, -11, 23, 19, -14],\n [-12, 6, 3, -4, 15, 23, -22, 26, 12, 7, 14, -22],\n [23, 17, -23, -11, -16, 24, 0, -4, 6, -4, -14, -22],\n [5, 13, -17, -12, -12, -4, 18, 7, -23, -14, 2, -18],\n [-22, -15, 7, 25, -19, -7, -11, -3, -7, -19, 2, -8],\n [25, 15, -2, 10, -24, -8, 25, 7, -20, -18, -19, -8],\n [10, -19, 20, -3, -25, 2, -15, 22, 21, -22, -26, -14],\n [12, -19, -8, 19, 1, -17, 22, 23, 7, -17, -9, -17],\n [-6, -25, -18, 21, 11, -20, -24, -1, -20, 25, 13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, 8, 19, 0, 11, 8, -20, 11, -7, -4, 23, 2],\n [26, -5, -6, 15, -22, 13, 26, 20, 21, 16, -17, 6],\n [-26, 22, 9, -11, -8, -22, -4, -24, 19, 23, -9, -24],\n [15, 24, -24, -13, -19, 5, 3, -8, -21, -18, 21, 3],\n [-21, 21, 4, 15, 26, -6, 13, -12, 16, -6, 16, -13],\n [11, -15, -12, 10, -16, 3, 8, 8, 15, 15, 25, 10],\n [1, 14, -17, -16, -25, -25, 19, -10, 13, 22, -14, 11],\n [-25, 25, -1, 0, 26, 23, 26, 12, 10, 6, -9, 2],\n [-23, 21, 3, 11, -10, 21, 13, -14, -7, 9, -22, 0],\n [-4, -16, 8, -9, 17, 26, -24, 4, 16, -12, 8, 12],\n [-21, 2, 0, 1, -24, -4, -1, 0, -21, 6, -13, 26],\n [25, -24, -8, 13, -8, 0, 23, 10, 24, 15, 21, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "552", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[13, 14, -25, 18, -13, 22, 1, -17, 11, 1, -14, 1],\n [18, -10, -22, 20, -22, -8, 7, 14, 16, 12, 4, -2],\n [24, -26, 23, -5, 11, 21, 2, -25, 14, 15, 3, -10],\n [9, 25, -13, -10, 1, 26, -21, -18, -16, -19, 20, 25],\n [-4, -21, -6, -10, 12, -16, 12, -22, 4, -11, -15, 3],\n [-2, -15, -24, -10, 26, -23, -21, 23, 21, -12, 5, -6],\n [-25, 19, 21, -24, -2, 0, 0, -4, -18, 9, -16, 12],\n [-20, -14, -20, 15, 20, 16, -14, 26, -21, -23, 16, -2],\n [-7, -18, -2, 10, -18, 14, 17, -8, -15, 8, -23, -8],\n [23, 17, 19, -21, 4, 20, 24, 5, -18, 21, -1, -21],\n [10, 16, 7, 13, 24, -6, 15, 0, 25, -8, 0, -24],\n [-2, 7, 24, -6, -16, 0, 1, -23, 17, 14, 26, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -6, 12, -23, 10, 22, 16, -23, 23, -4, -18, 13],\n [-3, 2, -20, -9, -25, 1, 16, 14, 2, 18, -10, 4],\n [-10, 4, -4, -17, -21, 11, 20, 0, -16, -7, 19, -22],\n [5, -22, -5, -26, -7, 24, -12, -16, 5, 1, 1, -10],\n [7, -3, -25, 0, -18, 25, -8, 9, 2, -16, 5, 0],\n [25, 12, -3, 0, 0, 13, 5, 18, 17, -5, 22, 15],\n [5, 21, 19, 8, -26, 26, 7, -26, 15, 8, 2, -9],\n [-21, -21, 0, 12, 26, -8, 11, -24, 26, 24, 11, -7],\n [-25, -20, -22, -2, 15, 26, -14, -15, -22, -15, -9, -24],\n [-23, 16, -8, -6, -2, -24, -20, -18, -23, -4, -16, -8],\n [-26, -23, -18, 15, -20, -1, -6, 21, -17, -17, -26, 9],\n [-24, 8, 18, -15, 0, -10, -8, -17, 16, -1, -19, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, -25, -15, 12, 13, 4, 2, -19, -12, -1, 21, 9],\n [14, -23, 23, 6, -15, 23, 26, -16, 3, 26, 18, -1],\n [23, 3, 9, 6, 18, 4, -25, -12, -25, 26, -15, -9],\n [-19, -24, 8, 6, 4, -23, -4, 10, 18, 18, 8, 13],\n [26, 11, -26, -24, -17, 25, 3, 1, -11, -23, 26, 21],\n [18, -23, -4, 13, -4, 23, -12, -14, -26, 10, -3, 17],\n [-26, 18, 23, 18, -14, 11, -10, 24, 3, -7, 15, -22],\n [14, -22, 19, 10, -11, -6, 7, 19, 23, -21, 15, -21],\n [-17, 4, -21, -24, 17, 25, -2, -7, 8, -26, 25, 4],\n [-13, -24, -11, -13, -24, -21, -18, 6, 14, -15, -25, 16],\n [19, -24, -14, 4, -18, 13, 14, -19, -5, -1, -11, 5],\n [8, 9, -26, -20, 23, 22, 13, 15, 21, -16, -16, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "590", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rounded largest singular value from the SVD of:\n[[14, -23, -2, -24, -17, -22, -15, 7, -15, 26, 11, -12],\n [-6, -23, -16, -17, -20, -18, -9, 20, 0, 16, 1, 5],\n [-17, 7, -22, -7, 3, 6, -8, -25, -9, -13, -22, -9],\n [18, 24, -12, -4, 23, -23, 7, -3, -15, 2, -21, -3],\n [20, -5, -10, 5, -2, 26, -1, 0, -20, 8, 7, 0],\n [-19, 8, -9, -4, 3, -11, 4, 11, 23, 7, -26, -18],\n [9, 17, -23, 18, -7, 18, -10, 17, -17, 19, 16, 13],\n [-14, 11, 17, -11, 12, 6, 0, 10, 21, -11, -12, -11],\n [-21, 2, 13, -10, 13, -20, 7, 18, 9, -1, -1, -16],\n [-2, 9, 15, 21, -25, 14, 1, -26, -21, 13, 9, -26],\n [22, -12, -26, -8, -2, -13, -5, -4, -20, 7, -16, -11],\n [20, 11, -18, -23, 18, 13, 8, -4, -3, -23, 3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 25, 11, 7, 7, 4, 4, 5, 9, -5, -8, 18],\n [8, 11, 15, -12, 11, -19, 5, 9, 10, 3, 24, 21],\n [-4, 16, -20, -5, 9, 12, 1, -15, -24, 18, 11, 17],\n [9, -6, -5, -4, -20, -20, -6, 17, -13, 15, -20, -22],\n [10, -8, -2, -15, -18, -26, 25, 16, 2, 16, -8, -12],\n [9, -9, -5, -5, 3, -20, 21, -21, -14, 25, -13, -25],\n [15, -11, 12, 19, 6, -26, 3, -16, -13, 10, 10, 26],\n [8, -13, 21, -5, 4, -9, -17, -3, -3, 5, 10, 7],\n [26, -17, 19, -13, -4, 5, 20, -15, 14, -3, 7, 20],\n [-7, 2, -11, 25, 13, 23, 15, -18, 17, 23, 25, -24],\n [-17, 13, -26, -20, 4, 14, -14, -5, -11, -5, -21, 26],\n [19, -26, -25, 0, -15, -21, -25, 10, -17, -10, -10, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525", "dataset": "MATH"}
{"messages": [{"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-26, -7, -9, -18, 5, -10, -8, 22, -14, -26, 18, 11],\n [17, 11, 9, -17, 8, -1, 21, 6, 13, -19, -7, -25],\n [12, 13, 1, 2, 26, -2, -1, -19, 3, 25, -26, 1],\n [3, -14, 14, 22, -6, -6, 13, -16, 0, -22, -14, -15],\n [13, 6, 3, -24, 21, -4, 4, -21, -16, 10, 12, 20],\n [18, 10, 12, 24, -21, -9, -26, -9, 25, -16, 15, -21],\n [-22, -3, -25, 21, 8, 7, 15, -25, 25, -15, -25, 20],\n [23, 8, 2, 6, -22, 16, 25, 16, 6, 12, -14, 4],\n [9, -8, -2, 16, 8, 26, 10, 12, 6, 16, -24, 24],\n [20, 15, -3, -24, -20, -14, -3, 11, 3, -22, -4, 14],\n [17, 0, -9, 13, -7, -21, 3, 23, -21, 23, -10, 16],\n [26, 9, -12, 25, -10, -2, 17, 3, 16, 13, -10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554", "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, 21, 22, 15, 15, 8, -16, 1, 17, -7, -25],\n [14, 6, 9, -17, 18, -8, -2, 0, 8, -4, 16, 7],\n [-19, -25, -2, -18, -2, 18, 2, -5, -13, 25, 21, 16],\n [21, -16, 23, 24, 24, -14, 6, -24, 20, 25, 9, 24],\n [21, 15, 5, 9, 16, 9, 8, -22, -15, -8, 13, 0],\n [8, -17, 24, 1, 6, 20, 20, 16, 9, 8, 22, -10],\n [-16, 9, 10, -9, 4, 8, 1, -26, 4, 25, 0, 13],\n [-15, -15, 0, 0, 24, 19, -10, 25, -2, 3, -17, 13],\n [-12, -8, -23, -12, 10, -12, 6, 24, -14, -10, -8, -14],\n [-21, 13, 3, 9, 4, 26, -14, -3, 2, 22, 19, -25],\n [-11, 25, -15, 1, -1, 5, 15, -23, -22, -10, -7, 13],\n [2, -2, -9, -5, 26, -19, 13, 20, 13, -17, -10, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[21, -7, 0, -25, 25, 2, -21, -7, 10, -8, -16, 21],\n [-9, 12, -5, 24, -13, 15, -21, -6, -19, -9, -5, -21],\n [8, 8, 19, 18, 26, -18, -11, -16, 21, -6, 15, -4],\n [18, -7, -10, 4, 25, -9, 2, 21, 5, -19, 23, -18],\n [19, -21, -22, 18, -14, -2, 4, 7, -10, -1, -7, 23],\n [-21, 5, 6, -7, 20, -16, 20, 25, -17, 16, 12, -8],\n [0, 13, 7, 9, -7, 19, -22, -17, 5, 13, 13, 1],\n [26, 2, 21, -5, -18, -25, -14, 8, 0, 3, 2, 8],\n [10, 24, -1, -23, 8, -17, -7, 22, -17, 3, -16, -11],\n [-20, -4, 13, -26, 18, -20, 14, -23, -25, -10, 13, -18],\n [-16, 17, -8, -13, -12, 20, -19, 6, -25, -25, -7, -4],\n [-9, 3, -6, 9, -24, -10, -3, 11, -23, -18, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}