{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[13, 3, -11, 17, -18, -5, 13, -7, -3],\n [0, -15, -2, 10, 14, -2, -23, -4, -24],\n [0, 0, 4, 12, -24, -5, 7, -14, -4],\n [0, 0, 0, 1, 16, 2, -10, -11, 21],\n [0, 0, 0, 0, 25, -19, -5, -17, 13],\n [0, 0, 0, 0, 0, -17, 0, -24, -6],\n [0, 0, 0, 0, 0, 0, 9, -12, -9],\n [0, 0, 0, 0, 0, 0, 0, -22, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1868", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 13, 19, -11, 17, 3, 10, -13, 6],\n [0, 25, -4, 2, -24, 16, 19, -20, 2],\n [0, 0, 18, -6, 4, -15, 2, -1, 13],\n [0, 0, 0, -13, 15, -23, 13, -20, -18],\n [0, 0, 0, 0, 25, 16, 18, -2, -11],\n [0, 0, 0, 0, 0, 23, -14, 13, -24],\n [0, 0, 0, 0, 0, 0, -24, -24, 2],\n [0, 0, 0, 0, 0, 0, 0, 18, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-119", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[8, -20, -4, -15, 22, -10, 7, -17, -20],\n [-10, 3, -23, -6, 10, -7, 0, -23, -7],\n [-6, 6, -19, 15, 7, 14, 13, -8, 14],\n [-25, -15, 2, -1, 24, -3, 5, 4, 16],\n [9, -19, -10, 0, 22, 23, -24, -25, 22],\n [-14, -21, 11, 6, -17, 15, 9, -7, 22],\n [-10, -23, -6, -2, 7, -2, -15, 23, -18],\n [10, 12, 14, -6, 9, 22, -1, 9, -1],\n [3, -8, 20, -8, -24, 9, -10, 15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 7) of the inverse. Round your answer to the nearest integer:\n[[7, -22, 7, -12, -5, 22, -6, -18, -19],\n [0, -9, 7, 22, -14, 25, -4, -4, 20],\n [0, 0, 12, 19, 25, -18, 1, 1, 8],\n [0, 0, 0, 2, 21, 7, -21, 22, -7],\n [0, 0, 0, 0, 18, 2, 4, 3, 20],\n [0, 0, 0, 0, 0, 3, 23, 20, 5],\n [0, 0, 0, 0, 0, 0, -23, -8, -1],\n [0, 0, 0, 0, 0, 0, 0, 6, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -17, 17, 22, 13, 3, 16, 0, 9],\n [24, -1, -2, -13, -19, 10, 19, -6, -25],\n [-18, 20, -10, -12, -14, 25, -3, -11, 2],\n [8, -24, 6, -3, -4, 25, -1, -4, -4],\n [23, 16, -20, -11, 17, 11, 7, -18, 18],\n [18, -21, 13, -22, -20, 19, 6, 4, 21],\n [9, 14, -10, -13, 24, 16, 4, -7, -9],\n [-7, 2, 0, 11, 0, -3, -17, -14, -25],\n [-25, 21, 8, 6, 22, -1, 14, 19, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "747", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 13, -21, -4, 3, -23, -14, 0, -10],\n [25, 11, -4, 3, -12, 2, -21, 21, 23],\n [4, 20, -21, -14, -10, 0, 0, 22, -5],\n [13, 10, 7, 4, 11, -3, -16, -21, 10],\n [8, 5, -16, -7, 6, -25, -21, 19, -22],\n [-10, -2, -10, -24, 23, 2, 6, 1, -6],\n [-2, -14, 24, 9, 7, 7, 25, 17, 11],\n [-14, -23, -25, 7, 14, -16, 17, 18, 3],\n [-13, -14, 5, 20, -24, 25, 24, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 4) rounded to the nearest integer?\n[[-9, 0, -18, 3, 0, -16, 0, 8, 25],\n [0, -19, -22, 24, 19, -15, 3, 10, -1],\n [0, 0, -16, 11, -17, -2, 9, 23, 9],\n [0, 0, 0, 23, 13, 6, -2, -3, 6],\n [0, 0, 0, 0, -3, -1, 9, 15, 4],\n [0, 0, 0, 0, 0, -4, -13, -7, 23],\n [0, 0, 0, 0, 0, 0, -19, 2, -12],\n [0, 0, 0, 0, 0, 0, 0, -1, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-21, 9, -3, 3, 17, -15, -8, 21, -14],\n [0, -16, 18, -9, 12, -19, 20, -13, 14],\n [0, 0, 24, 1, -24, -21, 3, 11, 12],\n [0, 0, 0, 19, -25, -4, -9, -19, -1],\n [0, 0, 0, 0, 5, -7, 18, 13, 1],\n [0, 0, 0, 0, 0, 19, -13, 24, 2],\n [0, 0, 0, 0, 0, 0, -23, -13, 2],\n [0, 0, 0, 0, 0, 0, 0, 6, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-6, -8, 21, 15, 23, -12, -11, 5, -25],\n [-23, -10, -3, -15, -14, -16, 6, -10, -18],\n [12, -14, -2, 2, -18, 2, 10, 0, -18],\n [24, 2, 2, 11, 15, 10, 1, -9, -17],\n [7, -6, -13, 2, 22, 3, -13, 20, 9],\n [-20, -8, 25, -21, 21, -1, -24, -16, 4],\n [24, 19, -21, 7, -25, -8, 6, 21, 23],\n [-15, -5, 0, -1, -4, 1, 23, -13, 7],\n [8, 15, 9, -25, -5, 22, -20, 2, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-21, -6, -1, 8, -2, 4, 12, 12, -6],\n [-6, -7, -11, -12, -16, -11, 22, -9, 2],\n [-1, -11, -22, -6, 14, 1, 7, 3, -7],\n [8, -12, -6, 0, 6, -24, 8, -12, -17],\n [-2, -16, 14, 6, -9, 4, 12, 0, -14],\n [4, -11, 1, -24, 4, 25, 1, 14, 0],\n [12, 22, 7, 8, 12, 1, 1, 25, 1],\n [12, -9, 3, -12, 0, 14, 25, -9, -12],\n [-6, 2, -7, -17, -14, 0, 1, -12, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[8, 0, -23, 6, -2, 2, 13, -3, 12],\n [0, -3, -6, -1, -20, -5, 0, -16, -5],\n [-23, -6, -23, 0, -22, 10, 12, 14, 22],\n [6, -1, 0, -21, 4, 2, 4, -4, -2],\n [-2, -20, -22, 4, -14, -8, 10, -2, 6],\n [2, -5, 10, 2, -8, 0, 16, -2, 23],\n [13, 0, 12, 4, 10, 16, -25, -8, 2],\n [-3, -16, 14, -4, -2, -2, -8, -3, -18],\n [12, -5, 22, -2, 6, 23, 2, -18, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-3, 4, 8, -1, 20, -14, -4, -4, 2],\n [4, -1, 14, 8, -17, 6, -14, -5, -14],\n [8, 14, -1, 5, 0, 1, 10, 2, -11],\n [-1, 8, 5, -8, 22, 14, 0, 0, 5],\n [20, -17, 0, 22, 18, -14, 10, 14, -2],\n [-14, 6, 1, 14, -14, 11, -4, 4, -14],\n [-4, -14, 10, 0, 10, -4, 4, 8, -6],\n [-4, -5, 2, 0, 14, 4, 8, -2, -8],\n [2, -14, -11, 5, -2, -14, -6, -8, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "473", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (5, 1) rounded to the nearest integer?\n[[4, 16, 10, -20, -16, -20, -4, -8, 4],\n [16, 18, 1, -5, -2, -6, -2, 1, -4],\n [10, 1, -14, 4, -20, -8, -4, -1, 13],\n [-20, -5, 4, 17, -2, -1, 2, 16, -2],\n [-16, -2, -20, -2, -24, -15, -4, -8, -9],\n [-20, -6, -8, -1, -15, -15, 4, -14, 8],\n [-4, -2, -4, 2, -4, 4, 24, 1, -3],\n [-8, 1, -1, 16, -8, -14, 1, -4, -1],\n [4, -4, 13, -2, -9, 8, -3, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-21, -7, -12, 0, -22, -1, 19, 16, -1],\n [0, 14, -18, 13, 14, -12, 6, 25, 12],\n [0, 0, -11, 7, -1, -9, 7, 21, -24],\n [0, 0, 0, 25, 13, 25, -20, -20, -23],\n [0, 0, 0, 0, -11, 21, 3, 7, 4],\n [0, 0, 0, 0, 0, 7, 11, 1, 7],\n [0, 0, 0, 0, 0, 0, 7, 12, -13],\n [0, 0, 0, 0, 0, 0, 0, -18, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1171", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (5, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, 10, 10, 0, 17, 1, -21, -6, -15],\n [-16, 14, 12, -20, -18, -3, 21, 0, 20],\n [17, -14, 0, -13, 14, -8, -1, 7, 21],\n [14, 17, -14, 18, 10, 22, -22, -21, 11],\n [-18, 16, 23, 2, 5, -17, 25, 3, -12],\n [14, 15, -4, -15, -3, -25, 20, 11, -5],\n [0, 20, 10, -3, -25, 25, 14, -11, -5],\n [21, -17, -17, -16, 0, 15, 9, -1, 0],\n [-15, 12, -24, -19, -8, 1, 8, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[17, 18, 25, -2, -1, -19, -20, -2, 7],\n [0, 3, 17, -4, 0, 2, 24, -5, 23],\n [0, 0, -6, 15, 23, -6, -4, 2, 14],\n [0, 0, 0, 6, -13, 4, -3, 25, -7],\n [0, 0, 0, 0, 19, 3, 4, -10, 14],\n [0, 0, 0, 0, 0, 21, 24, -24, 2],\n [0, 0, 0, 0, 0, 0, -25, -18, 3],\n [0, 0, 0, 0, 0, 0, 0, 8, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-2, -3, -18, 21, 11, -23, 25, 7, 2],\n [0, -18, 8, 9, 6, -2, -12, 6, 20],\n [0, 0, -22, 11, -5, -12, 5, 22, -8],\n [0, 0, 0, 7, -3, -5, -7, 22, -7],\n [0, 0, 0, 0, -25, 21, -21, -6, -15],\n [0, 0, 0, 0, 0, -6, -21, 11, 12],\n [0, 0, 0, 0, 0, 0, 18, -2, -9],\n [0, 0, 0, 0, 0, 0, 0, 25, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3696", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[17, 20, -22, 0, 3, 19, 8, -3, 11],\n [-15, -20, -8, -5, 16, 10, 15, 12, 8],\n [-9, 11, -1, 12, -14, -3, 16, -4, -5],\n [1, 5, -20, 1, 14, 8, -14, 19, -19],\n [-16, 19, -9, 0, -5, 2, 20, -24, 17],\n [-25, 25, 10, 25, 0, 3, -5, -15, 14],\n [-15, 10, 23, 13, 14, 9, 8, 21, -2],\n [-4, -21, 7, 10, 21, -6, -7, 9, 17],\n [-9, 19, 17, 8, -17, 0, -24, -17, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1399", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[14, 0, -8, 10, 7, 2, -2, -10, 9],\n [0, -23, 5, -2, 14, 9, 8, -6, 8],\n [-8, 5, -7, 0, 4, 19, -6, 4, 18],\n [10, -2, 0, -2, -14, 0, 2, 8, 0],\n [7, 14, 4, -14, -18, 0, -6, -10, -11],\n [2, 9, 19, 0, 0, 21, 1, 4, 3],\n [-2, 8, -6, 2, -6, 1, -19, -8, 1],\n [-10, -6, 4, 8, -10, 4, -8, 3, -8],\n [9, 8, 18, 0, -11, 3, 1, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -15, -13, 8, -1, -19, -22, -18, -6],\n [0, 25, 19, 20, -16, 17, 8, 0, 15],\n [0, 0, -20, -21, -21, 21, -3, 23, -17],\n [0, 0, 0, 16, 9, 24, -8, -9, -2],\n [0, 0, 0, 0, -13, 21, -1, -17, -22],\n [0, 0, 0, 0, 0, -23, 2, 3, -17],\n [0, 0, 0, 0, 0, 0, -11, 14, -1],\n [0, 0, 0, 0, 0, 0, 0, -21, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-353", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 16, 2, 9, 16, 4, 0, -9, -2],\n [16, 14, 8, 2, 12, 0, -7, 3, -12],\n [2, 8, 2, 8, 10, 12, -13, 8, 17],\n [9, 2, 8, 1, 14, -22, 0, 18, 12],\n [16, 12, 10, 14, -16, -3, 9, 6, 10],\n [4, 0, 12, -22, -3, -13, 13, 4, 8],\n [0, -7, -13, 0, 9, 13, 15, -14, 2],\n [-9, 3, 8, 18, 6, 4, -14, -7, 4],\n [-2, -12, 17, 12, 10, 8, 2, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-72", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, -4, -22, -6, 6, 10, 24, -22, 1],\n [0, -14, -4, -9, -16, -25, -4, 0, -8],\n [0, 0, 21, 3, -14, 10, 9, -14, -19],\n [0, 0, 0, -20, 21, -11, 6, 25, -15],\n [0, 0, 0, 0, 8, 3, -22, -9, 9],\n [0, 0, 0, 0, 0, 3, -15, 6, -24],\n [0, 0, 0, 0, 0, 0, -23, -9, 18],\n [0, 0, 0, 0, 0, 0, 0, -20, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-169", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -14, -8, -11, 18, -10, 1, -18, 20],\n [0, -9, 3, -18, -11, 1, 20, 24, -19],\n [0, 0, 18, -2, -23, -6, 20, -11, -1],\n [0, 0, 0, -9, 18, -6, 10, -17, 12],\n [0, 0, 0, 0, -18, -15, -13, -9, -18],\n [0, 0, 0, 0, 0, 21, 5, 12, 6],\n [0, 0, 0, 0, 0, 0, -18, -15, -4],\n [0, 0, 0, 0, 0, 0, 0, -11, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9344", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-24, 7, 7, 15, -13, 4, 7, -13, 0],\n [-4, 13, -24, 12, 13, 0, 20, 24, -11],\n [8, 16, 18, 23, 14, -15, -23, -20, -17],\n [-20, -17, 13, 5, 6, 15, 24, -14, -18],\n [-18, 24, 2, -6, 21, -19, -15, -6, -10],\n [-22, -20, -4, 0, -23, 15, 16, -12, -15],\n [-8, -14, -3, -14, -13, -1, 19, 25, -7],\n [20, 10, 19, -18, 3, 6, 25, 18, -8],\n [-20, -8, -7, -4, 11, 6, 15, -23, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 6) of the inverse. Round your answer to the nearest integer:\n[[-16, 14, 2, 6, 7, 8, -16, -13, 12],\n [14, -5, 2, -13, -10, 6, -17, 8, -3],\n [2, 2, 24, 6, 1, -6, -4, 4, 8],\n [6, -13, 6, 8, 14, -5, 12, 5, 18],\n [7, -10, 1, 14, -8, 18, -13, -18, -7],\n [8, 6, -6, -5, 18, 4, 4, 14, -4],\n [-16, -17, -4, 12, -13, 4, 19, -2, 18],\n [-13, 8, 4, 5, -18, 14, -2, -9, -8],\n [12, -3, 8, 18, -7, -4, 18, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[19, -3, 21, 5, -15, -16, -23, -12, -10],\n [-16, 3, -16, -14, 4, 15, -25, -21, -6],\n [-18, 17, -14, -25, -6, 2, 17, 11, 21],\n [11, -14, 11, 23, 23, 18, 2, 21, -11],\n [-20, 18, -6, 24, -12, -24, -17, 11, -6],\n [0, 3, -25, 9, -20, 11, -21, 7, 23],\n [25, -12, -14, 16, -6, 24, -2, 17, 8],\n [-1, 24, 3, 13, 5, 21, 17, 24, -3],\n [18, 12, -6, -3, 19, -10, 24, 16, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-48", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[24, -4, -16, -18, -4, -6, 14, -20, -2],\n [-4, 21, 0, -13, 11, 12, -16, 6, 11],\n [-16, 0, 0, 1, 0, 14, 0, -11, -9],\n [-18, -13, 1, -22, 11, -13, 0, -4, -6],\n [-4, 11, 0, 11, 0, 12, -6, 20, -12],\n [-6, 12, 14, -13, 12, -13, 2, -8, -3],\n [14, -16, 0, 0, -6, 2, -22, 2, -16],\n [-20, 6, -11, -4, 20, -8, 2, 19, -14],\n [-2, 11, -9, -6, -12, -3, -16, -14, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-60", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (6, 4) rounded to the nearest integer?\n[[-11, -5, -7, 3, -1, 7, 23, 6, 23],\n [9, 18, 12, 0, -15, 9, -18, 20, -12],\n [-16, -24, 20, -17, -23, -5, 0, -18, 22],\n [-24, -20, 2, 3, 0, -1, -14, -21, 8],\n [22, 11, -11, 18, 10, -11, 17, 22, -3],\n [-20, 20, 24, 18, 17, 19, -5, -3, 17],\n [-10, 21, -11, -1, 10, -15, 25, -11, -22],\n [-5, -13, -4, -7, 8, -12, -22, 22, 20],\n [1, 3, 21, 2, 9, -18, -10, 16, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -12, 0, 21, -6, 0, 6, -11, 0],\n [-12, -19, 10, 17, -16, 6, -14, 13, 2],\n [0, 10, 16, 16, -8, -10, -10, -1, 14],\n [21, 17, 16, -13, -10, 3, -6, 6, -14],\n [-6, -16, -8, -10, -2, -3, -12, 8, 0],\n [0, 6, -10, 3, -3, 24, 4, 0, 6],\n [6, -14, -10, -6, -12, 4, -16, 7, 2],\n [-11, 13, -1, 6, 8, 0, 7, -5, -2],\n [0, 2, 14, -14, 0, 6, 2, -2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1187", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, -12, 4, 4, 3, -3, 14, -14, -13],\n [-12, -23, 4, 12, -2, 12, -19, 11, -8],\n [4, 4, -22, 7, 14, 11, 1, 10, 11],\n [4, 12, 7, 11, 10, 2, -22, -10, -6],\n [3, -2, 14, 10, -22, -16, 0, -10, 0],\n [-3, 12, 11, 2, -16, 12, -10, 3, -16],\n [14, -19, 1, -22, 0, -10, 18, -14, 14],\n [-14, 11, 10, -10, -10, 3, -14, 18, 7],\n [-13, -8, 11, -6, 0, -16, 14, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2314", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 5) rounded to the nearest integer?\n[[-14, -9, -10, -14, -18, -6, -23, -10, 4],\n [0, -3, 2, 25, 14, -21, -6, 14, 18],\n [0, 0, -5, -6, -20, -4, -8, -18, 13],\n [0, 0, 0, -14, 12, 8, -12, 10, 7],\n [0, 0, 0, 0, 15, -5, -24, 1, -17],\n [0, 0, 0, 0, 0, -22, -8, -20, 9],\n [0, 0, 0, 0, 0, 0, -14, 21, 23],\n [0, 0, 0, 0, 0, 0, 0, 16, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[9, -24, 1, -24, 9, -8, -12, -6, -8],\n [0, -1, -24, -1, 7, 10, 5, -12, -25],\n [0, 0, 20, -23, 9, 15, -20, -1, -13],\n [0, 0, 0, 8, -22, -1, -11, -22, 19],\n [0, 0, 0, 0, -13, 5, -12, -6, -8],\n [0, 0, 0, 0, 0, -24, -3, -7, 5],\n [0, 0, 0, 0, 0, 0, -24, -15, 24],\n [0, 0, 0, 0, 0, 0, 0, -5, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, -22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14617", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[13, 14, -9, 11, 13, 3, 10, 12, 13],\n [24, 11, 9, -19, 1, 2, -4, -12, -19],\n [11, -4, -21, -24, 1, -5, 12, -11, -5],\n [-16, -3, 13, -21, -25, -13, -5, 0, 24],\n [19, -5, -8, 11, 19, 6, 10, -9, 9],\n [23, -15, -5, 0, -22, 8, 22, -8, 14],\n [9, 15, 3, 3, 12, 16, -5, 16, -13],\n [23, 15, -9, -17, 15, -25, -24, 22, 3],\n [7, -16, 24, 14, -5, 2, -15, 8, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "826", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, -18, 23, -11, -9, -3, -2, 19, -7],\n [-21, 6, 18, -25, -3, 11, -18, -13, -18],\n [-3, 17, -25, 19, 25, -2, 9, -2, -9],\n [-21, -6, -5, 14, 5, 20, 10, -15, -11],\n [-7, -19, 25, 2, 25, 17, -21, -21, 4],\n [6, -18, -16, 12, 21, 6, 22, 2, -9],\n [5, -18, 14, -1, -17, -24, -11, 24, -23],\n [23, 10, -22, -12, 15, 15, -1, 24, -16],\n [-5, 10, -14, 1, 14, -24, -13, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-10, 6, 6, 8, -15, -16, -11, -9, 14],\n [-8, -17, -1, 14, -12, -1, 24, -4, 4],\n [-6, -5, 18, 6, 25, 20, 23, -5, 9],\n [6, 4, 13, 23, -14, 15, 21, -8, -5],\n [-13, -5, -18, 20, 14, 20, -19, -3, 18],\n [6, -15, -4, -4, 17, -1, -4, 2, 3],\n [-13, -8, -24, 3, -5, -11, 1, 24, 5],\n [-11, 25, -3, -2, 18, -13, -4, 17, 11],\n [7, -23, -7, -3, 3, 4, 13, 18, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, 11, 21, -18, 16, -10, -18, -25, 18],\n [0, -23, -25, -22, 14, 9, 6, 16, 8],\n [0, 0, -16, -5, 20, 13, 1, 1, -24],\n [0, 0, 0, -17, 10, -4, 16, 0, -14],\n [0, 0, 0, 0, -6, -15, -10, 25, 5],\n [0, 0, 0, 0, 0, -22, -6, -16, -2],\n [0, 0, 0, 0, 0, 0, 13, -5, -16],\n [0, 0, 0, 0, 0, 0, 0, -22, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5886", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 9) of the inverse of matrix 1/450 * A where A =\n[[-8, 6, 8, 6, 6, 0, -14, 10, 4],\n [6, -14, 4, 10, -8, -3, -8, 0, 0],\n [8, 4, 23, -1, 6, 24, 10, 12, -8],\n [6, 10, -1, -20, -17, -14, 24, 16, -10],\n [6, -8, 6, -17, -15, 0, -12, -3, 2],\n [0, -3, 24, -14, 0, 17, 20, 14, 16],\n [-14, -8, 10, 24, -12, 20, 9, 8, 12],\n [10, 0, 12, 16, -3, 14, 8, -16, -6],\n [4, 0, -8, -10, 2, 16, 12, -6, -25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, 10, -20, 15, 20, 18, 5, -6, -2],\n [0, 10, -5, 4, -2, 18, 16, 4, -4],\n [0, 0, 9, 2, -12, -16, -10, -10, 5],\n [0, 0, 0, -20, 18, -17, 19, 10, 17],\n [0, 0, 0, 0, -22, 24, 7, 1, -19],\n [0, 0, 0, 0, 0, -6, -2, -11, 22],\n [0, 0, 0, 0, 0, 0, 11, -5, -8],\n [0, 0, 0, 0, 0, 0, 0, -7, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-331", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[-15, -24, 21, 18, 18, -17, -5, -2, 8],\n [0, -23, -14, 2, 4, 0, 22, -5, 2],\n [0, 0, -5, 9, 8, 15, 25, 21, -8],\n [0, 0, 0, -4, -9, -21, 18, -15, 4],\n [0, 0, 0, 0, -6, -10, 8, -24, 9],\n [0, 0, 0, 0, 0, -17, -6, -25, -18],\n [0, 0, 0, 0, 0, 0, -11, -5, 9],\n [0, 0, 0, 0, 0, 0, 0, 9, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[20, 3, -8, 6, -3, -3, -12, 13, -16],\n [3, 23, 10, 4, 4, -2, -12, 8, 10],\n [-8, 10, -7, 20, 20, -4, 16, -10, -12],\n [6, 4, 20, -19, -10, -14, 6, 15, 0],\n [-3, 4, 20, -10, 4, -6, 2, -8, -18],\n [-3, -2, -4, -14, -6, 15, -4, -1, 10],\n [-12, -12, 16, 6, 2, -4, -10, 14, 15],\n [13, 8, -10, 15, -8, -1, 14, -5, -11],\n [-16, 10, -12, 0, -18, 10, 15, -11, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-22, 3, -8, 6, 8, -10, -20, 0, 21],\n [3, 21, 7, 6, -18, 1, 0, 6, 1],\n [-8, 7, 3, -13, 5, -4, 12, 10, 3],\n [6, 6, -13, -19, 10, 7, -10, 5, 4],\n [8, -18, 5, 10, -24, -11, -5, -6, 18],\n [-10, 1, -4, 7, -11, -4, -4, 0, 7],\n [-20, 0, 12, -10, -5, -4, 16, -2, -8],\n [0, 6, 10, 5, -6, 0, -2, 19, 6],\n [21, 1, 3, 4, 18, 7, -8, 6, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1461", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-24, 25, -15, -13, -16, -12, -8, 25, -17],\n [0, 2, -23, -6, -20, 1, -24, 3, 12],\n [0, 0, 4, 14, -24, -9, 15, -14, 9],\n [0, 0, 0, -11, 0, 11, -5, 23, 5],\n [0, 0, 0, 0, 2, -5, 17, -8, 10],\n [0, 0, 0, 0, 0, 18, 8, 6, -23],\n [0, 0, 0, 0, 0, 0, 14, -15, 22],\n [0, 0, 0, 0, 0, 0, 0, 11, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159189", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, -5, 18, -15, 13, -22, 25, -25, 2],\n [0, 9, -13, 21, 8, -15, 10, 25, -9],\n [0, 0, 14, -4, -2, -7, 11, 13, -5],\n [0, 0, 0, -9, 11, 10, -7, 1, 8],\n [0, 0, 0, 0, -5, -15, 13, 2, -21],\n [0, 0, 0, 0, 0, -20, -9, 25, -7],\n [0, 0, 0, 0, 0, 0, 10, 12, -15],\n [0, 0, 0, 0, 0, 0, 0, 24, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, 19, 9, 22, -17, -18, 19, -9, -9],\n [23, 7, 6, -18, -7, 12, -23, -21, -13],\n [21, 20, 5, -10, 24, 6, -4, 3, -4],\n [17, -23, -16, 16, -5, -10, -14, -24, 15],\n [-2, 9, 4, 4, 21, 9, -7, 24, -18],\n [0, 23, 14, -19, 4, -19, -23, -25, 10],\n [-1, 11, -25, -11, 11, -13, 14, -18, -21],\n [-17, -25, 10, 9, -24, 14, -3, -17, 8],\n [20, -12, -22, 4, 5, 12, -15, 9, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (1, 6) rounded to the nearest integer?\n[[-23, -12, -13, 19, 6, 8, 19, -7, 12],\n [0, -24, 14, -9, 8, 16, -10, 12, -24],\n [0, 0, -13, 21, 5, 8, 13, -23, -18],\n [0, 0, 0, 3, 13, 13, -25, -9, 15],\n [0, 0, 0, 0, -7, -1, -4, 5, -9],\n [0, 0, 0, 0, 0, -18, -6, 6, 24],\n [0, 0, 0, 0, 0, 0, -4, 4, -22],\n [0, 0, 0, 0, 0, 0, 0, 8, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[0, -8, 6, -4, 12, -9, -3, -2, 24],\n [-18, 15, -20, -21, 18, 3, 2, -15, -25],\n [17, -7, -17, 1, 8, 18, -22, 10, -8],\n [-11, 25, -13, -7, 23, -20, 22, -14, 25],\n [11, -9, -3, 0, 3, 7, 1, -1, -16],\n [21, -3, -5, -5, 17, -13, 11, 7, -2],\n [18, -15, -9, -22, 21, -1, 4, -17, -5],\n [-6, -7, -7, -14, 11, 16, -9, 11, 22],\n [13, 2, 15, 9, 21, 22, -8, -12, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[18, 10, -4, -2, -6, -12, -6, 4, 5],\n [10, -24, 4, -4, -2, 15, -10, 4, 10],\n [-4, 4, -3, 6, -3, 14, -13, -6, -22],\n [-2, -4, 6, -23, 6, -18, 14, 2, -6],\n [-6, -2, -3, 6, -5, 18, -2, -8, 12],\n [-12, 15, 14, -18, 18, -13, -2, 8, -6],\n [-6, -10, -13, 14, -2, -2, 9, 8, -1],\n [4, 4, -6, 2, -8, 8, 8, -1, 0],\n [5, 10, -22, -6, 12, -6, -1, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[2, -14, 1, 16, 21, 4, 15, 8, 11],\n [-20, -19, 6, 6, -1, 7, -19, -14, -10],\n [-10, 17, 10, -13, -19, 10, 21, 25, -17],\n [6, -15, -18, 7, -3, -1, -18, 19, -4],\n [-22, 14, -23, 3, 15, 3, 8, 8, 2],\n [-13, -11, -3, 18, 0, -22, 0, 14, -17],\n [-21, 6, -6, 24, -15, -11, 6, 2, -4],\n [15, -9, 0, 18, -19, 16, 0, -1, -16],\n [19, -7, -15, -13, -18, 14, -22, 21, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[2, -15, 17, -25, 23, 21, 12, -2, 21],\n [5, 15, 20, 24, 0, 23, 24, -21, -6],\n [15, -15, 7, 24, 12, 1, 8, -11, 6],\n [-5, 20, -21, -20, 12, -4, -8, -12, -16],\n [20, -13, 5, 4, -23, 4, -20, 3, -18],\n [18, 19, 17, 18, 7, -9, 22, -15, -13],\n [24, -15, 5, 2, 18, -20, 15, -10, -22],\n [9, 22, 0, -14, -15, 11, -1, -8, -7],\n [-3, 12, -8, 0, -20, -22, 18, 25, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[8, -9, 17, 17, -10, -24, 8, -18, -13],\n [0, -18, 4, 6, 10, 21, 4, -25, 17],\n [0, 0, -6, -2, 24, -4, 3, -4, 18],\n [0, 0, 0, 10, 11, 2, 2, 16, 17],\n [0, 0, 0, 0, -24, -18, 22, 1, -4],\n [0, 0, 0, 0, 0, -13, 19, -16, 10],\n [0, 0, 0, 0, 0, 0, -1, 3, -19],\n [0, 0, 0, 0, 0, 0, 0, 23, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124056", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (7, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -22, -25, 24, -25, 0, 19, -6, -3],\n [0, -15, 15, 15, -21, -25, -9, -4, 8],\n [0, 0, 3, -22, -21, -15, 25, -5, 9],\n [0, 0, 0, -7, 19, -19, 21, -19, 0],\n [0, 0, 0, 0, -22, -3, 16, -6, -11],\n [0, 0, 0, 0, 0, 22, -7, 22, 13],\n [0, 0, 0, 0, 0, 0, 9, 11, -25],\n [0, 0, 0, 0, 0, 0, 0, 3, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-21, 5, 15, -20, 11, -16, 14, -19, 13],\n [0, -5, -6, -23, 25, -4, 21, -22, 2],\n [0, 0, 25, 10, 21, 15, -21, -13, -3],\n [0, 0, 0, -1, 22, 1, 25, -12, 22],\n [0, 0, 0, 0, -4, -5, -5, -18, 23],\n [0, 0, 0, 0, 0, 8, -17, -9, -15],\n [0, 0, 0, 0, 0, 0, 21, -1, -5],\n [0, 0, 0, 0, 0, 0, 0, -9, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-607", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, 13, -9, 8, 15, 3, -17, -13, -20],\n [0, -6, -23, -9, 23, -14, 22, 21, 19],\n [0, 0, -23, 0, -11, 10, 6, 6, -22],\n [0, 0, 0, 17, 9, 14, -12, 7, -12],\n [0, 0, 0, 0, -7, -20, 7, 23, 14],\n [0, 0, 0, 0, 0, -20, 14, -13, 22],\n [0, 0, 0, 0, 0, 0, -1, -6, 5],\n [0, 0, 0, 0, 0, 0, 0, -18, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-805", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[7, 23, -14, -15, -21, 1, -14, -9, -20],\n [0, -21, 2, -12, -21, 7, 24, 22, 15],\n [0, 0, -21, -24, 4, 21, 13, -22, 7],\n [0, 0, 0, -11, -3, -12, -3, -7, 3],\n [0, 0, 0, 0, -16, 15, -18, 0, 3],\n [0, 0, 0, 0, 0, 2, 15, -21, -8],\n [0, 0, 0, 0, 0, 0, -14, -19, -23],\n [0, 0, 0, 0, 0, 0, 0, -16, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10656", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 15, -6, 18, -7, -6, 9, 21, -24],\n [4, 8, -4, -23, -20, -11, 1, -16, -17],\n [7, 6, 22, -20, 15, 10, -24, 3, -22],\n [-25, -7, 0, -1, -16, -11, -4, 25, 22],\n [-5, -4, 10, 8, 4, -1, 19, 2, -25],\n [23, 19, -22, -19, 23, -17, 10, -7, -25],\n [-16, 10, -17, 19, 20, 16, 6, 6, -20],\n [22, 12, -9, -16, 24, 1, 24, 9, -5],\n [-1, 2, 21, -11, -22, 3, -17, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1398", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 8, -15, 1, 12, -1, 18, 6, 6],\n [8, 13, 20, -6, 4, 16, 22, 10, 14],\n [-15, 20, 22, 0, 17, 2, 13, -4, 2],\n [1, -6, 0, 4, 0, 0, 0, 11, -11],\n [12, 4, 17, 0, -16, 2, -7, 12, 4],\n [-1, 16, 2, 0, 2, -17, -18, 17, -12],\n [18, 22, 13, 0, -7, -18, -8, 3, -14],\n [6, 10, -4, 11, 12, 17, 3, -11, -8],\n [6, 14, 2, -11, 4, -12, -14, -8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, -22, 2, -11, -25, -23, -12, 12, 24],\n [0, 12, 12, -5, 22, 3, -21, 23, -16],\n [0, 0, 24, -19, -23, 19, 21, -6, -7],\n [0, 0, 0, -25, -22, -14, 1, 16, -3],\n [0, 0, 0, 0, 19, 20, 6, 6, -21],\n [0, 0, 0, 0, 0, 13, -10, 7, 23],\n [0, 0, 0, 0, 0, 0, 13, -4, 15],\n [0, 0, 0, 0, 0, 0, 0, -23, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11282", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, 22, -3, 19, -9, 14, -5, -24, 11],\n [-20, 18, -8, 4, -4, 7, 4, -9, 17],\n [6, 16, 25, -12, -16, 21, 25, 10, 8],\n [-17, 16, 2, -15, -12, 13, 21, -7, -11],\n [2, -2, -18, 17, -17, 21, 7, 7, -7],\n [-23, -16, 14, 21, 16, -25, 3, 24, 8],\n [25, -13, -25, 8, 3, 22, 21, -13, 22],\n [23, 3, 13, -2, 0, -9, -19, -13, -21],\n [0, 23, -23, -19, 23, 13, -25, 23, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[17, -1, -23, -11, 3, 17, 6, 0, -10],\n [-1, 2, -17, -25, 3, -4, -10, 15, 25],\n [18, 25, 15, -19, -12, 3, -7, -7, -24],\n [15, 19, -11, -23, -15, 20, 4, 14, -8],\n [25, 22, -24, 6, -18, -4, -20, -14, 21],\n [14, 10, -11, 2, 23, 19, -8, -24, -13],\n [19, -11, -6, 3, 16, 3, -23, -7, -23],\n [-12, 14, -22, -15, 5, 17, 6, 1, 4],\n [17, -24, 23, -17, 2, 5, 8, -11, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-88", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 5) rounded to the nearest integer?\n[[-1, 10, -18, -17, 11, 22, 19, 13, 6],\n [-9, 9, 11, -7, 18, 3, -19, 2, -17],\n [2, -20, 3, -9, -10, -3, 5, -23, -5],\n [0, 10, 16, 11, -4, 16, -14, 16, -13],\n [-15, -10, -18, 14, 14, 19, -24, 4, 4],\n [-14, -16, 18, -15, -11, -10, -9, 0, -24],\n [24, -14, 25, 0, -3, -8, 6, 23, 12],\n [21, -23, 12, -23, 4, -25, 4, 19, 6],\n [2, -5, 20, -13, 1, 10, -19, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (3, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -11, -11, -22, 6, -3, -20, -2, -6],\n [11, -6, -14, 7, 2, -18, -25, 11, -4],\n [-20, -5, 6, 9, -11, -21, 20, 24, 22],\n [-20, -1, 20, 14, 3, -19, 14, -13, 12],\n [-8, -24, -18, -15, 7, 12, 22, 1, -6],\n [-14, 17, 5, 1, 6, -16, -23, 19, 1],\n [9, 5, -11, -10, -13, 23, 9, -15, -5],\n [25, -15, 4, 22, 9, -4, 12, 5, -12],\n [-2, 24, 23, 6, 10, 6, -11, 17, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-23, -8, -12, -5, -14, -6, -4, -13, 14],\n [-8, 17, -13, -15, 1, 8, -16, 23, 8],\n [-12, -13, -15, 22, 7, -10, -20, 0, 16],\n [-5, -15, 22, -22, 4, 6, -14, 2, 8],\n [-14, 1, 7, 4, -8, 8, -16, 0, -13],\n [-6, 8, -10, 6, 8, -1, 2, 2, -9],\n [-4, -16, -20, -14, -16, 2, 14, -13, 5],\n [-13, 23, 0, 2, 0, 2, -13, 24, -6],\n [14, 8, 16, 8, -13, -9, 5, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-123", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, -23, 2, 0, 4, -13, -13, -24, 11],\n [23, 12, -24, 10, 0, -15, -18, 18, 14],\n [17, -4, -6, -18, 3, 14, 0, 4, -9],\n [-6, -10, 20, 17, -19, -10, 19, 21, 22],\n [1, -3, -2, -17, 9, 25, -6, 11, 16],\n [-9, 21, 5, -18, -11, 5, 4, 20, -6],\n [13, -14, 23, -9, 16, 4, 3, -7, 20],\n [-15, 8, 24, -19, 18, 8, -6, 24, 12],\n [-2, -16, 6, -11, 11, -6, -23, 11, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-600", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-18, 9, 14, -4, -1, -20, 10, -14, 2],\n [9, -16, 6, -11, 18, 8, 4, -2, 6],\n [14, 6, -4, -8, 12, -2, 2, 6, -4],\n [-4, -11, -8, -15, 0, 18, 16, -17, 2],\n [-1, 18, 12, 0, 9, 17, 4, -6, -11],\n [-20, 8, -2, 18, 17, 8, -2, 1, -12],\n [10, 4, 2, 16, 4, -2, -9, -14, 0],\n [-14, -2, 6, -17, -6, 1, -14, 14, -10],\n [2, 6, -4, 2, -11, -12, 0, -10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[12, -4, -13, -2, 20, -10, -16, 0, -8],\n [-4, 6, 0, -4, 14, -2, 11, 15, -22],\n [-13, 0, 0, 0, -2, -6, 14, -1, -6],\n [-2, -4, 0, 12, -1, -6, -9, 13, -18],\n [20, 14, -2, -1, 6, -6, -12, 2, -14],\n [-10, -2, -6, -6, -6, -14, 8, 0, 0],\n [-16, 11, 14, -9, -12, 8, 13, -8, -20],\n [0, 15, -1, 13, 2, 0, -8, -9, 17],\n [-8, -22, -6, -18, -14, 0, -20, 17, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-350", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[19, -3, 20, -18, -18, 0, 21, -13, 13],\n [11, 23, 2, -1, -10, -24, -8, -9, 4],\n [13, -13, 6, 24, 3, 20, 4, -8, -13],\n [17, -5, 4, -5, 22, -9, 14, -7, -11],\n [-17, -16, 18, 5, -3, 4, 7, -17, 21],\n [-25, 18, 9, -15, 8, -10, -17, 6, -11],\n [-14, 7, 19, -12, -18, -18, 1, -14, -25],\n [17, 14, 16, 25, -15, 13, 17, 5, -9],\n [7, 6, 3, -5, -5, 14, -3, -20, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[24, 12, 11, 19, 25, -18, 15, 23, 9],\n [25, -15, -2, 23, -5, 25, -24, 14, -7],\n [13, 2, -9, -20, -7, 12, 2, -24, 12],\n [11, 25, -22, -4, 0, 23, 17, 10, -13],\n [6, -9, 15, 10, 20, -7, 9, 20, 14],\n [2, -25, 16, -8, 22, 14, 7, -14, -18],\n [-2, -10, 24, -22, 12, 18, 1, -17, 21],\n [-10, -14, 5, -2, -12, 19, -1, 8, -23],\n [-2, 16, -17, 0, -6, 14, -16, -7, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1282", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (8, 3) rounded to the nearest integer?\n[[-2, -21, -23, 1, -10, 23, -11, 9, -14],\n [15, 18, 0, 21, 8, -3, 5, 24, -6],\n [-14, -3, -22, -3, 22, 22, -25, -1, -24],\n [4, -23, -5, -1, -6, 23, -4, -5, 7],\n [12, -11, 20, -11, 20, -1, -5, -2, -21],\n [-20, 23, 17, 22, 18, 21, -3, -22, 1],\n [-8, -5, 2, 9, -4, 14, -3, -23, 14],\n [24, -16, -1, 23, -18, -15, -21, 19, 11],\n [19, 12, 3, -21, -17, 22, -24, -25, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[25, 4, -15, 2, 18, -14, 13, 0, -13],\n [-18, 2, 4, -17, 13, 5, -5, 21, 8],\n [5, -1, -14, -25, -4, 14, 11, 21, -25],\n [-25, 16, 16, -5, -11, -9, -4, 12, 9],\n [19, -10, -18, 21, -9, -9, 0, -13, -9],\n [12, -9, 22, -12, 19, -20, 9, 20, -12],\n [21, -18, -11, 1, -13, 23, 5, 9, -20],\n [-21, -4, 23, -3, -1, 8, 0, 21, -21],\n [0, -6, -20, -20, 24, -8, -22, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-60", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-12, -13, -19, 18, -11, -7, 17, 21, 18],\n [9, -9, 9, -7, -6, 10, 9, 6, 22],\n [18, 14, -2, -9, -19, 17, 24, -25, 9],\n [6, 10, -13, -20, -12, 11, 22, -11, 21],\n [-22, 14, -10, 2, -10, -22, 19, 0, 2],\n [6, 19, -24, 5, -23, -18, -2, -11, 17],\n [5, -17, 13, 19, -24, -18, -19, 18, 25],\n [13, 16, -10, 9, 4, -16, 12, -8, 24],\n [-21, 3, 13, 8, 17, 19, -3, -21, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-20, 20, 18, -22, 3, -3, -20, 6, 16],\n [0, -11, 14, 6, -17, 11, -16, -6, -20],\n [0, 0, 16, -15, 17, -9, 6, -22, -22],\n [0, 0, 0, -21, 6, -4, -20, 9, -4],\n [0, 0, 0, 0, -15, -13, 16, -23, -17],\n [0, 0, 0, 0, 0, 23, 15, -17, -3],\n [0, 0, 0, 0, 0, 0, 4, -1, 2],\n [0, 0, 0, 0, 0, 0, 0, 16, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1678", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, 10, -24, -4, 6, -10, -8, -21, 10],\n [0, 19, -7, -3, 8, -13, 17, 3, 10],\n [0, 0, 10, -17, 13, 25, -7, 12, -20],\n [0, 0, 0, -17, 6, -22, 24, -8, -21],\n [0, 0, 0, 0, -4, -22, 3, 18, 8],\n [0, 0, 0, 0, 0, -19, -22, -7, 16],\n [0, 0, 0, 0, 0, 0, 5, 6, -24],\n [0, 0, 0, 0, 0, 0, 0, -10, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[0, 21, 24, -14, 5, -9, 7, -15, 2],\n [6, -25, 21, 2, 16, -19, -24, 16, -2],\n [-22, 18, -7, 0, -15, 14, 24, 17, -15],\n [19, -23, -14, -23, 16, 1, 23, -24, 23],\n [-10, -24, 4, -6, 12, 2, -1, 6, -16],\n [16, 14, 7, -13, 15, 16, 21, 11, -10],\n [19, -4, -6, 24, 17, 1, 15, -10, 8],\n [6, 0, -1, -24, -14, 14, -17, -14, 0],\n [-17, -16, 6, 8, 22, -6, 13, -24, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[25, 0, 9, -10, -9, 6, 0, -18, 10],\n [0, -14, 0, 6, 0, 16, 2, -12, -4],\n [9, 0, 11, 6, 8, -11, -2, 3, -12],\n [-10, 6, 6, 10, 3, -16, -15, 8, 9],\n [-9, 0, 8, 3, -6, -15, -1, -17, -1],\n [6, 16, -11, -16, -15, -5, 2, 22, -8],\n [0, 2, -2, -15, -1, 2, -9, 5, 6],\n [-18, -12, 3, 8, -17, 22, 5, 15, 4],\n [10, -4, -12, 9, -1, -8, 6, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[17, 7, 5, 9, -9, 2, -7, 20, -3],\n [6, 14, -13, -6, 9, -21, -17, 3, -20],\n [-1, 5, -4, -24, 19, -21, 1, -1, -18],\n [-25, -6, 18, -3, 6, -15, 13, 21, -2],\n [-15, 3, 0, -10, 9, -6, 20, -23, -25],\n [21, -25, -9, -24, 3, -6, -20, -18, 3],\n [22, 25, 7, -23, 9, -21, 1, 18, -14],\n [-6, 19, -6, -17, 13, -22, 25, -7, 12],\n [1, 19, 17, -13, -13, -4, 2, 21, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1435", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-4, 17, -7, -18, -18, 16, 0, 22, 25],\n [0, -3, 17, -13, 2, -17, -6, -7, 22],\n [13, 25, -14, -11, 5, -12, -15, 0, 16],\n [1, -15, 12, 8, 17, -7, -20, 20, 12],\n [23, 16, 2, -25, 9, 14, -18, 21, -19],\n [-15, 13, -22, -1, -14, 0, 12, 20, -14],\n [17, 25, 11, 20, -2, -10, -13, -1, -22],\n [-15, 6, 23, -19, 20, -15, 2, 15, -3],\n [19, -3, 24, 2, 17, 21, 0, -1, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, -8, 18, -8, 6, -6, 6, -5, 1],\n [-8, -10, 16, -2, 8, 18, -14, 6, -5],\n [18, 16, 16, 6, 6, -2, -2, 9, -3],\n [-8, -2, 6, 23, 11, -19, -12, -8, 22],\n [6, 8, 6, 11, -25, -4, 9, -16, 6],\n [-6, 18, -2, -19, -4, -19, 14, 16, -8],\n [6, -14, -2, -12, 9, 14, 17, 11, 14],\n [-5, 6, 9, -8, -16, 16, 11, 5, -4],\n [1, -5, -3, 22, 6, -8, 14, -4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-196", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, 4, 4, -4, -15, -24, 18, -14, 4],\n [0, -8, 0, -19, -25, 0, -3, 0, 19],\n [0, 0, 18, -18, -2, -4, -7, 11, -8],\n [0, 0, 0, 16, 7, -16, 11, -14, 4],\n [0, 0, 0, 0, -14, 3, 7, 17, -11],\n [0, 0, 0, 0, 0, -19, 17, -8, 18],\n [0, 0, 0, 0, 0, 0, -22, -8, -22],\n [0, 0, 0, 0, 0, 0, 0, -20, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[25, 20, -12, 16, -13, -8, -6, 7, -15],\n [20, 6, -16, 0, 7, 2, 9, 6, -12],\n [-12, -16, 2, 3, -8, -4, -12, 3, 20],\n [16, 0, 3, -7, -23, -15, -10, -12, 22],\n [-13, 7, -8, -23, 19, -16, 10, 6, -12],\n [-8, 2, -4, -15, -16, -19, 0, -10, 14],\n [-6, 9, -12, -10, 10, 0, 18, 0, -3],\n [7, 6, 3, -12, 6, -10, 0, -14, -2],\n [-15, -12, 20, 22, -12, 14, -3, -2, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1206", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (1, 6) of the inverse. Round your answer to the nearest integer:\n[[-20, 21, -21, 17, -1, -8, -13, 17, -12],\n [0, -8, 2, 25, 1, 6, 21, -17, 14],\n [0, 0, 2, 7, -22, 20, 8, 22, -23],\n [0, 0, 0, -10, -2, 22, 13, 4, 19],\n [0, 0, 0, 0, -8, 21, -8, -24, -16],\n [0, 0, 0, 0, 0, -13, 24, 21, -15],\n [0, 0, 0, 0, 0, 0, 19, 18, -2],\n [0, 0, 0, 0, 0, 0, 0, -8, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 9, 14, -10, 12, -13, -3, -4, -10],\n [2, 22, 9, 19, 20, -18, 18, -4, -5],\n [0, 14, -5, -1, 15, -25, -20, -3, 25],\n [-3, 17, 17, -3, 6, 4, -13, 17, -8],\n [-3, -11, 7, -5, 13, -3, 1, 19, 18],\n [-8, -2, 25, 21, 14, 25, 16, -19, 24],\n [22, -6, 1, -20, 1, -17, 19, 5, -5],\n [0, 14, 22, 19, -13, 23, -3, -6, 11],\n [2, -9, 2, 15, -24, -1, 24, 15, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-15, 12, -20, 19, -15, -12, -24, 14, -23],\n [9, 7, -2, -7, -8, 23, -2, 19, 9],\n [-25, 10, -1, 19, 23, 17, 8, -1, -10],\n [8, 3, -7, -3, -7, -1, -10, 25, -17],\n [-25, 16, -7, 7, 8, -10, 18, 14, -8],\n [8, -1, 19, -20, -5, -20, 6, 15, 22],\n [17, 13, 5, 16, -16, 4, -8, -2, -17],\n [5, -11, -22, 14, -17, 19, -17, 0, -22],\n [-9, -10, -11, 9, -21, -21, -6, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, -24, 3, -13, -22, 16, 19, -16, 5],\n [0, -18, -23, 22, 20, -17, 4, -15, 9],\n [0, 0, -13, 10, -13, -14, 11, -16, -17],\n [0, 0, 0, 13, 14, 13, -5, -3, 3],\n [0, 0, 0, 0, 5, -1, 5, 24, -6],\n [0, 0, 0, 0, 0, -13, 13, 2, 16],\n [0, 0, 0, 0, 0, 0, -21, -7, -4],\n [0, 0, 0, 0, 0, 0, 0, -1, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18681", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, -6, -1, 10, -4, 14, 0, -14, 8],\n [-6, -7, 13, -9, 2, -16, -22, 1, -16],\n [-1, 13, -1, 0, 5, 8, 0, -22, 10],\n [10, -9, 0, -2, -14, -3, 4, 4, 4],\n [-4, 2, 5, -14, 25, 11, 0, -8, 18],\n [14, -16, 8, -3, 11, 6, 2, -4, -4],\n [0, -22, 0, 4, 0, 2, -23, 0, 12],\n [-14, 1, -22, 4, -8, -4, 0, 18, 6],\n [8, -16, 10, 4, 18, -4, 12, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-191", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[9, 22, -21, 22, 6, -23, 21, 9, -12],\n [0, 5, 5, -9, -2, -3, -8, 24, -12],\n [0, 0, -11, -20, 1, -11, 24, 10, -18],\n [0, 0, 0, -13, 15, 8, -2, 14, 6],\n [0, 0, 0, 0, -25, 8, -11, 18, -12],\n [0, 0, 0, 0, 0, 5, -1, 12, -12],\n [0, 0, 0, 0, 0, 0, -1, 4, 3],\n [0, 0, 0, 0, 0, 0, 0, 23, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-220", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 6) of the inverse of matrix 1/450 * A where A =\n[[-9, 13, -1, -21, -21, -6, -10, 25, 15],\n [0, 14, -17, -21, 16, -24, -17, 17, 10],\n [0, 0, -4, 8, 3, 12, 20, 7, -8],\n [0, 0, 0, -25, -2, -22, -22, -8, 1],\n [0, 0, 0, 0, 16, 15, 10, -20, -10],\n [0, 0, 0, 0, 0, 23, -13, -8, -13],\n [0, 0, 0, 0, 0, 0, -11, -8, -3],\n [0, 0, 0, 0, 0, 0, 0, 16, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -5, 0, -12, -17, 21, -14, 16, 25],\n [25, -20, -6, -2, 1, 12, -18, -25, 23],\n [23, -2, 21, -19, -7, -4, 9, 4, 3],\n [-4, -15, -6, 3, 25, 15, 16, 8, -25],\n [5, 4, 22, -8, -9, 12, -12, -3, -1],\n [-11, 20, -4, -23, -7, 18, 8, 9, 24],\n [-25, -5, 3, -20, 11, -25, 25, -25, 1],\n [-5, -10, 18, 14, 0, -10, 2, -25, 10],\n [-16, 17, -9, -3, -19, 18, -19, 18, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 6, 12, -2, -6, -2, -10, -19, -3],\n [6, -24, 0, 16, -4, 0, -18, -22, 1],\n [12, 0, -6, -14, 14, -12, -5, -1, -20],\n [-2, 16, -14, -3, -6, 0, -8, -3, 16],\n [-6, -4, 14, -6, 10, 4, 4, -14, -20],\n [-2, 0, -12, 0, 4, -12, 5, 8, -5],\n [-10, -18, -5, -8, 4, 5, 15, -2, -2],\n [-19, -22, -1, -3, -14, 8, -2, 15, -8],\n [-3, 1, -20, 16, -20, -5, -2, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, -5, -9, 7, -16, 25, 21, 16, 25],\n [0, -10, 15, 6, -11, 1, 2, -9, 20],\n [0, 0, 10, 24, -19, -13, -11, -1, -3],\n [0, 0, 0, -15, -16, -1, 11, 22, 17],\n [0, 0, 0, 0, 14, 20, 7, -9, -2],\n [0, 0, 0, 0, 0, -22, -9, -9, 24],\n [0, 0, 0, 0, 0, 0, -8, 3, -2],\n [0, 0, 0, 0, 0, 0, 0, 11, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 12, 10, 4, -4, -19, -4, 0, -16],\n [12, 11, 8, 9, -9, 11, -10, 0, 10],\n [10, 8, -8, 6, -6, -12, -2, 2, -11],\n [4, 9, 6, -14, 2, -20, 6, 2, -12],\n [-4, -9, -6, 2, 20, 5, 0, -2, -7],\n [-19, 11, -12, -20, 5, -10, -18, 2, 16],\n [-4, -10, -2, 6, 0, -18, 15, 4, 10],\n [0, 0, 2, 2, -2, 2, 4, -6, 0],\n [-16, 10, -11, -12, -7, 16, 10, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, 6, -2, -18, 3, 12, 12, 8, -2],\n [6, 2, 4, -2, 17, -5, 14, -3, -10],\n [-2, 4, -3, 2, 1, -22, 8, -12, 8],\n [-18, -2, 2, -24, -2, -3, -14, -9, -4],\n [3, 17, 1, -2, 10, 9, -14, -18, 8],\n [12, -5, -22, -3, 9, -7, -18, -2, -8],\n [12, 14, 8, -14, -14, -18, -11, -22, -2],\n [8, -3, -12, -9, -18, -2, -22, -9, -1],\n [-2, -10, 8, -4, 8, -8, -2, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -12, -16, -14, 12, 18, 20, 8, 15],\n [0, -9, -9, -23, 5, 25, -25, -14, 13],\n [0, 0, -13, 8, 16, -5, -4, -22, -8],\n [0, 0, 0, -14, -9, -16, 8, -20, -18],\n [0, 0, 0, 0, -24, -18, -15, 10, -16],\n [0, 0, 0, 0, 0, 3, 16, -14, -12],\n [0, 0, 0, 0, 0, 0, 24, 4, 13],\n [0, 0, 0, 0, 0, 0, 0, 12, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 16, 2, -2, -6, -14, -10, -4, -14],\n [16, -8, 9, 2, 4, 21, -4, 8, -15],\n [2, 9, 6, 10, 4, -2, -8, -5, 3],\n [-2, 2, 10, 5, -4, -2, 8, -6, -8],\n [-6, 4, 4, -4, 8, -1, 8, 18, 3],\n [-14, 21, -2, -2, -1, 18, 2, 0, 8],\n [-10, -4, -8, 8, 8, 2, -13, 4, 10],\n [-4, 8, -5, -6, 18, 0, 4, -3, -16],\n [-14, -15, 3, -8, 3, 8, 10, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -14, 2, -7, -4, 4, 16, 4, -5],\n [-14, 18, -8, -1, 4, 0, -2, -6, -17],\n [2, -8, 0, -6, 11, 4, 0, 5, 10],\n [-7, -1, -6, 11, -12, -6, -9, -1, 2],\n [-4, 4, 11, -12, 16, -12, 8, -6, 2],\n [4, 0, 4, -6, -12, -20, -15, -12, 2],\n [16, -2, 0, -9, 8, -15, 22, 4, 2],\n [4, -6, 5, -1, -6, -12, 4, 4, -11],\n [-5, -17, 10, 2, 2, 2, 2, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-76", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (5, 9) of the inverse. Round your answer to the nearest integer:\n[[22, 8, -6, 4, 6, -11, 10, 16, -23],\n [8, 20, 12, -14, -2, 6, 14, 6, 0],\n [-6, 12, 12, -2, -4, -16, 12, -8, 8],\n [4, -14, -2, -11, -5, -2, -3, 10, -4],\n [6, -2, -4, -5, 5, 1, -11, 2, 0],\n [-11, 6, -16, -2, 1, 11, -22, -16, 7],\n [10, 14, 12, -3, -11, -22, 3, -3, 10],\n [16, 6, -8, 10, 2, -16, -3, 8, 7],\n [-23, 0, 8, -4, 0, 7, 10, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (5, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[20, 16, 13, 0, 23, 12, -3, -4, -22],\n [0, -17, -22, -19, -3, -24, 23, -2, 14],\n [0, 0, 5, 21, 14, 22, 25, 17, 8],\n [0, 0, 0, -10, 21, -13, -11, 1, -22],\n [0, 0, 0, 0, 10, -23, -4, 23, -4],\n [0, 0, 0, 0, 0, -22, 5, 18, 5],\n [0, 0, 0, 0, 0, 0, 11, -5, -11],\n [0, 0, 0, 0, 0, 0, 0, -8, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[8, -22, -10, -12, 6, 0, 18, 4, 4],\n [-22, -16, 4, -4, -6, 15, -4, -19, -8],\n [-10, 4, 13, -4, -8, -8, -6, 13, -1],\n [-12, -4, -4, 14, 10, -4, 2, 2, 19],\n [6, -6, -8, 10, 3, -1, 11, 8, -2],\n [0, 15, -8, -4, -1, 1, -2, -12, -6],\n [18, -4, -6, 2, 11, -2, -21, 7, 6],\n [4, -19, 13, 2, 8, -12, 7, -23, 14],\n [4, -8, -1, 19, -2, -6, 6, 14, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-541", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the inverse of matrix 1/450 * A where A =\n[[-6, 18, 19, 8, -5, 22, -3, -20, 25],\n [0, 23, -3, -17, -9, -24, -7, -7, -19],\n [0, 0, -6, -17, -9, 1, 21, -24, 10],\n [0, 0, 0, 13, -8, -19, -9, 13, 10],\n [0, 0, 0, 0, -1, -21, 4, -14, -22],\n [0, 0, 0, 0, 0, -2, -12, -21, -8],\n [0, 0, 0, 0, 0, 0, -2, -15, 9],\n [0, 0, 0, 0, 0, 0, 0, 2, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1460", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[23, 19, -25, -16, 21, 6, 13, -4, -8],\n [0, 20, 6, 1, 2, -8, 13, 23, 3],\n [0, 0, -18, 5, 8, -19, 10, -8, 12],\n [0, 0, 0, -18, 25, 9, -8, -21, -12],\n [0, 0, 0, 0, -6, -1, 2, -14, -24],\n [0, 0, 0, 0, 0, 22, -6, 12, -22],\n [0, 0, 0, 0, 0, 0, -14, 16, -21],\n [0, 0, 0, 0, 0, 0, 0, -24, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1438", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[13, 8, -20, 24, 12, 19, 25, 8, 18],\n [-11, -12, -20, 24, 11, 24, 6, -23, -23],\n [-4, -4, -16, 25, -23, -14, 3, 22, -9],\n [-19, -13, -24, -22, -16, 13, -2, -9, -20],\n [-7, -21, 6, -16, -17, 1, -13, -7, -5],\n [-2, 12, -22, -2, 9, -23, -22, 11, 14],\n [22, 9, 5, 18, -1, 14, -13, -22, 20],\n [-12, -13, 1, -20, -9, 10, 14, 23, 9],\n [-9, 15, -24, -13, -24, 2, 17, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[21, 15, -16, 12, -19, -8, 0, -2, 13],\n [15, -13, 17, 14, -17, -16, -18, -6, 3],\n [-16, 17, 9, -23, -3, 6, -2, -4, -2],\n [12, 14, -23, -18, 6, -12, -2, 2, 15],\n [-19, -17, -3, 6, -6, 14, 10, -2, 2],\n [-8, -16, 6, -12, 14, -15, -13, -4, 13],\n [0, -18, -2, -2, 10, -13, -1, 6, 14],\n [-2, -6, -4, 2, -2, -4, 6, 21, -18],\n [13, 3, -2, 15, 2, 13, 14, -18, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-256", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[16, 22, 18, -8, -3, 7, -10, 12, 9],\n [0, 2, -24, 4, -13, 15, -10, -21, 2],\n [0, 0, -6, -2, 1, 4, 19, 1, 0],\n [0, 0, 0, 12, -21, -3, 2, 8, -11],\n [0, 0, 0, 0, -7, -17, 3, 25, 13],\n [0, 0, 0, 0, 0, 12, -15, 1, 7],\n [0, 0, 0, 0, 0, 0, 1, 10, -15],\n [0, 0, 0, 0, 0, 0, 0, 13, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33407", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-16, -21, -17, -24, 8, 12, 5, -16, 24],\n [-14, 10, -5, 23, 21, -20, 22, 23, -23],\n [-16, -21, 20, 0, -5, 19, 0, 12, 18],\n [0, -18, -21, -11, -10, -25, -10, 11, -23],\n [21, 5, -13, -10, 17, -5, -24, 1, 12],\n [0, 12, 20, -1, -15, -18, -18, 7, -19],\n [12, -5, -18, 25, -5, -6, -18, 20, 5],\n [24, 3, 22, -17, -11, 4, 0, -16, 3],\n [-10, 10, -6, 19, 11, -4, -19, -3, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, 3, -10, 12, 2, 22, 12, 5, -12],\n [7, -17, 1, -2, -13, 0, 3, 25, 23],\n [17, 2, 2, -18, -3, 3, -21, 16, -19],\n [16, 10, 15, 1, 20, -24, -1, -17, 1],\n [-25, -3, -16, 16, -1, -23, -20, -20, -24],\n [-8, -3, -24, -14, -4, 11, -6, 13, -2],\n [22, -6, -25, -25, -9, -25, 19, 4, 15],\n [21, -23, 20, -15, -2, -4, 18, 19, 0],\n [-13, -25, -2, -16, 9, -2, 2, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[14, -10, -9, 25, -11, -10, -11, 8, -15],\n [0, -11, 0, 25, -22, 17, -21, 9, -13],\n [0, 0, -8, 8, 13, 15, 16, 24, -3],\n [0, 0, 0, -14, -19, 23, 0, 7, 11],\n [0, 0, 0, 0, -19, 6, -22, -6, 24],\n [0, 0, 0, 0, 0, 9, 22, 4, 10],\n [0, 0, 0, 0, 0, 0, -4, -2, 17],\n [0, 0, 0, 0, 0, 0, 0, 24, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "915", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[13, 3, 0, -5, -9, -10, 5, 25, -17],\n [0, -12, 23, 11, -24, 22, 20, -12, 7],\n [0, 0, 21, 25, -6, -24, 25, 15, -7],\n [0, 0, 0, -22, -14, 3, -19, -12, -14],\n [0, 0, 0, 0, 6, -16, 17, -9, -21],\n [0, 0, 0, 0, 0, 10, 10, -8, -17],\n [0, 0, 0, 0, 0, 0, 16, 3, -11],\n [0, 0, 0, 0, 0, 0, 0, -10, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-296", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 22, -1, 12, -13, -22, -12, 7, 2],\n [11, -18, 18, 8, 18, -21, -21, 5, 19],\n [-17, 16, 6, 7, -23, 4, 24, -14, 3],\n [-23, 0, 4, -17, 0, -24, -23, 20, -22],\n [-1, 25, -13, 13, 18, 9, -3, -17, -24],\n [15, 18, 5, 18, 21, -24, 6, -8, -13],\n [20, -21, 16, 18, -16, 17, -1, 8, 11],\n [4, -19, -20, -23, -13, -23, 0, -2, -20],\n [17, 23, 16, -14, 23, 10, -24, -15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "398", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 3) rounded to the nearest integer?\n[[8, 2, -7, -4, 6, 2, 11, 12, -7],\n [2, 24, 16, 2, -2, 2, 0, 0, 6],\n [-7, 16, -1, 4, -3, -17, 6, -10, 3],\n [-4, 2, 4, 6, 4, 0, -4, 16, 12],\n [6, -2, -3, 4, -7, 8, -14, 12, 10],\n [2, 2, -17, 0, 8, -14, -11, -14, 19],\n [11, 0, 6, -4, -14, -11, -11, 6, -12],\n [12, 0, -10, 16, 12, -14, 6, 4, 12],\n [-7, 6, 3, 12, 10, 19, -12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-24, 23, -20, 20, 24, 12, 16, -2, -8],\n [1, 15, -18, 2, -16, -9, 3, -20, -12],\n [-4, -20, 0, 13, -14, 9, -12, -4, 25],\n [-3, 22, -19, 14, 24, -1, -13, -5, 15],\n [-16, -17, -11, -24, -1, -13, 8, 25, 8],\n [9, 12, -23, 16, -20, 22, 23, -7, -23],\n [-8, 13, -17, -14, -21, -23, -15, 4, -22],\n [-21, -25, 1, 2, 3, -8, -14, -13, 15],\n [-24, 11, 19, -10, 22, -2, 9, -4, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-80", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-15, 18, -10, 4, 8, 4, 0, 8, 13],\n [18, -10, -2, 22, -10, 8, -14, 10, 11],\n [-10, -2, 5, 0, 4, 7, 4, -24, -5],\n [4, 22, 0, -23, 0, -16, -19, 5, 1],\n [8, -10, 4, 0, 16, -17, 0, 8, -6],\n [4, 8, 7, -16, -17, 13, -10, -8, 8],\n [0, -14, 4, -19, 0, -10, -15, -4, -8],\n [8, 10, -24, 5, 8, -8, -4, 4, 17],\n [13, 11, -5, 1, -6, 8, -8, 17, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 9, -24, 13, 11, -5, -21, 19, -5],\n [3, -6, 12, -6, 24, -1, -24, 6, 0],\n [-20, 15, -23, 7, -25, 25, -21, -13, -7],\n [-14, 22, -1, 25, 9, -14, 4, -21, 8],\n [-4, 13, -13, 21, -23, -6, 5, -21, -2],\n [14, 7, -18, -2, 24, -6, -10, 24, -14],\n [-13, 19, 16, 13, -1, 20, 6, -2, 22],\n [21, 18, -17, 14, 24, -3, 24, -13, 6],\n [24, -11, 10, 23, -21, -4, -10, 15, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1039", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (7, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 0, 11, -2, -2, -6, -2, -16, 4],\n [0, 0, -6, -2, -6, 0, -13, 16, 8],\n [11, -6, -9, 5, 0, 0, -6, -4, 8],\n [-2, -2, 5, -13, 0, -4, 5, 10, 2],\n [-2, -6, 0, 0, 6, -5, -4, -6, -7],\n [-6, 0, 0, -4, -5, -22, -6, -4, 6],\n [-2, -13, -6, 5, -4, -6, 23, 6, -20],\n [-16, 16, -4, 10, -6, -4, 6, -5, 11],\n [4, 8, 8, 2, -7, 6, -20, 11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, -1, -24, -17, 2, 12, -23, -6, -20],\n [13, 7, -25, 11, -20, 19, 8, 21, -11],\n [19, 0, -12, -19, 20, 5, -2, 5, 3],\n [16, 6, -9, -12, 14, 10, 22, -2, 19],\n [1, -1, 6, -8, 20, -8, 11, 0, -17],\n [9, -18, -6, 16, -4, -7, 4, 2, 9],\n [17, -15, 5, 23, 22, 13, 10, 4, -3],\n [-7, -14, -11, 5, 17, 11, 11, -11, 3],\n [24, 17, 0, 18, -24, -6, -11, -22, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2036", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[24, 12, -3, 0, 25, -15, 2, -24, -18],\n [3, -15, 11, -8, 24, -12, -16, 9, -17],\n [9, -15, 18, -14, -23, 13, -12, 2, -15],\n [13, -1, -5, -16, 17, -11, -7, 22, -4],\n [-5, 18, 6, 24, -3, -13, -21, -22, 2],\n [-12, -18, -17, 25, 9, 11, -5, -8, 7],\n [-18, 25, 23, -9, 17, 5, 8, -20, -4],\n [-12, -23, -14, 10, -14, 19, -24, -24, -11],\n [-3, 3, -9, 6, -19, 4, 2, -12, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "650", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[4, -8, -4, 17, -8, 20, 3, -3, 8],\n [-8, -2, 4, -10, 14, 14, 9, 12, -10],\n [-4, 4, -2, -14, -3, 0, -16, 15, 10],\n [17, -10, -14, -5, 0, -18, 4, 14, 16],\n [-8, 14, -3, 0, -12, -4, 12, 0, -10],\n [20, 14, 0, -18, -4, 10, -10, -2, 2],\n [3, 9, -16, 4, 12, -10, 11, 16, -4],\n [-3, 12, 15, 14, 0, -2, 16, 12, -10],\n [8, -10, 10, 16, -10, 2, -4, -10, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "443", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-23, 18, 5, 21, 16, -6, -7, 22, -15],\n [14, -23, -3, -19, -3, -19, 20, 8, 16],\n [-7, -17, 22, 25, -8, 15, 22, 19, 16],\n [-1, -12, 18, -1, -7, 13, -11, -10, 1],\n [14, -16, -22, 25, -7, 2, -5, 21, -12],\n [7, 22, -16, -7, 4, -4, -23, 11, 15],\n [-8, -15, 22, -24, -14, -20, 17, 14, 18],\n [3, 4, -24, -17, 21, -24, 3, 7, -16],\n [8, 18, -18, 11, 7, 21, -20, 18, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2542", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[19, -7, 6, 1, -25, 17, 7, 14, 6],\n [-21, -9, -18, 16, 8, -17, -3, 9, 24],\n [-19, -11, -6, 24, -1, -23, 20, -2, 8],\n [20, -4, -15, 22, -18, 13, 17, 9, 23],\n [20, 12, -18, 11, 1, 2, 14, 8, 6],\n [-11, 18, -9, 7, 21, 20, -10, 3, -17],\n [7, 23, 3, -13, -5, -5, -21, -16, -20],\n [25, -13, -25, -6, 21, 20, -18, -16, -17],\n [23, 15, -23, -15, -14, -16, -1, 23, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-1, -15, 10, 13, 0, -12, 13, 14, -25],\n [-22, 4, -14, 9, -13, 5, 12, 17, -3],\n [-22, -10, -19, -4, 3, -15, 7, 3, 13],\n [-14, -19, 13, 16, 22, 0, 14, -17, 15],\n [8, 19, -13, 10, -1, -2, 18, -9, -24],\n [-13, 5, 3, 24, 2, 1, -11, 5, 14],\n [-11, 7, -6, 16, -14, 11, -17, -3, -18],\n [6, 22, -12, 1, -1, -13, -5, 19, 5],\n [11, 22, 17, -21, -13, 2, 17, -1, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 16, 14, 2, 12, -2, -5, 16, 9],\n [16, 24, -9, -8, 2, -5, 0, 0, 4],\n [14, -9, 22, 22, 2, 2, -14, -6, 0],\n [2, -8, 22, -6, 2, 2, -2, -8, -16],\n [12, 2, 2, 2, 10, 8, -8, 0, -6],\n [-2, -5, 2, 2, 8, 22, 2, 2, -10],\n [-5, 0, -14, -2, -8, 2, 17, 8, 1],\n [16, 0, -6, -8, 0, 2, 8, 0, -12],\n [9, 4, 0, -16, -6, -10, 1, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7405", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, 3, -10, 20, -4, -18, -6, 25, -12],\n [13, 11, 24, 8, -15, 14, 7, 5, 18],\n [8, 24, -19, 23, -3, 20, -19, -1, -23],\n [12, -6, 8, 23, 18, 18, 4, -9, -16],\n [9, -6, -8, 19, 18, 1, 23, 10, -3],\n [6, -16, -15, 12, -20, 15, 21, 8, 10],\n [11, -9, 14, 14, -14, -5, 14, -7, -23],\n [-8, 25, -7, 21, -20, -10, -18, 22, -8],\n [22, 17, 13, 23, 23, -14, 19, -16, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1922", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[20, -4, 3, 13, -10, 10, 4, 5, -13],\n [-4, -9, -6, 8, -7, 10, -14, -13, -18],\n [3, -6, 9, -4, 6, -10, -9, 6, 5],\n [13, 8, -4, -2, -12, -4, 2, -4, -8],\n [-10, -7, 6, -12, 5, -10, 3, -6, 1],\n [10, 10, -10, -4, -10, -24, -14, -4, 0],\n [4, -14, -9, 2, 3, -14, 12, -9, -18],\n [5, -13, 6, -4, -6, -4, -9, -19, 3],\n [-13, -18, 5, -8, 1, 0, -18, 3, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-20, -1, -1, 2, 2, -4, -11, -2, 0],\n [-1, 25, -4, -8, -20, 0, 2, -8, -14],\n [-1, -4, -6, -2, -14, -4, 2, -6, 12],\n [2, -8, -2, 3, -6, 12, 10, -8, 10],\n [2, -20, -14, -6, -22, 2, -15, 1, -6],\n [-4, 0, -4, 12, 2, 7, -9, -7, -11],\n [-11, 2, 2, 10, -15, -9, 3, -4, -6],\n [-2, -8, -6, -8, 1, -7, -4, -4, -18],\n [0, -14, 12, 10, -6, -11, -6, -18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-70", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (6, 1) of the inverse. Round your answer to the nearest integer:\n[[-13, 1, -12, -2, -23, 21, 25, 23, 4],\n [0, 22, -12, -14, 2, 18, 3, 17, -9],\n [0, 0, -5, -3, -6, -15, 8, -16, -16],\n [0, 0, 0, -2, -14, 17, -3, 1, 19],\n [0, 0, 0, 0, 24, -4, 15, -2, -1],\n [0, 0, 0, 0, 0, 22, 12, -20, 9],\n [0, 0, 0, 0, 0, 0, -15, -14, 16],\n [0, 0, 0, 0, 0, 0, 0, -13, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-23, 0, 10, -4, -24, -10, -13, -2, 10],\n [0, 12, 10, 14, 10, -14, -6, -9, -2],\n [10, 10, -24, 15, -6, -8, 11, 6, -4],\n [-4, 14, 15, -21, -9, -10, -2, -2, -8],\n [-24, 10, -6, -9, -5, 2, -16, -20, 4],\n [-10, -14, -8, -10, 2, -2, -7, 16, -2],\n [-13, -6, 11, -2, -16, -7, -13, -8, 1],\n [-2, -9, 6, -2, -20, 16, -8, 25, 6],\n [10, -2, -4, -8, 4, -2, 1, 6, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "616", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-23, -16, 16, -12, -14, 21, 16, 4, 6],\n [6, 16, 6, 0, 25, -25, 16, -24, -9],\n [4, 13, -19, 1, -17, -4, 8, 20, 23],\n [-25, -17, -6, -7, 10, 14, 19, -22, -17],\n [15, -4, -8, -14, 16, 17, 13, -17, -20],\n [-7, 22, 21, -19, -10, -21, -10, -25, 25],\n [11, 13, -7, 11, -9, 0, -4, -18, 7],\n [-24, 4, 21, -6, -8, 17, -16, -2, -22],\n [11, -22, -13, -1, -13, -8, -2, -24, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-153", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, -6, -10, -8, 6, 4, -2, -25, 16],\n [-6, -17, 1, 6, -2, -10, 16, 4, 12],\n [-10, 1, -3, 12, 4, -10, 13, -12, 14],\n [-8, 6, 12, 25, -5, 0, 4, -8, 18],\n [6, -2, 4, -5, -11, -11, -4, 0, 14],\n [4, -10, -10, 0, -11, -14, -13, 2, 11],\n [-2, 16, 13, 4, -4, -13, 16, 4, 2],\n [-25, 4, -12, -8, 0, 2, 4, -16, -10],\n [16, 12, 14, 18, 14, 11, 2, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (2, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -13, -25, -21, -10, -11, 23, 2, 5],\n [0, 22, 19, 17, -9, 23, 8, -13, -12],\n [0, 0, 16, 6, 9, 5, -9, 21, -17],\n [0, 0, 0, -13, 24, -21, -20, 4, 5],\n [0, 0, 0, 0, -17, -24, 11, -25, -22],\n [0, 0, 0, 0, 0, -3, -14, -16, 8],\n [0, 0, 0, 0, 0, 0, -24, 4, -24],\n [0, 0, 0, 0, 0, 0, 0, 24, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, -4, -2, 10, -10, 5, -12, 16, -2],\n [-4, 0, -4, 3, 0, 18, 4, -1, -4],\n [-2, -4, -22, -10, 10, 10, 0, 3, -16],\n [10, 3, -10, 3, -10, 6, 6, 10, 14],\n [-10, 0, 10, -10, -1, -10, 10, -12, 0],\n [5, 18, 10, 6, -10, -1, -18, -6, -16],\n [-12, 4, 0, 6, 10, -18, 5, 0, 8],\n [16, -1, 3, 10, -12, -6, 0, 14, -7],\n [-2, -4, -16, 14, 0, -16, 8, -7, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-246", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 4) of the inverse of matrix 1/450 * A where A =\n[[-15, -12, 12, -14, 19, -9, -10, 9, -24],\n [-15, 15, -23, 3, -8, -6, 21, -12, 8],\n [23, 5, 14, 16, -8, 4, -1, -7, -18],\n [2, -18, 5, -23, -23, 18, -4, -9, 10],\n [-9, -12, 25, -17, 4, -5, -14, 11, 6],\n [-15, -6, 9, 21, 20, -15, -18, -22, 1],\n [18, 14, 12, 21, 4, 18, 22, 22, 1],\n [-5, -6, -22, -15, -13, -17, -22, -14, -17],\n [-13, 22, 0, 12, 16, -13, 13, 2, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-2, -10, 7, -4, 5, 2, -4, -9, -10],\n [-10, -17, 2, 2, 20, -4, 4, 0, 8],\n [7, 2, 4, -16, 22, 5, 1, -24, -6],\n [-4, 2, -16, -23, 6, -1, 5, -8, -16],\n [5, 20, 22, 6, 7, 6, 2, -8, -4],\n [2, -4, 5, -1, 6, 19, -13, -6, -14],\n [-4, 4, 1, 5, 2, -13, 3, -6, -6],\n [-9, 0, -24, -8, -8, -6, -6, -1, 21],\n [-10, 8, -6, -16, -4, -14, -6, 21, 19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-91", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-11, -25, -4, -23, 12, -12, 10, -8, 21],\n [0, -8, -23, -16, 23, 13, 21, -25, 1],\n [0, 0, 23, -21, -19, -7, 3, -11, 9],\n [0, 0, 0, 4, -6, 11, -23, -17, 15],\n [0, 0, 0, 0, -3, -5, -10, -17, -13],\n [0, 0, 0, 0, 0, 10, -25, -8, 25],\n [0, 0, 0, 0, 0, 0, 18, 20, -22],\n [0, 0, 0, 0, 0, 0, 0, -6, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-79", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-6, -1, -14, -5, -1, -15, -17, 24, -1],\n [0, 6, 23, -12, -25, -9, -1, -18, -21],\n [0, 0, 9, -7, -3, -17, 4, 24, -10],\n [0, 0, 0, 20, -25, 0, -1, -10, -11],\n [0, 0, 0, 0, -12, 3, -2, 21, -11],\n [0, 0, 0, 0, 0, -16, 9, -3, 23],\n [0, 0, 0, 0, 0, 0, 3, -25, -22],\n [0, 0, 0, 0, 0, 0, 0, 6, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-16, 15, 1, -17, 2, -25, -9, 5, 18],\n [0, 11, 3, -8, 21, 12, 13, 23, -20],\n [0, 0, -12, 18, -16, -6, -11, 5, -19],\n [0, 0, 0, 22, 13, 2, 4, 11, -23],\n [0, 0, 0, 0, 11, -14, -22, 21, -17],\n [0, 0, 0, 0, 0, 14, 18, -4, -2],\n [0, 0, 0, 0, 0, 0, 23, 24, 17],\n [0, 0, 0, 0, 0, 0, 0, 13, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, -17, 6, -6, 10, -4, 5, 12, -8],\n [-17, 6, -8, 1, -11, 16, 13, 6, 3],\n [6, -8, -5, 10, -2, -10, -8, 10, 6],\n [-6, 1, 10, -6, -6, 4, 9, -15, -9],\n [10, -11, -2, -6, -12, 2, 4, -14, 8],\n [-4, 16, -10, 4, 2, -7, 7, 0, 0],\n [5, 13, -8, 9, 4, 7, 3, -2, -6],\n [12, 6, 10, -15, -14, 0, -2, -23, 11],\n [-8, 3, 6, -9, 8, 0, -6, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, -25, 22, 13, -23, -22, 15, 11, 25],\n [-11, -18, 12, 24, -7, 21, 0, 13, -16],\n [12, -12, 23, 15, -7, 4, -21, 5, -19],\n [-7, 5, 13, -2, 8, -3, 22, 19, 14],\n [-20, 12, 15, 10, 1, -15, -21, -9, -19],\n [1, 21, -11, 20, -13, -15, 19, 0, -4],\n [2, -2, 3, -17, 16, -22, 23, 20, -8],\n [17, -10, 7, 3, 13, -16, -17, 5, 2],\n [-23, -12, -1, -11, -24, -2, -12, 22, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-25, -1, -25, 6, 16, 16, -23, 23, -7],\n [0, 3, 24, -24, -17, -9, 20, 10, -9],\n [0, 0, -6, 24, -23, 17, 24, -22, -9],\n [0, 0, 0, 16, -11, 7, -10, -15, -6],\n [0, 0, 0, 0, 8, -25, -2, -2, -17],\n [0, 0, 0, 0, 0, -11, 4, 25, 1],\n [0, 0, 0, 0, 0, 0, 5, 6, 6],\n [0, 0, 0, 0, 0, 0, 0, -19, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17429", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 5) of the inverse of matrix 1/450 * A where A =\n[[-15, 2, 4, 16, -2, 6, 5, -1, 16],\n [2, 11, 15, 16, -2, -3, -14, 7, -12],\n [4, 15, -7, 4, 2, -6, -10, 13, -10],\n [16, 16, 4, 11, -17, -9, 4, -2, 8],\n [-2, -2, 2, -17, -10, -6, 18, 12, 1],\n [6, -3, -6, -9, -6, -2, -4, 6, 4],\n [5, -14, -10, 4, 18, -4, -4, -10, -8],\n [-1, 7, 13, -2, 12, 6, -10, -10, -6],\n [16, -12, -10, 8, 1, 4, -8, -6, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-10, -7, -9, 0, -20, 17, 23, -17, 24],\n [-9, 5, -14, -3, -21, 17, 10, 10, -23],\n [-2, -9, 13, 0, -22, 19, -14, -25, -5],\n [-7, -5, -8, 17, -23, 23, 18, 6, -16],\n [14, -11, -21, -22, 2, 25, -22, -11, -9],\n [18, -23, -16, 21, 16, -3, -8, -25, 9],\n [5, 18, -25, -23, -23, 11, -7, 3, -1],\n [7, 10, 3, 0, -22, 23, -12, 24, 1],\n [7, -4, 22, -23, -3, -5, 15, -3, -22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-174", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, 4, 20, 8, -13, -6, 12, 8, 8],\n [4, -15, 6, 13, 0, -20, -1, 0, 6],\n [20, 6, -12, 4, -4, 8, -4, -7, -4],\n [8, 13, 4, 25, 1, -2, 0, -8, -8],\n [-13, 0, -4, 1, 5, 7, 10, 0, 7],\n [-6, -20, 8, -2, 7, 5, 3, -12, 2],\n [12, -1, -4, 0, 10, 3, 6, -8, 15],\n [8, 0, -7, -8, 0, -12, -8, 19, 0],\n [8, 6, -4, -8, 7, 2, 15, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, -23, -3, 25, -8, 0, 10, -18, -9],\n [0, 11, 19, 7, 1, 19, -22, -4, 0],\n [0, 0, 20, 9, 11, 6, -19, 7, 5],\n [0, 0, 0, -18, 6, 12, -4, 8, -7],\n [0, 0, 0, 0, -10, -22, 1, 2, 17],\n [0, 0, 0, 0, 0, -4, -17, -17, -17],\n [0, 0, 0, 0, 0, 0, -8, 7, -25],\n [0, 0, 0, 0, 0, 0, 0, -8, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32780", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[5, 7, 21, -8, 13, -10, -10, 21, 12],\n [0, -19, -12, 17, 22, -1, 6, 12, -4],\n [0, 0, -10, -14, -9, 11, 1, -1, -13],\n [0, 0, 0, 15, -23, 9, 7, -4, 24],\n [0, 0, 0, 0, 24, 3, 13, 1, 10],\n [0, 0, 0, 0, 0, -21, -12, -23, -3],\n [0, 0, 0, 0, 0, 0, -16, -1, -13],\n [0, 0, 0, 0, 0, 0, 0, 10, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2709", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (6, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -18, -14, 3, 5, -4, -3, -10, 6],\n [-18, -21, -16, 12, -5, -20, -4, -2, 4],\n [-14, -16, -16, 5, 7, 0, -14, -4, 16],\n [3, 12, 5, -18, -2, 0, 14, -4, 2],\n [5, -5, 7, -2, -13, -18, 10, -4, -12],\n [-4, -20, 0, 0, -18, 14, -6, 6, -3],\n [-3, -4, -14, 14, 10, -6, 14, -4, 6],\n [-10, -2, -4, -4, -4, 6, -4, -11, 7],\n [6, 4, 16, 2, -12, -3, 6, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 7, -21, 11, -12, 1, -3, -12, 14],\n [0, 13, -7, 21, -22, 4, -7, 5, 5],\n [0, 0, -12, 20, -16, 22, 5, 11, -3],\n [0, 0, 0, -24, 19, -13, 25, 24, -7],\n [0, 0, 0, 0, 22, 3, -24, 14, 12],\n [0, 0, 0, 0, 0, -18, -4, -22, -15],\n [0, 0, 0, 0, 0, 0, -20, -5, 0],\n [0, 0, 0, 0, 0, 0, 0, 11, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[16, -25, 10, -14, -17, 10, 15, 2, 12],\n [7, 16, 20, -4, -1, -8, -20, -8, -10],\n [-11, 22, -18, -13, 17, -19, -9, 24, 6],\n [-4, 25, -13, 21, -3, 3, -4, -25, 3],\n [22, -21, 9, -16, -7, 11, -19, 20, 9],\n [19, -13, -16, -24, -20, -18, 10, -1, 18],\n [21, 14, -19, 20, -3, -7, 20, -4, -13],\n [-5, -25, -7, 7, -22, 16, -23, 1, 15],\n [9, 2, -20, -20, 18, -3, 7, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1425", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-21, 15, 16, -13, 21, -14, -21, 11, 5],\n [2, 2, 4, -8, 18, 1, 9, 0, 13],\n [23, 25, -8, 7, -1, 5, 11, -24, 7],\n [13, 17, 17, 6, -8, -9, 8, 13, -19],\n [16, 9, 4, -14, 9, -15, 18, -22, -1],\n [22, 6, -6, 24, 5, -22, 12, 21, -25],\n [-23, 11, -4, -9, -12, 15, 9, -13, 9],\n [17, -24, 21, -13, 25, -10, -8, -19, 19],\n [10, 15, 4, 16, 15, -19, -11, 14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3352", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[17, 11, -24, 16, 22, -13, 14, 15, 17],\n [0, 5, -10, 16, 18, -20, 2, 6, 18],\n [0, 0, -8, -22, -17, -19, 24, -18, 17],\n [0, 0, 0, -23, -9, -24, -11, 20, 3],\n [0, 0, 0, 0, -20, 12, 0, -15, 0],\n [0, 0, 0, 0, 0, -13, 9, -10, -11],\n [0, 0, 0, 0, 0, 0, 23, 15, 1],\n [0, 0, 0, 0, 0, 0, 0, -14, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1711", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 7) rounded to the nearest integer?\n[[-25, 8, 13, 5, 0, -6, -8, 8, 20],\n [8, 17, 9, -4, -23, 0, -11, -2, -20],\n [13, 9, -17, -8, -12, -12, 0, 20, -2],\n [5, -4, -8, -14, 14, 2, -8, 8, -3],\n [0, -23, -12, 14, 1, 20, 2, 15, -15],\n [-6, 0, -12, 2, 20, -11, -11, 12, 2],\n [-8, -11, 0, -8, 2, -11, -3, 20, -12],\n [8, -2, 20, 8, 15, 12, 20, 4, 0],\n [20, -20, -2, -3, -15, 2, -12, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 1, 8, -6, -2, -4, -10, 14, 13],\n [1, 4, 18, -9, 12, -8, 2, 14, -14],\n [8, 18, -21, 4, 10, 4, 8, -16, 0],\n [-6, -9, 4, 25, -4, -14, 10, -6, 14],\n [-2, 12, 10, -4, -11, -18, 0, -7, -4],\n [-4, -8, 4, -14, -18, -13, -1, 0, -1],\n [-10, 2, 8, 10, 0, -1, -14, 5, -20],\n [14, 14, -16, -6, -7, 0, 5, -22, 0],\n [13, -14, 0, 14, -4, -1, -20, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34565", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-20, -18, -22, -21, -1, -4, 2, 13, -3],\n [0, -22, 21, -5, 11, 15, -24, -19, 23],\n [0, 0, -6, -3, 8, -15, 8, 7, 0],\n [0, 0, 0, -4, 8, -11, -16, -11, 16],\n [0, 0, 0, 0, 24, 10, -17, -10, 10],\n [0, 0, 0, 0, 0, -16, -10, -22, -4],\n [0, 0, 0, 0, 0, 0, -2, 3, -23],\n [0, 0, 0, 0, 0, 0, 0, -18, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-668", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -17, 6, 8, -15, 5, 8, -6, 0],\n [-17, 13, -16, 2, -7, 8, 10, -12, -2],\n [6, -16, 13, 20, -22, 8, 16, 6, 12],\n [8, 2, 20, 8, -20, 6, 0, 11, 1],\n [-15, -7, -22, -20, -17, -6, -13, -10, 0],\n [5, 8, 8, 6, -6, -20, 18, -2, -14],\n [8, 10, 16, 0, -13, 18, 22, 13, 23],\n [-6, -12, 6, 11, -10, -2, 13, -10, -2],\n [0, -2, 12, 1, 0, -14, 23, -2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1043", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -7, 9, 3, -25, -22, 2, -8, 0],\n [0, -7, -20, -25, -18, 7, 25, 17, -5],\n [0, 0, 21, 17, -7, 3, -16, -14, 7],\n [0, 0, 0, 5, -20, -9, 24, 11, -8],\n [0, 0, 0, 0, -2, -13, 3, 6, -2],\n [0, 0, 0, 0, 0, 7, -8, 11, -13],\n [0, 0, 0, 0, 0, 0, -1, 8, 13],\n [0, 0, 0, 0, 0, 0, 0, -9, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, 19, 9, -11, -25, 0, 9, -1, 16],\n [-11, -4, -20, -11, -2, -5, -19, 3, 6],\n [6, -21, -22, -4, -8, 9, -9, 24, 24],\n [-2, -24, -13, -11, -21, -23, 11, 11, 11],\n [-23, 9, -3, 2, 4, -8, 10, 7, 0],\n [22, 14, -9, 14, -19, -18, 5, -14, 22],\n [5, 18, -7, -16, 13, -14, -6, 11, 22],\n [15, -19, -12, -15, -19, 3, -16, 3, -17],\n [10, 22, -16, -7, 5, -9, -17, 19, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 6) rounded to the nearest integer?\n[[8, 22, -4, -2, 1, -10, -8, 6, -11],\n [22, 25, 4, -19, -2, -4, -18, -4, 1],\n [-4, 4, 10, 13, -8, 2, 4, -16, 2],\n [-2, -19, 13, 15, -3, -5, -4, -17, 3],\n [1, -2, -8, -3, 18, -4, 6, 22, 4],\n [-10, -4, 2, -5, -4, 16, -4, 6, 0],\n [-8, -18, 4, -4, 6, -4, 18, 2, 17],\n [6, -4, -16, -17, 22, 6, 2, -7, -15],\n [-11, 1, 2, 3, 4, 0, 17, -15, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 9) rounded to the nearest integer?\n[[-12, 19, 16, 24, -22, -18, -2, -15, -9],\n [0, -5, 0, 17, 22, 18, 19, 1, -10],\n [0, 0, 5, 22, 21, -20, 18, -18, -19],\n [0, 0, 0, -10, 17, -17, -16, -9, -14],\n [0, 0, 0, 0, 3, -20, -1, -2, -1],\n [0, 0, 0, 0, 0, -22, 8, 2, 12],\n [0, 0, 0, 0, 0, 0, 25, -25, 3],\n [0, 0, 0, 0, 0, 0, 0, 8, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[19, -2, 25, -3, -14, 23, 4, 5, 2],\n [-4, 18, 2, -13, -1, 18, 25, 20, -19],\n [19, -20, -2, -7, -7, 10, 25, -17, 22],\n [10, 12, 14, 3, -2, 22, -21, 16, 19],\n [0, -12, 13, 3, -20, -19, 11, -8, -3],\n [18, 12, -25, -22, 25, 18, 21, 9, -3],\n [1, 0, -18, 17, -10, 15, -23, 6, -21],\n [-6, -12, 6, 0, 21, -20, 10, 14, 25],\n [-21, -13, 6, -10, -25, -13, -15, -18, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[14, 0, 8, -4, -12, 12, 1, 12, -2],\n [0, 21, 4, -4, 14, 14, -9, 1, 18],\n [8, 4, 7, 0, -7, 2, 14, -4, -19],\n [-4, -4, 0, -11, 2, 6, 22, -6, -17],\n [-12, 14, -7, 2, -10, -7, -2, -4, 8],\n [12, 14, 2, 6, -7, 13, -4, 14, -10],\n [1, -9, 14, 22, -2, -4, -14, 4, 14],\n [12, 1, -4, -6, -4, 14, 4, 21, -5],\n [-2, 18, -19, -17, 8, -10, 14, -5, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107279", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -12, -22, -6, 8, -14, 7, -2, -6],\n [0, 12, 4, -2, 17, 14, -19, 10, 12],\n [0, 0, 20, -3, -14, 3, 18, 22, -11],\n [0, 0, 0, 23, -5, -11, -12, 16, 18],\n [0, 0, 0, 0, 1, -3, 3, 15, -17],\n [0, 0, 0, 0, 0, -21, -21, -15, 15],\n [0, 0, 0, 0, 0, 0, 20, -23, 24],\n [0, 0, 0, 0, 0, 0, 0, -6, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7652", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-3, 5, 13, 8, -3, -12, -2, -12, 0],\n [5, -23, -6, -12, -9, -6, 18, 10, -2],\n [13, -6, -17, -2, -16, -6, 12, 6, 12],\n [8, -12, -2, -16, -2, 2, -12, -11, 4],\n [-3, -9, -16, -2, 21, -2, 0, -16, 1],\n [-12, -6, -6, 2, -2, 1, -2, 5, 18],\n [-2, 18, 12, -12, 0, -2, 8, 11, -10],\n [-12, 10, 6, -11, -16, 5, 11, -4, -2],\n [0, -2, 12, 4, 1, 18, -10, -2, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, -4, -4, 11, 13, 8, 7, 18, 16],\n [0, 7, -14, -24, 2, -16, -4, -9, 0],\n [0, 0, 18, -18, -6, -14, 9, -9, 2],\n [0, 0, 0, 12, 7, -4, 18, 11, -13],\n [0, 0, 0, 0, 17, 14, 11, 8, 18],\n [0, 0, 0, 0, 0, -18, 13, 7, 18],\n [0, 0, 0, 0, 0, 0, -2, -5, -24],\n [0, 0, 0, 0, 0, 0, 0, 25, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-174", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-18, -11, -16, 0, 0, -10, 18, -19, 2],\n [-11, 21, 6, 0, -4, 10, -14, -17, 14],\n [-16, 6, -23, -16, 0, 19, -8, -12, 9],\n [0, 0, -16, 2, 7, -10, -1, -6, 16],\n [0, -4, 0, 7, 21, 0, -5, -6, 2],\n [-10, 10, 19, -10, 0, -25, 8, 4, -6],\n [18, -14, -8, -1, -5, 8, 13, 5, 4],\n [-19, -17, -12, -6, -6, 4, 5, -12, 0],\n [2, 14, 9, 16, 2, -6, 4, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, 9, 5, 9, 6, -21, -10, -9, 6],\n [0, 6, -6, 22, -24, -6, 21, -8, -25],\n [0, 0, -7, 18, 14, -20, 18, 13, 24],\n [0, 0, 0, -6, -12, -21, 15, 14, 8],\n [0, 0, 0, 0, -19, 1, -12, -12, 18],\n [0, 0, 0, 0, 0, 10, -19, 6, 22],\n [0, 0, 0, 0, 0, 0, 22, -2, 14],\n [0, 0, 0, 0, 0, 0, 0, -20, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1734", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[14, 4, 23, 15, -13, 8, 10, 4, -1],\n [-24, 10, -8, -21, -7, 16, -8, 6, -5],\n [-16, 11, 23, -4, -13, -9, -17, -2, 18],\n [-12, 20, -18, 11, -7, 2, 20, 15, 4],\n [-19, 0, 14, 20, 20, -15, -12, -5, -18],\n [-23, 2, 3, -3, -8, 9, -13, -14, 21],\n [24, -21, 13, -15, -15, 21, 16, 21, 5],\n [5, -13, -12, 23, 19, 16, -1, 7, 7],\n [-11, -10, 18, 12, -20, 18, -1, -11, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "671", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -3, 14, 19, 25, -4, -21, 5, -13],\n [0, -6, 7, -10, 3, -3, -2, 8, -19],\n [0, 0, -22, 8, 16, -4, -21, 24, 16],\n [0, 0, 0, -17, 17, -1, -1, 23, -5],\n [0, 0, 0, 0, 17, -3, 23, -22, 3],\n [0, 0, 0, 0, 0, 7, 15, 18, 10],\n [0, 0, 0, 0, 0, 0, 17, -17, -1],\n [0, 0, 0, 0, 0, 0, 0, 25, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4709", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -10, -14, -5, 19, -9, 14, -13, 6],\n [11, 24, -11, -14, 23, -11, 8, -20, -9],\n [22, 23, -6, -17, -21, -3, 7, 12, -12],\n [-9, -7, 7, -25, -13, 20, 1, -20, -20],\n [7, 4, 20, 9, -3, -16, 25, -7, 25],\n [2, -3, -22, -6, -7, 16, 1, 8, -22],\n [12, -19, 22, -19, 24, 0, 0, -7, -17],\n [-6, 16, 19, 24, -10, -9, -4, -13, -14],\n [-16, -25, 6, 4, -18, -5, -4, -8, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 7) of the inverse. Round your answer to the nearest integer:\n[[22, 9, -14, -5, -12, 3, 0, 6, 2],\n [9, 8, -14, -14, 4, 17, 6, -18, 6],\n [-14, -14, -8, 2, 15, -4, 14, 9, 0],\n [-5, -14, 2, 2, 6, 8, 0, 16, -12],\n [-12, 4, 15, 6, -17, 3, -6, -10, -6],\n [3, 17, -4, 8, 3, -19, 10, 4, -8],\n [0, 6, 14, 0, -6, 10, 6, -1, 19],\n [6, -18, 9, 16, -10, 4, -1, 6, 23],\n [2, 6, 0, -12, -6, -8, 19, 23, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, -3, -4, -22, 8, -20, 2, 5, 9],\n [13, 16, -3, -20, -10, -24, -2, -9, 19],\n [-25, -20, -21, 19, 24, 3, -14, 13, 21],\n [-23, 22, -25, 1, 22, -2, 18, -7, -18],\n [18, 21, -24, 4, 4, 23, 13, 19, 6],\n [-25, 12, -13, -15, -16, 22, 0, -6, -9],\n [-9, -22, -21, -3, 20, -16, 20, 2, 7],\n [17, 0, 24, 22, 3, 1, -8, 14, -16],\n [16, -21, -16, 24, -5, -2, 12, -23, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-73", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[5, 15, 11, -24, -24, 13, 23, 16, 18],\n [0, 16, -6, 7, -22, 19, 18, -15, 16],\n [0, 0, -1, 23, 11, 8, -17, -20, -8],\n [0, 0, 0, 14, -9, 9, 3, 16, -9],\n [0, 0, 0, 0, 10, -19, 20, -21, -2],\n [0, 0, 0, 0, 0, -23, 11, 0, -11],\n [0, 0, 0, 0, 0, 0, -25, -17, 5],\n [0, 0, 0, 0, 0, 0, 0, -21, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-497", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[1, -16, 0, -18, 6, -3, -8, 14, -2],\n [-16, 10, -8, 16, -16, -6, 19, -2, 12],\n [0, -8, -7, 17, 0, -2, -8, 16, 1],\n [-18, 16, 17, 6, 2, 8, 14, -2, 14],\n [6, -16, 0, 2, 18, 16, -7, -2, 14],\n [-3, -6, -2, 8, 16, -14, -19, -3, 5],\n [-8, 19, -8, 14, -7, -19, -6, -9, -8],\n [14, -2, 16, -2, -2, -3, -9, -6, -10],\n [-2, 12, 1, 14, 14, 5, -8, -10, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-387", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[21, -4, 12, 4, 6, -13, 14, 16, 14],\n [-4, -12, 2, 6, 4, -12, -2, 22, 10],\n [12, 2, 25, -2, -10, -4, 7, 12, 4],\n [4, 6, -2, 3, 6, -16, -3, -14, 7],\n [6, 4, -10, 6, -21, -16, -16, 20, 10],\n [-13, -12, -4, -16, -16, 11, 2, -6, -2],\n [14, -2, 7, -3, -16, 2, 3, 6, 16],\n [16, 22, 12, -14, 20, -6, 6, -12, -15],\n [14, 10, 4, 7, 10, -2, 16, -15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (4, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 1, 23, -22, -2, -3, 22, -7, 16],\n [0, 1, -23, 2, -9, 5, -16, 23, -4],\n [0, 0, -5, 10, -3, 12, -14, -1, -6],\n [0, 0, 0, -19, 3, 22, 3, -13, -23],\n [0, 0, 0, 0, -20, 19, -19, -21, -19],\n [0, 0, 0, 0, 0, -1, -5, -5, 2],\n [0, 0, 0, 0, 0, 0, 17, -15, -9],\n [0, 0, 0, 0, 0, 0, 0, 22, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-269", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[15, 1, 4, 1, -16, 11, -13, 18, 3],\n [1, -10, 3, -8, 9, 11, 7, 5, -8],\n [4, 3, 24, -3, -2, -8, 16, -14, -12],\n [1, -8, -3, 23, -14, -8, 1, 20, 0],\n [-16, 9, -2, -14, -4, 0, -10, 6, -7],\n [11, 11, -8, -8, 0, -19, 14, -2, 1],\n [-13, 7, 16, 1, -10, 14, -16, -18, -16],\n [18, 5, -14, 20, 6, -2, -18, -10, 8],\n [3, -8, -12, 0, -7, 1, -16, 8, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[23, 13, 12, -24, 17, 13, -5, 14, 11],\n [-8, 22, 20, -14, -9, 11, 20, 12, -11],\n [-19, -12, 24, -25, 12, -23, 11, 18, 5],\n [17, -13, 22, -8, -9, -9, -15, -6, -16],\n [3, 22, 8, -9, 16, -13, 18, 21, 13],\n [1, 0, 2, -13, -14, 18, 2, -24, 11],\n [8, -3, 19, 3, 9, -15, 22, 7, 25],\n [-15, -17, -12, -17, 13, 22, -23, 3, -7],\n [10, 6, -19, 2, 18, -8, -21, -3, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7567", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[19, -3, 20, 4, -5, -16, 17, -13, -14],\n [0, -22, 13, -2, 8, 13, 15, -21, -11],\n [0, 0, 25, 13, -18, 23, 19, -2, 2],\n [0, 0, 0, 8, -9, 11, 12, 0, -2],\n [0, 0, 0, 0, 25, 22, -13, 11, -23],\n [0, 0, 0, 0, 0, -4, -9, -22, 19],\n [0, 0, 0, 0, 0, 0, -15, 19, -3],\n [0, 0, 0, 0, 0, 0, 0, -7, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1163", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, -4, -13, -11, 12, 2, 12, -16, -2],\n [-4, -3, 4, -17, 2, 20, 20, -12, -2],\n [-13, 4, 21, 13, 16, -15, -10, -21, -8],\n [-11, -17, 13, -23, 8, -8, -2, 6, 4],\n [12, 2, 16, 8, 7, -2, -8, -6, -15],\n [2, 20, -15, -8, -2, -4, -6, -2, -24],\n [12, 20, -10, -2, -8, -6, 24, -9, -2],\n [-16, -12, -21, 6, -6, -2, -9, 0, -1],\n [-2, -2, -8, 4, -15, -24, -2, -1, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[9, -18, -1, -14, 6, 17, -14, -2, -10],\n [-18, 25, 10, 0, 11, 3, 20, -22, 4],\n [-1, 10, -19, 2, 8, -1, 9, -10, 6],\n [-14, 0, 2, -16, -8, 10, -14, 3, -14],\n [6, 11, 8, -8, 24, -2, -19, -10, 11],\n [17, 3, -1, 10, -2, 18, 4, 2, 10],\n [-14, 20, 9, -14, -19, 4, -21, -12, 12],\n [-2, -22, -10, 3, -10, 2, -12, 18, -3],\n [-10, 4, 6, -14, 11, 10, 12, -3, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 12, -22, -14, 18, 5, -1, -10, 16],\n [-12, -13, 15, -19, -14, 11, 24, -22, -24],\n [9, 18, -23, -22, 12, -14, -7, -16, -25],\n [-9, -10, -17, -17, -17, -14, 15, -11, -24],\n [-15, -15, -18, 6, -20, -6, 13, 9, -18],\n [24, 23, 17, 8, -7, -19, 5, -8, 14],\n [-12, 13, 10, -9, 11, 18, -17, -6, 19],\n [2, 24, -6, 15, 10, 1, -18, 6, -25],\n [-9, -17, -6, 19, 6, -24, 6, 19, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-230", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, -6, 12, -25, -21, 9, 10, -25, -12],\n [-17, 4, -2, -22, 24, -12, -1, -22, -1],\n [-16, 9, -19, 16, -13, -22, 24, 17, 10],\n [-12, -8, -18, 6, 1, 16, 11, -3, -19],\n [-14, -1, -23, 0, -22, 16, 10, -11, 6],\n [3, -16, -5, -10, 21, -7, 3, 25, -8],\n [18, -10, -25, 22, -24, -11, 13, 2, -25],\n [-21, 16, -4, 10, 20, -13, -25, -10, 15],\n [-4, 6, -10, 25, -11, 20, 16, -14, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, 0, 4, 18, 8, -16, -13, -7, -6],\n [0, -19, 20, 18, 3, 4, 4, -12, -16],\n [4, 20, -20, 11, 6, 3, 12, -10, 0],\n [18, 18, 11, -12, 2, -8, 12, -4, -6],\n [8, 3, 6, 2, -7, -2, 1, 4, -16],\n [-16, 4, 3, -8, -2, 7, -12, -1, -3],\n [-13, 4, 12, 12, 1, -12, 22, 6, 8],\n [-7, -12, -10, -4, 4, -1, 6, 22, -14],\n [-6, -16, 0, -6, -16, -3, 8, -14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-17, 12, -4, 16, 0, 12, -10, 22, -9],\n [12, -14, -2, 2, -8, 6, -4, 12, -7],\n [-4, -2, 12, -14, -3, 4, -2, -12, -13],\n [16, 2, -14, 24, 16, 8, -6, -7, 16],\n [0, -8, -3, 16, -10, 10, 6, 4, -12],\n [12, 6, 4, 8, 10, 7, 3, 8, 8],\n [-10, -4, -2, -6, 6, 3, 19, -2, -6],\n [22, 12, -12, -7, 4, 8, -2, -2, 4],\n [-9, -7, -13, 16, -12, 8, -6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[0, 4, 0, 6, -8, 6, 8, 7, -12],\n [4, -3, -2, -4, 3, 12, -8, 18, -4],\n [0, -2, -24, 9, 14, 0, -2, 14, 6],\n [6, -4, 9, -21, 18, -11, 3, 10, -13],\n [-8, 3, 14, 18, -19, -14, 8, 0, 16],\n [6, 12, 0, -11, -14, -2, 0, 14, 6],\n [8, -8, -2, 3, 8, 0, 21, 20, 18],\n [7, 18, 14, 10, 0, 14, 20, 3, -4],\n [-12, -4, 6, -13, 16, 6, 18, -4, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[10, 24, 11, 22, -12, 1, -7, 5, 20],\n [-17, 12, -9, -7, 18, -22, 22, -15, -4],\n [-22, -9, -18, 20, 8, -15, 5, -15, 12],\n [-5, 20, 4, -16, 0, 1, -18, 13, -18],\n [-18, 8, -10, 15, -13, -3, -14, 1, -4],\n [6, 23, 1, -24, 19, 7, 0, 2, -7],\n [17, -21, 7, -6, 4, 19, -18, 12, -9],\n [18, -25, -23, 20, 0, 5, -18, 17, 20],\n [-18, 9, 13, 2, 25, -22, -10, -13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, -21, 11, -6, -2, 10, 8, 19, 22],\n [0, -7, -9, -21, -1, -8, 24, -18, 1],\n [0, 0, -13, -10, -4, -6, -13, -6, -24],\n [0, 0, 0, 19, 11, -20, -12, -22, -4],\n [0, 0, 0, 0, 1, -19, -23, 21, 7],\n [0, 0, 0, 0, 0, -2, -11, 5, -12],\n [0, 0, 0, 0, 0, 0, 25, -9, -10],\n [0, 0, 0, 0, 0, 0, 0, 7, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4166", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-13, -3, -6, -4, 21, -3, 15, 9, -23],\n [0, 7, 20, -9, 19, -7, 4, -3, -11],\n [0, 0, 13, 23, -8, -20, 6, -5, 14],\n [0, 0, 0, 7, -10, 13, -4, 17, 21],\n [0, 0, 0, 0, 15, 2, -19, -8, 15],\n [0, 0, 0, 0, 0, 4, -2, -6, 20],\n [0, 0, 0, 0, 0, 0, -21, 18, -13],\n [0, 0, 0, 0, 0, 0, 0, -22, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3557", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -10, 9, -9, -17, 9, 3, 13, -8],\n [-14, -7, 22, -4, 23, -11, -25, -24, -18],\n [-4, -1, -24, 25, -17, -17, -13, -20, 4],\n [-11, 25, -11, 24, -19, -15, 14, 12, 14],\n [-24, 25, 22, 13, -16, 18, -9, -19, 14],\n [13, -22, 9, 25, 21, 10, 5, -1, 15],\n [-13, -8, -5, 22, -25, 10, 24, -18, 22],\n [-5, 17, -5, 1, -7, -3, 25, 24, 25],\n [17, 9, 14, 25, 16, 22, -21, 15, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1236", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, -10, 13, 21, -2, -5, -3, 23, 12],\n [21, -18, -19, -24, 4, -13, -3, 3, 12],\n [11, -6, 7, 3, 24, -11, -3, 16, -23],\n [11, 3, 19, -18, -4, 3, -24, 15, 23],\n [24, 19, -25, 18, -6, -5, 11, -18, 1],\n [21, 9, -20, 19, 18, -7, -8, -25, -1],\n [1, -19, 18, 16, 3, 5, 18, 17, 10],\n [-7, -20, -1, 5, -17, -6, -16, 11, 1],\n [-13, 15, -24, 24, -5, 7, -2, 18, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -4, -15, 2, -2, 10, -9, 2, -14],\n [-4, -13, -5, 3, 15, 6, -10, -20, -16],\n [-15, -5, 18, 2, 16, 0, -13, 6, 4],\n [2, 3, 2, -21, -13, 1, -1, 6, -8],\n [-2, 15, 16, -13, -25, 4, 4, -10, -6],\n [10, 6, 0, 1, 4, -1, -6, -10, -22],\n [-9, -10, -13, -1, 4, -6, -20, -6, -4],\n [2, -20, 6, 6, -10, -10, -6, -4, -4],\n [-14, -16, 4, -8, -6, -22, -4, -4, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-12, 0, -5, 6, 4, 13, -8, 4, 20],\n [0, -8, -4, 6, -5, 20, 14, 2, -2],\n [-5, -4, -18, 20, 0, 9, -4, 10, -18],\n [6, 6, 20, 12, 8, 0, 6, -18, 0],\n [4, -5, 0, 8, -13, 11, 4, -12, -10],\n [13, 20, 9, 0, 11, -12, -2, -16, 4],\n [-8, 14, -4, 6, 4, -2, 4, -1, 11],\n [4, 2, 10, -18, -12, -16, -1, 5, -12],\n [20, -2, -18, 0, -10, 4, 11, -12, -23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1544", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 3) of the inverse of matrix 1/450 * A where A =\n[[-21, 12, 0, 14, 12, 12, -22, -19, 4],\n [4, -7, 13, 9, 14, 7, 7, -12, 12],\n [-16, 2, -12, 10, 12, -10, -5, 2, 7],\n [-20, 15, -11, 18, -23, 17, 21, 9, -12],\n [-24, 3, -22, 0, 25, -14, -24, -9, 9],\n [-16, 22, -4, 15, 17, -5, -11, 9, 22],\n [-5, -5, -5, 18, 6, -21, 13, -17, -8],\n [-5, -18, 18, 8, -16, 25, 15, -2, 14],\n [-2, 6, 7, 12, 18, 25, 23, 8, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-53", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[5, -8, -3, -4, 17, -8, 14, 21, 15],\n [21, 13, -6, -13, 19, -25, -22, -2, 10],\n [10, 19, -24, 2, 0, -3, -11, 10, 1],\n [-20, 9, 13, 12, 9, 10, -16, 4, 15],\n [12, 3, 17, 13, 24, -22, -21, -22, 10],\n [19, -10, -1, -12, -15, 3, 8, -4, -12],\n [-2, 13, 0, 17, 10, 13, -10, 12, 6],\n [-20, 8, -18, 4, 1, -19, 1, -1, 20],\n [15, -11, -1, -4, -8, -14, -3, 25, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[13, 6, -17, -2, -12, 6, 18, -1, 13],\n [6, 15, 16, -4, -6, 14, -12, -6, -20],\n [-17, 16, 14, -18, 7, -4, 4, 4, 3],\n [-2, -4, -18, 24, 11, 12, -8, 7, 8],\n [-12, -6, 7, 11, 22, 8, 12, 16, -11],\n [6, 14, -4, 12, 8, 17, 4, 18, 4],\n [18, -12, 4, -8, 12, 4, 23, -5, -14],\n [-1, -6, 4, 7, 16, 18, -5, 14, -2],\n [13, -20, 3, 8, -11, 4, -14, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2283", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[15, 20, -10, -1, 0, 23, 19, -17, -11],\n [0, 7, -25, -21, -17, 18, -20, 2, 19],\n [0, 0, 14, -11, -20, 1, 12, -22, -15],\n [0, 0, 0, 9, -23, -14, 1, 4, -5],\n [0, 0, 0, 0, -11, -8, 3, 22, 12],\n [0, 0, 0, 0, 0, 11, 12, -14, -15],\n [0, 0, 0, 0, 0, 0, -5, -3, -17],\n [0, 0, 0, 0, 0, 0, 0, 13, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13541", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-6, 14, 9, 5, 5, 12, -4, 19, 15],\n [0, -17, -11, -13, -4, -10, 6, -24, 0],\n [0, 0, 8, -18, 10, -5, 20, 17, 2],\n [0, 0, 0, -20, -6, 5, 7, 18, -19],\n [0, 0, 0, 0, 19, 11, 16, 18, -9],\n [0, 0, 0, 0, 0, -20, -22, 25, 11],\n [0, 0, 0, 0, 0, 0, 4, 10, -24],\n [0, 0, 0, 0, 0, 0, 0, -13, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[3, 21, -7, 1, -17, 11, 11, 17, 2],\n [0, 2, 10, -8, -1, 9, -22, -12, 13],\n [0, 0, -2, -10, -6, -11, -19, -9, -4],\n [0, 0, 0, 20, 21, -11, 11, -10, -21],\n [0, 0, 0, 0, 5, 15, 10, 21, 17],\n [0, 0, 0, 0, 0, -10, 2, -4, -8],\n [0, 0, 0, 0, 0, 0, -21, 8, 13],\n [0, 0, 0, 0, 0, 0, 0, -2, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213789", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[1, -17, -19, 22, -16, -17, -4, -3, -19],\n [0, -17, 1, -2, 3, -9, -6, -19, 17],\n [0, 0, 2, -7, -6, 18, 13, 14, -19],\n [0, 0, 0, -13, 13, 14, -4, 23, -9],\n [0, 0, 0, 0, 23, 19, -8, -2, 16],\n [0, 0, 0, 0, 0, 13, -14, 6, 2],\n [0, 0, 0, 0, 0, 0, 24, -23, -25],\n [0, 0, 0, 0, 0, 0, 0, 8, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16364", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (6, 1) rounded to the nearest integer?\n[[24, 24, -1, 0, -12, -12, -12, -1, 10],\n [-22, 21, -11, 6, -8, -12, -25, 16, -6],\n [-16, -16, -2, 8, 2, 1, 14, -25, 7],\n [-22, -19, -17, -10, -21, 8, -3, 17, 24],\n [-1, 25, -13, -2, -15, 25, -9, 11, -13],\n [1, -6, 7, 16, 6, -18, 3, 14, -7],\n [-20, 18, 13, 22, 15, -5, -4, 16, -16],\n [-16, 3, -10, -25, -9, 4, 0, 20, -7],\n [-5, -9, 20, 14, -5, 15, 14, 19, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, 2, -10, -8, 16, -3, -2, -8, -8],\n [2, -21, 0, 4, -16, -3, 2, 14, -18],\n [-10, 0, -10, -14, -10, -4, -2, 3, 2],\n [-8, 4, -14, -17, -10, 0, 2, 10, 12],\n [16, -16, -10, -10, -16, -14, 12, 0, -6],\n [-3, -3, -4, 0, -14, 13, 2, -16, 10],\n [-2, 2, -2, 2, 12, 2, -16, 16, 12],\n [-8, 14, 3, 10, 0, -16, 16, -23, -14],\n [-8, -18, 2, 12, -6, 10, 12, -14, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-107", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 0, -8, -2, -15, 8, 20, -6, -6],\n [0, 25, -4, 2, -18, 8, 12, -2, -6],\n [-8, -4, 19, 20, 4, -14, -18, 4, -9],\n [-2, 2, 20, 20, -10, -4, 2, 0, -12],\n [-15, -18, 4, -10, -18, 2, 1, -11, 7],\n [8, 8, -14, -4, 2, -6, -2, -17, -14],\n [20, 12, -18, 2, 1, -2, 24, -3, -13],\n [-6, -2, 4, 0, -11, -17, -3, 23, 2],\n [-6, -6, -9, -12, 7, -14, -13, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-16, 13, -6, 22, 0, 12, 14, 2, 2],\n [13, -8, -16, 8, 0, -3, -4, -10, -5],\n [-6, -16, -7, 6, 22, 6, -14, -17, -18],\n [22, 8, 6, 3, 1, 18, -8, 3, -8],\n [0, 0, 22, 1, -22, 2, -22, -18, 3],\n [12, -3, 6, 18, 2, 22, 6, -7, 2],\n [14, -4, -14, -8, -22, 6, -2, 2, -2],\n [2, -10, -17, 3, -18, -7, 2, 18, -2],\n [2, -5, -18, -8, 3, 2, -2, -2, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2471", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (8, 8) rounded to the nearest integer?\n[[25, 18, 18, -8, -16, -19, 24, 18, -12],\n [0, -10, -24, 4, 4, -8, 5, 18, 22],\n [0, 0, 23, 24, 9, -3, 16, 7, 12],\n [0, 0, 0, -6, -23, -18, 14, 6, 3],\n [0, 0, 0, 0, 2, 22, 16, 10, 6],\n [0, 0, 0, 0, 0, -3, 24, -15, 23],\n [0, 0, 0, 0, 0, 0, 17, -15, 5],\n [0, 0, 0, 0, 0, 0, 0, -15, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (5, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -13, 25, -21, -6, -24, -15, 4, 6],\n [0, 24, 12, 2, -16, -4, -9, -4, 17],\n [0, 0, -2, 10, 6, 20, 10, 2, -12],\n [0, 0, 0, -5, -14, 4, 5, 14, -22],\n [0, 0, 0, 0, -20, -21, 25, 1, -18],\n [0, 0, 0, 0, 0, 6, -18, 21, 25],\n [0, 0, 0, 0, 0, 0, 2, -9, 16],\n [0, 0, 0, 0, 0, 0, 0, -23, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-79", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-16, -5, 3, 6, -16, -13, 21, -3, 24],\n [-3, 5, -22, 23, -23, -5, -24, -22, -25],\n [-11, 7, -20, -19, -7, 18, -25, 13, -7],\n [19, 0, 18, -14, -4, -13, 2, -12, -4],\n [4, 18, -6, 18, 1, 12, 16, 15, 8],\n [13, 15, 18, 11, -25, -11, 6, -18, 7],\n [-8, 19, 3, 6, 7, -21, -8, 22, -16],\n [10, 7, -3, 14, -21, 8, -2, -9, 5],\n [-19, -9, 2, 12, -4, -11, 11, -11, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[24, -1, -5, 12, -24, 1, 23, 6, -5],\n [-22, 18, -7, -24, 0, 8, -12, -11, -6],\n [8, 10, -7, -17, -19, 4, -13, 1, 18],\n [9, -13, -11, 20, -17, 19, -3, 10, 14],\n [-23, 8, -7, 2, -3, 14, 23, 19, -19],\n [15, -14, -12, 20, -11, -23, -11, 25, -2],\n [20, -18, -21, 25, -22, -12, -10, -6, -2],\n [-20, 5, -20, 9, -11, 3, -23, -15, -23],\n [2, -16, 24, 7, 22, -10, -16, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-88", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-23, -8, 6, -4, -9, -2, 16, 0, -16],\n [-8, 19, 3, 3, -14, 12, 2, 21, -10],\n [6, 3, 17, -6, -8, -1, 6, 3, -16],\n [-4, 3, -6, -15, -9, 10, -12, 0, -2],\n [-9, -14, -8, -9, 0, -3, -6, 10, 2],\n [-2, 12, -1, 10, -3, 11, -6, 8, 14],\n [16, 2, 6, -12, -6, -6, 15, 8, -16],\n [0, 21, 3, 0, 10, 8, 8, 6, 6],\n [-16, -10, -16, -2, 2, 14, -16, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[22, 4, -18, 5, 9, -20, 14, -7, 10],\n [4, -4, -7, -13, -12, 22, 16, -12, -16],\n [-18, -7, -14, 2, 9, 19, 0, -8, -7],\n [5, -13, 2, -12, -12, -8, -19, 7, 6],\n [9, -12, 9, -12, -7, 16, 23, -10, 0],\n [-20, 22, 19, -8, 16, -18, -14, -1, -9],\n [14, 16, 0, -19, 23, -14, 21, -8, -8],\n [-7, -12, -8, 7, -10, -1, -8, 20, -18],\n [10, -16, -7, 6, 0, -9, -8, -18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "736", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-8, 8, -3, 19, 1, 23, -9, 22, -5],\n [24, 14, 5, -23, -9, 24, 0, -3, -20],\n [2, -18, 19, -18, -7, 12, 3, -3, 21],\n [6, -16, 1, 23, -25, 13, 3, 19, -23],\n [25, 21, 11, 5, -15, -4, -8, 9, -20],\n [-23, -21, -17, 2, -7, 2, 1, -13, 12],\n [17, -5, 1, 20, -20, 12, 23, -15, 21],\n [15, -9, 13, -19, 4, -5, -25, -1, 6],\n [-18, -21, 4, 25, -18, 23, -7, 18, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-91", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-11, 12, 14, 10, -10, 2, -7, 24, 0],\n [12, 21, -12, -8, 21, -14, -1, -6, 8],\n [14, -12, 2, 8, -15, 10, -1, 9, 16],\n [10, -8, 8, 12, 5, -4, -6, 6, -12],\n [-10, 21, -15, 5, 25, 6, 0, -4, 10],\n [2, -14, 10, -4, 6, -17, 16, 2, 13],\n [-7, -1, -1, -6, 0, 16, -24, -2, 7],\n [24, -6, 9, 6, -4, 2, -2, 2, 17],\n [0, 8, 16, -12, 10, 13, 7, 17, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 14, 15, -8, 9, 23, -11, 1, -9],\n [0, -24, 23, 24, 5, 11, 15, 15, 8],\n [0, 0, -23, -9, -12, -12, 20, 12, 9],\n [0, 0, 0, -22, 7, -9, 2, 24, 0],\n [0, 0, 0, 0, 1, -10, -16, 14, -14],\n [0, 0, 0, 0, 0, 25, -25, 1, -23],\n [0, 0, 0, 0, 0, 0, 23, -22, -11],\n [0, 0, 0, 0, 0, 0, 0, 13, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3435", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, 9, 21, 12, 7, -12, 22, -25, 23],\n [0, -18, 24, -10, 12, -16, 16, 11, 0],\n [2, -14, -6, 23, -12, 20, 9, 3, -14],\n [-8, 18, -24, -24, -9, -16, -8, -4, -7],\n [-25, -2, 10, -1, 10, 5, 5, -24, -7],\n [-14, -16, 5, 19, -4, -3, -3, -11, 0],\n [-23, -3, -6, 19, 14, 13, -18, -8, 15],\n [-20, 1, 10, -11, 11, -21, 13, -17, -19],\n [15, -6, -16, 0, -22, 12, -2, -12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "775", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 8) rounded to the nearest integer?\n[[-25, -12, -2, 6, 12, -21, -14, 14, -2],\n [-12, -5, -10, -7, -6, -12, 5, 17, -8],\n [-2, -10, 14, 13, -6, -12, 14, 0, 0],\n [6, -7, 13, -8, 12, -2, -11, -16, 10],\n [12, -6, -6, 12, -4, 1, -18, 1, 8],\n [-21, -12, -12, -2, 1, 19, -6, 0, -12],\n [-14, 5, 14, -11, -18, -6, -3, 0, -6],\n [14, 17, 0, -16, 1, 0, 0, 18, -4],\n [-2, -8, 0, 10, 8, -12, -6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[5, -16, 0, -14, -11, 2, -22, 14, -6],\n [-16, 2, 14, -3, -5, 1, 21, 3, 0],\n [0, 14, -13, -16, -4, 7, 10, 1, -2],\n [-14, -3, -16, 9, 2, 13, -14, 0, 16],\n [-11, -5, -4, 2, 24, 1, 16, 17, -18],\n [2, 1, 7, 13, 1, -8, 4, -14, 2],\n [-22, 21, 10, -14, 16, 4, -4, -9, 12],\n [14, 3, 1, 0, 17, -14, -9, 12, 18],\n [-6, 0, -2, 16, -18, 2, 12, 18, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-848", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[10, -6, 6, 4, 2, -1, -2, 22, -11],\n [-6, 14, -2, 6, 3, 0, 6, 6, 0],\n [6, -2, -18, 16, 14, -7, 4, 16, -22],\n [4, 6, 16, -6, -8, -1, -6, -4, -8],\n [2, 3, 14, -8, -25, 24, 5, -4, -2],\n [-1, 0, -7, -1, 24, 13, 18, -6, 4],\n [-2, 6, 4, -6, 5, 18, -6, -19, 14],\n [22, 6, 16, -4, -4, -6, -19, -22, 6],\n [-11, 0, -22, -8, -2, 4, 14, 6, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "677", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[5, -19, -9, -7, 13, -23, 4, 9, 3],\n [0, -12, 9, 2, 4, 0, -19, 13, 5],\n [0, 0, 24, 21, -12, 10, 1, -2, 14],\n [0, 0, 0, -18, -11, 23, -21, -22, -15],\n [0, 0, 0, 0, -11, -20, -10, 21, 14],\n [0, 0, 0, 0, 0, 10, 1, -17, -21],\n [0, 0, 0, 0, 0, 0, 9, -20, 2],\n [0, 0, 0, 0, 0, 0, 0, -2, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16126", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 8) of the inverse of matrix 1/450 * A where A =\n[[-2, 5, 13, 20, -13, -16, -3, -8, 6],\n [0, 10, 2, -10, -10, -8, -18, 16, -10],\n [0, 0, -25, -14, 12, 2, 19, -9, -25],\n [0, 0, 0, 17, 20, -2, -16, 21, 13],\n [0, 0, 0, 0, 24, -16, -7, 20, 19],\n [0, 0, 0, 0, 0, 24, 3, 5, -9],\n [0, 0, 0, 0, 0, 0, -5, 15, 20],\n [0, 0, 0, 0, 0, 0, 0, -23, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (6, 6) rounded to the nearest integer?\n[[-12, -2, -12, 3, 4, -10, -16, -2, 6],\n [-2, -17, -6, -3, -4, 0, -2, 10, -2],\n [-12, -6, 13, 6, 8, -2, -2, 16, -14],\n [3, -3, 6, -17, -1, 5, 6, -5, -4],\n [4, -4, 8, -1, 4, -8, 13, -2, 12],\n [-10, 0, -2, 5, -8, 4, 9, -3, -22],\n [-16, -2, -2, 6, 13, 9, 9, -16, -2],\n [-2, 10, 16, -5, -2, -3, -16, 8, -6],\n [6, -2, -14, -4, 12, -22, -2, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[1, 0, 2, -4, -6, -6, -16, 10, 15],\n [0, -5, -3, 3, 0, -13, -22, -7, -14],\n [2, -3, -13, -4, 8, 3, -3, 1, -8],\n [-4, 3, -4, -5, -13, -18, 10, 11, 6],\n [-6, 0, 8, -13, 18, 4, 12, -16, -4],\n [-6, -13, 3, -18, 4, -8, 20, -14, -2],\n [-16, -22, -3, 10, 12, 20, 17, 13, -5],\n [10, -7, 1, 11, -16, -14, 13, -11, 6],\n [15, -14, -8, 6, -4, -2, -5, 6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 21, -16, -21, 22, 0, -4, 18, -3],\n [-13, -17, 23, -6, 2, 18, 11, -2, 18],\n [7, -6, 22, 4, 18, -17, 19, 23, -9],\n [10, -12, -7, -19, -23, 7, 18, 6, 21],\n [-15, 16, -24, 0, -22, -9, -9, 2, 4],\n [14, -3, 20, -2, 3, -22, 12, 3, -7],\n [1, 3, 10, 9, -20, -3, 13, 20, 18],\n [22, -18, -24, -13, 14, -5, 5, 22, 10],\n [22, 12, 1, 10, 22, -3, -5, -13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, 2, -2, -18, 22, 17, -1, 10, -4],\n [2, -8, -2, -12, 7, -5, -1, 5, 2],\n [-2, -2, -21, -10, 4, 6, -16, -2, 7],\n [-18, -12, -10, -9, 10, -11, -6, 12, 4],\n [22, 7, 4, 10, -20, -2, -22, -8, 6],\n [17, -5, 6, -11, -2, -13, -2, 6, -18],\n [-1, -1, -16, -6, -22, -2, -24, 2, 5],\n [10, 5, -2, 12, -8, 6, 2, 3, 10],\n [-4, 2, 7, 4, 6, -18, 5, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[18, -1, -3, 18, -25, 7, -11, -9, 8],\n [-9, 15, 18, -22, -13, -22, -19, 20, -17],\n [-3, 7, 7, -6, -22, -25, 16, 8, 1],\n [-5, -2, -11, 9, -1, -17, -9, -5, -13],\n [-23, -22, -22, 17, 2, -19, 0, -15, -2],\n [17, -16, 11, -13, 18, 16, 13, -7, 25],\n [-7, -14, -4, 21, 11, 4, 20, -14, 3],\n [-5, -15, 11, 22, -8, 18, 1, 11, 22],\n [-14, -3, 8, 12, -3, -1, -22, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "814", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 5) of the inverse. Round your answer to the nearest integer:\n[[-13, 8, 16, -13, 4, 1, 2, -15, -4],\n [8, -9, 3, 2, 0, -2, -12, 8, 1],\n [16, 3, 16, 10, 10, -4, 3, -1, 10],\n [-13, 2, 10, 7, -5, -5, 8, 16, 6],\n [4, 0, 10, -5, -8, 0, -9, 11, -17],\n [1, -2, -4, -5, 0, -21, -2, 10, 6],\n [2, -12, 3, 8, -9, -2, 1, 10, 3],\n [-15, 8, -1, 16, 11, 10, 10, -2, 0],\n [-4, 1, 10, 6, -17, 6, 3, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, -9, 18, -24, -20, -17, -21, -6, 3],\n [-5, -17, 2, -18, 5, -6, 1, -18, -5],\n [2, -3, -20, -23, -21, -17, -19, -22, 13],\n [-21, -15, -11, 8, -13, 22, -19, 14, -20],\n [13, 24, 4, -4, -1, 2, -6, 13, -23],\n [-21, -25, -11, 0, -23, 14, 15, 21, 16],\n [8, -21, 5, 25, -13, 17, -25, -4, -11],\n [0, -8, 22, -17, -25, 17, -17, -3, 17],\n [19, -24, -12, 12, 14, -8, -10, 3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-15, -22, -11, -8, -18, -5, 12, -10, -6],\n [-22, 24, 8, -8, -12, -2, 2, -16, 14],\n [-11, 8, 22, -9, 19, 0, -8, 6, -4],\n [-8, -8, -9, 8, 6, 2, 8, -4, -3],\n [-18, -12, 19, 6, 17, -6, -4, 16, -16],\n [-5, -2, 0, 2, -6, 13, -8, -17, 16],\n [12, 2, -8, 8, -4, -8, 12, 10, -10],\n [-10, -16, 6, -4, 16, -17, 10, 25, 15],\n [-6, 14, -4, -3, -16, 16, -10, 15, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "998", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (3, 5) of the inverse. Round your answer to the nearest integer:\n[[-8, 19, -4, 25, 13, 25, -17, 9, -3],\n [-14, -2, 24, 14, -17, -13, 14, 16, -9],\n [-19, -9, 24, -2, -24, 9, 2, -7, 7],\n [-5, -16, 20, 19, -17, 12, -20, 25, 16],\n [9, -8, -7, -21, -1, -15, -16, -9, 10],\n [0, 5, 6, -5, -8, -8, -25, -12, -18],\n [-24, 25, -11, 8, 10, -25, 25, -5, 16],\n [-25, 6, -6, 21, 10, 13, 4, -19, -4],\n [24, 19, -16, -18, 1, -16, -12, 20, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (5, 3) rounded to the nearest integer?\n[[-20, -5, 7, -7, 13, -2, -8, 9, 17],\n [11, -7, -2, 8, -4, -22, -16, -24, -18],\n [7, 12, 17, 2, -16, 19, -25, 8, -23],\n [-17, -21, 16, -16, -14, -8, -5, -5, -25],\n [-23, -21, -1, 23, -18, -9, -17, 6, -20],\n [23, 14, -5, -19, -19, 21, 13, 1, -18],\n [-17, 2, -11, -24, -19, 21, -8, -4, 24],\n [-16, 24, 7, -19, -23, -12, 18, 20, 10],\n [-13, -10, -10, -21, -1, 12, 12, 24, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[13, 22, 15, 0, -13, 18, 25, 0, -25],\n [-18, -22, -5, -4, 25, 11, 23, -23, -7],\n [-25, 3, -3, 7, 15, -3, -21, -19, -20],\n [23, -4, 23, -13, -14, -22, -18, 11, 5],\n [11, 19, 0, 17, -18, 14, 7, 19, 3],\n [-21, 2, 14, -9, -3, 19, -17, -24, 6],\n [25, 23, 5, -19, 4, -23, 25, 25, -17],\n [-16, 20, 24, 21, 0, -25, 4, 12, -11],\n [-1, -20, -8, -25, -23, -9, 22, -18, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1576", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[14, -5, -10, 15, -18, 12, -5, 8, -4],\n [-5, 3, -2, -22, -18, 8, 0, 6, -14],\n [-10, -2, -16, -8, -8, -3, -14, -17, 2],\n [15, -22, -8, -20, -6, 16, -8, 24, 16],\n [-18, -18, -8, -6, -5, -2, 4, -6, -6],\n [12, 8, -3, 16, -2, -3, 2, -2, -13],\n [-5, 0, -14, -8, 4, 2, -25, -14, -4],\n [8, 6, -17, 24, -6, -2, -14, 0, -10],\n [-4, -14, 2, 16, -6, -13, -4, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-17, -6, 10, 6, 13, -15, -8, -4, -7],\n [-6, 13, 18, -10, 3, -2, 12, 0, 2],\n [10, 18, -16, -1, 10, 11, -10, -2, -14],\n [6, -10, -1, 25, -9, -18, 4, -16, -2],\n [13, 3, 10, -9, 21, -4, 4, 0, 4],\n [-15, -2, 11, -18, -4, -18, -8, 8, -18],\n [-8, 12, -10, 4, 4, -8, -21, -20, -12],\n [-4, 0, -2, -16, 0, 8, -20, 5, 0],\n [-7, 2, -14, -2, 4, -18, -12, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1353", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-3, -14, -5, 2, 0, 2, -12, 16, -2],\n [-14, 25, 0, -12, 14, 12, -2, -3, 5],\n [-5, 0, -21, 4, 0, -22, -2, 10, 4],\n [2, -12, 4, 15, -16, -8, 16, -18, 8],\n [0, 14, 0, -16, 5, -10, -4, 10, -7],\n [2, 12, -22, -8, -10, -15, 11, -6, 0],\n [-12, -2, -2, 16, -4, 11, 15, -4, 7],\n [16, -3, 10, -18, 10, -6, -4, 23, 6],\n [-2, 5, 4, 8, -7, 0, 7, 6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, 8, 16, -11, -20, -24, -2, 23, 2],\n [-25, -25, 2, 10, -6, 22, -18, -25, 0],\n [25, 17, 23, -1, -16, -14, 15, -19, -14],\n [21, 14, -9, -21, -12, 8, 22, -9, 9],\n [-25, 24, 24, 10, -11, -7, 25, 16, -21],\n [-7, 17, 13, -21, -14, -7, 21, -14, 10],\n [-14, -8, 23, 25, 22, 17, 8, 22, 7],\n [23, -8, 3, 19, -21, -1, -2, 3, 12],\n [7, -16, 11, 7, -3, -15, -2, -2, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[24, -5, -6, -16, -1, 21, 10, 22, 21],\n [-11, 18, 14, 14, 24, -20, 11, -24, -14],\n [-22, -3, -13, -9, 5, -10, 15, 0, 2],\n [-25, 21, -14, 11, 24, -6, -24, 10, -11],\n [12, -4, 18, 24, 6, -6, 10, 7, -11],\n [24, 20, -23, 3, 21, 1, -21, 5, -4],\n [9, -19, -20, 0, -25, -7, -19, 10, -14],\n [-6, -3, -1, 4, 3, 5, -8, 15, -7],\n [-22, -25, 15, -11, -18, -11, -11, 24, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, -8, -10, -24, 10, -6, -10, -23, 4],\n [0, 9, 0, -21, -24, 25, -6, 8, 8],\n [0, 0, -1, -6, -1, -12, 21, 18, 17],\n [0, 0, 0, 22, -21, -24, -10, 4, 21],\n [0, 0, 0, 0, 16, -2, 25, 4, 11],\n [0, 0, 0, 0, 0, 24, -5, -22, 7],\n [0, 0, 0, 0, 0, 0, 19, -8, 18],\n [0, 0, 0, 0, 0, 0, 0, -21, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-419", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[14, 19, -11, -6, -6, 19, -21, 6, -20],\n [4, 0, 11, -13, 3, -21, -1, -13, -2],\n [5, -6, -18, -17, -5, 25, -6, -11, 0],\n [16, -15, 11, 15, -15, 1, 4, -7, 8],\n [12, -3, -25, -23, -23, 2, -12, 4, -21],\n [23, -11, 12, -12, -12, 23, -18, -18, -7],\n [6, 5, 3, 15, -15, 19, -13, 1, -7],\n [0, 25, 11, 22, -17, 2, 6, -23, 25],\n [6, -21, -18, -12, -23, -2, -13, 17, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-184", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 9) rounded to the nearest integer?\n[[-18, 25, 16, 5, 0, -8, -8, -19, 22],\n [0, 22, -10, 7, 25, -23, 12, -22, 10],\n [0, 0, -17, 14, 25, -9, -9, 7, -6],\n [0, 0, 0, 17, -23, -2, 4, -18, -4],\n [0, 0, 0, 0, 14, -25, -5, 13, -2],\n [0, 0, 0, 0, 0, 9, 10, 16, 10],\n [0, 0, 0, 0, 0, 0, 12, -7, -18],\n [0, 0, 0, 0, 0, 0, 0, 18, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-73", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-17, 2, 17, -10, -8, -1, 8, -16, 10],\n [2, -5, 2, 4, 4, 5, -3, -6, 4],\n [17, 2, 5, 6, 6, -4, 22, 9, 20],\n [-10, 4, 6, 8, 10, -8, 1, -4, -14],\n [-8, 4, 6, 10, -6, -4, 6, 22, 10],\n [-1, 5, -4, -8, -4, 11, -1, -16, 6],\n [8, -3, 22, 1, 6, -1, 9, 0, -8],\n [-16, -6, 9, -4, 22, -16, 0, -4, 4],\n [10, 4, 20, -14, 10, 6, -8, 4, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[12, -17, 8, 10, -17, -11, 19, -6, -18],\n [0, 25, -7, -10, -15, 16, -18, 7, -16],\n [0, 0, 17, 24, -23, 14, 1, 2, 20],\n [0, 0, 0, -19, -16, -11, 5, 3, 16],\n [0, 0, 0, 0, 18, -11, 0, -14, -1],\n [0, 0, 0, 0, 0, 15, 5, -23, -23],\n [0, 0, 0, 0, 0, 0, -15, -2, 9],\n [0, 0, 0, 0, 0, 0, 0, 25, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-175", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, 7, -13, 25, -25, -13, 17, 1, -19],\n [0, -1, 7, 14, -9, 19, -12, 11, -3],\n [0, 0, 12, 1, 12, 14, 19, 24, -3],\n [0, 0, 0, 11, -23, 10, -21, 20, -11],\n [0, 0, 0, 0, -3, 22, -9, 20, -6],\n [0, 0, 0, 0, 0, -4, 24, -20, -22],\n [0, 0, 0, 0, 0, 0, 18, -23, 2],\n [0, 0, 0, 0, 0, 0, 0, -11, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-166", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[5, -8, -14, 22, 4, 7, 21, -19, 2],\n [0, -23, 17, -20, 5, 12, -11, -19, 17],\n [0, 0, -9, -8, -4, 0, 25, 1, 14],\n [0, 0, 0, 3, 17, -5, -23, 5, 1],\n [0, 0, 0, 0, 7, 0, 2, 18, 17],\n [0, 0, 0, 0, 0, -11, 8, 24, -10],\n [0, 0, 0, 0, 0, 0, 2, -17, -24],\n [0, 0, 0, 0, 0, 0, 0, -9, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174608", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -23, -11, -16, -5, 11, -11, -3, -12],\n [0, -16, -17, 18, 13, -21, -1, 16, 0],\n [0, 0, -1, 22, -14, -17, -16, 22, -16],\n [0, 0, 0, 1, 5, -7, 17, 12, -20],\n [0, 0, 0, 0, -21, -12, -24, -3, 18],\n [0, 0, 0, 0, 0, 1, -2, -9, -1],\n [0, 0, 0, 0, 0, 0, -21, 18, 16],\n [0, 0, 0, 0, 0, 0, 0, 18, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112834", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-20, 12, 6, -5, 18, 18, 23, -19, 0],\n [-11, 23, 16, -3, 12, 15, -11, 22, 14],\n [-10, 6, 11, -8, -6, 20, -24, -3, 4],\n [-23, 20, 13, 21, 23, -25, 15, -4, 3],\n [-12, 22, 2, -5, 19, 6, -20, -25, -5],\n [-22, -23, 23, 4, 5, 8, -7, -6, -3],\n [14, -1, -11, 12, -3, -24, -11, 18, 9],\n [-16, -12, 1, -12, 9, 7, -25, 8, -7],\n [-2, 16, -22, 10, -13, 6, -17, 13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "754", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[24, -23, -6, -16, -4, 22, -23, -15, -1],\n [16, 22, -18, -17, -11, 6, -23, -22, 4],\n [-13, 18, -5, 15, 20, -7, 13, 22, -4],\n [-6, 11, 5, -16, -8, 17, 13, 20, -6],\n [-8, -15, -4, 18, -8, 8, -3, -25, -16],\n [-25, 12, 13, 23, -17, 5, -19, -9, 9],\n [22, 11, -8, 7, -22, -3, -15, -17, 4],\n [-18, 14, -21, -14, -25, -11, -1, -8, 12],\n [16, 20, 0, 14, -23, -4, 0, -7, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 5) of the inverse. Round your answer to the nearest integer:\n[[18, 16, 15, 17, -12, 2, 5, 7, -10],\n [16, -2, 10, 5, -12, -16, -8, 6, -16],\n [15, 10, 2, -6, -6, 10, -11, 10, 10],\n [17, 5, -6, 21, 0, -10, 8, -10, 5],\n [-12, -12, -6, 0, 0, -9, -1, -18, 19],\n [2, -16, 10, -10, -9, 23, 8, 10, -18],\n [5, -8, -11, 8, -1, 8, -24, -4, 16],\n [7, 6, 10, -10, -18, 10, -4, 24, -8],\n [-10, -16, 10, 5, 19, -18, 16, -8, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-19, 19, -13, 23, -25, -12, 3, -23, 20],\n [-2, -25, 22, -16, -13, 10, -17, -12, 10],\n [-16, 14, -3, 9, -19, 16, 9, -24, -11],\n [-17, 21, -9, 13, -8, -11, -8, -2, -3],\n [-14, -3, -5, 0, -18, 4, 8, -24, -21],\n [5, 7, -22, -20, -3, 19, -7, 17, 19],\n [-18, 13, -13, -25, -20, -19, 22, 1, -11],\n [8, -3, 22, 23, -2, -11, 9, -22, 18],\n [11, -9, 5, 12, -16, 24, 1, 16, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-87", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[15, 22, -14, -16, -20, 24, 8, 15, -7],\n [0, -24, -11, -9, -10, 2, -5, -18, -16],\n [0, 0, -16, -17, 2, -2, -7, 7, -22],\n [0, 0, 0, -8, -3, -6, -20, 8, 16],\n [0, 0, 0, 0, 16, 8, 14, -2, 23],\n [0, 0, 0, 0, 0, 5, 23, -17, -7],\n [0, 0, 0, 0, 0, 0, 13, 22, -10],\n [0, 0, 0, 0, 0, 0, 0, 17, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-906", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-18, 20, -7, 25, -18, 8, -22, 5, 12],\n [0, 9, -7, 17, 3, -16, -14, 20, 4],\n [0, 0, -2, 6, -17, 21, -2, 0, -23],\n [0, 0, 0, 24, 10, -13, 3, 12, -13],\n [0, 0, 0, 0, -12, 19, -12, -18, 22],\n [0, 0, 0, 0, 0, -4, 8, 24, 25],\n [0, 0, 0, 0, 0, 0, 23, -10, 16],\n [0, 0, 0, 0, 0, 0, 0, 21, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13661", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 7) of the inverse. Round your answer to the nearest integer:\n[[11, 19, 2, 24, -24, -6, -22, -13, -2],\n [0, 12, 14, 22, 19, 3, 10, -24, 15],\n [0, 0, -18, -11, 15, -9, -3, -24, -20],\n [0, 0, 0, 23, 8, -8, 16, -16, 12],\n [0, 0, 0, 0, 16, 1, -24, 8, 5],\n [0, 0, 0, 0, 0, 19, -14, -7, -17],\n [0, 0, 0, 0, 0, 0, -16, -14, -11],\n [0, 0, 0, 0, 0, 0, 0, 8, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -21, 9, 21, -12, -5, 21, -2, -9],\n [0, 8, -14, -10, -22, -1, 8, 2, 20],\n [0, 0, 5, -1, 13, -16, -2, -25, -1],\n [0, 0, 0, -20, -24, -23, 20, -18, 5],\n [0, 0, 0, 0, -12, -23, 22, -25, 18],\n [0, 0, 0, 0, 0, -19, 20, 11, 24],\n [0, 0, 0, 0, 0, 0, -14, -20, -8],\n [0, 0, 0, 0, 0, 0, 0, -22, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4662", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 4, -14, -8, 9, -7, -8, -14, 6],\n [4, 5, 3, 10, -4, 5, -4, -4, -4],\n [-14, 3, -10, 18, -8, 16, 24, 2, 8],\n [-8, 10, 18, 25, 6, -6, -16, -18, 1],\n [9, -4, -8, 6, 16, 4, 4, -22, -4],\n [-7, 5, 16, -6, 4, 13, 20, -4, 18],\n [-8, -4, 24, -16, 4, 20, 11, 6, 2],\n [-14, -4, 2, -18, -22, -4, 6, 2, 6],\n [6, -4, 8, 1, -4, 18, 2, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1091", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[2, 2, -16, -6, -1, -5, -12, -4, 0],\n [18, -15, -19, -9, -8, -19, -6, 12, -15],\n [18, -10, 25, 1, 25, -15, -10, -3, -14],\n [14, -23, -24, 12, 22, -2, 3, 21, 20],\n [8, -6, -8, -12, -8, -24, -25, -6, 8],\n [15, 15, 22, -15, 1, -3, 12, 18, -23],\n [-14, 4, 5, -3, -25, 15, -6, -20, -15],\n [9, -22, 3, -16, 25, 3, 12, -25, 14],\n [-18, 12, -9, -7, 7, -11, 19, 5, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1051", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (5, 8) of the inverse. Round your answer to the nearest integer:\n[[-23, -24, 9, 15, -10, 19, 25, 24, -5],\n [0, 2, -14, 7, -6, 14, 23, -5, 13],\n [0, 0, 16, 10, -4, 0, -19, -19, -18],\n [0, 0, 0, 14, 22, -14, 21, -18, -17],\n [0, 0, 0, 0, 21, -2, -22, -6, -10],\n [0, 0, 0, 0, 0, -15, 3, 19, -11],\n [0, 0, 0, 0, 0, 0, -24, 18, -10],\n [0, 0, 0, 0, 0, 0, 0, 6, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[22, -8, 6, 14, 21, -16, 12, 14, -2],\n [-8, 16, -1, 1, 9, -6, -6, 1, -19],\n [6, -1, -12, -12, -22, 4, -24, -16, -4],\n [14, 1, -12, 20, -8, 0, 10, 6, -5],\n [21, 9, -22, -8, -9, 3, 8, -4, -12],\n [-16, -6, 4, 0, 3, 3, 22, 13, 0],\n [12, -6, -24, 10, 8, 22, 20, 0, -2],\n [14, 1, -16, 6, -4, 13, 0, -11, -7],\n [-2, -19, -4, -5, -12, 0, -2, -7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 8) rounded to the nearest integer?\n[[-24, 4, -1, -4, -10, 0, 6, 8, 6],\n [4, 21, -2, 20, -9, -20, 8, 0, 0],\n [-1, -2, 6, 14, 13, 22, 15, -2, 18],\n [-4, 20, 14, 5, 18, -10, 4, 9, 0],\n [-10, -9, 13, 18, 9, -2, 14, 9, -3],\n [0, -20, 22, -10, -2, -2, -22, 12, 12],\n [6, 8, 15, 4, 14, -22, 6, -1, 20],\n [8, 0, -2, 9, 9, 12, -1, -8, 12],\n [6, 0, 18, 0, -3, 12, 20, 12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "407", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 7) of the inverse of matrix 1/450 * A where A =\n[[24, -25, 25, -10, 13, -11, 7, -3, 15],\n [8, -9, -1, 16, -20, 5, -21, 14, 14],\n [4, -21, -14, -19, 19, -13, 23, -22, 24],\n [16, -23, -14, -25, 1, 17, 24, -13, -9],\n [-18, 6, -6, 25, -9, 8, 9, 9, 12],\n [16, -2, -8, 24, 20, 22, 13, 7, 23],\n [-3, -1, 11, 1, -25, -5, 23, -16, 5],\n [18, -1, -6, -24, 22, -11, 2, -13, 24],\n [-12, 24, -24, 8, 9, 11, -1, 22, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-14, -17, 5, -12, 3, 22, 17, 12, 16],\n [0, 22, -23, -24, -10, -7, 4, 15, -10],\n [0, 0, -22, -16, 25, 19, -8, 21, 6],\n [0, 0, 0, 10, 3, -10, 2, -5, 21],\n [0, 0, 0, 0, 10, 5, 7, -3, 15],\n [0, 0, 0, 0, 0, -3, 22, 1, -1],\n [0, 0, 0, 0, 0, 0, -11, -9, 24],\n [0, 0, 0, 0, 0, 0, 0, 22, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-83", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[7, -6, 7, 14, 9, 8, 10, 1, -7],\n [17, -21, 3, -16, 14, -13, 3, -21, -14],\n [-13, -4, 14, -11, -13, -25, 12, 17, 19],\n [-25, -15, 17, 14, -4, 9, 25, 18, -20],\n [2, 5, -18, -21, 16, 22, 18, -9, 12],\n [-17, -16, -6, -12, -12, 0, 3, 23, 1],\n [-1, -10, 10, 8, -10, 7, -23, -3, -15],\n [22, -8, 21, 15, 18, 3, 24, -21, -2],\n [3, 3, 0, 14, -23, -24, -1, -7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12060", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-24, -7, -25, 1, 19, 23, 9, 15, -21],\n [0, -22, -9, -5, 22, 5, 22, -4, -15],\n [0, 0, -11, 24, -16, 12, 6, 22, 5],\n [0, 0, 0, 5, -20, -12, -3, -10, -1],\n [0, 0, 0, 0, 13, 8, 25, 14, 17],\n [0, 0, 0, 0, 0, 11, 1, 8, -15],\n [0, 0, 0, 0, 0, 0, -13, 6, -19],\n [0, 0, 0, 0, 0, 0, 0, 25, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, 16, -3, -15, 7, -6, -1, 0, 14],\n [-14, 6, 7, -16, -22, -11, 25, -20, 1],\n [-21, -21, -8, 2, 9, -4, 8, -22, -8],\n [15, 25, 0, 16, -4, 21, 7, 17, -12],\n [5, -16, 25, -2, -5, 22, -18, 6, 5],\n [8, -3, -1, -19, -7, -19, 21, -18, -12],\n [-25, -13, -23, 2, 12, 25, -11, 10, -23],\n [-22, -21, 24, 0, -1, -16, -18, -14, -23],\n [1, 24, -3, 14, 7, -12, -3, 5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-155", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-14, 12, -5, 10, -2, -2, 8, -6, 10],\n [12, 16, 10, -2, 0, 0, 0, -12, 6],\n [-5, 10, 4, 5, 14, -2, -9, 1, -13],\n [10, -2, 5, 0, 16, -12, 10, 10, 0],\n [-2, 0, 14, 16, -23, 0, -12, 14, 0],\n [-2, 0, -2, -12, 0, 16, -8, 16, 14],\n [8, 0, -9, 10, -12, -8, -11, -20, 4],\n [-6, -12, 1, 10, 14, 16, -20, 11, 7],\n [10, 6, -13, 0, 0, 14, 4, 7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-9, 24, -19, 24, -7, -19, 14, 19, 24],\n [0, -15, 15, -25, 6, 14, 18, -24, -11],\n [0, 0, 24, -9, 21, -17, 9, -6, -7],\n [0, 0, 0, 14, -25, -2, -2, 21, -7],\n [0, 0, 0, 0, 12, 3, -13, -22, 19],\n [0, 0, 0, 0, 0, -9, 24, 13, 22],\n [0, 0, 0, 0, 0, 0, -13, -18, -25],\n [0, 0, 0, 0, 0, 0, 0, -22, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-16, 8, -16, -1, 3, 4, -4, -2, 0],\n [8, 12, -1, -4, 6, 0, -2, -2, 6],\n [-16, -1, 17, 8, 0, 8, 4, 11, 18],\n [-1, -4, 8, 14, 4, 0, 4, 3, -3],\n [3, 6, 0, 4, -9, 8, 0, -14, -10],\n [4, 0, 8, 0, 8, 4, -12, 1, 14],\n [-4, -2, 4, 4, 0, -12, -22, -9, -11],\n [-2, -2, 11, 3, -14, 1, -9, -7, 0],\n [0, 6, 18, -3, -10, 14, -11, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-22, 4, -21, 2, -4, 19, 16, 16, 6],\n [4, -5, 12, 25, -14, -14, -2, -8, 12],\n [-21, 12, -16, -3, 0, -6, 0, -2, -3],\n [2, 25, -3, 18, 8, -1, 6, -3, 2],\n [-4, -14, 0, 8, 14, 5, 2, -3, -2],\n [19, -14, -6, -1, 5, 13, 5, 4, -10],\n [16, -2, 0, 6, 2, 5, 10, 12, 2],\n [16, -8, -2, -3, -3, 4, 12, 20, 8],\n [6, 12, -3, 2, -2, -10, 2, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-12, -14, 24, -22, 20, 25, -13, -8, 17],\n [2, 12, 15, 18, -7, 20, 21, 17, 12],\n [20, -23, -7, -6, -1, -15, -9, 23, 9],\n [-12, 13, -7, -23, 8, 23, 15, -4, 12],\n [1, -5, 15, 5, 1, 11, -24, 21, -17],\n [-7, 16, 10, -16, 14, 19, 13, -19, -22],\n [-11, -14, 22, -20, -17, 9, -18, -19, -22],\n [-13, -7, -19, -16, -1, 18, 9, -1, 3],\n [-14, 25, 21, 14, -14, -20, -16, -24, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-1, -19, 14, -3, 22, -15, 10, 23, 22],\n [0, -3, 17, -19, 1, -13, 25, -9, 6],\n [0, 0, -13, -14, -19, -25, 7, -12, 21],\n [0, 0, 0, -22, 25, 13, -25, 15, 19],\n [0, 0, 0, 0, -11, -9, -13, -19, -17],\n [0, 0, 0, 0, 0, -3, 0, -25, -12],\n [0, 0, 0, 0, 0, 0, -23, 23, 24],\n [0, 0, 0, 0, 0, 0, 0, -13, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112261", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, -17, 22, -8, 4, 6, 14, -3, -15],\n [0, -7, 10, 0, -16, -2, -13, 20, 8],\n [0, 0, -19, 25, 4, -9, 22, -13, -2],\n [0, 0, 0, -5, 18, -25, -11, -23, -20],\n [0, 0, 0, 0, -18, 0, -11, -12, 22],\n [0, 0, 0, 0, 0, -2, -16, 24, 8],\n [0, 0, 0, 0, 0, 0, -19, 21, -4],\n [0, 0, 0, 0, 0, 0, 0, 24, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2464", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[21, 18, 0, 15, 4, -6, -1, -7, 18],\n [18, 13, 12, 10, 10, 0, -1, 22, -12],\n [0, 12, -17, 5, 0, -6, 14, -17, -18],\n [15, 10, 5, 22, 6, -10, -18, 0, 19],\n [4, 10, 0, 6, 14, 22, -10, -1, 12],\n [-6, 0, -6, -10, 22, 9, 4, 6, 6],\n [-1, -1, 14, -18, -10, 4, -25, -5, -14],\n [-7, 22, -17, 0, -1, 6, -5, 13, -4],\n [18, -12, -18, 19, 12, 6, -14, -4, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[22, -1, 8, 11, 18, -13, 12, -20, -20],\n [-1, -1, 19, -18, 2, 20, 17, -10, -11],\n [8, 19, 2, 19, 17, 6, 6, -6, 4],\n [11, -18, 19, -14, 3, 6, -10, 0, 18],\n [18, 2, 17, 3, 5, 14, 22, 19, -4],\n [-13, 20, 6, 6, 14, 16, 0, -9, -7],\n [12, 17, 6, -10, 22, 0, 6, 4, -12],\n [-20, -10, -6, 0, 19, -9, 4, -5, -8],\n [-20, -11, 4, 18, -4, -7, -12, -8, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "460", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (1, 9) rounded to the nearest integer?\n[[-19, 8, -16, -2, 4, 8, -21, -8, -2],\n [8, 17, 2, -10, 4, 16, -2, 4, -20],\n [-16, 2, 19, 16, -6, 0, 6, -8, -6],\n [-2, -10, 16, 6, 16, 18, -5, 7, -4],\n [4, 4, -6, 16, -1, 14, 8, -6, -6],\n [8, 16, 0, 18, 14, -7, 6, -20, -15],\n [-21, -2, 6, -5, 8, 6, 22, 14, -12],\n [-8, 4, -8, 7, -6, -20, 14, -1, 2],\n [-2, -20, -6, -4, -6, -15, -12, 2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, -4, 15, 5, 0, -2, -6, 16, 0],\n [-4, -15, -14, 4, -6, -12, 8, 15, -18],\n [15, -14, 15, -16, -20, -12, -9, -16, -8],\n [5, 4, -16, -9, 4, 5, -6, -14, -8],\n [0, -6, -20, 4, 11, -8, 6, 2, 3],\n [-2, -12, -12, 5, -8, 8, -16, 4, 14],\n [-6, 8, -9, -6, 6, -16, -22, 15, -10],\n [16, 15, -16, -14, 2, 4, 15, 18, 22],\n [0, -18, -8, -8, 3, 14, -10, 22, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, 8, -8, -14, 9, -19, 15, 14, -1],\n [0, -25, 20, -10, 22, -22, 3, 12, 21],\n [0, 0, -18, 6, 7, -13, 1, -8, -8],\n [0, 0, 0, -15, 13, 24, -4, 10, -9],\n [0, 0, 0, 0, 3, -20, 24, -22, -15],\n [0, 0, 0, 0, 0, 9, -11, -18, -6],\n [0, 0, 0, 0, 0, 0, 14, 9, 7],\n [0, 0, 0, 0, 0, 0, 0, -3, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[19, 21, 1, -14, -13, -18, -10, 3, 9],\n [0, 5, -13, -14, 25, -24, 7, -18, 15],\n [0, 0, 15, 6, 12, 2, -11, -3, -2],\n [0, 0, 0, -13, 13, -3, 24, 20, 17],\n [0, 0, 0, 0, 8, 25, 22, -4, -16],\n [0, 0, 0, 0, 0, -13, -10, 4, 5],\n [0, 0, 0, 0, 0, 0, 18, 14, 19],\n [0, 0, 0, 0, 0, 0, 0, 18, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "924", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[22, 7, -10, 10, -20, -7, 5, -24, -8],\n [16, 2, -22, -25, 21, 16, 24, -10, 19],\n [21, -24, 10, -25, 13, -3, 0, -15, 16],\n [-25, -15, -2, -16, -12, -12, -19, -3, 17],\n [-4, 10, 1, -24, 13, 25, 20, -7, -19],\n [-14, -23, 21, -21, -18, -12, 10, -19, -19],\n [24, 20, 6, -18, -14, -16, -12, -17, 12],\n [4, -21, -25, -25, -6, 23, -15, 0, 18],\n [-23, -20, 17, 19, -15, -18, 3, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-2, 12, 21, -2, 6, -10, 11, -12, -10],\n [12, 22, 10, 6, -9, -8, 12, -19, 0],\n [21, 10, 16, -10, 10, -4, 14, 7, 10],\n [-2, 6, -10, -24, 16, -20, 2, -10, -12],\n [6, -9, 10, 16, -8, 20, 10, 15, 2],\n [-10, -8, -4, -20, 20, -18, 6, -5, 15],\n [11, 12, 14, 2, 10, 6, 14, 2, -12],\n [-12, -19, 7, -10, 15, -5, 2, 21, -10],\n [-10, 0, 10, -12, 2, 15, -12, -10, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 19, -24, 20, 13, 11, -12, -17, -16],\n [-19, 2, 20, -1, 20, 2, -24, -9, -22],\n [-13, -8, -23, 25, 11, 7, 15, -2, -18],\n [9, -24, 7, -14, -4, -13, -16, -9, 17],\n [-21, -17, -13, -3, 4, 17, -22, -5, 17],\n [-17, -19, -10, -3, -3, 5, -21, -20, 25],\n [-25, 22, 2, -8, -2, -13, 7, -16, -19],\n [11, 6, 19, -4, -10, -2, -12, -15, -7],\n [-3, 8, 14, -13, 13, 18, 2, 14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-111", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-5, 0, 2, 13, 7, 14, -7, 3, -6],\n [0, -16, -14, 7, -1, -1, -22, -22, -17],\n [0, 0, -11, 0, 2, -19, 6, -14, 9],\n [0, 0, 0, -13, 18, 7, 6, -7, 4],\n [0, 0, 0, 0, -8, -13, 3, -2, 12],\n [0, 0, 0, 0, 0, 17, 14, 8, 8],\n [0, 0, 0, 0, 0, 0, -6, 0, -11],\n [0, 0, 0, 0, 0, 0, 0, -11, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2803", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-3, -12, -22, -5, 20, -16, -4, 4, 4],\n [0, -15, -4, 3, -1, -12, -12, -24, -13],\n [0, 0, -8, 10, -5, -7, -10, 2, -22],\n [0, 0, 0, 22, 21, -10, -6, 7, -9],\n [0, 0, 0, 0, 18, 10, 4, -22, -3],\n [0, 0, 0, 0, 0, 5, -7, 12, -14],\n [0, 0, 0, 0, 0, 0, 14, 15, -21],\n [0, 0, 0, 0, 0, 0, 0, -5, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14327", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[0, -13, 18, 11, -13, 12, -1, 21, -3],\n [-4, -5, 4, -15, -22, 7, 21, -14, -17],\n [6, -15, 11, -2, -19, -18, 7, -1, -25],\n [-23, 14, 2, 17, 7, 20, -25, 12, 1],\n [12, 9, -16, -14, -16, 8, -2, 2, -4],\n [19, -10, -13, 10, 10, 17, -3, -12, 6],\n [-23, 1, -7, -4, -25, -21, 23, 7, 25],\n [-7, 10, 25, -20, -11, 10, 7, -2, 1],\n [23, -15, 23, -3, 7, 15, 20, 21, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2156", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -4, -4, 8, 0, -22, 20, -24, 0],\n [-4, 4, -6, 2, -12, -4, 0, -18, -13],\n [-4, -6, 1, -4, 0, -3, 8, -6, -8],\n [8, 2, -4, 7, -4, 6, 2, -24, -12],\n [0, -12, 0, -4, -4, 13, -12, -13, 6],\n [-22, -4, -3, 6, 13, -20, 17, 18, 0],\n [20, 0, 8, 2, -12, 17, -22, 21, 4],\n [-24, -18, -6, -24, -13, 18, 21, -19, 2],\n [0, -13, -8, -12, 6, 0, 4, 2, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-62", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-17, 20, 0, 14, -14, -12, -4, 0, 7],\n [20, -10, 5, -6, 4, 1, 12, -8, -6],\n [0, 5, 15, 2, 14, 0, 0, 0, -14],\n [14, -6, 2, -8, -15, 14, 10, -12, -2],\n [-14, 4, 14, -15, -3, -2, -10, 5, 8],\n [-12, 1, 0, 14, -2, -21, -11, 10, 4],\n [-4, 12, 0, 10, -10, -11, -13, -10, -14],\n [0, -8, 0, -12, 5, 10, -10, -15, 8],\n [7, -6, -14, -2, 8, 4, -14, 8, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-21, -19, -4, 4, -10, -6, -2, 14, -16],\n [-19, 20, -6, 20, -8, -1, -6, 17, 8],\n [-4, -6, 6, -6, -5, 6, 2, -2, -16],\n [4, 20, -6, -13, 6, 0, -2, -20, -11],\n [-10, -8, -5, 6, 21, -12, 2, -5, -1],\n [-6, -1, 6, 0, -12, 12, 8, 4, 12],\n [-2, -6, 2, -2, 2, 8, 0, 14, -11],\n [14, 17, -2, -20, -5, 4, 14, 19, 7],\n [-16, 8, -16, -11, -1, 12, -11, 7, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -13, 25, -22, -7, 24, -1, 12, 25],\n [5, 10, -22, 13, -19, -10, 22, -21, 21],\n [-3, 10, 6, -2, -1, 19, 2, -7, -19],\n [18, 15, -9, -24, -10, 13, -8, 13, -25],\n [-23, -5, 4, -15, -4, 21, -1, -23, 4],\n [-2, 19, 10, -3, -18, -22, 24, 13, 17],\n [5, 3, 10, -13, 15, -17, -5, 25, -23],\n [-1, -1, -14, 3, -15, -15, 23, 0, -12],\n [-10, -16, 5, 5, 10, -16, 0, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, -8, 4, 1, -6, -6, -3, -14, -4],\n [-8, -10, 8, -2, -10, 9, 9, 0, -9],\n [4, 8, -6, -20, 11, 14, -12, 4, -12],\n [1, -2, -20, 19, 2, 2, 2, -7, 3],\n [-6, -10, 11, 2, 0, 4, -13, 0, 12],\n [-6, 9, 14, 2, 4, 7, 2, 5, 6],\n [-3, 9, -12, 2, -13, 2, -23, 4, 7],\n [-14, 0, 4, -7, 0, 5, 4, 18, 6],\n [-4, -9, -12, 3, 12, 6, 7, 6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, 9, -4, -11, -15, 8, -2, -20, -9],\n [2, 24, 5, 10, -17, -16, -5, 8, 5],\n [3, 17, 17, -15, 7, 20, -25, -5, -3],\n [-17, -25, -5, -4, -22, -25, 25, -16, -11],\n [10, 3, 20, -21, 3, 21, 21, 1, -1],\n [-10, -10, 10, -1, 15, -25, -21, 15, -6],\n [-21, 10, 3, 22, 8, 22, -8, -24, -10],\n [3, 7, -10, 9, 21, 17, 16, -9, -22],\n [23, -22, 25, -1, 7, -12, -2, -15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 1) of the inverse of matrix 1/450 * A where A =\n[[2, -14, 16, -4, -8, 2, 11, 6, -12],\n [-14, 23, -10, -10, -4, -3, -14, 16, 0],\n [16, -10, -9, -2, 3, 0, -2, -14, 0],\n [-4, -10, -2, -1, -2, 23, 10, 1, 2],\n [-8, -4, 3, -2, -22, 4, -7, 20, 10],\n [2, -3, 0, 23, 4, -24, 14, -18, 18],\n [11, -14, -2, 10, -7, 14, 4, -12, -4],\n [6, 16, -14, 1, 20, -18, -12, 10, -23],\n [-12, 0, 0, 2, 10, 18, -4, -23, 20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[25, 15, 14, 3, 9, -8, 14, 22, 4],\n [0, -11, -10, 7, -16, -7, 11, 24, -23],\n [0, 0, -15, 15, 7, 2, 6, -10, -17],\n [0, 0, 0, 1, -14, -4, 14, 22, 11],\n [0, 0, 0, 0, 14, -16, -8, 21, -13],\n [0, 0, 0, 0, 0, -23, -4, 1, -23],\n [0, 0, 0, 0, 0, 0, 7, -19, -11],\n [0, 0, 0, 0, 0, 0, 0, -16, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "491", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-20, 16, 24, 22, -8, 12, -7, 23, 24],\n [4, -13, 13, -14, 8, -14, 18, -2, -22],\n [10, 24, 22, -12, -9, 23, -23, 12, -3],\n [-13, -17, -5, 15, -18, -9, -10, -10, 2],\n [25, -10, 20, 20, -12, 20, 18, 12, -6],\n [19, 22, 15, 8, 3, -23, -16, -6, -24],\n [1, 6, -16, 14, -9, 7, -20, 13, 21],\n [-8, -17, -18, -1, 5, 16, -22, -6, 2],\n [14, -25, 14, 18, -3, 21, -13, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, 14, -5, 8, 4, 16, -12, 16, 8],\n [14, -16, 4, -5, 22, -14, -6, -8, 4],\n [-5, 4, 24, 20, 3, -24, 2, 1, -4],\n [8, -5, 20, -23, 2, 4, -10, -5, 12],\n [4, 22, 3, 2, 5, 12, 2, 14, 4],\n [16, -14, -24, 4, 12, -16, 3, 8, -2],\n [-12, -6, 2, -10, 2, 3, -2, 0, 7],\n [16, -8, 1, -5, 14, 8, 0, -18, -17],\n [8, 4, -4, 12, 4, -2, 7, -17, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-134", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 8, -3, -12, -8, -6, 14, -2, -5],\n [8, -20, -2, 0, 10, 14, -13, -12, 6],\n [-3, -2, -4, 18, -4, -14, -20, 0, -8],\n [-12, 0, 18, 20, 2, -8, 2, 0, 10],\n [-8, 10, -4, 2, -4, -8, -14, 17, -7],\n [-6, 14, -14, -8, -8, -16, -4, -15, 7],\n [14, -13, -20, 2, -14, -4, -13, -22, 0],\n [-2, -12, 0, 0, 17, -15, -22, -23, 6],\n [-5, 6, -8, 10, -7, 7, 0, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-23, 9, -13, 8, -2, -25, -14, -18, -7],\n [0, 2, -12, 1, -8, 16, 15, -20, 7],\n [0, 0, -1, -13, -3, 10, 7, -5, 8],\n [0, 0, 0, -3, 18, -24, 9, -12, 21],\n [0, 0, 0, 0, -10, 17, 18, -1, -25],\n [0, 0, 0, 0, 0, 25, -16, -7, 16],\n [0, 0, 0, 0, 0, 0, 5, 19, -1],\n [0, 0, 0, 0, 0, 0, 0, -8, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5316290", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[10, -16, 24, 9, 9, 11, 22, -6, -13],\n [-15, 19, -7, 2, 12, 19, -22, 11, -7],\n [11, -12, 5, 2, 10, 18, 12, -7, 16],\n [-25, -3, 2, 22, -22, 15, -8, 23, 21],\n [25, 13, -1, -8, -20, -7, -14, -1, 9],\n [-25, -21, -25, -18, 13, 21, 17, -8, 20],\n [-17, -21, -22, 18, 3, -25, 4, 19, -25],\n [-23, -4, -18, -8, -1, 22, -6, 5, 4],\n [-10, -24, -9, -16, -19, 16, 25, -17, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-130", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-17, -20, -4, -6, 7, -4, 4, -12, 18],\n [-20, -16, 2, 0, 6, 8, 11, -8, -18],\n [-4, 2, 13, 15, -8, -16, -2, -4, 8],\n [-6, 0, 15, -14, -5, -22, -2, -12, 13],\n [7, 6, -8, -5, 1, 6, -11, 16, 16],\n [-4, 8, -16, -22, 6, -25, 0, -6, -2],\n [4, 11, -2, -2, -11, 0, -5, -4, 20],\n [-12, -8, -4, -12, 16, -6, -4, -16, 12],\n [18, -18, 8, 13, 16, -2, 20, 12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-19, 10, 2, -12, -11, 16, 10, 18, -6],\n [10, -16, 2, -4, -12, -7, -3, 9, -16],\n [2, 2, 19, 17, -6, -21, 2, 0, -9],\n [-12, -4, 17, 21, 4, -17, 6, -8, -4],\n [-11, -12, -6, 4, 9, -9, -6, 2, -5],\n [16, -7, -21, -17, -9, 20, 3, -18, 8],\n [10, -3, 2, 6, -6, 3, 16, -8, -2],\n [18, 9, 0, -8, 2, -18, -8, -14, 9],\n [-6, -16, -9, -4, -5, 8, -2, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1259", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-17, -23, 10, 22, -19, -4, -12, 22, 3],\n [24, -10, 22, 8, -16, -19, -1, 1, -11],\n [6, 2, -17, -19, -10, 0, 9, -9, -3],\n [-18, -24, 5, 6, 3, -23, -18, -24, 5],\n [25, 23, 11, -6, 3, -9, -16, 15, -4],\n [-20, 17, 8, 5, -14, -14, -10, -1, -4],\n [1, -2, -14, -8, 19, 21, -10, -22, -14],\n [23, 7, -4, -8, 22, 7, 1, 16, -7],\n [22, -12, -1, 8, -2, 12, -3, -21, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[10, -2, 10, -21, 13, -20, 19, 10, 19],\n [-22, -16, -25, -5, 14, 13, 11, -23, 21],\n [5, 1, -9, -3, -13, 21, 1, 25, -6],\n [20, -13, 18, -2, 15, -23, 17, -16, -25],\n [23, -13, -12, 7, -24, -24, 13, 15, 5],\n [-22, 8, -7, 11, -17, -2, -13, 18, 4],\n [-7, 15, -16, 25, 16, 18, -12, 14, 22],\n [23, -6, -22, 12, 18, 24, 13, -21, 16],\n [6, -20, -12, -20, -12, -14, 1, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-18, -16, -10, 0, -18, 15, 19, 3, -6],\n [0, -7, -9, 13, -25, 3, -12, -9, -13],\n [0, 0, 1, 20, 7, 3, 11, 13, -7],\n [0, 0, 0, 21, 11, -21, -2, 8, 24],\n [0, 0, 0, 0, 2, 16, 0, -8, 10],\n [0, 0, 0, 0, 0, 23, 22, -8, -19],\n [0, 0, 0, 0, 0, 0, 10, 5, 12],\n [0, 0, 0, 0, 0, 0, 0, -25, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22811", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[19, 18, -3, 16, 11, -18, -20, 11, -4],\n [0, 6, -9, 12, -9, 11, -3, 23, 23],\n [0, 0, -4, -19, -4, -5, -20, -12, -10],\n [0, 0, 0, -5, 24, 4, 4, 16, 16],\n [0, 0, 0, 0, -23, 11, -19, -23, 10],\n [0, 0, 0, 0, 0, -12, 11, 5, -24],\n [0, 0, 0, 0, 0, 0, 7, -7, 20],\n [0, 0, 0, 0, 0, 0, 0, -12, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24468", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-23, -8, 24, 12, 17, -23, 22, -21, -2],\n [0, 21, 22, 13, 22, -2, 10, 2, 22],\n [0, 0, -10, 10, -19, -8, -20, 24, 2],\n [0, 0, 0, 15, 3, -22, -12, -21, -1],\n [0, 0, 0, 0, -15, -6, 10, -8, -12],\n [0, 0, 0, 0, 0, 14, -25, -25, 25],\n [0, 0, 0, 0, 0, 0, 2, 23, 6],\n [0, 0, 0, 0, 0, 0, 0, -24, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10185", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-14, 20, 14, -16, -11, 4, 8, 11, 10],\n [20, -5, -2, 8, 1, -5, -16, 21, 1],\n [14, -2, -10, 14, 6, 8, -4, 6, -8],\n [-16, 8, 14, 21, 0, 4, 12, 0, -10],\n [-11, 1, 6, 0, -23, -18, -2, 6, 6],\n [4, -5, 8, 4, -18, 3, 14, 16, -1],\n [8, -16, -4, 12, -2, 14, 10, 4, 12],\n [11, 21, 6, 0, 6, 16, 4, -3, -4],\n [10, 1, -8, -10, 6, -1, 12, -4, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-87", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-25, 19, 0, 8, -16, -3, 25, 23, -2],\n [0, 3, 20, 1, 5, 17, -16, 5, 13],\n [0, 0, 7, -12, 9, 19, 8, -9, -5],\n [0, 0, 0, -18, 6, 12, 0, 4, -17],\n [0, 0, 0, 0, 15, -8, -7, -8, 11],\n [0, 0, 0, 0, 0, 1, 25, -21, -20],\n [0, 0, 0, 0, 0, 0, 6, 18, -11],\n [0, 0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "242493", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 6) rounded to the nearest integer?\n[[-20, 23, -10, 18, -2, -4, -2, 4, -6],\n [23, -14, 0, 12, -21, 12, -20, 10, -10],\n [-10, 0, 15, -3, 18, 0, 2, 8, 0],\n [18, 12, -3, -24, 5, 16, 0, -5, 7],\n [-2, -21, 18, 5, -19, -8, -14, -10, 4],\n [-4, 12, 0, 16, -8, 20, 16, -3, -7],\n [-2, -20, 2, 0, -14, 16, -16, -4, -17],\n [4, 10, 8, -5, -10, -3, -4, -20, 16],\n [-6, -10, 0, 7, 4, -7, -17, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, 0, -23, -24, 2, -24, -4, -19, -22],\n [0, 12, 13, -6, -20, -17, 5, 0, 10],\n [0, 0, -21, 25, -16, -8, -11, 7, -21],\n [0, 0, 0, -4, -4, -11, -9, 25, 19],\n [0, 0, 0, 0, -9, -21, -8, -9, -22],\n [0, 0, 0, 0, 0, 17, -17, -7, 25],\n [0, 0, 0, 0, 0, 0, 22, 13, -4],\n [0, 0, 0, 0, 0, 0, 0, 8, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3114", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -12, 19, 4, 14, 21, 18, 9, -5],\n [-21, 12, -24, 14, 11, 23, 8, -15, 10],\n [-15, -17, -20, 8, 21, 11, 6, -14, 19],\n [6, -9, -22, 16, 7, 17, 22, 17, -17],\n [8, 13, 25, 4, 24, -6, 13, -3, 15],\n [18, 9, -3, 22, 13, -3, 11, -3, 13],\n [2, -7, 23, 22, 4, -5, -2, -5, 0],\n [25, 24, 25, 10, 0, 7, 10, -22, -17],\n [-18, -24, 3, -3, -20, 17, 10, 20, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, -17, 8, 0, -25, 10, 18, -21, 15],\n [0, -22, 22, -24, -10, -10, -4, 17, -25],\n [0, 0, -22, -8, -9, -19, 24, 19, -16],\n [0, 0, 0, -4, 6, 3, 9, -9, -14],\n [0, 0, 0, 0, -6, 16, -19, 16, 24],\n [0, 0, 0, 0, 0, 23, 5, -8, 20],\n [0, 0, 0, 0, 0, 0, 9, 7, -5],\n [0, 0, 0, 0, 0, 0, 0, 4, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "619", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[18, -12, -21, 16, -24, -22, -14, -15, -22],\n [17, -17, -16, 1, -20, -11, 16, 5, -4],\n [-20, 7, 3, -5, 4, -5, 10, -4, 20],\n [-6, -4, 14, -15, 21, 5, 25, 14, -13],\n [-8, -4, -9, 12, -1, 6, -11, -13, 0],\n [24, -15, -13, 7, 24, 11, 12, -25, 13],\n [1, 10, 6, 15, -11, 5, -20, -1, 23],\n [-8, -4, 5, 10, -17, 20, -23, 7, 1],\n [17, -25, 18, -17, -21, -11, 24, -17, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-117", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[2, -13, -2, 19, -16, 16, -4, 13, -4],\n [11, 13, -6, -16, -16, 0, -1, 2, -13],\n [-11, -20, -14, -7, 6, -15, 12, 7, -24],\n [-11, 10, -21, -11, 17, -16, -9, 8, -2],\n [-16, 4, -23, 25, 11, -23, 14, -21, 2],\n [18, -12, 13, -15, -18, 11, -18, -14, -11],\n [-7, 22, 20, 2, -19, 14, -19, 4, -8],\n [-2, -20, 25, -22, -23, 23, 25, 21, -20],\n [0, 18, 25, 12, -15, 3, -6, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[22, 1, 24, -12, 10, -14, -3, -5, -18],\n [13, -17, -2, 5, -1, -9, 16, 3, -23],\n [-5, -18, -12, 13, -10, -8, 5, -15, 12],\n [-6, 20, 19, -22, -6, 5, -6, -15, 24],\n [-25, 18, -8, 13, 18, 7, 10, -8, 21],\n [5, 9, 13, 12, -11, 21, -20, -18, 14],\n [-4, -25, -13, -2, -5, 19, 17, -22, -19],\n [-14, -13, 18, -10, -20, -12, 25, 22, 5],\n [10, 11, 15, 9, -16, -9, 25, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2236", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[18, -2, 4, -9, -12, 6, 15, -10, 13],\n [-2, 4, -1, 16, 0, 8, 2, 0, 4],\n [4, -1, 22, 14, 4, 15, 16, -4, -13],\n [-9, 16, 14, -18, 0, -10, 6, 12, -6],\n [-12, 0, 4, 0, -11, -6, -22, 0, 24],\n [6, 8, 15, -10, -6, -12, -4, 13, -2],\n [15, 2, 16, 6, -22, -4, 13, 10, 8],\n [-10, 0, -4, 12, 0, 13, 10, -4, 5],\n [13, 4, -13, -6, 24, -2, 8, 5, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "387", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -1, -6, 2, 2, 18, 14, -7, 11],\n [-1, 2, -6, 0, 4, 6, 22, 2, -10],\n [-6, -6, -20, 10, 2, -4, -7, 0, 12],\n [2, 0, 10, -13, -4, -4, -15, 12, 4],\n [2, 4, 2, -4, 18, 5, 17, -14, -2],\n [18, 6, -4, -4, 5, -15, 6, 12, -15],\n [14, 22, -7, -15, 17, 6, 20, -4, -4],\n [-7, 2, 0, 12, -14, 12, -4, -9, -9],\n [11, -10, 12, 4, -2, -15, -4, -9, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3711", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -1, 2, -4, 16, -1, -9, 18, -14],\n [0, 11, -10, -9, 5, -11, -13, 14, 1],\n [0, 0, -18, 16, -19, -16, -22, 17, 15],\n [0, 0, 0, -23, -8, 25, 20, 17, -2],\n [0, 0, 0, 0, -16, -3, -11, -14, 17],\n [0, 0, 0, 0, 0, -14, -10, 6, -3],\n [0, 0, 0, 0, 0, 0, -19, 7, -22],\n [0, 0, 0, 0, 0, 0, 0, -6, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11342", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[22, 9, -18, 1, -4, -2, -24, 5, -4],\n [-25, -12, -1, 10, 10, 15, -23, -21, -25],\n [-7, 7, 16, 4, -14, -16, 8, -10, 14],\n [20, 3, -11, 22, -15, 18, 8, 10, 4],\n [9, -17, -8, -7, 13, -22, -20, 25, 7],\n [6, -10, -15, -4, 10, 24, -3, 0, 5],\n [3, -21, 12, -1, 8, -14, -4, -17, -6],\n [3, 18, 3, 19, 1, -9, -21, 19, -13],\n [16, -11, -11, -8, 24, -24, -3, 17, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "702", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -22, 21, -1, -15, 24, 22, 16, -14],\n [0, -17, 19, 12, -20, 17, 25, 17, -16],\n [0, 0, 19, -3, 14, 11, 8, -10, 19],\n [0, 0, 0, 6, 12, 14, 20, -21, -9],\n [0, 0, 0, 0, -8, 2, -13, 24, 16],\n [0, 0, 0, 0, 0, 17, -23, 15, -16],\n [0, 0, 0, 0, 0, 0, 20, 10, 17],\n [0, 0, 0, 0, 0, 0, 0, 20, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[-2, 0, -6, -8, 2, -15, 2, 7, -16],\n [0, 24, 5, -18, -2, -6, -3, -6, -2],\n [-6, 5, 2, 12, 12, -8, 7, -2, 21],\n [-8, -18, 12, 11, -4, -18, -4, 3, 8],\n [2, -2, 12, -4, 9, 3, 12, 0, -13],\n [-15, -6, -8, -18, 3, -5, 6, -8, -7],\n [2, -3, 7, -4, 12, 6, 10, 8, 10],\n [7, -6, -2, 3, 0, -8, 8, 21, -14],\n [-16, -2, 21, 8, -13, -7, 10, -14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[20, -3, -13, -10, 4, 14, -18, -9, 4],\n [0, 9, -25, 23, -2, 22, 23, -1, -24],\n [0, 0, 13, 25, 7, -9, 5, -16, -20],\n [0, 0, 0, 11, 4, 8, -8, -2, 23],\n [0, 0, 0, 0, -7, 13, -3, 13, 22],\n [0, 0, 0, 0, 0, 9, 25, -6, 2],\n [0, 0, 0, 0, 0, 0, 13, 17, -6],\n [0, 0, 0, 0, 0, 0, 0, -3, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, -6, -7, -12, 8, 2, 20, 0, 20],\n [-6, 12, 13, -14, -6, -16, -16, 2, -2],\n [-7, 13, -1, 16, 8, 18, 4, 6, -5],\n [-12, -14, 16, -2, -1, -1, -8, 1, 7],\n [8, -6, 8, -1, 13, -6, -6, -5, 5],\n [2, -16, 18, -1, -6, 22, -16, -4, 2],\n [20, -16, 4, -8, -6, -16, 12, -13, -5],\n [0, 2, 6, 1, -5, -4, -13, -17, 8],\n [20, -2, -5, 7, 5, 2, -5, 8, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3374", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[-12, -2, 10, 16, 18, 2, -3, 4, 17],\n [-2, 6, 1, 14, -10, 7, -9, 2, -12],\n [10, 1, -14, -12, -18, 8, -4, 4, 14],\n [16, 14, -12, -21, 11, -14, -12, 10, 8],\n [18, -10, -18, 11, -2, -10, -8, 4, 14],\n [2, 7, 8, -14, -10, -20, 16, -18, 10],\n [-3, -9, -4, -12, -8, 16, -15, -5, 4],\n [4, 2, 4, 10, 4, -18, -5, -8, -10],\n [17, -12, 14, 8, 14, 10, 4, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-250", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 7) of the inverse of matrix 1/450 * A where A =\n[[9, 4, 13, -8, 6, 10, -8, 18, -12],\n [4, -3, 4, 0, 0, 12, 22, -16, 5],\n [13, 4, 10, 6, -19, 7, 0, 2, 0],\n [-8, 0, 6, -19, -22, -4, 18, 4, -16],\n [6, 0, -19, -22, 10, 4, -12, -4, -14],\n [10, 12, 7, -4, 4, -18, 5, 1, -12],\n [-8, 22, 0, 18, -12, 5, 4, 0, 12],\n [18, -16, 2, 4, -4, 1, 0, -18, -21],\n [-12, 5, 0, -16, -14, -12, 12, -21, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 0, 7, -2, 7, 12, 2, 6, 4],\n [0, 6, -4, 2, -8, 4, 14, -12, 2],\n [7, -4, -1, 10, 10, 12, 6, 17, 16],\n [-2, 2, 10, 18, -3, -13, 12, 20, 16],\n [7, -8, 10, -3, 3, -12, -22, -10, -7],\n [12, 4, 12, -13, -12, 4, 2, 9, -6],\n [2, 14, 6, 12, -22, 2, 23, -2, 18],\n [6, -12, 17, 20, -10, 9, -2, -9, 4],\n [4, 2, 16, 16, -7, -6, 18, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-310", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-24, 0, 18, 10, -12, 6, 16, 11, -10],\n [0, 22, 25, -1, -6, -1, -2, 6, 8],\n [18, 25, -2, 8, 2, -2, -12, 4, -6],\n [10, -1, 8, 5, 8, -12, 5, -8, -4],\n [-12, -6, 2, 8, 25, -8, 0, -4, 11],\n [6, -1, -2, -12, -8, 4, 4, 6, 12],\n [16, -2, -12, 5, 0, 4, 11, 2, 4],\n [11, 6, 4, -8, -4, 6, 2, -10, -3],\n [-10, 8, -6, -4, 11, 12, 4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-6, 21, -7, -24, 14, 13, 1, -18, 19],\n [1, -11, -14, 21, -12, -19, -9, 0, 11],\n [-6, -16, -7, -8, 4, 4, -1, -2, -16],\n [-24, 12, 6, 9, 25, 11, -19, -19, 1],\n [-16, 7, 17, -19, -20, -20, -13, 22, -13],\n [-24, -7, 25, -7, 24, 12, -24, 25, 0],\n [-20, -6, -3, -11, -20, 2, 9, -15, -18],\n [24, 23, 25, 25, -2, -5, 23, 10, -19],\n [-21, 3, -10, -20, -12, -24, -1, 5, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-182", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[24, -13, -8, -9, 19, 2, -14, 9, -4],\n [0, -25, 11, -5, -25, -22, 6, -25, -13],\n [0, 0, -9, -14, -19, 25, -23, 24, 0],\n [0, 0, 0, -23, 18, 2, 18, -9, 12],\n [0, 0, 0, 0, -12, 11, 9, 16, 13],\n [0, 0, 0, 0, 0, 6, 14, -13, 17],\n [0, 0, 0, 0, 0, 0, -13, -4, -3],\n [0, 0, 0, 0, 0, 0, 0, -13, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[11, -23, -1, 8, -4, 12, -12, 13, -24],\n [6, 17, -23, 15, -18, 0, 6, -15, 24],\n [-25, -11, -22, -22, 2, -16, -15, 24, -3],\n [21, -23, 13, 13, -9, -4, 1, -10, -10],\n [14, -23, 21, 7, 16, -24, 13, 20, 22],\n [1, -11, -19, 19, 16, -17, 15, -20, -14],\n [4, -6, -6, 20, 1, -6, -19, 14, 14],\n [4, -18, -24, -12, -16, 24, -8, -8, -10],\n [-21, 5, 11, -6, -3, 6, 16, -9, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 8) of the inverse of matrix 1/450 * A where A =\n[[23, 24, -13, -9, -11, 0, 18, 2, 16],\n [19, 4, 17, 9, -4, -16, -15, 12, 7],\n [-20, 11, -19, 18, -14, -19, -24, -25, -3],\n [-1, -8, 18, -19, 25, -23, 3, -16, 17],\n [-21, 8, -18, -12, 14, -20, -25, 7, 14],\n [-15, 24, -2, -16, 18, -3, -10, 11, -10],\n [18, 5, -20, 4, 11, -25, 25, 16, -1],\n [20, -5, 9, 12, -21, 23, 24, -14, -21],\n [-17, 18, -17, 9, -25, 21, -16, 20, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (6, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 11, 22, 9, -9, -13, -20, 11, 22],\n [6, -15, -9, -21, -20, -16, 7, 4, -5],\n [16, -9, 1, -23, 3, -24, 3, 23, 10],\n [8, 11, 16, -25, 0, -25, -22, 13, -12],\n [20, -8, 8, -25, -4, -10, -4, 24, -10],\n [2, 2, -4, -20, -1, 16, -24, -19, -9],\n [9, -6, 18, -24, -19, 6, 23, -7, -14],\n [-17, 1, -12, -24, -5, -22, 25, -5, 22],\n [-4, 23, -24, -9, -7, 14, -2, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, -1, -3, 24, 8, 6, 25, -2, 16],\n [0, -23, -1, 2, -14, 0, 22, 18, -18],\n [0, 0, 16, 9, 1, 15, 18, 12, -7],\n [0, 0, 0, 2, 10, -8, -16, 6, -8],\n [0, 0, 0, 0, 20, 12, -12, -24, -17],\n [0, 0, 0, 0, 0, 13, 16, -9, 0],\n [0, 0, 0, 0, 0, 0, -18, 6, -7],\n [0, 0, 0, 0, 0, 0, 0, 15, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "328", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, -6, 7, 5, 14, -18, -16, -25, -5],\n [0, 6, 20, 20, -16, 25, 22, -17, -6],\n [0, 0, 14, -19, -15, -5, 12, 21, -7],\n [0, 0, 0, -16, 20, -10, 19, -15, 9],\n [0, 0, 0, 0, -12, 3, 21, -23, -25],\n [0, 0, 0, 0, 0, 7, -17, -23, -24],\n [0, 0, 0, 0, 0, 0, -8, -10, -18],\n [0, 0, 0, 0, 0, 0, 0, -3, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31533", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-12, -6, 18, -7, -16, -10, 4, 12, 10],\n [-6, 3, -12, -14, -6, 14, 6, 15, -21],\n [18, -12, 9, 8, 0, 23, 2, 2, 16],\n [-7, -14, 8, 8, -12, 8, -18, 0, -14],\n [-16, -6, 0, -12, 5, 12, -16, 8, 22],\n [-10, 14, 23, 8, 12, 14, 8, -10, 0],\n [4, 6, 2, -18, -16, 8, 22, -8, 0],\n [12, 15, 2, 0, 8, -10, -8, 23, -6],\n [10, -21, 16, -14, 22, 0, 0, -6, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 16, -15, 0, -5, -24, 14, 25, -6],\n [0, -10, 16, -21, -12, -2, 25, -22, 22],\n [0, 0, -17, -23, -17, -8, 10, -7, -2],\n [0, 0, 0, -25, 25, 9, -16, -14, -8],\n [0, 0, 0, 0, -2, -25, 4, -11, -18],\n [0, 0, 0, 0, 0, -11, -21, 19, -19],\n [0, 0, 0, 0, 0, 0, -13, -9, 15],\n [0, 0, 0, 0, 0, 0, 0, -22, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-895", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-18, -9, -8, 24, -14, 7, -3, -14, -15],\n [-13, 9, 1, -1, 14, -23, 23, -1, 19],\n [-16, -9, -23, 19, -4, 12, -12, 1, 16],\n [-6, 22, -8, -13, 16, -20, -16, 11, 3],\n [-20, 13, -15, 22, -1, 18, 18, 4, -6],\n [11, -10, 5, 3, -20, 3, 6, -17, 11],\n [-3, -10, -8, -7, 18, -24, -16, -14, 20],\n [-8, -7, 12, 11, 1, 22, -12, 19, 8],\n [-24, 18, 7, -7, 1, 22, 4, -19, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -19, 22, -1, 12, -8, 7, 7, 6],\n [0, -12, 12, 12, -22, 18, -8, -16, 9],\n [0, 0, -3, -1, -25, -8, -11, -1, 6],\n [0, 0, 0, -13, -1, -6, -1, 16, 19],\n [0, 0, 0, 0, 22, 2, -5, 4, -23],\n [0, 0, 0, 0, 0, 7, -15, 19, -21],\n [0, 0, 0, 0, 0, 0, 13, 23, 14],\n [0, 0, 0, 0, 0, 0, 0, 20, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1152", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-14, 10, -16, -20, -19, 5, 1, -18, -23],\n [14, 21, -5, -25, 19, 24, -11, -19, -11],\n [-1, -23, 4, -12, -22, 10, -23, -21, -1],\n [5, -15, -18, 0, -24, 2, 22, -16, 24],\n [13, 11, 13, -5, 2, 12, 7, -15, 19],\n [18, -25, 21, 7, -23, 0, -11, 15, -12],\n [-3, -18, 10, -6, -20, 7, 2, 24, 12],\n [4, 20, 17, -9, -17, 2, -19, 20, 2],\n [-9, 14, 22, 18, 18, -21, -21, -12, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3243", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 3) of the inverse of matrix 1/450 * A where A =\n[[-19, -9, -17, 5, -4, 19, -17, -10, 10],\n [0, 19, -13, -7, -14, 10, -16, -10, 2],\n [0, 0, -20, -22, 4, 13, 5, 20, 1],\n [0, 0, 0, -17, 9, 16, 21, -5, -9],\n [0, 0, 0, 0, 24, 11, -13, -1, 6],\n [0, 0, 0, 0, 0, 14, 14, 21, 17],\n [0, 0, 0, 0, 0, 0, -20, -5, 10],\n [0, 0, 0, 0, 0, 0, 0, 8, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, -24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[16, -12, 10, 0, -2, -1, 4, 14, -3],\n [-12, 6, 21, -8, 6, -10, 10, -22, 2],\n [10, 21, 23, 12, 15, -4, 12, -4, -6],\n [0, -8, 12, 22, 0, -10, -6, -7, 23],\n [-2, 6, 15, 0, 13, 4, -14, -9, 6],\n [-1, -10, -4, -10, 4, -12, -4, -16, 2],\n [4, 10, 12, -6, -14, -4, -8, -6, 6],\n [14, -22, -4, -7, -9, -16, -6, -14, 1],\n [-3, 2, -6, 23, 6, 2, 6, 1, -19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-209", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-16, 3, 10, -2, 20, -12, -12, -1, 20],\n [-4, 24, 21, -3, 6, 0, 25, 1, 19],\n [-14, -7, -7, 8, 6, 3, -5, 9, 16],\n [-21, -14, -19, 15, -24, -1, -16, 12, 18],\n [-20, 1, 9, -16, -17, -6, 11, 9, 11],\n [14, -18, 20, 5, 23, 17, -10, 2, -20],\n [6, 2, -15, 16, -3, 4, -17, 2, -2],\n [2, -2, -11, 13, 24, 7, 21, 8, -4],\n [3, 8, 16, 21, -16, 25, 19, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, -5, -13, -1, -5, -25, -21, -4, -19],\n [-13, 19, -3, -5, -20, -6, -14, 14, -17],\n [24, 2, -15, 6, -15, -2, -11, 15, 9],\n [-9, -1, 23, 9, -7, 15, 5, -9, 24],\n [-3, 21, -25, -16, -18, 16, 0, 8, -7],\n [-12, -18, 25, -25, 22, -1, -2, 21, -6],\n [4, -21, -23, 6, -9, 16, -21, -15, 12],\n [-22, 13, -7, 13, 20, 23, -3, -9, -13],\n [1, -25, -24, -8, 10, 19, 7, 10, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1086", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 3, 25, -3, 7, -18, 16, -13, -21],\n [0, -16, -12, -2, -15, 20, -23, 3, 22],\n [0, 0, 11, -19, -9, -6, -15, 18, -1],\n [0, 0, 0, -7, 3, 11, -15, -7, 2],\n [0, 0, 0, 0, -20, -15, -12, 10, 14],\n [0, 0, 0, 0, 0, 13, -22, 3, 20],\n [0, 0, 0, 0, 0, 0, 11, 14, 17],\n [0, 0, 0, 0, 0, 0, 0, 4, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-21, -12, -16, 15, 7, 10, -2, -6, -6],\n [-12, -12, -6, 20, 8, 10, -2, -6, -12],\n [-16, -6, -23, 0, -18, -8, 10, 16, -15],\n [15, 20, 0, -24, 3, 7, 1, 24, 19],\n [7, 8, -18, 3, -23, 18, -6, 14, -19],\n [10, 10, -8, 7, 18, 18, -8, -6, -1],\n [-2, -2, 10, 1, -6, -8, -1, 7, 6],\n [-6, -6, 16, 24, 14, -6, 7, 19, -4],\n [-6, -12, -15, 19, -19, -1, 6, -4, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-257", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[3, 8, -7, 22, -8, -24, 1, -20, 13],\n [0, -20, 5, 15, 14, 4, -5, 15, 18],\n [0, 0, 12, -3, 2, 10, -1, -19, -8],\n [0, 0, 0, 16, 14, 7, -11, 9, 21],\n [0, 0, 0, 0, -19, 15, 24, 18, 14],\n [0, 0, 0, 0, 0, 20, -18, 12, -22],\n [0, 0, 0, 0, 0, 0, 15, -2, -10],\n [0, 0, 0, 0, 0, 0, 0, -21, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1563", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, -6, 2, 10, 2, -2, 10, 2, 2],\n [-6, -22, -6, 12, -2, -5, 8, 18, -12],\n [2, -6, 14, 3, 21, -6, 0, -6, -2],\n [10, 12, 3, -10, -6, 3, 13, 8, 0],\n [2, -2, 21, -6, -11, 12, -7, -4, -1],\n [-2, -5, -6, 3, 12, 13, 16, -8, 10],\n [10, 8, 0, 13, -7, 16, 3, -12, -5],\n [2, 18, -6, 8, -4, -8, -12, 12, -2],\n [2, -12, -2, 0, -1, 10, -5, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-21, -4, -22, 8, -19, 24, -9, -15, 24],\n [0, 2, 18, 7, -1, -5, -14, 0, 3],\n [0, 0, 11, 20, 18, 19, 19, 3, 23],\n [0, 0, 0, 6, 18, 8, 10, -6, -14],\n [0, 0, 0, 0, 1, -9, -15, 13, -24],\n [0, 0, 0, 0, 0, -2, -10, 5, 23],\n [0, 0, 0, 0, 0, 0, -1, 17, 18],\n [0, 0, 0, 0, 0, 0, 0, 19, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-13, -25, 14, 11, 5, -9, -17, 19, -13],\n [0, -12, -15, -1, 5, -12, -19, -2, 23],\n [0, 0, 16, 21, 18, 15, -23, 21, 18],\n [0, 0, 0, -25, -11, -15, 11, -19, -14],\n [0, 0, 0, 0, 4, 6, 10, 19, 25],\n [0, 0, 0, 0, 0, 22, -10, 22, 2],\n [0, 0, 0, 0, 0, 0, 8, 20, 14],\n [0, 0, 0, 0, 0, 0, 0, 1, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58182", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (9, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-24, -22, 1, -1, -22, 6, -9, -25, 7],\n [4, -21, -14, 12, 6, 12, -9, 19, 14],\n [6, -2, -14, 21, 5, -7, 3, -5, 0],\n [2, -9, -17, -5, 24, 8, -15, -6, 23],\n [24, 21, 13, -10, 3, -25, -8, -4, -18],\n [-19, -1, 4, 8, 18, 22, 15, -15, -11],\n [9, -3, 19, -5, 2, -13, 8, 12, -20],\n [18, -22, -21, 14, -20, -5, 2, -23, -3],\n [-18, -7, -15, 24, -16, 2, -6, 18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[3, -18, -7, 22, -5, -8, -17, -22, 15],\n [0, 8, -17, -17, -8, -15, -13, 12, -17],\n [0, 0, 8, -19, -11, 12, -15, 6, 1],\n [0, 0, 0, -7, -19, 17, 19, -5, 2],\n [0, 0, 0, 0, -8, 11, 19, 19, -2],\n [0, 0, 0, 0, 0, -13, -22, -3, -16],\n [0, 0, 0, 0, 0, 0, -18, -10, 5],\n [0, 0, 0, 0, 0, 0, 0, -9, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5855", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[25, -6, 15, 22, 1, 13, -13, -22, 6],\n [0, 14, 8, 13, 17, -9, -2, 3, 20],\n [0, 0, 21, -4, 2, -1, 15, -23, -13],\n [0, 0, 0, -8, 11, 17, 8, -9, -5],\n [0, 0, 0, 0, -14, 2, -15, 22, 11],\n [0, 0, 0, 0, 0, 19, -19, 21, -23],\n [0, 0, 0, 0, 0, 0, 9, -14, -5],\n [0, 0, 0, 0, 0, 0, 0, 22, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, 8, 21, 11, 24, 3, 22, 10, 1],\n [16, -4, -24, 21, 10, 22, 4, -19, -14],\n [-23, -9, 15, 6, -18, -3, 12, 4, -11],\n [-16, 12, -11, 4, 20, 0, 25, 19, -12],\n [-23, 10, 0, -12, 5, -12, 14, -16, -17],\n [20, 14, 17, 16, -8, 10, 10, -14, 24],\n [14, -23, -8, -19, 5, -25, 5, -13, 3],\n [-23, 3, 9, -11, -5, -7, 2, -22, 19],\n [-13, -11, 25, 22, 13, 6, -23, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "580", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-24, 24, -1, -15, -25, 22, 23, 22, -16],\n [-9, 4, 9, 24, -7, 20, 8, 6, -14],\n [17, -9, -20, 25, -13, 13, -4, -15, -19],\n [19, 19, -5, -25, 4, -7, 25, 21, 20],\n [3, 9, -6, 10, 13, -25, -3, 5, 25],\n [9, 21, 19, -4, 20, -19, 7, 19, 10],\n [18, -19, 1, -24, -9, -25, 20, 4, -4],\n [2, 7, 0, 9, -15, -19, 2, -1, 15],\n [5, -23, 7, 25, 8, -5, 11, 23, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -5, -12, -16, -19, 3, 14, -18, 13],\n [-13, 20, -7, -15, -24, 23, -20, 3, 15],\n [25, -21, 15, 4, 13, 10, 1, 24, -8],\n [23, 10, -10, -21, -17, 8, 8, 10, 5],\n [-6, -9, -6, 2, -5, -7, -23, 4, -21],\n [16, -20, -23, 23, 16, -2, 18, -25, 24],\n [25, 10, -11, 15, 12, 18, -8, -3, 21],\n [3, 25, 15, -4, -2, 19, 22, -13, 7],\n [24, -4, 9, -9, -4, -21, -1, -20, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-14, 22, -25, -18, 7, 25, -22, -12, 3],\n [0, -17, -17, 0, 23, 21, 16, -9, 15],\n [0, 0, -23, 3, -1, -5, -14, -25, -25],\n [0, 0, 0, -19, -16, -11, 14, -15, 20],\n [0, 0, 0, 0, 15, -9, 24, 25, -13],\n [0, 0, 0, 0, 0, 5, -18, -2, -15],\n [0, 0, 0, 0, 0, 0, 6, -15, 4],\n [0, 0, 0, 0, 0, 0, 0, -6, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30531", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-22, 10, 12, -6, 19, 4, 12, 6, 10],\n [10, 7, -15, 11, -6, 2, 17, -8, -8],\n [12, -15, -8, 6, 16, 24, 7, 8, -12],\n [-6, 11, 6, -8, -12, -4, 17, -6, -14],\n [19, -6, 16, -12, -4, -14, 9, -16, 16],\n [4, 2, 24, -4, -14, 10, -1, -4, 10],\n [12, 17, 7, 17, 9, -1, -8, 2, -7],\n [6, -8, 8, -6, -16, -4, 2, 12, 22],\n [10, -8, -12, -14, 16, 10, -7, 22, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[25, 1, -13, -19, -18, 20, 25, 25, -3],\n [0, 18, 1, -17, 20, 12, 21, -13, -19],\n [0, 0, 7, 13, 24, -23, 15, 3, 11],\n [0, 0, 0, 18, 24, 17, 23, -19, -11],\n [0, 0, 0, 0, 25, -24, -23, 20, -1],\n [0, 0, 0, 0, 0, 6, 25, 15, 10],\n [0, 0, 0, 0, 0, 0, -20, -18, -11],\n [0, 0, 0, 0, 0, 0, 0, -11, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3680", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, 14, 12, -11, -11, 11, 19, -12, 17],\n [0, 18, -6, 7, -23, 14, -3, 18, 21],\n [0, 0, 9, -1, 6, -4, -18, 25, 12],\n [0, 0, 0, -15, -14, -24, 11, -22, 15],\n [0, 0, 0, 0, -3, -13, -19, 6, -3],\n [0, 0, 0, 0, 0, 11, 8, 22, 3],\n [0, 0, 0, 0, 0, 0, 14, -15, -12],\n [0, 0, 0, 0, 0, 0, 0, 16, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-593", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-9, -16, -22, -3, -12, -21, -24, 20, -2],\n [0, 1, -2, 3, -15, 22, -8, 22, -22],\n [0, 0, 18, 16, 6, 25, -22, -6, -5],\n [0, 0, 0, 21, -15, -10, 10, -20, 5],\n [0, 0, 0, 0, 11, 16, 11, 18, 7],\n [0, 0, 0, 0, 0, -6, 6, 18, -10],\n [0, 0, 0, 0, 0, 0, -12, 11, -4],\n [0, 0, 0, 0, 0, 0, 0, 24, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18467", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 22, -18, -20, 2, -22, 4, 17, -9],\n [8, -20, 10, 9, 13, 13, -10, -24, -18],\n [-11, 1, -10, -25, -16, -19, 22, -16, -14],\n [-9, 19, -14, -11, 20, 25, 6, 6, 25],\n [0, -12, 24, 0, -21, 12, 24, 20, -22],\n [2, -25, -13, 17, -23, 23, 24, -1, 16],\n [-10, -5, -13, 18, 10, -18, 18, -7, 21],\n [-10, -14, -6, -8, -14, 22, -1, -15, -4],\n [20, 8, -13, 20, 12, -14, 13, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-98", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 2, -12, -2, 8, 12, 19, -3, -18],\n [2, 0, 20, -7, 18, -2, -1, 8, -4],\n [-12, 20, 3, -12, 18, 22, 6, -6, -20],\n [-2, -7, -12, -12, 16, 2, 3, -17, 0],\n [8, 18, 18, 16, -17, 8, -4, 12, 2],\n [12, -2, 22, 2, 8, 24, 4, 8, 10],\n [19, -1, 6, 3, -4, 4, -11, 1, 8],\n [-3, 8, -6, -17, 12, 8, 1, 24, 2],\n [-18, -4, -20, 0, 2, 10, 8, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-15, -8, -2, -14, 10, -3, 15, -18, -5],\n [-8, -2, -2, 14, -7, -1, 4, 7, -7],\n [-2, -2, -14, -11, -8, 2, 4, -4, 7],\n [-14, 14, -11, -19, 6, 5, 1, 3, 10],\n [10, -7, -8, 6, 1, -6, 4, -1, -21],\n [-3, -1, 2, 5, -6, -3, -12, 4, 1],\n [15, 4, 4, 1, 4, -12, 5, -2, 11],\n [-18, 7, -4, 3, -1, 4, -2, -22, 15],\n [-5, -7, 7, 10, -21, 1, 11, 15, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-284", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, -11, -7, 4, 12, 6, 14, 3, -20],\n [0, 1, 9, 2, -21, 15, 22, -10, 15],\n [0, 0, 17, -1, -16, 3, -16, -20, -10],\n [0, 0, 0, 11, 8, -7, 7, -22, 18],\n [0, 0, 0, 0, -24, 23, -24, 10, -20],\n [0, 0, 0, 0, 0, 20, -10, 17, 18],\n [0, 0, 0, 0, 0, 0, 15, -12, 18],\n [0, 0, 0, 0, 0, 0, 0, 13, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "675", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, -6, -10, -3, 0, 11, -6, -5, -19],\n [-6, -1, 6, -2, -4, 2, 7, 9, 18],\n [-10, 6, 2, 10, 22, -6, 10, -11, -5],\n [-3, -2, 10, 22, 7, 13, -17, 10, -20],\n [0, -4, 22, 7, -18, 5, 11, 0, -8],\n [11, 2, -6, 13, 5, 15, 8, 6, -16],\n [-6, 7, 10, -17, 11, 8, -13, -14, 2],\n [-5, 9, -11, 10, 0, 6, -14, 8, -1],\n [-19, 18, -5, -20, -8, -16, 2, -1, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-75", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-12, 14, -12, -5, 23, 1, 20, 0, 1],\n [-2, -21, 16, 12, 2, 16, 17, 6, -2],\n [-20, -16, 20, -23, -19, 3, 8, -19, -9],\n [-13, -5, 5, -17, 19, 21, -13, -9, -18],\n [-17, -17, 14, 22, 4, -19, -9, 13, 12],\n [-21, -9, 14, -25, -10, -9, 4, 5, 9],\n [19, -18, 22, 4, 13, -5, -11, 8, 1],\n [-24, -16, -21, 1, -22, 21, -13, -9, -5],\n [-3, 7, 24, -11, -12, -17, 18, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-63", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[3, -3, 8, -19, -17, 24, -22, -24, 1],\n [0, 6, 18, 19, 20, 11, 1, 2, -23],\n [0, 0, 25, 17, -18, 18, 24, 24, 15],\n [0, 0, 0, 12, -4, -12, -11, 20, -22],\n [0, 0, 0, 0, 16, 24, -9, -7, 10],\n [0, 0, 0, 0, 0, -19, 16, -18, -2],\n [0, 0, 0, 0, 0, 0, -14, 1, 20],\n [0, 0, 0, 0, 0, 0, 0, 5, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5339", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 20, -13, -22, -24, 8, 17, -4, -21],\n [-17, -6, -5, -9, -14, 2, -8, -23, -21],\n [-12, 22, 0, -7, 15, -9, 13, 16, -22],\n [16, 9, -2, 15, -13, 7, -11, -11, 5],\n [17, 2, -16, -19, 7, -19, -21, 0, -10],\n [-18, -4, 8, 14, 2, 20, 10, 21, -19],\n [14, 17, 2, -24, -17, -20, -25, -23, -16],\n [11, 18, -3, 7, -17, -13, 2, 25, -19],\n [0, -10, 14, 0, 25, 13, 6, 10, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-182", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, 23, -5, -13, 25, 0, 19, -17, 11],\n [-3, -25, -24, 17, 2, 10, 5, 15, -21],\n [11, -1, -18, 8, 13, 23, 6, -15, 21],\n [-1, -23, 19, 24, 6, 9, 6, 8, 11],\n [-21, 19, 2, 2, -18, 1, -10, -8, -1],\n [22, -25, -18, -5, 8, -2, 11, 0, 21],\n [-12, 3, 4, -23, -19, 10, -15, 6, -14],\n [-11, 12, -2, -25, -8, 20, -19, 16, 15],\n [-24, 14, 5, 7, 4, 5, 8, -19, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -21, -8, -22, -25, 24, -6, -20, -6],\n [0, 20, 1, 0, 6, -16, -8, 15, -14],\n [0, 0, -2, 25, 12, 20, -1, -18, -12],\n [0, 0, 0, -10, -6, 12, 21, -11, -12],\n [0, 0, 0, 0, 20, -21, 1, 15, -13],\n [0, 0, 0, 0, 0, -24, -19, 22, -15],\n [0, 0, 0, 0, 0, 0, 6, 22, -5],\n [0, 0, 0, 0, 0, 0, 0, -11, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26633", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-21, -22, -12, -10, -4, 19, 8, -10, -11],\n [-22, -15, -9, -4, -5, 19, 19, -6, -2],\n [-12, -9, 2, -10, 0, -14, 1, 17, 8],\n [-10, -4, -10, 17, 0, 14, 8, -4, 6],\n [-4, -5, 0, 0, -21, 11, -11, -12, 5],\n [19, 19, -14, 14, 11, 8, 13, 4, 0],\n [8, 19, 1, 8, -11, 13, 18, 9, -12],\n [-10, -6, 17, -4, -12, 4, 9, -14, -8],\n [-11, -2, 8, 6, 5, 0, -12, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3453", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, 4, -4, 10, -14, -10, -14, -1, 8],\n [4, -11, 17, 3, 3, 0, -11, -2, -19],\n [-4, 17, 7, -14, -4, -6, 2, 0, 8],\n [10, 3, -14, -4, 4, 4, -4, -2, 14],\n [-14, 3, -4, 4, 5, -10, 7, 12, -2],\n [-10, 0, -6, 4, -10, -12, -8, 6, -10],\n [-14, -11, 2, -4, 7, -8, -12, 4, -3],\n [-1, -2, 0, -2, 12, 6, 4, -8, 9],\n [8, -19, 8, 14, -2, -10, -3, 9, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1183", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -5, -20, -10, 9, 21, -6, 16, 15],\n [0, 6, -12, -2, 18, 13, 17, 5, -9],\n [0, 0, -4, 19, 22, 9, 11, -9, 2],\n [0, 0, 0, -13, 21, 6, 2, 5, -18],\n [0, 0, 0, 0, 11, 22, -1, 25, 7],\n [0, 0, 0, 0, 0, 22, 20, 6, -21],\n [0, 0, 0, 0, 0, 0, -5, -24, -5],\n [0, 0, 0, 0, 0, 0, 0, -24, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-495", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -24, -24, -3, 21, -15, 3, 16, 9],\n [23, -17, 6, 4, -11, -12, 25, -9, -4],\n [4, -9, -10, -18, 13, 5, -14, 7, -14],\n [-1, 12, 22, -8, -7, -23, 9, -21, 9],\n [25, 1, 11, 20, -5, -10, 2, -1, 7],\n [-9, 17, 4, 15, -22, -24, -17, 5, -1],\n [11, 10, -21, -2, -2, 3, 24, 19, 5],\n [11, -7, -3, 9, 24, -20, -20, 11, 4],\n [-25, -18, 2, -1, 7, 12, -12, -15, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-329", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 4, -22, -13, -19, 12, -23, -17, -12],\n [-15, 11, -12, -7, -18, -19, -19, -23, -23],\n [-8, 19, 7, 11, 2, 10, -10, -11, 3],\n [-8, 23, 20, 20, -7, 3, -20, 19, 24],\n [21, 1, -19, 1, -7, -9, 15, -15, -21],\n [-24, 21, -14, 16, 16, -15, -16, 2, -19],\n [-12, -13, -21, 25, 16, -18, 24, -25, -21],\n [-15, 17, 22, -16, -11, 13, 21, 3, -1],\n [22, -20, -15, -9, -11, -10, -24, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[12, 24, -5, -15, 15, -23, 8, -8, -11],\n [0, 24, 25, -11, 4, -9, -8, 5, 24],\n [0, 0, 9, -13, -12, 10, -8, -21, -12],\n [0, 0, 0, -14, 14, 2, 9, -25, -23],\n [0, 0, 0, 0, 10, -3, -2, -16, 24],\n [0, 0, 0, 0, 0, -4, -23, 14, 1],\n [0, 0, 0, 0, 0, 0, 10, 3, -15],\n [0, 0, 0, 0, 0, 0, 0, -3, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-120", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-11, -3, 23, -23, -8, 17, 0, -20, 18],\n [-9, 20, 12, 16, 22, 24, 1, -6, -20],\n [25, 9, -14, 22, -23, 22, -22, 19, -22],\n [-22, 13, -5, 18, -24, -10, -19, -7, 17],\n [7, -17, 11, -9, 1, 7, 23, -14, 19],\n [-15, -13, 5, -13, 12, 0, 5, -4, -20],\n [-6, -5, -16, -7, 9, 0, -19, 11, -18],\n [-21, 18, 10, 25, 2, 24, -23, 13, -18],\n [-11, 1, 23, 25, 10, -10, 0, 19, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-22, -14, -9, 15, 18, 0, 5, -11, 8],\n [3, -17, -12, 10, -22, 12, 11, -2, -9],\n [-13, -6, -9, 25, 1, 7, -5, -9, -4],\n [-1, -23, 1, 1, 20, -14, -11, 12, -6],\n [-4, -24, -22, 19, -13, 6, -4, -1, 1],\n [-9, -20, 17, 25, -10, -18, 7, -16, 8],\n [-7, -12, -23, 15, -3, 14, -15, 21, -20],\n [8, -25, 9, -1, 3, -3, -8, -12, -9],\n [-24, 5, -7, 6, 2, 15, -18, 16, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[14, 13, -4, -2, 12, -24, 15, 15, -7],\n [0, -24, 2, 6, -7, -10, 4, -4, -12],\n [0, 0, -24, -4, 20, 7, -11, 24, 15],\n [0, 0, 0, 15, 15, -15, -22, -19, -5],\n [0, 0, 0, 0, -9, -6, 5, 0, 5],\n [0, 0, 0, 0, 0, -5, -10, 25, -10],\n [0, 0, 0, 0, 0, 0, 11, 14, -10],\n [0, 0, 0, 0, 0, 0, 0, -21, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18669", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, 17, -8, 0, -5, 4, -18, 3, -11],\n [17, 8, -13, 6, -6, 1, -2, 0, 16],\n [-8, -13, 16, 14, 1, -1, 3, -2, -4],\n [0, 6, 14, -25, -4, -16, -4, -2, -2],\n [-5, -6, 1, -4, 15, -4, -8, -2, -6],\n [4, 1, -1, -16, -4, 1, -3, 6, -8],\n [-18, -2, 3, -4, -8, -3, 13, -2, 2],\n [3, 0, -2, -2, -2, 6, -2, -4, -20],\n [-11, 16, -4, -2, -6, -8, 2, -20, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "249", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 1) of the inverse of matrix 1/450 * A where A =\n[[-7, -8, -4, -4, -2, 3, 1, -2, -4],\n [-8, -3, 0, -1, 0, 2, -24, 22, 4],\n [-4, 0, 22, -4, -16, 0, 2, 5, -15],\n [-4, -1, -4, -10, -16, 6, -14, 0, -2],\n [-2, 0, -16, -16, -4, 10, 9, -2, -1],\n [3, 2, 0, 6, 10, 19, 20, 4, 6],\n [1, -24, 2, -14, 9, 20, 5, -16, -10],\n [-2, 22, 5, 0, -2, 4, -16, -8, 1],\n [-4, 4, -15, -2, -1, 6, -10, 1, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-24, -2, -20, 2, -10, 0, -6, -24, -2],\n [-2, -23, 3, 16, -18, -10, 22, 4, -4],\n [-20, 3, 2, 14, -8, -13, -2, -20, 0],\n [2, 16, 14, 1, -2, 0, 17, 19, -2],\n [-10, -18, -8, -2, -1, 18, -8, 4, -10],\n [0, -10, -13, 0, 18, 25, -9, 13, 12],\n [-6, 22, -2, 17, -8, -9, -18, 14, -9],\n [-24, 4, -20, 19, 4, 13, 14, -2, -12],\n [-2, -4, 0, -2, -10, 12, -9, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-16, 12, -6, 1, 6, 2, -12, 7, 2],\n [12, -14, -10, -6, 4, -22, -8, -8, -10],\n [-6, -10, -18, 18, 8, -1, -1, -6, 2],\n [1, -6, 18, -1, 4, 16, -2, 24, -6],\n [6, 4, 8, 4, 0, 2, -4, -14, 2],\n [2, -22, -1, 16, 2, 16, -16, 0, 12],\n [-12, -8, -1, -2, -4, -16, -11, -2, -6],\n [7, -8, -6, 24, -14, 0, -2, 23, -10],\n [2, -10, 2, -6, 2, 12, -6, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[2, -5, -3, -15, -24, -6, -2, -1, 11],\n [0, -2, -11, -14, 20, 5, 17, 5, 4],\n [0, 0, -18, 18, 4, 9, -5, 21, 14],\n [0, 0, 0, -14, 24, -8, 21, 2, -23],\n [0, 0, 0, 0, 23, 5, 5, -25, -15],\n [0, 0, 0, 0, 0, 18, -7, 19, -13],\n [0, 0, 0, 0, 0, 0, 11, 5, 5],\n [0, 0, 0, 0, 0, 0, 0, -5, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16491", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[12, 15, 5, -18, -3, 24, -1, 21, -25],\n [0, -8, -7, 25, 16, -20, -9, 20, 19],\n [0, 0, -17, 11, 1, 10, -20, -20, 19],\n [0, 0, 0, 1, 11, -24, -17, -15, -6],\n [0, 0, 0, 0, 12, 4, 10, 12, 9],\n [0, 0, 0, 0, 0, 6, 3, -3, 10],\n [0, 0, 0, 0, 0, 0, 18, 18, 1],\n [0, 0, 0, 0, 0, 0, 0, 13, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5035", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -2, -12, 2, -10, 6, 21, -14, -10],\n [-7, -21, -14, 3, -21, 16, -9, 21, -18],\n [14, 14, 4, -16, -6, 19, -10, 15, -10],\n [16, -23, -3, -4, 2, 20, 19, 10, -22],\n [12, -2, -7, -15, 14, 20, 14, 20, 13],\n [-8, -14, -12, 21, -8, 18, 16, -14, 14],\n [1, -20, -2, 25, 7, 19, -10, 24, -14],\n [5, 11, -13, -18, 12, -23, -6, -22, 18],\n [19, -24, 25, 10, -3, 19, -7, 14, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-394", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-10, 17, -8, 10, -2, -25, -25, 20, 10],\n [-15, -8, -10, -9, -2, 8, -22, 9, -11],\n [-24, 25, 5, -17, -16, -1, 25, -21, -12],\n [16, 22, 12, 14, -24, -8, 3, -6, -18],\n [11, 23, 22, 0, 11, 23, -22, 7, -4],\n [-20, 7, 2, -2, -22, -24, -13, 20, 23],\n [-15, 9, 13, -16, 17, -16, -18, -21, -3],\n [8, 21, 6, -10, -22, 2, 22, 18, -12],\n [-14, -5, 22, -10, 18, -24, -3, 3, 20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "549", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 6) rounded to the nearest integer?\n[[17, -17, -19, 3, 18, -9, -17, -20, 18],\n [0, -16, -17, -14, 7, 6, 8, -7, 7],\n [0, 0, 24, 24, -3, 0, 19, 18, 15],\n [0, 0, 0, -13, 22, 16, -10, 20, -24],\n [0, 0, 0, 0, -15, -12, 21, -1, -19],\n [0, 0, 0, 0, 0, -18, 4, 10, 24],\n [0, 0, 0, 0, 0, 0, -5, 12, -15],\n [0, 0, 0, 0, 0, 0, 0, -7, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (5, 8) rounded to the nearest integer?\n[[4, -12, 7, 16, -19, -8, -14, -24, 24],\n [0, -5, -19, 1, -14, -6, -12, -16, 15],\n [0, 0, 21, 5, -16, -7, -7, 18, -3],\n [0, 0, 0, -6, -22, 7, 22, -25, -13],\n [0, 0, 0, 0, 15, 10, -24, -4, -4],\n [0, 0, 0, 0, 0, 9, 24, -17, 21],\n [0, 0, 0, 0, 0, 0, 7, -15, 11],\n [0, 0, 0, 0, 0, 0, 0, 16, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 23, -9, -5, -10, 0, -17, -24, 17],\n [-11, 9, -2, 22, 25, 12, -12, 11, 11],\n [-20, -8, -4, -8, 25, -24, 6, -9, -25],\n [-17, -13, 10, 11, 4, 5, -3, 24, 2],\n [-16, -1, 10, 0, 0, 19, -13, -9, 14],\n [-22, -3, 9, -15, -14, -17, -11, 19, 11],\n [-21, -7, -15, -17, 9, 24, 1, -13, -14],\n [-17, 16, 2, -13, -6, -13, 1, 0, 3],\n [3, -4, -17, -2, 16, -7, 12, 5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 8, 11, 0, 5, 10, 6, 14, -2],\n [8, -20, 13, -16, 14, 16, 19, -10, 2],\n [11, 13, 2, -6, -11, 2, -4, -13, 10],\n [0, -16, -6, -1, -4, -2, -18, 13, 20],\n [5, 14, -11, -4, -15, 14, 6, -22, -5],\n [10, 16, 2, -2, 14, -21, -17, 4, 1],\n [6, 19, -4, -18, 6, -17, 11, 0, -6],\n [14, -10, -13, 13, -22, 4, 0, -1, -6],\n [-2, 2, 10, 20, -5, 1, -6, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[19, -2, -4, -6, 8, -14, -18, -18, -20],\n [-2, 20, -2, 8, 11, 14, 6, 7, 0],\n [-4, -2, 19, 0, -2, -9, 0, -2, 4],\n [-6, 8, 0, -3, 12, 16, 0, 22, -4],\n [8, 11, -2, 12, -21, -4, 9, -5, -12],\n [-14, 14, -9, 16, -4, -13, -12, -10, 0],\n [-18, 6, 0, 0, 9, -12, -20, -3, 0],\n [-18, 7, -2, 22, -5, -10, -3, 19, 2],\n [-20, 0, 4, -4, -12, 0, 0, 2, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "518", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, 8, -20, -20, 22, -6, 13, 10, 8],\n [8, 15, -2, -24, 6, -2, 2, 0, 8],\n [-20, -2, 10, -3, -8, -4, 8, -2, 16],\n [-20, -24, -3, 5, -4, 10, 18, 0, -16],\n [22, 6, -8, -4, 0, 0, 4, 16, 16],\n [-6, -2, -4, 10, 0, -18, 0, -16, -4],\n [13, 2, 8, 18, 4, 0, 18, 16, -14],\n [10, 0, -2, 0, 16, -16, 16, -11, 3],\n [8, 8, 16, -16, 16, -4, -14, 3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-48", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[8, -8, 4, -22, -11, -6, 13, -9, -4],\n [-8, -25, 1, 10, 16, 8, 12, 1, -4],\n [4, 1, -9, -22, -18, 13, 22, 1, 3],\n [-22, 10, -22, -16, -5, -4, 16, -16, 10],\n [-11, 16, -18, -5, 1, 14, -2, -4, 2],\n [-6, 8, 13, -4, 14, 6, 6, 20, -10],\n [13, 12, 22, 16, -2, 6, 23, -15, 10],\n [-9, 1, 1, -16, -4, 20, -15, 21, 0],\n [-4, -4, 3, 10, 2, -10, 10, 0, -24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-10, -25, -22, 21, -25, 21, 9, -13, 24],\n [0, 16, 5, -6, -19, 14, 7, 2, 24],\n [0, 0, 18, -6, 6, -17, 8, -12, -22],\n [0, 0, 0, -7, 12, -17, 1, 23, -11],\n [0, 0, 0, 0, -5, 8, -7, 11, -22],\n [0, 0, 0, 0, 0, -14, 15, -10, -12],\n [0, 0, 0, 0, 0, 0, 20, -4, -14],\n [0, 0, 0, 0, 0, 0, 0, -12, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, -19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-217", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[6, -1, 5, -10, 15, -12, -1, 4, -19],\n [-14, -23, 1, 20, -7, 17, 11, 19, 16],\n [-19, 23, -10, 6, -18, 23, -13, -15, -6],\n [-8, 11, -20, -6, 6, 20, 18, 3, -22],\n [-19, 17, -6, 8, 10, -19, 7, -11, 6],\n [-4, 14, 3, -1, -21, -12, 24, 9, -24],\n [-1, -10, 20, -10, -15, 23, 9, -3, -21],\n [9, 3, 21, -21, -23, -20, -3, 20, -24],\n [-8, 4, 12, -21, 20, 23, -15, -25, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[15, 18, 0, 7, 1, 24, -14, -24, -25],\n [-25, 7, -4, -14, 13, 10, -5, -6, 10],\n [0, 21, 5, -25, 12, -12, 0, 20, 16],\n [-19, -14, -2, -7, -17, 9, -22, 19, 16],\n [6, 20, -20, 2, 2, 14, 25, 3, 16],\n [-21, -21, 11, 15, 2, 15, 21, -17, 3],\n [-12, 12, 14, 8, 11, 23, 16, -12, -8],\n [7, 8, 2, 10, 19, 22, 11, -3, 16],\n [-9, -15, 6, 11, -11, -22, 13, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-3, -10, 0, -20, 6, 6, -14, -2, -18],\n [-10, 14, -12, 16, -10, -15, -10, -5, -6],\n [0, -12, -9, -4, 2, -15, 8, 16, 6],\n [-20, 16, -4, 23, -12, -5, 10, 0, 0],\n [6, -10, 2, -12, 17, 12, -2, -14, -5],\n [6, -15, -15, -5, 12, 10, -2, 10, -4],\n [-14, -10, 8, 10, -2, -2, -18, 14, 18],\n [-2, -5, 16, 0, -14, 10, 14, 16, 12],\n [-18, -6, 6, 0, -5, -4, 18, 12, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-366", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 9) of the inverse of matrix 1/450 * A where A =\n[[13, -11, -24, -18, 18, 17, -20, -6, 1],\n [19, -3, 22, 14, -9, -13, -22, -6, 16],\n [-1, -4, 22, -9, 14, -15, -1, -21, -5],\n [0, -10, 14, -5, 22, 6, -22, 12, -18],\n [-17, 19, -9, 15, -13, -17, -20, 1, 16],\n [11, 13, 17, -2, -17, 16, -15, 9, 3],\n [-18, -9, -19, -14, 22, -11, 3, 19, 24],\n [24, -2, 11, -12, -15, 9, -9, 1, 18],\n [-23, -24, -22, -8, -6, -5, -12, -18, -24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[10, -7, -24, 8, -9, -2, -17, -25, 16],\n [0, -11, -5, -11, -3, -24, 20, 10, 24],\n [0, 0, -24, -8, -9, 15, -18, 8, 8],\n [0, 0, 0, 2, -10, -12, -24, 14, -22],\n [0, 0, 0, 0, 25, 8, 5, 22, -15],\n [0, 0, 0, 0, 0, -13, 1, -18, 21],\n [0, 0, 0, 0, 0, 0, -23, -19, -12],\n [0, 0, 0, 0, 0, 0, 0, -8, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8133", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[25, -2, -24, -8, -8, -9, -2, -4, 2],\n [-2, 22, 4, -4, -4, 6, 4, 6, 0],\n [-24, 4, 10, -10, 7, 6, 20, 16, -3],\n [-8, -4, -10, 6, 8, 2, 16, -14, 4],\n [-8, -4, 7, 8, -2, 0, -6, 4, 2],\n [-9, 6, 6, 2, 0, -15, -5, -10, -14],\n [-2, 4, 20, 16, -6, -5, 15, 2, 20],\n [-4, 6, 16, -14, 4, -10, 2, 2, 2],\n [2, 0, -3, 4, 2, -14, 20, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[16, -8, 1, -2, -16, -10, 0, -16, 6],\n [-8, -15, -2, 2, -18, 12, 4, 6, 20],\n [1, -2, -22, -8, 18, -14, -7, -8, 6],\n [-2, 2, -8, 2, 8, 0, 0, -11, -5],\n [-16, -18, 18, 8, -7, 11, -6, -10, 0],\n [-10, 12, -14, 0, 11, 15, 4, 14, 8],\n [0, 4, -7, 0, -6, 4, -13, -4, -4],\n [-16, 6, -8, -11, -10, 14, -4, -3, -10],\n [6, 20, 6, -5, 0, 8, -4, -10, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[-15, -22, 0, 20, -21, 10, 7, -12, 6],\n [0, -16, -24, -16, 9, -5, 14, 16, -18],\n [0, 0, -17, 15, 4, -22, 9, -12, -12],\n [0, 0, 0, 3, -3, 21, -5, 5, 6],\n [0, 0, 0, 0, -18, -14, 10, -10, 0],\n [0, 0, 0, 0, 0, 5, 20, 15, -8],\n [0, 0, 0, 0, 0, 0, 11, -12, 13],\n [0, 0, 0, 0, 0, 0, 0, 22, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[14, 2, -3, 6, 22, -21, 0, 13, 0],\n [-23, -2, 8, 8, -6, 4, 16, -6, 15],\n [-8, 12, -6, -20, 16, -1, 15, 15, -23],\n [18, 17, 20, -7, -16, 25, -21, -4, -17],\n [7, -11, -2, 4, 10, 13, -20, -11, 12],\n [13, -4, -23, 3, 3, 5, 19, -24, 9],\n [19, -17, -4, -7, 24, 11, -16, 20, -5],\n [-9, -23, -19, 15, 11, 10, -23, -13, 15],\n [4, -3, -19, 4, 3, -18, -16, 7, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, 3, -5, -25, 25, 8, 18, 6, 19],\n [0, 11, 9, -2, 23, -25, 20, -20, 23],\n [0, 0, -25, 15, 5, 10, -17, 15, 19],\n [0, 0, 0, 23, -5, -23, 0, -20, -6],\n [0, 0, 0, 0, -3, -11, 20, 5, -22],\n [0, 0, 0, 0, 0, 22, 13, 17, 18],\n [0, 0, 0, 0, 0, 0, -13, -21, 4],\n [0, 0, 0, 0, 0, 0, 0, -11, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 7) of the inverse. Round your answer to the nearest integer:\n[[6, -7, -17, -8, -11, 9, -11, 3, 8],\n [-7, -25, -2, -4, -11, 12, 6, 5, 10],\n [-17, -2, -5, 21, -7, 4, 5, -6, -4],\n [-8, -4, 21, 6, -14, 12, -8, 1, -15],\n [-11, -11, -7, -14, -2, -6, 0, 8, -8],\n [9, 12, 4, 12, -6, -21, 0, 0, -10],\n [-11, 6, 5, -8, 0, 0, 24, 9, 6],\n [3, 5, -6, 1, 8, 0, 9, -5, -6],\n [8, 10, -4, -15, -8, -10, 6, -6, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-24, 9, 12, 19, -11, 17, 16, -23, 5],\n [0, 16, -3, -14, -18, -5, -5, 6, -9],\n [0, 0, -18, -8, -15, -16, 0, 21, -20],\n [0, 0, 0, 16, 11, 2, -10, -14, -5],\n [0, 0, 0, 0, 7, -24, 11, -7, 2],\n [0, 0, 0, 0, 0, 9, 6, 2, -17],\n [0, 0, 0, 0, 0, 0, -4, 14, 13],\n [0, 0, 0, 0, 0, 0, 0, 8, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[15, 22, 6, -2, -23, 1, -17, 14, -3],\n [-19, -9, 11, -19, 4, -13, -8, 5, -4],\n [-12, -8, 9, -9, -7, 5, 13, 10, -11],\n [3, 14, -10, 7, -1, -10, 4, 8, -24],\n [14, 18, 17, 12, 25, -8, -21, 21, 14],\n [-20, -14, 25, -14, -14, -17, 16, -4, 23],\n [24, -10, -22, 24, -23, -10, -12, 15, 12],\n [-22, -24, -16, -15, 13, 0, 11, 0, -22],\n [0, 12, 2, -24, -24, -10, -3, -3, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 5, 7, 14, 8, -2, 0, -1, -17],\n [5, -22, 4, 12, -2, 0, -4, -4, 2],\n [7, 4, -21, -4, 22, -10, -4, 2, -10],\n [14, 12, -4, -2, 14, 4, 0, -2, 6],\n [8, -2, 22, 14, -17, 0, 4, 16, 0],\n [-2, 0, -10, 4, 0, -11, 17, -2, 2],\n [0, -4, -4, 0, 4, 17, -15, -10, -24],\n [-1, -4, 2, -2, 16, -2, -10, -12, -7],\n [-17, 2, -10, 6, 0, 2, -24, -7, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-113", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, -1, -4, 17, -16, 24, 7, 23, 22],\n [18, 4, 4, -10, -17, -9, 9, 24, 21],\n [-11, 22, 2, -6, 7, 7, 10, -13, -22],\n [-3, -18, -13, -2, 14, 20, 4, 4, -1],\n [7, -17, 0, -2, 7, 13, -1, 19, -11],\n [15, 22, 23, 15, -20, -6, 18, -10, -5],\n [-11, 13, 16, -22, -2, -23, 24, -25, 4],\n [-13, -8, 14, -15, 16, 3, -22, -1, 10],\n [10, 18, 14, 2, 19, -18, -5, 9, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "590", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 21, -1, 20, 15, -21, 21, -18, -3],\n [-23, 18, 11, 5, 3, 15, -6, -23, -3],\n [14, -5, -13, -18, -21, -1, 13, 11, 15],\n [-21, -18, 18, -22, 15, -4, -12, -7, -13],\n [9, -22, 7, -4, -25, -15, -10, -22, 3],\n [13, 18, 12, -2, -17, -18, -12, -11, -4],\n [11, -11, -20, -25, -6, 15, 10, -24, -20],\n [-24, -23, -19, -6, 23, 15, 15, 25, -21],\n [-1, 12, -8, -25, -1, -9, 20, -11, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1875", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 7) rounded to the nearest integer?\n[[-9, -5, -3, 17, -16, -9, -25, 11, 22],\n [-19, -14, 14, 24, -25, -6, 18, 5, -22],\n [0, -14, -4, -25, -25, -23, -14, -5, -13],\n [-13, 15, -8, 7, -20, -1, -3, -2, 11],\n [0, -22, 12, 9, 23, -15, 10, -1, -6],\n [-25, 4, -22, -3, 9, 16, -4, 5, -25],\n [-22, -7, 4, -25, 22, -7, -5, -4, 24],\n [-24, -20, -5, 7, -7, 1, 11, 3, 2],\n [8, -25, 22, -1, -5, 8, 0, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 4, 6, 11, -1, 6, 3, 8, -8],\n [4, 11, 2, -5, -10, -15, 8, -16, -12],\n [6, 2, -24, -4, -10, -2, -9, 12, 8],\n [11, -5, -4, -11, 0, 3, 10, -14, 0],\n [-1, -10, -10, 0, -3, -8, -8, 0, 0],\n [6, -15, -2, 3, -8, 12, 0, 2, 10],\n [3, 8, -9, 10, -8, 0, 19, -4, -3],\n [8, -16, 12, -14, 0, 2, -4, -18, 20],\n [-8, -12, 8, 0, 0, 10, -3, 20, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "634", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[17, 11, 8, 17, 0, 8, 11, -12, -16],\n [11, -12, 11, -6, -14, -4, 4, 20, 14],\n [8, 11, -6, 2, 4, -1, -20, -6, 10],\n [17, -6, 2, 20, -2, -2, -12, -8, 12],\n [0, -14, 4, -2, 1, 18, 15, -1, 4],\n [8, -4, -1, -2, 18, -23, 6, 9, 6],\n [11, 4, -20, -12, 15, 6, -2, -2, -13],\n [-12, 20, -6, -8, -1, 9, -2, 15, 1],\n [-16, 14, 10, 12, 4, 6, -13, 1, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 1, 10, -9, 23, -5, 11, 5, 19],\n [0, 1, -3, 6, -9, -15, -25, 2, -8],\n [0, 0, -6, -19, 11, -10, 13, 19, 19],\n [0, 0, 0, 23, -9, -7, 16, 8, -12],\n [0, 0, 0, 0, 23, -11, -7, 17, -11],\n [0, 0, 0, 0, 0, -7, -2, 3, -21],\n [0, 0, 0, 0, 0, 0, 3, -10, 10],\n [0, 0, 0, 0, 0, 0, 0, -17, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the inverse of matrix 1/450 * A where A =\n[[-10, -25, 16, -8, -4, 0, -12, 11, 23],\n [-12, 0, 24, 10, -3, -24, 13, -19, 13],\n [19, 25, -4, 2, 12, -6, 23, -8, -2],\n [7, 19, 0, -7, 22, 16, -13, -16, -12],\n [-17, -15, -23, 14, -14, 9, 13, 20, 13],\n [6, 13, -12, 18, -25, 1, 11, 17, -25],\n [19, 3, -2, -9, 9, 5, 16, 6, -7],\n [5, 13, -6, 2, -23, 6, -4, 18, 16],\n [18, -11, 12, -7, 5, 0, -21, -6, -24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, 5, 8, 4, -10, -3, -1, 16, -4],\n [5, -23, 16, -12, 9, 22, 10, -4, 10],\n [8, 16, 16, -6, -4, -2, 16, -8, 10],\n [4, -12, -6, 21, 18, 18, 6, -18, -7],\n [-10, 9, -4, 18, 7, 10, 6, -10, 4],\n [-3, 22, -2, 18, 10, -9, -22, -4, -20],\n [-1, 10, 16, 6, 6, -22, 18, -18, 4],\n [16, -4, -8, -18, -10, -4, -18, 15, -4],\n [-4, 10, 10, -7, 4, -20, 4, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-21, 19, -20, -4, -9, -11, 13, 14, 2],\n [0, -8, 1, -5, -3, -19, 22, -7, -17],\n [0, 0, 4, -19, -24, -9, -15, 24, -14],\n [0, 0, 0, -11, 25, 16, 15, -16, 10],\n [0, 0, 0, 0, -1, 1, 7, -15, -13],\n [0, 0, 0, 0, 0, 13, -3, -16, 22],\n [0, 0, 0, 0, 0, 0, 21, -16, -10],\n [0, 0, 0, 0, 0, 0, 0, -10, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8088", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[11, -12, 17, -10, 2, -1, -1, -4, 14],\n [-12, 6, 0, -6, -2, 0, -2, -12, -11],\n [17, 0, 12, 18, -7, 3, 20, -20, -10],\n [-10, -6, 18, -17, -18, 12, -4, 8, -5],\n [2, -2, -7, -18, -3, -2, -2, -10, -6],\n [-1, 0, 3, 12, -2, 8, -16, 6, 2],\n [-1, -2, 20, -4, -2, -16, 1, -18, 4],\n [-4, -12, -20, 8, -10, 6, -18, -12, -14],\n [14, -11, -10, -5, -6, 2, 4, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1383", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[9, 6, 9, 9, 2, -22, 2, -1, 4],\n [6, 13, -3, -12, -1, -8, 8, -12, 4],\n [9, -3, 6, -14, -4, -14, -6, -2, 6],\n [9, -12, -14, 7, -19, 8, 20, 0, -6],\n [2, -1, -4, -19, 7, -1, 2, -14, -7],\n [-22, -8, -14, 8, -1, 13, 4, -2, -6],\n [2, 8, -6, 20, 2, 4, -2, 2, -2],\n [-1, -12, -2, 0, -14, -2, 2, -9, 0],\n [4, 4, 6, -6, -7, -6, -2, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-47", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 9) of the inverse of matrix 1/450 * A where A =\n[[-7, -10, -14, 10, 8, -4, -7, 5, -6],\n [-10, 3, 16, 0, 2, -6, -2, 14, -5],\n [-14, 16, 17, 0, 4, 4, 5, -4, -8],\n [10, 0, 0, 21, 8, -2, 5, 8, 0],\n [8, 2, 4, 8, 21, -14, 4, 4, 6],\n [-4, -6, 4, -2, -14, 10, 2, 4, 6],\n [-7, -2, 5, 5, 4, 2, -8, 5, -19],\n [5, 14, -4, 8, 4, 4, 5, 6, 1],\n [-6, -5, -8, 0, 6, 6, -19, 1, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-14, 8, -3, -10, 23, -21, 18, 21, 2],\n [-20, -13, 17, 4, 0, -9, -17, -10, 23],\n [-8, -13, 3, 17, 19, -2, 19, 18, 20],\n [-13, -1, 15, 20, -25, -17, -22, 2, -14],\n [-2, 20, -17, 9, 12, 9, 7, 9, 20],\n [-6, -24, 18, 0, 16, -13, 4, 6, 10],\n [-7, -4, -25, -15, 0, 22, -7, -7, -14],\n [-23, -8, 23, -21, 22, -2, -12, 25, 12],\n [-23, -20, -14, -15, 13, 0, -25, -10, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1146", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[23, 21, -17, -21, -18, -5, 7, 13, 17],\n [0, 19, -4, -13, 13, -15, -8, 4, 7],\n [0, 0, -25, 10, -20, 11, 3, -15, -13],\n [0, 0, 0, -1, -11, -13, 16, 7, -13],\n [0, 0, 0, 0, -9, 24, -2, 0, 14],\n [0, 0, 0, 0, 0, 8, 1, 2, -4],\n [0, 0, 0, 0, 0, 0, -17, -13, -16],\n [0, 0, 0, 0, 0, 0, 0, -4, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-728", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -3, -1, -10, -2, 5, -15, -3, 15],\n [13, -4, 7, 15, 16, 22, -8, -12, 2],\n [-15, -2, 10, -7, -13, 7, -7, 21, 6],\n [-11, -15, -3, -21, -4, 16, -8, -19, 7],\n [-23, 2, -25, 23, 21, 11, -4, 22, 18],\n [-7, -12, -23, -7, 7, -5, -25, 0, -16],\n [9, -13, -20, 17, -20, 9, -10, 15, -18],\n [-23, -21, -5, 5, -12, 11, -7, 11, -6],\n [-24, -19, 7, 24, 16, -20, -19, 18, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-58", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[17, 3, -7, -1, -22, 25, -13, 6, 1],\n [25, 8, 2, -17, -18, -5, 20, 4, 3],\n [-17, -13, -8, 12, -4, 5, 9, 16, 16],\n [-16, -17, 5, 18, 14, -2, 15, 23, -18],\n [24, -6, -9, 2, -20, 16, 7, 2, -25],\n [15, 9, -2, -20, -19, -17, 11, -10, 8],\n [9, 9, -6, -3, 16, 9, 21, 20, -3],\n [-22, -16, 17, -15, 14, -17, 14, -14, -9],\n [6, -3, -11, 25, 2, 12, -21, 14, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-62", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -6, -23, 9, -2, 4, 8, -12, 0],\n [-6, 15, -5, 2, 18, 7, -8, -15, -3],\n [-23, -5, 5, -4, 12, 7, 20, -14, 14],\n [9, 2, -4, 0, 10, 10, 5, -9, 0],\n [-2, 18, 12, 10, -8, -2, 8, 6, -20],\n [4, 7, 7, 10, -2, -12, 22, -4, -8],\n [8, -8, 20, 5, 8, 22, -1, -16, 1],\n [-12, -15, -14, -9, 6, -4, -16, -9, 12],\n [0, -3, 14, 0, -20, -8, 1, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-448", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 0, -4, 6, -24, 15, -10, 0, 14],\n [0, 7, -14, -10, 2, 14, 22, -14, 7],\n [-4, -14, -6, 4, 2, -6, 15, -8, 2],\n [6, -10, 4, -3, 20, 18, -10, -14, 12],\n [-24, 2, 2, 20, -10, -2, 6, -9, 19],\n [15, 14, -6, 18, -2, 3, 7, 15, 2],\n [-10, 22, 15, -10, 6, 7, 12, 0, -2],\n [0, -14, -8, -14, -9, 15, 0, 11, 4],\n [14, 7, 2, 12, 19, 2, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-173", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, -6, 10, -13, 14, -15, -2, -7, -3],\n [5, 11, 11, -23, 8, 3, -23, -11, -19],\n [-23, 21, 17, -10, 19, 8, -6, 18, 13],\n [7, -12, 16, 9, -15, -6, 4, 2, -11],\n [12, 24, -13, 21, 9, 21, -2, -25, 16],\n [-2, 1, -8, 0, 3, -18, 18, 0, -21],\n [7, 14, -21, 23, 21, 10, -13, -9, -13],\n [-1, -24, -2, 10, -1, 8, -14, -7, 24],\n [16, 4, 11, 17, -25, -23, 23, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (6, 2) rounded to the nearest integer?\n[[20, 21, 22, 2, -22, -7, -2, 14, -20],\n [0, 6, 4, 9, -18, -21, 11, -14, -1],\n [0, 0, -2, -15, 16, 9, 14, -25, -18],\n [0, 0, 0, -15, -19, 4, 22, 13, -13],\n [0, 0, 0, 0, 17, -13, 11, -1, -3],\n [0, 0, 0, 0, 0, 4, 5, -13, 16],\n [0, 0, 0, 0, 0, 0, -18, -23, -7],\n [0, 0, 0, 0, 0, 0, 0, 11, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-23, -23, 1, -24, -23, -9, 20, 13, 12],\n [0, -7, -7, 18, -21, -21, -12, 1, 23],\n [0, 0, 14, 9, -5, -21, -2, 13, 24],\n [0, 0, 0, 20, 24, -13, 12, 19, -25],\n [0, 0, 0, 0, -10, 11, -10, -3, 0],\n [0, 0, 0, 0, 0, 7, 6, -17, -15],\n [0, 0, 0, 0, 0, 0, 4, -8, -14],\n [0, 0, 0, 0, 0, 0, 0, -11, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1560", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-4, -15, 10, 18, 3, 16, 6, -12, -8],\n [12, 11, 8, 19, -3, 6, 20, -23, 17],\n [-4, -3, -22, -13, 6, 3, 14, 14, 19],\n [-16, -13, 19, -9, 12, -24, -9, 18, 0],\n [12, 11, -21, -1, -17, 2, -4, 3, 9],\n [-6, -21, 13, 18, 6, 13, -16, 14, -9],\n [11, -11, -17, 6, -3, -15, -13, -8, 23],\n [-17, 16, -21, 17, -4, 6, 21, -24, -5],\n [2, -2, -2, -12, 11, 1, -2, -20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-69", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 7) rounded to the nearest integer?\n[[-11, -10, 11, -15, 3, 25, -20, 4, -16],\n [-10, -22, 2, -10, 10, 2, -10, -2, -16],\n [11, 2, -25, -13, 4, 7, 12, 2, 8],\n [-15, -10, -13, -18, -14, 18, 4, -8, 4],\n [3, 10, 4, -14, 24, 2, 8, 21, -13],\n [25, 2, 7, 18, 2, -23, 0, -14, 6],\n [-20, -10, 12, 4, 8, 0, -13, 21, 9],\n [4, -2, 2, -8, 21, -14, 21, 24, 0],\n [-16, -16, 8, 4, -13, 6, 9, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-17, -6, -9, -16, -12, 2, -16, -6, 4],\n [-6, -12, 10, -8, -4, 5, -18, -14, 14],\n [-9, 10, 22, -12, 10, -10, -14, 2, 16],\n [-16, -8, -12, 14, 22, 7, -1, 11, 14],\n [-12, -4, 10, 22, -8, -6, -18, -15, -5],\n [2, 5, -10, 7, -6, -3, -2, 22, -20],\n [-16, -18, -14, -1, -18, -2, 2, -8, -12],\n [-6, -14, 2, 11, -15, 22, -8, -18, 14],\n [4, 14, 16, 14, -5, -20, -12, 14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -1, -8, 8, 12, -23, -6, -7, -13],\n [-9, -12, 4, -4, 17, 22, 17, 3, 24],\n [-24, -18, -12, 8, -13, -16, -18, -19, -13],\n [0, 6, -7, -11, -24, 11, -7, 7, 13],\n [24, 7, -25, 13, 2, -9, -20, 18, -6],\n [21, -13, -14, 4, -5, -24, -8, 2, -22],\n [16, 17, -20, 12, -17, -6, 19, 4, 11],\n [12, -22, 12, 24, -13, 9, 4, 16, -22],\n [-1, 5, 21, -14, -11, 0, -16, -14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[9, 24, 6, -12, 9, -15, -16, -9, -13],\n [0, 19, 25, -21, 22, -16, 6, -14, -13],\n [0, 0, 7, 15, 22, 25, 21, 24, 6],\n [0, 0, 0, 10, 12, 22, 2, -13, -14],\n [0, 0, 0, 0, -13, 9, -13, 8, -7],\n [0, 0, 0, 0, 0, -24, -11, -7, 5],\n [0, 0, 0, 0, 0, 0, 12, -7, 11],\n [0, 0, 0, 0, 0, 0, 0, -11, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6206", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-2, -22, -5, 13, -19, -3, 14, -5, -25],\n [15, -1, 5, 18, 12, 19, -21, 5, 25],\n [-25, 4, -8, -18, 0, 14, -11, -7, -16],\n [-2, -10, 17, 5, 18, -10, -10, 2, -6],\n [9, -17, 14, -16, 19, -8, 19, 19, -11],\n [19, 4, 22, 6, 14, 1, 1, -7, -16],\n [18, 20, -20, -2, -17, 1, -19, -20, 7],\n [-5, 20, 12, 18, -9, 5, 11, -15, 2],\n [-21, -14, -23, 15, 12, -24, 0, -24, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-97", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[14, -24, 15, -10, 4, 21, 20, 10, -22],\n [-15, -2, -8, 1, 11, -24, -11, -15, 1],\n [23, 22, 21, -3, 9, 4, 21, -2, -7],\n [3, -13, 22, -3, -14, 23, 22, 15, 3],\n [-20, 25, -3, 5, 19, -5, -2, -18, 18],\n [-17, -4, -22, -13, 8, -23, 11, 2, 0],\n [24, 20, 8, -11, -18, 22, 9, -2, 11],\n [-22, -14, -7, -11, 4, 19, 11, -14, -7],\n [8, -19, 2, 2, 3, 11, -6, -15, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[24, 13, 16, -3, 20, -6, -6, -15, -24],\n [0, -13, 15, 23, -11, 5, -3, -4, -10],\n [0, 0, -6, 2, 1, 18, 3, -21, 23],\n [0, 0, 0, 18, 25, -24, 19, -6, 17],\n [0, 0, 0, 0, 20, -18, 2, 15, -11],\n [0, 0, 0, 0, 0, 21, 21, -19, -8],\n [0, 0, 0, 0, 0, 0, -20, -5, -16],\n [0, 0, 0, 0, 0, 0, 0, -16, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-417", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, 8, 12, 15, 17, 2, -11, 8, -8],\n [8, -23, -8, 24, -10, 8, 16, 5, 6],\n [12, -8, -16, 1, 1, 16, 2, 2, -14],\n [15, 24, 1, -2, -14, -12, 8, -2, -12],\n [17, -10, 1, -14, -6, 11, -7, 16, 4],\n [2, 8, 16, -12, 11, -11, 6, -2, -1],\n [-11, 16, 2, 8, -7, 6, 7, 5, 15],\n [8, 5, 2, -2, 16, -2, 5, -7, 8],\n [-8, 6, -14, -12, 4, -1, 15, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[17, -11, -4, 1, -16, 12, 3, 8, 2],\n [-11, 13, 4, 0, -13, 8, -15, 2, -2],\n [-4, 4, 1, -4, 4, -4, 4, -6, -1],\n [1, 0, -4, 9, 8, -6, -2, 3, 7],\n [-16, -13, 4, 8, 6, -2, 1, 0, -4],\n [12, 8, -4, -6, -2, 13, -14, -5, -8],\n [3, -15, 4, -2, 1, -14, -23, 12, 4],\n [8, 2, -6, 3, 0, -5, 12, -14, 15],\n [2, -2, -1, 7, -4, -8, 4, 15, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3381", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 4, 22, 16, -2, 20, 17, 8, -7],\n [0, -22, -15, -13, 24, -8, -7, 18, 7],\n [0, 0, 23, 9, -25, 9, 10, 12, 13],\n [0, 0, 0, -22, -20, -15, -25, -18, 8],\n [0, 0, 0, 0, 13, 16, 11, 16, 18],\n [0, 0, 0, 0, 0, 2, -19, 17, 18],\n [0, 0, 0, 0, 0, 0, 6, -24, 10],\n [0, 0, 0, 0, 0, 0, 0, -8, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6136", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -10, 8, 9, 2, -2, 8, -3, 16],\n [-10, -20, 4, 2, -19, 6, -8, -18, -4],\n [8, 4, 17, -1, -6, 18, -9, -2, -4],\n [9, 2, -1, -7, 8, 8, -8, 6, -8],\n [2, -19, -6, 8, -7, 8, -8, 14, 0],\n [-2, 6, 18, 8, 8, -6, -8, 9, -15],\n [8, -8, -9, -8, -8, -8, 7, 5, 4],\n [-3, -18, -2, 6, 14, 9, 5, -16, -12],\n [16, -4, -4, -8, 0, -15, 4, -12, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 0, 14, 8, -24, -2, -12, 15, 16],\n [-13, 3, -25, 20, 8, -22, 2, -7, -25],\n [10, 17, -13, 24, 16, -21, 7, -12, -10],\n [6, 24, 1, 9, -23, -22, -19, -13, 15],\n [-23, -9, 21, -16, 21, -25, 2, -16, -19],\n [13, -23, -19, -17, 14, 9, 0, -21, -13],\n [19, 4, 14, 24, 13, -16, 16, -3, -15],\n [-14, -13, 14, 23, 20, 23, 25, -10, -17],\n [-16, 3, -17, 7, -2, 9, -15, 13, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 6, 12, 20, -9, -1, 6, -3, 16],\n [6, -7, 12, 12, 16, -17, 25, -4, 13],\n [12, 12, -21, 17, 18, -16, 16, -16, -12],\n [20, 12, 17, 21, 4, 10, -12, 0, -12],\n [-9, 16, 18, 4, -3, -23, -19, 20, 7],\n [-1, -17, -16, 10, -23, -14, 3, 0, 18],\n [6, 25, 16, -12, -19, 3, 2, -22, -14],\n [-3, -4, -16, 0, 20, 0, -22, 6, 23],\n [16, 13, -12, -12, 7, 18, -14, 23, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-17, 4, 0, -14, -2, 15, -7, 18, -10],\n [0, -3, 7, 16, 4, -3, -16, 10, 5],\n [0, 0, 17, 17, 12, 21, -24, -3, 9],\n [0, 0, 0, -14, 9, 15, -23, 8, 12],\n [0, 0, 0, 0, -25, -18, -11, 24, 19],\n [0, 0, 0, 0, 0, 20, -11, -20, 7],\n [0, 0, 0, 0, 0, 0, 18, 6, -23],\n [0, 0, 0, 0, 0, 0, 0, 11, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3039", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, -1, 4, 11, -23, -22, 3, 6, -3],\n [-7, -11, 25, -10, -3, 14, 20, 11, -25],\n [-7, 11, 9, 4, -9, 13, 23, 0, -13],\n [-4, 20, -3, 18, 17, 7, 1, 9, -14],\n [-17, 8, -12, 11, -23, 18, 18, -5, -19],\n [7, 9, -15, 19, 6, -4, 16, -7, 10],\n [11, -15, 15, -13, 2, 23, -11, -13, 17],\n [7, -18, 6, 11, 22, -22, 25, -8, -3],\n [3, -24, -13, -10, -18, -7, 6, -23, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-181", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 6) of the inverse of matrix 1/450 * A where A =\n[[19, -20, -20, 24, 11, 23, -23, 11, 5],\n [0, 19, -11, -9, -11, -21, -4, 20, -15],\n [0, 0, 13, -23, 16, -15, 4, 12, -21],\n [0, 0, 0, 25, 25, -5, 11, -1, -5],\n [0, 0, 0, 0, 21, 9, -3, -19, 20],\n [0, 0, 0, 0, 0, -22, 23, -1, -20],\n [0, 0, 0, 0, 0, 0, 12, 6, 9],\n [0, 0, 0, 0, 0, 0, 0, -19, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-19, -4, 10, -24, -2, 25, -24, 22, -14],\n [21, 16, 0, 12, 19, -20, -3, -24, 0],\n [-12, -8, 12, 6, 25, -12, 4, -13, 14],\n [5, 11, 19, 12, -4, 2, -7, 17, -10],\n [-21, 18, 23, -24, -16, 21, -7, -6, 3],\n [-1, -9, 25, 25, -13, 19, -10, 9, 10],\n [13, -23, -17, 14, 24, 20, 3, -21, -23],\n [-16, 5, -15, -9, 14, 15, -18, -24, -22],\n [-10, 15, 15, -5, -21, 9, -12, -11, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-10, 8, 9, 13, 10, -2, -2, -8, -4],\n [8, -13, 17, -8, 6, 14, 4, -3, -8],\n [9, 17, 3, -14, 13, 17, 10, -6, -13],\n [13, -8, -14, -23, 3, 11, -10, 14, 9],\n [10, 6, 13, 3, 18, 16, -11, 16, 2],\n [-2, 14, 17, 11, 16, 5, -2, 12, 6],\n [-2, 4, 10, -10, -11, -2, -20, 18, -4],\n [-8, -3, -6, 14, 16, 12, 18, 24, -10],\n [-4, -8, -13, 9, 2, 6, -4, -10, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (1, 6) of the inverse. Round your answer to the nearest integer:\n[[-23, 3, -6, -10, 4, 4, 12, 6, -14],\n [3, -25, -4, -12, 2, -17, -14, 7, 6],\n [-6, -4, 18, 3, -13, 1, 16, 3, 8],\n [-10, -12, 3, 16, 16, -11, -4, 17, -3],\n [4, 2, -13, 16, 14, 17, 0, 5, -10],\n [4, -17, 1, -11, 17, 9, 2, -7, 1],\n [12, -14, 16, -4, 0, 2, 3, 5, 22],\n [6, 7, 3, 17, 5, -7, 5, 5, 2],\n [-14, 6, 8, -3, -10, 1, 22, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[19, -2, 2, -2, 6, -9, -8, 2, 13],\n [-2, 18, -2, -20, 10, 14, -3, 8, 18],\n [2, -2, 14, 6, -10, 21, -6, -6, -4],\n [-2, -20, 6, -8, -12, -7, 4, -8, 12],\n [6, 10, -10, -12, -4, -4, -6, 6, 6],\n [-9, 14, 21, -7, -4, 19, 1, 4, -16],\n [-8, -3, -6, 4, -6, 1, -23, 0, -12],\n [2, 8, -6, -8, 6, 4, 0, 1, 18],\n [13, 18, -4, 12, 6, -16, -12, 18, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-139", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-3, 19, -4, -25, -1, 15, 2, 11, -15],\n [-4, -1, -5, 10, -6, -10, 2, 3, 24],\n [0, 14, -24, 23, -16, -13, -11, -17, 1],\n [-18, -20, 10, 24, -2, -23, 0, 10, -5],\n [-13, -15, -18, 20, 20, 22, -12, 7, -24],\n [-25, -15, -20, 6, -11, -14, 11, 3, 18],\n [-4, 20, -12, -7, -21, 9, -1, 24, 12],\n [-17, -19, -8, -24, -16, 18, -24, 19, -18],\n [-19, 9, -3, -18, -5, 7, 21, -25, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, 0, 14, -8, 16, 2, 0, -20, 2],\n [0, 24, -5, -2, -9, -23, -13, 7, -6],\n [14, -5, -18, -3, -16, -21, -12, 6, -2],\n [-8, -2, -3, -5, -17, -5, -4, -5, -5],\n [16, -9, -16, -17, 0, -2, 0, 18, -4],\n [2, -23, -21, -5, -2, 0, -6, -1, 24],\n [0, -13, -12, -4, 0, -6, 7, 4, 1],\n [-20, 7, 6, -5, 18, -1, 4, 11, 16],\n [2, -6, -2, -5, -4, 24, 1, 16, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-185", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 7) rounded to the nearest integer?\n[[-18, 5, -15, -18, -1, 23, -6, 12, -19],\n [0, 13, 17, -16, -18, 16, 17, -6, -9],\n [0, 0, 11, 16, 6, 0, 11, -17, 9],\n [0, 0, 0, -19, -24, -1, 14, -14, 4],\n [0, 0, 0, 0, 25, -3, -9, -13, 7],\n [0, 0, 0, 0, 0, -10, 16, -19, -23],\n [0, 0, 0, 0, 0, 0, -25, -1, 11],\n [0, 0, 0, 0, 0, 0, 0, -2, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, 12, 20, 9, -16, -17, -3, 4, 25],\n [0, 21, -17, -7, -18, -22, -21, -7, 20],\n [0, 0, -7, -20, -21, 17, -21, -18, 1],\n [0, 0, 0, 12, 11, -8, 0, 16, -10],\n [0, 0, 0, 0, -23, -23, -14, -3, 21],\n [0, 0, 0, 0, 0, 3, -20, 20, -10],\n [0, 0, 0, 0, 0, 0, -7, 6, 24],\n [0, 0, 0, 0, 0, 0, 0, -25, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 1, 20, 16, 0, 18, -2, 0, -24],\n [1, -6, -15, -19, 14, 14, -2, 12, 8],\n [20, -15, 17, 12, 6, -7, 12, -14, 20],\n [16, -19, 12, 22, -3, -9, 0, -6, -14],\n [0, 14, 6, -3, 5, -3, -8, -2, -16],\n [18, 14, -7, -9, -3, -18, -9, 6, -6],\n [-2, -2, 12, 0, -8, -9, 16, 7, 6],\n [0, 12, -14, -6, -2, 6, 7, 22, 16],\n [-24, 8, 20, -14, -16, -6, 6, 16, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-2, 9, 2, 16, 3, -5, 22, -1, 13],\n [5, -11, 21, 16, 9, 12, 24, -4, -21],\n [22, -13, 6, -23, -11, 1, 1, 4, -20],\n [-1, 2, -4, -22, -11, 0, -8, -17, -22],\n [22, 24, -21, 19, -20, 25, -14, 5, 21],\n [-17, -19, 3, -12, 25, -6, 22, 6, -4],\n [10, 18, -8, 14, 23, -1, 5, 9, 0],\n [-22, 16, 22, -6, 8, -14, -10, 16, -21],\n [18, 9, 18, 1, -25, 8, 17, 6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 7, -8, -10, 16, -16, -3, -14, -12],\n [7, 13, 2, 2, -10, -2, 1, -2, -6],\n [-8, 2, -4, 6, -6, 3, -5, 6, -7],\n [-10, 2, 6, -1, -12, 1, -10, 2, 9],\n [16, -10, -6, -12, 19, 2, -6, -6, 12],\n [-16, -2, 3, 1, 2, -21, -3, -6, -6],\n [-3, 1, -5, -10, -6, -3, -3, 16, 2],\n [-14, -2, 6, 2, -6, -6, 16, 23, 0],\n [-12, -6, -7, 9, 12, -6, 2, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "423", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, 8, 23, -3, -16, 25, 4, -4, -21],\n [18, 24, -17, 17, -22, 16, -25, 8, 15],\n [0, -8, -10, -3, 20, 10, 0, -24, 18],\n [-21, 3, -22, 21, 9, -4, 23, -18, 18],\n [-5, -18, -21, -5, 1, 12, -21, -5, -18],\n [-4, -8, -22, -22, 11, -11, 12, 1, -5],\n [22, 20, 20, 22, -22, -15, -7, -7, 1],\n [14, 16, 2, -21, 22, -1, -23, 0, -16],\n [-2, 3, 19, -19, 18, -3, 20, 1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1452", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 3) of the inverse of matrix 1/450 * A where A =\n[[-17, 16, -12, -10, -10, 14, -8, 5, -6],\n [16, -22, -10, -14, -8, 18, 2, -10, 2],\n [-12, -10, -6, -13, -10, 8, 4, 5, -11],\n [-10, -14, -13, -23, -7, -3, -7, -18, 2],\n [-10, -8, -10, -7, -9, 2, 17, -8, 2],\n [14, 18, 8, -3, 2, 3, 0, -1, -13],\n [-8, 2, 4, -7, 17, 0, -16, -5, 14],\n [5, -10, 5, -18, -8, -1, -5, -19, -12],\n [-6, 2, -11, 2, 2, -13, 14, -12, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, 0, -2, 2, -9, 4, -10, 8, -16],\n [0, -23, -16, -6, 12, 3, -5, 8, 16],\n [-2, -16, -3, 10, -10, 6, -4, -8, 2],\n [2, -6, 10, -25, 13, 2, 5, 19, 1],\n [-9, 12, -10, 13, 8, -3, 16, 18, 4],\n [4, 3, 6, 2, -3, -25, -12, 12, -12],\n [-10, -5, -4, 5, 16, -12, 14, 8, 14],\n [8, 8, -8, 19, 18, 12, 8, 23, -13],\n [-16, 16, 2, 1, 4, -12, 14, -13, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[13, -2, 18, 10, -14, -12, -18, -2, -18],\n [-2, -11, -4, -10, -15, -2, -6, -10, 18],\n [18, -4, -2, -2, -8, -19, -7, -6, 11],\n [10, -10, -2, -11, 10, -4, 4, 4, -3],\n [-14, -15, -8, 10, -17, -4, -9, 4, 14],\n [-12, -2, -19, -4, -4, 2, 4, -2, 24],\n [-18, -6, -7, 4, -9, 4, -23, -2, 3],\n [-2, -10, -6, 4, 4, -2, -2, 2, -6],\n [-18, 18, 11, -3, 14, 24, 3, -6, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-140", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[1, 1, -8, 4, 19, 20, 5, 16, -23],\n [0, -19, -8, -10, 23, 6, 12, -1, 18],\n [0, 0, -23, 9, 24, 3, -15, -20, -7],\n [0, 0, 0, -21, 0, 9, -7, -9, 9],\n [0, 0, 0, 0, 4, 22, 17, -9, 11],\n [0, 0, 0, 0, 0, 19, 7, 12, -15],\n [0, 0, 0, 0, 0, 0, -4, 3, 20],\n [0, 0, 0, 0, 0, 0, 0, 4, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-20, -2, 0, 2, -4, 6, 13, 10, 7],\n [-2, 17, 2, -2, -12, -4, 0, 2, -12],\n [0, 2, 24, 2, 2, 18, 1, -10, -6],\n [2, -2, 2, -11, -12, -18, 10, -13, -8],\n [-4, -12, 2, -12, -25, -7, 14, -18, 6],\n [6, -4, 18, -18, -7, -21, 16, -22, -4],\n [13, 0, 1, 10, 14, 16, -4, 18, 14],\n [10, 2, -10, -13, -18, -22, 18, -13, 8],\n [7, -12, -6, -8, 6, -4, 14, 8, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -4, 0, 2, -12, -12, 6, 16, -15],\n [-4, 11, 13, -4, -16, 14, 16, 16, 7],\n [0, 13, 13, -10, -6, 19, -16, -10, 0],\n [2, -4, -10, 24, -9, 16, 2, -2, -2],\n [-12, -16, -6, -9, -14, -5, -18, 18, 10],\n [-12, 14, 19, 16, -5, -21, 10, -4, 16],\n [6, 16, -16, 2, -18, 10, -10, 7, -8],\n [16, 16, -10, -2, 18, -4, 7, -3, -18],\n [-15, 7, 0, -2, 10, 16, -8, -18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[20, 0, 22, 1, 2, 7, -4, 1, -6],\n [0, -18, -6, 14, 2, 11, -18, -6, 4],\n [22, -6, 23, 4, -4, -6, 4, 11, -10],\n [1, 14, 4, 10, -4, 0, 4, 16, 22],\n [2, 2, -4, -4, 18, -8, -17, 0, 12],\n [7, 11, -6, 0, -8, -16, 0, 12, 2],\n [-4, -18, 4, 4, -17, 0, 13, -16, 13],\n [1, -6, 11, 16, 0, 12, -16, 25, -16],\n [-6, 4, -10, 22, 12, 2, 13, -16, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-70", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[22, 0, -20, 12, -6, -15, 0, 4, -16],\n [0, -22, -12, 6, -18, -22, 0, -14, 6],\n [-20, -12, 12, 13, -1, 2, -6, -15, -12],\n [12, 6, 13, -18, 6, 6, 6, -18, -13],\n [-6, -18, -1, 6, -17, -14, -6, 13, 0],\n [-15, -22, 2, 6, -14, 5, 7, -1, 2],\n [0, 0, -6, 6, -6, 7, 16, 0, -11],\n [4, -14, -15, -18, 13, -1, 0, 8, 6],\n [-16, 6, -12, -13, 0, 2, -11, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (2, 5) rounded to the nearest integer?\n[[19, 21, -2, 20, 14, -5, 4, -15, -17],\n [-14, 0, 12, 25, -23, 7, -11, 21, -21],\n [-2, -15, 7, -3, -16, 17, 2, 13, -9],\n [18, 0, -1, 10, -14, -23, 24, 3, 18],\n [-2, -7, -13, -10, 14, 1, -20, 16, -16],\n [12, -18, -8, 6, -9, 16, -24, 18, -6],\n [-16, -17, 22, 13, 15, -1, -1, -2, -20],\n [4, -16, 13, 5, -8, 17, 7, -7, -3],\n [-21, 0, 3, -2, -20, 13, -22, 22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 9, 21, 21, 24, -19, 11, -18, -1],\n [0, -16, 4, 7, -15, 9, 1, -23, 21],\n [0, 0, -18, -13, 16, -23, -6, 20, 19],\n [0, 0, 0, -2, -17, 4, -1, -10, -18],\n [0, 0, 0, 0, -2, 23, 3, -11, -8],\n [0, 0, 0, 0, 0, -21, 0, -24, 7],\n [0, 0, 0, 0, 0, 0, 15, -22, -7],\n [0, 0, 0, 0, 0, 0, 0, 3, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-75", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 7) of the inverse of matrix 1/450 * A where A =\n[[5, -3, -12, 2, -12, -25, 17, 6, 15],\n [0, -21, 16, -11, 16, -10, 10, 10, 14],\n [0, 0, -3, -15, -1, 19, 25, 17, -24],\n [0, 0, 0, -13, 16, 11, 4, -15, -3],\n [0, 0, 0, 0, 19, -23, -17, -18, 21],\n [0, 0, 0, 0, 0, -25, 14, -21, 4],\n [0, 0, 0, 0, 0, 0, -8, 11, 1],\n [0, 0, 0, 0, 0, 0, 0, -12, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[6, -14, -6, 21, 19, -14, -18, -4, 1],\n [15, 15, -9, 6, 7, 5, -20, 13, -17],\n [16, 6, 10, -10, -14, 15, -23, 1, 1],\n [-17, -9, 20, -21, 0, -5, -25, -25, 9],\n [-17, -3, 12, 15, -22, -7, 11, -21, 2],\n [20, 16, 22, -3, 12, -3, 20, -8, 3],\n [2, -17, 13, 24, -16, -24, -13, 12, 1],\n [15, -6, 14, -16, -10, -11, -13, 24, 12],\n [-6, -2, 15, 24, -19, -3, -2, 3, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-261", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[17, 19, 9, -25, 10, 25, -8, -20, -3],\n [-16, -19, 18, -18, -13, 4, -8, -12, -15],\n [16, 12, -13, 16, 18, 7, 24, -13, -1],\n [-2, 3, 10, -20, -8, 2, -21, -8, 11],\n [-19, -17, 9, -14, 20, 14, 18, 13, -2],\n [-17, -14, 10, 11, -17, 13, 20, -4, -9],\n [7, 21, -2, -11, 3, 6, 7, 3, -11],\n [1, 8, -22, 23, 22, -8, -5, 22, -18],\n [-20, -6, -24, 25, 19, -4, -5, -20, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2385", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, -14, -21, -10, 12, 2, 10, 3, 8],\n [-14, 0, -4, -12, -4, -2, 4, -15, 14],\n [-21, -4, 16, 20, -20, -7, -16, 4, -12],\n [-10, -12, 20, 7, -1, 4, -2, 18, 10],\n [12, -4, -20, -1, 11, 20, -18, 18, 6],\n [2, -2, -7, 4, 20, -3, 6, -2, -5],\n [10, 4, -16, -2, -18, 6, 18, -1, 13],\n [3, -15, 4, 18, 18, -2, -1, 14, 8],\n [8, 14, -12, 10, 6, -5, 13, 8, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "902", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[25, 11, -15, -19, 9, -15, 23, 17, 21],\n [25, 14, 22, -5, 21, -23, 4, -2, 12],\n [-23, 11, 7, -4, 5, 20, -14, 19, -12],\n [-14, 1, -13, -2, 12, 21, 22, -17, -18],\n [11, -11, -19, -2, 23, -10, -2, 17, -19],\n [17, 2, -24, 8, 12, -23, -25, 5, -3],\n [-6, -10, 20, 6, -9, -8, -22, 9, 14],\n [10, -3, -11, -13, -12, -12, 11, -21, -4],\n [2, 19, -22, 24, 12, 3, 11, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "695", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 2, -5, -18, 6, 5, 14, 6, -4],\n [2, 3, 6, 0, -10, 2, -20, -6, -2],\n [-5, 6, 6, 2, 8, 2, 14, -3, -10],\n [-18, 0, 2, -19, 8, -7, -2, -20, 6],\n [6, -10, 8, 8, -6, 6, 4, -10, -14],\n [5, 2, 2, -7, 6, -7, -22, 7, 4],\n [14, -20, 14, -2, 4, -22, -7, 16, -3],\n [6, -6, -3, -20, -10, 7, 16, 11, -7],\n [-4, -2, -10, 6, -14, 4, -3, -7, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1610", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -8, 7, -12, -20, -15, 20, -6, 3],\n [0, -10, 22, -19, 14, 10, 18, 18, 5],\n [0, 0, 17, 17, 21, -20, 3, 1, 17],\n [0, 0, 0, -15, -10, 19, -13, -8, -1],\n [0, 0, 0, 0, 23, -25, 7, 23, -11],\n [0, 0, 0, 0, 0, -7, -24, 22, -6],\n [0, 0, 0, 0, 0, 0, -11, -6, 8],\n [0, 0, 0, 0, 0, 0, 0, -6, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 21, -1, -1, -9, -14, 25, -15, -16],\n [0, 19, -10, -6, 23, -21, 15, 6, 1],\n [0, 0, 22, -19, 20, -12, 13, -2, 22],\n [0, 0, 0, 25, 14, -25, -9, 0, 25],\n [0, 0, 0, 0, 2, -5, 12, 7, 4],\n [0, 0, 0, 0, 0, 7, 17, 3, 5],\n [0, 0, 0, 0, 0, 0, -6, -22, -18],\n [0, 0, 0, 0, 0, 0, 0, -8, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8004", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[19, 0, 23, 21, -24, -20, 3, 0, 2],\n [-19, 8, 19, -16, 22, 15, 14, 21, -4],\n [1, 13, -4, -7, 10, -17, -7, -24, 2],\n [13, -4, 25, -20, 21, -19, -20, 7, -12],\n [-25, -1, -20, 2, -8, 1, 23, -24, 14],\n [-5, -3, -24, -10, -22, 8, -21, 23, 8],\n [-4, 20, -6, 13, 21, 24, -13, 18, 8],\n [18, -20, 3, 7, -25, 21, 22, -19, -4],\n [6, -12, 25, -2, -7, 1, -3, 19, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1379", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[18, 3, -25, 5, 1, 18, 10, 1, -11],\n [0, 22, -11, 14, -7, 21, 24, -15, 15],\n [0, 0, -3, -14, -24, 17, -5, -12, 8],\n [0, 0, 0, -5, 24, -12, -5, -14, 16],\n [0, 0, 0, 0, -4, -20, 18, -24, 3],\n [0, 0, 0, 0, 0, -12, 17, -14, 17],\n [0, 0, 0, 0, 0, 0, 1, 25, -19],\n [0, 0, 0, 0, 0, 0, 0, 14, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-125411", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, -10, 13, -16, 0, -17, 8, 14, 15],\n [-10, 19, -16, 10, 10, 13, 6, -22, -10],\n [13, -16, 5, -17, -18, -2, 24, 2, -6],\n [-16, 10, -17, -13, 4, -2, -2, 9, 0],\n [0, 10, -18, 4, 24, -4, 16, 2, 4],\n [-17, 13, -2, -2, -4, -23, 8, 18, 4],\n [8, 6, 24, -2, 16, 8, 5, 21, 0],\n [14, -22, 2, 9, 2, 18, 21, -16, 7],\n [15, -10, -6, 0, 4, 4, 0, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1985", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (5, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-23, -4, 6, -4, 20, -12, 13, -23, 2],\n [-4, -2, 10, 22, -2, 6, 6, 7, -5],\n [6, 10, 4, -14, -11, -1, -11, -4, 7],\n [-4, 22, -14, 13, 20, -22, -16, 12, -20],\n [20, -2, -11, 20, -25, 0, 6, -3, -2],\n [-12, 6, -1, -22, 0, 16, 12, 12, 10],\n [13, 6, -11, -16, 6, 12, -2, 16, -4],\n [-23, 7, -4, 12, -3, 12, 16, 8, 2],\n [2, -5, 7, -20, -2, 10, -4, 2, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[16, 4, 6, -4, 12, -12, 8, 17, 21],\n [0, 14, -13, 4, -7, 16, 15, 24, 13],\n [0, 0, -14, -11, 19, 12, 14, -12, 9],\n [0, 0, 0, -9, -8, 16, -9, -10, -5],\n [0, 0, 0, 0, 1, 13, -9, -1, 25],\n [0, 0, 0, 0, 0, 4, 7, 13, 0],\n [0, 0, 0, 0, 0, 0, 13, -13, 4],\n [0, 0, 0, 0, 0, 0, 0, -21, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73334", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[0, -6, -6, 1, 12, -10, -1, 20, 12],\n [-6, -6, 5, -8, -23, 12, 0, 8, -19],\n [-6, 5, 13, 17, 2, 5, 10, -6, 18],\n [1, -8, 17, 0, 14, -2, -6, 2, -8],\n [12, -23, 2, 14, 21, 11, -8, 13, -6],\n [-10, 12, 5, -2, 11, 1, 11, 6, -6],\n [-1, 0, 10, -6, -8, 11, -9, 5, -6],\n [20, 8, -6, 2, 13, 6, 5, 12, 4],\n [12, -19, 18, -8, -6, -6, -6, 4, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1626", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 8) of the inverse of matrix 1/450 * A where A =\n[[-21, 13, 3, 18, 20, 7, -2, -16, -1],\n [0, -16, 13, -10, 2, -14, 18, 6, 25],\n [0, 0, 24, 1, 0, -23, 0, 13, -25],\n [0, 0, 0, -22, -7, -4, -20, -17, -15],\n [0, 0, 0, 0, 17, -16, 8, 5, -4],\n [0, 0, 0, 0, 0, -11, -7, 12, -11],\n [0, 0, 0, 0, 0, 0, 17, 13, 10],\n [0, 0, 0, 0, 0, 0, 0, 18, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (9, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-21, -1, -7, 21, -6, -19, 0, 2, -12],\n [-1, -11, -5, -4, -10, -10, 10, 5, -4],\n [-7, -5, -21, -18, -14, 5, -17, -4, 8],\n [21, -4, -18, 3, -2, 4, -2, -12, 8],\n [-6, -10, -14, -2, -18, -2, 0, -3, 18],\n [-19, -10, 5, 4, -2, 0, 7, -6, 2],\n [0, 10, -17, -2, 0, 7, -7, -7, 23],\n [2, 5, -4, -12, -3, -6, -7, -10, 0],\n [-12, -4, 8, 8, 18, 2, 23, 0, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (3, 5) of the inverse. Round your answer to the nearest integer:\n[[-1, 22, -6, 11, -7, 16, -13, 21, -14],\n [23, -11, -22, -11, -9, 1, -15, -3, -11],\n [5, 0, -19, -13, -13, -6, 8, -16, 24],\n [11, 25, 1, 8, 10, -10, -5, -10, -9],\n [-11, -13, 7, -21, 1, -25, 18, 4, -3],\n [-11, 10, -7, 4, -10, -8, 0, -9, -15],\n [19, 3, -17, 23, -9, 1, 11, -4, -18],\n [-23, 12, 9, 6, -18, 18, 1, 6, 10],\n [8, -1, 5, 16, 21, -13, -11, 25, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-13, 7, 5, -1, 22, 14, -3, 12, -23],\n [0, -24, -3, 8, 4, 21, -16, -25, -4],\n [0, 0, -1, -4, -10, 4, -8, -2, -21],\n [0, 0, 0, 1, -14, -16, 8, 7, -10],\n [0, 0, 0, 0, 10, 1, -16, -16, -15],\n [0, 0, 0, 0, 0, -7, -1, -16, -11],\n [0, 0, 0, 0, 0, 0, 4, 14, -14],\n [0, 0, 0, 0, 0, 0, 0, 25, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34165", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[7, 4, 11, -10, -1, 12, 16, -16, -21],\n [0, 7, 11, -25, 5, -19, 21, -3, -2],\n [0, 0, -17, -18, -18, -23, 6, -22, 23],\n [0, 0, 0, 20, -25, 23, -15, 3, 0],\n [0, 0, 0, 0, 2, 5, -7, 22, 0],\n [0, 0, 0, 0, 0, -5, 12, 8, 14],\n [0, 0, 0, 0, 0, 0, 5, -25, 13],\n [0, 0, 0, 0, 0, 0, 0, 3, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25446", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -18, 20, -1, 16, 12, 22, 8, -5],\n [-18, -11, -4, -2, 2, -16, 0, -8, 9],\n [20, -4, 22, -3, 6, -14, -12, -8, 24],\n [-1, -2, -3, 24, -8, -14, -19, 5, -1],\n [16, 2, 6, -8, -11, -15, 18, 0, 7],\n [12, -16, -14, -14, -15, -22, -10, -8, 2],\n [22, 0, -12, -19, 18, -10, -19, -10, -12],\n [8, -8, -8, 5, 0, -8, -10, -9, 8],\n [-5, 9, 24, -1, 7, 2, -12, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, -4, 0, -2, -8, 1, 6, -5, 7],\n [-4, -15, 0, -2, -8, -18, -6, 6, 7],\n [0, 0, 9, -9, 8, 8, 6, 2, -10],\n [-2, -2, -9, 11, -4, -5, -2, 18, -3],\n [-8, -8, 8, -4, 13, 4, 12, -16, -8],\n [1, -18, 8, -5, 4, -9, -14, 9, 16],\n [6, -6, 6, -2, 12, -14, -13, -2, 13],\n [-5, 6, 2, 18, -16, 9, -2, -12, 4],\n [7, 7, -10, -3, -8, 16, 13, 4, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, 0, -4, -7, -2, -10, -4, 6, 3],\n [0, 9, -12, 6, -20, 13, 15, -1, -9],\n [-4, -12, -4, 20, 4, 12, -6, 23, 20],\n [-7, 6, 20, 1, -16, 6, 10, 6, -5],\n [-2, -20, 4, -16, 7, 9, 10, 6, 4],\n [-10, 13, 12, 6, 9, 0, 11, -12, 10],\n [-4, 15, -6, 10, 10, 11, 4, 7, 0],\n [6, -1, 23, 6, 6, -12, 7, -10, 14],\n [3, -9, 20, -5, 4, 10, 0, 14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-47", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[17, 19, -16, 0, -18, -2, -4, -4, -18],\n [19, -3, -20, 2, -8, 4, 10, -11, -12],\n [-16, -20, -1, -2, 4, 4, 14, -13, -10],\n [0, 2, -2, 23, 8, 2, -3, 4, 25],\n [-18, -8, 4, 8, 11, -4, 2, -8, -4],\n [-2, 4, 4, 2, -4, 3, -6, -8, -10],\n [-4, 10, 14, -3, 2, -6, 15, -12, 16],\n [-4, -11, -13, 4, -8, -8, -12, -19, 18],\n [-18, -12, -10, 25, -4, -10, 16, 18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-22, 4, 13, -6, 2, 4, 17, -12, -20],\n [4, -3, 11, 0, 4, -18, -6, -2, -4],\n [13, 11, 22, 4, 13, -22, -6, 12, 2],\n [-6, 0, 4, 10, 8, 8, -5, -10, -17],\n [2, 4, 13, 8, 15, 7, -6, -4, 9],\n [4, -18, -22, 8, 7, -2, -9, 5, 0],\n [17, -6, -6, -5, -6, -9, -17, 2, 8],\n [-12, -2, 12, -10, -4, 5, 2, -16, 8],\n [-20, -4, 2, -17, 9, 0, 8, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-743", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, 13, 18, 19, 3, 19, 20, 21, 5],\n [0, -20, -17, -11, -6, 22, -24, -23, 4],\n [0, 0, -5, 13, 17, -13, 14, 15, 22],\n [0, 0, 0, -25, 1, -2, 25, 23, -4],\n [0, 0, 0, 0, -23, 7, 25, 21, -5],\n [0, 0, 0, 0, 0, 15, 6, -2, -15],\n [0, 0, 0, 0, 0, 0, 17, 12, -25],\n [0, 0, 0, 0, 0, 0, 0, 1, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "324", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[24, -22, -8, 8, 6, -14, -13, 8, 4],\n [-22, -18, -4, -1, 14, 2, 15, -7, -2],\n [-8, -4, -24, -16, 6, 2, -6, 16, 0],\n [8, -1, -16, -14, 24, -8, -13, -15, 14],\n [6, 14, 6, 24, -20, 4, 4, 14, 9],\n [-14, 2, 2, -8, 4, 20, 2, 11, 4],\n [-13, 15, -6, -13, 4, 2, 24, 14, -15],\n [8, -7, 16, -15, 14, 11, 14, -21, 14],\n [4, -2, 0, 14, 9, 4, -15, 14, -24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[19, -22, 24, -2, 22, 16, -24, 20, -24],\n [24, -25, -13, -20, -4, -9, 23, -4, 17],\n [-20, -23, 20, -20, -9, 9, 23, 25, 24],\n [11, 21, 9, -3, -18, -19, 24, -16, 0],\n [-16, -7, -3, 5, 7, -24, 2, 6, 7],\n [-17, 3, -11, -8, -8, -19, -12, 3, 24],\n [-7, -21, 15, 24, 19, -21, -11, 0, -2],\n [-7, -6, 17, -17, 2, -10, -15, 8, -1],\n [14, -5, -21, -15, 17, -17, -15, 11, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, 0, -16, 14, -7, -10, 19, 11, 24],\n [15, -22, -12, 4, -19, -14, -2, 13, 17],\n [-4, 21, 4, 13, -6, 0, 23, -21, 14],\n [16, -20, 8, -21, -16, 2, -23, -13, 22],\n [21, -24, 9, 24, 21, 2, 11, -3, 17],\n [-3, 9, 15, 13, 6, -24, 21, 18, 22],\n [-10, -10, 25, -23, 2, 3, -6, 10, 7],\n [-4, -18, 21, -2, 11, -6, -14, -6, -6],\n [-22, 4, 5, -4, -11, 12, 11, 2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-12, -15, -17, -2, -16, 12, 17, 15, 11],\n [16, 6, -6, -12, 12, -22, -2, 6, -16],\n [17, -10, 13, 6, -8, -1, -19, 21, 25],\n [-8, 21, -8, -23, -25, 7, -19, -16, 18],\n [-18, 6, -3, -9, -12, -9, -1, -5, -20],\n [-6, 23, -6, 0, 6, -18, 19, 22, 18],\n [3, -9, -8, 14, -8, -15, 19, -14, -11],\n [0, -23, -23, 12, 9, -17, 17, 14, -22],\n [-6, -11, 3, -21, 13, 14, -19, -18, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-107", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[10, 12, 10, 4, 6, 8, 8, 2, 2],\n [12, 6, -18, -16, 14, 12, 4, -10, -14],\n [10, -18, -19, -10, 15, 0, -7, 10, -6],\n [4, -16, -10, -9, -22, -14, -8, 20, -2],\n [6, 14, 15, -22, -3, 8, 2, 22, -10],\n [8, 12, 0, -14, 8, -22, 0, -8, 10],\n [8, 4, -7, -8, 2, 0, -8, 0, -1],\n [2, -10, 10, 20, 22, -8, 0, 15, -14],\n [2, -14, -6, -2, -10, 10, -1, -14, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "637", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[9, 4, -8, -4, -4, 3, 8, -4, 1],\n [4, -3, -1, 12, 18, -20, -18, 11, 8],\n [-8, -1, -17, -2, 18, 4, -11, -10, -10],\n [-4, 12, -2, -19, 0, 5, 10, -12, -2],\n [-4, 18, 18, 0, -3, -8, 8, 22, 3],\n [3, -20, 4, 5, -8, -10, -6, -4, 4],\n [8, -18, -11, 10, 8, -6, 9, 2, -20],\n [-4, 11, -10, -12, 22, -4, 2, 16, 9],\n [1, 8, -10, -2, 3, 4, -20, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -17, -8, 6, 5, 18, -6, -3, 6],\n [-17, 8, 11, -11, -6, 10, 20, -16, -1],\n [-8, 11, -15, -7, 9, -3, 6, 1, -20],\n [6, -11, -7, 0, 11, 17, -12, 6, 3],\n [5, -6, 9, 11, -23, -2, -20, -12, 4],\n [18, 10, -3, 17, -2, -1, 22, -21, 18],\n [-6, 20, 6, -12, -20, 22, -6, -4, -6],\n [-3, -16, 1, 6, -12, -21, -4, 4, -6],\n [6, -1, -20, 3, 4, 18, -6, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29843", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[-21, -20, -16, 17, -24, -19, 20, -22, 11],\n [0, 2, -6, 4, 16, 12, -24, -23, 21],\n [0, 0, 13, -1, -24, 13, -11, -23, -21],\n [0, 0, 0, 25, 14, 12, 11, 1, -21],\n [0, 0, 0, 0, -14, 16, 5, 7, 17],\n [0, 0, 0, 0, 0, 14, 4, 21, -4],\n [0, 0, 0, 0, 0, 0, -22, 3, 19],\n [0, 0, 0, 0, 0, 0, 0, -17, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[12, -16, 2, 4, -16, 14, 2, -18, 9],\n [-16, 0, 2, -10, 11, -4, 15, -11, -8],\n [2, 2, -24, 0, -12, 2, 1, -5, 4],\n [4, -10, 0, -9, 2, -5, -2, 2, -19],\n [-16, 11, -12, 2, -1, 6, -4, 20, -16],\n [14, -4, 2, -5, 6, -9, 0, -1, 6],\n [2, 15, 1, -2, -4, 0, -2, -16, 6],\n [-18, -11, -5, 2, 20, -1, -16, 22, -8],\n [9, -8, 4, -19, -16, 6, 6, -8, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1082", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, -10, -24, 20, -14, 1, -7, 2, 9],\n [25, 17, -22, 23, 23, -19, 11, 25, -1],\n [25, 15, -9, 15, -12, 11, -24, -2, -11],\n [22, 25, 7, -14, -7, 21, -21, -25, 17],\n [-17, 13, 8, 3, 23, 22, 22, 20, -24],\n [-7, 2, 9, 14, 25, 22, -4, -22, -18],\n [-25, 10, -19, -1, 3, -25, -8, -22, -6],\n [20, -18, 1, 24, 13, 9, -1, -12, 18],\n [21, 14, 5, -21, -9, -16, 17, -10, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1216", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 2) of the inverse. Round your answer to the nearest integer:\n[[-22, -15, 5, 15, 10, 24, 0, -12, -18],\n [-15, 15, -16, 0, 6, 10, -4, 12, 0],\n [5, -16, 25, -1, -10, 15, 4, -14, -4],\n [15, 0, -1, -8, 5, 14, -9, 7, 4],\n [10, 6, -10, 5, -12, -12, -6, 4, 1],\n [24, 10, 15, 14, -12, 22, -15, -8, 1],\n [0, -4, 4, -9, -6, -15, -23, 18, -11],\n [-12, 12, -14, 7, 4, -8, 18, 0, 2],\n [-18, 0, -4, 4, 1, 1, -11, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "195", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (9, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -10, -13, 4, 10, 2, 14, 11, -20],\n [-10, -10, -8, -7, 0, -10, -6, -7, 16],\n [-13, -8, 3, -5, -2, -8, -11, -5, 0],\n [4, -7, -5, -25, -8, 10, 2, 5, -14],\n [10, 0, -2, -8, 15, -12, -18, -4, 14],\n [2, -10, -8, 10, -12, 0, 8, 4, -11],\n [14, -6, -11, 2, -18, 8, 4, -9, 8],\n [11, -7, -5, 5, -4, 4, -9, 25, 2],\n [-20, 16, 0, -14, 14, -11, 8, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[6, 4, -25, 6, -6, -5, -7, 4, 24],\n [0, 6, 4, -3, 1, 11, 0, -23, 5],\n [0, 0, 12, -7, 5, 3, -1, 6, -9],\n [0, 0, 0, -3, -8, -15, -6, -13, -2],\n [0, 0, 0, 0, 2, 9, -5, -20, -19],\n [0, 0, 0, 0, 0, 6, -16, 20, 17],\n [0, 0, 0, 0, 0, 0, 19, 25, 12],\n [0, 0, 0, 0, 0, 0, 0, 8, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34104", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[8, 3, 4, 8, 8, 0, -20, -18, 10],\n [3, -7, -12, -22, 8, -7, 6, -14, 14],\n [4, -12, 2, 1, 1, 2, 12, 10, -2],\n [8, -22, 1, 18, -24, 10, -16, -8, 8],\n [8, 8, 1, -24, 12, 0, 8, -2, -6],\n [0, -7, 2, 10, 0, 20, -10, -17, 4],\n [-20, 6, 12, -16, 8, -10, 4, 6, 12],\n [-18, -14, 10, -8, -2, -17, 6, -9, 6],\n [10, 14, -2, 8, -6, 4, 12, 6, 19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (7, 3) of the inverse. Round your answer to the nearest integer:\n[[0, -12, 22, -5, 2, -11, 4, -1, 25],\n [-15, 18, -15, 2, -21, 2, -18, 0, -20],\n [6, 22, 6, -14, -20, -13, 13, 14, 18],\n [8, -3, 15, 19, -9, 19, 22, -25, -19],\n [-13, -12, -9, 4, 22, 21, 23, 8, 1],\n [-1, 18, 9, -17, -20, 0, 12, 13, 1],\n [14, 5, -23, -2, -11, -20, -15, 4, 9],\n [22, 12, 17, 14, 3, -3, 16, 16, -23],\n [0, -12, -7, -5, -5, -17, -13, 15, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[20, 11, 12, 19, 19, -2, 12, 20, -15],\n [0, 19, 18, 22, 12, 15, -9, 22, 0],\n [0, 0, -8, -17, -23, -16, 17, -24, -18],\n [0, 0, 0, 5, -12, 13, 7, 3, 18],\n [0, 0, 0, 0, 6, 10, 20, 24, -3],\n [0, 0, 0, 0, 0, 14, 2, -1, -19],\n [0, 0, 0, 0, 0, 0, 7, 19, 6],\n [0, 0, 0, 0, 0, 0, 0, -19, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 9) of the inverse. Round your answer to the nearest integer:\n[[20, 7, 0, -10, -17, -3, -11, -7, 16],\n [0, -1, 9, 25, -13, 20, -19, 8, -12],\n [0, 0, -9, -13, 1, -24, 11, 4, -22],\n [0, 0, 0, -15, 14, -3, 15, 22, 6],\n [0, 0, 0, 0, 22, -17, -14, -25, -10],\n [0, 0, 0, 0, 0, 7, 12, 15, 25],\n [0, 0, 0, 0, 0, 0, 13, 0, 18],\n [0, 0, 0, 0, 0, 0, 0, 21, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[21, -2, -4, 3, 8, -1, -22, 20, -14],\n [-2, 17, -4, -4, 9, -1, -14, -15, -16],\n [-4, -4, 20, 2, 6, 16, -4, -19, 18],\n [3, -4, 2, -6, -2, -10, 8, 13, 6],\n [8, 9, 6, -2, 5, -12, 8, 12, -4],\n [-1, -1, 16, -10, -12, 6, 2, -2, 5],\n [-22, -14, -4, 8, 8, 2, -10, -8, -14],\n [20, -15, -19, 13, 12, -2, -8, -11, 4],\n [-14, -16, 18, 6, -4, 5, -14, 4, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-79", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-18, 22, 10, 0, 19, -18, 6, 6, -25],\n [0, -25, -11, 24, -6, -23, -11, 11, -5],\n [0, 0, -3, 14, 9, -8, -9, 5, 22],\n [0, 0, 0, 10, 9, -15, 1, 8, -8],\n [0, 0, 0, 0, 16, -15, -21, -8, -1],\n [0, 0, 0, 0, 0, 10, -5, -12, -18],\n [0, 0, 0, 0, 0, 0, 13, 24, -24],\n [0, 0, 0, 0, 0, 0, 0, -21, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, -19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-3, 23, 16, -6, -6, -4, 12, -9, -1],\n [23, 25, 0, -12, -18, -2, 12, -8, 4],\n [16, 0, 8, -16, 12, -2, 0, 2, -7],\n [-6, -12, -16, -7, -1, -8, 12, 0, 1],\n [-6, -18, 12, -1, -10, 10, -10, 0, 0],\n [-4, -2, -2, -8, 10, 11, -14, 18, -10],\n [12, 12, 0, 12, -10, -14, 13, -14, -7],\n [-9, -8, 2, 0, 0, 18, -14, -5, -2],\n [-1, 4, -7, 1, 0, -10, -7, -2, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-409", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-23, -2, -3, 19, 22, -25, 6, 7, 22],\n [4, -24, -8, 4, -8, -21, -21, -18, -17],\n [6, -12, -13, -8, -22, 24, -4, -6, -11],\n [-19, -13, 8, 15, 4, -21, -25, 5, 25],\n [-6, -7, 3, 19, 12, -16, 3, 5, -15],\n [-3, 4, -1, -10, -3, 7, 25, 11, 2],\n [1, -20, 12, 11, -20, -1, -13, 7, 7],\n [-1, -12, 14, 15, 16, 12, -17, -8, -11],\n [-22, 8, 12, -9, -19, 6, -3, -6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-24, -5, -14, 16, 23, 1, 24, 22, -16],\n [0, -5, -4, -13, 22, 14, -14, -9, 22],\n [0, 0, 23, 14, -14, -17, 4, -20, -1],\n [0, 0, 0, 2, 3, 10, -15, -5, 12],\n [0, 0, 0, 0, 15, -11, -3, 15, -20],\n [0, 0, 0, 0, 0, -17, 25, 4, 18],\n [0, 0, 0, 0, 0, 0, 9, 0, 4],\n [0, 0, 0, 0, 0, 0, 0, -14, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "781", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-7, 3, 21, 24, 22, 13, 16, -1, -10],\n [-9, 2, 13, 17, 23, -21, -25, -23, 22],\n [-2, 3, -11, -22, 18, -25, 23, -11, -2],\n [5, -6, -16, -15, -8, 8, 2, 12, -10],\n [-2, 13, 25, -14, 24, 16, -19, 10, -9],\n [23, -22, 11, 7, -7, 0, -15, 5, -25],\n [14, 10, 3, -1, 21, 23, -8, -23, -8],\n [-19, 2, -9, -1, -8, 14, 17, -23, -1],\n [-19, 21, -16, 18, 18, 25, -7, -11, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 11, 2, 19, 6, 15, 1, -3, -16],\n [0, 15, -20, -2, -8, -16, -11, 19, 17],\n [0, 0, 24, 9, 1, -1, -23, -5, 13],\n [0, 0, 0, -17, 24, -25, -22, -22, 23],\n [0, 0, 0, 0, 19, 6, 15, -19, 18],\n [0, 0, 0, 0, 0, 6, 15, 0, 22],\n [0, 0, 0, 0, 0, 0, -1, -8, 19],\n [0, 0, 0, 0, 0, 0, 0, 5, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-307", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, -20, -14, 16, -7, 14, -21, 1, -16],\n [0, 20, -12, 8, 23, -11, 3, 0, 1],\n [0, 0, 9, 9, 24, -20, -12, 0, -23],\n [0, 0, 0, 3, -17, 6, -4, -4, 8],\n [0, 0, 0, 0, -23, -7, 7, 21, 0],\n [0, 0, 0, 0, 0, 17, -3, 22, -12],\n [0, 0, 0, 0, 0, 0, 10, -20, -3],\n [0, 0, 0, 0, 0, 0, 0, -21, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2499", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, -12, -19, 0, 6, 3, 20, 13, -17],\n [0, -9, 23, -1, 4, 19, 3, 3, -8],\n [0, 0, -9, -20, -14, 12, -23, 21, 9],\n [0, 0, 0, -23, -21, -12, 10, 2, 15],\n [0, 0, 0, 0, -13, -24, -1, -6, -19],\n [0, 0, 0, 0, 0, 1, 16, -24, 9],\n [0, 0, 0, 0, 0, 0, -7, -10, 6],\n [0, 0, 0, 0, 0, 0, 0, -21, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65480", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-7, 3, -24, 11, 0, 3, -21, 6, 12],\n [22, -24, -21, 21, 7, 25, 9, -7, -11],\n [9, -18, 21, -25, 12, -4, -9, -10, 19],\n [-25, -23, -20, -23, 21, 4, 21, -15, 1],\n [-4, -20, 12, 15, 20, 5, 17, -20, 24],\n [-6, 21, 15, -15, -24, 5, 12, 0, 1],\n [20, 20, 5, -2, -13, -1, 11, 15, -1],\n [3, 5, 17, 13, -24, -14, -21, 1, 8],\n [-12, -19, 11, 10, -16, 3, -10, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[12, -2, 14, -9, 12, -4, -6, 2, -10],\n [-2, 6, -7, -7, 2, -6, -7, 7, -21],\n [14, -7, 14, -1, 15, 2, 14, -10, 4],\n [-9, -7, -1, -24, 2, 10, -20, -6, 0],\n [12, 2, 15, 2, 17, -18, -10, -6, -10],\n [-4, -6, 2, 10, -18, 12, 12, 12, 14],\n [-6, -7, 14, -20, -10, 12, -4, -2, 10],\n [2, 7, -10, -6, -6, 12, -2, 13, 4],\n [-10, -21, 4, 0, -10, 14, 10, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9977", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-3, -8, -2, 16, 3, 12, 12, -13, 6],\n [-7, -9, -24, -8, 13, 1, -12, -11, -18],\n [-17, -5, 17, 9, -12, 1, -18, 9, -8],\n [-12, -18, 23, -18, 11, 18, -24, -9, -13],\n [-12, 15, 15, -17, 1, -6, 12, -14, 16],\n [-4, 11, 24, 13, 5, -13, -25, 12, 14],\n [-17, 13, -16, 3, 14, 4, -24, -8, 2],\n [21, 6, -2, 12, -12, -1, -1, 6, 1],\n [6, 5, 24, -2, 9, 4, 7, 7, 20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "949", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 9) rounded to the nearest integer?\n[[1, 6, -2, -16, -1, 2, -2, 2, 0],\n [6, 10, 13, 2, 20, 12, 17, 5, 1],\n [-2, 13, -16, -12, -10, -8, -8, 12, 8],\n [-16, 2, -12, 16, -10, -6, 14, -18, 16],\n [-1, 20, -10, -10, 13, -14, 2, 2, -4],\n [2, 12, -8, -6, -14, -21, -23, 0, 14],\n [-2, 17, -8, 14, 2, -23, -3, 14, -1],\n [2, 5, 12, -18, 2, 0, 14, 18, -10],\n [0, 1, 8, 16, -4, 14, -1, -10, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-110", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 10, 16, 16, 18, 19, -8, 3, -14],\n [10, -23, 4, 22, 6, -8, 6, 14, 6],\n [16, 4, 1, 8, -20, -18, -10, 5, 4],\n [16, 22, 8, -25, 0, -10, -8, -2, -2],\n [18, 6, -20, 0, -8, -7, 7, -6, 10],\n [19, -8, -18, -10, -7, 15, 18, -17, -14],\n [-8, 6, -10, -8, 7, 18, -24, 12, -8],\n [3, 14, 5, -2, -6, -17, 12, -10, 14],\n [-14, 6, 4, -2, 10, -14, -8, 14, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "788", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, 21, 3, 17, -2, 14, 6, 13, -14],\n [21, -7, -6, -14, -3, -6, 14, -2, -11],\n [3, -6, -16, 10, -2, 16, -16, 18, 21],\n [17, -14, 10, -3, -4, 5, 18, -1, -6],\n [-2, -3, -2, -4, -18, -9, 10, 0, -15],\n [14, -6, 16, 5, -9, -16, 13, 12, -9],\n [6, 14, -16, 18, 10, 13, -18, -20, -3],\n [13, -2, 18, -1, 0, 12, -20, 8, 6],\n [-14, -11, 21, -6, -15, -9, -3, 6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-21, -17, 24, -16, 23, -16, -12, 10, -16],\n [0, 11, 15, 12, 22, -4, -3, -10, -15],\n [0, 0, 9, 22, -6, 11, 15, -21, 10],\n [0, 0, 0, 18, -6, 13, 7, 4, -10],\n [0, 0, 0, 0, 17, 14, -25, -23, -18],\n [0, 0, 0, 0, 0, 14, 0, -5, -17],\n [0, 0, 0, 0, 0, 0, 21, 14, 2],\n [0, 0, 0, 0, 0, 0, 0, 1, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, 23, -22, 11, -8, 5, 23, 13, -16],\n [-17, 2, 2, -13, -8, -14, -18, -3, 24],\n [-21, -19, -11, -23, -8, 12, 0, 12, 7],\n [-5, -9, 17, -24, -1, 15, -7, 12, -1],\n [13, -22, -23, 8, 16, -16, 23, 1, 22],\n [0, 1, -25, 18, -6, -1, -16, -25, -10],\n [-15, -22, 9, -13, -5, -11, -16, 12, -15],\n [6, 7, -6, 10, 4, -16, -11, 3, -25],\n [-5, -11, -23, 7, 12, -7, -22, -14, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -16, -20, 6, 0, 4, -14, 1, 0],\n [-16, -24, 2, -2, 5, 9, -6, 8, 8],\n [-20, 2, -4, -11, 6, -2, -12, -8, 0],\n [6, -2, -11, -20, 23, 14, -2, 8, -8],\n [0, 5, 6, 23, 1, -11, -10, 0, 7],\n [4, 9, -2, 14, -11, -12, -6, -4, 8],\n [-14, -6, -12, -2, -10, -6, 2, 14, -10],\n [1, 8, -8, 8, 0, -4, 14, 21, 1],\n [0, 8, 0, -8, 7, 8, -10, 1, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[16, -2, -1, 7, 15, -14, 19, 6, -3],\n [-2, -10, -18, 14, -16, 8, 2, -6, -5],\n [-1, -18, -5, 4, 4, 7, 16, 0, -2],\n [7, 14, 4, -8, 0, -2, 12, -14, 11],\n [15, -16, 4, 0, 7, -10, 19, 6, -9],\n [-14, 8, 7, -2, -10, -11, 0, -8, 8],\n [19, 2, 16, 12, 19, 0, 10, 11, -12],\n [6, -6, 0, -14, 6, -8, 11, 7, -18],\n [-3, -5, -2, 11, -9, 8, -12, -18, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "807", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[13, -10, 7, 1, -25, 18, -10, -21, 20],\n [0, 15, 8, 18, -1, 16, 8, -11, -22],\n [0, 0, -1, 15, -13, 16, 20, -1, -23],\n [0, 0, 0, -12, -4, 22, -17, -2, -3],\n [0, 0, 0, 0, -12, -6, 13, 10, 1],\n [0, 0, 0, 0, 0, -7, 15, 14, 13],\n [0, 0, 0, 0, 0, 0, -14, 3, 4],\n [0, 0, 0, 0, 0, 0, 0, -8, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6092", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, 16, 6, 17, 9, 23, -15, -9, 25],\n [0, -24, -2, 20, -11, 2, -23, 3, 19],\n [0, 0, -4, 5, -19, 22, 22, 0, 5],\n [0, 0, 0, 9, 7, -23, -7, -17, 20],\n [0, 0, 0, 0, -4, 22, -18, -2, 0],\n [0, 0, 0, 0, 0, 24, -24, 7, -14],\n [0, 0, 0, 0, 0, 0, -22, 14, -3],\n [0, 0, 0, 0, 0, 0, 0, -18, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-112", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-16, -15, 14, 12, -15, 22, 4, -22, -24],\n [0, 13, -9, -3, 19, -16, -13, 16, 13],\n [0, 0, -10, -23, 10, -22, 10, -10, 15],\n [0, 0, 0, 10, -3, -14, 16, 5, -14],\n [0, 0, 0, 0, -7, -4, -2, 7, 10],\n [0, 0, 0, 0, 0, -18, -13, 4, -25],\n [0, 0, 0, 0, 0, 0, 9, 2, -14],\n [0, 0, 0, 0, 0, 0, 0, 7, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "862", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 9) of the inverse of matrix 1/450 * A where A =\n[[-13, 10, 0, -6, -9, -1, 0, 3, -12],\n [10, -17, -4, 1, 6, -2, 2, 10, 10],\n [0, -4, -6, -2, 14, -12, 8, 4, -14],\n [-6, 1, -2, 16, -10, -19, 0, -4, -12],\n [-9, 6, 14, -10, 1, -8, 20, -2, -7],\n [-1, -2, -12, -19, -8, 20, -12, -10, 16],\n [0, 2, 8, 0, 20, -12, -7, 11, -6],\n [3, 10, 4, -4, -2, -10, 11, -25, -4],\n [-12, 10, -14, -12, -7, 16, -6, -4, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 7, -3, -4, 7, 12, -8, 2, 8],\n [7, 6, -20, -11, 3, -10, -16, -4, 6],\n [-3, -20, 11, 10, 18, -6, -18, -22, -12],\n [-4, -11, 10, -16, -6, 2, 16, -16, 9],\n [7, 3, 18, -6, 22, -12, -16, 12, -23],\n [12, -10, -6, 2, -12, 22, 0, -3, 1],\n [-8, -16, -18, 16, -16, 0, -14, 2, 14],\n [2, -4, -22, -16, 12, -3, 2, -4, 16],\n [8, 6, -12, 9, -23, 1, 14, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[1, -4, -5, -11, 21, 9, 2, 7, 4],\n [-4, -18, -19, -12, -18, -1, 7, -22, 18],\n [-5, -19, -20, 8, -18, -2, 7, -8, 12],\n [-11, -12, 8, 6, -10, -11, 2, 8, 2],\n [21, -18, -18, -10, -14, -18, 19, 0, 4],\n [9, -1, -2, -11, -18, 21, 16, 9, 0],\n [2, 7, 7, 2, 19, 16, -16, 13, -1],\n [7, -22, -8, 8, 0, 9, 13, -17, -6],\n [4, 18, 12, 2, 4, 0, -1, -6, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 3) rounded to the nearest integer?\n[[-12, 22, 14, -6, 22, 4, 18, 12, -10],\n [22, -14, -9, -2, -4, -3, -11, -4, -2],\n [14, -9, -6, 7, -12, -10, -7, -4, -14],\n [-6, -2, 7, 23, 10, -1, -10, 6, -3],\n [22, -4, -12, 10, 23, 10, -3, -4, -12],\n [4, -3, -10, -1, 10, 6, 2, -8, 10],\n [18, -11, -7, -10, -3, 2, -12, -6, 6],\n [12, -4, -4, 6, -4, -8, -6, -17, -13],\n [-10, -2, -14, -3, -12, 10, 6, -13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-145", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[8, -16, -4, 2, -8, 22, -2, 9, 8],\n [-16, 20, 2, 12, 6, 4, 18, -8, 7],\n [-4, 2, -1, -4, 6, -13, -3, -11, 0],\n [2, 12, -4, -17, -2, -14, 8, 16, -9],\n [-8, 6, 6, -2, 7, -2, 10, 8, -15],\n [22, 4, -13, -14, -2, 6, -7, 1, 14],\n [-2, 18, -3, 8, 10, -7, 4, -5, -7],\n [9, -8, -11, 16, 8, 1, -5, -5, 6],\n [8, 7, 0, -9, -15, 14, -7, 6, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-83", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[23, -19, 14, 16, -2, 9, -13, 23, -13],\n [0, -7, 3, -4, 15, -5, -10, 4, -21],\n [0, 0, -20, -5, 16, 24, -15, -2, 2],\n [0, 0, 0, 14, 25, 21, -7, 24, -9],\n [0, 0, 0, 0, 5, 16, 23, 21, -18],\n [0, 0, 0, 0, 0, 19, 7, 24, -15],\n [0, 0, 0, 0, 0, 0, -9, -8, -15],\n [0, 0, 0, 0, 0, 0, 0, 11, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -17, 0, 14, -4, -11, -12, 8, -2],\n [-17, 3, -1, 2, -15, 6, 4, 1, 14],\n [0, -1, -22, 8, -16, 8, 6, 10, -3],\n [14, 2, 8, 6, -7, -11, 0, 8, -8],\n [-4, -15, -16, -7, -19, -18, 18, -4, -10],\n [-11, 6, 8, -11, -18, 13, 19, 19, 1],\n [-12, 4, 6, 0, 18, 19, -24, 1, 0],\n [8, 1, 10, 8, -4, 19, 1, 6, -17],\n [-2, 14, -3, -8, -10, 1, 0, -17, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-25, 6, -2, 22, 16, -17, 24, -25, 16],\n [0, -16, 18, 17, 15, 4, -21, -22, 19],\n [0, 0, -25, 23, -11, -2, -11, 24, -20],\n [0, 0, 0, 13, 15, 8, 13, 6, 3],\n [0, 0, 0, 0, -2, -11, -14, -6, -22],\n [0, 0, 0, 0, 0, -3, -19, -14, 22],\n [0, 0, 0, 0, 0, 0, 24, 25, -19],\n [0, 0, 0, 0, 0, 0, 0, -3, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1970", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[21, -8, 21, 17, -1, 1, 1, -14, -3],\n [0, 18, -19, -2, -19, 3, 2, -3, -16],\n [0, 0, 22, 8, -1, -24, 24, -21, -12],\n [0, 0, 0, 2, -17, -20, -9, 14, 9],\n [0, 0, 0, 0, 8, 20, -25, -11, -8],\n [0, 0, 0, 0, 0, -6, 22, 10, 12],\n [0, 0, 0, 0, 0, 0, -19, -3, -15],\n [0, 0, 0, 0, 0, 0, 0, -18, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6572", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 13, 6, 3, -10, -25, -14, -7, -17],\n [22, -19, 4, -11, 18, -22, -20, 12, 21],\n [9, -24, -21, -18, 25, 4, 22, -7, 4],\n [5, -10, 12, -4, 7, 24, -4, -18, 11],\n [-14, 24, -21, -1, 3, -13, 0, -4, 3],\n [-14, 22, 20, 17, 2, -17, -16, 22, 25],\n [16, 0, 10, 14, -15, -20, -22, 1, -2],\n [-21, 24, -23, -19, -2, -4, -14, 9, -9],\n [-23, -15, -20, 17, 10, -9, -4, -25, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-23, -10, 9, -12, 23, 25, -19, 0, 17],\n [22, 5, -2, -7, 11, -25, -1, -16, -8],\n [16, -25, 3, -13, -22, -14, 22, -7, 0],\n [18, 12, -10, 18, -1, -16, 11, 2, 2],\n [-1, -1, 25, -14, -18, 10, 13, -2, -3],\n [11, -15, -9, 2, -23, -24, 25, 3, 8],\n [-12, 7, 22, 21, -8, 3, -24, -15, 5],\n [23, -13, 18, 0, 8, 24, -16, -14, 23],\n [-4, 20, 5, -7, 19, -2, -1, 9, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1193", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-21, 10, 12, -14, 8, -10, 8, -17, 10],\n [10, 0, 16, -18, -12, -7, 5, -10, 6],\n [12, 16, -3, 6, -20, -4, 10, 3, 9],\n [-14, -18, 6, 8, -12, -10, -20, -12, -10],\n [8, -12, -20, -12, -7, -19, 1, 8, 2],\n [-10, -7, -4, -10, -19, 21, -6, 4, -1],\n [8, 5, 10, -20, 1, -6, -17, 4, -18],\n [-17, -10, 3, -12, 8, 4, 4, 22, -12],\n [10, 6, 9, -10, 2, -1, -18, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-137", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, -6, -16, -15, 13, -7, -7, 17, -20],\n [0, -25, -3, 14, 11, -16, -24, 10, -24],\n [0, 0, 16, -5, 4, -2, -24, 12, -4],\n [0, 0, 0, -2, 0, -24, 20, 19, 8],\n [0, 0, 0, 0, -23, -14, 12, 25, -9],\n [0, 0, 0, 0, 0, -5, 14, -2, -2],\n [0, 0, 0, 0, 0, 0, 9, 22, 9],\n [0, 0, 0, 0, 0, 0, 0, -6, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84716", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[14, 8, 6, 1, -6, 6, 3, -4, -11],\n [8, -14, -1, -6, 4, 8, 3, 4, 12],\n [6, -1, -25, -4, -11, -22, 4, -6, -13],\n [1, -6, -4, 0, 6, 4, -7, -16, -21],\n [-6, 4, -11, 6, 18, 6, 3, -5, -2],\n [6, 8, -22, 4, 6, 4, 0, -1, 4],\n [3, 3, 4, -7, 3, 0, -2, -10, 3],\n [-4, 4, -6, -16, -5, -1, -10, -4, -10],\n [-11, 12, -13, -21, -2, 4, 3, -10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 9) of the inverse of matrix 1/450 * A where A =\n[[-16, -23, -7, -24, -9, 3, -24, -10, 23],\n [-16, -22, 17, 0, 23, -2, -14, -5, 16],\n [-10, 10, 9, -17, -20, 18, -25, -12, -2],\n [-16, -8, 19, -17, 1, -7, 10, -23, 12],\n [-17, -16, -17, -9, 16, 12, 22, 23, 17],\n [-6, -19, -22, -16, -5, -12, -1, -9, 2],\n [-12, -13, 8, 15, -23, -22, 18, -11, -6],\n [-18, 24, -21, -24, 2, -4, -17, 2, 20],\n [-25, 10, 23, 16, -24, 12, 0, 5, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[15, 22, -6, 6, -8, -2, 3, -14, 5],\n [22, 19, -16, 0, -2, 2, 2, -22, 7],\n [-6, -16, 14, 2, -10, 18, -2, -2, 14],\n [6, 0, 2, 3, 14, 4, -8, 15, 0],\n [-8, -2, -10, 14, -3, 2, -6, -9, -4],\n [-2, 2, 18, 4, 2, 19, -25, -4, -6],\n [3, 2, -2, -8, -6, -25, 21, -8, 12],\n [-14, -22, -2, 15, -9, -4, -8, 1, -12],\n [5, 7, 14, 0, -4, -6, 12, -12, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-249", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 18, -9, -23, 5, -5, 7, -25, -20],\n [25, -22, -4, -13, 18, 4, 14, 0, 13],\n [13, -19, -12, 0, -8, 25, -2, 25, -1],\n [24, 6, -20, -10, -23, -5, 6, -24, 21],\n [-6, -15, 25, -8, -15, 9, 10, 12, -14],\n [5, 10, 4, 18, -22, -24, 18, -13, 0],\n [3, 22, 10, 2, -18, -21, 6, 4, -12],\n [21, 17, -16, -16, -20, -10, 0, -5, 10],\n [15, 16, 4, -21, -16, 22, 5, -15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-19, -14, 19, 23, 15, -18, 2, -10, -23],\n [0, 6, -5, 19, -8, 22, 20, -15, 24],\n [0, 0, 25, -24, 15, -4, -17, -12, -11],\n [0, 0, 0, -1, 11, -20, 11, 7, -1],\n [0, 0, 0, 0, 5, 0, -15, 4, -15],\n [0, 0, 0, 0, 0, 2, -4, 16, 25],\n [0, 0, 0, 0, 0, 0, 20, -15, 16],\n [0, 0, 0, 0, 0, 0, 0, -7, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142435", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[6, 17, -3, -6, -7, 3, -18, 3, -8],\n [0, -14, -16, 21, 11, -9, 6, -22, 5],\n [0, 0, -8, -18, 6, -6, 23, 14, -13],\n [0, 0, 0, 13, 24, -5, -19, 0, -3],\n [0, 0, 0, 0, 13, 20, -11, -10, 0],\n [0, 0, 0, 0, 0, -2, 10, -8, -3],\n [0, 0, 0, 0, 0, 0, 18, 18, 19],\n [0, 0, 0, 0, 0, 0, 0, -12, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22779", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[22, -12, 8, 0, -8, -6, -7, 2, -2],\n [-12, -20, -10, -12, 12, -4, -1, 21, -5],\n [8, -10, -15, -5, -8, 8, -17, 16, -6],\n [0, -12, -5, 22, -2, 2, 22, 11, -14],\n [-8, 12, -8, -2, -11, 0, 6, 0, 11],\n [-6, -4, 8, 2, 0, -15, 16, -5, 6],\n [-7, -1, -17, 22, 6, 16, 7, 20, 1],\n [2, 21, 16, 11, 0, -5, 20, -1, 7],\n [-2, -5, -6, -14, 11, 6, 1, 7, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-533", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (5, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 9, 21, 1, 3, -21, -25, 17, 25],\n [-21, 3, -9, 25, 23, 11, -2, 1, -17],\n [12, -13, 0, -15, -2, 7, 23, -20, 9],\n [-10, -13, 18, -15, -3, -24, 4, -7, 14],\n [19, 20, 21, 23, -11, 16, 7, 18, 15],\n [-21, -4, 1, 21, 9, -7, 13, -19, 13],\n [8, 8, 1, 18, -21, -22, -19, 22, -23],\n [-5, 8, 23, -17, -6, 14, -14, 13, 20],\n [2, 22, 7, -16, -15, -19, -8, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, -3, -7, 19, -23, 8, -1, 15, 5],\n [13, -12, 11, 21, -6, 6, 7, 5, -19],\n [-21, -22, -15, -7, 12, -6, 1, 3, -8],\n [11, 21, -1, -6, -20, 10, 23, -11, -8],\n [12, -1, -6, -4, 25, -14, 15, 14, 21],\n [7, 3, -24, 0, 6, -23, 4, -7, -16],\n [-1, 20, -7, 17, -5, -20, 25, -12, -18],\n [-24, -8, -4, 4, 10, 2, 9, -24, 10],\n [-8, 17, -17, 2, -18, -18, -21, -13, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4407", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, 0, 8, 16, 12, 4, 6, 18, -4],\n [0, -15, 6, 12, -10, -6, -10, -2, 4],\n [8, 6, -13, -18, 16, 12, -2, -5, -13],\n [16, 12, -18, 16, 4, 13, -3, -2, 18],\n [12, -10, 16, 4, 23, 9, 6, 2, 3],\n [4, -6, 12, 13, 9, -15, -17, 15, 8],\n [6, -10, -2, -3, 6, -17, 25, -14, 16],\n [18, -2, -5, -2, 2, 15, -14, 20, 15],\n [-4, 4, -13, 18, 3, 8, 16, 15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1442", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-7, 17, -21, 4, -1, 4, -1, -17, 1],\n [-2, 14, 17, 12, -11, 12, 0, 4, -15],\n [3, -11, 18, -17, 16, 3, -11, -9, -10],\n [-4, 14, 23, 17, -15, 12, -1, 4, -24],\n [-25, 12, 11, -17, -21, 24, -2, 1, 4],\n [25, -11, 21, -17, 20, 11, 4, 23, -11],\n [-6, 23, -1, -17, 19, -4, -13, 11, 2],\n [-12, 4, 13, -21, -14, 9, 15, 16, -25],\n [20, -25, 16, 17, -6, 8, 8, -2, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "681", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-15, -18, 9, 15, -10, -10, 16, -20, -6],\n [0, -18, -6, 6, 7, -20, 2, -18, -12],\n [0, 0, -4, 7, 17, -5, -20, 14, -19],\n [0, 0, 0, -18, -2, 1, 25, 2, -21],\n [0, 0, 0, 0, 21, 19, -13, 11, -24],\n [0, 0, 0, 0, 0, -1, 13, 20, 5],\n [0, 0, 0, 0, 0, 0, -10, 10, -19],\n [0, 0, 0, 0, 0, 0, 0, -22, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2825", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, 20, 6, 3, -22, 8, 0, -5, 10],\n [20, -25, 18, -9, 10, -9, 0, -2, -20],\n [6, 18, 17, 10, 8, 6, 0, -20, -6],\n [3, -9, 10, 16, 16, 5, -4, -12, 6],\n [-22, 10, 8, 16, 23, 16, 14, -12, -1],\n [8, -9, 6, 5, 16, 24, 2, 0, 14],\n [0, 0, 0, -4, 14, 2, 18, 4, 6],\n [-5, -2, -20, -12, -12, 0, 4, 3, 6],\n [10, -20, -6, 6, -1, 14, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "591", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[20, -16, 6, 18, 11, -5, -4, -13, 0],\n [-16, -12, -13, 10, 6, -13, 9, 18, 0],\n [6, -13, 18, 2, 2, -17, 7, 7, 2],\n [18, 10, 2, 14, -1, -22, -1, 5, -8],\n [11, 6, 2, -1, -10, -6, 10, 0, 7],\n [-5, -13, -17, -22, -6, 20, -4, -17, 22],\n [-4, 9, 7, -1, 10, -4, -9, -10, -8],\n [-13, 18, 7, 5, 0, -17, -10, -2, 0],\n [0, 0, 2, -8, 7, 22, -8, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[5, -12, 0, -4, 8, 7, -13, 6, -18],\n [-4, 15, -6, -5, 8, 23, 4, -20, 9],\n [1, -6, 23, 12, 14, -12, -16, 16, -11],\n [14, 17, 22, -23, -11, 19, 5, -15, 20],\n [13, -7, -11, 12, -6, -4, -19, -12, -22],\n [-17, 13, -1, 21, 9, 11, 23, 1, 2],\n [-2, 7, 7, -10, -3, 20, -15, 20, 14],\n [-7, 8, -3, -16, 11, 21, -25, -24, 25],\n [-4, -9, 21, -2, 24, -5, 14, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25928", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-18, 4, -4, -3, 14, 25, -13, 2, 4],\n [-21, -16, 13, -17, -12, 12, -16, 7, -15],\n [14, -20, -9, 10, -20, 21, -16, 23, 16],\n [-21, -7, -19, -2, 25, 16, -7, -15, -23],\n [4, 17, 12, -20, 21, 9, -4, -15, -18],\n [1, 3, -18, -3, 3, -10, 9, -18, -18],\n [19, 7, 16, -21, 11, -9, -4, -12, 12],\n [6, -12, 18, -6, -4, 4, 7, -21, -8],\n [20, -19, 3, 21, -17, 21, 22, 15, -19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-19, -1, 11, -10, 16, -2, -2, 4, -16],\n [-1, -20, 12, -6, -1, 4, -4, -19, 22],\n [11, 12, -19, -2, 4, 0, -16, -8, -3],\n [-10, -6, -2, -20, -11, -10, -2, 2, 2],\n [16, -1, 4, -11, 9, -16, -9, 6, -6],\n [-2, 4, 0, -10, -16, 13, -8, -2, 10],\n [-2, -4, -16, -2, -9, -8, 1, -4, 3],\n [4, -19, -8, 2, 6, -2, -4, 17, -7],\n [-16, 22, -3, 2, -6, 10, 3, -7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-15, -6, -14, -2, 7, -4, -8, 16, 8],\n [-6, -22, 16, -16, -10, 20, 20, 10, 10],\n [-14, 16, -22, 4, 6, -4, 0, 11, 11],\n [-2, -16, 4, -23, 24, 2, 6, 3, 15],\n [7, -10, 6, 24, 4, -6, -15, 6, -3],\n [-4, 20, -4, 2, -6, 6, 0, 0, 8],\n [-8, 20, 0, 6, -15, 0, -24, -21, -4],\n [16, 10, 11, 3, 6, 0, -21, 11, 4],\n [8, 10, 11, 15, -3, 8, -4, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -25, -18, 16, -11, 8, -7, 18, 4],\n [0, 18, 1, -6, -1, -17, 14, 8, -5],\n [0, 0, -22, 25, -18, -13, -5, 9, -21],\n [0, 0, 0, 16, -10, -22, 4, 20, 4],\n [0, 0, 0, 0, 23, 23, -15, -7, -8],\n [0, 0, 0, 0, 0, 3, -9, 0, -21],\n [0, 0, 0, 0, 0, 0, 22, 9, 18],\n [0, 0, 0, 0, 0, 0, 0, -5, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2126", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -17, -21, -21, 15, 15, 8, -19, 0],\n [0, 8, 0, 6, -14, -20, -6, -7, -10],\n [0, 0, -8, -21, 24, -20, -12, 23, -8],\n [0, 0, 0, -8, -22, 6, 21, -20, 0],\n [0, 0, 0, 0, -21, -12, -24, 25, 14],\n [0, 0, 0, 0, 0, 10, 24, -7, -6],\n [0, 0, 0, 0, 0, 0, -23, 11, -1],\n [0, 0, 0, 0, 0, 0, 0, -1, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-55472", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[23, 17, -4, 2, -10, 18, -10, -10, 11],\n [17, -16, 5, 0, 1, -2, 4, -3, 12],\n [-4, 5, -1, 3, -6, -17, -7, -6, 0],\n [2, 0, 3, -25, 4, -4, 8, 3, -18],\n [-10, 1, -6, 4, 1, -10, 10, 10, -4],\n [18, -2, -17, -4, -10, -21, 2, 9, -9],\n [-10, 4, -7, 8, 10, 2, 14, 10, -10],\n [-10, -3, -6, 3, 10, 9, 10, 13, 4],\n [11, 12, 0, -18, -4, -9, -10, 4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (6, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-23, -1, 1, 7, -6, 13, -12, -2, 6],\n [-1, -17, -12, -9, 12, 0, 3, 8, -16],\n [1, -12, -15, 7, -6, 9, 2, 10, 8],\n [7, -9, 7, 7, 4, 10, -11, -18, 7],\n [-6, 12, -6, 4, 20, 3, 4, 12, 1],\n [13, 0, 9, 10, 3, 6, 8, 2, 10],\n [-12, 3, 2, -11, 4, 8, -10, 2, -4],\n [-2, 8, 10, -18, 12, 2, 2, 11, 5],\n [6, -16, 8, 7, 1, 10, -4, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-15, -6, 22, 22, 22, 12, -11, 9, -17],\n [7, -15, -4, -20, 11, 24, -5, -14, -19],\n [-24, 13, 15, -2, 0, -1, -6, 14, 15],\n [16, 18, -24, 16, 9, 7, -9, -4, -25],\n [11, 4, 20, -20, 15, -12, 10, 7, 12],\n [13, -20, 0, -2, 7, -18, 18, 17, 8],\n [8, -2, -24, -18, -1, 4, 6, 4, -19],\n [22, -2, -17, -10, -24, 9, 8, -4, -7],\n [23, -5, -14, -15, -7, -20, 16, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1560", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (3, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, 12, -13, 0, -12, 19, -2, 22, -25],\n [20, 19, 4, -16, -16, 2, -22, -12, -14],\n [12, 21, 11, -16, 15, 1, 16, -14, -4],\n [-22, 3, 10, 19, -12, -14, 19, -6, 19],\n [-3, -4, 8, -5, 25, -17, -16, 23, -16],\n [19, 4, 7, -24, 23, 6, 19, -9, 2],\n [19, -9, 25, -12, -16, 8, -12, -9, 11],\n [-4, -8, 9, 22, 25, -8, 4, 11, 14],\n [-20, -11, 9, 0, 15, 1, 4, -15, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -3, -17, 16, 21, -8, 25, 13, -7],\n [-21, -8, 7, 18, 12, -13, 23, -17, 0],\n [-25, -14, -2, -25, -22, -19, 2, 11, -21],\n [13, 6, 23, 5, 18, -11, -23, 23, 20],\n [21, 21, -11, 25, 17, -8, -5, -16, -5],\n [0, 15, -23, -25, -5, -15, -10, 9, -5],\n [15, -15, 5, 23, -25, 15, 6, -23, 6],\n [16, -21, 17, 11, -14, -12, 18, 25, -17],\n [-19, -10, 2, -19, -12, 6, -18, 1, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the inverse of matrix 1/450 * A where A =\n[[-23, 4, -10, 16, 6, -4, -3, 20, 8],\n [4, 15, -24, 17, -8, 14, -20, 4, 14],\n [-10, -24, 2, -9, -11, -7, -11, 6, 0],\n [16, 17, -9, -25, -12, -18, 7, 2, -4],\n [6, -8, -11, -12, 12, 8, 13, 18, -2],\n [-4, 14, -7, -18, 8, -17, -1, -6, 7],\n [-3, -20, -11, 7, 13, -1, 3, 2, -16],\n [20, 4, 6, 2, 18, -6, 2, -12, 9],\n [8, 14, 0, -4, -2, 7, -16, 9, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 3) of the inverse of matrix 1/450 * A where A =\n[[-20, 14, 2, -13, 3, 19, -6, -9, 9],\n [19, 13, 11, 17, -3, -8, 10, -6, -19],\n [10, 16, -25, 23, 11, 23, 9, 15, -23],\n [9, 3, -17, 11, 16, 21, -1, -14, 12],\n [-19, -19, -22, 19, 21, 5, 24, 24, 13],\n [-16, 22, -3, 0, -3, 3, -18, -7, 3],\n [17, -20, 3, -2, -16, 25, -12, -20, -22],\n [-11, 11, 22, 13, 2, -24, -13, -24, 15],\n [6, -21, -23, -24, -12, 14, 18, 23, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-198", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (2, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[22, 12, -20, 24, 8, -18, 20, -24, 0],\n [0, -2, 5, -10, 24, -5, 12, 0, -9],\n [0, 0, 16, -22, 24, 17, 22, -22, -7],\n [0, 0, 0, -8, 25, -8, 22, -19, -9],\n [0, 0, 0, 0, 10, 0, 22, -12, -9],\n [0, 0, 0, 0, 0, -14, -9, -17, 18],\n [0, 0, 0, 0, 0, 0, -6, -25, -17],\n [0, 0, 0, 0, 0, 0, 0, 9, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1463", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 3) of the inverse of matrix 1/450 * A where A =\n[[-23, 13, -2, -5, -20, 7, -18, 7, 22],\n [0, -24, 12, 14, 13, 13, -2, -5, 25],\n [0, 0, -15, -15, -23, -3, -25, -3, -4],\n [0, 0, 0, -9, 15, 24, -6, -17, -15],\n [0, 0, 0, 0, 18, 24, -18, 3, -18],\n [0, 0, 0, 0, 0, -18, -12, -13, 14],\n [0, 0, 0, 0, 0, 0, -1, -19, -9],\n [0, 0, 0, 0, 0, 0, 0, 13, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[16, -15, -16, -14, -12, 4, 15, -13, 4],\n [0, -15, -25, 1, 21, 13, 17, 23, 11],\n [0, 0, 17, 0, -1, -9, -20, -11, -23],\n [0, 0, 0, 18, 25, -8, 22, 14, 6],\n [0, 0, 0, 0, -14, 21, 16, -9, 13],\n [0, 0, 0, 0, 0, -8, 22, 17, -17],\n [0, 0, 0, 0, 0, 0, 14, 17, 1],\n [0, 0, 0, 0, 0, 0, 0, -16, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1123", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[15, -8, -17, -4, -16, 14, -3, 17, -13],\n [-2, -13, 22, 19, -1, 18, 21, 3, -10],\n [14, -20, -18, 8, -8, 17, 6, 23, -16],\n [8, -3, -7, -6, 8, 12, -9, 18, -21],\n [-24, 15, 8, -6, 20, 21, -24, 2, -8],\n [18, 13, 22, 25, 9, -11, 21, 13, 14],\n [13, -23, -7, -3, -7, -8, 4, 13, -7],\n [-21, -13, 8, -2, -8, -22, 10, -18, 17],\n [-25, 15, 12, 10, 12, -13, -4, 3, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, 20, 18, -22, 14, -9, 11, -23, -22],\n [0, -10, -15, 1, 0, 5, 8, -18, 13],\n [0, 0, 1, 19, 17, -23, 8, -10, -25],\n [0, 0, 0, 22, 6, 0, -20, 20, -15],\n [0, 0, 0, 0, -25, -5, 19, -6, -17],\n [0, 0, 0, 0, 0, -25, -23, 6, -6],\n [0, 0, 0, 0, 0, 0, 19, 3, 16],\n [0, 0, 0, 0, 0, 0, 0, -15, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175226", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-20, -16, 11, -14, 18, -9, 1, -24, -1],\n [0, 18, 2, 19, 11, 11, -9, -21, -7],\n [0, 0, 23, 17, 12, 19, 18, 4, 6],\n [0, 0, 0, 16, -15, 15, -13, 9, -9],\n [0, 0, 0, 0, 4, 0, -10, -15, -22],\n [0, 0, 0, 0, 0, -22, 9, -5, 10],\n [0, 0, 0, 0, 0, 0, 24, -18, -18],\n [0, 0, 0, 0, 0, 0, 0, -25, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (5, 5) rounded to the nearest integer?\n[[-2, 16, -4, -16, -22, -18, 13, -11, -18],\n [0, 16, 13, 25, 9, 15, 22, -12, 6],\n [0, 0, 7, 22, 9, 1, -25, -20, -24],\n [0, 0, 0, 3, -10, 3, 5, -4, -16],\n [0, 0, 0, 0, 14, -18, -3, -19, 6],\n [0, 0, 0, 0, 0, 10, 1, -20, 16],\n [0, 0, 0, 0, 0, 0, 20, -13, -1],\n [0, 0, 0, 0, 0, 0, 0, 19, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[17, -18, 4, -25, 8, -6, 10, 8, 8],\n [-13, -20, 10, -1, 1, 21, 5, -23, 2],\n [-22, -9, 12, 8, -6, -13, 21, -21, -2],\n [25, 12, -9, 5, 2, -25, -24, 7, 14],\n [3, -22, -8, -2, 6, -17, 21, -10, -5],\n [4, -23, 7, 5, 19, -12, -20, -21, 3],\n [11, 10, -5, -14, 20, -3, -12, 17, 16],\n [-16, 1, 15, -24, -12, -19, -9, -6, -18],\n [-6, 10, -21, -13, 13, 12, -9, -20, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -4, 0, -4, 4, 2, -17, -16, -18],\n [-4, -3, 7, 4, -5, 4, -4, -15, 2],\n [0, 7, 10, 4, 8, -4, 1, -8, 10],\n [-4, 4, 4, -22, 2, -2, 14, 14, 14],\n [4, -5, 8, 2, 7, 1, -6, -10, 12],\n [2, 4, -4, -2, 1, -8, 5, 10, 8],\n [-17, -4, 1, 14, -6, 5, 1, -6, 4],\n [-16, -15, -8, 14, -10, 10, -6, 22, -6],\n [-18, 2, 10, 14, 12, 8, 4, -6, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-344", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-21, 5, 3, -11, -1, -13, 18, -2, -11],\n [-2, 0, -7, -2, -7, 16, -9, 22, -21],\n [-22, -4, -16, -5, -1, -20, 4, 3, -15],\n [-15, 22, 20, 1, -7, -4, 2, -22, 11],\n [-7, -9, 24, 14, 10, -3, 24, 2, -15],\n [-12, -13, -2, -10, 2, 4, 18, 15, 13],\n [16, 1, -9, 24, 0, -19, 9, -11, -10],\n [-5, -9, 19, 0, 9, -6, -6, -3, -21],\n [-17, -3, -8, 3, -15, 17, 22, -18, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-77", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-24, -8, 5, -15, 1, -22, -4, 2, 10],\n [-8, 22, 8, -2, 5, 2, -2, -2, 0],\n [5, 8, 22, -4, 12, -1, 3, 2, 7],\n [-15, -2, -4, 11, -6, -1, -2, 9, -12],\n [1, 5, 12, -6, 4, 7, -4, 1, -1],\n [-22, 2, -1, -1, 7, -9, 10, -3, -9],\n [-4, -2, 3, -2, -4, 10, 16, 18, 4],\n [2, -2, 2, 9, 1, -3, 18, -12, -14],\n [10, 0, 7, -12, -1, -9, 4, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the inverse of matrix 1/450 * A where A =\n[[24, 14, -5, -6, -9, 16, -22, 1, 15],\n [14, 8, -6, -17, 6, -11, -2, -16, -2],\n [-5, -6, -12, 0, 10, -12, -10, 8, 20],\n [-6, -17, 0, -3, -4, 8, -16, -4, -4],\n [-9, 6, 10, -4, 22, -2, -24, 4, -19],\n [16, -11, -12, 8, -2, -14, -2, -15, 20],\n [-22, -2, -10, -16, -24, -2, -25, 3, -2],\n [1, -16, 8, -4, 4, -15, 3, -3, -6],\n [15, -2, 20, -4, -19, 20, -2, -6, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, 2, -20, 13, -7, -9, -20, -11, -4],\n [0, 8, -21, -3, -21, 18, -16, -22, -14],\n [0, 0, 4, 24, -2, -21, -13, 10, -17],\n [0, 0, 0, -2, 17, -22, 15, 0, 18],\n [0, 0, 0, 0, -17, -25, -10, 20, -13],\n [0, 0, 0, 0, 0, 2, -6, -25, -14],\n [0, 0, 0, 0, 0, 0, 19, -4, 19],\n [0, 0, 0, 0, 0, 0, 0, -3, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-68", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[0, -10, -10, 18, 15, -12, 18, 0, 1],\n [22, -9, 18, -22, -9, 7, 4, -5, -9],\n [-15, 25, 4, -8, -6, 8, 15, 2, -17],\n [18, 5, 19, -10, 5, 3, -13, -3, -12],\n [13, -24, -14, 2, 6, 23, -2, 11, 3],\n [16, -8, -23, -13, -13, 16, 3, -24, 2],\n [22, -22, 25, -21, 13, 15, -21, -18, 8],\n [-1, 1, -19, 10, 6, -5, 21, -8, -24],\n [20, 16, -21, 18, 16, 24, 12, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-302", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[18, 8, -8, 11, -15, -2, 0, 2, 6],\n [8, 19, 10, 16, -9, -2, 15, 10, -3],\n [-8, 10, -11, 12, 0, 6, 13, 11, 6],\n [11, 16, 12, -8, 16, 6, 4, -18, 10],\n [-15, -9, 0, 16, 18, 4, 2, -10, 0],\n [-2, -2, 6, 6, 4, 13, 2, 4, -16],\n [0, 15, 13, 4, 2, 2, -23, 12, 4],\n [2, 10, 11, -18, -10, 4, 12, 9, 8],\n [6, -3, 6, 10, 0, -16, 4, 8, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, 6, -14, -15, -16, 9, 18, -22, 16],\n [-24, 18, 2, 17, 20, 21, -12, 18, 3],\n [-24, 8, 7, -6, 21, 4, 16, 0, -6],\n [-25, -25, -1, 7, -3, -15, 18, -11, -12],\n [-25, 7, -20, -3, 0, -23, 20, -20, 14],\n [-1, 21, -9, 2, 6, 3, -3, 15, -10],\n [6, 0, 7, 22, -7, 15, -9, 12, -12],\n [-8, -5, 20, 13, 16, 22, 13, 2, -6],\n [-20, 0, -20, 13, 0, -9, 14, -24, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-78", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -19, 18, -6, -23, 10, 17, 18, 25],\n [-7, 4, -15, -13, 7, 12, 22, -24, 20],\n [-3, 24, 23, -6, 24, 25, 4, -11, -24],\n [4, -1, -22, -25, -18, -12, -15, -2, -2],\n [6, -1, 20, 2, -10, 16, 13, -10, 10],\n [-14, -14, 8, 12, -6, 21, -11, -4, -10],\n [-2, -23, -25, 18, 21, 25, 12, 25, -9],\n [15, -5, 19, 21, 22, -13, -24, -24, 17],\n [-1, 2, 22, 23, 0, 9, 2, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1314", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-12, 15, -17, 18, 4, -23, 8, 7, 1],\n [-17, -13, 4, -10, 25, 16, 0, -21, 20],\n [1, -11, 2, -23, 15, -25, -25, 25, -20],\n [-15, 24, 20, -10, 7, -2, 6, -16, -1],\n [-16, -13, -25, 9, -12, -5, 22, 12, -25],\n [-6, -21, 14, 18, 6, -25, 19, 15, 14],\n [19, -24, 5, 21, 20, 25, 0, -17, 25],\n [4, 20, -18, -21, 13, -22, 14, 10, -5],\n [7, 0, 14, 13, -15, -5, 22, -4, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, -11, 1, -7, -11, 19, -19, 17, 14],\n [0, -2, -3, -15, -2, -21, 13, 22, 4],\n [0, 0, 3, -9, -7, 0, -11, -1, -11],\n [0, 0, 0, 21, 9, 18, -20, 11, -15],\n [0, 0, 0, 0, -8, 20, 10, 14, 22],\n [0, 0, 0, 0, 0, 25, -11, 18, -14],\n [0, 0, 0, 0, 0, 0, 2, 19, 11],\n [0, 0, 0, 0, 0, 0, 0, -5, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9970", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-5, 15, 25, 4, -1, -2, -15, 9, -22],\n [11, 10, -13, -17, 2, 20, -10, -20, 1],\n [-16, -3, -5, 0, 19, -23, 17, 9, -19],\n [1, 16, 7, -22, 0, -18, -6, -9, -21],\n [23, -17, -18, -19, 11, 10, -23, -18, -21],\n [-21, -9, 21, 1, 14, 13, 23, -14, 2],\n [-22, 2, -1, 24, 10, 16, -23, 5, 11],\n [-14, 11, 11, -22, 4, 12, 16, 12, 1],\n [-4, -25, 22, 17, 12, -6, -8, -20, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-14, -9, -4, -8, -16, -2, -6, -14, -22],\n [16, -21, 0, 10, -10, -21, 0, -7, -20],\n [-2, 5, 5, -19, -16, 13, -4, -12, 2],\n [16, -4, 6, -15, -12, 5, 18, -22, 19],\n [-4, 3, 9, -13, -6, -7, -11, 25, 0],\n [-6, 10, -20, -11, -22, -20, -24, 10, 24],\n [-11, -14, 14, 18, 15, -19, -4, -18, 16],\n [-15, -24, 4, -22, -1, -5, -1, -17, -18],\n [-21, 20, 2, -24, -5, 23, -18, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2641", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, 1, -24, 2, -15, 20, -5, 16, 6],\n [0, -19, -4, -12, -13, -5, -4, 8, -16],\n [0, 0, -2, -23, 5, 17, 25, 15, -13],\n [0, 0, 0, 8, 15, -8, 10, 0, 7],\n [0, 0, 0, 0, -23, -4, 23, 9, -22],\n [0, 0, 0, 0, 0, -23, -5, 14, -25],\n [0, 0, 0, 0, 0, 0, 6, 3, 19],\n [0, 0, 0, 0, 0, 0, 0, -7, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10297", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[14, 10, 0, 4, 9, 0, 4, 8, 8],\n [10, 2, -10, 4, -20, 6, 4, 10, -8],\n [0, -10, -11, 0, -2, 20, 10, 2, -10],\n [4, 4, 0, -1, -10, -14, 5, 2, 3],\n [9, -20, -2, -10, -15, -3, 12, -6, 0],\n [0, 6, 20, -14, -3, -1, -4, 4, -13],\n [4, 4, 10, 5, 12, -4, 7, 14, -7],\n [8, 10, 2, 2, -6, 4, 14, -7, 3],\n [8, -8, -10, 3, 0, -13, -7, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[23, -21, -21, -1, -2, 11, 5, 20, 8],\n [15, -12, 1, 21, -22, -3, 12, 20, -21],\n [1, 17, -12, -19, 20, 19, -8, 6, -24],\n [15, 17, -6, 3, 17, 0, 12, -25, -21],\n [-12, -1, 22, -17, 4, -7, 14, -18, -10],\n [24, -18, -3, -17, 6, 11, 8, 20, -8],\n [19, 18, -11, -11, 3, -3, -3, -25, -4],\n [-19, 19, 6, 2, 24, 6, 7, 17, -13],\n [2, -17, 22, 17, -23, -9, 8, 6, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "391", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[15, 22, -25, 23, 16, -6, -21, 14, 19],\n [-5, -21, -22, -18, -1, -19, 11, 16, 6],\n [-9, 2, -20, 16, 22, 16, 10, -24, 5],\n [-25, -23, -13, 5, 3, 18, 7, -16, 12],\n [-17, -25, 18, 11, 6, 7, -24, 20, -24],\n [-21, -16, 12, 11, -24, 15, 16, 14, -1],\n [12, 11, -8, 1, -6, 24, 8, 18, -18],\n [-22, 4, 10, -17, 15, -14, -12, 9, -20],\n [21, -3, 25, -22, -25, -17, 22, -17, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[20, -11, -2, 22, -18, 2, 16, 20, -9],\n [9, 5, -22, 22, -12, -1, 20, 22, 14],\n [24, -19, 5, 9, 12, -6, -10, -4, 10],\n [-7, -24, -22, 8, -19, 21, 23, -12, 17],\n [6, -9, 11, -12, -9, 6, -24, 13, -22],\n [14, 4, 4, 7, 16, -25, 7, 10, 23],\n [5, 11, -12, -20, -19, 14, -2, 24, -22],\n [-1, -23, 2, -3, 10, 22, -13, -4, -1],\n [17, -2, 17, 11, 7, -12, -2, -4, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 5) of the inverse. Round your answer to the nearest integer:\n[[11, 0, -14, 6, -5, -4, 14, 0, -10],\n [0, -19, 7, -18, 18, 6, -12, 17, -4],\n [-14, 7, -18, -8, -2, -8, 10, 0, -18],\n [6, -18, -8, 9, 2, -2, -7, -20, 12],\n [-5, 18, -2, 2, -16, 0, 9, -9, -20],\n [-4, 6, -8, -2, 0, 14, 0, 3, 8],\n [14, -12, 10, -7, 9, 0, 12, -4, -20],\n [0, 17, 0, -20, -9, 3, -4, 17, 8],\n [-10, -4, -18, 12, -20, 8, -20, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -7, -23, -17, 13, -24, -17, -20, 12],\n [2, 22, 8, 3, 22, -23, -10, 18, 9],\n [-15, 17, -3, 4, 22, -21, -18, 17, 17],\n [24, 25, -16, 2, 10, -16, -12, 12, 11],\n [21, -21, -20, 4, -7, 23, -12, -15, 20],\n [-21, 19, 5, 18, 6, -2, 25, -16, -13],\n [21, -13, 10, -4, -17, -7, -19, -11, -9],\n [20, -12, 15, 22, -24, -12, -22, -23, -23],\n [-15, -21, 22, 3, 2, -3, 4, -3, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, 8, 16, -18, -8, 5, 4, 19, -14],\n [8, -3, 18, -5, 10, -9, 9, 4, 11],\n [16, 18, -23, 0, -6, 18, -13, 18, 4],\n [-18, -5, 0, 9, -6, -4, 0, 8, 8],\n [-8, 10, -6, -6, 4, -6, -2, -10, 12],\n [5, -9, 18, -4, -6, -9, -4, -6, 2],\n [4, 9, -13, 0, -2, -4, -4, -5, 10],\n [19, 4, 18, 8, -10, -6, -5, -8, -4],\n [-14, 11, 4, 8, 12, 2, 10, -4, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, 7, 4, 4, 19, 12, 18, 0, 10],\n [7, -20, -9, 8, 0, -17, 14, 18, -19],\n [4, -9, -10, -1, -18, -5, 4, 4, -4],\n [4, 8, -1, -24, 18, 0, -3, 0, 22],\n [19, 0, -18, 18, 13, 16, -4, 18, 2],\n [12, -17, -5, 0, 16, -25, 8, 10, 10],\n [18, 14, 4, -3, -4, 8, -7, 12, -6],\n [0, 18, 4, 0, 18, 10, 12, -17, 4],\n [10, -19, -4, 22, 2, 10, -6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 4) of the inverse of matrix 1/450 * A where A =\n[[10, -8, 5, 23, 9, 15, 2, 0, -20],\n [8, 2, 18, 21, -17, 3, 8, -14, -10],\n [-19, 5, 7, -19, -23, -6, -21, -23, 21],\n [12, -11, 9, -3, 7, -24, 10, -5, -12],\n [-12, 16, -15, -22, 21, 4, 10, -6, -10],\n [8, 19, -18, 19, -6, -5, 14, 4, 10],\n [-21, -5, 12, -3, -7, -16, 1, 9, -13],\n [-17, -9, 5, 16, 18, 19, -2, 16, 25],\n [-7, 23, 4, -21, -18, 11, 21, 10, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[19, 23, -21, 7, -4, 21, 16, -1, 17],\n [0, 3, 19, 4, 22, 25, 4, 18, 20],\n [0, 0, 2, -16, -22, 7, -9, -15, -19],\n [0, 0, 0, 15, -16, 0, -20, -9, -10],\n [0, 0, 0, 0, -6, 23, 15, -15, -3],\n [0, 0, 0, 0, 0, 11, -25, -20, 19],\n [0, 0, 0, 0, 0, 0, 5, 2, 19],\n [0, 0, 0, 0, 0, 0, 0, 22, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 9) of the inverse of matrix 1/450 * A where A =\n[[-17, 2, 10, -3, 8, 10, 12, 6, -6],\n [2, -1, 0, 14, 3, -16, -16, -3, -3],\n [10, 0, 19, -15, -6, -10, 4, 0, -8],\n [-3, 14, -15, 25, 4, 4, 6, -22, -2],\n [8, 3, -6, 4, 4, 8, 14, 4, -4],\n [10, -16, -10, 4, 8, -25, -2, -10, 4],\n [12, -16, 4, 6, 14, -2, -4, 1, -2],\n [6, -3, 0, -22, 4, -10, 1, 11, 18],\n [-6, -3, -8, -2, -4, 4, -2, 18, -19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[20, 16, -18, -11, -10, -18, 10, 6, -9],\n [0, -4, 6, -15, 19, -20, -4, -12, 2],\n [0, 0, 1, -25, -16, 7, -10, 13, -20],\n [0, 0, 0, 10, -3, -10, -25, 4, 1],\n [0, 0, 0, 0, 21, -2, 22, 15, 13],\n [0, 0, 0, 0, 0, -14, -13, -23, 17],\n [0, 0, 0, 0, 0, 0, 16, 1, -11],\n [0, 0, 0, 0, 0, 0, 0, -8, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "675", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[1, 12, -2, -4, 6, 18, -7, -12, 4],\n [12, 22, -4, -10, -14, 4, 8, 24, -16],\n [-2, -4, -6, 14, 2, 0, -10, 4, -6],\n [-4, -10, 14, -9, 6, 9, 8, -4, 16],\n [6, -14, 2, 6, -2, -17, 13, -4, 1],\n [18, 4, 0, 9, -17, -15, 10, -15, 4],\n [-7, 8, -10, 8, 13, 10, 12, -14, -2],\n [-12, 24, 4, -4, -4, -15, -14, 14, -12],\n [4, -16, -6, 16, 1, 4, -2, -12, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -21, -24, 25, -12, 3, 15, -25, -13],\n [0, 6, 8, -12, 12, 12, 24, 25, 15],\n [0, 0, -20, 3, 11, -7, -25, -5, 13],\n [0, 0, 0, -18, 5, -14, 16, -20, 0],\n [0, 0, 0, 0, -2, 19, -6, -19, -19],\n [0, 0, 0, 0, 0, 3, -11, -18, 13],\n [0, 0, 0, 0, 0, 0, -12, -15, 6],\n [0, 0, 0, 0, 0, 0, 0, -24, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-117", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[-20, 17, 19, -8, -12, -6, -15, 11, 14],\n [-22, 18, -20, -3, -18, 4, 10, 16, -15],\n [21, -21, -23, -11, -24, -24, -18, 20, 4],\n [15, -21, 4, 18, -16, 7, -2, -7, 4],\n [-1, -15, 23, 9, -25, -9, 5, -20, -13],\n [0, 10, -21, 21, -12, 25, -11, -14, 24],\n [20, 16, -18, 5, 0, 3, -22, 24, 2],\n [-1, 14, 6, 10, -15, 11, -16, 12, 10],\n [24, 1, -9, -19, -17, 9, -17, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1225", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -7, 15, -3, -6, -20, 17, -2, 21],\n [-4, -20, -2, 16, -4, -8, -10, 10, -13],\n [11, -2, -7, 24, -6, 1, -9, -10, -25],\n [-5, 1, -25, 4, -6, -2, 20, -24, -11],\n [3, 9, -13, -7, -25, 19, 21, -10, 17],\n [-23, 14, -20, 5, -21, 0, 2, -11, -17],\n [-4, 11, -5, 16, 3, 0, -20, -15, 10],\n [-6, 18, -6, 1, -20, 7, 4, 24, 8],\n [-21, -10, -14, -14, -15, 25, -5, -19, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6550", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -20, 10, 8, 23, -18, 11, -16, -10],\n [0, -7, -19, -24, 19, -3, 5, -22, -10],\n [0, 0, -5, 2, 20, -14, -13, 14, -9],\n [0, 0, 0, -13, 8, 23, -20, -14, 3],\n [0, 0, 0, 0, -10, -7, 21, 0, 6],\n [0, 0, 0, 0, 0, 11, -23, -20, 5],\n [0, 0, 0, 0, 0, 0, -2, -4, -1],\n [0, 0, 0, 0, 0, 0, 0, 14, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-311", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, -6, -6, -7, 25, -8, -13, -9, 7],\n [0, -21, 2, -1, -6, -5, -13, -20, 3],\n [0, 0, 3, 12, -25, 4, 24, 6, -3],\n [0, 0, 0, -5, 0, -11, -9, 9, -1],\n [0, 0, 0, 0, -20, 2, 3, 22, -5],\n [0, 0, 0, 0, 0, -8, -16, -4, 18],\n [0, 0, 0, 0, 0, 0, 18, -25, 8],\n [0, 0, 0, 0, 0, 0, 0, -14, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "855", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the inverse of matrix 1/450 * A where A =\n[[-21, 11, -24, 12, -19, -25, -23, -6, -24],\n [0, 17, -5, 19, 6, 22, -6, 17, 24],\n [0, 0, 7, -2, -8, -6, 6, -21, -24],\n [0, 0, 0, -4, 13, -4, -15, -15, 19],\n [0, 0, 0, 0, 18, 2, 16, -4, 14],\n [0, 0, 0, 0, 0, -19, 3, 0, 15],\n [0, 0, 0, 0, 0, 0, 7, -10, -3],\n [0, 0, 0, 0, 0, 0, 0, -1, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[6, 11, 18, 3, -4, -24, 24, -17, 3],\n [7, -16, 2, 20, 20, 13, -14, -4, -20],\n [19, 14, -3, 8, 16, 12, -10, -16, 21],\n [-5, -16, -15, -5, -1, 8, 5, 1, -1],\n [16, 6, 18, -15, 21, 0, 10, 11, 7],\n [7, 16, 10, -13, -12, 25, 11, 17, 14],\n [-25, -21, 4, -8, 19, 11, 13, -14, 8],\n [19, -12, 12, -10, 16, -15, 7, -11, 22],\n [16, -16, -23, -15, -15, -10, 12, 4, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-327", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-25, 12, 24, 19, 8, -7, 8, 10, -22],\n [0, -9, -10, -5, 2, -18, 3, -20, 4],\n [0, 0, 5, -1, -3, 17, -5, -10, -22],\n [0, 0, 0, -20, 1, 25, 10, 10, -2],\n [0, 0, 0, 0, 15, -10, 12, -17, 25],\n [0, 0, 0, 0, 0, -24, -6, -22, 2],\n [0, 0, 0, 0, 0, 0, 10, -17, 12],\n [0, 0, 0, 0, 0, 0, 0, -5, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (5, 8) of the inverse. Round your answer to the nearest integer:\n[[10, -17, -16, -23, 23, 3, -19, 0, -18],\n [0, -13, 9, -7, 20, -4, -10, -11, -24],\n [0, 0, 4, -19, 5, 15, 15, 23, 9],\n [0, 0, 0, -16, 4, 6, -23, -16, -17],\n [0, 0, 0, 0, 9, -22, -22, 23, 6],\n [0, 0, 0, 0, 0, -20, 9, 20, 6],\n [0, 0, 0, 0, 0, 0, 12, -15, 24],\n [0, 0, 0, 0, 0, 0, 0, -21, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-93", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-16, 12, 10, -7, 14, -20, -2, 5, -12],\n [12, 7, -14, -18, -4, 5, 7, 2, -1],\n [10, -14, -18, -17, 10, 6, 4, -22, -2],\n [-7, -18, -17, -6, -18, 5, -7, -4, 8],\n [14, -4, 10, -18, 8, 8, -6, 6, -12],\n [-20, 5, 6, 5, 8, -18, 15, 14, 6],\n [-2, 7, 4, -7, -6, 15, 11, 22, 14],\n [5, 2, -22, -4, 6, 14, 22, -3, 14],\n [-12, -1, -2, 8, -12, 6, 14, 14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-337", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (5, 1) rounded to the nearest integer?\n[[1, -6, 7, 5, -2, 11, -20, -2, 14],\n [-6, -3, 2, -16, -12, 19, 2, 2, 5],\n [7, 2, -17, -16, -19, -3, -4, -8, -8],\n [5, -16, -16, -13, -2, -18, 5, -2, -8],\n [-2, -12, -19, -2, 14, -12, 3, 0, 0],\n [11, 19, -3, -18, -12, -12, 2, 2, 8],\n [-20, 2, -4, 5, 3, 2, -8, 8, 16],\n [-2, 2, -8, -2, 0, 2, 8, 22, 20],\n [14, 5, -8, -8, 0, 8, 16, 20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 1) rounded to the nearest integer?\n[[-4, 17, 2, 22, 14, 8, -4, 10, 2],\n [17, 10, -11, 17, -4, -15, 14, 2, -16],\n [2, -11, -1, -6, 12, 18, 8, 0, 18],\n [22, 17, -6, -9, 15, 2, -2, 9, -4],\n [14, -4, 12, 15, -19, 4, -2, 6, -2],\n [8, -15, 18, 2, 4, -6, 14, 2, -14],\n [-4, 14, 8, -2, -2, 14, 18, -10, 1],\n [10, 2, 0, 9, 6, 2, -10, 21, 1],\n [2, -16, 18, -4, -2, -14, 1, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (7, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -5, 10, -13, 20, -17, 9, 20, 10],\n [23, 21, 18, 20, 25, -16, -21, 5, -2],\n [6, 23, 23, -23, -10, 15, 23, -6, 18],\n [-2, 8, 22, -3, 12, -24, 15, -21, -8],\n [24, 3, -16, 16, 16, 24, -10, -3, 4],\n [-20, 18, 10, -6, -10, 2, 0, -4, -15],\n [-25, -21, 23, 17, 20, 15, 16, 10, -24],\n [-20, 1, 0, 9, -13, -14, -8, 12, 16],\n [-20, 2, 2, -1, -21, -11, 21, 18, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[19, 22, -24, 23, -17, 0, -3, 25, 2],\n [-20, -22, 4, 21, -8, 4, 1, 18, 5],\n [18, 23, 13, 4, 11, -14, -9, 8, 2],\n [-22, 8, 20, -12, -13, 23, 23, 24, -23],\n [-5, -10, 25, 12, 0, -20, -8, 15, 24],\n [-20, 15, 24, -1, 22, -2, 4, -3, 19],\n [17, -18, 23, -17, -20, 7, 7, 19, -19],\n [16, -8, -20, 19, 11, -5, 0, -11, 18],\n [4, -15, -18, -21, -18, -21, -16, -11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, -20, 10, 4, -8, 15, 8, -2, -2],\n [-20, 13, -4, 4, -2, -4, -12, 10, 15],\n [10, -4, 24, 0, 2, 6, -10, 14, 2],\n [4, 4, 0, -8, 7, 10, 14, -3, -2],\n [-8, -2, 2, 7, 8, -15, 5, 10, 16],\n [15, -4, 6, 10, -15, 4, 14, -9, 9],\n [8, -12, -10, 14, 5, 14, -17, 6, -12],\n [-2, 10, 14, -3, 10, -9, 6, 17, -24],\n [-2, 15, 2, -2, 16, 9, -12, -24, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-107", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, 19, -12, 2, 7, -1, 14, -8, 20],\n [8, -14, 1, -2, 7, -11, 17, 6, 24],\n [-9, 9, 21, 19, 9, -13, -17, -16, -25],\n [8, 20, 11, -1, -4, -16, 0, -7, 14],\n [19, 15, 24, -22, 14, -21, 3, 12, -21],\n [-25, 2, -7, 10, -25, 3, 25, 10, 6],\n [-12, 6, 20, -17, -7, -15, 22, 25, -22],\n [15, -1, -9, 21, -18, 19, -25, -24, -16],\n [1, 1, -13, -15, -12, 6, -10, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 9, -18, -12, -4, -5, 2, 0, -7],\n [9, -7, 4, 20, -16, -5, -18, 20, 4],\n [-18, 4, -8, 2, -6, 0, -20, -3, -7],\n [-12, 20, 2, 24, 1, 18, -5, -7, 5],\n [-4, -16, -6, 1, 17, -14, -5, 4, 0],\n [-5, -5, 0, 18, -14, -6, 14, -19, 2],\n [2, -18, -20, -5, -5, 14, 6, -16, 10],\n [0, 20, -3, -7, 4, -19, -16, -12, 4],\n [-7, 4, -7, 5, 0, 2, 10, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[1, -3, -10, 5, -14, 7, 12, 19, 6],\n [0, 24, 23, 25, -3, 6, -11, 14, 15],\n [0, 0, 17, 24, 23, -4, 12, 8, -25],\n [0, 0, 0, -2, 20, -2, 22, -12, 0],\n [0, 0, 0, 0, 10, -2, 0, 3, 22],\n [0, 0, 0, 0, 0, -23, -5, -15, -18],\n [0, 0, 0, 0, 0, 0, 6, -13, -20],\n [0, 0, 0, 0, 0, 0, 0, -5, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220728", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[4, 24, -21, -20, 16, 25, -16, -20, -16],\n [0, -5, 18, -22, -13, -16, -10, -7, -20],\n [0, 0, 20, -16, 14, -23, 23, -7, 9],\n [0, 0, 0, -7, 24, 18, -11, 12, -5],\n [0, 0, 0, 0, -6, 16, 24, -24, 19],\n [0, 0, 0, 0, 0, -23, -1, 22, -17],\n [0, 0, 0, 0, 0, 0, -2, 1, 19],\n [0, 0, 0, 0, 0, 0, 0, -15, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-75981", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, -4, 0, 8, 12, -3, 1, -9, -3],\n [-4, 16, 19, -22, 10, -20, 16, 2, -16],\n [0, 19, 5, -9, -8, 2, -14, -12, -10],\n [8, -22, -9, 13, 2, 0, -16, -6, -18],\n [12, 10, -8, 2, -18, 5, 1, -4, 6],\n [-3, -20, 2, 0, 5, -8, 6, 18, 12],\n [1, 16, -14, -16, 1, 6, -15, -4, 9],\n [-9, 2, -12, -6, -4, 18, -4, 11, -6],\n [-3, -16, -10, -18, 6, 12, 9, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "688", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-25, 14, -17, 5, -2, 19, 23, -4, -17],\n [0, -3, -6, 16, -5, 1, -21, -9, 8],\n [0, 0, -16, 18, -24, 21, -1, -23, 8],\n [0, 0, 0, -15, 3, -10, 13, 3, -13],\n [0, 0, 0, 0, -18, -19, -21, -20, 25],\n [0, 0, 0, 0, 0, -5, -12, 23, 9],\n [0, 0, 0, 0, 0, 0, -20, -16, -6],\n [0, 0, 0, 0, 0, 0, 0, -13, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-380", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-21, -18, 16, 19, -17, 13, -6, 25, -15],\n [0, -4, -10, 16, 12, 16, -16, -1, -7],\n [0, 0, -23, -9, -12, -16, -20, 5, 5],\n [0, 0, 0, 18, 20, 0, -24, 16, -22],\n [0, 0, 0, 0, 2, -13, 20, 10, -16],\n [0, 0, 0, 0, 0, -4, 20, 13, -24],\n [0, 0, 0, 0, 0, 0, -22, -5, 4],\n [0, 0, 0, 0, 0, 0, 0, -2, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-227", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[5, 21, -18, -11, -4, 6, -21, 18, 18],\n [-17, 15, -11, 21, 18, 11, 7, -4, 25],\n [-15, 24, -20, -9, 20, 18, -21, 13, 22],\n [-17, 3, -3, 21, 10, 5, -6, -3, -19],\n [20, 10, -22, -2, -12, -1, -19, -11, 18],\n [20, -13, -7, -14, 22, 0, 22, 7, -11],\n [11, -20, -1, -9, 17, 10, 24, 20, -17],\n [2, 9, -23, -15, -6, -3, 4, 11, 10],\n [18, -14, 10, 9, 8, -22, -2, 10, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -24, 17, -21, 2, -13, 10, -17, 13],\n [0, 1, -13, 16, 13, 24, 2, -8, 8],\n [0, 0, 19, -3, 8, 10, -17, -18, 24],\n [0, 0, 0, 10, -8, -24, -15, 10, 5],\n [0, 0, 0, 0, 6, 23, 4, -18, 7],\n [0, 0, 0, 0, 0, 16, -13, -4, -21],\n [0, 0, 0, 0, 0, 0, 19, -15, 0],\n [0, 0, 0, 0, 0, 0, 0, -16, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1102", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, 0, -13, 16, -7, 4, -2, 6, 7],\n [0, -22, -6, -2, 9, 10, -3, 1, 4],\n [-13, -6, 8, -10, 3, 1, 16, 4, -19],\n [16, -2, -10, 16, -10, -15, -2, 3, 8],\n [-7, 9, 3, -10, -7, 10, 14, -12, -7],\n [4, 10, 1, -15, 10, -15, -22, 14, -12],\n [-2, -3, 16, -2, 14, -22, 17, -6, -6],\n [6, 1, 4, 3, -12, 14, -6, 2, -12],\n [7, 4, -19, 8, -7, -12, -6, -12, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-445", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-15, 8, 1, 24, -4, -23, 24, 22, 14],\n [0, -20, -1, -24, -10, 15, 25, -5, -11],\n [0, 0, 17, -6, 18, 5, -11, 22, 2],\n [0, 0, 0, -3, -23, 19, 18, -18, -24],\n [0, 0, 0, 0, 10, 21, -22, 18, -10],\n [0, 0, 0, 0, 0, 17, -10, 21, -4],\n [0, 0, 0, 0, 0, 0, -14, 24, 14],\n [0, 0, 0, 0, 0, 0, 0, 10, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "901", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[8, 4, 14, 5, 4, -15, -3, -7, -2],\n [4, -10, -1, 14, 13, 0, -18, 2, -8],\n [14, -1, 17, 6, -23, 4, 1, -2, 16],\n [5, 14, 6, 17, -10, -10, 16, 8, -16],\n [4, 13, -23, -10, 20, -12, 0, 10, -4],\n [-15, 0, 4, -10, -12, -16, 8, -3, 13],\n [-3, -18, 1, 16, 0, 8, -8, -1, -24],\n [-7, 2, -2, 8, 10, -3, -1, -25, -14],\n [-2, -8, 16, -16, -4, 13, -24, -14, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-3, -12, -11, 12, 1, 10, 0, 6, -6],\n [-12, 11, 10, 8, -18, -13, -14, -12, 8],\n [-11, 10, 2, 14, 4, -2, 11, -3, -15],\n [12, 8, 14, -18, 8, -14, -19, 3, -11],\n [1, -18, 4, 8, -22, 12, -2, -4, 6],\n [10, -13, -2, -14, 12, -2, 5, 4, -8],\n [0, -14, 11, -19, -2, 5, -17, 15, 16],\n [6, -12, -3, 3, -4, 4, 15, -9, 6],\n [-6, 8, -15, -11, 6, -8, 16, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "391", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -2, 7, 20, 16, 15, 2, 2, 4],\n [-2, -22, -3, -20, 0, -10, -6, -1, 6],\n [7, -3, -18, 16, 5, 10, -17, 11, 5],\n [20, -20, 16, 20, 23, 12, -10, 5, 11],\n [16, 0, 5, 23, -10, 4, 12, 3, -18],\n [15, -10, 10, 12, 4, -12, -4, 6, -6],\n [2, -6, -17, -10, 12, -4, -24, -18, 8],\n [2, -1, 11, 5, 3, 6, -18, -3, 4],\n [4, 6, 5, 11, -18, -6, 8, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-23, 10, -10, -15, 2, -6, 8, -2, -14],\n [10, 18, 18, 0, 0, 1, 7, -7, -12],\n [-10, 18, -24, 16, 18, -3, 11, -10, 3],\n [-15, 0, 16, 7, 0, -8, 11, -14, 8],\n [2, 0, 18, 0, -6, 4, -2, -2, 4],\n [-6, 1, -3, -8, 4, -24, -8, -18, -1],\n [8, 7, 11, 11, -2, -8, 17, 2, 8],\n [-2, -7, -10, -14, -2, -18, 2, 18, -6],\n [-14, -12, 3, 8, 4, -1, 8, -6, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2899", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-11, 5, 18, -4, -14, -16, -5, 21, 5],\n [0, -16, -7, -3, 20, -16, 23, 1, 17],\n [0, 0, -15, -18, -7, -10, -22, -12, -4],\n [0, 0, 0, 9, 10, 19, 23, 4, -5],\n [0, 0, 0, 0, -18, 9, 3, 16, -19],\n [0, 0, 0, 0, 0, -12, -14, -18, -19],\n [0, 0, 0, 0, 0, 0, 17, 16, -16],\n [0, 0, 0, 0, 0, 0, 0, -15, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, -25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-249", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, 22, 12, 0, 17, 23, -8, 1, -4],\n [22, -6, -6, 2, -8, -15, -17, 22, 6],\n [12, -6, 9, -16, 6, 10, 6, 17, -10],\n [0, 2, -16, 6, 5, -9, -4, -11, 8],\n [17, -8, 6, 5, -22, 8, 4, -20, -13],\n [23, -15, 10, -9, 8, -19, 24, 18, 2],\n [-8, -17, 6, -4, 4, 24, -17, 6, 4],\n [1, 22, 17, -11, -20, 18, 6, 24, 7],\n [-4, 6, -10, 8, -13, 2, 4, 7, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[17, 13, 20, -22, 14, 18, -13, 15, -17],\n [-24, 9, -14, -9, -22, -12, -5, 15, -18],\n [7, 19, 2, -23, -12, -7, -20, 10, -6],\n [-25, -16, -13, -14, -15, 10, -9, 21, 3],\n [-23, 3, -16, 20, -7, -22, 20, 12, -14],\n [5, -24, 23, -25, -9, -1, -21, 22, -12],\n [-16, -5, -1, 9, -23, -8, 24, 10, 13],\n [7, 22, -9, 14, -20, 8, 0, 16, 5],\n [23, 25, 2, 10, -13, -5, 0, 25, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4898", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 5, -13, 4, 6, -21, -14, 13, 15],\n [0, -22, 16, 22, 17, 3, 15, -21, -15],\n [0, 0, 23, 2, -4, -15, -5, -20, 0],\n [0, 0, 0, 9, 16, 10, -4, -24, -13],\n [0, 0, 0, 0, -17, 18, -19, -9, -16],\n [0, 0, 0, 0, 0, 1, 4, 4, 17],\n [0, 0, 0, 0, 0, 0, -3, 3, 17],\n [0, 0, 0, 0, 0, 0, 0, 9, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[-11, 10, -2, 14, 3, 24, -12, -24, 22],\n [-4, 21, -20, -17, -14, 16, 13, -21, 14],\n [18, -25, -16, -15, 1, -3, -6, -21, -13],\n [24, -16, 23, 25, 10, 15, 24, -10, -19],\n [6, -1, 18, 0, 10, 2, 18, -14, 0],\n [-22, 18, -3, 14, -2, 5, 4, -23, -10],\n [8, 12, 2, 23, 18, 15, 22, -19, -18],\n [-19, 11, -19, 24, -8, 22, 13, -5, 8],\n [23, 1, -18, 8, -8, 25, 15, -14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[25, 14, -4, -18, 16, 2, 24, 21, 6],\n [0, -5, 0, -12, -11, -12, -14, 10, -23],\n [0, 0, 13, 25, 20, -25, 13, -1, 5],\n [0, 0, 0, -13, -18, -17, -11, -18, 7],\n [0, 0, 0, 0, -7, 21, 20, 0, -25],\n [0, 0, 0, 0, 0, -8, 7, -17, -19],\n [0, 0, 0, 0, 0, 0, 12, 11, -16],\n [0, 0, 0, 0, 0, 0, 0, -3, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[18, 6, 2, -22, 13, 19, -18, -12, 4],\n [-23, -24, -16, -20, -19, -10, -20, -10, 1],\n [-14, -4, -11, -4, 9, 22, 24, -11, -3],\n [12, 23, -24, -24, 23, -7, -21, -22, 2],\n [-8, 14, 15, 24, 5, -4, -15, 22, -10],\n [-22, -5, 15, 19, -1, -6, -18, 17, -17],\n [-8, 5, 9, 4, -8, -7, 15, -2, 24],\n [-4, 22, -12, -7, 3, -4, 4, -11, -5],\n [0, 10, -14, -19, -15, 13, -6, 9, -22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-53", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-24, -6, 21, -6, -14, -9, -8, 14, -2],\n [0, 11, 15, 4, -6, -3, 11, -16, 7],\n [0, 0, -10, 24, 2, -14, -6, 21, -8],\n [0, 0, 0, -19, 17, 21, -5, 17, 6],\n [0, 0, 0, 0, 6, 0, 10, -2, -25],\n [0, 0, 0, 0, 0, -21, -24, 6, 8],\n [0, 0, 0, 0, 0, 0, 24, -16, -20],\n [0, 0, 0, 0, 0, 0, 0, -6, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-265", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 8, 22, -18, -10, 14, -3, 6, -13],\n [0, 12, -25, -24, 13, -13, 1, -22, 15],\n [0, 0, -23, -3, -24, -10, -16, 2, 18],\n [0, 0, 0, 18, -6, 14, -3, -19, 19],\n [0, 0, 0, 0, 24, -21, -3, 15, -16],\n [0, 0, 0, 0, 0, 21, 25, -18, -15],\n [0, 0, 0, 0, 0, 0, 23, 16, 11],\n [0, 0, 0, 0, 0, 0, 0, -9, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1860", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, 12, 23, -14, -19, 11, -10, 12, 14],\n [0, 14, 3, 13, -9, 25, 0, -6, 20],\n [0, 0, 13, 11, -7, -5, 6, 2, 13],\n [0, 0, 0, -11, 2, -5, -10, -3, 0],\n [0, 0, 0, 0, 9, 5, 1, 6, 7],\n [0, 0, 0, 0, 0, 11, 24, -21, -8],\n [0, 0, 0, 0, 0, 0, -12, 25, -14],\n [0, 0, 0, 0, 0, 0, 0, 6, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6010", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-14, 23, -23, -6, 24, -14, -2, -10, -16],\n [0, 15, -12, -12, -4, -22, 21, 8, -8],\n [0, 0, 14, 5, 16, -6, 10, 16, -16],\n [0, 0, 0, -16, -19, -4, -3, -14, 13],\n [0, 0, 0, 0, 5, 22, 25, 2, -7],\n [0, 0, 0, 0, 0, -19, 21, 0, -20],\n [0, 0, 0, 0, 0, 0, 8, 23, 21],\n [0, 0, 0, 0, 0, 0, 0, -20, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4151", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[5, 6, -11, 13, 5, -23, 25, 6, -16],\n [0, 1, 22, 20, 14, 17, 5, 25, 8],\n [0, 0, -19, -18, -9, 18, 24, 13, 15],\n [0, 0, 0, 4, 25, 24, -11, -22, -13],\n [0, 0, 0, 0, 23, -16, 4, 0, 18],\n [0, 0, 0, 0, 0, -14, 19, -5, 4],\n [0, 0, 0, 0, 0, 0, 4, -9, -23],\n [0, 0, 0, 0, 0, 0, 0, -10, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "331036", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, 12, 2, -17, -3, -4, 8, -11, 2],\n [12, 3, -17, -5, -6, 12, 13, 14, -19],\n [2, -17, 5, -8, 14, 3, -18, 0, -8],\n [-17, -5, -8, 3, -14, 1, 6, -10, -3],\n [-3, -6, 14, -14, 18, 6, 16, 12, -4],\n [-4, 12, 3, 1, 6, -21, -20, -3, 0],\n [8, 13, -18, 6, 16, -20, -9, 16, -4],\n [-11, 14, 0, -10, 12, -3, 16, 21, 14],\n [2, -19, -8, -3, -4, 0, -4, 14, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 9) of the inverse. Round your answer to the nearest integer:\n[[21, 19, -8, 23, 7, -11, -2, 10, 8],\n [0, 25, 14, -4, -10, 14, 16, -10, -21],\n [25, -20, 16, -2, 4, 11, 6, -7, 25],\n [19, 2, 21, -18, 17, -25, -22, -4, -4],\n [4, 1, 1, -13, 13, 1, 13, 12, -18],\n [-14, -2, -8, -11, -10, 7, -16, 21, -2],\n [19, -7, 1, 19, 15, 5, -5, -10, -3],\n [-12, -3, 15, -8, 10, -14, 11, -15, -21],\n [25, -5, 6, 3, -19, 10, 14, 1, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -22, 20, 9, -16, 12, 24, 4, 16],\n [-17, -10, -22, 0, 3, 2, -15, 2, 18],\n [6, -2, 25, 16, 13, -19, -8, -23, 18],\n [20, -6, 8, 4, -17, -16, -20, -9, -11],\n [7, -13, 16, 18, -4, -10, 8, -23, -18],\n [-6, 21, -2, 25, -8, -3, -25, 25, -24],\n [-21, -8, -10, -16, 3, 9, -1, 16, -2],\n [-13, -5, 16, 17, 13, 8, -7, 2, 1],\n [24, 0, -15, 23, 9, -6, -14, 2, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-25, -17, -4, 25, 14, 1, -17, -19, 10],\n [22, 12, 24, -24, 17, -21, -9, 11, 9],\n [25, -18, 17, -23, -23, -25, -2, 19, 4],\n [16, 0, 12, 17, 14, 25, 17, 12, 18],\n [24, -23, -13, 10, 15, 22, -14, -6, 13],\n [18, -18, 21, -24, -15, -5, 11, -20, -7],\n [4, 20, 13, 18, 23, 10, -6, -16, -2],\n [7, 3, 4, 10, 19, -20, 21, -12, -23],\n [-2, -7, 12, 8, -17, 4, 6, -13, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-225", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, -4, -22, -3, -19, 18, -15, 13, 16],\n [15, 8, -21, 16, -1, 2, -12, 1, -10],\n [1, -24, -7, -3, 15, -12, 21, 25, 0],\n [-18, 1, 21, 14, 2, -22, 12, -15, 18],\n [-2, 2, 15, -8, 23, -5, 0, -23, -13],\n [12, 2, -12, -25, 2, 10, 24, -15, 17],\n [14, -22, 8, -25, -16, -9, -19, 13, -13],\n [-4, -25, 2, 7, -13, -25, 12, -1, 16],\n [-5, 7, 11, 8, -23, 4, -23, -8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-18, -17, -24, -24, 1, 22, 13, 10, -21],\n [-25, -4, -16, 19, -2, -11, 7, 24, -3],\n [-12, -8, -1, -4, 18, 18, 11, -19, 0],\n [-2, -13, 15, -20, -5, -19, -8, -11, -18],\n [-10, 23, -23, 19, -17, 21, 0, 0, 4],\n [1, -10, 22, 25, -22, 25, -7, 8, -20],\n [19, -11, -16, 16, 10, 20, 14, -20, 18],\n [14, -20, -11, 3, -1, -7, -12, -23, 24],\n [16, 20, -12, 13, 13, -5, -15, 24, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 12, 20, 4, 0, 6, 8, -6, 9],\n [12, 25, -8, -2, 16, 2, 8, 2, -8],\n [20, -8, 15, -8, 1, -11, 6, -19, -6],\n [4, -2, -8, 12, -20, -9, 4, 2, 9],\n [0, 16, 1, -20, 10, 4, 1, 1, 3],\n [6, 2, -11, -9, 4, -23, -8, 11, 14],\n [8, 8, 6, 4, 1, -8, -2, -21, -4],\n [-6, 2, -19, 2, 1, 11, -21, 24, -14],\n [9, -8, -6, 9, 3, 14, -4, -14, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (9, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, 12, 19, -5, 3, 8, -14, 13, 6],\n [0, -9, 6, -18, 12, 3, 5, -7, -17],\n [0, 0, 24, 25, 13, 14, 5, -7, 7],\n [0, 0, 0, -15, -24, 9, -13, 13, 8],\n [0, 0, 0, 0, -14, 7, -8, -21, -7],\n [0, 0, 0, 0, 0, -11, 20, 22, -22],\n [0, 0, 0, 0, 0, 0, -13, 15, -25],\n [0, 0, 0, 0, 0, 0, 0, 5, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-9, -22, 24, -8, 2, 24, -10, 17, -18],\n [0, -8, 24, 3, 14, -10, 4, 23, 8],\n [0, 0, -4, 21, -1, -4, 2, 13, 7],\n [0, 0, 0, -14, -9, 10, -10, 13, -3],\n [0, 0, 0, 0, 21, 0, 10, -23, -16],\n [0, 0, 0, 0, 0, 25, -7, 24, -13],\n [0, 0, 0, 0, 0, 0, 14, 1, -2],\n [0, 0, 0, 0, 0, 0, 0, -8, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5293", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-14, -2, 25, 18, -4, 0, -4, -19, -11],\n [22, 4, -22, -20, 22, 21, -24, 5, -2],\n [9, 21, 5, -1, -18, -14, -24, -11, 14],\n [6, -15, -9, -5, -4, 7, 3, -11, -5],\n [-24, 16, 12, -23, -1, -13, -2, 5, -11],\n [-20, 15, -16, -17, 24, 15, 24, 15, -21],\n [19, 18, 15, -7, -6, 7, 17, 11, 5],\n [13, -13, 12, 19, -20, 21, -18, 17, -16],\n [15, -22, -12, -22, -2, 21, -5, -16, 20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-1, -20, -10, 18, 2, 10, 7, 4, 10],\n [-1, -13, 13, -11, 12, 4, -12, 24, -22],\n [-25, -23, 19, 24, 10, -22, 17, -12, -1],\n [13, -23, -19, -18, 18, -19, 22, -1, -9],\n [0, -22, 23, -8, -22, -9, 21, -9, 19],\n [-1, -23, -14, 1, -9, -4, 13, 13, 17],\n [22, 10, -10, 11, 25, 3, -12, -19, 15],\n [2, -13, -10, -5, -22, 13, 9, -11, 0],\n [20, -19, -8, -1, 11, -5, -18, -6, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -13, -1, -2, 15, -10, 17, 15, 16],\n [0, -5, 5, -11, 19, 23, 10, 17, -25],\n [0, 0, -23, -11, 7, 6, -3, 0, 22],\n [0, 0, 0, 3, -20, 21, 15, 9, 25],\n [0, 0, 0, 0, 9, 20, -24, 16, -17],\n [0, 0, 0, 0, 0, -25, 14, -4, 22],\n [0, 0, 0, 0, 0, 0, -1, -14, 5],\n [0, 0, 0, 0, 0, 0, 0, 8, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "302504", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-21, -6, 25, -19, 17, -3, -25, 13, -23],\n [0, -23, -20, 5, 1, 3, -11, 10, -21],\n [0, 0, -1, 6, -5, 22, -9, -17, 0],\n [0, 0, 0, -3, -15, -16, -3, -21, 0],\n [0, 0, 0, 0, 8, -23, 24, 6, 0],\n [0, 0, 0, 0, 0, 9, 5, 16, 11],\n [0, 0, 0, 0, 0, 0, 12, -15, -24],\n [0, 0, 0, 0, 0, 0, 0, 10, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-340", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 20, -8, 20, -10, 21, -6, 13, -18],\n [0, 12, 3, -13, -9, 14, 17, -9, -17],\n [0, 0, -2, -5, 20, -24, -21, -9, -2],\n [0, 0, 0, -4, -2, 0, -18, -14, -12],\n [0, 0, 0, 0, 20, 1, 10, -25, 15],\n [0, 0, 0, 0, 0, 14, -12, 10, 1],\n [0, 0, 0, 0, 0, 0, -19, -9, -14],\n [0, 0, 0, 0, 0, 0, 0, 3, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17694", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[3, -24, -8, 2, 21, 16, 23, -19, -15],\n [0, 17, -2, -11, 5, 25, -7, -16, 22],\n [0, 0, -24, 3, 16, -16, 16, -17, 24],\n [0, 0, 0, -2, 11, 17, -20, -18, 14],\n [0, 0, 0, 0, -1, 20, -15, 9, -25],\n [0, 0, 0, 0, 0, -14, 12, 14, 5],\n [0, 0, 0, 0, 0, 0, -15, -21, -19],\n [0, 0, 0, 0, 0, 0, 0, 4, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63347", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, 22, 24, 15, -18, 17, 9, -21, 5],\n [0, 5, 11, -18, -20, -3, -10, 18, 23],\n [0, 0, 6, 23, -23, 24, -10, 8, -13],\n [0, 0, 0, -2, -23, 7, 4, 0, 8],\n [0, 0, 0, 0, -1, 2, 7, -3, 0],\n [0, 0, 0, 0, 0, 23, 21, -18, -5],\n [0, 0, 0, 0, 0, 0, -22, -2, 1],\n [0, 0, 0, 0, 0, 0, 0, 1, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 9, 4, 16, 7, 9, 10, 10, 13],\n [9, -4, -12, 20, 0, -2, -4, -2, -4],\n [4, -12, -2, 15, -18, 4, -1, 0, -6],\n [16, 20, 15, -13, -2, -6, -8, 0, -14],\n [7, 0, -18, -2, -18, -9, 20, -10, 0],\n [9, -2, 4, -6, -9, 11, -6, 20, -18],\n [10, -4, -1, -8, 20, -6, 23, 2, 7],\n [10, -2, 0, 0, -10, 20, 2, -5, 12],\n [13, -4, -6, -14, 0, -18, 7, 12, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[20, 23, -3, -1, -1, -23, -22, 4, 7],\n [3, -22, -12, -5, -19, -5, -19, -25, 8],\n [-3, -23, -8, 17, -14, -12, 15, 2, 16],\n [19, -2, -2, -23, -17, -2, -24, 14, 2],\n [-19, -17, 19, 13, 13, 7, 8, -5, 3],\n [1, -9, 16, 21, 22, -3, 19, -5, -18],\n [-17, 7, -22, -8, 6, 4, -1, 7, 9],\n [16, 8, 24, -24, -13, 15, -3, -3, 5],\n [-24, -24, -21, -12, -3, 9, 20, -25, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[22, 23, 14, -11, 4, -5, -18, -19, 15],\n [8, 16, 11, 22, 6, 7, -20, 16, -16],\n [0, 25, 19, 0, -7, 9, 19, -22, -1],\n [-18, -14, -2, -2, -9, -1, 7, 1, -24],\n [-17, 7, -7, 23, -21, 21, -6, -2, 5],\n [18, -22, 6, 21, 9, -12, 10, 25, -20],\n [-9, -8, -18, 25, -14, -9, 5, 25, -25],\n [-15, 16, -10, 11, 23, 2, -17, -18, -1],\n [-16, 14, -23, -3, -3, 18, -22, 24, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-85", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, -14, -8, 6, -15, 9, 4, 6, -2],\n [-14, 8, 6, 14, 16, 9, -5, 3, 8],\n [-8, 6, -14, -2, 8, -11, -14, -12, -7],\n [6, 14, -2, -9, -10, 2, -7, 0, 13],\n [-15, 16, 8, -10, 9, -2, 2, 4, 4],\n [9, 9, -11, 2, -2, -12, 4, -8, -14],\n [4, -5, -14, -7, 2, 4, 3, -6, 8],\n [6, 3, -12, 0, 4, -8, -6, -9, 22],\n [-2, 8, -7, 13, 4, -14, 8, 22, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-22, -17, -18, 2, 6, -12, -6, -14, 3],\n [-17, -25, 7, -9, 16, -7, 2, -2, -16],\n [-18, 7, 23, 2, 10, -7, -3, -16, 2],\n [2, -9, 2, 2, -6, -3, 6, -2, 11],\n [6, 16, 10, -6, 1, -12, -2, 0, -14],\n [-12, -7, -7, -3, -12, 10, 2, -4, -8],\n [-6, 2, -3, 6, -2, 2, -11, 20, -14],\n [-14, -2, -16, -2, 0, -4, 20, -22, 0],\n [3, -16, 2, 11, -14, -8, -14, 0, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-49", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 5) of the inverse of matrix 1/450 * A where A =\n[[-23, 11, 12, 15, -22, 0, 13, 19, 16],\n [0, 16, -15, -15, 12, 12, -6, 0, 12],\n [0, 0, -12, 24, -1, 25, 16, 16, 13],\n [0, 0, 0, -21, -4, -15, 3, -19, -8],\n [0, 0, 0, 0, -19, 4, -22, 25, 4],\n [0, 0, 0, 0, 0, -16, -12, 10, -3],\n [0, 0, 0, 0, 0, 0, 25, -11, 16],\n [0, 0, 0, 0, 0, 0, 0, 5, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, -22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[15, -7, -19, 21, 9, 0, 18, -3, 8],\n [0, -19, -15, 25, -18, -13, 6, 15, 8],\n [0, 0, 17, -2, 21, -5, -8, -12, -7],\n [0, 0, 0, 8, 23, 0, -4, -6, 3],\n [0, 0, 0, 0, 1, 9, 3, -20, 11],\n [0, 0, 0, 0, 0, -10, -12, -20, -15],\n [0, 0, 0, 0, 0, 0, -8, 7, 9],\n [0, 0, 0, 0, 0, 0, 0, -11, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50218", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[25, -11, 9, -9, 22, -13, -4, 14, -5],\n [0, 20, -22, -19, -16, -11, 0, -10, 14],\n [0, 0, 12, -10, 8, 3, -8, -15, -14],\n [0, 0, 0, 12, 7, -17, -11, 2, -18],\n [0, 0, 0, 0, 16, 24, 24, -7, -22],\n [0, 0, 0, 0, 0, 19, -3, 4, 5],\n [0, 0, 0, 0, 0, 0, -2, -6, 13],\n [0, 0, 0, 0, 0, 0, 0, 24, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1151", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, -1, 8, -6, -2, -6, 2, -2, 1],\n [-1, 2, -6, -6, -10, 6, -14, -4, 1],\n [8, -6, 9, -10, -21, -4, -2, 10, -8],\n [-6, -6, -10, -11, -8, 16, -8, -1, 15],\n [-2, -10, -21, -8, -7, -14, -6, 15, -2],\n [-6, 6, -4, 16, -14, -20, -10, 8, 12],\n [2, -14, -2, -8, -6, -10, -13, 8, -9],\n [-2, -4, 10, -1, 15, 8, 8, -2, -2],\n [1, 1, -8, 15, -2, 12, -9, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89189", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the inverse of matrix 1/450 * A where A =\n[[-13, 17, -5, -25, -22, -23, 24, -3, -10],\n [0, -13, 13, 5, -2, 21, -11, -21, 23],\n [0, 0, -15, -2, 19, -16, 21, 8, -15],\n [0, 0, 0, 7, -18, 23, 6, 14, 19],\n [0, 0, 0, 0, -20, -1, -1, 5, -12],\n [0, 0, 0, 0, 0, -24, -22, -6, 15],\n [0, 0, 0, 0, 0, 0, -23, 11, 19],\n [0, 0, 0, 0, 0, 0, 0, -19, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 0, 9, -16, 19, -4, -11, -2, -1],\n [0, 8, 4, -4, 6, 16, 16, -18, -2],\n [9, 4, 7, 18, 2, -2, 5, -4, -10],\n [-16, -4, 18, 23, -4, 2, 8, -2, 10],\n [19, 6, 2, -4, 14, -7, 4, 24, 16],\n [-4, 16, -2, 2, -7, 1, 6, -4, -11],\n [-11, 16, 5, 8, 4, 6, -21, -18, -16],\n [-2, -18, -4, -2, 24, -4, -18, -22, 12],\n [-1, -2, -10, 10, 16, -11, -16, 12, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-14, 2, 2, 0, 0, -1, 13, -10, 2],\n [2, 4, 10, 8, 1, 18, 0, -14, 22],\n [2, 10, 24, 0, 2, 8, -18, -16, -18],\n [0, 8, 0, -13, 16, -6, -2, 1, 5],\n [0, 1, 2, 16, 25, -4, -2, -1, 6],\n [-1, 18, 8, -6, -4, 5, 6, 12, 5],\n [13, 0, -18, -2, -2, 6, -1, 2, -8],\n [-10, -14, -16, 1, -1, 12, 2, 15, 22],\n [2, 22, -18, 5, 6, 5, -8, 22, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (6, 7) rounded to the nearest integer?\n[[6, 6, 13, -5, 18, 16, 13, 20, 1],\n [0, 10, -18, -7, 3, -7, -21, -4, 9],\n [0, 0, -24, 16, -4, 22, 9, 13, -7],\n [0, 0, 0, 19, -6, 25, -19, -2, -23],\n [0, 0, 0, 0, 3, -3, -22, -21, 8],\n [0, 0, 0, 0, 0, -23, 17, 23, 16],\n [0, 0, 0, 0, 0, 0, -22, -6, -1],\n [0, 0, 0, 0, 0, 0, 0, -10, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 16, 21, 1, 2, 5, 21, -19, -18],\n [0, -15, 22, 0, -1, -19, -6, 15, 25],\n [0, 0, -8, -18, 3, 14, -4, 6, 14],\n [0, 0, 0, -19, -23, -11, 17, 8, -4],\n [0, 0, 0, 0, 10, 20, 13, 21, 12],\n [0, 0, 0, 0, 0, -14, -8, 5, -11],\n [0, 0, 0, 0, 0, 0, 7, -24, -18],\n [0, 0, 0, 0, 0, 0, 0, 2, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89821", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (2, 9) rounded to the nearest integer?\n[[-19, -9, 16, -14, 4, 22, 8, -4, -5],\n [0, -14, -9, -10, -21, -7, 2, -9, -4],\n [0, 0, -11, -7, 21, 24, 0, 18, 18],\n [0, 0, 0, -16, -4, 21, -15, 0, -25],\n [0, 0, 0, 0, 19, -9, -11, -5, -25],\n [0, 0, 0, 0, 0, -9, -4, -4, 10],\n [0, 0, 0, 0, 0, 0, -4, -11, -6],\n [0, 0, 0, 0, 0, 0, 0, 19, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-284", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, -22, 6, 3, 4, -23, -21, -7, -18],\n [0, 5, 1, -13, 16, -20, -25, 4, -15],\n [0, 0, -10, -11, -21, -11, -25, -11, 10],\n [0, 0, 0, -4, 1, 8, 4, -14, -24],\n [0, 0, 0, 0, 25, -9, 9, 16, 19],\n [0, 0, 0, 0, 0, -9, -18, 24, -19],\n [0, 0, 0, 0, 0, 0, -1, -15, 14],\n [0, 0, 0, 0, 0, 0, 0, -1, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1033", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[19, 22, -25, 25, 10, -23, 8, -14, 19],\n [0, 24, 11, -1, -14, 25, 7, -17, -25],\n [0, 0, 2, -23, 12, 10, 18, 18, -21],\n [0, 0, 0, -22, -20, 25, 12, -20, -15],\n [0, 0, 0, 0, -22, 1, -10, -8, -19],\n [0, 0, 0, 0, 0, -20, 12, -24, 5],\n [0, 0, 0, 0, 0, 0, 2, 19, 1],\n [0, 0, 0, 0, 0, 0, 0, 15, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9883", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (4, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 7, -16, 18, -8, 7, 3, 5, -2],\n [0, -6, -20, -18, -12, -21, 10, 22, 12],\n [0, 0, -4, -18, -12, -19, -22, -7, 17],\n [0, 0, 0, -20, 18, -18, -1, 6, -1],\n [0, 0, 0, 0, 20, -23, -17, -8, 23],\n [0, 0, 0, 0, 0, -2, 12, -23, -10],\n [0, 0, 0, 0, 0, 0, 19, 9, 4],\n [0, 0, 0, 0, 0, 0, 0, -9, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, -23, 14, -4, -8, 19, 4, -25, -6],\n [23, -21, -14, -15, -2, -8, -18, 3, -4],\n [19, -24, -3, -10, 18, -18, -22, -12, -17],\n [-15, 22, 12, 18, 25, -10, -13, 10, 18],\n [10, -9, -12, 3, -9, -25, -6, 7, -24],\n [-9, -3, -4, -25, -14, -13, -12, -16, -14],\n [-4, -8, 13, -7, 4, -11, 13, -12, -17],\n [-21, 7, 22, -21, -2, -18, -7, -14, -18],\n [-18, 12, -6, 3, 15, 8, -8, -25, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[21, 18, 9, 25, 6, 25, 16, -10, -20],\n [-17, 14, -4, 22, -18, 6, 0, -8, 11],\n [-14, 12, 8, -22, -10, -2, -12, -9, 25],\n [5, -22, 24, 18, 8, 12, 12, -23, -18],\n [-14, 9, -24, 3, -3, 7, 24, -8, 14],\n [-4, -12, 3, 19, -11, -11, 19, -22, 10],\n [-21, -23, -14, -6, 18, -6, 13, 13, -25],\n [18, -23, 21, -17, -6, -17, 5, 20, 2],\n [9, 14, 12, 18, -24, -23, -12, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2542", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (8, 1) rounded to the nearest integer?\n[[-22, 21, 4, 13, 25, -12, 22, 1, -13],\n [-6, 23, 23, -2, -16, -19, -9, -4, 18],\n [-15, 16, -3, -4, 14, 21, -8, 19, 0],\n [22, 4, -13, -22, 17, 1, 25, 14, -16],\n [18, 2, -5, -15, -6, 10, -7, -16, -11],\n [19, 19, -8, -19, 4, -12, 11, 15, 4],\n [1, 23, 11, 22, 15, -9, 4, -8, -23],\n [2, 11, 4, -5, 23, -6, -4, 10, 10],\n [-5, -2, -5, -19, -18, -4, -4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (7, 8) of the inverse. Round your answer to the nearest integer:\n[[3, -16, -21, 23, 13, 8, 12, -16, -17],\n [6, -21, 9, -15, 16, -10, 1, -6, 25],\n [-25, 0, -15, -11, 13, 14, 22, -8, -2],\n [2, -1, -3, -15, 7, -10, 10, -3, -20],\n [17, -2, 12, 16, -20, -16, -4, -3, -21],\n [2, -17, 13, 23, 18, 2, -1, 17, 12],\n [1, -2, 17, 17, 20, -10, -24, -24, -21],\n [20, -5, -16, 16, -8, 0, -6, 15, 10],\n [23, -5, -24, 20, 7, -3, 13, 5, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[15, -23, 11, -16, 16, 6, 10, 23, 1],\n [0, -7, 12, -25, 0, 20, -13, 9, -24],\n [0, 0, 2, 18, -24, -15, 22, 11, 0],\n [0, 0, 0, -23, -12, -10, 23, 25, 10],\n [0, 0, 0, 0, -15, 11, 17, 19, -5],\n [0, 0, 0, 0, 0, -15, 3, 21, 2],\n [0, 0, 0, 0, 0, 0, 6, 3, -24],\n [0, 0, 0, 0, 0, 0, 0, -20, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1813", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, 15, -5, 6, -14, 11, 14, 21, -19],\n [0, 19, 5, -25, -15, 19, 8, -7, -15],\n [0, 0, -18, 19, -18, 8, 14, 1, 3],\n [0, 0, 0, 11, -25, -17, -16, 4, 17],\n [0, 0, 0, 0, -2, 10, 7, 7, -8],\n [0, 0, 0, 0, 0, -24, 11, -6, -9],\n [0, 0, 0, 0, 0, 0, -13, -17, -21],\n [0, 0, 0, 0, 0, 0, 0, -2, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7045", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 4, 3, -4, -5, 17, -8, -14, 20],\n [4, 20, 0, -2, -2, -2, 10, -2, -8],\n [3, 0, -21, -3, -14, -4, 2, -5, 16],\n [-4, -2, -3, -23, -2, -3, 8, 14, 4],\n [-5, -2, -14, -2, 7, -16, -16, 5, 8],\n [17, -2, -4, -3, -16, 24, 0, -14, 12],\n [-8, 10, 2, 8, -16, 0, -21, 6, 2],\n [-14, -2, -5, 14, 5, -14, 6, 15, -8],\n [20, -8, 16, 4, 8, 12, 2, -8, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 25, -15, 12, 25, -12, 2, 1, -4],\n [0, -2, -7, -2, 0, -1, 19, 18, 3],\n [0, 0, -15, -2, -2, -14, -19, 14, -9],\n [0, 0, 0, -11, 6, -3, -19, 12, 5],\n [0, 0, 0, 0, 1, -22, -5, -17, 23],\n [0, 0, 0, 0, 0, -16, 12, -20, -5],\n [0, 0, 0, 0, 0, 0, 20, -21, -11],\n [0, 0, 0, 0, 0, 0, 0, -3, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66806", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-24, -12, -2, -4, 2, 17, -18, -11, 6],\n [-12, 13, 16, -2, -16, 6, 12, 18, -13],\n [-2, 16, -12, -4, 8, 16, 12, -1, -8],\n [-4, -2, -4, 24, -6, -7, 2, 17, -11],\n [2, -16, 8, -6, 24, 23, 1, -9, -8],\n [17, 6, 16, -7, 23, -2, -4, -4, 4],\n [-18, 12, 12, 2, 1, -4, -24, -9, 12],\n [-11, 18, -1, 17, -9, -4, -9, 6, 2],\n [6, -13, -8, -11, -8, 4, 12, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, -10, 24, -16, 3, 1, 9, 16, 19],\n [0, -3, -23, 10, 19, -12, -22, 18, 22],\n [0, 0, -6, -9, 3, 13, 6, -22, -2],\n [0, 0, 0, -12, 14, 16, 12, 8, 20],\n [0, 0, 0, 0, 10, -4, -21, 12, 15],\n [0, 0, 0, 0, 0, 16, 3, 7, -4],\n [0, 0, 0, 0, 0, 0, -1, 8, -17],\n [0, 0, 0, 0, 0, 0, 0, -9, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151675", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-25, 4, -6, 8, 10, 4, -6, -12, 16],\n [4, 11, -8, 0, 5, -10, -1, 2, 11],\n [-6, -8, -17, 8, 10, -9, 4, -7, 2],\n [8, 0, 8, 24, -10, 11, 16, 6, 0],\n [10, 5, 10, -10, -3, 12, -6, 0, -13],\n [4, -10, -9, 11, 12, -9, -5, 18, 6],\n [-6, -1, 4, 16, -6, -5, -20, -5, -4],\n [-12, 2, -7, 6, 0, 18, -5, 10, 6],\n [16, 11, 2, 0, -13, 6, -4, 6, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, 5, -9, -11, 0, 1, -8, -20, 5],\n [5, -13, -12, 10, 16, 0, 8, 1, 10],\n [-9, -12, 6, -18, 20, 4, -6, -12, -9],\n [-11, 10, -18, 9, -15, 6, 10, -11, -4],\n [0, 16, 20, -15, -3, -22, 10, -14, 2],\n [1, 0, 4, 6, -22, -4, -11, -8, 5],\n [-8, 8, -6, 10, 10, -11, -5, 10, 6],\n [-20, 1, -12, -11, -14, -8, 10, -11, 18],\n [5, 10, -9, -4, 2, 5, 6, 18, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "742", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-25, 10, 4, -3, 11, 2, 23, -21, 10],\n [0, -16, -21, -12, -2, 2, -5, 19, 25],\n [0, 0, -6, 25, 6, 25, 12, 14, 16],\n [0, 0, 0, 25, 18, 2, -24, -9, 13],\n [0, 0, 0, 0, -8, 14, 8, 17, -25],\n [0, 0, 0, 0, 0, 23, -10, -7, 11],\n [0, 0, 0, 0, 0, 0, 22, 15, -20],\n [0, 0, 0, 0, 0, 0, 0, -12, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "397", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-15, 6, -6, 11, 5, -4, 12, -12, -2],\n [6, -20, 4, -2, 12, -2, 14, 15, -12],\n [-6, 4, -7, -2, -2, -12, 0, 1, 1],\n [11, -2, -2, -15, -6, -4, 0, -1, -20],\n [5, 12, -2, -6, -9, -2, 6, 2, -6],\n [-4, -2, -12, -4, -2, -11, -24, -10, -1],\n [12, 14, 0, 0, 6, -24, -8, -8, 12],\n [-12, 15, 1, -1, 2, -10, -8, 3, -11],\n [-2, -12, 1, -20, -6, -1, 12, -11, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "195", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -14, -9, -2, 10, 2, 2, 5, -4],\n [-14, -5, 13, -11, -11, -1, -22, 6, 13],\n [-9, 13, -7, -6, -4, 2, 20, -10, -6],\n [-2, -11, -6, 9, 8, -5, -15, 8, 14],\n [10, -11, -4, 8, -18, -3, -16, 10, 21],\n [2, -1, 2, -5, -3, 14, 11, -4, -1],\n [2, -22, 20, -15, -16, 11, 1, -4, 10],\n [5, 6, -10, 8, 10, -4, -4, 16, 10],\n [-4, 13, -6, 14, 21, -1, 10, 10, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 14, -6, 8, -18, 6, 4, 3, -21],\n [0, -14, 13, 1, -13, 21, -16, 10, 5],\n [0, 0, 19, 10, 0, 18, -6, 8, 11],\n [0, 0, 0, 5, -24, -1, 12, -23, 20],\n [0, 0, 0, 0, -10, -17, 22, -17, 23],\n [0, 0, 0, 0, 0, -8, -8, 16, 17],\n [0, 0, 0, 0, 0, 0, -15, -9, 9],\n [0, 0, 0, 0, 0, 0, 0, 17, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-81", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (7, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -17, 23, 24, -19, 1, -23, -4, -10],\n [-18, -21, 23, 4, 2, 25, 1, 24, -4],\n [4, 11, -19, 24, 4, -13, -4, -15, -21],\n [-4, -11, 13, 11, 5, 3, 13, -9, 15],\n [-20, 15, -9, 8, -3, 4, -13, 4, 23],\n [-6, -20, 5, -7, -20, 8, 2, -13, -16],\n [15, 19, -19, -8, -4, -12, 10, -18, -14],\n [14, 22, 7, -2, 16, 13, -12, 23, 25],\n [-21, -7, -23, -25, 14, 15, 11, 7, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[20, -9, -17, 5, 9, -23, -13, 11, 12],\n [0, -20, 3, 23, -17, 10, -3, -11, 24],\n [0, 0, -19, 21, -1, 11, -3, -15, 20],\n [0, 0, 0, 13, -25, 18, -13, -10, 20],\n [0, 0, 0, 0, 20, -14, 2, -4, -6],\n [0, 0, 0, 0, 0, -11, 4, 3, 6],\n [0, 0, 0, 0, 0, 0, 15, 22, 13],\n [0, 0, 0, 0, 0, 0, 0, 25, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3634", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-10, -16, 18, 8, 7, -16, 16, 0, 16],\n [-1, -24, 0, -6, -23, 6, -25, -2, 24],\n [17, 18, 7, 12, 22, 9, -9, 22, 17],\n [22, 18, 7, -15, -3, 12, 6, -7, -14],\n [2, -24, -16, -7, 2, 21, -18, 17, -3],\n [22, 19, 4, 2, -13, 11, -14, -16, 25],\n [-9, -25, -4, -11, -10, -6, -16, 16, 0],\n [23, -3, -9, 8, 15, -4, -22, -19, -21],\n [5, -7, -22, 24, -4, -23, -3, -22, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 9) rounded to the nearest integer?\n[[-2, -12, 23, 15, 25, -23, 21, -5, 0],\n [0, 4, 25, -22, -12, -8, -14, 12, 16],\n [0, 0, -25, -23, 13, 9, -11, 12, -10],\n [0, 0, 0, -15, 2, 1, 12, -8, 21],\n [0, 0, 0, 0, -24, -6, -14, 3, 20],\n [0, 0, 0, 0, 0, 9, 13, 5, -10],\n [0, 0, 0, 0, 0, 0, 9, -3, -18],\n [0, 0, 0, 0, 0, 0, 0, -2, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-96", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-24, 16, 17, 0, -23, -2, 0, -18, 21],\n [11, -18, -8, -8, -14, 10, 14, -24, -6],\n [-23, 14, 18, 8, 23, 20, 20, -20, 14],\n [-16, -2, -8, 7, 13, -19, 19, 22, 18],\n [3, -7, 12, 13, -1, -9, 25, 11, -23],\n [-2, -8, 23, 0, -5, -15, 15, -9, 25],\n [19, 12, -5, -22, 6, -8, 18, 2, 10],\n [11, 18, 24, 0, 23, -2, -16, 12, 23],\n [-18, -24, 18, 9, -5, 1, -3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-19, 14, -4, 2, 16, -11, 23, 12, 11],\n [14, -8, 14, 8, 4, 4, -4, 6, -6],\n [-4, 14, -3, -14, 18, -2, -6, -4, -12],\n [2, 8, -14, 11, -4, -4, -2, 9, 14],\n [16, 4, 18, -4, 20, 0, -13, -10, 18],\n [-11, 4, -2, -4, 0, -10, -7, -3, -6],\n [23, -4, -6, -2, -13, -7, -9, 12, -4],\n [12, 6, -4, 9, -10, -3, 12, -15, -5],\n [11, -6, -12, 14, 18, -6, -4, -5, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 0, 14, 3, -17, -8, -19, 16, -5],\n [-10, -23, 6, -16, 6, -18, 6, 24, -22],\n [3, -14, 11, 10, 25, -7, 11, 21, 5],\n [18, 0, 19, -20, 3, -9, -6, 16, 20],\n [21, -16, -20, 22, 6, -24, -16, 11, 1],\n [15, -7, 25, 15, -10, 25, -6, 10, -21],\n [-8, -18, -13, 15, -16, 10, -7, 5, 10],\n [3, 19, -3, 6, 23, -15, -24, 6, -21],\n [5, -13, -4, 9, -7, 3, -3, -7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[5, -10, 0, -23, -3, -17, 25, -2, 7],\n [0, 2, -2, 17, 24, -19, 12, 18, -1],\n [0, 0, -25, -3, 21, 14, -8, 21, -18],\n [0, 0, 0, 3, -13, -25, 3, 24, 11],\n [0, 0, 0, 0, 24, -24, 21, -4, 4],\n [0, 0, 0, 0, 0, -13, -23, -16, -22],\n [0, 0, 0, 0, 0, 0, -8, 13, -4],\n [0, 0, 0, 0, 0, 0, 0, -22, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-98985", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[19, -4, 18, 8, -17, 7, 12, 8, 9],\n [21, 0, -19, 19, 22, 19, 1, -14, -9],\n [-5, 17, -4, 0, 13, -13, 16, 16, 19],\n [-3, 25, 4, -9, 1, -6, -19, -22, 23],\n [5, 4, 5, -22, -8, -6, 14, 14, 22],\n [21, 24, -3, 25, 12, -17, -10, -5, -17],\n [-1, 23, 10, 21, 17, -12, -9, 2, 19],\n [15, 22, -18, -12, -11, 13, -1, -15, 3],\n [-23, 13, -4, 11, 15, -6, -7, -13, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3334", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (1, 8) of the inverse. Round your answer to the nearest integer:\n[[-7, -10, -24, -25, -23, -2, 18, 12, -24],\n [-10, 3, 11, 18, -22, -12, -9, 18, 19],\n [-9, -6, 21, 3, 15, 0, 16, 12, -9],\n [-14, 2, -17, 6, 8, -10, 22, 5, 1],\n [3, -25, 1, 6, -15, 9, -24, 20, -25],\n [-20, -19, -24, -24, 21, -21, -13, -7, -7],\n [21, -25, 9, -8, 23, 6, 6, -18, -15],\n [-6, -18, 2, -5, 12, 12, -20, -24, -16],\n [16, -17, -23, -24, 10, -18, -17, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[22, 4, 12, -18, -23, -15, -1, -21, -14],\n [4, 1, 17, -21, -6, -5, -23, 15, 24],\n [18, -22, -2, -19, -2, -15, -24, 18, 15],\n [-20, -19, 12, -8, 19, -17, 2, -7, -22],\n [-22, -13, 2, -15, -24, -20, -14, 14, 11],\n [-2, -17, 0, -22, 15, 18, -22, 23, 8],\n [-4, -13, -11, 14, 12, 15, 17, 18, -24],\n [-24, 17, -18, 12, -8, 3, -15, -20, -17],\n [-4, 20, 25, -1, 5, -5, 12, -7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[20, 10, -19, -4, -20, -4, 3, -8, 22],\n [10, 12, 10, 4, 0, 8, 3, -10, 8],\n [-19, 10, -18, -2, 0, 6, 13, 18, -13],\n [-4, 4, -2, -24, 16, -8, -5, -16, -6],\n [-20, 0, 0, 16, -23, 16, 6, 10, 12],\n [-4, 8, 6, -8, 16, -4, 3, 2, 3],\n [3, 3, 13, -5, 6, 3, -8, 6, 4],\n [-8, -10, 18, -16, 10, 2, 6, -13, -19],\n [22, 8, -13, -6, 12, 3, 4, -19, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1558", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-18, 6, -7, -14, -16, -12, 1, 18, -5],\n [-6, -22, -7, 3, -19, 7, -18, -15, 7],\n [-1, 7, 10, 0, 10, -15, 4, 7, -16],\n [3, -1, 6, -22, 13, 8, -4, -13, 25],\n [10, -20, -9, 0, -2, -17, -24, -6, 1],\n [-20, 24, 1, -2, -11, 22, 7, 16, -16],\n [-5, -20, 4, -3, 10, 20, 23, -23, 0],\n [8, 4, -8, -9, 19, 25, 16, -5, -2],\n [-22, 23, 22, -1, 25, -2, 20, 1, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3359", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (6, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, 25, 9, -6, -10, 5, -19, -8, -18],\n [1, -12, -8, -25, 5, -6, -20, 19, -25],\n [-7, 13, 1, -10, -12, 8, -19, -6, 5],\n [-4, -6, -11, -1, 20, -25, -9, -10, 11],\n [-5, 1, 9, -2, 25, -24, 20, -1, -7],\n [19, -13, 3, 6, -20, -17, -25, -2, -16],\n [9, -20, 22, -6, 12, -14, -23, -8, -5],\n [9, 11, -7, -1, -8, 14, 4, 16, 25],\n [16, 8, -16, -4, 24, -22, -23, 23, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 6, -18, 16, -6, -1, 9, 0, -10],\n [6, -9, 14, -8, -12, -6, -10, 16, -4],\n [-18, 14, 14, -24, 14, 6, 8, 4, -1],\n [16, -8, -24, -17, 8, 15, -9, -12, 6],\n [-6, -12, 14, 8, 1, 6, 10, -22, -3],\n [-1, -6, 6, 15, 6, 20, -11, -2, 2],\n [9, -10, 8, -9, 10, -11, -12, 2, 5],\n [0, 16, 4, -12, -22, -2, 2, -14, 6],\n [-10, -4, -1, 6, -3, 2, 5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1100", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[16, 3, 8, 14, -8, -18, 10, -2, -2],\n [3, 20, 19, 10, 14, 4, -16, 16, -4],\n [8, 19, -2, -7, 6, 10, -14, -3, 2],\n [14, 10, -7, -4, 11, -13, -2, 6, -19],\n [-8, 14, 6, 11, -11, 6, 5, 24, -6],\n [-18, 4, 10, -13, 6, -18, 3, 8, -14],\n [10, -16, -14, -2, 5, 3, -25, 2, 7],\n [-2, 16, -3, 6, 24, 8, 2, 20, 1],\n [-2, -4, 2, -19, -6, -14, 7, 1, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-108", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (3, 7) rounded to the nearest integer?\n[[16, -13, -1, -24, -12, -9, 15, 14, 14],\n [13, -1, 1, 22, 25, -2, 23, 7, 1],\n [19, 5, 22, 12, -11, 18, 14, -25, -15],\n [-11, 7, 22, 6, -1, 13, 7, 3, 8],\n [-18, -15, -13, -21, 24, -7, -5, -23, 0],\n [7, 4, -4, -21, -7, -17, -2, 13, -14],\n [20, 22, 19, 1, 24, 16, -5, 12, 9],\n [6, 10, 7, 17, -9, -21, 18, -6, -3],\n [13, -22, 0, 4, 22, 21, 20, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-16, -6, -2, 8, 11, -13, -3, -16, -4],\n [19, -12, -1, -8, -6, 2, -18, -21, -5],\n [-6, 18, -10, -6, 25, -1, -19, -1, 10],\n [25, -16, 14, -10, -22, -16, 25, 22, 5],\n [-14, -6, 6, -24, -15, -6, -3, -13, 9],\n [-9, -16, 14, 12, -12, -7, 6, 7, 17],\n [-1, -1, -12, 19, 18, 12, 10, -2, 15],\n [13, 13, -13, -24, 8, -11, 22, -24, -1],\n [-21, 8, 13, -21, 17, -18, 23, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, 11, -22, 9, -19, 0, 6, 17, 7],\n [0, 24, -25, 3, 22, 19, 12, 12, -5],\n [0, 0, -21, 4, 14, -8, -20, -21, 16],\n [0, 0, 0, 12, -5, -22, -13, -8, -13],\n [0, 0, 0, 0, 12, 14, 1, 0, -14],\n [0, 0, 0, 0, 0, -18, 14, 20, 10],\n [0, 0, 0, 0, 0, 0, -2, 9, -24],\n [0, 0, 0, 0, 0, 0, 0, 20, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-64", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-5, 14, -4, 8, -1, 10, 24, 14, 4],\n [14, -5, -18, -4, -5, 12, 0, 8, -2],\n [-4, -18, 19, -5, -12, -4, 16, -8, -22],\n [8, -4, -5, 11, 0, -10, 2, 1, -12],\n [-1, -5, -12, 0, -9, -8, -2, -4, -9],\n [10, 12, -4, -10, -8, -21, -12, -22, 2],\n [24, 0, 16, 2, -2, -12, 21, 0, -10],\n [14, 8, -8, 1, -4, -22, 0, 5, 12],\n [4, -2, -22, -12, -9, 2, -10, 12, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4108", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[19, 4, -4, 6, 6, -20, 4, -4, 2],\n [4, -25, -10, 0, -7, 5, -6, 4, 17],\n [-4, -10, 5, -4, -4, -4, -3, 8, -1],\n [6, 0, -4, -10, 2, 0, 18, 18, 2],\n [6, -7, -4, 2, 8, -2, -13, -6, -10],\n [-20, 5, -4, 0, -2, -1, -17, 4, 4],\n [4, -6, -3, 18, -13, -17, 16, -22, 1],\n [-4, 4, 8, 18, -6, 4, -22, -7, -10],\n [2, 17, -1, 2, -10, 4, 1, -10, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "705", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-2, 17, 1, -17, -2, -9, 2, 13, -22],\n [3, 19, 2, 11, 3, 18, 3, -21, -15],\n [-24, -22, -16, 13, 18, -18, -3, 1, -3],\n [22, 8, 9, -9, 21, 24, -16, -24, -9],\n [5, -10, -2, -19, -7, -10, 7, 10, 19],\n [-16, 17, 25, -11, 17, -23, -24, 17, 16],\n [9, 1, -21, -11, 10, 23, 7, -25, -14],\n [16, 15, -17, -6, 4, -12, -3, 3, 25],\n [16, 9, 1, 23, 1, 4, -23, -14, 21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "938", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[5, 11, 1, 21, -2, 22, 15, 14, -15],\n [0, -17, -10, -12, 21, 4, 20, -2, 16],\n [0, 0, -17, 23, 0, 23, 16, 19, 24],\n [0, 0, 0, 2, -2, -13, 16, -6, 13],\n [0, 0, 0, 0, -1, 9, -13, 17, -18],\n [0, 0, 0, 0, 0, -5, -12, 19, 7],\n [0, 0, 0, 0, 0, 0, 10, 10, -11],\n [0, 0, 0, 0, 0, 0, 0, -16, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120281", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (7, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, 22, -14, -21, -20, -15, 25, 12, -16],\n [-11, 24, 13, 2, -23, -10, 19, -9, 10],\n [-7, -22, -1, 1, -14, 1, -22, -2, -9],\n [0, -8, -4, -20, -7, 11, 8, -15, -2],\n [19, 11, -3, 14, 17, -22, -8, 4, -11],\n [11, -3, -14, -22, -22, 15, 15, -12, -18],\n [-3, -25, -15, 1, -22, 3, -9, 23, -7],\n [19, 25, 23, -2, 18, 20, 15, 18, 6],\n [5, 23, -10, 6, 18, 16, 8, 9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-10, 3, -3, -8, -24, -6, 11, -8, -7],\n [3, 9, 9, -8, 17, 0, -2, -14, -7],\n [-3, 9, 14, 13, -8, -6, -8, -10, -15],\n [-8, -8, 13, -19, -12, 4, 6, -17, 6],\n [-24, 17, -8, -12, 16, -20, -10, 0, 1],\n [-6, 0, -6, 4, -20, -6, -6, 0, 1],\n [11, -2, -8, 6, -10, -6, 2, -5, 18],\n [-8, -14, -10, -17, 0, 0, -5, 22, -1],\n [-7, -7, -15, 6, 1, 1, 18, -1, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[25, -23, -9, -13, -23, 2, -22, -8, 9],\n [-12, -10, -14, -15, -24, 7, -13, 4, 0],\n [24, -8, -13, -22, 7, -11, -9, -20, -21],\n [7, -10, 20, -2, -21, -23, 9, 1, -14],\n [24, 15, -1, -9, 23, -6, 2, 24, 9],\n [24, -11, 7, -23, -19, -16, 15, 0, 15],\n [14, -20, 7, -10, -2, 4, -16, -15, 18],\n [-4, -23, 12, 14, -3, 19, -7, 14, -13],\n [10, -23, -4, -1, -6, 2, -23, -4, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, 2, -8, 4, 8, -6, 12, -7, 8],\n [2, -14, 9, -2, 8, 13, 0, 0, -8],\n [-8, 9, -2, 8, 18, -18, -24, -2, -6],\n [4, -2, 8, 9, -16, -6, -10, -3, 0],\n [8, 8, 18, -16, -17, 1, -4, -5, -8],\n [-6, 13, -18, -6, 1, 10, -1, 7, 22],\n [12, 0, -24, -10, -4, -1, 25, -20, 8],\n [-7, 0, -2, -3, -5, 7, -20, 23, 20],\n [8, -8, -6, 0, -8, 22, 8, 20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-21, 14, 3, -9, 4, -1, -12, 16, -4],\n [0, -21, 14, 2, -14, 10, -13, -5, 6],\n [0, 0, 11, 12, -17, 11, -24, -23, 17],\n [0, 0, 0, 14, 22, 6, -5, 8, -1],\n [0, 0, 0, 0, -4, -1, -25, 19, 10],\n [0, 0, 0, 0, 0, 2, -7, -12, -3],\n [0, 0, 0, 0, 0, 0, 5, 11, -11],\n [0, 0, 0, 0, 0, 0, 0, 1, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177124", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[18, -8, 8, 2, -6, 8, 3, -6, 6],\n [-8, 12, -5, 3, -8, -17, 2, 4, -4],\n [8, -5, 19, -18, 10, -2, -18, 0, 10],\n [2, 3, -18, 8, 14, 12, 13, 18, -8],\n [-6, -8, 10, 14, 13, -4, -12, 8, -2],\n [8, -17, -2, 12, -4, 25, 12, 12, 22],\n [3, 2, -18, 13, -12, 12, -17, 10, -2],\n [-6, 4, 0, 18, 8, 12, 10, 8, -5],\n [6, -4, 10, -8, -2, 22, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, -21, -1, -16, -21, -4, 16, -1, 11],\n [-6, 2, -5, -15, 3, -21, 11, 23, -21],\n [7, 19, 10, -18, -20, -11, -11, 22, -17],\n [-21, 0, -3, -10, 13, 9, -16, 1, -10],\n [-5, -14, -17, -10, -17, 3, -3, 13, 17],\n [23, -2, -4, 5, -16, 21, 16, 1, 8],\n [22, 13, -2, -5, -11, -9, 19, -7, -1],\n [14, -4, 15, 25, 23, 16, -12, 2, -14],\n [1, -2, -4, 13, 15, 24, 13, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2078", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-18, -6, 4, 10, -8, 0, -16, -4, -4],\n [-6, 16, 0, -2, -8, 8, -18, 18, -8],\n [4, 0, 6, -10, -8, 4, 0, -11, -2],\n [10, -2, -10, -8, -4, 0, -4, -2, -8],\n [-8, -8, -8, -4, 20, -9, -8, 16, 5],\n [0, 8, 4, 0, -9, 8, -6, 14, 14],\n [-16, -18, 0, -4, -8, -6, 1, 8, 18],\n [-4, 18, -11, -2, 16, 14, 8, 3, 4],\n [-4, -8, -2, -8, 5, 14, 18, 4, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "767", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, -13, 0, 13, -4, 8, -6, 13, -17],\n [-13, -10, 2, -20, -20, -16, -10, 15, 13],\n [0, 2, 9, 6, -2, 3, -8, 3, -18],\n [13, -20, 6, 16, 10, -4, 0, 2, -7],\n [-4, -20, -2, 10, 15, -14, 6, -7, 0],\n [8, -16, 3, -4, -14, 7, -14, -2, -3],\n [-6, -10, -8, 0, 6, -14, -20, -9, 1],\n [13, 15, 3, 2, -7, -2, -9, 3, -2],\n [-17, 13, -18, -7, 0, -3, 1, -2, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, 6, 15, 6, 16, 4, -9, 14, 12],\n [-5, 0, 17, -23, 12, -9, 13, -20, -5],\n [19, 20, 25, 14, -13, -17, -21, 17, -19],\n [12, 18, 18, 12, 5, -22, -13, 18, -11],\n [14, -13, 17, 17, 17, 0, -7, 23, -25],\n [-13, -1, -6, 15, -3, -2, 17, 15, 23],\n [13, 14, 4, 8, 20, -16, 15, -25, -14],\n [20, 25, 3, -15, 15, -9, -6, 12, -20],\n [-6, -16, -16, 5, 0, -9, -12, -21, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (4, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, 25, -6, 25, 20, -11, -23, -23, -3],\n [-17, -15, 21, 23, 18, 23, 15, -13, -18],\n [-4, 12, 1, 0, -3, 13, 5, 3, -25],\n [-16, 21, 20, -22, 5, -22, 3, -17, -11],\n [18, 15, -23, -11, -15, -20, 21, -19, 25],\n [20, -22, -5, -25, -3, -13, 17, 2, 3],\n [-8, -3, 2, -17, 17, -20, -10, 11, -25],\n [-4, 20, -3, -5, 25, 5, 12, 2, 18],\n [1, 13, 16, 16, -13, 6, -19, 25, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[21, 20, -13, 6, -19, -14, 14, -11, 23],\n [0, -14, -13, 14, 16, 13, -24, 3, 22],\n [0, 0, 12, -19, 4, -3, 25, 2, -3],\n [0, 0, 0, -22, -6, -21, 20, -15, -24],\n [0, 0, 0, 0, -4, 21, -20, -2, 3],\n [0, 0, 0, 0, 0, 25, 15, -23, -1],\n [0, 0, 0, 0, 0, 0, -12, 17, 6],\n [0, 0, 0, 0, 0, 0, 0, 5, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-486", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[5, 10, -11, -2, -6, 10, -20, -8, 4],\n [10, -24, 12, 1, -9, 2, 5, -16, 10],\n [-11, 12, -5, -12, -7, -8, -12, -4, -13],\n [-2, 1, -12, -7, -12, -15, 4, -10, -22],\n [-6, -9, -7, -12, 20, -15, -4, -12, 16],\n [10, 2, -8, -15, -15, 9, 4, -20, -12],\n [-20, 5, -12, 4, -4, 4, -23, 6, 0],\n [-8, -16, -4, -10, -12, -20, 6, -7, -12],\n [4, 10, -13, -22, 16, -12, 0, -12, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-116", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[12, -14, -7, -6, -6, 3, 12, -11, -14],\n [-14, -6, -12, -4, -4, -4, -4, -15, 4],\n [-7, -12, 19, 7, -8, 6, 2, -6, 6],\n [-6, -4, 7, -9, 2, 6, -1, -4, 10],\n [-6, -4, -8, 2, -18, 0, -5, -4, 11],\n [3, -4, 6, 6, 0, 10, -4, 14, 3],\n [12, -4, 2, -1, -5, -4, 5, 0, 8],\n [-11, -15, -6, -4, -4, 14, 0, -8, 5],\n [-14, 4, 6, 10, 11, 3, 8, 5, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-561", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-6, -15, 15, -9, 15, -1, 3, -3, -17],\n [0, 15, -3, -24, 19, -25, 12, -20, 22],\n [0, 0, -19, -24, 4, 3, -14, 8, 4],\n [0, 0, 0, 24, -23, 16, -14, -22, -19],\n [0, 0, 0, 0, 1, -11, -18, -8, 3],\n [0, 0, 0, 0, 0, -16, 14, -6, -24],\n [0, 0, 0, 0, 0, 0, -8, -12, 19],\n [0, 0, 0, 0, 0, 0, 0, -13, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8342", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[23, -14, -2, 11, 6, -7, 3, 12, 23],\n [3, -7, -6, -23, 14, -21, -3, -21, 4],\n [6, -2, 23, 25, 25, 16, 9, 6, 19],\n [22, 18, -4, -5, 2, 23, 8, -10, -15],\n [7, 18, 12, -7, 2, 3, 11, -23, -8],\n [-8, -14, -8, 6, 16, 10, -7, -22, -15],\n [-23, 1, 21, -10, 18, -8, 4, -2, -20],\n [21, 8, -14, 16, -3, 10, 14, -11, 25],\n [-10, 19, 21, -12, -11, -14, 17, 9, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-71", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-12, -24, -8, 9, -17, -15, 0, -23, -21],\n [6, 15, -16, 12, -20, -15, -9, -24, 15],\n [-2, 24, -21, -5, -20, -22, -17, -21, -22],\n [-17, -8, 17, -10, -24, 3, 22, 25, 16],\n [10, -14, 15, 19, 11, 8, 9, 14, -20],\n [11, 10, -6, -10, -18, 18, -4, -21, -21],\n [19, -15, 17, -7, 13, -9, 11, 12, -8],\n [24, -17, 24, 25, -9, 15, 7, -6, -8],\n [-2, -13, 14, 2, 20, -23, 10, -15, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 18, -10, -16, -13, 4, 11, 11, 6],\n [18, 14, -13, -6, 5, -2, -2, -4, 13],\n [-10, -13, 3, -3, -24, -6, 9, 3, -6],\n [-16, -6, -3, 3, 12, 4, 2, -6, 10],\n [-13, 5, -24, 12, -10, -4, 5, 9, 4],\n [4, -2, -6, 4, -4, 16, 23, 19, 11],\n [11, -2, 9, 2, 5, 23, -17, 8, -16],\n [11, -4, 3, -6, 9, 19, 8, 14, -10],\n [6, 13, -6, 10, 4, 11, -16, -10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-143", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[17, -17, 25, -15, -20, 21, 23, -14, 8],\n [0, 6, 10, -1, 9, 8, -7, 11, -9],\n [0, 0, 18, -22, 23, 4, 25, 8, -21],\n [0, 0, 0, -9, -14, -2, -14, -11, -10],\n [0, 0, 0, 0, 18, 5, 17, -11, -5],\n [0, 0, 0, 0, 0, 12, -20, -9, 14],\n [0, 0, 0, 0, 0, 0, 5, 20, -15],\n [0, 0, 0, 0, 0, 0, 0, 11, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8091", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (7, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, -6, -10, 12, 4, -1, 0, 18, 18],\n [-6, -21, -4, -8, -2, -6, 4, 6, 4],\n [-10, -4, -24, 2, 0, -13, 12, -14, 12],\n [12, -8, 2, -16, -4, 12, 7, -12, 2],\n [4, -2, 0, -4, -5, -2, -10, 6, 12],\n [-1, -6, -13, 12, -2, -7, 13, 12, 0],\n [0, 4, 12, 7, -10, 13, 13, 12, 16],\n [18, 6, -14, -12, 6, 12, 12, 23, 9],\n [18, 4, 12, 2, 12, 0, 16, 9, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -6, -3, -2, 17, -2, 10, -17, 14],\n [-10, 1, 19, 11, -13, 25, -24, -14, 15],\n [7, -3, -12, 13, 23, 4, 20, 23, 8],\n [-17, -11, -2, 22, 15, -1, 10, 6, 21],\n [-5, 16, 13, -20, 21, -1, -24, 5, 4],\n [-11, -8, 6, -12, -8, 9, -4, -12, 12],\n [-12, 8, -4, -10, 22, 23, -10, -10, 14],\n [12, -8, -3, 20, 22, 14, -8, 20, 23],\n [-4, 14, 4, 22, 16, 16, -8, -8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 8) of the inverse of matrix 1/450 * A where A =\n[[-25, 17, 16, 0, -4, 9, 0, -2, 4],\n [17, 0, -14, -5, 6, -5, 0, -2, -8],\n [16, -14, -15, 6, 9, 10, 8, -10, 5],\n [0, -5, 6, -3, -2, -4, -1, -8, -3],\n [-4, 6, 9, -2, 0, -1, 16, 3, 2],\n [9, -5, 10, -4, -1, -20, 4, -7, -6],\n [0, 0, 8, -1, 16, 4, -17, 16, -6],\n [-2, -2, -10, -8, 3, -7, 16, -19, 10],\n [4, -8, 5, -3, 2, -6, -6, 10, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[22, 10, 18, -3, 11, 11, -7, -1, -6],\n [10, -18, -13, -18, -2, 2, 2, -4, 14],\n [18, -13, 14, 16, -4, -1, -2, 19, 12],\n [-3, -18, 16, -25, -5, -10, -6, -8, 8],\n [11, -2, -4, -5, 20, 9, -11, -18, -2],\n [11, 2, -1, -10, 9, -6, -8, -20, -12],\n [-7, 2, -2, -6, -11, -8, 17, -12, -2],\n [-1, -4, 19, -8, -18, -20, -12, 20, -4],\n [-6, 14, 12, 8, -2, -12, -2, -4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4670", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-4, 8, -14, 6, -4, -12, 1, 8, 2],\n [8, 8, -6, 0, 0, -9, 8, -14, 10],\n [-14, -6, -18, 18, 8, 10, 1, 14, 8],\n [6, 0, 18, 0, -10, 6, -20, 4, -4],\n [-4, 0, 8, -10, -17, -2, 20, 2, 4],\n [-12, -9, 10, 6, -2, -17, -20, 12, 8],\n [1, 8, 1, -20, 20, -20, -17, -2, 20],\n [8, -14, 14, 4, 2, 12, -2, 19, 6],\n [2, 10, 8, -4, 4, 8, 20, 6, -19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "644", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-24, -15, 24, -23, 20, -6, -13, -3, -9],\n [3, 17, 13, 6, 9, 9, 8, -5, -10],\n [-3, -15, -12, -23, -19, 14, 19, 25, -15],\n [7, -7, 19, 23, 15, 25, 25, -3, -3],\n [3, -20, 13, -21, 6, 14, 0, -12, -8],\n [-5, -1, -6, -2, -23, -4, -18, 20, 20],\n [3, -19, -20, -20, -14, -4, 21, 0, -1],\n [-7, 10, 9, -13, -1, 22, 19, 6, 4],\n [-5, 16, 19, 14, 18, -18, 15, 16, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1176", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (1, 9) of the inverse. Round your answer to the nearest integer:\n[[-23, 11, -23, -8, 25, 16, -17, -2, -19],\n [7, -1, 16, 8, 12, -5, 12, 14, -8],\n [13, 24, 7, 2, -1, -12, -6, 13, -6],\n [-19, -22, 5, 4, 11, -5, -25, -23, -13],\n [-19, -20, -20, 8, 6, -10, 12, -18, -5],\n [-15, 24, -3, -20, 20, -11, -15, 1, -11],\n [19, 12, -22, -12, 19, -16, 3, -14, 14],\n [-6, 11, -24, -6, -14, 12, 4, 21, -8],\n [24, -16, -19, 16, -21, 22, 3, 25, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[13, 25, -14, -16, 11, -24, -23, -12, 21],\n [-6, 19, 23, -22, 25, 0, 21, -11, -17],\n [-23, -24, 13, 15, 4, 11, -9, -23, -17],\n [-18, -17, -9, -2, -18, -12, -10, -8, 23],\n [-2, 13, 21, 1, 2, -19, 8, 1, 8],\n [13, -7, -20, 4, 2, -14, -11, 19, 13],\n [13, -11, 10, -23, -25, -19, -17, -25, -21],\n [21, 10, -16, -24, -3, 13, 3, -7, 12],\n [21, -6, -14, -15, 9, 23, -19, -3, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 12, -20, -8, -10, -4, -16, -10, 4],\n [12, 9, -16, 8, -6, 12, -3, 7, 4],\n [-20, -16, 25, -2, 8, -6, -19, 9, 14],\n [-8, 8, -2, 17, 5, 10, -11, -7, -19],\n [-10, -6, 8, 5, -2, -10, -6, 6, -11],\n [-4, 12, -6, 10, -10, -10, -4, -2, -4],\n [-16, -3, -19, -11, -6, -4, 21, 8, -6],\n [-10, 7, 9, -7, 6, -2, 8, 19, 8],\n [4, 4, 14, -19, -11, -4, -6, 8, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 22, -21, 7, -17, -23, -12, -8, -14],\n [-3, -12, -10, 11, -6, -6, -11, 15, -1],\n [-9, -14, 19, 16, 13, -19, -18, -2, 21],\n [-1, -5, 24, 7, -16, -4, -7, 3, -23],\n [13, -22, 11, 5, -20, 2, -16, -14, 20],\n [-24, -23, -25, 9, -2, 21, 22, 8, -6],\n [-10, 4, 21, 13, -1, -21, 3, 11, 2],\n [15, -3, 6, 20, 25, -8, 15, 9, 17],\n [-2, 21, 2, 10, -5, -21, 0, 24, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "955", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 6) of the inverse. Round your answer to the nearest integer:\n[[18, 7, 0, -4, -6, -24, 15, -8, -21],\n [6, 20, -15, -5, -4, -23, -17, -24, 20],\n [2, 8, -16, -7, 3, -24, 22, -20, 18],\n [-19, 10, -18, -7, -16, 7, 11, 12, 1],\n [3, -7, -8, 25, 25, -3, -25, 17, -23],\n [-16, -19, 23, 0, -10, 13, 19, 6, -14],\n [18, -18, -18, 19, -15, 7, -1, -9, 5],\n [-7, 19, -11, 18, 23, 9, 13, -24, 8],\n [-1, 12, -22, -10, 6, -11, 16, -12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 8) of the inverse. Round your answer to the nearest integer:\n[[18, 24, -20, -19, 0, -9, 11, -3, 1],\n [0, 14, -7, 1, -1, 14, -1, -5, -1],\n [0, 0, 9, -20, 14, 24, -11, -2, 23],\n [0, 0, 0, -9, 12, 4, 19, 13, -17],\n [0, 0, 0, 0, 11, -7, -20, -14, -11],\n [0, 0, 0, 0, 0, -20, 23, 2, -18],\n [0, 0, 0, 0, 0, 0, 23, -2, -5],\n [0, 0, 0, 0, 0, 0, 0, -23, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[-7, 18, -25, 15, -2, 22, -9, 6, 24],\n [-12, -9, 6, 7, 4, 21, 25, 8, 2],\n [-2, -12, 8, 21, -25, -4, 7, 18, 21],\n [-8, 21, 13, -14, -16, -24, -24, -20, -6],\n [12, 2, 16, -23, 22, 11, 11, 16, -1],\n [-3, -13, -2, -23, 24, 25, 12, 2, 0],\n [-6, 1, -25, -16, -16, -25, 6, 25, 6],\n [17, 1, -13, -9, 2, -1, 24, 10, 21],\n [-24, 6, 6, -20, 5, -17, 17, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 9) of the inverse of matrix 1/450 * A where A =\n[[14, 2, -9, 5, -3, 5, 0, -22, 13],\n [17, 17, 17, -11, 11, 12, -3, -21, 15],\n [17, -1, 4, 0, -23, -22, 21, -8, 11],\n [-15, -15, 10, -10, 17, -1, -25, 0, 19],\n [4, 25, -20, 1, -7, 12, 19, 17, -7],\n [13, 18, 6, 22, -25, -1, 21, -13, -16],\n [-8, 10, -4, -20, 1, -18, -2, -6, -4],\n [-17, 14, 24, 13, -7, 24, -25, -15, 15],\n [16, -16, -25, 1, -9, 18, 18, 25, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-259", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (7, 3) of the inverse. Round your answer to the nearest integer:\n[[13, 17, -24, 22, -3, 15, -16, 16, 4],\n [9, -1, -9, 20, -7, -8, -8, 20, 9],\n [-16, -3, 19, -4, 18, -17, 6, 0, 3],\n [16, -7, 22, 3, 9, -14, -18, -1, 1],\n [21, 17, 19, -20, -13, -15, 12, -20, -21],\n [-19, -7, 17, -20, -1, -17, -6, -1, 24],\n [-18, 24, 11, 12, -24, -4, 10, 25, -22],\n [22, -25, 22, 7, -2, 23, -21, 22, 9],\n [16, 24, 24, 0, 23, 17, 15, 17, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, 23, -21, 18, -8, -1, 22, 15, 14],\n [12, 23, 20, -5, -2, 2, 20, -22, -18],\n [23, 7, -23, 23, -6, 9, 13, 17, 21],\n [-19, 1, -21, 23, 11, -25, -4, -19, 23],\n [-18, 18, 4, 2, 0, 8, 23, 6, -4],\n [-6, -12, -3, -23, -7, -12, 14, 13, 11],\n [9, -25, -7, -11, -1, -25, 5, 11, 17],\n [20, -4, 24, -6, 15, 21, 17, -21, -11],\n [-24, -14, -19, -24, -18, -17, 1, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 6) of the inverse of matrix 1/450 * A where A =\n[[-11, -7, 4, 25, -13, 19, -20, 4, -25],\n [0, 12, -1, 9, 0, -13, -7, -16, 19],\n [0, 0, -3, 10, 17, 5, -18, 4, 8],\n [0, 0, 0, 24, -15, 1, -4, 14, -7],\n [0, 0, 0, 0, 13, -6, -23, -25, -3],\n [0, 0, 0, 0, 0, 22, 1, 13, -3],\n [0, 0, 0, 0, 0, 0, 21, 22, -18],\n [0, 0, 0, 0, 0, 0, 0, 12, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-11, -11, -4, -2, -8, 0, -12, -1, 6],\n [-11, -20, 8, 5, 12, -12, 4, -10, -1],\n [-4, 8, 10, 7, 14, 15, -8, -6, 6],\n [-2, 5, 7, -5, -3, 7, 0, 14, -2],\n [-8, 12, 14, -3, 12, 5, 8, 2, 12],\n [0, -12, 15, 7, 5, -11, 4, -4, -4],\n [-12, 4, -8, 0, 8, 4, 8, 10, -2],\n [-1, -10, -6, 14, 2, -4, 10, 0, -1],\n [6, -1, 6, -2, 12, -4, -2, -1, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "134", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 14, 2, 4, -6, -2, 12, -24, -6],\n [14, -8, -2, 12, -2, -6, -13, -10, 2],\n [2, -2, 8, -2, -18, 2, -18, -14, -2],\n [4, 12, -2, -3, -13, 6, -9, 0, 0],\n [-6, -2, -18, -13, 25, 16, -16, -2, -2],\n [-2, -6, 2, 6, 16, -24, 14, 4, 4],\n [12, -13, -18, -9, -16, 14, -5, 9, -13],\n [-24, -10, -14, 0, -2, 4, 9, 12, 2],\n [-6, 2, -2, 0, -2, 4, -13, 2, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-4, -23, 15, 14, 3, 13, 1, 13, 14],\n [0, -23, -7, 8, -12, -5, -24, -16, 16],\n [0, 0, 1, -25, 24, 10, 7, -4, 23],\n [0, 0, 0, 10, -23, 18, -10, -15, -16],\n [0, 0, 0, 0, 9, -20, 20, 18, -18],\n [0, 0, 0, 0, 0, 12, 1, -13, 17],\n [0, 0, 0, 0, 0, 0, -12, -21, 17],\n [0, 0, 0, 0, 0, 0, 0, 19, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, -22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66905", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-25, 2, -8, 20, -13, 14, -20, 23, 17],\n [0, 13, -4, 4, 1, -18, 17, 2, -24],\n [0, 0, -12, -2, -13, -18, 18, -5, -4],\n [0, 0, 0, -15, -10, 24, -17, -23, 10],\n [0, 0, 0, 0, 18, -15, -2, -21, -24],\n [0, 0, 0, 0, 0, -15, -3, -25, 16],\n [0, 0, 0, 0, 0, 0, 19, 1, 8],\n [0, 0, 0, 0, 0, 0, 0, -12, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-94", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-20, -20, 21, 23, -4, -23, -7, 8, 15],\n [15, -19, -10, 12, -17, -13, 8, 20, 11],\n [17, 21, -20, 12, 22, -22, -21, -20, -13],\n [20, -2, 2, -13, 16, 23, -8, -19, -22],\n [5, -2, -4, -5, 22, 16, 0, 4, 25],\n [9, 25, -3, 19, 14, 24, 4, -7, 6],\n [24, -7, -4, -22, 19, -14, -11, -11, -16],\n [-7, -18, 25, 5, -17, 3, -19, -18, 15],\n [-9, -11, -10, -19, 16, -7, 12, -1, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 1) of the inverse. Round your answer to the nearest integer:\n[[6, 18, -20, 11, 4, -4, -1, -2, 10],\n [18, 13, 10, -13, 6, 0, -10, 14, 0],\n [-20, 10, -10, 14, 12, -21, 12, 0, 0],\n [11, -13, 14, 1, 0, -10, 8, 4, -5],\n [4, 6, 12, 0, -11, 0, 8, 21, 14],\n [-4, 0, -21, -10, 0, 0, 14, 0, 2],\n [-1, -10, 12, 8, 8, 14, 10, 2, -10],\n [-2, 14, 0, 4, 21, 0, 2, -1, -14],\n [10, 0, 0, -5, 14, 2, -10, -14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[25, 10, -11, 24, -25, 25, 8, 16, 5],\n [0, 6, 10, 3, -16, -5, 10, -2, 1],\n [0, 0, -22, 21, -8, -17, 23, 4, 9],\n [0, 0, 0, 20, -20, -12, 20, 3, 6],\n [0, 0, 0, 0, -14, -12, -3, 22, 8],\n [0, 0, 0, 0, 0, -21, 13, -16, -4],\n [0, 0, 0, 0, 0, 0, -23, -22, 1],\n [0, 0, 0, 0, 0, 0, 0, 21, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1168", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-21, -14, 18, -16, 16, -10, -6, 16, -2],\n [-14, -16, 19, -7, 12, 2, 8, -22, -8],\n [18, 19, 18, -17, 22, 18, -10, -12, 8],\n [-16, -7, -17, 2, 7, 0, 10, 4, 2],\n [16, 12, 22, 7, -13, -19, -10, -6, 10],\n [-10, 2, 18, 0, -19, -16, -7, 5, 11],\n [-6, 8, -10, 10, -10, -7, 13, 16, -14],\n [16, -22, -12, 4, -6, 5, 16, -23, -8],\n [-2, -8, 8, 2, 10, 11, -14, -8, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-19, 23, 14, -7, 22, 20, -16, -3, -24],\n [0, -2, 22, -13, -21, -8, -15, 11, 6],\n [0, 0, 19, 2, -25, -20, -15, 16, 7],\n [0, 0, 0, 22, 21, 13, 20, -2, 17],\n [0, 0, 0, 0, -23, -14, -19, -6, -11],\n [0, 0, 0, 0, 0, 8, 23, -1, 5],\n [0, 0, 0, 0, 0, 0, -12, -13, -13],\n [0, 0, 0, 0, 0, 0, 0, -18, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1523", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, 25, 21, 12, -13, -8, -8, -25, 6],\n [-1, -5, 1, -15, 22, -25, -7, 6, -18],\n [-7, -10, 9, -24, -14, 3, -16, -4, 8],\n [-5, 11, -21, -20, 6, -23, -16, -21, -2],\n [-6, 11, 5, 21, -9, 23, -2, -8, 0],\n [16, -19, 17, -12, 15, 23, -24, 4, 23],\n [-9, -6, -16, -2, 18, -14, 1, -11, -17],\n [-8, 22, -19, 2, 20, 10, -23, 18, -10],\n [10, -22, 9, -17, 20, -14, -16, 20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1745", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[18, -22, 3, -12, 19, 0, -8, -8, -4],\n [-22, -23, 4, -2, 6, 2, 6, -14, -4],\n [3, 4, 18, 1, -14, -16, -4, 14, -14],\n [-12, -2, 1, 10, -8, 2, -2, 1, -14],\n [19, 6, -14, -8, -21, -10, 14, -8, 22],\n [0, 2, -16, 2, -10, -10, 1, -8, 2],\n [-8, 6, -4, -2, 14, 1, -19, 20, -9],\n [-8, -14, 14, 1, -8, -8, 20, -23, -6],\n [-4, -4, -14, -14, 22, 2, -9, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, 4, -5, -23, -5, 2, 2, -21, -19],\n [0, -17, 21, -5, -6, 12, 14, 11, -9],\n [0, 0, 5, 7, 6, 6, 22, -3, -5],\n [0, 0, 0, -20, 23, 2, -24, 6, 0],\n [0, 0, 0, 0, -8, 23, -12, 2, 4],\n [0, 0, 0, 0, 0, 17, 25, -14, -1],\n [0, 0, 0, 0, 0, 0, 6, 17, -20],\n [0, 0, 0, 0, 0, 0, 0, -7, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-17, -1, -10, -11, 22, -8, -3, 16, -23],\n [-19, 13, -15, -2, 9, 24, -1, 2, -14],\n [-3, -9, 15, 11, -8, -17, 19, 9, 10],\n [-8, -6, -5, 21, -6, -20, -17, 17, 3],\n [3, -13, 10, 1, 21, 23, 18, -20, 13],\n [6, 23, 17, 18, 2, 19, -25, 24, 25],\n [17, 5, 4, -8, 3, 16, 12, -3, -4],\n [-24, -21, 16, -11, 6, 20, -20, -12, -2],\n [-5, -12, -14, -22, 18, -5, -9, 3, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (3, 7) of the inverse. Round your answer to the nearest integer:\n[[-10, -8, 12, 15, 25, 18, -15, 6, 2],\n [-10, 8, 24, 4, 12, -4, -21, -17, -13],\n [13, -3, 1, 6, 5, 7, 16, 0, -8],\n [-14, -23, -21, -12, 21, -14, -22, -10, -15],\n [10, 12, 22, -24, -13, -18, 18, -5, 0],\n [12, 9, -11, 14, 4, -24, -10, -13, -25],\n [17, 2, -25, 14, 8, -13, -24, -22, -1],\n [8, -13, 10, 6, -5, 0, -11, 3, 0],\n [-5, -14, -14, -21, 16, 0, 6, -24, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 0, -2, -10, 0, -8, 6, -14, 4],\n [0, -2, -4, 0, -14, 0, -18, -20, 0],\n [-2, -4, -24, 4, -2, 3, -1, -16, 10],\n [-10, 0, 4, -10, -20, 4, -11, -8, 14],\n [0, -14, -2, -20, -9, 0, 0, -5, -2],\n [-8, 0, 3, 4, 0, 22, 4, 1, 6],\n [6, -18, -1, -11, 0, 4, 4, 6, -1],\n [-14, -20, -16, -8, -5, 1, 6, -16, -2],\n [4, 0, 10, 14, -2, 6, -1, -2, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2985", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-15, 14, 3, -19, 1, -4, 5, 4, 2],\n [0, -11, -11, -14, -9, -3, -20, 19, -10],\n [0, 0, -25, 19, -19, 19, 13, 14, 24],\n [0, 0, 0, 14, 13, -8, 10, -4, -24],\n [0, 0, 0, 0, -3, 14, 20, -8, -7],\n [0, 0, 0, 0, 0, 23, 12, 5, 14],\n [0, 0, 0, 0, 0, 0, -24, 25, 4],\n [0, 0, 0, 0, 0, 0, 0, 22, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-868", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[13, -6, -12, 0, -14, 5, 2, 12, -6],\n [-6, -22, 4, -10, -21, 2, -2, 20, -6],\n [-12, 4, -21, 1, -9, 12, 2, -4, 4],\n [0, -10, 1, -25, 7, -4, 0, -16, -8],\n [-14, -21, -9, 7, 23, 6, -12, -10, -2],\n [5, 2, 12, -4, 6, -12, -2, 0, -16],\n [2, -2, 2, 0, -12, -2, -11, 14, 10],\n [12, 20, -4, -16, -10, 0, 14, 6, -8],\n [-6, -6, 4, -8, -2, -16, 10, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "772", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-13, 2, 20, -11, 3, -5, 18, 5, -3],\n [0, -23, 24, 9, -12, -24, 24, -13, -24],\n [0, 0, 8, 14, -21, -1, -15, -13, 2],\n [0, 0, 0, 25, 0, 1, 0, -11, 24],\n [0, 0, 0, 0, -13, -17, 16, -12, 2],\n [0, 0, 0, 0, 0, -11, 21, 13, -11],\n [0, 0, 0, 0, 0, 0, 21, 15, -20],\n [0, 0, 0, 0, 0, 0, 0, 1, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[19, -16, 21, 6, -11, 13, 20, -18, 25],\n [-1, -8, -11, 0, 15, 18, -5, -4, 20],\n [8, 11, 11, -12, -22, -2, -24, -25, -24],\n [-13, 1, -9, 19, -9, -21, -2, -18, 18],\n [-17, -8, -10, 25, 6, 14, 13, 15, 18],\n [20, 6, 16, 22, -24, 12, 17, -22, -21],\n [11, 23, 11, 0, 17, -17, -11, -2, -2],\n [9, 22, 15, -1, 0, -3, -20, 15, 1],\n [-7, 5, 12, 17, 6, -24, -8, 2, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, 10, -2, 2, -1, 13, 23, -22, 19],\n [-7, -22, -13, -25, 8, -19, -1, -3, 4],\n [23, -19, 19, -9, 7, -24, 12, 18, -13],\n [6, -4, -17, -9, -8, 14, 14, 1, -15],\n [2, -18, 24, -8, -13, 7, -11, -4, 12],\n [4, -20, 19, 8, -7, 23, 7, -12, 22],\n [21, 15, -7, 14, -11, -16, -24, 24, -24],\n [-5, -14, -16, -14, 13, -24, -25, -24, -3],\n [2, -9, 14, -5, 18, 8, -17, -9, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[16, -1, 2, -12, -7, 0, 21, -4, -14],\n [-1, 12, -10, 0, 2, -2, -4, -18, -12],\n [2, -10, -11, 11, -19, -1, 8, 14, -10],\n [-12, 0, 11, 11, -3, -18, 12, 16, 0],\n [-7, 2, -19, -3, -19, 7, 4, -4, -7],\n [0, -2, -1, -18, 7, 16, -12, -2, -10],\n [21, -4, 8, 12, 4, -12, 17, -8, -9],\n [-4, -18, 14, 16, -4, -2, -8, -20, -8],\n [-14, -12, -10, 0, -7, -10, -9, -8, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 0, 0, -2, 3, 18, 4, 4, -8],\n [0, -3, -13, 18, -2, 0, 4, 17, -4],\n [0, -13, -10, 14, 15, 10, 10, -8, -24],\n [-2, 18, 14, 16, 15, 6, -18, -1, -6],\n [3, -2, 15, 15, -5, -16, 8, 12, -3],\n [18, 0, 10, 6, -16, 9, -9, 8, -8],\n [4, 4, 10, -18, 8, -9, 20, 16, -14],\n [4, 17, -8, -1, 12, 8, 16, 0, 0],\n [-8, -4, -24, -6, -3, -8, -14, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (7, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, 12, 0, 10, -18, 2, 13, 2, 15],\n [12, -21, -8, -3, 6, -4, 4, -1, 6],\n [0, -8, -2, 14, 2, -14, 2, -17, -6],\n [10, -3, 14, -25, 10, -12, 5, 14, 4],\n [-18, 6, 2, 10, 11, -4, -16, 18, 16],\n [2, -4, -14, -12, -4, -7, 18, 12, -7],\n [13, 4, 2, 5, -16, 18, 25, -10, 6],\n [2, -1, -17, 14, 18, 12, -10, 21, -2],\n [15, 6, -6, 4, 16, -7, 6, -2, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (7, 2) of the inverse of matrix 1/450 * A where A =\n[[-9, -8, -13, 0, 19, 14, 13, 5, 14],\n [0, 6, -25, 9, 10, -7, 2, -24, 3],\n [0, 0, 17, -7, 2, 8, 5, 11, -7],\n [0, 0, 0, -19, -14, 25, 5, -8, 2],\n [0, 0, 0, 0, 8, 21, -2, -10, 2],\n [0, 0, 0, 0, 0, 12, 15, -15, -22],\n [0, 0, 0, 0, 0, 0, -2, -15, 22],\n [0, 0, 0, 0, 0, 0, 0, 6, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[4, 18, -4, -4, 12, 3, -5, -8, 22],\n [-15, -16, 9, 0, 24, 18, 20, -22, -16],\n [13, -10, 15, 4, -23, 8, -1, 12, 16],\n [10, -22, 16, -16, -13, -20, -19, 2, 11],\n [-11, 4, 14, -16, -14, -9, 22, 4, -25],\n [10, 14, -2, 12, -5, 16, 6, -8, -13],\n [11, 18, -5, -8, 14, 20, 21, 0, -21],\n [-21, 5, 2, 23, -13, 23, -15, -25, -2],\n [-13, -8, -2, 3, 2, 12, 19, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-87", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-15, 24, -5, -5, -4, 14, 6, 0, 2],\n [24, -9, -8, 2, 0, -14, -2, -1, 1],\n [-5, -8, -13, 5, -16, -10, -2, 6, -2],\n [-5, 2, 5, -4, 4, -20, 7, 16, 10],\n [-4, 0, -16, 4, -23, 0, -10, -8, -20],\n [14, -14, -10, -20, 0, 9, 12, -13, 16],\n [6, -2, -2, 7, -10, 12, -21, 18, 6],\n [0, -1, 6, 16, -8, -13, 18, 20, -14],\n [2, 1, -2, 10, -20, 16, 6, -14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "710", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[25, -22, 8, 11, -2, -5, -24, -19, -15],\n [0, -22, 9, 14, 0, -8, 11, -10, -14],\n [0, 0, 11, -7, -11, -4, -6, 17, -13],\n [0, 0, 0, 19, 6, -5, -9, 3, 3],\n [0, 0, 0, 0, -12, 13, -3, 15, -24],\n [0, 0, 0, 0, 0, 22, 8, -22, -3],\n [0, 0, 0, 0, 0, 0, 11, -23, -4],\n [0, 0, 0, 0, 0, 0, 0, 21, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1162", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-1, 6, -6, 12, 4, 12, -5, 10, 5],\n [6, -3, -10, -7, -5, 13, 4, 4, 1],\n [-6, -10, 1, -6, 6, 16, 20, -12, 18],\n [12, -7, -6, 24, -10, 0, -16, -20, 12],\n [4, -5, 6, -10, -7, -10, -14, -20, -10],\n [12, 13, 16, 0, -10, -24, 3, 17, 11],\n [-5, 4, 20, -16, -14, 3, -20, 12, 0],\n [10, 4, -12, -20, -20, 17, 12, -22, 14],\n [5, 1, 18, 12, -10, 11, 0, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[11, 2, 1, -1, 4, -20, 4, -17, -20],\n [3, -3, -20, -4, -24, 5, -20, 16, -21],\n [-6, -14, 12, 12, -18, 23, 24, 17, 7],\n [13, 14, 5, -23, -7, 22, -18, 4, 5],\n [3, -20, -24, -3, 18, 4, 12, 20, 13],\n [-17, -19, 21, 18, 23, -11, -11, -5, -12],\n [-15, -15, -6, -13, 19, 4, 14, 13, -6],\n [19, 17, 25, 12, -18, 25, 11, 16, 7],\n [0, 18, 13, -18, -8, 13, -12, -8, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-3, -23, -20, 11, -14, -10, 6, -2, 13],\n [-23, 15, 12, -12, 15, 1, 1, -2, 20],\n [-20, 12, 15, -4, -11, 9, -12, 3, 5],\n [11, -12, -4, -6, -2, 10, 2, -4, 4],\n [-14, 15, -11, -2, -18, -1, -12, 16, -8],\n [-10, 1, 9, 10, -1, -1, -16, -4, 4],\n [6, 1, -12, 2, -12, -16, 23, 4, 6],\n [-2, -2, 3, -4, 16, -4, 4, 24, 17],\n [13, 20, 5, 4, -8, 4, 6, 17, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-24, -14, 7, -11, 19, -25, 7, -22, 2],\n [-12, 23, 19, -14, -20, 25, -6, 22, -5],\n [-10, -14, -6, 19, 7, 24, -24, 8, 0],\n [7, 16, 4, -25, 20, -18, -25, 20, -16],\n [6, 25, 14, -24, 5, -22, -14, 5, 15],\n [-3, 7, -18, 23, -10, -11, 15, 14, 0],\n [-12, -14, 1, 21, 5, -22, 4, -22, 5],\n [8, -22, -6, -8, 21, -18, 16, -24, -17],\n [-10, -4, -14, -21, 13, -11, 19, -18, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1905", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[25, -7, 11, -8, -5, 23, 13, -12, -11],\n [23, -23, 19, -15, -23, 4, -20, -20, 5],\n [-4, -5, 12, 12, -20, 3, 20, -15, 22],\n [-4, 25, 13, -20, 4, 17, -1, 10, -25],\n [-4, -17, 19, -18, 8, -10, -7, -18, -14],\n [17, 15, 5, 16, 7, -7, 1, -2, 23],\n [2, -22, -14, -3, -6, 14, 2, 22, -25],\n [15, -15, 18, 5, 15, 12, -17, -20, -20],\n [-23, 6, 9, -10, -24, 10, 15, -19, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "251", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[4, 19, 20, 3, 15, -25, 18, -25, 15],\n [0, -23, 10, 13, 5, -1, 21, -2, -25],\n [0, 0, 11, -15, 23, -23, -14, -6, 4],\n [0, 0, 0, -5, -8, 6, -7, 4, 7],\n [0, 0, 0, 0, -22, 24, -14, 10, -22],\n [0, 0, 0, 0, 0, -19, -14, -16, 3],\n [0, 0, 0, 0, 0, 0, 25, -2, -10],\n [0, 0, 0, 0, 0, 0, 0, -20, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-15, 1, 14, 10, 16, -6, 16, -18, 20],\n [10, 0, 9, -23, -22, 18, 3, 24, 2],\n [-7, 17, 2, -8, -12, 17, -12, 3, -23],\n [8, -17, 14, -21, 3, 15, -21, 19, 17],\n [17, 18, 25, -13, 0, -17, -22, 13, 5],\n [-21, -19, 2, 14, -12, -2, 16, 12, -21],\n [21, 22, 8, 2, 21, -18, -5, -2, -2],\n [-13, 23, -11, 20, -1, 25, 19, 2, 13],\n [-18, 5, -19, 25, 21, 13, -9, 24, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[9, -4, -19, -16, 2, 13, 17, 3, 9],\n [0, -17, 10, -18, 4, 4, 5, -4, 18],\n [0, 0, 21, 2, 20, -21, -9, -15, -4],\n [0, 0, 0, 10, 19, 19, -15, -21, -12],\n [0, 0, 0, 0, 6, 12, 14, -2, 2],\n [0, 0, 0, 0, 0, 24, 10, -16, 11],\n [0, 0, 0, 0, 0, 0, -1, 6, -18],\n [0, 0, 0, 0, 0, 0, 0, -16, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9640", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-10, 10, -14, -4, 8, -4, 6, 2, 5],\n [10, 2, 2, -4, -8, 16, 6, 8, -14],\n [-14, 2, 18, -10, 4, -6, -18, 0, -2],\n [-4, -4, -10, -14, 10, -4, 6, -7, -6],\n [8, -8, 4, 10, 25, -12, -5, -6, 8],\n [-4, 16, -6, -4, -12, -23, 0, -1, -1],\n [6, 6, -18, 6, -5, 0, -13, -1, 0],\n [2, 8, 0, -7, -6, -1, -1, -7, 9],\n [5, -14, -2, -6, 8, -1, 0, 9, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-9, 8, -2, 2, -17, 0, 3, -12, 1],\n [8, -15, 24, 17, 0, -8, 18, 4, -6],\n [-2, 24, -21, -9, -8, -2, -14, -10, -12],\n [2, 17, -9, 0, 5, -8, 4, -10, -5],\n [-17, 0, -8, 5, -15, -5, 7, 8, -2],\n [0, -8, -2, -8, -5, -7, -2, -3, -4],\n [3, 18, -14, 4, 7, -2, -4, -11, -13],\n [-12, 4, -10, -10, 8, -3, -11, 12, 8],\n [1, -6, -12, -5, -2, -4, -13, 8, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (4, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 21, -10, 7, 7, -16, -24, 18, -22],\n [0, 25, 1, 7, 7, 15, -6, -13, -15],\n [0, 0, 6, -23, -13, 2, -4, -7, 5],\n [0, 0, 0, -17, 25, -7, -3, -1, 7],\n [0, 0, 0, 0, -23, 2, 11, 9, -12],\n [0, 0, 0, 0, 0, 8, -17, -8, -24],\n [0, 0, 0, 0, 0, 0, -12, 19, 22],\n [0, 0, 0, 0, 0, 0, 0, -23, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -6, -4, 14, 5, 5, 2, -14, -10],\n [0, 9, 18, -22, -16, 8, 15, -23, 5],\n [0, 0, -21, -21, -24, -11, -25, -5, 11],\n [0, 0, 0, 16, -24, 4, -12, -21, 5],\n [0, 0, 0, 0, 5, 1, -8, -21, -9],\n [0, 0, 0, 0, 0, -5, -2, 4, -10],\n [0, 0, 0, 0, 0, 0, 11, -24, -15],\n [0, 0, 0, 0, 0, 0, 0, 19, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2404", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-6, -23, 16, 13, -16, 0, -16, 14, -13],\n [-5, 8, 18, 6, -17, 4, -25, -14, 18],\n [9, -2, 14, 19, 23, -16, 21, -2, 15],\n [-8, -18, 20, 17, -13, -10, -12, -17, -17],\n [25, -21, 21, -15, -7, 12, -16, -10, 3],\n [-21, -8, 25, 16, 16, 18, 9, 10, -4],\n [-2, -14, 13, -14, 9, 24, -7, 11, -12],\n [-3, 14, -4, 21, 22, 24, -15, -24, -16],\n [17, -21, 4, -5, 23, 7, -1, 20, 21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, 0, -4, 5, 10, 9, -22, 22, 4],\n [0, -7, 16, -16, -22, -22, -2, 11, 2],\n [-4, 16, 24, -6, -7, -4, -2, 4, -11],\n [5, -16, -6, -7, -2, -15, -14, -2, 8],\n [10, -22, -7, -2, -12, 8, -5, -4, -4],\n [9, -22, -4, -15, 8, 23, -2, 8, -4],\n [-22, -2, -2, -14, -5, -2, 9, 18, 2],\n [22, 11, 4, -2, -4, 8, 18, -1, -2],\n [4, 2, -11, 8, -4, -4, 2, -2, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, -16, 0, 14, 3, 8, -8, -24, -1],\n [-5, 25, 5, -4, -17, 1, -1, -1, 1],\n [-16, 4, -22, -5, 4, 7, 17, 0, -24],\n [-3, 5, -22, 21, -6, -1, 19, -25, -24],\n [-20, -19, 25, -22, -8, 15, 17, -21, -1],\n [-25, 8, -23, -9, 6, -2, -24, -25, 8],\n [-18, 19, 20, 18, -17, 2, -7, -6, -19],\n [16, 9, -7, -9, 14, -8, -19, 1, 13],\n [4, -3, -6, -3, 0, 22, 21, -12, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1088", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[5, 6, 0, 11, -6, 0, -10, -10, -1],\n [6, 14, 14, 6, -12, 14, 1, 4, -8],\n [0, 14, -4, 6, 6, 9, -10, 7, -5],\n [11, 6, 6, 2, -5, 11, 10, 2, 14],\n [-6, -12, 6, -5, 21, -4, 6, 4, 9],\n [0, 14, 9, 11, -4, -11, 2, -17, 4],\n [-10, 1, -10, 10, 6, 2, -5, 11, 4],\n [-10, 4, 7, 2, 4, -17, 11, -22, 2],\n [-1, -8, -5, 14, 9, 4, 4, 2, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-63", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-13, -22, 8, 4, 12, -12, -7, -10, 4],\n [-22, -4, 8, -5, -4, 4, -12, 0, -8],\n [8, 8, -4, -2, 8, -13, -1, 18, 9],\n [4, -5, -2, 18, -6, -20, -2, -14, 0],\n [12, -4, 8, -6, 7, -10, 18, -15, 2],\n [-12, 4, -13, -20, -10, -24, 4, -6, -10],\n [-7, -12, -1, -2, 18, 4, -23, -19, 0],\n [-10, 0, 18, -14, -15, -6, -19, -12, -11],\n [4, -8, 9, 0, 2, -10, 0, -11, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1784", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-22, -2, -2, -12, -6, -11, -4, 8, 12],\n [-2, 14, -15, 14, 17, -19, -8, 4, 11],\n [-2, -15, -17, 4, 3, 10, 16, 13, -6],\n [-12, 14, 4, 8, 14, -12, 14, 2, 4],\n [-6, 17, 3, 14, 7, -8, 2, 9, -17],\n [-11, -19, 10, -12, -8, -21, 6, -1, 3],\n [-4, -8, 16, 14, 2, 6, -12, -8, 6],\n [8, 4, 13, 2, 9, -1, -8, 3, -13],\n [12, 11, -6, 4, -17, 3, 6, -13, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1741", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 8) of the inverse. Round your answer to the nearest integer:\n[[13, -6, -19, -11, -11, -3, 7, 18, -24],\n [0, 6, -11, -19, -17, 2, -4, -23, 16],\n [0, 0, -1, -1, 6, 18, -19, 5, 11],\n [0, 0, 0, -17, -20, 20, 5, 8, 18],\n [0, 0, 0, 0, -4, 22, 3, -15, -20],\n [0, 0, 0, 0, 0, -16, -16, 23, -2],\n [0, 0, 0, 0, 0, 0, -1, 5, 23],\n [0, 0, 0, 0, 0, 0, 0, 10, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "936", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, 24, -8, 18, 8, 3, -5, -25, -10],\n [23, 7, -5, 9, 1, -6, 5, -10, -12],\n [22, 6, 15, 6, -24, 19, -4, 11, -9],\n [6, 12, -9, 8, -19, 3, -9, -2, -18],\n [-3, 7, 3, -7, -21, 11, -3, 0, -2],\n [-5, 7, 0, -16, 16, 3, 9, 2, -14],\n [18, -19, -10, -6, 3, 9, 2, -19, -4],\n [-12, 10, -16, -24, -4, -10, 9, 21, 14],\n [22, -15, 17, 17, 7, 8, 7, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-16, -8, -4, 6, -16, 0, 8, -8, 18],\n [-8, 7, 12, -15, 18, -4, -4, -2, -4],\n [-4, 12, -6, -16, 16, -12, -10, 8, 0],\n [6, -15, -16, -12, 10, 6, 0, -2, 5],\n [-16, 18, 16, 10, -1, 4, -18, -11, -10],\n [0, -4, -12, 6, 4, 3, 13, 6, 4],\n [8, -4, -10, 0, -18, 13, 24, -19, -2],\n [-8, -2, 8, -2, -11, 6, -19, -9, 18],\n [18, -4, 0, 5, -10, 4, -2, 18, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[7, -10, -20, -5, 4, 6, -6, 5, -4],\n [-10, -25, -18, -12, -2, -10, -15, 0, -2],\n [-20, -18, -16, 0, 6, -15, -10, -10, 6],\n [-5, -12, 0, 22, -6, -12, -14, -20, 15],\n [4, -2, 6, -6, -3, 0, 7, -10, -2],\n [6, -10, -15, -12, 0, 14, 2, 0, 18],\n [-6, -15, -10, -14, 7, 2, 11, 13, -1],\n [5, 0, -10, -20, -10, 0, 13, 7, -11],\n [-4, -2, 6, 15, -2, 18, -1, -11, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the inverse of matrix 1/450 * A where A =\n[[-9, 24, 11, 4, 1, 4, -4, 10, 14],\n [24, 21, -13, -6, -10, 6, 10, -4, 4],\n [11, -13, -14, -6, -12, -8, 20, -2, -14],\n [4, -6, -6, -21, 4, 2, 3, 16, 3],\n [1, -10, -12, 4, 3, -2, 13, 3, -19],\n [4, 6, -8, 2, -2, 17, -5, -12, 0],\n [-4, 10, 20, 3, 13, -5, -10, 12, 8],\n [10, -4, -2, 16, 3, -12, 12, -13, -6],\n [14, 4, -14, 3, -19, 0, 8, -6, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, 14, -3, 14, -5, -6, 6, -12, -2],\n [0, -8, 21, 4, 2, 22, -12, 16, -5],\n [0, 0, 5, -23, -3, 13, 18, 4, 16],\n [0, 0, 0, 10, 12, -19, -21, -20, 23],\n [0, 0, 0, 0, 5, 20, 1, -10, -24],\n [0, 0, 0, 0, 0, -21, 10, -19, 6],\n [0, 0, 0, 0, 0, 0, 22, 1, -20],\n [0, 0, 0, 0, 0, 0, 0, -16, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28216", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-20, 10, -2, 1, 4, -4, 4, 4, 16],\n [10, 11, 6, 6, 0, -22, 2, 15, -6],\n [-2, 6, 7, 18, 22, -14, -2, 16, -11],\n [1, 6, 18, -8, -22, -17, 2, -2, 12],\n [4, 0, 22, -22, 22, 12, -15, -6, -4],\n [-4, -22, -14, -17, 12, 21, -10, -14, 11],\n [4, 2, -2, 2, -15, -10, -2, 5, -10],\n [4, 15, 16, -2, -6, -14, 5, 11, 2],\n [16, -6, -11, 12, -4, 11, -10, 2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1144", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, 3, 0, 7, 1, 4, -16, 1, -10],\n [3, 18, -17, 12, -4, -1, 4, 16, 10],\n [0, -17, -20, 10, 16, -7, 10, -8, 16],\n [7, 12, 10, 7, -4, 12, 4, -4, -6],\n [1, -4, 16, -4, 6, 14, -8, -24, -6],\n [4, -1, -7, 12, 14, 15, 14, 2, 5],\n [-16, 4, 10, 4, -8, 14, -4, -4, -6],\n [1, 16, -8, -4, -24, 2, -4, 4, -14],\n [-10, 10, 16, -6, -6, 5, -6, -14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "218", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[17, -24, 6, -10, 25, -13, 23, 1, 5],\n [0, -5, -7, 22, -13, -7, 9, 9, 7],\n [0, 0, -5, 14, -3, 22, 19, 19, -15],\n [0, 0, 0, 2, 10, -18, -2, 8, -11],\n [0, 0, 0, 0, 9, 17, -19, -10, -4],\n [0, 0, 0, 0, 0, -24, -18, -19, 12],\n [0, 0, 0, 0, 0, 0, -17, 23, -24],\n [0, 0, 0, 0, 0, 0, 0, -21, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38552", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[0, -2, -10, 20, -14, -14, -17, -14, 22],\n [-2, -19, 16, -18, 2, 5, -4, -17, 10],\n [-10, 16, 11, 10, 5, -8, 1, 0, 19],\n [20, -18, 10, 0, 6, 4, -3, 18, 6],\n [-14, 2, 5, 6, 5, -4, -11, 18, 16],\n [-14, 5, -8, 4, -4, -17, -24, -1, 9],\n [-17, -4, 1, -3, -11, -24, -20, 7, -8],\n [-14, -17, 0, 18, 18, -1, 7, -13, -14],\n [22, 10, 19, 6, 16, 9, -8, -14, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, 6, 8, 10, 2, 0, 0, 1, -16],\n [6, 24, 6, -10, -19, -24, -14, 10, -22],\n [8, 6, 6, -4, 1, 2, 16, -2, -12],\n [10, -10, -4, 12, -10, 8, -16, 4, 4],\n [2, -19, 1, -10, -8, 2, 12, -8, -4],\n [0, -24, 2, 8, 2, 23, 6, -4, -8],\n [0, -14, 16, -16, 12, 6, 21, -22, 16],\n [1, 10, -2, 4, -8, -4, -22, -25, 3],\n [-16, -22, -12, 4, -4, -8, 16, 3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (3, 9) of the inverse. Round your answer to the nearest integer:\n[[22, -3, -7, -12, 1, 10, 12, -4, -15],\n [0, 6, 14, 15, -2, 8, -23, 12, -24],\n [0, 0, -6, -18, 9, 23, 17, -23, 6],\n [0, 0, 0, 5, -25, -14, -8, -2, 10],\n [0, 0, 0, 0, 4, -9, 19, 23, 4],\n [0, 0, 0, 0, 0, -17, 13, 22, 18],\n [0, 0, 0, 0, 0, 0, -4, 12, -4],\n [0, 0, 0, 0, 0, 0, 0, 3, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-184", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -2, 18, 17, 8, 2, -2, -21, -13],\n [0, -9, 4, 12, -7, -4, 23, 23, -8],\n [0, 0, 2, 4, 2, -6, -22, -22, 11],\n [0, 0, 0, -3, 9, 17, 9, -15, -24],\n [0, 0, 0, 0, 6, 8, 24, -4, 3],\n [0, 0, 0, 0, 0, -24, -14, -5, -14],\n [0, 0, 0, 0, 0, 0, -17, -2, -18],\n [0, 0, 0, 0, 0, 0, 0, -5, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14982", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[17, 2, -15, -4, -9, -4, -4, -12, 9],\n [2, -2, 2, 20, 19, -24, -1, -13, 18],\n [-15, 2, 6, -16, -23, 5, -16, -9, -9],\n [-4, 20, -16, 20, -12, -7, -8, -18, -15],\n [-9, 19, -23, -12, 8, -18, -22, 0, 11],\n [-4, -24, 5, -7, -18, -18, 4, 22, -15],\n [-4, -1, -16, -8, -22, 4, 4, -9, 2],\n [-12, -13, -9, -18, 0, 22, -9, 8, 5],\n [9, 18, -9, -15, 11, -15, 2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 16, 17, -5, 2, -4, 8, 12, 4],\n [16, 15, -4, 6, 0, 3, 19, 5, 0],\n [17, -4, 14, -2, -2, -2, -6, 6, -14],\n [-5, 6, -2, 14, 6, 8, 22, -2, 12],\n [2, 0, -2, 6, -2, -12, 0, -2, -5],\n [-4, 3, -2, 8, -12, 7, 0, 6, -6],\n [8, 19, -6, 22, 0, 0, -13, -3, -17],\n [12, 5, 6, -2, -2, 6, -3, -9, -22],\n [4, 0, -14, 12, -5, -6, -17, -22, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 3, -15, -4, 5, 13, -25, -11, -7],\n [0, -17, -13, 19, 0, -20, 14, 18, -24],\n [0, 0, -14, -3, 24, -23, 24, -15, -21],\n [0, 0, 0, -20, -10, 5, -3, 4, 14],\n [0, 0, 0, 0, 21, -23, 21, 8, -14],\n [0, 0, 0, 0, 0, 2, -19, 22, 19],\n [0, 0, 0, 0, 0, 0, 23, 15, -11],\n [0, 0, 0, 0, 0, 0, 0, -25, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[25, 3, -22, -5, 8, 8, 0, -21, 9],\n [3, -22, 3, 2, 4, 10, 13, 4, -8],\n [-22, 3, 17, 20, -11, 16, 4, 12, 10],\n [-5, 2, 20, -22, -13, 0, 9, 8, -4],\n [8, 4, -11, -13, -6, -6, 14, 15, -4],\n [8, 10, 16, 0, -6, -22, 18, 8, 4],\n [0, 13, 4, 9, 14, 18, -20, 16, 2],\n [-21, 4, 12, 8, 15, 8, 16, 17, -8],\n [9, -8, 10, -4, -4, 4, 2, -8, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "446", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-2, 8, -3, -6, -4, -2, 12, -4, 2],\n [8, 14, -6, 18, 11, -2, -8, 17, -8],\n [-3, -6, 17, 1, 20, 6, 18, 6, 0],\n [-6, 18, 1, 20, -8, -6, -6, -4, 0],\n [-4, 11, 20, -8, 12, 10, -14, 0, 6],\n [-2, -2, 6, -6, 10, -11, 18, -4, 7],\n [12, -8, 18, -6, -14, 18, 3, -8, -4],\n [-4, 17, 6, -4, 0, -4, -8, 7, 9],\n [2, -8, 0, 0, 6, 7, -4, 9, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, 23, 6, -10, -25, 20, -23, -6, 2],\n [0, 10, 15, -25, -12, 19, -11, 6, -8],\n [0, 0, -4, -10, -15, -19, -17, -25, 16],\n [0, 0, 0, 3, -20, -14, 17, 13, -19],\n [0, 0, 0, 0, 10, -7, -5, -7, 17],\n [0, 0, 0, 0, 0, -15, -1, 9, -21],\n [0, 0, 0, 0, 0, 0, -8, -20, 25],\n [0, 0, 0, 0, 0, 0, 0, -18, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476034", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (7, 9) of the inverse. Round your answer to the nearest integer:\n[[12, 15, -13, -21, 20, -12, 24, -19, -20],\n [0, 20, 25, -10, 25, 6, 16, -15, -22],\n [0, 0, -17, -16, -18, 10, 6, 19, -20],\n [0, 0, 0, -17, 12, -21, 8, -12, -16],\n [0, 0, 0, 0, -15, -13, -9, 11, 18],\n [0, 0, 0, 0, 0, -13, -1, 18, 7],\n [0, 0, 0, 0, 0, 0, 1, 24, 10],\n [0, 0, 0, 0, 0, 0, 0, 18, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "767", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 17, -14, 0, 16, -4, -4, -6, 8],\n [17, -1, -6, -8, 0, 17, -10, 2, -4],\n [-14, -6, 6, -8, 6, -3, 10, -22, 10],\n [0, -8, -8, 15, -1, -8, -6, 0, 21],\n [16, 0, 6, -1, 10, 0, -10, -20, -13],\n [-4, 17, -3, -8, 0, 3, -18, -12, 2],\n [-4, -10, 10, -6, -10, -18, 8, 18, -12],\n [-6, 2, -22, 0, -20, -12, 18, 2, -2],\n [8, -4, 10, 21, -13, 2, -12, -2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -21, 2, 5, -13, -1, -20, -23, -4],\n [0, 13, 6, 4, -19, -1, -24, -18, 24],\n [0, 0, -16, 12, -8, -13, -5, 7, -3],\n [0, 0, 0, -5, -21, 9, -8, 12, 10],\n [0, 0, 0, 0, 12, 24, -8, 3, 5],\n [0, 0, 0, 0, 0, 14, -20, -24, -18],\n [0, 0, 0, 0, 0, 0, -4, -16, 9],\n [0, 0, 0, 0, 0, 0, 0, 23, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 7) of the inverse of matrix 1/450 * A where A =\n[[-20, 11, 25, 1, 16, 15, 20, -21, 13],\n [0, -3, -9, 15, -3, 13, 7, -24, -16],\n [0, 0, -17, -11, 17, -2, -14, -4, -8],\n [0, 0, 0, 13, -17, -4, -9, -12, 5],\n [0, 0, 0, 0, 8, -23, -24, 19, 1],\n [0, 0, 0, 0, 0, -5, -19, -1, 19],\n [0, 0, 0, 0, 0, 0, 18, -22, -5],\n [0, 0, 0, 0, 0, 0, 0, -16, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1036", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, 9, -18, -9, -2, -21, -10, -11, 2],\n [9, 3, 13, 21, -10, -6, -9, 24, -10],\n [-18, 13, -21, 5, -4, 4, 0, 8, -12],\n [-9, 21, 5, 16, 4, 0, -5, -12, -6],\n [-2, -10, -4, 4, 7, 4, -4, -10, -14],\n [-21, -6, 4, 0, 4, 7, -10, -9, 4],\n [-10, -9, 0, -5, -4, -10, -1, -2, -6],\n [-11, 24, 8, -12, -10, -9, -2, -15, -3],\n [2, -10, -12, -6, -14, 4, -6, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-101", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 23, -21, -3, -23, 13, 11, -16, 1],\n [-19, 23, 3, 23, 13, -20, -17, -18, -12],\n [12, -17, -15, -15, 14, 9, -15, 10, -23],\n [19, -7, -18, 2, -25, 14, 4, 15, 12],\n [-15, 3, 5, -16, 9, 14, 3, 11, -24],\n [22, -25, 6, -2, -24, -23, -17, 23, -2],\n [-14, 8, 8, -3, -7, 6, 23, 2, 0],\n [23, 19, -14, 17, 5, -15, 14, 24, -22],\n [-8, 3, 21, 13, 21, 5, 25, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 4) rounded to the nearest integer?\n[[4, 23, 16, -15, -12, -22, 10, -25, 18],\n [0, 11, 7, -5, -2, 14, 24, -13, 23],\n [0, 0, 3, 10, 14, 21, -21, -6, 3],\n [0, 0, 0, 23, 15, -8, 4, -12, -17],\n [0, 0, 0, 0, -23, 3, 11, 1, -22],\n [0, 0, 0, 0, 0, -19, 1, 4, -14],\n [0, 0, 0, 0, 0, 0, 11, 8, 24],\n [0, 0, 0, 0, 0, 0, 0, -16, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, 2, -11, 6, -24, -20, -4, 2, -9],\n [2, -19, 7, 7, -9, -1, 4, 5, 2],\n [-11, 7, -9, 6, 2, 20, -3, 8, -12],\n [6, 7, 6, 14, -10, -4, -4, -5, -1],\n [-24, -9, 2, -10, 2, -11, 10, 10, -5],\n [-20, -1, 20, -4, -11, 22, 18, 19, -15],\n [-4, 4, -3, -4, 10, 18, 14, 6, -19],\n [2, 5, 8, -5, 10, 19, 6, 8, -2],\n [-9, 2, -12, -1, -5, -15, -19, -2, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 3) of the inverse of matrix 1/450 * A where A =\n[[23, -4, 5, 1, 1, 14, 0, -19, -15],\n [0, 14, -7, 12, -6, -7, -7, 10, 21],\n [0, 0, -8, -6, 18, 16, 15, -18, 14],\n [0, 0, 0, -3, -20, 9, -11, 12, 2],\n [0, 0, 0, 0, -20, 6, 3, 8, -25],\n [0, 0, 0, 0, 0, 6, 10, -1, -11],\n [0, 0, 0, 0, 0, 0, -14, 9, 25],\n [0, 0, 0, 0, 0, 0, 0, -14, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-22, -17, 19, -11, 16, -5, 6, -17, 22],\n [6, -10, 19, -21, 16, 5, -1, -25, -23],\n [-5, 2, -23, 16, 6, 6, 23, 4, 24],\n [-13, 8, 22, -22, -8, 6, -12, 6, -20],\n [17, -9, -18, 9, -2, -23, -9, 10, 25],\n [14, -9, 4, -1, -4, 11, -15, -14, -5],\n [-11, -14, -4, 13, 9, 16, -10, 7, 17],\n [23, -12, -8, 18, -10, 14, -23, 17, 0],\n [-11, 10, 1, 22, -9, -12, -24, 1, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-2, 0, 14, 2, -20, -2, 16, -10, 10],\n [0, 14, 2, 0, -25, -5, -20, 6, 1],\n [14, 2, 13, -4, -12, 2, -2, -8, -8],\n [2, 0, -4, 10, 14, 10, 4, 6, 18],\n [-20, -25, -12, 14, 22, -12, 10, 15, -8],\n [-2, -5, 2, 10, -12, 18, 10, 6, -8],\n [16, -20, -2, 4, 10, 10, -13, 8, -19],\n [-10, 6, -8, 6, 15, 6, 8, 2, -3],\n [10, 1, -8, 18, -8, -8, -19, -3, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-113", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[10, -12, 8, -8, -2, 4, 25, -7, 10],\n [-5, -7, 0, 9, 14, -22, -5, -23, -21],\n [17, 3, -7, 25, -9, 8, -6, 2, -17],\n [-23, -16, -5, 15, -22, -4, -19, -14, -15],\n [-4, 3, 1, 21, -6, -12, -19, -11, 20],\n [2, 17, -16, 25, -23, -14, -13, 13, 18],\n [8, -25, 12, -1, -7, -1, -20, 19, -22],\n [0, 0, 0, -12, 6, 22, 2, -24, 15],\n [19, -5, 20, -12, 11, -24, -21, 12, -24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-25, 22, 10, 7, -6, 8, 10, -4, -2],\n [22, -16, 4, 5, -5, -12, -12, 6, 16],\n [10, 4, 24, 10, -8, 12, -6, -20, -8],\n [7, 5, 10, -22, -14, 5, 5, 4, 10],\n [-6, -5, -8, -14, 18, -18, -16, -2, 2],\n [8, -12, 12, 5, -18, -4, -14, 18, 4],\n [10, -12, -6, 5, -16, -14, -7, -4, -6],\n [-4, 6, -20, 4, -2, 18, -4, 2, -5],\n [-2, 16, -8, 10, 2, 4, -6, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-121", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (8, 6) rounded to the nearest integer?\n[[19, -10, 18, -25, -11, -4, 6, 11, -3],\n [7, 23, 14, -4, 14, 21, -14, 22, -8],\n [6, -23, 10, 21, 20, -25, -1, -6, -9],\n [23, -4, 24, 7, 0, 1, 8, -3, -10],\n [-12, 24, 15, -12, 19, 0, 20, 25, 23],\n [1, 14, -22, -17, 1, 17, 13, -11, -1],\n [-8, 4, 11, -10, -14, -9, -1, -11, -1],\n [-5, -7, -2, -19, -14, 23, 13, -15, 7],\n [23, -1, 13, 8, -15, -10, 6, -11, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, -19, 11, 14, -24, -20, 10, 13, 12],\n [2, -4, 11, -21, -8, -15, -18, -6, -15],\n [1, 3, -1, 25, -7, -24, 16, 13, 18],\n [-24, -19, 25, 5, 7, -15, 14, 14, 20],\n [-13, -16, 23, 12, -6, -5, -12, -2, 14],\n [-19, -21, -20, 14, 9, -17, 16, -25, 13],\n [-6, -20, 6, -13, 13, 14, -5, 11, -14],\n [-20, -11, -5, -5, 2, 10, -9, 20, -19],\n [-3, 19, -4, -16, -8, -24, -14, 19, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[24, -5, 7, -9, 3, -14, 2, 3, 14],\n [-5, -20, -3, 8, 10, -4, 20, -12, -8],\n [7, -3, 20, -8, -4, -6, 1, -8, 7],\n [-9, 8, -8, -17, -2, -4, -4, 8, -10],\n [3, 10, -4, -2, -2, 13, -8, -23, -6],\n [-14, -4, -6, -4, 13, 2, -9, 13, -14],\n [2, 20, 1, -4, -8, -9, -23, -6, 14],\n [3, -12, -8, 8, -23, 13, -6, 22, -14],\n [14, -8, 7, -10, -6, -14, 14, -14, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-226", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -17, 3, 5, 19, 20, 1, -20, 17],\n [5, 15, 19, 10, -24, -5, 8, -4, -13],\n [-7, 7, 12, 14, 23, -23, 12, -7, -19],\n [-11, 12, -1, -4, -3, 24, -16, 10, 11],\n [24, 16, 16, 16, -19, 20, -1, 14, 15],\n [-2, -21, -5, 14, -6, 3, 11, -6, -8],\n [-22, -15, -4, 17, -12, 19, 2, -22, -10],\n [12, -3, -13, -6, -21, -7, -5, 16, -21],\n [-12, 10, -20, -21, -2, 3, 3, -24, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -8, 2, -22, 20, 6, -22, -14, -8],\n [-8, 9, 6, -13, -10, -5, -1, -3, -10],\n [2, 6, -20, -13, 12, -2, 2, 0, -6],\n [-22, -13, -13, 19, -25, 9, -16, -6, 6],\n [20, -10, 12, -25, -3, 2, -15, 4, -12],\n [6, -5, -2, 9, 2, 13, -7, 0, 0],\n [-22, -1, 2, -16, -15, -7, -10, -2, 20],\n [-14, -3, 0, -6, 4, 0, -2, -6, 16],\n [-8, -10, -6, 6, -12, 0, 20, 16, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, -21, 14, 3, -8, 3, -11, 24, 19],\n [0, -11, 19, -23, 18, 18, 16, 7, -2],\n [0, 0, -2, -13, 1, 7, -7, -1, -20],\n [0, 0, 0, 23, -9, -5, 17, -6, -14],\n [0, 0, 0, 0, 7, -23, -9, 13, 6],\n [0, 0, 0, 0, 0, 17, 9, 3, -14],\n [0, 0, 0, 0, 0, 0, 22, 18, 4],\n [0, 0, 0, 0, 0, 0, 0, -21, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9329", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[21, -16, 2, -5, 23, 2, -4, 12, -7],\n [0, 20, -2, 2, 19, -13, -17, -17, -5],\n [0, 0, 3, 14, -16, -22, -23, -13, -5],\n [0, 0, 0, -25, -12, -14, 10, -4, 10],\n [0, 0, 0, 0, 8, -1, 0, -23, -6],\n [0, 0, 0, 0, 0, -15, -10, -6, 16],\n [0, 0, 0, 0, 0, 0, 19, -1, -22],\n [0, 0, 0, 0, 0, 0, 0, -15, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6605", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[23, 17, 19, 18, -23, -3, -6, 19, -11],\n [0, -10, -19, 7, -7, -8, 15, -8, -23],\n [0, 0, -10, 17, -3, -3, -11, -17, 14],\n [0, 0, 0, -20, 18, 11, 20, -20, -5],\n [0, 0, 0, 0, -12, -25, 1, 6, 3],\n [0, 0, 0, 0, 0, -10, 18, -15, -8],\n [0, 0, 0, 0, 0, 0, -2, 0, -10],\n [0, 0, 0, 0, 0, 0, 0, -18, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9641", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 5, -16, -24, 20, 18, -22, -4, 19],\n [2, -16, -24, 23, 5, 16, -3, -10, -17],\n [25, 17, -20, -1, -22, 22, -14, -2, 1],\n [22, -23, -14, 21, 4, -14, 15, 16, 14],\n [19, -4, -11, 2, -9, 18, 22, -1, 17],\n [25, 19, -23, 10, 5, -11, 20, 2, 17],\n [5, 19, -6, 24, 19, -5, 1, -7, 10],\n [-14, 9, 22, 7, 10, 15, -3, -13, 4],\n [-16, 15, -6, -20, 5, -7, -23, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-151", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, -24, 19, 13, 19, 4, 20, 2, -8],\n [-12, 19, -7, 14, 10, 15, -14, -6, 8],\n [10, -5, -7, 15, 15, 17, 16, 9, -18],\n [-4, 17, 12, -8, -18, -24, -6, -21, 16],\n [4, -8, 18, -3, -24, 16, 18, 25, 11],\n [16, 6, -25, 13, -25, 23, 18, 5, 13],\n [-18, -23, 21, -14, 23, 8, 23, -1, 10],\n [-19, -11, -5, -1, 22, 12, 11, -10, -25],\n [21, 11, 19, -12, 8, -24, 5, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 8) rounded to the nearest integer?\n[[18, -3, 4, -9, -24, -15, 23, -12, 15],\n [3, -7, 2, 25, -25, -21, 25, 8, -12],\n [-7, -2, 14, -9, -24, 5, -9, -18, 20],\n [-9, 12, 0, 17, 14, 19, 14, -19, -2],\n [4, 0, 4, 9, -24, 18, -22, -21, 22],\n [-24, 5, 1, -2, 19, -22, 2, -21, 1],\n [18, 21, -21, -21, 22, -17, 21, 1, -22],\n [23, -2, 1, -25, 6, -10, -3, 2, -6],\n [-9, 10, 19, -18, -8, -13, -17, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -10, 10, 0, -4, -2, 20, -1, -2],\n [-10, 8, -10, 11, 12, 16, -10, -14, -6],\n [10, -10, -25, -8, -6, -9, 0, -4, 12],\n [0, 11, -8, -18, 4, -4, 18, 10, 6],\n [-4, 12, -6, 4, 7, 10, 7, -2, 4],\n [-2, 16, -9, -4, 10, 25, 7, 1, 11],\n [20, -10, 0, 18, 7, 7, -18, 14, 15],\n [-1, -14, -4, 10, -2, 1, 14, 18, 17],\n [-2, -6, 12, 6, 4, 11, 15, 17, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-23, 17, 14, 6, 10, 16, 15, 19, -7],\n [5, 4, 21, 11, -1, -13, -14, -17, 14],\n [-17, 19, 1, 15, 5, -20, 3, 4, 12],\n [-15, 16, 20, -20, 13, 15, 5, 9, -14],\n [22, 19, -20, 19, 0, 11, 6, -22, 14],\n [-23, -24, -6, -7, 13, -14, 10, 16, 2],\n [-17, 18, -15, 4, 25, -24, 12, 12, 7],\n [-19, 18, -5, -14, -5, -3, -20, -12, 6],\n [23, 23, 24, 19, -13, 1, -15, 6, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, -24, 4, -24, 13, 3, -4, -1, 16],\n [0, -7, 23, -10, -9, 24, 1, 17, -7],\n [0, 0, 4, -12, 20, 16, 6, -3, 10],\n [0, 0, 0, -15, 24, 12, -11, 6, 1],\n [0, 0, 0, 0, -23, 4, 5, -25, 20],\n [0, 0, 0, 0, 0, 15, 17, -11, 12],\n [0, 0, 0, 0, 0, 0, 17, -24, 25],\n [0, 0, 0, 0, 0, 0, 0, 7, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-244", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -10, -7, 4, -2, -12, 20, 5, 0],\n [-10, 13, -2, -2, 6, 8, -2, 14, -16],\n [-7, -2, 22, -7, 2, 11, -4, -11, -22],\n [4, -2, -7, 16, -7, 9, 4, 8, 4],\n [-2, 6, 2, -7, -6, -10, -20, -14, -15],\n [-12, 8, 11, 9, -10, 24, 20, -7, 6],\n [20, -2, -4, 4, -20, 20, -19, -16, 10],\n [5, 14, -11, 8, -14, -7, -16, -5, 0],\n [0, -16, -22, 4, -15, 6, 10, 0, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1193", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[3, -4, 10, 11, 4, 14, 0, 8, 0],\n [-4, -6, -8, -18, 14, 16, 15, -4, -15],\n [10, -8, -12, -4, -3, -13, -13, 12, 10],\n [11, -18, -4, -5, 12, -14, -2, 5, -22],\n [4, 14, -3, 12, 6, -12, 12, 16, -8],\n [14, 16, -13, -14, -12, 2, -4, 2, -10],\n [0, 15, -13, -2, 12, -4, -14, 18, 10],\n [8, -4, 12, 5, 16, 2, 18, -7, 1],\n [0, -15, 10, -22, -8, -10, 10, 1, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-10, -4, 7, -24, 19, 3, 20, 8, -10],\n [0, 13, 20, 24, 23, -21, 17, -8, 22],\n [0, 0, -20, -12, -24, 1, -17, -13, -5],\n [0, 0, 0, -13, -5, 7, -6, 10, -8],\n [0, 0, 0, 0, 12, -11, 24, -9, 20],\n [0, 0, 0, 0, 0, 17, -13, -9, -5],\n [0, 0, 0, 0, 0, 0, 2, -7, -15],\n [0, 0, 0, 0, 0, 0, 0, -21, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7623", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, 5, 6, -19, 17, 12, 8, 20, -22],\n [0, -4, 3, 8, 8, 19, 19, -23, -5],\n [0, 0, -9, 3, 7, 13, 0, -19, 19],\n [0, 0, 0, -15, -4, 6, 17, -16, 23],\n [0, 0, 0, 0, -16, -14, 12, -5, 1],\n [0, 0, 0, 0, 0, 8, 23, 14, -4],\n [0, 0, 0, 0, 0, 0, -16, 23, -3],\n [0, 0, 0, 0, 0, 0, 0, 6, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2334", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-20, -18, 7, 6, 20, 10, 16, 22, 10],\n [0, -24, -13, 17, -16, 12, -19, 21, 25],\n [0, 0, -12, 4, 8, -3, 22, -9, -11],\n [0, 0, 0, -23, -17, -23, 22, 9, 14],\n [0, 0, 0, 0, -13, -11, 13, -14, 9],\n [0, 0, 0, 0, 0, 24, -14, -4, 1],\n [0, 0, 0, 0, 0, 0, -16, -7, 18],\n [0, 0, 0, 0, 0, 0, 0, -17, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-552", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -4, 12, 5, -2, -4, 4, 8, -7],\n [-4, -23, -20, 10, -5, -7, 17, 4, 12],\n [12, -20, 1, -16, -9, -9, 14, -10, 14],\n [5, 10, -16, 22, 0, -5, -2, -1, -7],\n [-2, -5, -9, 0, 0, -17, 16, -8, 4],\n [-4, -7, -9, -5, -17, -21, 6, 7, -12],\n [4, 17, 14, -2, 16, 6, 12, 6, 8],\n [8, 4, -10, -1, -8, 7, 6, -11, -4],\n [-7, 12, 14, -7, 4, -12, 8, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, -23, -17, -2, 18, 21, 6, -9, 15],\n [0, -18, -20, -17, -11, -2, 24, -15, 5],\n [0, 0, 19, -13, 4, -1, 22, -14, -5],\n [0, 0, 0, -14, 11, 23, -5, -3, -25],\n [0, 0, 0, 0, 22, 2, -25, 25, -18],\n [0, 0, 0, 0, 0, -19, -15, -18, 17],\n [0, 0, 0, 0, 0, 0, 1, -6, 12],\n [0, 0, 0, 0, 0, 0, 0, -11, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "459", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-22, 8, 12, 18, 13, 15, -20, -4, 11],\n [0, 2, 0, -22, -16, 1, -6, 10, -21],\n [0, 0, 6, 9, -3, -13, -25, 5, -7],\n [0, 0, 0, 22, 22, 23, 18, 8, 4],\n [0, 0, 0, 0, 23, -8, 10, 9, -1],\n [0, 0, 0, 0, 0, 3, -19, 22, 14],\n [0, 0, 0, 0, 0, 0, 10, -12, -8],\n [0, 0, 0, 0, 0, 0, 0, -17, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12575", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-16, -17, 23, -12, 13, -8, 16, -1, 10],\n [5, 20, 9, 1, -4, -15, -16, -18, 15],\n [2, -3, -20, -12, -2, -17, 20, 14, 12],\n [-1, 12, 4, -4, -24, -1, -2, 11, -23],\n [17, 0, 4, 3, -19, -17, 19, 4, -10],\n [18, 14, -12, 0, 20, 11, -16, 4, -4],\n [4, 6, -12, -3, -9, 10, 3, -2, 21],\n [-15, 15, -11, -4, 1, 8, 7, -5, -2],\n [-6, 23, -22, 11, 11, 20, 7, 5, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "491", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-4, 16, 4, -21, 15, 19, -3, -13, -17],\n [-12, -9, 9, -8, -14, 15, -10, 4, -13],\n [-8, -14, 8, 25, 7, -20, -8, -23, -20],\n [10, 23, 24, -4, -19, 4, -24, 6, -11],\n [-4, 23, 12, -18, -18, 13, 10, -6, 11],\n [-18, -12, -6, 9, -1, -8, 21, -5, 11],\n [21, 5, -20, 16, 21, -6, 2, 15, 10],\n [14, 0, -13, 23, -22, 8, 11, 8, -10],\n [-3, -3, -11, -1, 3, 10, -11, 11, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1530", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[20, 13, 21, 11, 15, 2, 19, 4, -19],\n [0, -19, 7, 21, 21, -8, -11, 9, 11],\n [0, 0, -3, -16, -1, -4, 5, -3, 2],\n [0, 0, 0, -19, 20, 12, 14, -11, 23],\n [0, 0, 0, 0, -7, 0, 4, 2, -11],\n [0, 0, 0, 0, 0, -2, -15, 13, 17],\n [0, 0, 0, 0, 0, 0, 13, -4, 9],\n [0, 0, 0, 0, 0, 0, 0, -1, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54800", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (3, 7) rounded to the nearest integer?\n[[-14, -8, -20, -21, 16, 12, 0, 13, -7],\n [-8, 10, 0, 0, -2, -4, -16, -6, 18],\n [-20, 0, 12, -2, 2, -20, 3, 0, 0],\n [-21, 0, -2, 4, -10, -9, -8, -14, -3],\n [16, -2, 2, -10, -13, -10, -6, -16, -4],\n [12, -4, -20, -9, -10, 12, -2, 2, 6],\n [0, -16, 3, -8, -6, -2, -23, 13, -4],\n [13, -6, 0, -14, -16, 2, 13, 7, -6],\n [-7, 18, 0, -3, -4, 6, -4, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -6, 10, -7, 20, -22, 6, -18, 25],\n [0, 25, -25, 0, 21, 17, -17, 9, -8],\n [-7, 22, -10, 2, -23, -8, -13, 1, 14],\n [13, -2, 3, -4, 25, 0, -6, -2, -14],\n [-8, 21, -14, 12, 6, 23, -3, -22, -14],\n [-9, -5, 11, 3, -20, 21, 2, -18, 5],\n [-6, -10, -13, -11, -13, 21, -24, -6, 2],\n [-8, -19, -5, 15, 13, -17, 18, -16, 5],\n [16, -13, -21, 14, 16, 12, 17, 10, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-20, -13, 3, 18, -12, 4, -1, 14, 9],\n [0, -19, 24, 12, -8, -18, -19, 8, 10],\n [0, 0, 25, -16, 14, 3, -10, -1, 3],\n [0, 0, 0, 1, -13, 0, 16, -1, 2],\n [0, 0, 0, 0, 21, -4, -25, -14, -2],\n [0, 0, 0, 0, 0, -20, -7, -5, 19],\n [0, 0, 0, 0, 0, 0, -19, -19, 7],\n [0, 0, 0, 0, 0, 0, 0, -7, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7388", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -12, -14, -12, -16, -1, -4, -10, -24],\n [-12, -23, -16, 12, 5, 18, 9, -12, 0],\n [-14, -16, 18, 8, -12, -2, 11, 9, 5],\n [-12, 12, 8, 25, 0, 5, 16, -9, 5],\n [-16, 5, -12, 0, 11, -16, -5, 4, 6],\n [-1, 18, -2, 5, -16, 10, -4, 0, -10],\n [-4, 9, 11, 16, -5, -4, 11, 1, -2],\n [-10, -12, 9, -9, 4, 0, 1, -7, -14],\n [-24, 0, 5, 5, 6, -10, -2, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1134", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[21, -15, -8, -18, 2, -14, -4, 23, 2],\n [-15, -9, 4, 6, 4, 14, -6, -6, 18],\n [-8, 4, -18, -4, 0, 18, 13, 20, -8],\n [-18, 6, -4, -21, 2, 4, 8, -4, 0],\n [2, 4, 0, 2, -17, 16, -4, -4, 12],\n [-14, 14, 18, 4, 16, -5, 13, 16, 7],\n [-4, -6, 13, 8, -4, 13, -21, 8, -17],\n [23, -6, 20, -4, -4, 16, 8, 23, -24],\n [2, 18, -8, 0, 12, 7, -17, -24, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[10, -2, 4, 4, -12, -7, 6, 13, -4],\n [-2, -7, 8, 0, -13, -6, 18, -2, -9],\n [4, 8, 1, -8, -22, 2, -8, -6, 5],\n [4, 0, -8, -25, 7, -4, -10, 8, 9],\n [-12, -13, -22, 7, 14, -6, 12, 14, 2],\n [-7, -6, 2, -4, -6, -1, -9, -4, -6],\n [6, 18, -8, -10, 12, -9, -15, -12, -14],\n [13, -2, -6, 8, 14, -4, -12, -20, 6],\n [-4, -9, 5, 9, 2, -6, -14, 6, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-158", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, 8, -23, -3, 23, -21, 3, 8, 18],\n [-21, 3, 19, -2, 13, -5, 6, 17, -21],\n [-8, 12, 9, 12, -10, 9, 24, -2, 10],\n [-21, -17, -22, 7, 1, -4, -15, -21, -16],\n [-23, -11, 20, 11, 14, -9, -6, 25, -22],\n [8, 8, 5, 8, -23, 2, 15, 11, 3],\n [-11, 10, 9, 15, -16, -9, 4, -18, -3],\n [-7, 11, 17, 10, -22, 0, 21, 14, 1],\n [-13, 18, 8, 7, 20, 0, -6, -18, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1217", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (8, 7) rounded to the nearest integer?\n[[-21, 8, 21, 1, 10, -22, 16, 24, -19],\n [0, 10, -2, -11, 24, 23, -20, 0, 0],\n [0, 0, -23, -17, 11, 12, 4, 1, -13],\n [0, 0, 0, 9, -2, 11, -14, -6, -8],\n [0, 0, 0, 0, 22, 6, 4, -24, -18],\n [0, 0, 0, 0, 0, 16, 19, 2, -13],\n [0, 0, 0, 0, 0, 0, 16, 17, 8],\n [0, 0, 0, 0, 0, 0, 0, 8, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-6, 17, 0, -6, -13, -8, 9, -1, -17],\n [17, 8, -16, 20, 0, 4, -8, 2, -8],\n [0, -16, -23, -6, -15, 6, 18, -22, -8],\n [-6, 20, -6, 10, -6, 2, -6, 2, 7],\n [-13, 0, -15, -6, 1, -6, -7, -1, -16],\n [-8, 4, 6, 2, -6, 1, -12, -11, 6],\n [9, -8, 18, -6, -7, -12, -10, -1, -16],\n [-1, 2, -22, 2, -1, -11, -1, -25, -1],\n [-17, -8, -8, 7, -16, 6, -16, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-159", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, -22, -2, -7, -2, 15, 19, -5, -9],\n [-18, 5, -7, -15, 20, 24, -3, 11, 2],\n [-3, -14, -10, -10, -12, -19, -5, -5, 15],\n [9, 20, -2, -25, -12, -6, 2, -8, -23],\n [1, -20, -22, -25, -5, 9, 2, -8, 9],\n [-5, -10, 0, 13, -17, -3, -24, -23, 7],\n [-2, -3, -20, -5, 21, -21, -13, 14, -13],\n [-7, -17, -23, 5, 20, 13, -13, 15, -15],\n [15, -15, 20, 21, 23, -25, 9, 9, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-107", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-22, -2, 4, 6, 23, -6, 10, -13, 13],\n [-22, 2, 14, 17, 25, -19, -17, -4, -22],\n [10, 7, -20, -23, 9, 7, -19, 15, 9],\n [21, -23, 17, -8, -23, 13, 1, -17, -9],\n [15, 16, 19, -21, 20, -22, -12, 3, -15],\n [-4, 16, -21, -14, -5, -11, -2, -13, 6],\n [0, 14, 0, 10, 19, 4, 21, -17, -2],\n [12, -8, -17, -4, 12, -5, -19, -14, 10],\n [-15, -23, 1, -19, -24, -16, -23, -9, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-70", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-25, 4, -18, -17, -17, 1, 2, 6, 12],\n [4, 18, 6, 15, 14, -8, -12, -16, 8],\n [-18, 6, 16, 4, -3, -10, 2, 18, -14],\n [-17, 15, 4, -13, -12, -12, 0, -4, 10],\n [-17, 14, -3, -12, 23, -16, -12, 8, -4],\n [1, -8, -10, -12, -16, 21, 0, 2, -8],\n [2, -12, 2, 0, -12, 0, -12, 18, 3],\n [6, -16, 18, -4, 8, 2, 18, 20, -6],\n [12, 8, -14, 10, -4, -8, 3, -6, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "721", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-19, -12, -24, -14, 17, 23, -24, 2, 2],\n [-14, 4, 21, 14, 14, -4, -8, -12, -1],\n [-16, 10, 22, 22, 23, -17, -15, 1, -13],\n [-25, 13, -15, -23, -24, 20, 16, -2, -6],\n [23, 14, -11, -20, -6, -4, -24, -11, 22],\n [8, 20, 5, 4, 2, 7, 15, 23, -5],\n [20, -3, 16, -13, 19, 0, -7, 1, 14],\n [-19, -1, 23, 14, 10, -19, -6, -2, 2],\n [23, -21, 10, 5, 25, 7, -2, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the inverse of matrix 1/450 * A where A =\n[[18, 23, -21, 5, -17, 6, 15, -21, 25],\n [0, 2, 17, -14, -21, -18, -9, -18, 8],\n [0, 0, 25, -16, 13, 15, 18, 18, -21],\n [0, 0, 0, -15, 21, 22, -7, -5, 18],\n [0, 0, 0, 0, -2, 10, -20, -16, 21],\n [0, 0, 0, 0, 0, -6, 12, 9, 8],\n [0, 0, 0, 0, 0, 0, 18, 23, -25],\n [0, 0, 0, 0, 0, 0, 0, 5, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, -7, -7, -23, -23, 0, -20, -13, 20],\n [0, 1, 15, -2, -16, -10, -3, 21, -14],\n [0, 0, -8, -24, 20, -9, -3, -3, -25],\n [0, 0, 0, -12, 23, 18, 12, 15, 18],\n [0, 0, 0, 0, 22, -16, -7, 4, -22],\n [0, 0, 0, 0, 0, 13, 23, 7, 9],\n [0, 0, 0, 0, 0, 0, 24, 3, 9],\n [0, 0, 0, 0, 0, 0, 0, -5, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 5, 24, 15, 4, -23, -10, -22, 20],\n [0, 2, 24, 24, 24, 2, -23, 0, 13],\n [0, 0, -13, -22, -10, 2, 21, -13, 16],\n [0, 0, 0, -7, 4, 21, 15, 22, 2],\n [0, 0, 0, 0, -25, -17, -14, -3, -14],\n [0, 0, 0, 0, 0, -10, -13, 9, 24],\n [0, 0, 0, 0, 0, 0, -14, -2, 2],\n [0, 0, 0, 0, 0, 0, 0, -4, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6651", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 14, 7, 1, 0, 10, -8, 20, 8],\n [14, 22, 8, 0, 2, 18, 8, -2, -6],\n [7, 8, 19, -10, -4, 11, 2, 4, -9],\n [1, 0, -10, 17, 15, -8, 8, 6, -14],\n [0, 2, -4, 15, 13, 6, 19, 14, -3],\n [10, 18, 11, -8, 6, 14, 6, 6, -22],\n [-8, 8, 2, 8, 19, 6, 16, 15, -2],\n [20, -2, 4, 6, 14, 6, 15, -10, -5],\n [8, -6, -9, -14, -3, -22, -2, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[7, -17, -12, -14, 5, -14, -6, 1, 6],\n [-17, -24, -9, -2, 7, 10, 13, -11, -14],\n [-12, -9, 21, 7, -1, 20, 8, -2, 10],\n [-14, -2, 7, 4, 10, 14, 2, 8, 2],\n [5, 7, -1, 10, -16, -2, -10, 7, -14],\n [-14, 10, 20, 14, -2, 17, 0, 4, -8],\n [-6, 13, 8, 2, -10, 0, -21, 6, -16],\n [1, -11, -2, 8, 7, 4, 6, 19, -6],\n [6, -14, 10, 2, -14, -8, -16, -6, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-205", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[13, -6, 6, -14, -16, 15, 2, 4, 0],\n [-6, 15, -14, -14, 12, 18, -10, 10, 0],\n [6, -14, 16, 6, -20, -2, 4, -14, 0],\n [-14, -14, 6, 4, -6, -6, 19, -1, 13],\n [-16, 12, -20, -6, -15, -4, 6, 5, 1],\n [15, 18, -2, -6, -4, 22, 7, 4, -8],\n [2, -10, 4, 19, 6, 7, 6, 14, -6],\n [4, 10, -14, -1, 5, 4, 14, -18, -3],\n [0, 0, 0, 13, 1, -8, -6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 0, 18, 14, 2, -9, 4, -14, 4],\n [0, 15, 19, -6, -13, -9, -4, 4, -1],\n [18, 19, -18, -6, -15, 0, -4, 2, 8],\n [14, -6, -6, -17, 0, -12, -16, 5, -4],\n [2, -13, -15, 0, -21, 13, -2, 12, 2],\n [-9, -9, 0, -12, 13, 5, 21, -5, -9],\n [4, -4, -4, -16, -2, 21, 4, -12, -4],\n [-14, 4, 2, 5, 12, -5, -12, 12, 9],\n [4, -1, 8, -4, 2, -9, -4, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "398", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (6, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -24, -19, 17, 5, -8, -6, -19, -4],\n [11, 8, 20, 13, 16, 24, 14, -10, -12],\n [15, 6, 12, 13, 0, 4, 15, 13, -17],\n [6, -19, -14, -3, -9, -5, -14, -4, -3],\n [-21, -8, 11, 11, -19, -23, -25, -20, -19],\n [1, 5, -18, -12, -11, -19, -19, 7, 15],\n [-19, -6, -19, 24, -12, -11, -8, -16, 9],\n [1, 17, -25, 2, 8, 22, -23, 23, -23],\n [-15, -22, 4, 13, 6, -10, -9, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, -23, 2, 10, -24, 20, -6, 14, 24],\n [0, -18, 13, -1, -11, 4, 21, 8, -22],\n [0, 0, -17, -3, 13, 24, -14, -12, -19],\n [0, 0, 0, -7, -5, -7, 21, -7, 18],\n [0, 0, 0, 0, -1, 7, -5, 8, 20],\n [0, 0, 0, 0, 0, 23, 23, 8, -24],\n [0, 0, 0, 0, 0, 0, -22, -7, 3],\n [0, 0, 0, 0, 0, 0, 0, 21, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11245", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[10, -25, 0, -9, 10, -9, 11, 1, -1],\n [4, 15, -1, 12, 6, -14, 23, -5, 16],\n [8, -25, -13, -5, -25, -13, 5, -3, -23],\n [-15, 3, 22, -8, -1, 8, -8, 23, -25],\n [2, -22, -5, -20, -5, 11, 4, -6, 15],\n [6, 5, 10, -1, -21, -18, -9, -11, -6],\n [19, 21, 3, 10, 24, 25, 2, -18, -12],\n [7, 8, 3, -4, -23, 22, -3, -23, -20],\n [14, -3, -14, -21, -21, -23, -22, -2, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 9, 16, -7, -18, 2, 12, -3, -19],\n [0, -13, 19, -5, 11, -20, -16, 1, 0],\n [0, 0, -10, 24, 2, -23, -25, -23, 4],\n [0, 0, 0, -7, 10, 22, 11, -21, 8],\n [0, 0, 0, 0, 16, 16, 25, -2, 22],\n [0, 0, 0, 0, 0, 14, 6, 25, 7],\n [0, 0, 0, 0, 0, 0, -4, 23, -8],\n [0, 0, 0, 0, 0, 0, 0, -9, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-130", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[14, -16, -12, -1, 4, -4, -5, 12, 1],\n [-16, 19, 2, -8, 15, 4, -6, 1, -16],\n [-12, 2, -25, -7, 6, 4, 18, 5, -14],\n [-1, -8, -7, -13, 8, -4, -2, 11, 14],\n [4, 15, 6, 8, -15, -18, 5, 6, 7],\n [-4, 4, 4, -4, -18, 8, 16, 18, 16],\n [-5, -6, 18, -2, 5, 16, -1, 1, 0],\n [12, 1, 5, 11, 6, 18, 1, -19, 14],\n [1, -16, -14, 14, 7, 16, 0, 14, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "131", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, -3, 1, 7, 25, 21, 23, -6, 2],\n [0, -4, 9, 5, 18, -2, -11, 24, 19],\n [0, 0, -4, -9, 2, -23, -7, 12, 1],\n [0, 0, 0, -5, 11, 25, -15, -25, 4],\n [0, 0, 0, 0, 24, 10, 0, 16, 1],\n [0, 0, 0, 0, 0, 11, 8, 0, -4],\n [0, 0, 0, 0, 0, 0, -19, 2, -2],\n [0, 0, 0, 0, 0, 0, 0, 25, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-203", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[17, -13, -10, 8, -20, 22, -8, -9, 21],\n [13, -12, -19, -20, -14, 8, -25, 24, 3],\n [2, -21, -5, 13, 21, 12, 8, -5, -2],\n [23, -13, 19, 20, -3, 6, -18, 21, -15],\n [-13, -6, -25, -24, -15, 20, 4, -21, -19],\n [-2, 5, 22, 4, 17, -11, 10, -16, -25],\n [-19, 18, 0, 17, 17, 23, 4, -25, -11],\n [-6, -4, -1, 24, 10, 25, 11, 20, 19],\n [1, -7, -7, -10, -5, 25, 7, 16, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-353", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -12, 3, -5, -4, 8, 8, -6, -16],\n [-12, -7, -8, 11, 0, 18, 8, 6, 14],\n [3, -8, 22, 23, 4, -18, -1, -8, -12],\n [-5, 11, 23, -8, -2, -2, -20, -2, 18],\n [-4, 0, 4, -2, 5, -6, -15, 5, 16],\n [8, 18, -18, -2, -6, 7, -2, -2, 18],\n [8, 8, -1, -20, -15, -2, 9, 23, 7],\n [-6, 6, -8, -2, 5, -2, 23, -19, -10],\n [-16, 14, -12, 18, 16, 18, 7, -10, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1198", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[12, -11, 24, 17, -1, -9, 7, -24, 13],\n [-16, -12, -14, -9, -12, 25, -16, 18, 13],\n [14, 3, 19, -20, 14, 5, 11, -17, 17],\n [19, 7, -19, 12, -18, 8, -9, -9, 4],\n [-8, 13, -11, 19, -6, -1, -12, 1, 21],\n [9, 2, -20, 15, 5, -12, -10, 23, 18],\n [10, -21, 6, -15, -4, 17, 14, 2, 24],\n [-20, 13, -20, 20, -6, 12, -22, -1, -13],\n [23, -14, -17, -23, 6, -15, -21, 9, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "835", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-2, 15, -20, -8, 12, -20, -4, 16, 17],\n [-12, -14, -1, -6, -8, -2, -11, 5, 16],\n [-25, -11, 8, -24, 10, -3, -2, 20, 6],\n [25, 20, -13, 7, 16, -12, -9, -10, 6],\n [-11, 17, 5, -14, 7, -23, -15, 17, -21],\n [21, 1, -10, 9, 14, -10, -10, -4, -22],\n [6, 1, -11, -7, 0, -11, 19, -16, 8],\n [12, 23, 0, -18, -10, 3, 6, -5, 6],\n [19, -14, 22, 13, -16, -20, 11, -8, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (5, 7) rounded to the nearest integer?\n[[5, 9, -23, -21, 8, 7, 10, -16, 19],\n [-23, -15, -23, 2, 16, 2, -17, 0, 3],\n [-16, 1, 19, 6, -8, -8, -4, -9, 23],\n [-1, 0, -21, -17, 18, 18, -2, 25, -19],\n [-6, 18, 15, -18, -7, 9, 17, 18, -1],\n [-9, 13, -1, 9, 13, 13, 20, -24, -10],\n [16, -12, 3, 13, -24, -16, -24, 1, -13],\n [-24, 16, -12, -9, 25, 18, 23, 12, 10],\n [8, 3, 21, -3, -3, -10, 18, -19, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-25, -4, -2, 5, 0, -3, -1, 8, -8],\n [-4, 5, -2, 0, -22, -4, 6, -2, -22],\n [-2, -2, 20, 8, 6, -6, -11, 15, -14],\n [5, 0, 8, -11, -16, 8, -8, -10, 1],\n [0, -22, 6, -16, -6, -5, -9, 7, -7],\n [-3, -4, -6, 8, -5, -17, -9, 3, 10],\n [-1, 6, -11, -8, -9, -9, -16, -4, -8],\n [8, -2, 15, -10, 7, 3, -4, -14, -12],\n [-8, -22, -14, 1, -7, 10, -8, -12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-86", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (5, 6) rounded to the nearest integer?\n[[2, 2, -4, 0, 15, -8, 4, 4, -11],\n [2, 23, -12, -11, 14, -6, -8, 2, 15],\n [-4, -12, -8, 14, -19, 8, -2, 6, -6],\n [0, -11, 14, 3, 22, 0, -3, 20, 2],\n [15, 14, -19, 22, -11, -3, -4, 8, 4],\n [-8, -6, 8, 0, -3, 19, -14, -8, 8],\n [4, -8, -2, -3, -4, -14, -25, -10, 10],\n [4, 2, 6, 20, 8, -8, -10, -16, 6],\n [-11, 15, -6, 2, 4, 8, 10, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[12, -4, -4, -18, -12, 2, -3, -2, 2],\n [-4, -15, -19, 0, -17, 0, 14, -4, -6],\n [-4, -19, -5, 4, -4, -17, 17, -2, 4],\n [-18, 0, 4, 25, 12, -22, -12, -6, -10],\n [-12, -17, -4, 12, 11, -18, -9, -14, 0],\n [2, 0, -17, -22, -18, 20, 21, 0, 16],\n [-3, 14, 17, -12, -9, 21, 6, 2, -7],\n [-2, -4, -2, -6, -14, 0, 2, 1, 16],\n [2, -6, 4, -10, 0, 16, -7, 16, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-15, 16, 7, 4, 6, 14, 11, -13, -19],\n [0, -15, 5, 18, -12, 18, 0, -25, -20],\n [0, 0, 17, -14, -25, -20, 3, 4, -13],\n [0, 0, 0, 13, -16, -8, -20, -18, -6],\n [0, 0, 0, 0, -2, -7, -22, -23, -11],\n [0, 0, 0, 0, 0, -1, -25, 14, -24],\n [0, 0, 0, 0, 0, 0, -15, 16, -12],\n [0, 0, 0, 0, 0, 0, 0, -7, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16217", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-24, -4, -22, 19, 20, -6, -23, -17, -8],\n [0, 25, -17, -7, -20, 18, -11, -20, -21],\n [0, 0, 1, 25, 24, 19, 15, 0, 2],\n [0, 0, 0, 4, 5, -14, -17, 8, -23],\n [0, 0, 0, 0, -4, 0, -7, -5, 11],\n [0, 0, 0, 0, 0, -25, -22, 11, 17],\n [0, 0, 0, 0, 0, 0, 14, -25, 13],\n [0, 0, 0, 0, 0, 0, 0, -9, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "363", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-21, -24, 10, 24, 14, 20, 19, 13, -17],\n [0, -21, -11, -17, -1, 24, 2, 1, 20],\n [0, 0, 25, 7, 12, -18, -22, 22, 17],\n [0, 0, 0, -16, 23, 15, 16, -18, 4],\n [0, 0, 0, 0, 20, -23, 3, -10, -16],\n [0, 0, 0, 0, 0, -11, -15, -3, 12],\n [0, 0, 0, 0, 0, 0, 19, 11, -3],\n [0, 0, 0, 0, 0, 0, 0, 25, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2288", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 1, 21, 6, 4, 2, -4, -7, 11],\n [1, 14, -2, -2, 19, 7, 10, -12, -14],\n [21, -2, 3, -14, 9, 3, 8, 2, -8],\n [6, -2, -14, 24, 9, 3, 12, -14, 4],\n [4, 19, 9, 9, -10, 17, 6, 6, -12],\n [2, 7, 3, 3, 17, -17, 23, -6, 8],\n [-4, 10, 8, 12, 6, 23, -14, 6, -18],\n [-7, -12, 2, -14, 6, -6, 6, -25, -2],\n [11, -14, -8, 4, -12, 8, -18, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3173", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-17, -4, -4, 2, 8, 5, 4, 10, 8],\n [-4, 4, 1, -10, 6, 0, 12, -4, 10],\n [-4, 1, -12, 4, -20, 2, 8, -12, 8],\n [2, -10, 4, 9, 15, 1, 6, -17, 8],\n [8, 6, -20, 15, 18, 2, 4, -3, -11],\n [5, 0, 2, 1, 2, 9, 24, 8, -1],\n [4, 12, 8, 6, 4, 24, 15, 22, 10],\n [10, -4, -12, -17, -3, 8, 22, 8, -2],\n [8, 10, 8, 8, -11, -1, 10, -2, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 8) of the inverse of matrix 1/450 * A where A =\n[[-20, 8, 13, -14, 12, 6, 0, 24, 19],\n [8, -16, 20, 14, 4, -6, 10, -4, 2],\n [13, 20, -1, -18, 12, 0, 6, 2, 0],\n [-14, 14, -18, -7, -10, -10, 4, 7, 2],\n [12, 4, 12, -10, -19, 13, -6, -4, 6],\n [6, -6, 0, -10, 13, 24, 8, 4, 6],\n [0, 10, 6, 4, -6, 8, 25, 15, 10],\n [24, -4, 2, 7, -4, 4, 15, -1, -18],\n [19, 2, 0, 2, 6, 6, 10, -18, 19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, -11, 15, 7, 23, -16, 11, -15, 9],\n [0, 6, -4, -22, -24, 7, -17, 9, 12],\n [0, 0, 5, 7, 18, -10, -6, 25, 24],\n [0, 0, 0, 23, 19, 7, 3, -18, 8],\n [0, 0, 0, 0, 24, -11, 16, 24, -6],\n [0, 0, 0, 0, 0, -3, 10, -14, -3],\n [0, 0, 0, 0, 0, 0, 3, -20, 5],\n [0, 0, 0, 0, 0, 0, 0, 4, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31362", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-17, -22, 20, 14, -13, -20, 20, -17, 0],\n [23, 13, 15, 21, 16, -12, 22, 8, -22],\n [-5, 5, 21, 17, -5, 17, 3, -2, 19],\n [-10, -17, -5, -24, -24, 11, 11, -21, 20],\n [-20, 22, 22, -18, 6, 11, -13, -23, -17],\n [-22, 2, 14, -10, -15, -7, 16, -4, 13],\n [-14, 4, 14, 16, -21, 11, 19, 6, 8],\n [-14, 17, -24, 21, -19, 6, 14, 9, 23],\n [-20, -4, -1, 21, -13, -3, 19, 18, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, 16, 11, 11, 4, -6, 12, 18, 23],\n [-10, 24, -4, 12, -16, -6, 15, -24, -23],\n [16, -18, -17, 2, -5, 25, 7, 8, -22],\n [22, -1, 6, -14, -24, 21, 24, 22, -14],\n [24, 20, 0, -5, 18, 11, 10, -8, -2],\n [4, -9, -10, 16, -9, 18, -14, 1, -22],\n [9, -25, -14, 3, -18, -18, -14, 10, 22],\n [8, 10, -22, -15, -23, -16, -14, 23, -17],\n [-5, 8, -4, -8, 18, -20, -1, 24, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, -9, 12, -15, 18, 6, -3, 2, 0],\n [-9, -16, -4, -4, 14, 9, -9, 8, 4],\n [12, -4, 24, 2, -1, 20, 4, 6, 12],\n [-15, -4, 2, -10, 0, -11, 11, -3, -16],\n [18, 14, -1, 0, -23, -3, -10, 16, -16],\n [6, 9, 20, -11, -3, 9, -6, 10, 4],\n [-3, -9, 4, 11, -10, -6, -14, 12, -2],\n [2, 8, 6, -3, 16, 10, 12, 3, 10],\n [0, 4, 12, -16, -16, 4, -2, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[10, 9, 2, 20, -23, -10, -11, -7, -16],\n [23, -22, -4, -8, -4, 16, -10, -23, 18],\n [25, 9, 15, 13, -10, -5, -5, -25, 4],\n [21, 8, 22, 13, 20, -3, 8, 4, 24],\n [7, -10, 15, 4, -23, 19, -24, 0, -8],\n [-24, 14, -23, -9, -2, -24, -20, 14, 0],\n [23, -20, -14, -5, -10, -20, 8, -23, 15],\n [-7, 3, 6, -16, 1, 3, -13, -6, 2],\n [1, -13, -1, 3, -11, 19, 19, 4, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8891", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, 24, -19, 9, 7, -14, -3, -21, 17],\n [18, 5, -10, 7, 24, -25, -4, 2, -21],\n [-22, -25, -11, 11, 13, 23, 12, 19, -2],\n [-3, 21, -19, 5, -19, -13, -22, -8, 14],\n [-7, -10, -8, -10, 22, 5, -1, -24, 20],\n [25, 2, -10, 10, 19, 14, 9, -2, 9],\n [4, 11, -15, 19, 8, 12, 13, -2, 3],\n [-22, 15, 24, 4, -12, -2, 12, 8, 10],\n [-11, 9, 3, 10, -22, -11, -15, 23, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-5, 9, -3, -16, -22, 19, -1, -24, 12],\n [0, -2, -18, -20, -6, -12, 14, -20, -14],\n [0, 0, 19, 4, -10, -18, -12, 22, -6],\n [0, 0, 0, -22, 10, -23, -16, 12, 1],\n [0, 0, 0, 0, 14, 9, 18, -13, -3],\n [0, 0, 0, 0, 0, 24, 5, -23, 10],\n [0, 0, 0, 0, 0, 0, -13, -14, -7],\n [0, 0, 0, 0, 0, 0, 0, -4, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-367", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-24, -23, 19, -5, 13, -13, 22, -12, 4],\n [-8, -13, -12, 15, 14, -1, 11, 1, -3],\n [-19, 22, -16, -1, 9, -2, 23, 16, -15],\n [-6, -16, 24, -5, 2, 2, 1, 7, -22],\n [9, -6, -20, -20, -9, -7, 23, -9, 23],\n [-23, 20, 8, -22, -3, -8, 8, 3, 18],\n [-11, 19, -15, 13, -17, 21, 9, -16, 14],\n [12, 3, 20, -20, -7, 0, -17, 15, 22],\n [19, -13, 0, 18, -6, -24, -22, -19, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[9, -15, -7, 6, -12, 23, -21, -1, -12],\n [13, -14, 23, -6, -8, -25, 17, -22, -14],\n [0, 6, 11, -11, 9, 0, -11, -18, 2],\n [4, 17, 18, -23, -20, 5, 0, -18, 13],\n [3, -9, -10, 23, 19, -22, -16, -10, -7],\n [13, 24, -13, -22, 6, -8, -10, -1, 24],\n [-10, -4, -2, 2, -3, -5, -17, -24, 12],\n [2, 0, 1, -1, -5, 12, -1, 12, 20],\n [-15, 2, 23, 10, -22, -7, -2, -4, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-1, -18, 25, -6, -25, -22, -14, -1, -5],\n [0, 8, -20, 9, -23, 7, -17, -19, 15],\n [0, 0, 14, -8, 9, -9, 13, -15, 11],\n [0, 0, 0, -13, 2, 12, 21, 8, 2],\n [0, 0, 0, 0, -10, -18, 14, -15, 19],\n [0, 0, 0, 0, 0, -10, -2, -16, 8],\n [0, 0, 0, 0, 0, 0, -3, 14, -12],\n [0, 0, 0, 0, 0, 0, 0, 10, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439445", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-25, -8, 0, -12, -7, -8, 19, -19, -24],\n [0, 2, 2, 16, -9, 4, -5, 11, -17],\n [0, 0, -11, -12, 1, -8, -16, 22, -4],\n [0, 0, 0, 22, -21, 25, -1, -25, -2],\n [0, 0, 0, 0, -11, -15, 18, -9, 23],\n [0, 0, 0, 0, 0, -16, 11, -16, 16],\n [0, 0, 0, 0, 0, 0, -18, -15, -6],\n [0, 0, 0, 0, 0, 0, 0, -14, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "537", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, 14, -11, 13, -20, 6, 22, -18, 9],\n [5, 16, 0, 16, -2, 25, -24, 15, -25],\n [-16, 24, -3, 7, 18, 11, -15, -6, 0],\n [20, 21, -24, -1, -22, -7, -13, -7, -13],\n [-14, -24, 11, 24, -3, -7, -23, -2, -3],\n [-22, -8, -14, 9, 1, 17, -12, 5, -23],\n [-21, 3, 13, -9, -7, 9, 7, -18, 11],\n [9, -6, -9, 19, -13, -22, 24, 4, -20],\n [-24, -11, 8, -6, -10, 17, 23, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "718", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -13, 14, 6, -23, -12, 2, 20, 0],\n [-5, 20, 25, -15, 1, 18, -25, 7, 20],\n [-8, -24, -22, 24, -22, -9, 22, -10, -17],\n [0, -16, -19, -17, 22, 1, 6, 23, -3],\n [1, -1, 3, -2, -10, -10, 2, -6, -7],\n [-16, 0, -24, -23, 13, -24, -1, 19, -22],\n [-11, -8, -19, 1, -8, -19, 3, 15, 18],\n [7, -24, -8, 20, -3, -20, 17, -1, -7],\n [-18, 11, 0, 3, 2, -19, 10, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1037", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-21, 3, -9, 19, 1, -9, 25, -22, 23],\n [0, -3, 24, -15, 10, -14, -17, -2, -8],\n [0, 0, 7, -20, 25, 7, 14, -20, -22],\n [0, 0, 0, 8, -13, 21, -18, -14, -18],\n [0, 0, 0, 0, -5, -3, 1, -1, -19],\n [0, 0, 0, 0, 0, 16, 14, -14, -9],\n [0, 0, 0, 0, 0, 0, -8, -9, 1],\n [0, 0, 0, 0, 0, 0, 0, -9, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8210", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[17, 24, 6, 3, -9, 2, 15, -5, -2],\n [20, 9, -6, -4, -22, -10, -5, 18, -5],\n [14, 15, -15, 11, 18, -4, -6, -24, 17],\n [-15, -5, 7, 23, -9, 10, -12, 11, 5],\n [-22, -20, 24, -5, -13, 12, -11, -21, 12],\n [-2, -8, 3, 6, -19, 4, 12, 0, -18],\n [-1, 4, -2, 4, -21, -22, 25, 16, -17],\n [7, 25, 3, 5, 18, -7, 19, 21, -24],\n [-6, -14, 24, -5, 5, 10, -6, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[19, 9, 18, -11, -21, 13, -18, -16, 14],\n [9, -11, -16, -12, 12, -16, 12, 12, 11],\n [18, -16, 21, 3, 12, -1, -4, -16, 3],\n [-11, -12, 3, 2, 2, 4, -1, -1, -20],\n [-21, 12, 12, 2, 21, -16, 6, 20, -8],\n [13, -16, -1, 4, -16, -23, 10, 7, 0],\n [-18, 12, -4, -1, 6, 10, -18, -8, -2],\n [-16, 12, -16, -1, 20, 7, -8, 9, 0],\n [14, 11, 3, -20, -8, 0, -2, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3425", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-16, -16, 7, -8, -16, -19, 14, 6, 17],\n [-20, -7, 15, 17, 8, 17, -21, -7, 23],\n [24, -12, -16, 23, -15, 5, -24, -16, -5],\n [-25, 20, 5, -15, 17, -16, -6, -5, 11],\n [11, -12, -21, -20, -2, -10, -3, 21, 12],\n [-10, 25, -13, 25, 19, -18, 12, 6, -4],\n [-9, -21, -18, 24, 4, -7, -14, -1, 18],\n [-13, -22, -16, 22, 2, -21, 2, 18, 5],\n [-10, -3, 3, 21, -5, -24, -3, -10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2120", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-17, -24, -8, -13, 19, -18, -16, 1, -9],\n [-2, -5, -25, -10, 17, 7, -20, -14, 6],\n [22, -15, -8, -24, 6, 23, 23, -6, -5],\n [10, 12, 1, 21, -15, -8, -9, 8, 19],\n [0, -20, 17, 4, 13, 24, 6, -9, -13],\n [20, 15, -13, -20, -4, 7, 7, -22, -12],\n [24, 22, 9, 1, -20, -25, 17, 2, 3],\n [6, 2, 1, -16, -8, -22, 12, 25, 15],\n [16, 6, -21, -4, 22, -4, -24, 15, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-67", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[8, 1, -6, 12, 6, 7, -9, 13, 3],\n [1, -8, 2, -2, 18, 1, 12, -10, 6],\n [-6, 2, -25, 10, -18, 17, 14, -6, 2],\n [12, -2, 10, -14, 6, -10, -16, 18, 2],\n [6, 18, -18, 6, 7, -4, -8, -1, 9],\n [7, 1, 17, -10, -4, 11, 10, -14, -16],\n [-9, 12, 14, -16, -8, 10, 4, -4, -4],\n [13, -10, -6, 18, -1, -14, -4, -15, 11],\n [3, 6, 2, 2, 9, -16, -4, 11, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 15, -21, 7, -15, -18, -5, 6, -21],\n [8, -17, 12, 17, 6, -16, -14, 9, 13],\n [-8, -3, -14, 5, -15, 8, 1, -5, -16],\n [-13, 19, 21, -1, -13, 15, -20, 9, 2],\n [-6, -6, 15, -22, -6, -21, -4, -2, 18],\n [-9, -21, 0, 10, -18, -17, -9, -18, -21],\n [-16, 24, -12, 1, 1, -21, -11, 2, -21],\n [-4, -14, 16, -18, -25, 9, -10, 4, 17],\n [15, -16, 8, -15, -6, 17, -19, -5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-505", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[11, -3, 18, 5, -8, -2, -4, 11, 21],\n [0, -25, 24, -20, 12, 3, 17, -15, -10],\n [0, 0, 22, 9, -2, 12, -23, 25, 14],\n [0, 0, 0, -4, 20, 20, -22, -2, -7],\n [0, 0, 0, 0, 14, 1, -11, 11, -25],\n [0, 0, 0, 0, 0, -15, -15, 4, -6],\n [0, 0, 0, 0, 0, 0, 19, 2, -20],\n [0, 0, 0, 0, 0, 0, 0, 10, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2688", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (1, 3) rounded to the nearest integer?\n[[23, 1, 4, -11, 13, 16, -8, -15, -4],\n [0, -22, -23, -2, -12, -23, 5, 9, 5],\n [0, 0, -6, -8, 18, 10, 25, -7, -9],\n [0, 0, 0, 11, 19, 10, 19, 22, 18],\n [0, 0, 0, 0, 3, -1, -18, 22, -7],\n [0, 0, 0, 0, 0, -7, -13, 23, -18],\n [0, 0, 0, 0, 0, 0, -10, -14, -1],\n [0, 0, 0, 0, 0, 0, 0, 17, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 7, 8, -12, -6, 7, 8, 2, -8],\n [7, 18, -12, -4, -21, -23, -8, 4, 18],\n [8, -12, -21, 11, 7, 9, 14, 10, 0],\n [-12, -4, 11, 11, -10, 4, -4, 22, 10],\n [-6, -21, 7, -10, -23, 14, 10, 13, -4],\n [7, -23, 9, 4, 14, -8, 9, 11, 6],\n [8, -8, 14, -4, 10, 9, -24, -3, 2],\n [2, 4, 10, 22, 13, 11, -3, -20, -7],\n [-8, 18, 0, 10, -4, 6, 2, -7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "688", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 4) of the inverse. Round your answer to the nearest integer:\n[[-15, -24, -8, 2, 4, 8, -14, 16, -11],\n [-24, -22, 12, 12, -12, -10, -7, 8, -6],\n [-8, 12, 3, -3, -2, 1, 20, 10, 16],\n [2, 12, -3, -19, -6, 8, 0, 2, 2],\n [4, -12, -2, -6, -20, -14, 11, 2, -18],\n [8, -10, 1, 8, -14, -5, -6, 1, -7],\n [-14, -7, 20, 0, 11, -6, -8, 10, 4],\n [16, 8, 10, 2, 2, 1, 10, 13, -5],\n [-11, -6, 16, 2, -18, -7, 4, -5, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, 22, -3, 24, -19, -12, -17, 2, -20],\n [17, 19, -4, -8, 18, 12, -4, -17, -8],\n [-5, -11, -17, 16, -24, -12, -5, 17, 19],\n [8, -19, -11, 13, -14, -19, -21, 21, 13],\n [-3, 2, 8, -1, -24, 25, -17, 8, 20],\n [21, 6, -14, -7, 21, 12, -16, -16, 9],\n [15, 11, 6, -19, 25, -16, 17, 12, 1],\n [6, 25, -19, 22, 0, -4, -14, -2, 24],\n [20, 3, 6, -10, 0, -20, -25, -13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1361", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-20, 12, -14, -17, -6, 13, 1, -23, -2],\n [0, 8, 24, 6, -5, -25, 7, -15, -23],\n [0, 0, 18, 12, -2, -19, 23, 23, 10],\n [0, 0, 0, -9, -15, -23, -16, -24, 6],\n [0, 0, 0, 0, 13, -16, 10, 4, -17],\n [0, 0, 0, 0, 0, -14, -10, 22, -18],\n [0, 0, 0, 0, 0, 0, 9, 11, 13],\n [0, 0, 0, 0, 0, 0, 0, -11, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -12, 2, -5, 3, 10, 0, -12, 10],\n [-12, -10, 10, -3, -13, 6, -12, 14, 2],\n [2, 10, -1, 19, 0, 4, -20, -18, -2],\n [-5, -3, 19, 9, 15, -4, 0, 17, 8],\n [3, -13, 0, 15, 8, 2, 2, 1, -18],\n [10, 6, 4, -4, 2, -22, 10, 2, 8],\n [0, -12, -20, 0, 2, 10, -12, 12, 3],\n [-12, 14, -18, 17, 1, 2, 12, 14, 14],\n [10, 2, -2, 8, -18, 8, 3, 14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-51", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-21, -5, -20, -25, 5, 19, 15, 2, -23],\n [12, -3, 14, -22, -20, -14, -14, -19, 2],\n [0, 22, -19, -23, -13, 15, -15, 13, -3],\n [21, -25, 8, 5, 7, 21, 10, 10, -12],\n [11, 6, 2, -25, 21, -19, -10, 6, -2],\n [-12, 21, -11, -25, 2, -7, -19, -8, 21],\n [-13, 25, -8, -22, 24, -22, 1, -10, -12],\n [-12, -19, 19, -12, 16, 19, -20, 17, 12],\n [1, -15, 5, 25, 23, -23, -25, -10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 1) of the inverse of matrix 1/450 * A where A =\n[[1, 20, 24, -23, -18, 24, -10, 21, -24],\n [3, -10, 3, 5, 16, -15, 25, 6, -2],\n [-7, 6, -16, 23, 6, -3, 7, 4, 4],\n [-19, -10, 17, 24, -25, 4, 8, 8, 12],\n [5, -18, -6, 20, 3, 5, -5, 0, 5],\n [-6, -4, 14, 0, -9, -1, 11, 1, -23],\n [-2, -1, 24, -16, 10, 16, -8, 19, -9],\n [-12, -7, -8, -3, -18, 24, -10, -1, 17],\n [6, 23, 24, -7, -8, 6, 20, 23, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 4) rounded to the nearest integer?\n[[-11, 23, -5, -15, 3, 6, -20, -7, -10],\n [-14, -11, -15, 13, -16, 25, 11, 23, -2],\n [25, 10, -25, 20, -9, -12, 12, -1, 11],\n [9, -4, 21, -19, -15, -16, -12, 9, 20],\n [23, 10, -20, -21, 16, -19, -11, -5, -8],\n [-25, -22, -15, -16, 19, -7, 16, 4, 24],\n [15, 15, -6, 1, -14, -12, 8, 16, 24],\n [12, -24, 23, 6, -8, 24, -5, 20, -15],\n [4, -7, 22, 14, 24, 4, 9, -22, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-21, 0, 7, -4, -4, 8, -10, -4, -11],\n [0, 20, 18, 1, 2, 12, 14, 10, -5],\n [7, 18, -1, 12, 16, 16, -2, 11, -10],\n [-4, 1, 12, 2, -8, 14, 8, 4, -15],\n [-4, 2, 16, -8, -12, 0, -2, 2, -10],\n [8, 12, 16, 14, 0, 17, 10, 6, 4],\n [-10, 14, -2, 8, -2, 10, -5, 2, -10],\n [-4, 10, 11, 4, 2, 6, 2, 6, -2],\n [-11, -5, -10, -15, -10, 4, -10, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-23, 10, -5, 12, -4, 18, -4, 6, 9],\n [10, 22, -10, -18, 11, -4, 6, 2, 3],\n [-5, -10, -4, -14, -10, -4, -2, -2, 12],\n [12, -18, -14, 19, 22, 14, 16, 17, 8],\n [-4, 11, -10, 22, 4, 14, -11, 2, 15],\n [18, -4, -4, 14, 14, -19, -2, 10, 14],\n [-4, 6, -2, 16, -11, -2, 1, 3, 1],\n [6, 2, -2, 17, 2, 10, 3, 15, 6],\n [9, 3, 12, 8, 15, 14, 1, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-12, 10, -19, 17, 8, 24, 6, 16, 7],\n [-12, -1, 2, 16, 24, 13, 4, 5, -2],\n [25, -22, -12, -17, 10, -20, -2, 0, 8],\n [-25, -3, -9, 10, 11, 24, 19, -6, 0],\n [-15, -6, -25, 18, -13, 10, 18, 12, -13],\n [-12, -14, 8, 1, -14, 12, 10, -25, 0],\n [14, 14, -5, 6, -1, -14, -1, 0, 10],\n [-10, -12, 20, 8, 23, -2, -18, 1, 13],\n [-13, 3, 5, 17, -7, 25, -16, 17, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-91", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[14, 8, 20, 23, 23, 17, -25, -7, -25],\n [0, -1, -22, -2, 13, -6, 7, 2, 17],\n [0, 0, -2, 14, 18, -24, -3, 7, -12],\n [0, 0, 0, -22, -6, 5, -19, -25, -21],\n [0, 0, 0, 0, -19, 18, 13, 24, -10],\n [0, 0, 0, 0, 0, 19, -19, 25, -24],\n [0, 0, 0, 0, 0, 0, -6, 15, 20],\n [0, 0, 0, 0, 0, 0, 0, -13, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17497", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[6, -1, 4, 14, -9, -14, -5, 2, 2],\n [-1, 15, -4, 4, 0, 10, 6, -13, -8],\n [4, -4, -23, 1, 15, 6, -6, 15, 0],\n [14, 4, 1, 13, -1, 6, -2, -6, -2],\n [-9, 0, 15, -1, -24, 6, 2, -14, 15],\n [-14, 10, 6, 6, 6, 18, -7, -5, -7],\n [-5, 6, -6, -2, 2, -7, -22, -6, 16],\n [2, -13, 15, -6, -14, -5, -6, -3, -6],\n [2, -8, 0, -2, 15, -7, 16, -6, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "863", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-11, 9, 8, 14, 4, 22, -3, -17, 6],\n [0, 23, 6, 19, -10, 6, -1, 4, 11],\n [0, 0, 19, -18, 14, 23, 21, 10, -1],\n [0, 0, 0, -25, -22, 0, -15, -11, 6],\n [0, 0, 0, 0, 25, 6, -6, -12, 9],\n [0, 0, 0, 0, 0, 15, -22, -14, 25],\n [0, 0, 0, 0, 0, 0, 10, 16, 9],\n [0, 0, 0, 0, 0, 0, 0, -2, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-621", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-8, -11, 7, 13, 25, -21, 14, 11, -21],\n [0, 17, -19, -24, 4, 23, -15, 11, 13],\n [0, 0, -15, -14, -16, -15, 7, -6, -21],\n [0, 0, 0, 5, 16, 18, -12, -7, 16],\n [0, 0, 0, 0, -5, 25, 10, -1, 25],\n [0, 0, 0, 0, 0, 10, 22, -14, 24],\n [0, 0, 0, 0, 0, 0, 22, 9, 23],\n [0, 0, 0, 0, 0, 0, 0, 17, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29988", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[4, -7, -2, 20, -11, 9, -2, 10, 23],\n [-12, -4, 13, -18, 22, -10, 20, -9, -21],\n [15, 9, 11, -8, -5, 16, -25, -9, -18],\n [3, -6, 23, 24, 11, 13, -21, -16, -20],\n [-19, 9, 1, 16, -5, -2, 3, 1, 12],\n [-24, -1, -24, 12, -8, 16, -19, 23, -22],\n [18, 14, 15, -16, 25, 15, 2, 4, -2],\n [10, -10, 7, -16, 22, -5, 1, -5, 1],\n [6, -21, 9, -4, 10, -16, 8, -20, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-245", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -7, 6, -6, -5, -11, -9, 18, 19],\n [-2, -5, 22, -11, -15, 11, 4, -8, 2],\n [-13, 17, -16, 21, 13, -14, 24, 12, 15],\n [22, 14, 0, 18, -7, -3, 22, 10, 1],\n [-10, -19, -13, -14, 1, 7, 5, -15, -9],\n [12, -24, -23, 8, 24, 6, -2, -2, -13],\n [-4, -7, 4, 13, -5, 22, -3, -10, 16],\n [-19, -6, 22, 16, -12, 0, -4, 15, 10],\n [0, -14, 23, 5, 14, -22, 14, 1, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-14, 3, 2, -10, -18, 21, 23, -13, -12],\n [-11, -17, 18, 6, -4, 25, -1, 15, 0],\n [19, 3, -8, 10, -6, 7, -6, -23, 17],\n [8, -20, 5, 9, 6, 16, -17, 20, 22],\n [1, -2, 24, -4, 4, 10, 0, 24, -24],\n [16, 18, -19, 1, -10, 23, 20, 3, -5],\n [0, -8, -25, -24, -12, 12, -11, 10, -2],\n [-1, -17, -11, 11, -20, 17, 19, -14, 1],\n [-19, 2, -14, 16, 9, -24, 0, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, -25, 2, 12, -13, 4, -16, 19, -4],\n [0, -21, -18, -15, 0, -7, -7, 4, 10],\n [0, 0, -19, -8, -17, -20, -20, 19, -4],\n [0, 0, 0, -20, -3, -9, 6, 6, 11],\n [0, 0, 0, 0, 15, 25, -12, -12, 4],\n [0, 0, 0, 0, 0, 13, -17, 10, -16],\n [0, 0, 0, 0, 0, 0, 2, -1, 0],\n [0, 0, 0, 0, 0, 0, 0, -12, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-15, -2, -7, 7, 8, -10, -8, -4, -6],\n [-2, 8, -22, -14, 0, 10, 2, 2, 11],\n [-7, -22, 19, -14, 6, 22, 2, -16, 13],\n [7, -14, -14, 1, 8, -12, -8, -6, 4],\n [8, 0, 6, 8, 14, -20, 14, 8, -17],\n [-10, 10, 22, -12, -20, -10, 2, -19, 7],\n [-8, 2, 2, -8, 14, 2, -22, 0, -4],\n [-4, 2, -16, -6, 8, -19, 0, 16, 8],\n [-6, 11, 13, 4, -17, 7, -4, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-53", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 3) of the inverse of matrix 1/450 * A where A =\n[[-9, 20, -19, 25, 13, 18, 4, 12, 14],\n [0, 24, -16, 6, 0, 22, -9, -25, 13],\n [0, 0, -17, 18, 7, 0, 16, -16, 16],\n [0, 0, 0, 16, 22, 22, 7, 1, 17],\n [0, 0, 0, 0, 21, 2, 12, -16, -23],\n [0, 0, 0, 0, 0, -8, -22, -21, -5],\n [0, 0, 0, 0, 0, 0, -2, -6, 24],\n [0, 0, 0, 0, 0, 0, 0, -1, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[14, -7, 19, -22, -20, 10, -15, -5, 16],\n [22, -1, 4, -8, -1, 25, -5, -3, 4],\n [18, 20, -8, 7, 19, 9, 20, -4, 24],\n [-2, -3, 25, -25, -11, 22, 2, 16, -6],\n [10, 17, -10, -21, 25, 17, 24, -11, -24],\n [-2, -13, -3, -14, 20, 7, 18, 19, -1],\n [9, 9, -25, 17, -22, 5, 2, -15, 6],\n [-24, 25, 18, -13, -9, 25, -22, 5, 12],\n [-23, 17, -14, 18, -8, 4, 20, -15, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 23, 22, 9, -22, 0, -18, -2, 17],\n [0, -14, -21, -10, 6, 3, 7, 15, -12],\n [0, 0, 1, 9, -4, -19, 10, 21, -14],\n [0, 0, 0, 9, 13, -7, 2, 3, -18],\n [0, 0, 0, 0, 3, 9, 7, 6, -5],\n [0, 0, 0, 0, 0, -13, -11, 16, 10],\n [0, 0, 0, 0, 0, 0, -13, -6, 23],\n [0, 0, 0, 0, 0, 0, 0, 1, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529176", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[23, 1, -20, -2, -4, -17, -16, -23, -20],\n [0, 19, -12, 10, 16, -7, 22, 13, -3],\n [0, 0, -11, 4, 7, 12, -7, -21, -17],\n [0, 0, 0, -10, 11, -16, -5, -5, 21],\n [0, 0, 0, 0, 14, -18, 17, 15, 12],\n [0, 0, 0, 0, 0, -19, -25, -7, 4],\n [0, 0, 0, 0, 0, 0, -10, -1, 20],\n [0, 0, 0, 0, 0, 0, 0, -7, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-593", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-24, 17, -2, 7, -7, 0, 20, 15, -23],\n [0, -12, -6, 9, -3, -1, -22, -24, -24],\n [0, 0, -3, -5, 19, -1, 1, -15, -12],\n [0, 0, 0, 25, 5, 8, 10, 14, 18],\n [0, 0, 0, 0, 18, 13, 2, 0, 22],\n [0, 0, 0, 0, 0, 5, 14, 15, 24],\n [0, 0, 0, 0, 0, 0, 10, 13, 6],\n [0, 0, 0, 0, 0, 0, 0, -20, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 3, 24, 0, 8, 25, -9, -8, 6],\n [0, 4, 5, -8, -21, 6, 3, -14, -11],\n [0, 0, 9, 17, -12, 13, -8, 12, -4],\n [0, 0, 0, -12, 18, -1, -12, 21, 5],\n [0, 0, 0, 0, -19, 23, -12, 3, 21],\n [0, 0, 0, 0, 0, -3, -18, -13, 10],\n [0, 0, 0, 0, 0, 0, -1, -7, -6],\n [0, 0, 0, 0, 0, 0, 0, -21, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-196588", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -9, 2, 6, 18, 24, 8, -4, 16],\n [-7, 22, -18, -24, -21, 2, -22, 10, -25],\n [-11, -13, 5, -9, -20, -2, -13, -5, -2],\n [-4, 3, -2, 18, -14, -6, 16, 8, -11],\n [25, -22, -12, -25, 7, 24, 21, 17, 24],\n [3, -16, 10, -12, -4, 24, 7, 2, -19],\n [10, 10, 24, 15, 8, 11, -20, 9, 1],\n [4, 6, -7, -4, -5, -21, -5, 15, -6],\n [12, 5, 11, -20, 5, 21, 17, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "609", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[3, 2, -7, -14, 13, -8, 0, -18, -5],\n [2, 16, 2, -3, 15, 14, -4, 21, 23],\n [-7, 2, 20, 7, 10, 3, -12, 3, -3],\n [-14, -3, 7, 25, 16, -14, -1, -10, 6],\n [13, 15, 10, 16, -19, 6, -4, 16, -3],\n [-8, 14, 3, -14, 6, -4, -1, -14, -6],\n [0, -4, -12, -1, -4, -1, 22, 15, 22],\n [-18, 21, 3, -10, 16, -14, 15, 16, 7],\n [-5, 23, -3, 6, -3, -6, 22, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[19, -13, 19, -8, -2, 5, 7, 5, 1],\n [0, -5, -21, -15, 8, 8, 22, -23, -20],\n [0, 0, 11, 13, -19, -9, 12, 10, 8],\n [0, 0, 0, -8, 16, 1, 13, 15, 25],\n [0, 0, 0, 0, -1, -2, -1, -14, 4],\n [0, 0, 0, 0, 0, 3, 25, -12, -1],\n [0, 0, 0, 0, 0, 0, 12, -9, 5],\n [0, 0, 0, 0, 0, 0, 0, -17, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-181", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -2, 15, -6, 23, -20, 7, 24, 2],\n [-15, 10, -6, -20, -18, -7, -11, -4, 25],\n [-24, 2, 10, 10, 18, -8, -14, -7, 0],\n [-1, 2, -11, -16, 13, 8, -13, -10, 14],\n [5, -25, 23, 21, -3, -12, 13, 4, 25],\n [16, -6, -1, -15, 0, -5, -21, -19, -14],\n [-24, 13, -5, 6, -21, 1, 5, -14, 10],\n [-5, -7, -23, -9, 4, 10, -17, 8, 3],\n [-16, -17, 14, 24, -15, -7, -4, 24, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, -4, 23, 21, -10, -9, 14, -19, 5],\n [0, 3, -19, 17, 4, -23, -1, 8, 7],\n [0, 0, 12, 20, -22, 22, -16, -1, 11],\n [0, 0, 0, 20, -19, -12, -25, -20, 13],\n [0, 0, 0, 0, -7, 2, -24, 1, 18],\n [0, 0, 0, 0, 0, 14, 3, -17, -8],\n [0, 0, 0, 0, 0, 0, 14, 17, 9],\n [0, 0, 0, 0, 0, 0, 0, -24, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3205", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-21, 8, 5, 8, -14, 8, -2, -4, 8],\n [8, 20, 12, 2, 0, 5, 10, -4, 11],\n [5, 12, 17, -12, 1, 14, 7, -10, -12],\n [8, 2, -12, -10, 6, 3, -12, 10, -15],\n [-14, 0, 1, 6, -8, -25, 21, -10, -4],\n [8, 5, 14, 3, -25, 12, -17, 9, -8],\n [-2, 10, 7, -12, 21, -17, 9, -16, -7],\n [-4, -4, -10, 10, -10, 9, -16, 4, -24],\n [8, 11, -12, -15, -4, -8, -7, -24, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-68", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -24, 22, 14, 9, -22, 10, 14, -20],\n [-12, -11, 23, 11, 7, 18, -7, -14, 17],\n [-17, -7, 6, 2, 2, 5, 10, -13, 16],\n [7, 16, -8, 3, 19, 13, -18, 23, -4],\n [-25, 22, 5, -6, 10, -3, -9, 19, -16],\n [-17, 20, -9, -23, 7, -25, -6, -24, -10],\n [-17, -12, -25, 9, -8, -25, 17, -21, -15],\n [12, -2, 13, 19, 6, -10, -23, 21, -18],\n [6, -4, 22, -9, 1, 19, -23, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-13, -9, 4, 3, -12, 4, 11, 18, 22],\n [0, -17, 22, 6, -22, -20, 25, -25, -1],\n [0, 0, -23, -5, -12, 4, -24, 22, -4],\n [0, 0, 0, 17, -15, 22, -16, 23, 18],\n [0, 0, 0, 0, -7, 2, 16, 22, 25],\n [0, 0, 0, 0, 0, -23, -2, -16, 18],\n [0, 0, 0, 0, 0, 0, 13, 13, -1],\n [0, 0, 0, 0, 0, 0, 0, -7, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-202", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[25, -10, 7, 8, 25, -12, 21, -24, -13],\n [3, 17, 16, 8, -9, -23, 4, -22, 5],\n [-21, -24, -22, 18, 12, 1, 1, -11, 13],\n [12, -12, -8, 3, -19, 12, -2, 12, -20],\n [-6, 16, 10, -16, -4, 7, -3, 20, 24],\n [15, 16, 25, -22, -5, -13, 16, -13, -14],\n [-2, 9, -7, -17, -13, -4, 14, 10, 2],\n [15, -19, 4, 5, -15, 4, -11, -13, 9],\n [9, -6, 17, -3, 11, -6, -7, 18, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[-22, -5, 13, -4, 14, 4, -2, 0, -2],\n [-5, 14, -14, 8, -4, -18, 0, -10, -1],\n [13, -14, 0, 16, -2, -10, 6, -15, 2],\n [-4, 8, 16, 14, -16, 12, -18, 18, 14],\n [14, -4, -2, -16, 23, -18, -8, 8, -2],\n [4, -18, -10, 12, -18, 13, 0, 6, 18],\n [-2, 0, 6, -18, -8, 0, -10, -16, -8],\n [0, -10, -15, 18, 8, 6, -16, -17, 10],\n [-2, -1, 2, 14, -2, 18, -8, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-16, -13, 4, 8, 2, -2, -4, -2, 14],\n [-13, -11, -2, -16, -3, 15, 10, 13, 13],\n [4, -2, -23, 22, -8, 12, -1, -4, 0],\n [8, -16, 22, 22, -6, -8, -11, -6, 12],\n [2, -3, -8, -6, -16, -14, 0, -2, -4],\n [-2, 15, 12, -8, -14, -14, -22, -10, -13],\n [-4, 10, -1, -11, 0, -22, 5, 12, -18],\n [-2, 13, -4, -6, -2, -10, 12, -16, 23],\n [14, 13, 0, 12, -4, -13, -18, 23, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 19, 7, 7, -9, -8, 23, 18, 12],\n [-19, 23, 0, 22, -25, -15, -16, 5, -1],\n [-25, 17, -23, 22, -25, -19, 17, 23, 25],\n [-12, -3, 22, -9, -12, -17, -5, 19, -24],\n [6, -18, 10, 0, 11, -11, 8, -5, -3],\n [-17, 14, 0, 17, -4, -13, -1, -19, 25],\n [1, -11, -14, 19, 7, -5, -1, 14, 21],\n [-4, -12, -18, -2, -23, -14, 21, -4, -10],\n [-19, -8, 19, -3, 0, 12, -24, -24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[25, -6, 4, 1, 4, 1, 7, 7, 12],\n [-6, 9, -12, -10, 16, 19, 10, 24, -2],\n [4, -12, 12, 0, -18, 6, 4, -2, -10],\n [1, -10, 0, -19, 8, 17, -6, 10, 16],\n [4, 16, -18, 8, -10, 2, -10, 10, -4],\n [1, 19, 6, 17, 2, 13, 5, -10, 4],\n [7, 10, 4, -6, -10, 5, -11, 2, -16],\n [7, 24, -2, 10, 10, -10, 2, 19, -2],\n [12, -2, -10, 16, -4, 4, -16, -2, -25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[-17, -2, 13, -8, 22, 13, -8, 15, 2],\n [-24, 11, 15, 10, 22, -2, 9, -20, -9],\n [4, 25, -18, 16, -16, -10, 12, 0, 5],\n [-18, 9, 8, -16, 14, 18, -14, 15, 1],\n [-7, 0, -11, 5, 20, 11, -8, 3, 18],\n [1, 12, -6, -5, 3, 17, -11, -4, -3],\n [-22, -2, -12, 11, -5, 17, 13, -13, -7],\n [0, 10, 18, 20, 7, 14, -10, -7, 11],\n [-12, 18, 18, 4, 5, -6, 18, 17, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, 16, 11, 21, -24, -4, -13, 20, 12],\n [5, -25, 21, 17, -13, -9, -22, 17, 5],\n [7, -12, -5, -4, -21, 11, 6, -23, 15],\n [-13, -15, 24, 16, 12, -2, -17, -13, -4],\n [-8, -16, 21, -14, 4, 21, 20, -7, -7],\n [-16, -25, -19, -15, -22, 10, -5, -4, -16],\n [-3, -21, 22, -14, 4, 7, 11, -8, -22],\n [1, 21, -3, -20, -19, -7, 20, -11, 22],\n [-4, 6, -11, -20, -20, -20, -14, -24, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-22, -20, 16, 25, 11, 12, -12, 21, -7],\n [25, -19, -8, 18, -18, 2, -5, 9, 21],\n [-16, 2, -7, 18, 9, 2, 20, 23, -23],\n [13, 1, -9, -11, 16, 13, -4, -6, 1],\n [9, 21, -21, -24, 15, 24, 19, -6, -19],\n [10, -18, 1, -20, -2, 10, -21, -6, -6],\n [15, 14, 8, 13, 24, -16, -23, 23, 8],\n [9, 11, 19, 19, 12, 20, -3, 11, -5],\n [1, -25, -17, -23, 12, 10, 8, 4, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -14, 10, 0, 0, -8, 2, 4, -10],\n [-14, 23, 10, 10, 14, 10, 12, 2, 8],\n [10, 10, -25, -6, -4, -10, 9, -22, 16],\n [0, 10, -6, -14, -13, -8, -3, 16, -10],\n [0, 14, -4, -13, -13, -14, 10, 0, 16],\n [-8, 10, -10, -8, -14, 15, -8, -19, 12],\n [2, 12, 9, -3, 10, -8, -7, -16, -6],\n [4, 2, -22, 16, 0, -19, -16, -10, 6],\n [-10, 8, 16, -10, 16, 12, -6, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "989", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (7, 4) of the inverse of matrix 1/450 * A where A =\n[[-12, -13, -4, 17, 22, -8, -6, 4, 9],\n [7, 20, -9, 9, -14, -24, 8, -14, 0],\n [6, -5, -21, 2, -3, 22, 6, -21, 9],\n [-20, -7, 18, 14, -20, -12, -23, -15, 13],\n [15, -2, 17, 19, -8, 5, -16, 0, 3],\n [-24, 4, 13, 21, -16, -14, -6, 15, -7],\n [-20, -3, -7, 5, 7, -24, -11, -15, 0],\n [-8, -25, 6, -22, -4, 10, 3, 10, 24],\n [7, 13, -12, 22, 21, 11, 19, -21, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-347", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-4, -21, 11, 12, 20, 8, -11, 22, 11],\n [1, 22, -25, 3, -18, 7, -19, 3, 5],\n [12, -18, 5, 11, -11, 6, 0, 22, 23],\n [-15, -3, 8, 7, -9, 7, -24, 23, -22],\n [-14, 3, 16, 16, 21, 17, 13, 16, -7],\n [24, -24, -19, 20, -4, -15, 7, -6, -21],\n [-22, -12, -23, 24, -8, 1, -22, -23, 1],\n [2, -4, 16, 3, -10, 9, -7, 4, -11],\n [-21, 5, 17, 5, -17, -13, 17, -5, 20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[5, -5, 17, -17, 9, -2, -10, -6, 10],\n [-5, 8, -10, -20, -2, -11, 7, 4, -22],\n [17, -10, 7, -2, 4, -12, -5, 10, 10],\n [-17, -20, -2, 19, -8, -10, -11, -4, -18],\n [9, -2, 4, -8, -10, 0, -10, -14, 1],\n [-2, -11, -12, -10, 0, 12, -10, -8, 8],\n [-10, 7, -5, -11, -10, -10, 21, -4, 4],\n [-6, 4, 10, -4, -14, -8, -4, 21, 4],\n [10, -22, 10, -18, 1, 8, 4, 4, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-104", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, -17, -9, 12, 20, 9, -1, 24, -19],\n [15, 21, 5, 6, 25, 22, -7, 25, -9],\n [-20, -1, 7, -7, -11, 9, 23, 6, 12],\n [10, 6, 6, 14, 10, 8, -16, 18, 7],\n [18, -16, 18, 25, 9, -4, 25, -3, -19],\n [-5, -25, -13, -17, 22, 24, 21, -6, 21],\n [21, -16, 0, 24, 21, 18, -25, 19, -9],\n [-9, 13, 17, -14, 15, -11, -25, 6, -15],\n [-21, 25, -8, 24, -8, -3, -19, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-25, 2, -6, 15, 22, -3, 6, 12, 13],\n [0, 7, -1, 6, 22, 24, 24, 25, 2],\n [0, 0, -23, 1, -9, 17, 3, 23, 18],\n [0, 0, 0, 2, -6, 19, 8, -10, 13],\n [0, 0, 0, 0, 22, -6, -8, 2, 2],\n [0, 0, 0, 0, 0, 19, 11, -8, -21],\n [0, 0, 0, 0, 0, 0, 1, -23, 25],\n [0, 0, 0, 0, 0, 0, 0, -14, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1164", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[23, 15, 13, -22, -9, -11, 15, 2, -10],\n [-20, 2, 6, -9, -1, 13, -9, 20, -11],\n [24, 25, -8, 20, -6, -3, -21, 13, -14],\n [-9, 4, -7, 6, -10, -24, -14, 23, -23],\n [-18, 11, -2, 23, -1, -1, -12, 20, 10],\n [-11, 6, -24, -5, -22, 3, 23, 3, -3],\n [-23, -5, -10, 18, -6, 9, -21, 22, 0],\n [-19, -10, -9, -24, -14, -13, -21, -10, 2],\n [-18, 2, 20, -18, 3, -8, 18, 17, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-314", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[0, 0, 3, -14, 6, 2, 20, 0, -22],\n [0, -25, -24, -14, -12, 2, 10, -3, -4],\n [3, -24, 25, 2, -2, -4, -4, -18, -1],\n [-14, -14, 2, 1, 6, -14, -18, 22, 2],\n [6, -12, -2, 6, 11, -6, -2, -1, -19],\n [2, 2, -4, -14, -6, 19, 12, -19, 9],\n [20, 10, -4, -18, -2, 12, -10, 13, 18],\n [0, -3, -18, 22, -1, -19, 13, 24, -19],\n [-22, -4, -1, 2, -19, 9, 18, -19, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[8, -5, -20, 13, 0, 10, 14, -8, 16],\n [0, 13, -21, 0, -15, 24, -10, -7, -21],\n [0, 0, -1, -16, 25, -21, 6, 6, -21],\n [0, 0, 0, 5, -9, -4, 21, 24, 15],\n [0, 0, 0, 0, 17, -20, -14, 17, 1],\n [0, 0, 0, 0, 0, 13, -11, -24, 23],\n [0, 0, 0, 0, 0, 0, -21, -12, -12],\n [0, 0, 0, 0, 0, 0, 0, -14, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5200", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-23, -13, -20, -15, 12, -7, -7, 10, -3],\n [-13, -21, 10, 0, -13, 8, 12, -2, 6],\n [-20, 10, -5, 24, 24, -6, -12, -2, 14],\n [-15, 0, 24, 20, -20, -16, 6, 4, 3],\n [12, -13, 24, -20, 4, 12, 18, 1, -8],\n [-7, 8, -6, -16, 12, -19, 6, -2, 11],\n [-7, 12, -12, 6, 18, 6, -9, 9, 8],\n [10, -2, -2, 4, 1, -2, 9, -25, 9],\n [-3, 6, 14, 3, -8, 11, 8, 9, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2037", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 10, 15, 1, 21, 24, 0, 1, -22],\n [0, 22, 12, -14, 21, -11, 21, 22, 4],\n [0, 0, 2, 5, -24, -11, 14, 17, 22],\n [0, 0, 0, -14, -16, -22, 25, -16, 3],\n [0, 0, 0, 0, 17, -13, 8, 20, -6],\n [0, 0, 0, 0, 0, -23, 18, -23, -5],\n [0, 0, 0, 0, 0, 0, -18, -1, 23],\n [0, 0, 0, 0, 0, 0, 0, 2, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, -11, 3, 2, -4, 3, -16, -4, -21],\n [-11, -16, 8, 22, 16, 0, -4, -21, 5],\n [3, 8, -7, 8, -15, 21, 2, -5, 10],\n [2, 22, 8, 2, 0, -13, 2, 2, -11],\n [-4, 16, -15, 0, 23, 6, -12, -20, 14],\n [3, 0, 21, -13, 6, 8, 5, 2, 20],\n [-16, -4, 2, 2, -12, 5, 1, 12, -4],\n [-4, -21, -5, 2, -20, 2, 12, 9, 8],\n [-21, 5, 10, -11, 14, 20, -4, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3789", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[-25, -17, 15, 5, -4, 12, 20, 15, -24],\n [15, 19, -6, -3, -14, -16, 6, -21, 18],\n [3, 7, -3, 10, -13, 24, -24, -15, 2],\n [-1, 10, -8, 13, -17, -24, 10, 20, -9],\n [7, 9, 7, 6, -6, 4, -4, -1, 19],\n [20, 18, -15, 24, 8, 2, 9, -22, -17],\n [17, -4, -1, -5, -1, 15, -9, -11, 15],\n [-19, 6, -18, -23, 7, 10, -9, -25, 10],\n [14, -9, 18, 22, 11, -1, -1, -13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, -4, 2, 11, 13, -2, 10, -2, 1],\n [-4, 16, 6, 14, -5, 8, 24, 16, -22],\n [2, 6, 9, 10, 16, -18, -3, 14, 4],\n [11, 14, 10, 5, 6, 17, 12, 0, 10],\n [13, -5, 16, 6, 4, -8, -1, -6, -12],\n [-2, 8, -18, 17, -8, -2, 1, 0, 6],\n [10, 24, -3, 12, -1, 1, 13, -8, 6],\n [-2, 16, 14, 0, -6, 0, -8, 7, -17],\n [1, -22, 4, 10, -12, 6, 6, -17, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[16, 20, -11, 16, -17, -14, -16, -2, 15],\n [0, -7, 25, -9, -24, -16, -21, 13, -20],\n [0, 0, -22, 24, 5, 10, -18, 5, -9],\n [0, 0, 0, -18, -1, -12, -3, 17, 15],\n [0, 0, 0, 0, 8, 23, -15, 1, -17],\n [0, 0, 0, 0, 0, -6, 16, 3, -22],\n [0, 0, 0, 0, 0, 0, 11, -10, -4],\n [0, 0, 0, 0, 0, 0, 0, -7, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-180", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, -13, -10, -2, 10, -3, -16, 0, -2],\n [-13, -10, -24, 2, -2, 6, -6, -17, -11],\n [-10, -24, -11, 7, 12, 10, 2, -16, 8],\n [-2, 2, 7, -8, -3, 16, -20, 24, 15],\n [10, -2, 12, -3, 3, -13, -1, -8, 2],\n [-3, 6, 10, 16, -13, -5, 10, 8, 0],\n [-16, -6, 2, -20, -1, 10, -10, 10, -7],\n [0, -17, -16, 24, -8, 8, 10, 22, 16],\n [-2, -11, 8, 15, 2, 0, -7, 16, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-191", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[14, -18, 10, 10, 7, 3, 5, 4, -18],\n [0, -3, 24, 25, 17, 0, 16, 12, 13],\n [0, 0, -8, 1, 24, -9, 19, -11, 17],\n [0, 0, 0, 1, 14, -9, 6, -10, 4],\n [0, 0, 0, 0, -4, -10, 23, 23, -10],\n [0, 0, 0, 0, 0, -19, -17, 18, 0],\n [0, 0, 0, 0, 0, 0, -17, -14, -18],\n [0, 0, 0, 0, 0, 0, 0, 15, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 7) rounded to the nearest integer?\n[[-24, -3, 15, -22, 11, -15, 10, 10, -11],\n [11, -23, 22, 4, -3, 7, -25, -25, -23],\n [-17, 6, -13, 19, 5, -5, -3, -13, 0],\n [-1, -18, 14, 4, 25, -21, -2, -16, -7],\n [9, -4, 13, 12, -19, 13, -6, 14, 6],\n [-24, -11, -16, -5, -11, 8, 9, 25, -21],\n [-7, -19, 20, 18, 16, 16, 10, -8, -20],\n [-22, -21, -12, 15, 21, 7, -5, -13, -24],\n [-11, 21, -10, 9, 19, -6, -25, 20, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-9, -9, 15, -6, -6, -22, -15, -11, 19],\n [1, -2, -6, 18, -11, -20, -8, -4, 23],\n [-5, -2, -9, -15, -8, 9, 5, 2, -2],\n [10, 19, -2, 7, 25, 4, 11, -13, -10],\n [22, 17, -17, 24, 21, -13, -19, 9, 18],\n [0, 24, -17, 9, -2, 7, -5, -4, 13],\n [-7, 18, 20, 19, 6, -21, -14, 14, -20],\n [-8, -19, -7, -11, 16, -17, -6, 22, -6],\n [-22, -16, 16, 14, -25, 9, -2, 18, -19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2328", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -3, -25, -2, -6, 6, 5, 7, 10],\n [-8, 11, 7, 7, -21, -8, -17, 16, 5],\n [-19, -11, 20, -22, 20, 13, -18, -2, -18],\n [-21, -3, 17, 8, -11, 25, 24, 21, -7],\n [-1, 13, -22, 20, -18, 3, 16, -13, 12],\n [10, 11, 16, 19, 25, 17, 5, -7, 11],\n [-1, 11, -25, -5, 15, 13, 15, 0, 16],\n [-23, 24, 15, -21, 17, 3, 7, -24, -8],\n [-12, 14, 4, 3, 3, -7, 20, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[14, -17, 20, 18, -13, 12, 5, -12, 5],\n [0, 8, 24, -16, -5, 13, -1, 11, 14],\n [0, 0, -19, -8, 15, 18, 0, -9, 16],\n [0, 0, 0, 11, -3, 21, 22, 22, -16],\n [0, 0, 0, 0, -15, 7, 5, 18, -2],\n [0, 0, 0, 0, 0, 23, 16, -19, 1],\n [0, 0, 0, 0, 0, 0, 11, 21, 19],\n [0, 0, 0, 0, 0, 0, 0, -25, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2691", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, 8, 0, -10, 2, -12, 6, -9, -5],\n [8, -11, -9, 21, -1, -12, 13, -4, -3],\n [0, -9, -23, -2, 0, -3, -4, 4, 12],\n [-10, 21, -2, -13, 14, 0, 2, 1, 7],\n [2, -1, 0, 14, 11, -2, -14, 0, -10],\n [-12, -12, -3, 0, -2, 8, 9, 8, 10],\n [6, 13, -4, 2, -14, 9, 17, 20, 5],\n [-9, -4, 4, 1, 0, 8, 20, 0, -3],\n [-5, -3, 12, 7, -10, 10, 5, -3, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-117", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-16, -20, -22, -25, -20, 12, 3, 18, -23],\n [0, -2, 16, -17, -9, 17, 12, 16, 24],\n [0, 0, 19, 7, -6, 8, -23, -6, -23],\n [0, 0, 0, 17, 5, 13, 23, -5, 25],\n [0, 0, 0, 0, -16, 0, -23, -12, -18],\n [0, 0, 0, 0, 0, 1, 7, -5, 0],\n [0, 0, 0, 0, 0, 0, 22, 15, 3],\n [0, 0, 0, 0, 0, 0, 0, 1, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179998", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -23, -24, -21, -8, 8, -11, 24, 24],\n [14, 18, 15, 25, -25, -4, -1, -9, 7],\n [-9, 12, -21, 11, 17, 17, -15, -14, 18],\n [8, 9, 13, 20, -10, -2, 5, -12, 23],\n [21, 6, 17, -13, 12, -9, 18, 10, 16],\n [-8, -7, -19, 4, -14, -15, 3, -23, 8],\n [8, 5, -4, -24, 1, 21, 10, 6, 9],\n [-9, 8, 0, -16, 13, -17, -1, -6, -11],\n [14, 23, 1, -15, -10, 4, -4, -2, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-522", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-2, 10, -8, -6, -18, -11, -13, 10, -12],\n [21, 21, -2, 11, -2, 21, -8, 6, 9],\n [-6, 16, 6, 11, 11, 21, 7, -25, 22],\n [2, 1, -9, 20, -11, -12, 5, 8, -23],\n [-14, 0, -2, 8, -18, -14, -17, 0, 20],\n [12, 23, 17, -7, -5, -13, 9, -23, -1],\n [6, -5, -12, 5, -18, -19, 10, 9, -7],\n [-24, -21, 18, -24, -8, -11, -10, -14, 18],\n [10, -4, 2, 14, 17, -4, -22, -14, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[1, -6, 8, 3, -1, -6, 6, 4, -6],\n [-6, 1, -10, 7, 6, 0, -4, 12, 15],\n [8, -10, -2, -2, -6, 2, -4, -21, -19],\n [3, 7, -2, 19, -20, -4, 22, -10, -17],\n [-1, 6, -6, -20, 22, 16, -4, 0, 2],\n [-6, 0, 2, -4, 16, 8, -6, 22, 4],\n [6, -4, -4, 22, -4, -6, 3, -13, 1],\n [4, 12, -21, -10, 0, 22, -13, 10, 12],\n [-6, 15, -19, -17, 2, 4, 1, 12, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[7, -7, 11, -8, -2, 6, 2, 2, -6],\n [-7, -20, 16, -16, 3, 0, 8, -14, -8],\n [11, 16, -16, -6, 2, -6, 8, 8, 20],\n [-8, -16, -6, -3, -16, -4, 0, 0, 1],\n [-2, 3, 2, -16, 10, 16, -12, -5, -4],\n [6, 0, -6, -4, 16, -11, -2, 10, 14],\n [2, 8, 8, 0, -12, -2, 25, -19, 0],\n [2, -14, 8, 0, -5, 10, -19, 22, 2],\n [-6, -8, 20, 1, -4, 14, 0, 2, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-140", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, -20, -19, -20, 9, -1, -5, 21, 22],\n [-9, 15, 0, 15, -9, -19, -1, 8, 0],\n [-20, -16, -9, -12, -23, 22, -10, -21, 22],\n [-3, 1, -21, 11, 12, -8, -14, -5, -19],\n [-9, 16, -17, 15, -2, -15, -1, 20, 11],\n [-19, -9, 15, -7, -5, 19, -17, 19, 20],\n [-18, 20, 19, 1, -3, -16, -24, 18, 22],\n [-19, -24, -10, -20, -10, -1, 19, -16, -17],\n [6, 6, -24, -5, 22, -23, 8, 3, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-6, -3, 11, -18, 18, 10, -12, -3, 1],\n [-11, 9, -4, 21, 10, -11, 6, 15, -8],\n [19, 5, 15, 10, -1, 19, -16, 14, -12],\n [22, 0, -7, 4, 13, -14, 5, 19, 21],\n [21, -8, -24, -12, -6, 13, -6, 8, 8],\n [11, -23, 9, 7, -7, 5, 18, -4, 1],\n [12, 2, -5, -6, 12, -13, 3, -5, 16],\n [7, 6, 22, 20, 2, 24, -12, 16, -4],\n [11, 8, -9, 7, 7, 12, 0, 13, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, 22, 25, 4, 15, 7, 24, 13, 2],\n [-8, -16, -24, 17, 24, 17, -12, -13, -25],\n [6, -1, -16, -11, 25, 3, -9, 16, 14],\n [-3, -19, 24, 10, -20, -24, 19, 6, 18],\n [-21, -7, -24, 17, -3, 14, -22, -22, -15],\n [20, 15, -6, -12, 9, 19, -12, 23, -23],\n [-11, -5, -24, -5, -16, 1, 21, -7, -14],\n [23, -10, -18, 11, -1, -2, 21, 14, -8],\n [-5, -18, -7, 23, 4, 1, 10, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-6, 16, 4, -8, -18, 10, 10, 6, 3],\n [16, 2, -10, 12, 12, 8, 6, -15, -16],\n [4, -10, 14, -4, -4, -2, 7, -12, -14],\n [-8, 12, -4, -14, 14, 18, 10, 22, 13],\n [-18, 12, -4, 14, 6, 24, 11, 12, -6],\n [10, 8, -2, 18, 24, -8, -12, -10, -3],\n [10, 6, 7, 10, 11, -12, -7, -2, -2],\n [6, -15, -12, 22, 12, -10, -2, -9, 2],\n [3, -16, -14, 13, -6, -3, -2, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, 18, 12, -14, -23, 14, 3, -4, 8],\n [0, 9, 13, -10, 5, 23, 18, -11, 20],\n [0, 0, -6, -3, -6, 6, 20, 22, -1],\n [0, 0, 0, 19, 4, -23, -2, -14, 5],\n [0, 0, 0, 0, -16, -11, -5, -5, 3],\n [0, 0, 0, 0, 0, -11, 20, 0, -15],\n [0, 0, 0, 0, 0, 0, -5, -9, 5],\n [0, 0, 0, 0, 0, 0, 0, 12, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-70", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[17, -14, 0, 0, 20, 7, -2, 17, 10],\n [-14, -5, 3, 16, 2, -9, -8, 6, 22],\n [0, 3, -16, -7, -6, 6, 6, 15, 2],\n [0, 16, -7, -13, -16, 0, 17, -23, -18],\n [20, 2, -6, -16, 11, 2, -5, -12, -10],\n [7, -9, 6, 0, 2, 19, 8, 9, -18],\n [-2, -8, 6, 17, -5, 8, 11, 0, -14],\n [17, 6, 15, -23, -12, 9, 0, 14, -5],\n [10, 22, 2, -18, -10, -18, -14, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[24, 14, 18, 18, 2, -8, 17, 24, -6],\n [14, 12, 12, -2, 8, 8, 8, -10, 12],\n [18, 12, -24, -4, 6, -2, -18, -16, 13],\n [18, -2, -4, -13, -2, 12, 14, -12, -12],\n [2, 8, 6, -2, 3, 19, 11, 20, 6],\n [-8, 8, -2, 12, 19, 23, -15, 4, -2],\n [17, 8, -18, 14, 11, -15, 12, 2, 6],\n [24, -10, -16, -12, 20, 4, 2, -2, -2],\n [-6, 12, 13, -12, 6, -2, 6, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[2, 6, -19, -12, -12, 6, -17, -20, 25],\n [-11, 4, 4, -10, -3, 5, -14, -5, -23],\n [-23, 12, -4, -5, 25, 18, -10, -8, -22],\n [-6, 19, -13, 5, -24, 4, 5, 2, -17],\n [-15, 9, 23, 18, 11, 20, 25, -9, 0],\n [-22, 7, -9, 16, -18, 0, 17, -6, 16],\n [25, 12, 17, 22, 16, 7, 14, -9, 25],\n [-17, -6, -18, 15, 22, 20, -20, -17, -15],\n [21, 21, -21, -18, 9, -1, 10, 13, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "572", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, -20, -2, -5, 10, -8, 22, -25, 3],\n [-9, -21, 24, -20, 19, -18, -1, -7, 22],\n [24, 13, -17, 2, 5, -25, 15, -16, 24],\n [-4, -25, -13, -12, -3, 13, 2, 3, 14],\n [7, -24, 17, 7, -2, -14, 14, 2, 9],\n [-16, 21, 18, 8, -21, 15, -8, -20, -15],\n [20, -25, -3, -22, -19, 15, 23, -9, -15],\n [1, -14, 21, 8, -18, -3, 0, 8, 6],\n [-20, -25, 24, -22, -1, -18, 14, 20, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-12, 7, -23, -11, 1, -7, -25, 9, 7],\n [25, -9, -13, 22, -14, 13, 0, 1, -2],\n [-9, -15, -4, -18, 16, 22, 6, 3, 16],\n [6, 14, -21, 23, -13, -1, 16, -16, 0],\n [0, -5, -3, 18, -14, 13, 17, -1, -14],\n [10, 6, -8, 16, -6, -24, 7, 20, -9],\n [10, 4, -17, 5, 13, -5, -4, -9, -23],\n [6, 7, -16, -21, -22, 25, 12, 6, 12],\n [15, -6, -17, -11, -18, 8, 4, -16, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 5) of the inverse of matrix 1/450 * A where A =\n[[8, 2, -14, 4, 4, 11, -14, 8, -18],\n [2, 11, -10, -11, 0, 4, 20, -6, -7],\n [-14, -10, -2, -2, 0, 3, -18, -6, 22],\n [4, -11, -2, -11, 8, -5, -3, 14, -4],\n [4, 0, 0, 8, -6, 8, 10, 18, -4],\n [11, 4, 3, -5, 8, -18, -7, 11, 5],\n [-14, 20, -18, -3, 10, -7, -8, -4, 4],\n [8, -6, -6, 14, 18, 11, -4, -8, -14],\n [-18, -7, 22, -4, -4, 5, 4, -14, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, -2, -25, -15, 17, 0, 0, -20, 7],\n [-12, -2, 12, 23, 15, -9, -12, -7, -18],\n [-3, 18, -24, -23, -13, -21, -8, -25, 11],\n [-5, 18, -7, 12, 8, -24, -6, 5, -13],\n [-12, 12, -14, -13, -2, 14, 5, -12, 24],\n [4, 1, 10, -20, -20, -11, -2, -13, -19],\n [19, -5, 12, 12, -12, -23, 17, 19, 9],\n [-14, -5, -6, 1, -21, 19, -15, 23, 16],\n [18, -20, -21, -4, -25, -6, -2, -6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-211", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 4) of the inverse. Round your answer to the nearest integer:\n[[22, 4, 7, -6, 2, 13, 4, 10, 10],\n [4, -20, 4, 18, -9, -10, 0, 11, -2],\n [7, 4, -12, -6, -10, -7, -16, 12, 8],\n [-6, 18, -6, 19, -9, 21, -9, 3, -17],\n [2, -9, -10, -9, 24, -8, -8, -8, -4],\n [13, -10, -7, 21, -8, 4, 0, 0, 8],\n [4, 0, -16, -9, -8, 0, 11, 0, 4],\n [10, 11, 12, 3, -8, 0, 0, -17, -14],\n [10, -2, 8, -17, -4, 8, 4, -14, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[22, 20, -2, 16, -6, -2, 8, -4, -8],\n [20, -12, -12, 0, 2, 8, 10, 14, 2],\n [-2, -12, -17, 6, 6, -16, -2, -11, -4],\n [16, 0, 6, -18, -16, -9, -2, 18, 19],\n [-6, 2, 6, -16, -24, 18, -8, -2, -7],\n [-2, 8, -16, -9, 18, 19, 12, -11, -12],\n [8, 10, -2, -2, -8, 12, -18, -14, 8],\n [-4, 14, -11, 18, -2, -11, -14, 22, 10],\n [-8, 2, -4, 19, -7, -12, 8, 10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-59", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[6, -21, -1, 7, -19, -10, 23, 3, -11],\n [-6, -4, -16, -18, 6, 2, -17, 5, -3],\n [-7, 6, -16, -6, 9, 5, -15, 17, 14],\n [-16, -17, 16, -16, 24, 11, 11, -19, -6],\n [-6, -18, -9, 12, -1, -13, 19, -13, 22],\n [-24, 11, 16, 16, -15, -6, -17, 19, 19],\n [3, 8, -21, 5, 0, 11, 18, -6, -18],\n [-20, -8, -18, -1, -24, 2, 16, -1, -6],\n [-20, 11, -10, 9, 10, -25, -12, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 12, 18, -8, -17, -13, 25, 19, 25],\n [-7, -16, 12, -23, 22, 15, -9, -3, 1],\n [-17, -21, -7, 3, -11, 16, 10, -14, -12],\n [-11, 25, 5, -21, 18, -23, 21, 4, 21],\n [-14, -11, 12, 2, 23, -3, 21, -11, -15],\n [4, -14, -7, 6, -25, -10, -15, 5, 7],\n [10, 4, 12, -22, -1, 8, -9, 7, 4],\n [-13, -14, 6, -3, 3, 8, -7, -14, -22],\n [-1, 0, -8, 4, 8, 7, 5, 5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "661", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-2, -6, 4, -2, -8, 6, -12, -2, 0],\n [-6, 3, -6, -20, 6, -17, 16, -10, 1],\n [4, -6, -8, 7, 20, -22, 5, 6, -2],\n [-2, -20, 7, 10, -3, 2, 1, 4, 16],\n [-8, 6, 20, -3, -6, 2, -2, 6, 1],\n [6, -17, -22, 2, 2, 21, 7, -10, 14],\n [-12, 16, 5, 1, -2, 7, -16, 9, -6],\n [-2, -10, 6, 4, 6, -10, 9, -21, 6],\n [0, 1, -2, 16, 1, 14, -6, 6, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (5, 2) of the inverse. Round your answer to the nearest integer:\n[[19, 9, 10, 3, 7, 0, -18, -17, -4],\n [0, 18, 15, 10, 6, 4, 23, 18, 19],\n [0, 0, 4, 21, -17, -22, -14, 9, -6],\n [0, 0, 0, 13, 18, 16, -18, -17, 20],\n [0, 0, 0, 0, -6, -6, 1, 1, -19],\n [0, 0, 0, 0, 0, -24, -25, -19, -2],\n [0, 0, 0, 0, 0, 0, -2, 12, 18],\n [0, 0, 0, 0, 0, 0, 0, -11, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-24, -6, -3, -5, 5, -10, -13, -22, -24],\n [24, -25, 0, 4, 12, -6, -1, -7, 1],\n [-16, 15, -9, 21, -24, -9, -19, -10, 23],\n [1, -25, -4, -4, 1, -10, 10, -10, -2],\n [9, 7, -9, -21, 9, -7, 17, 21, 8],\n [6, -1, -4, 13, 24, 1, 7, -18, 4],\n [22, 0, -11, 10, 19, -14, 15, 19, 17],\n [-14, -22, -23, 11, 12, 6, 0, -22, -25],\n [-21, -24, 20, -15, -17, -18, 13, -11, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3361", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[16, 24, 4, 3, 25, -1, -4, 8, -4],\n [20, 4, -16, -21, -21, -24, 4, -4, -13],\n [13, -1, 1, 21, 1, -5, 5, -11, 12],\n [13, 10, 10, -25, -15, -21, 8, 11, -21],\n [-6, 19, 18, 16, -13, -17, -21, 12, 6],\n [4, 23, 2, 11, 2, 17, -20, 15, 18],\n [3, -22, -8, -11, -1, -22, -12, 24, -9],\n [8, -7, 3, -4, -12, 10, -24, 19, -19],\n [2, -18, 3, -16, -5, 9, -22, -5, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}