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[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, -6, -4, -2],\n [-6, -6, -6, -4],\n [-4, -6, 11, -3],\n [-2, -4, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-15
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[-4, -2, -8, 4],\n [-2, 3, 4, 2],\n [-8, 4, 6, 1],\n [4, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[11, 2, -5, 3],\n [2, 7, -6, -2],\n [-5, -6, -4, 2],\n [3, -2, 2, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-37
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, -12, -9, -12],\n [0, -6, 7, 11],\n [0, 0, -2, -11],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2112
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-7, 1, 0, -2],\n [0, -11, -6, -3],\n [0, 0, -11, 2],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -12, -10, 1],\n [3, 11, 3, 0],\n [-5, -11, 12, -9],\n [-8, 1, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, 1, 1, 0],\n [1, 1, 12, 4],\n [1, 12, -9, -3],\n [0, 4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-6, -8, 6, 11],\n [-2, -9, -9, 0],\n [-7, -2, -2, 5],\n [-10, -9, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, 5, -4, 2],\n [5, -6, -8, 0],\n [-4, -8, -5, -2],\n [2, 0, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
83
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, 3, -11, -11],\n [9, -7, -2, -4],\n [-11, 6, -11, -12],\n [10, 4, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
227
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, 3, -6, 6],\n [3, -11, 10, -2],\n [-6, 10, -8, 0],\n [6, -2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, 0, -1, -4],\n [0, -12, 6, 3],\n [-1, 6, 0, -6],\n [-4, 3, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-126
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 0, 10, -11],\n [4, 6, 10, -2],\n [-7, -5, 9, -5],\n [-4, -6, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[12, 0, 1, -1],\n [0, 10, -2, 1],\n [1, -2, 7, 2],\n [-1, 1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6757
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -5, -4, 3],\n [9, -6, -5, -12],\n [-4, -12, -1, 6],\n [2, -12, -6, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-24
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 11, -9, -9],\n [0, 12, 12, 4],\n [0, 0, 8, 12],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
258
MATH
[ { "content": "Find the value at position (2, 2) of the inverse of matrix 1/96 * A where A =\n[[-2, -12, -4, 6],\n [5, 3, 5, -12],\n [-1, -7, -9, 5],\n [-10, 10, -10, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-5
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, 11, 7, -4],\n [-10, 2, -3, -5],\n [-11, 7, -8, 12],\n [-3, -1, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16
MATH
[ { "content": "Find the inverse of 1/96 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[[-1, 4, 2, -2],\n [4, -3, -5, -8],\n [2, -5, 4, -2],\n [-2, -8, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-1, 11, -3, -3],\n [10, -12, 3, 11],\n [0, 11, -12, -1],\n [0, -4, -5, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
248
MATH
[ { "content": "Find the inverse of 1/96 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, 0, -10, -3],\n [0, 1, 9, -9],\n [0, 0, -10, -12],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
317
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -11, -8, 11],\n [0, 11, -6, -2],\n [0, 0, -5, 4],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-4, -2, 7, 6],\n [-12, -6, -9, 1],\n [8, -2, 6, 8],\n [-1, 12, -4, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-12
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, -3, -6, 8],\n [0, 3, -7, 11],\n [0, 0, -8, 2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
201
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, 0, -4, -11],\n [0, -12, -6, 11],\n [0, 0, 5, -12],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, 9, 2, -5],\n [0, 7, 3, 1],\n [0, 0, -10, -12],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
194
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, -6, 5, -12],\n [0, -12, 3, -2],\n [0, 0, -7, -8],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-90
MATH
[ { "content": "Find the inverse of 1/96 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, 1, 6, 2],\n [0, 7, -10, 4],\n [0, 0, -5, -2],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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[[12, 7, -11, -3],\n [9, -9, -3, -10],\n [-6, -7, 9, 4],\n [-6, -4, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-5
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[2, -6, -3, 6],\n [-6, 4, 6, 4],\n [-3, 6, -9, 10],\n [6, 4, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
65
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[6, -11, 0, -6],\n [-11, 1, 0, 2],\n [0, 0, 10, 6],\n [-6, 2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-15
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-2, 1, 5, 1],\n [-7, 6, 6, -4],\n [9, 12, -9, -9],\n [-11, 12, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
83
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, 4, -6, -2],\n [4, -8, 6, 4],\n [-6, 6, 1, 6],\n [-2, 4, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
99
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, -9, 0, 6],\n [-9, 10, 1, 5],\n [0, 1, 11, 6],\n [6, 5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -1, -3, -3],\n [11, -12, 7, 2],\n [4, 6, -11, -6],\n [1, 10, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-90
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[5, -2, -11, -6],\n [11, -2, 8, 12],\n [-11, -8, -9, -2],\n [11, 5, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16
MATH
[ { "content": "Find the inverse of 1/96 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, 6, 2, -2],\n [6, 10, -2, 0],\n [2, -2, -8, -1],\n [-2, 0, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-30
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-2, -2, 10, 6],\n [-2, -12, 2, 0],\n [10, 2, -10, -11],\n [6, 0, -11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-37
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-1, -8, -10, -1],\n [-8, 6, 5, -8],\n [-10, 5, -1, -4],\n [-1, -8, -4, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1752
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[4, 0, 2, -6],\n [0, -3, -6, 2],\n [2, -6, 3, 2],\n [-6, 2, 2, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-145
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[9, -11, 8, 2],\n [-5, 1, -2, -5],\n [10, 9, -7, 1],\n [0, 6, -7, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-37
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -4, -2, 6],\n [-4, 0, 2, -2],\n [-2, 2, 10, 0],\n [6, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-107
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[1, 3, -11, 0],\n [0, 7, -7, 5],\n [0, 0, 9, -12],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 2, 1, -3],\n [9, 2, 10, -4],\n [4, -7, -4, 6],\n [9, -4, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-99
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, 8, 5, -3],\n [8, -11, 6, -2],\n [5, 6, 8, 2],\n [-3, -2, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, 1, 4, 0],\n [1, -3, 7, 3],\n [4, 7, 2, 0],\n [0, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-61
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-3, 11, 10, 10],\n [-2, 8, -2, -10],\n [-4, -3, 6, -5],\n [0, -12, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-2, -12, 12, -6],\n [0, 7, 6, -12],\n [0, 0, -7, -2],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
MATH
[ { "content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[2, -1, 4, 12],\n [-1, 3, 3, 2],\n [4, 3, -10, 2],\n [12, 2, 2, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, 7, 7, -7],\n [0, -12, -12, 3],\n [0, 0, -9, -6],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "Find the inverse of 1/96 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, -11, -3, -12],\n [7, -12, 2, -5],\n [-1, 11, -11, 9],\n [3, -4, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
203
MATH
[ { "content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[12, 10, -6, -2],\n [10, 1, 0, -5],\n [-6, 0, -5, 12],\n [-2, -5, 12, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[12, 10, -6, -1],\n [1, -3, -11, 4],\n [-3, 5, -5, 6],\n [11, 11, 10, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[-8, -5, 2, -9],\n [0, 6, 2, 8],\n [0, 0, 8, 9],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the inverse of 1/96 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, 0, 0, 4],\n [0, 3, 0, 4],\n [0, 0, 2, -7],\n [4, 4, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
123
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, 6, -5],\n [2, 12, -8, -12],\n [-5, 3, 0, -2],\n [-12, 10, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4902
MATH
[ { "content": "Find the value at position (2, 2) of the inverse of matrix 1/96 * A where A =\n[[-11, -5, -2, 5],\n [0, -8, -5, 1],\n [0, 0, -11, 3],\n [0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-12
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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[[3, 11, 0, -3],\n [0, -4, 6, -9],\n [0, 0, -9, 7],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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[[-5, 4, 2, -8],\n [4, -2, 11, 9],\n [2, 11, -12, -10],\n [-8, 9, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, 4, 3, -2],\n [4, 9, 7, -5],\n [3, 7, -7, 2],\n [-2, -5, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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[[-9, -8, -3, -4],\n [-8, -1, 10, -2],\n [-3, 10, 12, -3],\n [-4, -2, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -6, 9, 11],\n [0, 0, 6, 11],\n [-8, -5, -12, -2],\n [1, -12, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[10, 9, 2, -9],\n [0, 8, 2, 7],\n [0, 0, 8, -8],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -3, 0, -5],\n [-3, -4, 6, -2],\n [0, 6, -2, -4],\n [-5, -2, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, -4, -1, -1],\n [-4, 12, 0, -9],\n [-1, 0, -5, 0],\n [-1, -9, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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[[-10, 11, 9, 3],\n [-6, -10, 5, 0],\n [-3, -10, 1, -1],\n [-10, 3, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 7, 4, -7],\n [0, -11, 5, 0],\n [0, 5, -11, -2],\n [5, 11, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, 1, 9, -12],\n [9, -8, -10, -11],\n [12, -8, -10, 8],\n [-1, 1, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
MATH
[ { "content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[-1, 11, 0, -1],\n [-1, 10, -5, -6],\n [4, 6, 2, -3],\n [-2, -6, 8, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-8
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, 6, -6, -5],\n [6, -10, 11, -10],\n [-6, 11, -6, 2],\n [-5, -10, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Find the inverse of 1/96 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, -11, 0, -10],\n [0, -11, 1, -6],\n [0, 0, -12, 11],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
318
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, -12, -9, 6],\n [0, -5, 10, -2],\n [0, 0, 12, -1],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-33
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[11, 8, -6, -8],\n [-4, 11, 4, -6],\n [7, -3, 3, -11],\n [-5, -11, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-29
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-12, -8, 7, 2],\n [-6, -1, 11, -11],\n [-7, 12, 9, 11],\n [9, 9, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, 0, 6, 7],\n [0, -3, -6, -8],\n [6, -6, -8, 4],\n [7, -8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-71
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, -4, 2, -4],\n [-4, 11, 4, 4],\n [2, 4, 2, -6],\n [-4, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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[[8, 11, 7, -8],\n [0, 3, 12, 7],\n [0, 0, 4, 12],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the inverse of 1/96 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, -2, 2, 10],\n [-2, -3, 4, -7],\n [2, 4, 2, 2],\n [10, -7, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Find the inverse of 1/96 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, -6, 5, -6],\n [-6, 2, 2, 3],\n [5, 2, -2, -9],\n [-6, 3, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-21
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, -1, 11, 5],\n [0, 3, -8, -6],\n [0, 0, -10, 0],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, 6, 10, 4],\n [0, 9, -10, -11],\n [6, 0, 12, 1],\n [-5, -2, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
61
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, 10, 8],\n [6, -8, -2, 6],\n [10, -2, -10, 1],\n [8, 6, 1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
MATH
[ { "content": "Find the inverse of 1/96 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, 1, 1, 9],\n [-2, 4, -6, 2],\n [12, -3, 5, 10],\n [5, 12, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "Find the inverse of 1/96 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, 7, 4, 2],\n [0, -3, -2, -9],\n [0, 0, 1, 1],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, 12, 12, -12],\n [5, 2, 10, 11],\n [3, -2, 8, -6],\n [-5, 11, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Find the inverse of 1/96 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[[1, -8, -6, -2],\n [5, 5, 7, -1],\n [-6, 0, 7, -7],\n [-4, 3, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-26
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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[[10, 2, -10, 5],\n [8, 7, -6, -3],\n [-4, 9, 10, -11],\n [-2, 10, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
453
MATH
[ { "content": "Find the inverse of 1/96 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, 4, 3, -6],\n [4, -4, -2, -3],\n [3, -2, 1, 5],\n [-6, -3, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
116
MATH
[ { "content": "Find the value at position (4, 3) of the inverse of matrix 1/96 * A where A =\n[[-4, -10, -9, -4],\n [-8, 11, 10, 11],\n [9, 11, 5, 6],\n [-5, 0, -8, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, 10, 10, 8],\n [3, 10, -6, 0],\n [2, -7, -3, 0],\n [-7, -11, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, 11, -7, 6],\n [0, 9, -7, -3],\n [0, 0, -3, -3],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-32
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[-1, 2, 5, 11],\n [0, -1, 9, -11],\n [0, 0, 11, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-45
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-9, -2, -9, 9],\n [0, 9, -9, 2],\n [0, 0, 12, -12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -10, -6, 10],\n [10, -2, 9, -3],\n [-9, -5, -1, 6],\n [-6, 5, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -12, 8, 4],\n [0, 9, 10, -7],\n [0, 0, -3, 11],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-93
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[3, -6, -3, 10],\n [0, -11, 9, 12],\n [0, 0, -1, 12],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1356
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -10, -8, 11],\n [0, -10, 9, -6],\n [0, 0, 10, 10],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
897
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -4, -6, 4],\n [2, -3, -3, 3],\n [-8, -6, 1, -11],\n [1, 12, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-66
MATH
[ { "content": "Find the inverse of 1/96 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, 11, -10, -12],\n [0, 2, -3, 11],\n [0, 0, 2, -9],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-75
MATH
[ { "content": "Calculate the inverse matrix of 1/96 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, -8],\n [-1, 11, 0, -5],\n [10, 12, -3, -10],\n [6, 12, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH