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[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[2, -7, 12, 9],\n [0, -2, -5, 10],\n [0, 0, 7, 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" } ]
-927
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, -7, 3, -4],\n [0, -12, 7, 5],\n [0, 0, -10, 2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-50
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, -10, -9, -11],\n [-1, 5, -2, 4],\n [2, 4, -6, 1],\n [10, -6, 9, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
109
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, 7, 8, 5],\n [4, -4, -2, -11],\n [5, 12, 0, 6],\n [10, -12, 2, -12]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 0, 6, 4],\n [0, -5, -12, 6],\n [6, -12, 1, -10],\n [4, 6, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
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[[6, -8, 1, 4],\n [2, -7, 11, 6],\n [2, 1, 0, -2],\n [2, 9, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
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[[-1, -8, 3, 1],\n [-8, -8, 4, 2],\n [3, 4, 1, -2],\n [1, 2, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
97
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, 3, -3, -2],\n [3, 12, 1, -8],\n [-3, 1, 3, -9],\n [-2, -8, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 3, -9, -12],\n [-1, 9, 1, 0],\n [1, 7, -7, -11],\n [-9, -5, -9, -6]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 0, 12, -2],\n [0, -4, 1, -8],\n [0, 0, -11, 9],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-50
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[10, 2, 12, 9],\n [1, 4, -5, -3],\n [9, 12, 8, -7],\n [-6, 7, 6, -10]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, -12, -6, 3],\n [0, 6, -7, 10],\n [0, 0, -11, -7],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
137
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[4, -10, -10, 2],\n [0, 6, -11, 9],\n [0, 0, -4, -10],\n [0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
703
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[[12, -3, 0, 0],\n [-3, 1, -2, 3],\n [0, -2, 1, -6],\n [0, 3, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
334
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[[-11, -6, -5, 11],\n [0, 1, 11, 8],\n [0, 0, 11, -7],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1440
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, -5, 9, 2],\n [-3, 11, 1, -8],\n [-11, -6, -7, -7],\n [-4, -1, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
465
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[[-7, 10, 0, -1],\n [0, 6, -10, 2],\n [0, 0, 5, -9],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
49
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[[-4, -7, -12, -9],\n [0, -5, -6, 2],\n [0, 0, 5, -8],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
105
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, -10, -12, 10],\n [0, 3, 10, -5],\n [0, 0, -6, 2],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
251
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-12, 4, -10, 2],\n [4, 4, -6, 4],\n [-10, -6, 8, -6],\n [2, 4, -6, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1488
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 6, -8, -12],\n [0, 5, 3, -4],\n [0, 0, -12, 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" } ]
129
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[[-12, -11, -11, -3],\n [-5, 6, -10, 5],\n [8, 11, -7, 8],\n [-1, 3, 6, 12]]\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 all entries rounded to the nearest integer?\n[[-12, 9, 4, 10],\n [9, 10, -2, -8],\n [4, -2, 2, -10],\n [10, -8, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-53
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, 11, 12, 8],\n [0, 6, -9, 2],\n [0, 0, -9, -6],\n [0, 0, 0, -5]]\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, -4, -9, 4],\n [0, -5, -7, 11],\n [0, 0, -1, 3],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-720
MATH
[ { "content": "Find the value at position (1, 1) of the inverse of matrix 1/96 * A where A =\n[[2, -5, 10, -4],\n [0, 12, 11, 7],\n [0, 0, -1, 1],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
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, -10, 12, -2],\n [9, -12, 12, 0],\n [-7, -5, -11, -10],\n [-5, 12, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
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[[-10, 10, -7, -8],\n [1, -12, 3, -1],\n [0, -3, 10, -3],\n [-6, -5, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-27
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, -4, -2, 2],\n [-4, -4, 1, -3],\n [-2, 1, -7, 3],\n [2, -3, 3, 7]]\nRound your answer to the nearest integer.\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 (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 2, -2, 10],\n [0, 3, 7, -1],\n [0, 0, -1, 4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-9
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 10, 1, 10],\n [10, 7, -4, 9],\n [1, -4, -2, -10],\n [10, 9, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
152
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, 9, 2, 8],\n [9, -7, 1, 9],\n [2, 1, -11, -1],\n [8, 9, -1, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
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, -8, 4, -2],\n [-8, -7, -2, -2],\n [4, -2, -4, -2],\n [-2, -2, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
105
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, -6, -1, 6],\n [-6, 11, -4, 0],\n [-1, -4, 1, 0],\n [6, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[10, 11, -1, -5],\n [8, -4, 1, 2],\n [-8, -1, -12, -3],\n [1, 9, -3, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
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[[-12, -1, -9, -8],\n [-2, 7, -3, 7],\n [2, -3, 12, -11],\n [0, 10, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-24
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, -10, -8, -9],\n [-7, -4, 5, -6],\n [-12, 4, 1, 9],\n [7, 10, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[10, -6, -7, -3],\n [-6, -3, 1, 7],\n [2, 7, 2, -6],\n [8, -10, -2, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2816
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, -9, 2, 7],\n [2, -1, -12, 3],\n [2, 12, 10, 3],\n [-5, -3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
198
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[12, 2, -9, -4],\n [2, -7, 8, -10],\n [-9, 8, -9, 2],\n [-4, -10, 2, 1]]\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[[-5, 5, -2, 3],\n [5, 0, -8, -1],\n [-2, -8, 11, -4],\n [3, -1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
278
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, 4, 10],\n [0, -5, -5, 2],\n [0, 0, -6, -12],\n [0, 0, 0, 6]]\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[[-11, -12, 6, -11],\n [0, -9, 7, 4],\n [0, 0, 10, 7],\n [0, 0, 0, -10]]\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 value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 0, -3, 6],\n [0, -1, -7, -1],\n [0, 0, 12, -2],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[4, 11, 5, 3],\n [-8, 1, 2, 9],\n [-1, -5, 5, 0],\n [8, 7, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[6, -7, 11, -2],\n [-7, -9, -9, 1],\n [11, -9, -9, 0],\n [-2, 1, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-9
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, -3, 9, -11],\n [2, -8, 7, 4],\n [7, 12, -10, 12],\n [-12, 4, -2, 1]]\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[[10, -11, -5, -1],\n [12, -6, -12, 4],\n [-7, 7, 6, 7],\n [12, -8, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
111
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, -9, 10, -1],\n [0, 9, 10, 7],\n [0, 0, -12, -5],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
193
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[2, 2, 5, 5],\n [0, -9, 7, -2],\n [0, 0, 4, 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" } ]
85
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[[8, 2, 1, -1],\n [2, -9, 8, -6],\n [1, 8, 5, -1],\n [-1, -6, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-35
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-4, -2, 8, 3],\n [-2, -9, 2, 2],\n [8, 2, -2, 0],\n [3, 2, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
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[[-12, -9, 3, 7],\n [8, -2, -2, -10],\n [-8, -3, -7, -8],\n [12, 8, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[-8, 4, 10, 5],\n [0, 8, 1, 7],\n [0, 0, 4, 9],\n [0, 0, 0, 1]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, 1, -7, 8],\n [12, 12, -3, -11],\n [-1, 2, 12, -5],\n [-3, 9, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
189
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, -12, -1, 9],\n [6, -8, -12, -10],\n [4, 6, 3, -6],\n [12, -2, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[9, 6, -5, 5],\n [-9, 6, 10, 3],\n [10, -12, -12, 9],\n [-4, 10, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
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, 7, 10, 0],\n [0, 5, 11, 6],\n [0, 0, 1, -12],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-442
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, -9, -12, 11],\n [0, -10, 10, 10],\n [0, 0, -11, -11],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-66
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[4, -9, -3, -4],\n [-9, -3, 11, -5],\n [1, 5, -1, 4],\n [8, 1, 1, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
79
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[[5, 2, -9, 4],\n [1, 10, -6, -3],\n [8, -5, -6, 3],\n [-3, 9, -6, -2]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 9, 7, 4],\n [0, 7, -2, 10],\n [0, 0, -4, -7],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-51
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[[0, 8, -8, -6],\n [8, -4, 2, -4],\n [-8, 2, 10, 1],\n [-6, -4, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[11, 2, 10, 4],\n [2, 7, 10, 8],\n [-1, -4, -10, 4],\n [4, -5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
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, 0, -4, -2],\n [0, -6, 5, -4],\n [-4, 5, -10, 4],\n [-2, -4, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-27
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, -3, -9, -3],\n [0, -3, 4, -12],\n [0, 0, 9, -6],\n [0, 0, 0, 1]]\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 value at position (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 8, 10, 7],\n [4, -11, -3, 6],\n [-7, 9, 0, 4],\n [8, 10, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[1, 7, 9, -5],\n [-1, -3, -4, -9],\n [6, 7, 10, -8],\n [-7, 10, 4, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
231
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[[0, 1, 4, 6],\n [1, 1, -4, 7],\n [4, -4, -8, 4],\n [6, 7, 4, -2]]\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 sum of all entries rounded to the nearest integer?\n[[10, 0, -3, 7],\n [-3, 5, 7, -10],\n [8, 9, 2, 2],\n [7, -3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
169
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, -12, -7, 1],\n [-12, 1, -3, -6],\n [5, 0, -10, 9],\n [-6, 5, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-26
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[[5, -12, -3, -8],\n [0, 12, -1, 8],\n [0, 0, -6, -11],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
138
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, 2, -6, -11],\n [2, 5, -2, -1],\n [-6, -2, 9, -8],\n [-11, -1, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
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[[5, -6, -5, 8],\n [-6, 12, 11, -11],\n [6, 0, -11, -3],\n [-7, -7, -11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
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, -11, 9, -1],\n [0, 1, 9, -2],\n [0, -3, 4, 2],\n [9, 2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-1, -2, -11, 11],\n [0, 12, 10, 0],\n [0, 0, -8, -2],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
727
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[[-12, -6, 4, -6],\n [-6, -11, 8, 8],\n [4, 8, -11, -6],\n [-6, 8, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-36
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[[3, 2, -11, 0],\n [2, 6, -8, -1],\n [-11, -8, 12, -2],\n [0, -1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
302
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-8, 1, -11, 6],\n [-1, 7, -4, 9],\n [-6, 3, -5, 10],\n [-12, -10, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
912
MATH
[ { "content": "Find the value at position (3, 2) of the inverse of matrix 1/96 * A where A =\n[[6, 10, 2, 9],\n [0, -9, 6, 12],\n [0, 0, 5, 8],\n [0, 0, 0, -10]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -6, -12, -5],\n [-8, -5, -11, 4],\n [6, -12, 10, 10],\n [-8, -9, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-92
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[[-8, 2, -8, -4],\n [2, 3, -6, 4],\n [-8, -6, -2, -2],\n [-4, 4, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
391
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 3) rounded to the nearest integer?\n[[6, -10, 4, 3],\n [-1, 0, -5, -4],\n [-11, 5, -2, 10],\n [5, -2, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2
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, -6, 4, 11],\n [2, -9, 4, -10],\n [6, -2, 0, -1],\n [-6, -12, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
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[[9, -10, 10, -7],\n [0, -1, 10, -12],\n [0, 0, 5, -12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
579
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[[2, -2, -2, 0],\n [-2, 12, 0, -1],\n [-2, 0, -5, 0],\n [0, -1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
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[[10, -10, 7, -5],\n [0, 6, 11, 10],\n [0, 0, 3, 7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
38
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[[2, -11, -1, -3],\n [3, -7, -5, 2],\n [1, -6, -2, -11],\n [-4, 0, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
155
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, -2, 10, -1],\n [-2, -2, 2, -3],\n [10, 2, -12, -8],\n [-1, -3, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-143
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[[12, -5, -12, -9],\n [-12, 5, 10, 3],\n [4, -7, 5, 2],\n [-7, -1, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-30
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, 0, 3, -4],\n [-4, 7, 4, 9],\n [-9, 3, -7, 6],\n [-12, 7, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[6, -4, -6, 2],\n [-4, -8, 0, 2],\n [-6, 0, 5, -5],\n [2, 2, -5, -9]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, 12, 2, -1],\n [0, -5, 6, -7],\n [0, 0, -8, -2],\n [0, 0, 0, 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 sum of absolute values of all entries rounded to the nearest integer?\n[[6, 4, -9, -7],\n [-3, 6, -8, 2],\n [-7, -2, -2, -6],\n [5, -1, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
107
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, -6, 8, -6],\n [-6, -8, -8, 4],\n [8, -8, 12, -2],\n [-6, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
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, -7, -2],\n [4, -3, -7, -5],\n [-7, -7, 4, 8],\n [-2, -5, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-35
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[[-11, 5, 8, -3],\n [0, 12, -3, -7],\n [0, 0, -2, -3],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-48
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[[-2, -10, 5, 12],\n [4, 7, -1, -9],\n [11, 2, 7, 12],\n [8, 6, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
190
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[[-4, -2, 7, -6],\n [-2, -10, 4, 0],\n [7, 4, -4, 10],\n [-6, 0, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-9
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, 7, 4, -8],\n [8, 3, 1, -5],\n [1, 9, -8, 0],\n [0, 0, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
66
MATH