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[ { "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, -9, 0, 0],\n [0, 6, -2, 0],\n [0, 0, -4, 10],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-120
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -2, 12, 0],\n [-2, 10, 11, 0],\n [12, 11, 1, -2],\n [0, 0, -2, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-17
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, 11, -4, 11],\n [0, -9, -5, -2],\n [0, 0, -11, -6],\n [0, 0, 0, -7]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[2, -4, -4, 5],\n [0, 1, 5, 5],\n [0, 0, -6, -7],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1152
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, 6, -8, -6],\n [0, 10, -11, -3],\n [0, 0, -2, 5],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-199
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-8, -12, -10, -3],\n [6, -10, 11, 8],\n [-10, -2, 12, 5],\n [0, 7, 9, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-67
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, 8, 10, 1],\n [1, 1, -12, -12],\n [1, -12, -1, 12],\n [-3, -9, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
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[[1, 9, 4, 4],\n [-10, 3, 9, 12],\n [3, 0, 10, -5],\n [-12, -1, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
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, -7, -7, 2],\n [0, 2, 10, 12],\n [0, 0, -3, -1],\n [0, 0, 0, 10]]\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 at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[-3, 0, -2, -6],\n [0, 12, -2, 2],\n [-2, -2, -10, 7],\n [-6, 2, 7, -2]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 8, -2, -1],\n [8, 11, 2, 4],\n [-2, 2, -2, -8],\n [-1, 4, -8, 3]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -12, -8, 4],\n [0, 1, 3, 9],\n [0, 0, 7, -1],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-288
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, 5, -2, -6],\n [5, 0, -4, -8],\n [-2, -4, -2, -4],\n [-6, -8, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2131
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, -5, 1, 9],\n [12, -12, -1, -8],\n [-8, -5, -7, -6],\n [6, -4, -7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[-6, -1, 0, 8],\n [-1, 5, 3, 6],\n [0, 3, 2, 0],\n [8, 6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
288
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[0, -2, -7, 7],\n [-2, 0, -10, 2],\n [-7, -10, -11, 6],\n [7, 2, 6, -3]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-12, -3, 5, -2],\n [8, -6, 3, 7],\n [-9, -5, 3, 8],\n [-4, -12, -11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
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[[8, 4, -2, -1],\n [4, -11, -4, -3],\n [-2, -4, 8, 2],\n [-1, -3, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
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[[10, -10, 6, 4],\n [-9, 2, 6, 4],\n [12, 0, 7, -2],\n [-10, 4, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, 2, 10, -7],\n [2, -5, -8, 4],\n [10, -8, 0, 6],\n [-7, 4, 6, 4]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, 11, -6, 11],\n [0, 1, -5, -3],\n [0, 0, -10, 2],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
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[[-11, -5, -2, -1],\n [-5, 2, 0, 0],\n [-2, 0, 11, 0],\n [-1, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
68
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, -10, -6, -7],\n [11, 4, -1, -3],\n [11, -6, 5, -10],\n [8, -4, 12, 1]]\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[11, 3, 8, -10],\n [11, -6, -2, -10],\n [2, 11, 10, 3],\n [3, -5, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
223
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[[-5, 4, 4, 3],\n [0, -11, 8, 1],\n [0, 0, -4, 3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
145
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[11, -11, -7, 6],\n [12, 3, -5, 7],\n [-6, -12, 10, -8],\n [-10, 1, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-4
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, 6, -9, 11],\n [-11, -9, -8, -4],\n [7, 2, 12, 11],\n [2, 0, 7, -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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 0, 8, 5],\n [0, 10, -5, 0],\n [0, 0, -4, -7],\n [0, 0, 0, 10]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, 0, 6, -2],\n [0, 2, 2, -6],\n [6, 2, 12, 0],\n [-2, -6, 0, 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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 11, 2, -1],\n [-4, -1, -4, -4],\n [-4, 8, -10, -6],\n [-6, 2, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-22
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[[-6, -2, -12, 6],\n [-6, -2, 9, 1],\n [-11, -3, -3, 3],\n [-12, -2, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-10, 11, 4, 7],\n [-12, -6, -6, 12],\n [-5, 12, 2, 3],\n [2, 11, -12, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
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, 4, -6, -5],\n [4, 4, -10, 6],\n [-6, -10, -9, 2],\n [-5, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[2, 10, 7, 7],\n [0, 0, 9, -3],\n [-4, -9, 8, 12],\n [-10, -3, -7, 12]]\nRound your answer to the nearest integer.\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 value at position (4, 2) rounded to the nearest integer?\n[[-4, 0, 0, -2],\n [0, 4, 2, 8],\n [0, 2, 6, -7],\n [-2, 8, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
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, 1, 6, -4],\n [-9, 9, -7, -1],\n [-12, 5, 5, 11],\n [8, 1, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-2, 5, -3, 9],\n [4, -9, 4, 10],\n [8, -6, -7, -4],\n [2, -12, -1, 8]]\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[[12, 10, 1, -6],\n [10, 8, 2, 6],\n [1, 2, -1, -6],\n [-6, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
176
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[[3, -10, 8, 8],\n [0, -6, -10, 3],\n [0, 0, -12, -6],\n [0, 0, 0, 5]]\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, -6, 8, -2],\n [0, 10, 9, 6],\n [0, 0, 8, 0],\n [0, 0, 0, -10]]\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 value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -3, -3, 0],\n [-3, 0, 5, 5],\n [-3, 5, -9, -7],\n [0, 5, -7, 1]]\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 value at position (2, 2) rounded to the nearest integer?\n[[-9, 7, -8, 5],\n [-12, -11, 8, -8],\n [-4, -1, -8, 9],\n [7, 0, -3, -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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[3, 2, 3, -2],\n [2, 7, 0, -2],\n [3, 0, 4, -2],\n [-2, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
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, 4, -1, -2],\n [4, 4, 6, 2],\n [-1, 6, 8, -4],\n [-2, 2, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34872
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, 2, -4, -8],\n [2, -8, 0, 6],\n [-4, 0, -9, 2],\n [-8, 6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
134
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[[-2, 6, 2, 6],\n [6, 6, 8, -4],\n [2, 8, 4, 10],\n [6, -4, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-32
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[[11, 2, -9, -11],\n [0, 12, -2, -5],\n [0, 0, -6, -7],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
107
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, -6, 8, 10],\n [-6, -3, -4, 4],\n [8, -4, 10, -4],\n [10, 4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-91
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, 11, 5, -10],\n [6, 6, 1, -8],\n [-9, 7, -9, -5],\n [8, -3, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-21
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 1) rounded to the nearest integer?\n[[-8, 2, -6, -7],\n [2, 11, -2, 5],\n [-6, -2, 2, 6],\n [-7, 5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-5
MATH
[ { "content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[-5, -8, -10, 4],\n [0, -5, 5, -1],\n [0, 0, 5, -10],\n [0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-69
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[4, -8, 10, 7],\n [-4, 2, 2, 5],\n [-9, 2, 1, 10],\n [-2, -8, 8, 0]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[9, 0, -8, -9],\n [7, 7, -3, -8],\n [-3, -9, 2, -6],\n [-8, 3, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-45
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 1) of the inverse. Round your answer to the nearest integer:\n[[2, -9, -5, 4],\n [0, -8, 2, 10],\n [-8, -6, 1, -7],\n [12, 4, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
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[[6, 0, -1, -6],\n [0, 7, 2, -8],\n [-1, 2, 0, 0],\n [-6, -8, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-423
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[[0, -4, 4, -2],\n [0, 0, 6, 2],\n [8, 7, 9, -1],\n [12, 10, 5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
38
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[11, 2, -3, 0],\n [2, 12, -10, -4],\n [-3, -10, 10, 0],\n [0, -4, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
296
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[[-8, 1, -8, 1],\n [-7, 4, 6, 0],\n [-10, -12, 7, -1],\n [2, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
82
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, -10, -6, -1],\n [-10, -11, 2, -4],\n [-6, 2, -1, -1],\n [-1, -4, -1, 3]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -9, -9, 2],\n [0, 12, -2, -8],\n [0, 0, -11, 0],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
387
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[9, -8, 11, -2],\n [-8, 3, 2, 4],\n [11, 2, -1, 0],\n [-2, 4, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
101
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 2, 4, 2],\n [2, 9, 4, -6],\n [4, 4, -6, -2],\n [2, -6, -2, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[-5, 7, 9, -1],\n [-6, 0, -8, 5],\n [7, -5, 1, -12],\n [-8, -5, -7, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3
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, 4, -4, -7],\n [9, 7, 6, -7],\n [9, -9, -7, -6],\n [11, 7, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/96 * A where A =\n[[5, -10, 9, 9],\n [3, 1, -11, 5],\n [-12, -4, 8, -5],\n [3, -1, 9, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[10, 0, -2, 4],\n [0, -3, -10, 6],\n [-2, -10, -6, 6],\n [4, 6, 6, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
114
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[9, 2, -2, 5],\n [0, -2, -9, -4],\n [0, 0, -1, 4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, -2, 3, 11],\n [0, 8, 9, 7],\n [0, 0, 11, -2],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
94
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, 1, -3, -10],\n [0, 7, 11, 6],\n [0, 0, -11, -8],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-105
MATH
[ { "content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[-4, 8, 4, 2],\n [0, 7, -5, 12],\n [0, 0, 3, 10],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
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, 0, 1],\n [-1, 8, 2, 5],\n [0, 2, 2, -4],\n [1, 5, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
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[[-1, 5, 10, -11],\n [-7, 5, 1, 12],\n [-9, 9, 7, -2],\n [0, -5, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[-12, -11, 5, -6],\n [11, 1, 11, 12],\n [0, 11, 1, 8],\n [5, 9, 6, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
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[[12, 10, 3, -2],\n [0, 7, -5, -7],\n [0, 0, -9, -9],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[3, 9, -3, -1],\n [6, -1, 9, 6],\n [-5, -8, 4, 1],\n [10, -7, -5, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
530
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, -9, -5, -3],\n [0, -11, -2, 8],\n [0, 0, -10, 1],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
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, -11, 0, -9],\n [0, -8, -11, -9],\n [0, 0, -6, -11],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
258
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[[12, 0, -12, 4],\n [8, 12, -12, -2],\n [1, -5, 6, 4],\n [5, -2, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[3, 3, 5, 7],\n [-2, 10, 11, 9],\n [6, 0, -12, -6],\n [-3, -9, 4, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[9, 2, -3, 11],\n [0, 9, 12, 1],\n [0, 0, -6, -12],\n [0, 0, 0, -12]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -6, 4, 8],\n [0, 9, -5, -3],\n [0, 0, -12, 2],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
113
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, 5, 9, 10],\n [5, -5, 2, 2],\n [9, 2, -8, -2],\n [10, 2, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3
MATH
[ { "content": "Find the value at position (3, 1) of the inverse of matrix 1/96 * A where A =\n[[10, -7, -11, 7],\n [9, -7, 0, 8],\n [-10, 7, -3, -4],\n [10, 1, 2, -3]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 3, 2, -5],\n [3, -7, -4, -2],\n [2, -4, 12, -5],\n [-5, -2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
141
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, -6, -3, -6],\n [-6, -12, -8, 9],\n [-3, -8, 0, 4],\n [-6, 9, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[5, 0, -9, 7],\n [0, -2, 4, 5],\n [0, 0, -4, 9],\n [0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-763
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, 11, 1, -11],\n [0, -7, -2, -7],\n [0, 0, -6, 8],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-58
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, -10, 4, -7],\n [-1, -7, -9, -4],\n [4, 6, 3, 5],\n [-3, 5, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
619
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, -8, -1, -8],\n [-2, -6, -5, 6],\n [11, -1, 6, -7],\n [8, -10, 9, 8]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -2, 6, -2],\n [-2, 3, 3, -9],\n [6, 3, -10, 10],\n [-2, -9, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
59
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[[-10, -11, -4, -7],\n [0, -10, 8, -6],\n [-8, -5, -5, 0],\n [-1, 7, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-3, 9, -10, -4],\n [2, -1, 3, -12],\n [-5, 12, 7, 3],\n [-6, 10, 6, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-78
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[[4, 0, 2, -6],\n [0, 6, -6, -5],\n [2, -6, -3, 4],\n [-6, -5, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-39
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-2, 4, -3, 8],\n [0, -7, 3, 0],\n [0, 0, 6, -10],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
223
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[[-1, -1, -8, 5],\n [-1, -8, -4, 2],\n [-8, -4, -9, 0],\n [5, 2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
229
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, -5, 11],\n [0, -9, -7, 3],\n [0, 0, 9, -8],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
106
MATH
[ { "content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[2, 1, 7, 1],\n [8, -8, -5, -9],\n [6, 7, -4, 0],\n [-8, 11, -2, -7]]\nRound your answer to the nearest integer.\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[[-10, 8, 6, 5],\n [0, -3, 12, 5],\n [0, 0, 1, 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" } ]
1395
MATH
[ { "content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[5, 8, -10, 12],\n [0, -2, -8, 2],\n [0, 0, -8, 11],\n [0, 0, 0, 12]]\nRound your answer to the nearest integer.\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 all entries of the inverse. Round your answer to the nearest integer:\n[[-10, -2, 2, 0],\n [-2, -3, -2, 2],\n [2, -2, -12, -4],\n [0, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH