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[ { "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, -8, -11, 10],\n [-8, 4, 4, -5],\n [5, 7, -10, -7],\n [11, -12, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
53
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, -11, -12, -8],\n [0, 4, 3, 11],\n [0, 0, -9, -11],\n [0, 0, 0, 6]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[0, 10, 6, -6],\n [3, 8, 8, -9],\n [-3, 12, 12, 1],\n [-10, -1, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-33
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, -6, 4],\n [-12, 2, -1, -2],\n [-6, -1, -3, 8],\n [4, -2, 8, -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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -2, 2, -4],\n [-2, 0, -9, 0],\n [2, -9, -3, 2],\n [-4, 0, 2, 8]]\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 at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[3, 0, 12, 10],\n [12, 2, -10, -11],\n [-4, -9, 11, -5],\n [7, 12, 10, 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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, -1, 9, 8],\n [0, 7, 12, 4],\n [0, 0, 7, 3],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, 4, 0, 7],\n [4, -1, 8, 6],\n [0, 8, -2, -1],\n [7, 6, -1, -1]]\nRound your answer to the nearest integer.\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[2, 0, -2, 2],\n [9, -12, 10, -7],\n [-1, -4, -5, -12],\n [-12, 3, 4, 10]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, -10, 11, 10],\n [0, -9, -4, -9],\n [0, 0, -12, -8],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-17
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, 1, -2, 8],\n [0, 7, -6, 1],\n [0, 0, -10, 2],\n [0, 0, 0, -5]]\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[[-9, 0, -3, 3],\n [0, -6, -11, 0],\n [-3, -11, -1, 6],\n [3, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[5, -2, 2, 4],\n [-2, -4, -2, -10],\n [2, -2, -12, -6],\n [4, -10, -6, -2]]\nRound your answer to the nearest integer.\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 10, -8, -10],\n [-1, -12, 11, 7],\n [-1, 9, -4, 12],\n [6, 9, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
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, 6, 4, -8],\n [6, -4, -4, -1],\n [4, -4, 10, 6],\n [-8, -1, 6, -4]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[6, 3, -8, 11],\n [0, -2, -2, -12],\n [0, 0, -4, 4],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-336
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, -6, -5, -2],\n [-6, -2, -9, 2],\n [-5, -9, 8, -2],\n [-2, 2, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
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, 9, 11],\n [2, -4, -2, 2],\n [-11, -7, -3, 1],\n [0, -9, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
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, -9, -9, -8],\n [0, 7, -11, 5],\n [0, 0, 3, 5],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1800
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, 0, -11],\n [-1, 12, 11, 9],\n [4, -7, 11, -4],\n [7, -3, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
824
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[2, 10, 2, -6],\n [0, -12, 5, -10],\n [0, 0, 1, 5],\n [0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
864
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[[12, 4, -8, 0],\n [-6, -6, -5, 11],\n [5, 12, -3, 3],\n [-4, 10, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-58
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, -4, -5, -7],\n [-4, -7, 6, 1],\n [-5, 6, -4, -4],\n [-7, 1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
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, -10, 9, 1],\n [-10, -11, 2, -2],\n [-11, -2, -2, 5],\n [2, 12, 11, -11]]\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 value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -2, 4, -6],\n [-2, -9, -2, -2],\n [4, -2, 2, 4],\n [-6, -2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
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[[0, -7, 4, 9],\n [4, -5, -5, 11],\n [-1, -9, -5, 11],\n [-10, -10, 3, -2]]\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[[8, -7, 10, 8],\n [7, 1, -5, -3],\n [-9, -8, 11, 12],\n [-5, 1, 11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
250
MATH
[ { "content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[-2, 10, -2, 9],\n [10, -6, -9, -12],\n [-8, -2, 9, 3],\n [6, 8, -7, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-154
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, -9, 8, -5],\n [2, -11, 0, -6],\n [-7, 12, 11, 12],\n [-10, 7, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
108
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, -6, -8, -6],\n [-6, 7, -3, -2],\n [-8, -3, -10, -8],\n [-6, -2, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
110
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[[9, 9, 2, 7],\n [9, 4, -8, 10],\n [2, -8, 7, -4],\n [7, 10, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
148
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[5, 1, 10, 2],\n [-8, 12, -12, 10],\n [-11, 9, 8, 2],\n [12, -7, 3, 7]]\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[[10, 0, 7, 1],\n [0, -8, -8, -6],\n [0, 0, -6, 6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, 4, -4, -2],\n [4, 3, 4, -3],\n [-4, 4, -3, 3],\n [-2, -3, 3, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
77
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, 3, -3, 2],\n [3, 1, 2, 10],\n [-3, 2, 9, 2],\n [2, 10, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-52
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[11, -6, 10, -8],\n [0, -2, -11, -1],\n [0, 0, -4, -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" } ]
-50
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -2, -2, 4],\n [-2, -10, -6, 4],\n [-2, -6, -6, -4],\n [4, 4, -4, 6]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-4, -2, -6, 5],\n [4, 11, 2, 7],\n [1, 3, 10, 10],\n [12, 12, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
117
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[6, 12, -2, 8],\n [0, 10, -5, 12],\n [0, 0, -11, -12],\n [0, 0, 0, -12]]\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 absolute values of all entries rounded to the nearest integer?\n[[-2, -7, -2, 6],\n [0, -3, -8, -8],\n [0, 0, -5, 8],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
845
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[[-10, 5, -11, -3],\n [0, -12, 10, 8],\n [0, 0, -12, 8],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
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[[7, 8, -11, -11],\n [-11, -12, 8, 8],\n [-10, 4, 9, 1],\n [8, -2, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-21
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, 0, -4, -4],\n [0, 4, 4, 4],\n [-4, 4, -11, -9],\n [-4, 4, -9, 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 value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[5, -4, 12, -4],\n [5, -10, -10, 7],\n [0, -8, 11, -9],\n [9, 1, 10, -5]]\nRound your answer to the nearest integer.\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[5, 8, -5, 1],\n [0, -5, -11, -12],\n [0, 0, -12, 1],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
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[[1, 11, -1, 2],\n [-12, 7, -11, 12],\n [0, -10, -10, 1],\n [-12, -11, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
62
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, 9, -3, -7],\n [0, -5, -11, 7],\n [0, 0, -2, -3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-49
MATH
[ { "content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[-10, 2, 8, -6],\n [2, 10, -2, 2],\n [8, -2, 3, -3],\n [-6, 2, -3, -8]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -11, -8, 5],\n [0, -3, 0, 6],\n [0, 0, 4, 3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
278
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, 1, -3, -3],\n [-8, 12, 8, -8],\n [-9, -2, 10, -7],\n [-11, 12, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
113
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, -9, 9, -12],\n [11, -10, 5, -6],\n [-4, -6, 1, -9],\n [-6, 2, -8, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
133
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, -3, -11],\n [-2, -5, 1, 12],\n [-2, -10, -11, 3],\n [-7, -10, -8, -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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, 1, 8, 8],\n [-4, 0, 10, -1],\n [8, 8, 6, 6],\n [3, -1, -6, 7]]\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 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, -4, 2],\n [-6, 2, -10, 2],\n [-4, -10, -7, -6],\n [2, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
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, 8, 1, 6],\n [8, -8, -2, 0],\n [1, -2, 4, 4],\n [6, 0, 4, 1]]\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 (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -10, 7, -7],\n [1, -6, -3, -10],\n [3, 11, -10, -10],\n [12, 10, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, 7, 2, -2],\n [0, -8, 4, -5],\n [0, 0, -3, -6],\n [0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
841
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, 1, -6, 4],\n [1, -3, 0, 2],\n [-6, 0, -6, 2],\n [4, 2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
521
MATH
[ { "content": "Find the value at position (3, 2) of the inverse of matrix 1/96 * A where A =\n[[0, 4, -4, -5],\n [4, -9, 4, 2],\n [-4, 4, -4, 2],\n [-5, 2, 2, -12]]\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[5, 8, -3, 0],\n [8, 7, 0, 6],\n [-3, 0, 11, 6],\n [0, 6, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
193
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[[-9, -1, -2, -12],\n [0, -2, -5, 4],\n [0, 0, 8, 2],\n [0, 0, 0, 8]]\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[[10, 10, 8, 11],\n [7, -5, 5, 0],\n [-7, -11, -9, 9],\n [2, -11, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-31
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[[4, -12, 12, 8],\n [11, 0, -10, -8],\n [-11, -8, -12, 11],\n [-3, 0, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2622
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[0, -1, 6, -12],\n [-9, -2, 12, -7],\n [2, -4, 9, 8],\n [-3, 12, 2, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[1, 2, 2, 2],\n [2, -5, 7, -4],\n [2, 7, -11, -6],\n [2, -4, -6, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
933
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[[-12, -3, -1, 9],\n [2, 11, 8, -3],\n [-10, -5, 12, 1],\n [8, 12, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
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, 7, 0, 3],\n [0, 5, -9, -5],\n [0, 0, 11, 6],\n [0, 0, 0, -4]]\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 all entries rounded to the nearest integer?\n[[4, 4, 9, 2],\n [4, -11, 4, -4],\n [9, 4, 10, -8],\n [2, -4, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
49
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 12, 4, 10],\n [0, 12, -5, -6],\n [0, 0, -3, -5],\n [0, 0, 0, 11]]\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 absolute values of all entries rounded to the nearest integer?\n[[9, 12, 6, -7],\n [2, 0, -10, -7],\n [-5, -11, -12, 0],\n [7, -11, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
349
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, 3, 2],\n [0, 1, -6, -3],\n [3, -6, 6, -4],\n [2, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-19
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[[11, -3, 2, 3],\n [0, 8, -2, -1],\n [0, 0, -11, -12],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
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, -12, -4, -10],\n [-11, 2, -5, 3],\n [-10, 3, -2, 2],\n [11, -12, 7, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
63
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, -9, -7, -8],\n [5, -11, 9, 3],\n [8, 12, 12, 4],\n [5, -6, 10, -11]]\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[[-4, -2, 0, -1],\n [-2, -6, 2, -4],\n [0, 2, -5, 10],\n [-1, -4, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-29
MATH
[ { "content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[-4, -4, -2, 4],\n [-4, 10, 0, 0],\n [-2, 0, -12, 4],\n [4, 0, 4, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-44
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, -9, 11, 11],\n [1, -5, 10, -2],\n [-11, -2, 11, -4],\n [1, -1, 5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
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[[-7, -4, -8, -5],\n [8, 3, 9, -3],\n [6, 3, 1, -12],\n [6, -10, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 2, 1, -8],\n [2, -8, 4, -10],\n [1, 4, -2, 4],\n [-8, -10, 4, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4960
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, -6, -4],\n [-8, 2, 6, 1],\n [-6, 6, 8, 9],\n [-4, 1, 9, -6]]\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[4, 4, -4, -10],\n [4, 0, 10, -1],\n [-4, 10, -2, 8],\n [-10, -1, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
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, 2, -12],\n [0, 3, 9, 0],\n [0, 0, -2, 9],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-176
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, -1, 6, -4],\n [-1, 10, 7, -3],\n [6, 7, -5, 10],\n [-4, -3, 10, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
122
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -7, -4, 0],\n [0, 7, 0, -4],\n [0, 0, 3, 9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[5, -11, 0, -1],\n [-10, -3, 8, 4],\n [-3, 11, -6, -9],\n [6, -1, -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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, 0, 2, -4],\n [0, -11, 3, 8],\n [2, 3, -2, 0],\n [-4, 8, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-324
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, 12, -5, -8],\n [0, -6, 10, 10],\n [0, 0, 7, 9],\n [0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-5
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, 4, -3, -1],\n [4, 9, -2, 6],\n [-3, -2, -9, -3],\n [-1, 6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
146
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[[8, -11, 3, -6],\n [0, 12, 11, -3],\n [-6, -4, 6, -5],\n [-11, 1, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[7, -3, 8, 8],\n [9, 10, 2, 9],\n [8, -5, -6, 8],\n [2, -8, 3, -5]]\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 value at position (2, 2) rounded to the nearest integer?\n[[-12, 3, -7, 6],\n [12, 4, -5, -2],\n [-2, -7, -5, 10],\n [-9, 3, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[3, 0, 11, 3],\n [0, -6, 4, -7],\n [0, 0, 4, 2],\n [0, 0, 0, -9]]\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, 0, 3, 6],\n [-3, 11, -5, 0],\n [-3, 10, 12, 2],\n [4, -5, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Find the value at position (2, 3) of the inverse of matrix 1/96 * A where A =\n[[-8, 12, -2, 10],\n [0, 7, -4, -1],\n [0, 0, 2, 0],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
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, 5, 2, 8],\n [0, 1, 9, 1],\n [0, 0, 5, 2],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2021
MATH
[ { "content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[3, -7, -4, -10],\n [-8, 3, 10, 9],\n [-11, 12, 9, -1],\n [6, -10, -10, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
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, 6, -10, -10],\n [0, 9, 3, 6],\n [0, 0, -9, -6],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
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, -8, -6, -2],\n [-8, -11, 9, -8],\n [-6, 9, 2, 6],\n [-2, -8, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
472
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, 0, 2, 4],\n [-4, 11, -11, -7],\n [-11, -2, -5, -5],\n [8, -8, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
69
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, 11, -3, -6],\n [1, 0, 5, 8],\n [12, 7, -7, -4],\n [5, 7, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-46
MATH