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[ { "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[[-9, -7, -2, 5],\n [4, -10, -6, -10],\n [6, -4, -10, 6],\n [-5, 7, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
59
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[[-9, 11, -2, -7],\n [-12, 2, 5, -9],\n [2, -3, 12, -6],\n [5, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
133
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, 4, -8],\n [4, 9, -10, 8],\n [4, -10, 8, -5],\n [-8, 8, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
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, -8, 2, 5],\n [-8, -12, 2, -6],\n [2, 2, 3, 0],\n [5, -6, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
126
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, -9, -9, -8],\n [0, -6, -5, -5],\n [0, 0, 3, -2],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
131
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, 6, 12, 8],\n [0, 1, -7, 6],\n [0, 0, 8, -4],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -3, 2, -10],\n [-6, 10, -12, -7],\n [2, -10, 12, 0],\n [-4, 6, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
332
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 6, 10, -7],\n [0, 4, 11, -3],\n [-9, 10, -7, 0],\n [-6, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
135
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, -4, -9, -6],\n [-4, 1, 6, -4],\n [-9, 6, -8, -3],\n [-6, -4, -3, 9]]\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 sum of all entries rounded to the nearest integer?\n[[-11, 2, 3, 7],\n [0, 2, 11, 11],\n [0, 0, 1, -2],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1189
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[6, -4, -3, -11],\n [-3, -11, -4, -4],\n [3, 4, -12, 5],\n [-1, 3, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, -10, 11, 8],\n [-1, 3, -10, 6],\n [8, 12, 10, -11],\n [-2, 6, -4, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[-3, -11, 3, -6],\n [0, 7, 0, -6],\n [0, 0, 1, -8],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, -2, 7, -4],\n [-2, -2, -2, 0],\n [7, -2, 4, -4],\n [-4, 0, -4, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-96
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[8, 1, 0, 4],\n [1, -12, 4, 4],\n [0, 4, -7, 5],\n [4, 4, 5, 9]]\nRound your answer to the nearest integer.\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[[4, -8, 11, -4],\n [8, -7, -3, -7],\n [-5, -11, 12, 4],\n [11, 1, 1, 11]]\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[[9, -7, 6, 2],\n [1, -6, 12, 3],\n [-4, 0, 12, -12],\n [-8, 7, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-390
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[1, 3, -3, -10],\n [11, -10, 12, -4],\n [-6, -5, 6, 11],\n [-8, 5, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-64
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[[11, 10, -10, 4],\n [0, 1, -5, -12],\n [0, 0, 5, 3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[-5, -6, 10, 0],\n [-6, -5, -2, 0],\n [10, -2, -3, 0],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 9, 0, 1],\n [9, 8, -1, -4],\n [0, -1, -5, 8],\n [1, -4, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
67
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, 0, 6, -12],\n [-2, 0, 6, 5],\n [8, 3, 4, -12],\n [5, -9, 1, 5]]\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[[8, 4, -2, 3],\n [4, 10, 1, -8],\n [-2, 1, 10, 1],\n [3, -8, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, -2, -7, -1],\n [0, 3, 6, -7],\n [0, 0, 5, 7],\n [0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
201
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, 7, 3, -4],\n [2, 8, 0, 12],\n [-4, -7, -12, -9],\n [-9, -7, 11, -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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[10, -7, -6, -3],\n [0, -10, -5, 12],\n [0, 0, 3, -3],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
475
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 7, -2, -2],\n [7, -12, 2, 4],\n [-2, 2, 10, -4],\n [-2, 4, -4, -3]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 4, -3, -2],\n [0, 12, -3, -3],\n [0, 0, -7, 11],\n [0, 0, 0, -7]]\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 value at position (2, 3) rounded to the nearest integer?\n[[-4, 3, -12, 9],\n [8, 7, -2, 7],\n [-3, 7, 4, 5],\n [12, -1, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-4, 3, -5, -6],\n [-12, -6, 7, 11],\n [7, 1, 6, -6],\n [6, -8, -7, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-40
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, 11, -4],\n [0, 2, -5, 0],\n [0, 0, -8, 5],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
63
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-2, 6, 5, 7],\n [0, -1, 11, -2],\n [0, 0, -9, -8],\n [0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1426
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -4, -11, 2],\n [0, 11, 4, 2],\n [0, 0, -7, -1],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-24
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[4, 8, 1, -2],\n [8, 8, -4, 5],\n [1, -4, 9, -10],\n [-2, 5, -10, 5]]\nRound your answer to the nearest integer.\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 value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[2, 3, 12, 2],\n [3, -8, 0, -1],\n [12, 0, -9, -4],\n [2, -1, -4, 2]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 10, -6, -6],\n [10, 9, -4, 0],\n [-6, -4, 1, 4],\n [-6, 0, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-12, -8, -1, -8],\n [-8, 6, 4, 4],\n [-1, 4, -1, 7],\n [-8, 4, 7, 6]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, 11, -9, 5],\n [12, -7, -6, 8],\n [-9, 4, -9, -5],\n [-9, 11, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
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, 12, -8, -3],\n [0, 6, 6, -11],\n [0, 0, 11, -2],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-141
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, 0, 2, 4],\n [-2, -11, -1, -9],\n [-2, -6, 6, 3],\n [-8, 11, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-127
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[[2, 4, 6, 7],\n [3, 5, 9, 1],\n [11, 1, 3, 4],\n [5, 4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
129
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, -5, 4, -12],\n [-6, -9, -3, 2],\n [8, 0, 6, 5],\n [1, 7, -11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-46
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -1, -2, -2],\n [-11, 8, -4, -11],\n [-7, 6, -2, -3],\n [-1, 9, 8, 0]]\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[[5, -4, -4, -10],\n [11, 2, -11, -7],\n [-4, 7, -9, -5],\n [-6, 6, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
284
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 3, 11, -10],\n [-4, -3, 2, 6],\n [9, 3, -6, 4],\n [-6, 1, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
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, -9, -11, 2],\n [7, 6, -4, -11],\n [-4, 7, 2, -7],\n [-10, 7, -2, 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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-9, -2, 11, -12],\n [4, 5, 6, 4],\n [12, 4, -11, -11],\n [-3, 8, -10, 5]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 4, 1, 0],\n [4, -3, -6, 0],\n [1, -6, 10, -1],\n [0, 0, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-238
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, -3, 3, 2],\n [-2, 11, 7, -8],\n [5, 8, -10, -9],\n [1, -6, -1, -5]]\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, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -3, 0, 4],\n [6, 1, 0, 0],\n [-11, -6, 4, -7],\n [3, -7, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 4) rounded to the nearest integer?\n[[-10, -10, -8, -5],\n [-7, -9, -11, -9],\n [9, -4, -11, -9],\n [-12, -5, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
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, 6, -3, -4],\n [6, -7, -8, 6],\n [-3, -8, 12, 0],\n [-4, 6, 0, 9]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -7, -2, -4],\n [0, -12, 7, 4],\n [0, 0, -1, -11],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2406
MATH
[ { "content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[1, -8, -9, 4],\n [-10, 3, 6, 12],\n [-8, 5, 3, 9],\n [-4, 3, -5, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-9, 4, 8, -11],\n [3, 5, 0, 3],\n [-1, -12, 0, 11],\n [4, -6, 0, 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 value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-2, -5, -3, -4],\n [0, 2, 4, -3],\n [0, 0, 4, -10],\n [0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
168
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, -7, -8, 10],\n [0, -8, 10, 11],\n [0, 0, -12, 12],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-897
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, -5, 7, 2],\n [0, 12, -5, 10],\n [0, 0, -1, 4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-118
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, -4, 6, -8],\n [-4, -12, -4, 6],\n [6, -4, 9, 3],\n [-8, 6, 3, 4]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-9, 4, 8, 2],\n [4, -7, 0, -4],\n [8, 0, 8, 6],\n [2, -4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-181
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, 1, 9, -12],\n [-4, 3, 6, -5],\n [-1, -4, -2, -10],\n [9, 2, 7, 8]]\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, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -2, 2, 9],\n [-2, 4, 7, 10],\n [2, 7, 10, 0],\n [9, 10, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[3, -1, -7, 3],\n [-3, -5, 1, 1],\n [2, 2, 9, -1],\n [-8, -10, 4, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[8, -2, -1, -1],\n [0, -4, 6, 11],\n [0, 0, -9, 10],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
226
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-1, -6, 2, -1],\n [-6, 8, 8, 0],\n [2, 8, -11, -4],\n [-1, 0, -4, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-30
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-12, -2, 2, -8],\n [0, -10, 5, -7],\n [0, 0, -5, -9],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
294
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[5, 4, -8, -3],\n [4, 8, -8, 0],\n [-8, -8, 11, -6],\n [-3, 0, -6, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
142
MATH
[ { "content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[0, 10, -1, -8],\n [10, 10, -9, 5],\n [-7, 0, -5, 11],\n [0, -2, 12, -4]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-7, -10, -2, -10],\n [0, 9, 8, -3],\n [0, 0, 6, 7],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
165
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[[-6, 10, 11, 2],\n [8, -12, -7, 0],\n [11, -3, 6, 3],\n [-6, 8, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-39
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[[7, -5, -2, -6],\n [1, 1, 6, -3],\n [11, 2, 2, 9],\n [9, -3, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[8, -8, -5, 4],\n [0, -7, -10, 2],\n [0, 0, 2, 8],\n [0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
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[[6, -8, -4, 4],\n [-8, -7, 0, 6],\n [-4, 0, -8, -12],\n [4, 6, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-22
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[12, -4, 6, 5],\n [-4, -7, -4, 0],\n [6, -4, -3, -2],\n [5, 0, -2, 9]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 9, 0, 9],\n [0, -8, 6, -9],\n [0, 0, -8, -1],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
102
MATH
[ { "content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[3, 1, -7, -12],\n [0, 8, -2, -9],\n [0, 0, -4, -1],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-74
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, 2, -2, -2],\n [2, 5, -2, 4],\n [-2, -2, -2, -2],\n [-2, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-9, 9, 3, 11],\n [0, 11, -7, -9],\n [0, 0, -10, -11],\n [0, 0, 0, -5]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[8, -4, -7, -5],\n [0, -8, -6, 2],\n [0, 0, -11, -10],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
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, 7, 6, 1],\n [-1, -1, 8, -8],\n [-8, -3, 2, 10],\n [1, -12, -3, 9]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, -4, 1, -9],\n [-4, -5, 3, 11],\n [-4, -9, 11, 9],\n [2, 9, 9, -10]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 11, -8, -5],\n [4, 3, 7, 6],\n [-5, 8, 8, 10],\n [12, 6, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
549
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, 3, -7, -11],\n [0, -10, 11, -11],\n [0, 0, 5, 11],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -5, 2, 0],\n [-5, -9, 4, 2],\n [2, 4, -3, 0],\n [0, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -3, -8, 5],\n [-3, -7, -10, 4],\n [-8, -10, -8, 0],\n [5, 4, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
253
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[2, -1, 11, 2],\n [0, 2, 11, 4],\n [-12, -12, 8, 11],\n [-4, 6, 2, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
93
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, -5, 4, -10],\n [0, -10, -4, 7],\n [0, 0, -6, 3],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[3, -5, -3, -3],\n [9, -3, -5, 8],\n [1, -1, -7, -11],\n [9, 7, 3, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
129
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[1, -2, -8, 2],\n [-2, -1, 2, 4],\n [-8, 2, 11, 4],\n [2, 4, 4, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-224
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, 0, -4, -7],\n [0, 11, -4, -6],\n [-4, -4, 4, 0],\n [-7, -6, 0, 5]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 7, 0, -4],\n [7, 7, 9, -1],\n [-5, 6, -1, -3],\n [-8, 12, -11, 2]]\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 sum of all entries rounded to the nearest integer?\n[[-7, 3, 3, -6],\n [3, -9, -6, 7],\n [3, -6, 12, -2],\n [-6, 7, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-77
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[[0, 4, 2, 2],\n [4, -11, 0, -2],\n [2, 0, 8, -2],\n [2, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1463
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, -8, 11],\n [-1, -12, -1, 5],\n [7, -5, 0, 7],\n [4, 11, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
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, 9, 5, -4],\n [6, 10, 8, -5],\n [-6, 10, 6, 8],\n [-1, 2, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, 12, 0, -3],\n [0, -9, -6, 5],\n [0, 0, -10, 12],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-39
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, -9, 3, -1],\n [-9, 4, 8, 2],\n [3, 8, 1, -2],\n [-1, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-125
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[3, -11, -11, -4],\n [11, 0, -1, -4],\n [10, 10, -12, 3],\n [-6, 3, -11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2
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, 10, 4, -10],\n [0, 8, 3, 10],\n [0, 0, 2, 12],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-20
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, 3, 7, -2],\n [6, -5, -1, -5],\n [7, -6, 5, 2],\n [-6, -10, 9, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH