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[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[0, 12, 12, -1],\n [-11, 5, -8, 7],\n [7, 7, 0, -3],\n [-11, -5, 7, 5]]\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[[3, 2, -8, 4],\n [2, -9, -10, 6],\n [-8, -10, 9, 2],\n [4, 6, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1249
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-7, -6, -7, 2],\n [0, -7, 8, -3],\n [0, 0, -11, 2],\n [0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 3, -2, -2],\n [3, -11, -9, 2],\n [-2, -9, -4, 4],\n [-2, 2, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
149
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -2, -9, -7],\n [0, 5, 8, 2],\n [0, 0, -7, -7],\n [0, 0, 0, -10]]\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 value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[5, 2, -7, 8],\n [2, -12, -4, -5],\n [-7, -4, 0, 2],\n [8, -5, 2, 12]]\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 at position (3, 4) rounded to the nearest integer?\n[[-8, -4, 2, 8],\n [12, -11, -8, 8],\n [-8, -8, -2, -1],\n [5, 11, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-70
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-6, 8, 3, -6],\n [8, -12, -4, -8],\n [3, -4, 12, -8],\n [-6, -8, -8, 0]]\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[[1, -11, -8, -6],\n [5, 10, 7, -11],\n [-6, -11, -10, 8],\n [-12, 6, 9, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-54
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 0, -10, 4],\n [0, 1, 0, 6],\n [-10, 0, 9, 2],\n [4, 6, 2, -9]]\nRound your answer to the nearest integer.\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[[12, -10, 10, 4],\n [0, -5, 8, -10],\n [0, 0, 12, 12],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
583
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, -6, 4, -8],\n [-6, -2, -4, 3],\n [4, -4, -5, 0],\n [-8, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-70
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[1, -6, 10, -2],\n [-6, 11, 2, -2],\n [10, 2, 6, 0],\n [-2, -2, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, 4, 7, -6],\n [0, 12, -7, 9],\n [0, 0, 9, -6],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-33
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 8, -6, -6],\n [8, -11, 0, -8],\n [-6, 0, -4, -8],\n [-6, -8, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
139
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -12, -10, 7],\n [-6, -9, 4, 2],\n [1, -8, -2, 6],\n [3, 8, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, -8, -12, 4],\n [-7, -8, 11, 7],\n [2, 9, -1, 8],\n [-11, -8, 4, -12]]\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 all entries rounded to the nearest integer?\n[[-3, -12, 6, 9],\n [0, 9, -1, -3],\n [7, -12, -12, 1],\n [-6, 4, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2782
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[[2, -5, -5, 12],\n [6, -10, -6, 5],\n [-3, 2, 2, -4],\n [-2, -3, -2, 0]]\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[[-9, 4, -4, 2],\n [4, -6, 4, 10],\n [-4, 4, 2, 1],\n [2, 10, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, 9, -1, -9],\n [1, -3, 7, -3],\n [-8, -1, -4, 10],\n [11, -7, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, 4, 8, -6],\n [0, 8, -9, 2],\n [0, 0, 6, -3],\n [0, 0, 0, 7]]\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 value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 8, -1, 11],\n [8, 0, 0, 8],\n [-1, 0, 2, 1],\n [11, 8, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[-12, 5, 12, -7],\n [0, -12, -11, 4],\n [0, 0, 10, -10],\n [0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-3, 8, -2, 8],\n [8, 0, 2, -2],\n [-2, 2, 0, 4],\n [8, -2, 4, -2]]\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 all entries rounded to the nearest integer?\n[[-12, 2, 5, -8],\n [3, -5, -7, 3],\n [3, -3, -6, 7],\n [1, -6, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
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, 10, 8, 1],\n [12, 4, -11, 3],\n [9, -2, 0, -12],\n [-3, -7, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-38
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 4) rounded to the nearest integer?\n[[2, -2, 11, -3],\n [0, 12, -10, -3],\n [0, 0, -9, 3],\n [0, 0, 0, 6]]\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 at position (1, 4) rounded to the nearest integer?\n[[-6, -12, -4, -5],\n [0, -7, 8, -3],\n [0, 0, 7, -11],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-63
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, 2, 0, -4],\n [2, 1, -4, -6],\n [0, -4, 3, 8],\n [-4, -6, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-17
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, -6, 0, -1],\n [-6, -1, -5, -2],\n [0, -5, 9, -7],\n [-1, -2, -7, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
579
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[[5, 4, -5, -6],\n [4, -5, -2, 6],\n [-5, -2, -11, -2],\n [-6, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, 6, 8, 8],\n [0, -7, -9, -3],\n [0, 0, -3, 3],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
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, -1, 3, -10],\n [-1, -6, -4, 7],\n [3, -4, 2, 0],\n [-10, 7, 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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -8, 4, 6],\n [-8, 4, -8, 0],\n [4, -8, -11, 5],\n [6, 0, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-23
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -10, 0, -7],\n [10, -1, -1, -7],\n [12, -12, 5, -5],\n [-11, 5, 5, 4]]\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 value at position (4, 1) rounded to the nearest integer?\n[[-3, -9, -5, 7],\n [0, 7, -1, 2],\n [0, 0, -5, -8],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 5, 10, 7],\n [0, 3, -1, 9],\n [0, 0, 7, -11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
102
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[[-7, -8, -3, 3],\n [-8, 9, 2, 10],\n [-3, 2, -8, 4],\n [3, 10, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-38
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[1, 5, -10, 11],\n [0, -11, 0, -3],\n [-10, 6, -2, -5],\n [2, -5, 11, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
43
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, -6, 9, -2],\n [-6, 2, -3, 1],\n [9, -3, -1, 0],\n [-2, 1, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
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, -2, -2],\n [1, -7, 0, 0],\n [-2, 0, -9, -10],\n [-2, 0, -10, 11]]\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[[-6, -11, 8, -8],\n [0, 5, 6, 1],\n [0, 0, 9, 12],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-50
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[10, 4, 6, 0],\n [4, 4, 3, -1],\n [6, 3, -6, 5],\n [0, -1, 5, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
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[[-7, 2, 1, 2],\n [2, -11, -4, -4],\n [1, -4, -4, -2],\n [2, -4, -2, 8]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[7, 10, 5, -6],\n [0, 7, 3, -1],\n [-9, 11, -1, 9],\n [-11, -12, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
377
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, 5, 2, -7],\n [0, -6, 1, 3],\n [0, 0, 7, 9],\n [0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
129
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[0, -4, -1, -1],\n [-4, 2, -9, -10],\n [-1, -9, 9, 4],\n [-1, -10, 4, 3]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[5, 4, 10, 5],\n [1, 11, -9, -11],\n [-10, 2, -10, -5],\n [-10, 12, 1, -11]]\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[[-3, 7, 6, 6],\n [-12, -5, -11, -4],\n [-3, 9, 6, 2],\n [-1, 3, -11, 5]]\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 value at position (3, 4) rounded to the nearest integer?\n[[6, -4, 6, -6],\n [0, 9, -6, -1],\n [0, 0, -4, -11],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
44
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, -2, 6, 3],\n [-2, -12, 1, 10],\n [6, 1, 7, 8],\n [3, 10, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 2, 11, -1],\n [2, 3, 8, 2],\n [11, 8, -8, -8],\n [-1, 2, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 0, 2, 8],\n [0, -8, -4, 7],\n [2, -4, -8, -2],\n [8, 7, -2, -1]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[12, -4, 3, 5],\n [-9, -10, -4, -10],\n [0, 6, -2, 4],\n [10, 6, -12, 0]]\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[[-9, -4, 8, 3],\n [0, -2, -9, -6],\n [0, 0, -2, -3],\n [0, 0, 0, -7]]\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[[9, -11, 2, -11],\n [7, 4, -12, 10],\n [3, -6, -3, -3],\n [-6, 9, 9, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
348
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -11, -11, -1],\n [0, -4, -9, 10],\n [0, 0, -12, -9],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-24
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[[9, 0, -4, -8],\n [0, -1, 6, -2],\n [-4, 6, 0, -6],\n [-8, -2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-4
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, 5, -11, 8],\n [-2, 8, 10, -5],\n [8, 2, -1, 10],\n [7, 12, -9, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -2, 4, 6],\n [-2, -4, -4, 2],\n [4, -4, 11, 0],\n [6, 2, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
MATH
[ { "content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[4, 3, 1, 1],\n [3, 10, 4, 9],\n [1, 4, -12, 6],\n [1, 9, 6, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[8, 2, 0, 4],\n [2, -2, 6, 3],\n [0, 6, -7, -2],\n [4, 3, -2, 2]]\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, 8, 5, 8],\n [0, 7, -9, 9],\n [0, 0, -12, 9],\n [0, 0, 0, -3]]\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 sum of all entries rounded to the nearest integer?\n[[8, 3, -2, -1],\n [3, 3, -2, -2],\n [-2, -2, -5, -9],\n [-1, -2, -9, 6]]\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 value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[8, -8, -4, -9],\n [0, 4, -8, -6],\n [0, 0, 9, 5],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
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, -3, 12, 10],\n [10, 3, -8, 6],\n [-3, -7, -1, -1],\n [1, 8, 11, -7]]\nRound your answer to the nearest integer.\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[[8, 0, -4, -1],\n [0, 12, -6, -2],\n [-4, -6, 8, -2],\n [-1, -2, -2, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
343
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, -1, 6],\n [2, -4, 0, 4],\n [-1, 0, 12, 2],\n [6, 4, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[9, 12, 2, -2],\n [3, 2, 11, 4],\n [-6, 4, -2, -9],\n [0, 9, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 5, 10, 12],\n [1, 8, 11, 4],\n [10, 0, -9, -7],\n [0, -6, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
396
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[[0, 11, 8, 3],\n [4, 4, -2, 12],\n [-9, 3, -2, -11],\n [8, -11, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1329
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, 9, -2],\n [-4, 10, -3, 4],\n [9, -3, -7, 0],\n [-2, 4, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-209
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, 3, -8, 7],\n [3, 11, 8, 4],\n [-8, 8, -4, -1],\n [7, 4, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-9
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-7, -4, 8, -6],\n [0, -5, -2, -12],\n [0, 0, 1, -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" } ]
75
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -9, 12, 3],\n [7, -3, -12, -2],\n [4, 2, -10, -1],\n [-5, 2, -2, 7]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[12, 6, 6, 8],\n [6, 0, 0, 8],\n [6, 0, 2, -2],\n [8, 8, -2, 12]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, -5, -8, -6],\n [-5, 10, 7, -7],\n [-8, 7, 0, -4],\n [-6, -7, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
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, -9, -11, -5],\n [0, -8, -8, -12],\n [0, 0, 2, -5],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
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, -7, -6, 4],\n [-7, 0, 7, -7],\n [-6, 7, -2, -2],\n [4, -7, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-353
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, 6, -6, 2],\n [6, 2, 4, 6],\n [-6, 4, 6, 0],\n [2, 6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
116
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, 4, 4, -6],\n [1, -1, 6, 6],\n [3, -1, 8, -5],\n [10, 10, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
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[[-12, 3, 2, -11],\n [0, 8, -1, -3],\n [0, 0, 1, 5],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-8
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[10, 1, -7, -11],\n [0, -1, 9, 6],\n [0, 0, 4, -4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
597
MATH
[ { "content": "Find the value at position (1, 1) of the inverse of matrix 1/96 * A where A =\n[[-4, 3, -10, 3],\n [-10, -10, -8, 4],\n [-9, 12, 7, -2],\n [-2, -9, -2, 1]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -2, 1, 10],\n [0, -1, -5, -10],\n [0, 0, -8, 0],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1900
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, 2, 2, 0],\n [2, 5, -3, 10],\n [2, -3, -1, -2],\n [0, 10, -2, -9]]\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 11, -5, 9],\n [0, 10, 9, -5],\n [0, 0, -7, -7],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2016
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, -1, -8, 9],\n [10, -9, 12, -5],\n [-12, -4, 1, 2],\n [-12, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
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, -1, 4, -6],\n [-1, -8, -10, 1],\n [4, -10, -11, 4],\n [-6, 1, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[2, -9, 1, -9],\n [0, -11, -11, -2],\n [0, 0, 4, -6],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-120
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, -12, 11, 6],\n [0, 12, -9, 8],\n [0, 0, 2, -3],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
123
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[11, 5, -10, 12],\n [0, -10, 9, 6],\n [0, 0, -8, 9],\n [0, 0, 0, 4]]\nRound your answer to the nearest integer.\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[11, 2, -1, 4],\n [2, -8, 11, -1],\n [-1, 11, 1, -6],\n [4, -1, -6, -10]]\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 at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[4, -4, 4, 1],\n [-4, -6, 0, -5],\n [4, 0, -8, -6],\n [1, -5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16
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[[6, 8, -12, 0],\n [12, -9, 4, 12],\n [12, 10, 1, -4],\n [-2, -1, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-151
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, -3, 3, -3],\n [12, -9, -5, 0],\n [1, -1, -6, 9],\n [5, -9, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
117
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-4, -10, 8, -6],\n [-10, 6, -6, 0],\n [8, -6, -3, 8],\n [-6, 0, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-5
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 1, 7, 1],\n [-7, 7, 11, -8],\n [12, 12, 10, 12],\n [-7, -3, -6, 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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -2, 0, 2],\n [-2, 5, -5, 4],\n [0, -5, -7, 11],\n [2, 4, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH