messages
listlengths 1
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stringlengths 1
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| dataset
stringclasses 1
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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
|
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