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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 12, 11, 12],\n [7, -3, -3, 9],\n [-2, -9, 7, 10],\n [-10, 6, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-1
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, -6, 7, 4],\n [0, -9, -12, -11],\n [0, 0, -10, 2],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-48
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 2, 7, -8],\n [2, -4, 6, -2],\n [7, 6, 0, 3],\n [-8, -2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
57
|
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[[5, -9, 2, -6],\n [0, -1, 5, 3],\n [0, 0, -6, 11],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
848
|
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, -12, 1, 3],\n [-5, 4, -1, -4],\n [7, -4, 4, 0],\n [2, 10, 7, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-39
|
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, 12, 4, -12],\n [9, 11, -6, 7],\n [11, 10, -4, -6],\n [0, -5, 11, 3]]\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 value at position (1, 3) rounded to the nearest integer?\n[[-10, -3, -9, 0],\n [0, -10, 9, 11],\n [0, 0, 7, -1],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-16
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-1, -7, -6, 1],\n [-2, 5, 4, 0],\n [-3, 12, -5, -9],\n [2, 6, 6, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-101
|
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[[-5, 3, 9, 0],\n [-6, -7, -8, -3],\n [-9, 9, 9, 1],\n [11, 10, 12, -11]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 2, -7, 1],\n [6, -3, -5, 0],\n [-4, 4, 9, -5],\n [7, 6, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
144
|
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[[5, -7, 10, -3],\n [0, 12, 11, 5],\n [0, 0, -5, 1],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
98
|
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, 0, -12, -9],\n [0, -10, -12, 5],\n [0, 0, 5, 3],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
290
|
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, 8, -2, 9],\n [8, 0, -12, 0],\n [-12, -7, -10, 4],\n [10, 12, -12, -12]]\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 at position (1, 4) rounded to the nearest integer?\n[[7, 7, 7, -8],\n [0, 7, 2, -8],\n [0, 0, 10, 7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24
|
MATH
|
[
{
"content": "Find the value at position (4, 3) of the inverse of matrix 1/96 * A where A =\n[[2, 5, -9, 1],\n [6, -1, -1, 6],\n [-7, 9, 11, 11],\n [-1, -6, -6, 5]]\nRound your answer to the nearest integer.\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-11, -8, -6, -3],\n [0, 6, 7, 7],\n [0, 0, -5, -4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-96
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, -12, 4, -8],\n [0, 9, 6, 0],\n [0, 0, 4, -8],\n [0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
54
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[2, -6, -4, 3],\n [-6, -7, 6, 4],\n [-4, 6, -5, 2],\n [3, 4, 2, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-58
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[5, 3, 9, -9],\n [9, -7, 4, 8],\n [10, -11, 12, 3],\n [-9, 2, 3, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
47
|
MATH
|
[
{
"content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[-5, 10, -10, -1],\n [-2, 7, -4, -9],\n [4, 3, -3, -12],\n [1, -11, 4, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-10
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[9, 7, -6, -3],\n [0, 1, -4, -10],\n [0, 0, 4, -9],\n [0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
139
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[11, -10, 2, 1],\n [-10, 4, -6, 4],\n [2, -6, -3, 1],\n [1, 4, 1, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
497
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -7, -7, -5],\n [1, 6, -8, 11],\n [-9, 11, -4, -3],\n [8, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-4
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -3, -6, 5],\n [-3, -8, 2, -4],\n [-6, 2, -10, 7],\n [5, -4, 7, 2]]\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[[-11, 6, -2, -4],\n [-11, 12, -2, 11],\n [-10, 8, 9, 4],\n [-11, 1, -1, -5]]\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, -5, -9, 4],\n [5, -9, -6, 12],\n [-6, 0, 2, -8],\n [9, -5, 4, 1]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, -11, 3, -6],\n [-12, 11, 12, 9],\n [12, 8, -12, 4],\n [11, 4, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
233
|
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, -6, 6, -2],\n [-6, 12, -2, 4],\n [6, -2, -10, 9],\n [-2, 4, 9, -7]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 6, 5, 10],\n [0, 10, 1, -5],\n [0, 0, 11, 3],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
79
|
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, 0, 3, -11],\n [-7, -12, 5, 11],\n [5, 0, -12, 2],\n [-2, -6, 10, -11]]\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, -3, 0, 5],\n [0, -11, 10, 1],\n [0, 0, -5, -12],\n [0, 0, 0, -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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[1, -5, 0, 8],\n [-5, 5, -1, -2],\n [0, -1, 0, 2],\n [8, -2, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1941
|
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[[-9, 11, -10, -8],\n [-1, -3, 2, -6],\n [-12, -12, -1, 2],\n [5, 1, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
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[[-8, 6, -2, 9],\n [-2, -7, 1, 11],\n [3, 6, -6, -1],\n [11, 12, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[5, 0, -7, -9],\n [-3, 10, -7, -5],\n [9, 6, -12, -12],\n [-8, -1, 9, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
175
|
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[[12, -2, 0, -10],\n [-3, -12, -2, 3],\n [2, 3, -10, -5],\n [-3, 10, -4, -9]]\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 value at position (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -4, 2, -8],\n [-4, 2, 0, -2],\n [2, 0, 5, 1],\n [-8, -2, 1, 1]]\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 value at position (4, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -5, 11, 2],\n [6, 12, 0, 0],\n [6, 2, 0, -10],\n [-9, -9, 4, -2]]\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 all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 6, -4, -12],\n [-2, 7, 4, 6],\n [3, 8, 12, 5],\n [-3, 0, -3, -8]]\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 sum of all entries rounded to the nearest integer?\n[[-1, 3, -3, 8],\n [-8, -5, 11, 0],\n [-6, -11, -1, 10],\n [-7, 0, -11, -1]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, 7, -10, 12],\n [4, -1, 11, -9],\n [-1, 7, 4, -8],\n [-4, 12, -11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 9, 4, 3],\n [9, 12, -2, 3],\n [4, -2, 5, 10],\n [3, 3, 10, -9]]\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[[9, 5, 0, 9],\n [5, -1, 4, 4],\n [0, 4, -1, -8],\n [9, 4, -8, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[3, 5, 7, -5],\n [0, 1, 7, 1],\n [0, 0, 1, 2],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4960
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, -4, -6, -3],\n [0, -2, 8, 0],\n [0, 0, -9, 6],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
412
|
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[[12, -8, -4, 1],\n [11, -1, 0, -6],\n [11, 1, 11, 10],\n [-4, 8, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-85
|
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[[12, 11, 2, 8],\n [0, 5, 5, -5],\n [0, 0, 12, -4],\n [0, 0, 0, -2]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -1, 4, 1],\n [-8, -2, -10, -6],\n [8, 0, -2, 3],\n [-5, 5, 12, -8]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -1, 8, -2],\n [0, 12, 7, 1],\n [0, 0, 6, -1],\n [0, 0, 0, -5]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-12, -11, -4, -8],\n [0, -12, 3, -4],\n [0, 0, -6, 11],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-48
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[4, 3, 4, -2],\n [3, 5, -10, -2],\n [4, -10, -3, -9],\n [-2, -2, -9, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
51
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 1) of the inverse. Round your answer to the nearest integer:\n[[9, -12, -5, -10],\n [0, -3, -10, 9],\n [0, 0, -2, 1],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-1, 8, -6, 1],\n [0, 2, 8, 1],\n [0, 0, 12, 3],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-56
|
MATH
|
[
{
"content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[2, -5, 4, 1],\n [7, 4, 11, -8],\n [-4, 0, 1, -7],\n [-9, 2, 7, -9]]\nRound your answer to the nearest integer.\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[5, -6, 11, -2],\n [-8, -5, 2, 4],\n [10, -5, -9, 6],\n [4, -4, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
68
|
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, 10, 9],\n [0, -2, -10, 0],\n [0, 0, 6, 0],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-92
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -7, 7, -4],\n [4, 1, 0, 6],\n [11, 5, -3, -3],\n [9, 11, -11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
47
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, -1, 5, 1],\n [0, 4, -4, -1],\n [0, 0, 4, 3],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
168
|
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, -1, -2, -4],\n [-1, -6, -3, -4],\n [-2, -3, -4, 10],\n [-4, -4, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-209
|
MATH
|
[
{
"content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[-9, 0, 11, -6],\n [0, -5, -8, -2],\n [0, 0, -10, -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"
}
] |
0
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, -2, 1, 12],\n [-4, -12, 10, -4],\n [2, 1, 12, 9],\n [4, -10, -1, 2]]\nRound your answer to the nearest integer.\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[[5, -11, 6, -7],\n [7, -5, 9, -4],\n [-6, 0, -10, 8],\n [0, 0, 11, 10]]\nRound your answer to the nearest integer.\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -9, 6, 2],\n [0, -3, -1, 10],\n [0, 0, -10, -2],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
163
|
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, -8, 0, -9],\n [0, 2, -2, -3],\n [0, 0, 8, 3],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1080
|
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, -4, 8, -8],\n [0, -11, -2, 6],\n [0, 0, -7, -8],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
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, 10, -3],\n [-6, -3, 2, -8],\n [10, 2, 0, -4],\n [-3, -8, -4, 3]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-9, -12, -11, 3],\n [11, 3, 10, -8],\n [-7, 5, 0, 12],\n [1, 1, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[7, 2, 5, -12],\n [-7, -9, -12, -9],\n [-5, 11, -9, -10],\n [-12, 4, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-34
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -1, -1, 0],\n [-1, -6, -2, -2],\n [-1, -2, 9, 6],\n [0, -2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
MATH
|
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[10, 4, -11, 7],\n [0, -1, -7, -11],\n [0, 0, -12, -6],\n [0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
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[[-2, 6, 9, 1],\n [0, -2, -5, 11],\n [0, 0, -3, 10],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-29
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[12, -6, -4, 4],\n [-6, 6, -7, 11],\n [-4, -7, 1, 7],\n [4, 11, 7, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
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, -7, -7, 0],\n [-7, 4, 7, 11],\n [-1, -12, -7, -9],\n [-11, 1, 2, -8]]\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 sum of all entries rounded to the nearest integer?\n[[1, -10, -8, 8],\n [-5, 4, 9, -5],\n [2, 11, 11, -8],\n [8, -11, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
46
|
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, -12],\n [0, 7, 3, 1],\n [0, 0, -10, -10],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
64
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, -4, 7, 10],\n [-11, -4, -8, 5],\n [-3, 4, -9, -12],\n [-4, 1, -4, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6589
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[9, 6, 10, 6],\n [6, 0, -1, 8],\n [10, -1, -8, 6],\n [6, 8, 6, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
778
|
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[[12, 8, -11, -2],\n [10, 4, 11, -10],\n [-12, 8, 1, -8],\n [-5, -8, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-20
|
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[[-2, -3, 8, -7],\n [0, 6, -10, 6],\n [0, 0, 11, -6],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
178
|
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, -12, 8],\n [0, -8, -9, 4],\n [0, 0, -9, 7],\n [0, 0, 0, -11]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -7, 11, -3],\n [0, 3, -2, 11],\n [0, 0, 5, -11],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
277
|
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[[-12, 1, -6, 0],\n [1, -12, 2, 2],\n [-6, 2, 10, 0],\n [0, 2, 0, -9]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -11, 5, 6],\n [1, -3, -4, -12],\n [11, -8, -2, -12],\n [12, -9, 0, -2]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[7, 4, -11, 9],\n [0, 6, -7, -4],\n [0, 0, 6, -12],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-29
|
MATH
|
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[12, 5, -3, -3],\n [0, -6, -3, -3],\n [0, 0, -9, -3],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-16
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-8, -7, -2, 7],\n [0, -6, 10, -8],\n [0, 0, -5, -7],\n [0, 0, 0, 7]]\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[[10, -8, 8, 2],\n [-8, -10, -6, -4],\n [8, -6, 4, -1],\n [2, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
216
|
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[[3, -10, 4, -11],\n [-10, -2, 6, -2],\n [4, 6, 9, 0],\n [-11, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
147
|
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[[2, -8, -2, -7],\n [0, 2, -8, -7],\n [0, 0, 3, -8],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2541
|
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[[-12, 9, 6, -3],\n [8, 4, -1, 2],\n [7, 2, 11, 1],\n [-1, 8, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[-9, -3, 6, -1],\n [-10, 0, -3, -11],\n [9, 4, -7, -6],\n [-3, 7, -4, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-6
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, 10, 8, -6],\n [10, -1, -8, -4],\n [8, -8, -9, 6],\n [-6, -4, 6, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-217
|
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, -10, 5],\n [4, 2, -7, 1],\n [-10, -7, -1, 0],\n [5, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-57
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[12, 4, 2, 6],\n [4, 5, -8, -2],\n [2, -8, -11, -9],\n [6, -2, -9, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[3, -10, -2, -8],\n [0, -4, 12, -11],\n [0, 0, -12, 6],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-120
|
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, 4, 0, -1],\n [4, 12, 2, 4],\n [0, 2, 11, -4],\n [-1, 4, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
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, 1, 3, 2],\n [-10, -11, 6, 8],\n [-12, 3, 5, 10],\n [-5, -10, 8, -2]]\nRound your answer to the nearest integer.\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 all entries rounded to the nearest integer?\n[[-5, 0, 9, -4],\n [0, 1, 1, -8],\n [9, 1, 12, -6],\n [-4, -8, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-15
|
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[[-5, 3, 2, 1],\n [3, -12, -1, -4],\n [2, -1, -2, 6],\n [1, -4, 6, -2]]\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[[4, 7, -4, 2],\n [1, -12, 4, -8],\n [3, -3, -7, -11],\n [-6, -10, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
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