messages
listlengths 1
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stringlengths 1
6
| dataset
stringclasses 1
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|---|---|---|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[0, 6, -2, 2],\n [6, -2, -1, -4],\n [-2, -1, -10, 2],\n [2, -4, 2, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
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[[4, -6, -1, 11],\n [-12, 2, 6, 3],\n [-4, 12, -11, 7],\n [8, -4, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
156
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -4, 0, 8],\n [-4, -12, 0, -1],\n [0, 0, -10, 0],\n [8, -1, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
189
|
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[[12, -10, -11, 6],\n [0, -7, -8, -3],\n [0, 0, -5, 2],\n [0, 0, 0, -4]]\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[[11, 5, 3, -4],\n [0, -8, -10, 7],\n [0, 0, -12, -12],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
68
|
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, 6, -3, 12],\n [6, 11, -4, 7],\n [-3, -4, 6, -4],\n [12, 7, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
471
|
MATH
|
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/96 * A where A =\n[[-10, 5, 6, -8],\n [0, 10, -4, 10],\n [0, 0, 2, 11],\n [0, 0, 0, -7]]\nRound your answer to the nearest integer.\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 all entries rounded to the nearest integer?\n[[-3, 0, -6, 4],\n [0, 3, 2, 7],\n [-6, 2, 8, -3],\n [4, 7, -3, 3]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 9, 11, 4],\n [0, -6, -12, 1],\n [0, 0, -12, -4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
277
|
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, -2, -9, 6],\n [5, -2, -1, -2],\n [-10, 5, 12, -3],\n [-7, -9, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
97
|
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, 0, -10, 12],\n [-12, 3, 8, -3],\n [-2, 3, -10, 5],\n [5, -12, 4, -12]]\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, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 2, 1, -2],\n [0, 6, -10, -5],\n [0, 0, -1, -9],\n [0, 0, 0, -11]]\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 value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -6, 11, 7],\n [0, -10, 4, 5],\n [0, 0, 3, -1],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-10
|
MATH
|
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[1, -1, 1, -1],\n [2, -11, -5, -10],\n [-7, 6, 6, 1],\n [3, -9, 6, -2]]\nRound your answer to the nearest integer.\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[[-7, -8, -6, -7],\n [0, -3, -9, -3],\n [-3, -10, 0, -6],\n [7, -11, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
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, -2, 1, -7],\n [-2, 0, 4, -8],\n [1, 4, -1, 0],\n [-7, -8, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-92
|
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[[6, 11, -3, 8],\n [-10, 0, -2, -5],\n [-7, 1, 11, 11],\n [6, 11, 8, -3]]\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 (4, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -1, -3, -8],\n [0, 5, 0, 8],\n [0, 0, 6, -8],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[6, -7, 11, -11],\n [0, -5, 1, 6],\n [0, 0, -11, 12],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
126
|
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[[-11, 1, 1, -8],\n [0, 2, -1, 5],\n [0, 0, -10, -1],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
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, 2, 1, 10],\n [-1, -4, 6, 10],\n [2, 0, 3, -2],\n [5, -2, -12, 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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-10, -8, 9, -6],\n [-8, -6, -8, 4],\n [9, -8, 0, -8],\n [-6, 4, -8, -8]]\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[[7, -4, 5, 11],\n [-4, 8, 10, 0],\n [5, 10, 7, 1],\n [11, 0, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
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[[5, 7, 5, 2],\n [12, 5, 1, 10],\n [-1, 12, 1, -2],\n [-4, -6, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
MATH
|
[
{
"content": "Find the value at position (4, 3) of the inverse of matrix 1/96 * A where A =\n[[-12, 3, -12, 6],\n [10, -12, 12, 12],\n [-6, 6, 0, -4],\n [-2, -5, -8, -4]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 11, 10, -11],\n [0, 2, -9, -12],\n [0, 0, -8, -7],\n [0, 0, 0, -10]]\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 value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -3, 5, 4],\n [-8, 11, -7, -4],\n [1, 6, -7, 11],\n [8, 8, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, -8, -8, -6],\n [-8, -5, 1, -4],\n [-8, 1, -10, 1],\n [-6, -4, 1, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
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, -8, 4, -9],\n [0, 7, 5, 3],\n [0, 0, -6, 7],\n [0, 0, 0, 9]]\nRound your answer to the nearest integer.\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 2, -12, -2],\n [0, 5, 5, 0],\n [0, 0, -2, -10],\n [0, 0, 0, -5]]\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[[-12, -11, 3, 6],\n [8, -11, 5, 9],\n [-9, -1, 5, 1],\n [1, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-45
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-12, -8, -4, 0],\n [-8, 0, -10, 5],\n [-4, -10, 9, 0],\n [0, 5, 0, -3]]\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[[3, -6, 6, -7],\n [0, -7, 8, 0],\n [0, 0, 9, -10],\n [0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
596
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[10, 4, 3, -8],\n [-12, 2, 5, -9],\n [4, 6, -2, -11],\n [8, 12, 9, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, -6, -11, -4],\n [6, 10, 9, 5],\n [-8, 0, -11, -12],\n [-11, -2, -6, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4261
|
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[[-7, -8, 3, -7],\n [-6, 5, -6, 12],\n [-5, -9, -2, -5],\n [6, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-659
|
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, 2, 0, 12],\n [-4, 10, 4, -6],\n [-6, -7, 0, 9],\n [-1, -11, 7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
39
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, 4, 0, 5],\n [4, -2, 10, -6],\n [0, 10, -3, 2],\n [5, -6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
111
|
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[[-2, 4, -6, 7],\n [-4, -7, -12, -4],\n [9, -2, -10, 6],\n [-12, 11, -12, -7]]\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 (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -1, 12, -12],\n [0, -5, -12, -2],\n [-8, 8, 8, -12],\n [10, 10, 7, -4]]\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 (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -9, 0, 8],\n [7, 12, 7, -1],\n [4, -6, 5, 7],\n [3, -11, 5, 0]]\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 (4, 2) of the inverse. Round your answer to the nearest integer:\n[[2, -12, -9, 8],\n [-3, -2, 5, 6],\n [3, 0, 3, 8],\n [2, 0, 4, 3]]\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[[-2, -6, 2, 2],\n [0, -8, 7, -4],\n [0, 0, -10, -1],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
338
|
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, 10, -10, 8],\n [10, -11, -2, 4],\n [-10, -2, 1, 8],\n [8, 4, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-9, 2, -2, -4],\n [-6, 3, -3, 1],\n [11, 5, 12, 5],\n [-6, -12, -2, -3]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, -10, 10, -11],\n [0, -10, 5, -9],\n [0, 0, -4, -7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
110
|
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, 2, 5, 7],\n [12, -7, -9, 4],\n [10, -6, 2, 1],\n [5, 7, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[6, -8, 0, -8],\n [-8, -7, -4, 0],\n [0, -4, 0, -3],\n [-8, 0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 2, -8, -11],\n [0, -10, 6, 0],\n [0, 0, 11, 0],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
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, 4, 3, -10],\n [0, 7, -1, -8],\n [0, 0, 4, 3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-26
|
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[[7, -1, -2, -3],\n [6, -10, -5, 7],\n [-7, -3, -9, -11],\n [-4, 4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[6, -8, 10, 11],\n [0, -11, -1, -6],\n [0, 0, -11, -11],\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": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[5, -4, -7, 7],\n [0, -9, -5, 7],\n [0, 0, 5, 7],\n [0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
38
|
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, 2, 12],\n [0, 12, -8, 11],\n [0, 0, -3, 3],\n [0, 0, 0, -7]]\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[[3, 0, -4, 9],\n [-10, 8, 0, -9],\n [-12, 4, -4, 5],\n [4, 1, -12, -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 value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[7, 12, 10, -5],\n [0, 4, 8, 10],\n [0, 0, -9, 0],\n [0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
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, -2, -12, -11],\n [0, -10, -9, 5],\n [0, 0, 3, 7],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
481
|
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[[10, 5, 10, 0],\n [0, -10, -7, -5],\n [0, 0, -10, 5],\n [0, 0, 0, -4]]\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 value at position (4, 2) rounded to the nearest integer?\n[[12, -6, 6, 2],\n [0, 9, 7, -1],\n [0, 0, -6, 8],\n [0, 0, 0, -2]]\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 (1, 1) rounded to the nearest integer?\n[[-6, -9, 8, -10],\n [1, -1, 8, 7],\n [-11, 10, 6, -10],\n [12, -12, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-98
|
MATH
|
[
{
"content": "Find the value at position (2, 2) of the inverse of matrix 1/96 * A where A =\n[[6, 0, 8, 5],\n [-5, -12, -4, -3],\n [-9, -10, -12, -9],\n [4, -2, -1, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-2
|
MATH
|
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[-7, -8, -3, 2],\n [-8, 6, 0, 8],\n [-3, 0, -8, 2],\n [2, 8, 2, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-13
|
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[[9, 0, -3, -6],\n [0, 3, 3, 5],\n [-3, 3, -10, 4],\n [-6, 5, 4, -3]]\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 (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 0, -8, -9],\n [0, 10, 3, 10],\n [0, 0, 11, 11],\n [0, 0, 0, -4]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, 10, 3, 2],\n [10, 8, 8, -2],\n [3, 8, -8, 6],\n [2, -2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
175
|
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, -11, -1, -2],\n [0, 10, 9, 10],\n [0, 0, 3, -11],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1572
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 9, -10, 0],\n [0, -6, -6, -5],\n [0, 0, 8, 10],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
422
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, 3, 1, 2],\n [0, -1, -5, 6],\n [0, 0, 2, -6],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-45
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[1, 1, 2, 2],\n [1, 2, 5, -6],\n [2, 5, -5, 6],\n [2, -6, 6, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
77
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, -10, 7, 8],\n [-6, 6, -1, -6],\n [-3, -8, -9, 12],\n [4, 10, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-61
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, -11, -2, -9],\n [-11, 7, -2, 4],\n [-2, -2, -8, 10],\n [-9, 4, 10, 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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[11, 4, 0, -11],\n [3, -10, 12, 5],\n [-11, 4, 10, 12],\n [-8, -6, 3, 4]]\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, -4, 6, -4],\n [0, 8, -8, 4],\n [0, 0, -8, -3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
117
|
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, 10, -2, -4],\n [10, 2, -2, 0],\n [-2, -2, 8, 2],\n [-4, 0, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-16
|
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[[0, -12, 2, -8],\n [-4, 12, 12, 0],\n [11, 5, -8, 0],\n [-11, -1, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
278
|
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, -3, 8, -2],\n [-3, 8, 6, 6],\n [8, 6, 1, 6],\n [-2, 6, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-3
|
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[[-3, -2, 7, 11],\n [0, -8, 2, -8],\n [-8, -2, -6, 9],\n [-1, -12, 1, -3]]\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 (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 11, -11, -12],\n [0, 6, -3, 1],\n [0, 0, 12, 6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
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[[11, 7, -6, 1],\n [0, -8, 0, 5],\n [0, 0, -8, -1],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
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, 12, 8, -5],\n [-6, 0, -11, 12],\n [-11, 3, 5, 1],\n [-6, 12, -12, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
41
|
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, 8, -5, 0],\n [0, 7, -8, -3],\n [0, 0, -6, 10],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
45
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[7, 9, -12, -5],\n [-10, -1, -5, -5],\n [-8, 9, -8, -3],\n [-6, 4, 1, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
139
|
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[[7, 0, -1, 2],\n [0, 7, 12, -10],\n [0, 0, 4, -4],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
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, -1, 10, 1],\n [0, 3, -7, 6],\n [0, 0, -6, 3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-40
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[11, 7, 4, 9],\n [7, -3, -8, -2],\n [4, -8, 8, 4],\n [9, -2, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
56
|
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, -1, -9, -2],\n [-1, 8, 7, 5],\n [-9, 7, 10, 12],\n [-2, 5, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
195
|
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, 2, 2, -8],\n [2, 9, -11, 1],\n [2, -11, 0, -3],\n [-8, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-27
|
MATH
|
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[-6, 3, -12, -7],\n [9, 12, -9, 10],\n [-6, 8, -1, -10],\n [11, -7, 7, 6]]\nRound your answer to the nearest integer.\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[[0, 8, 6, -7],\n [-4, -11, -1, 8],\n [4, 0, 8, -2],\n [-8, 5, 10, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
425
|
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, -11, 11, 5],\n [0, 3, -7, 0],\n [0, 0, -8, 2],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
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, 0, -3],\n [1, 4, 9, 4],\n [0, 9, -3, 5],\n [-3, 4, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-42
|
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, -7, -12, 8],\n [0, -1, -9, 12],\n [0, 0, -1, -1],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4718
|
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, -3, 11, -8],\n [0, 11, -5, 4],\n [0, 0, -12, -5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
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, 12, 10, -11],\n [-12, -7, 2, 11],\n [-2, 10, -1, -12],\n [5, 12, 5, -5]]\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, 12, -8, 4],\n [0, 6, 8, -10],\n [0, 0, -5, 2],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
182
|
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, 1, -5, -1],\n [-6, 3, 6, -7],\n [12, 11, 4, -3],\n [-1, -5, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-21
|
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[[-5, -4, -7, 10],\n [0, -6, 6, 11],\n [0, 0, -5, 9],\n [0, 0, 0, -10]]\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[[-12, 3, -4, 7],\n [3, -1, -2, -11],\n [11, 0, -8, -10],\n [-3, -8, 10, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-85
|
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, -3, 3],\n [-12, -6, 2, -9],\n [10, 0, -7, 10],\n [-3, 2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-38
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[11, -8, -8, 9],\n [-10, 4, -12, -2],\n [7, 5, 3, -7],\n [-5, 11, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-60
|
MATH
|
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