messages
listlengths 1
1
| ground_truth
stringlengths 1
6
| dataset
stringclasses 1
value |
|---|---|---|
[
{
"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[[-10, 1, -2, -2],\n [1, 0, 6, 4],\n [-2, 6, -4, -5],\n [-2, 4, -5, -10]]\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 value at position (4, 1) rounded to the nearest integer?\n[[8, 2, -4, 2],\n [2, -11, 6, 6],\n [-4, 6, 7, -1],\n [2, 6, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-4
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, 8, -10, -2],\n [7, -12, 7, -9],\n [-9, 2, -11, 1],\n [-3, 0, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-145
|
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, -4, 0, -8],\n [-4, -6, 0, 1],\n [0, 0, -9, 0],\n [-8, 1, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 5, 2, 10],\n [11, -12, -12, -7],\n [-9, -7, -7, -3],\n [-9, 0, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-54
|
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, 11, 9, 7],\n [0, 1, -7, -4],\n [0, 0, 8, -1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-988
|
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, -12, -5],\n [8, -10, -9, 7],\n [-11, -12, 8, -9],\n [11, 8, -9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-21
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[-8, 0, -2, 0],\n [0, -12, -10, -6],\n [-2, -10, -8, -1],\n [0, -6, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-242
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[9, -4, -3, 8],\n [0, -4, -10, 2],\n [0, 0, 8, 8],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
158
|
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, -9, -8, 5],\n [-8, 1, -6, -7],\n [1, 4, -12, -6],\n [-3, -11, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-20
|
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, 2, 0, 8],\n [12, -7, 11, 0],\n [-5, 0, 7, 7],\n [-9, 6, -4, 2]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-2, -3, 2, 3],\n [0, 3, -2, 9],\n [0, 0, -1, -9],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-101
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -8, 1, 7],\n [2, -8, -6, 12],\n [7, -11, 11, -6],\n [-1, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
47
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[10, 9, -2, 11],\n [-4, -1, 5, 4],\n [9, 2, -3, -9],\n [11, 3, -8, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[7, 8, 11, 12],\n [-8, 1, 8, 2],\n [11, 5, 2, -12],\n [9, 12, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
71
|
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[[-8, -9, -8, 6],\n [-9, 1, -4, 1],\n [-8, -4, -5, 0],\n [6, 1, 0, 4]]\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[[0, -6, -10, -1],\n [4, 7, 1, -3],\n [-2, 12, -1, 5],\n [8, 7, 1, 1]]\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 sum of all entries rounded to the nearest integer?\n[[5, -11, 10, 9],\n [-10, 11, -9, -3],\n [3, 2, -4, -7],\n [1, -2, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-564
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[12, 2, 0, -10],\n [2, 0, 9, 0],\n [0, 9, 7, 0],\n [-10, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-8
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, -2, 6, -8],\n [-2, 10, -5, 3],\n [6, -5, 4, 0],\n [-8, 3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
43
|
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, -10, -6, 10],\n [2, 1, -3, 10],\n [-5, -7, 12, 6],\n [-3, -8, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-17
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, -9, 2, 6],\n [0, -8, 9, -8],\n [0, 0, -1, 5],\n [0, 0, 0, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
697
|
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, -8, -10, -11],\n [-11, 7, -6, -9],\n [8, 1, -1, -7],\n [-1, -5, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
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, 6, 7, 8],\n [1, 12, -3, 6],\n [-3, 0, -10, 8],\n [1, -1, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-1236
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[10, -10, -6, 8],\n [0, -9, 12, -2],\n [0, 0, 6, -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"
}
] |
40
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[5, 7, -11, -2],\n [9, -9, 10, -9],\n [3, -7, -1, 4],\n [11, 8, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-9
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, 5, -8, -2],\n [0, 7, -12, 8],\n [0, 0, -1, 7],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-362
|
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[[11, -10, 4, 10],\n [-10, 0, 2, 6],\n [4, 2, 0, 8],\n [10, 6, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[12, 3, 8, 6],\n [3, 9, 0, 2],\n [8, 0, 2, -2],\n [6, 2, -2, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-9, -9, -10, -8],\n [0, -11, 4, -9],\n [0, 0, -11, 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"
}
] |
-39
|
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, 4, -1, -6],\n [-7, 2, 0, 11],\n [9, 3, 1, -4],\n [1, 1, -5, 12]]\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[[2, 6, -11, 1],\n [0, -11, 12, -9],\n [0, 0, -12, -1],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
79
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, -8, -8, 9],\n [0, -3, 1, 3],\n [-4, 7, 11, 11],\n [8, -5, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
111
|
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[[-2, -10, 0, 1],\n [0, 11, -1, -5],\n [0, 0, -11, -11],\n [0, 0, 0, 8]]\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[[11, -6, 0, -2],\n [-6, 12, -10, -11],\n [0, -10, -11, -4],\n [-2, -11, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-14
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, 6, 10, 1],\n [0, -3, 7, 1],\n [0, 0, -8, 1],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
354
|
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[[6, -6, 0, 12],\n [-6, -6, 2, 2],\n [-12, 11, -11, -6],\n [-4, -1, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9
|
MATH
|
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[8, -3, -3, -2],\n [0, 4, 12, -9],\n [0, 0, -4, 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"
}
] |
-24
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-9, 9, -10, -2],\n [9, 3, -1, 4],\n [-10, -1, -11, -4],\n [-2, 4, -4, -1]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -6, -2, -4],\n [-6, -3, -2, 8],\n [-2, -2, 0, 2],\n [-4, 8, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
73
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[7, 0, 2, -11],\n [0, -8, 2, -7],\n [0, 0, -12, -4],\n [0, 0, 0, 7]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 10, -3, 0],\n [10, -3, 4, -10],\n [-3, 4, -2, -10],\n [0, -10, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-16
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, 2, 2, 0],\n [2, -7, 0, 4],\n [2, 0, -3, 0],\n [0, 4, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-115
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[3, -6, 5, 1],\n [0, 7, 8, 3],\n [-10, 2, 8, 12],\n [8, 1, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-142
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 7, -12, -3],\n [3, -1, 0, -6],\n [2, 2, -1, 7],\n [-9, 12, -11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
MATH
|
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[5, 2, 4, 6],\n [2, 2, 10, 0],\n [4, 10, 9, -2],\n [6, 0, -2, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-1
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[1, -6, 2, 12],\n [1, -8, -3, -4],\n [-2, 8, 3, 5],\n [9, -3, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-123
|
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, -7, 12, -7],\n [2, -2, 9, -7],\n [-11, 10, -12, 8],\n [5, -1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/96 * A where A =\n[[-8, 6, -5, -6],\n [6, -2, -4, -12],\n [-5, -4, -3, -9],\n [-6, -12, -9, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-6
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, 0, 1, -5],\n [-9, -5, 6, -10],\n [0, -4, 3, -3],\n [0, -11, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
299
|
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[[1, 2, -3, 10],\n [2, 8, -2, 1],\n [-3, -2, -12, 8],\n [10, 1, 8, 12]]\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[[-3, -6, 12, -11],\n [0, 11, -9, -4],\n [0, 0, 10, 9],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-60
|
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, -9, -9],\n [-7, 11, 11, 12],\n [-6, 2, -5, -4],\n [3, 1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
162
|
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, -2, -5, -8],\n [-2, 9, -1, -6],\n [-5, -1, 3, 2],\n [-8, -6, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
54
|
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, -12, 0],\n [2, 4, 0, -2],\n [-12, 0, 8, 6],\n [0, -2, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
106
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-11, -9, -4, -1],\n [-11, -8, -9, -3],\n [2, -1, -7, -12],\n [11, 11, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
654
|
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, 8, -6, 0],\n [8, 7, 2, -1],\n [-6, 2, 11, 4],\n [0, -1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
597
|
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, -7, -4],\n [-1, 10, -12, 7],\n [5, 0, 0, -11],\n [-4, -9, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
660
|
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[[0, 3, 2, -2],\n [3, 8, 4, -1],\n [2, 4, -9, 0],\n [-2, -1, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-144
|
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, -6, -12, -9],\n [1, 3, -12, 11],\n [-2, -8, -2, 6],\n [4, -11, 11, 8]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-10, -2, 2, 2],\n [-2, 6, 2, -4],\n [2, 2, -7, 0],\n [2, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-52
|
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, 9, 12, -6],\n [0, -5, 10, 2],\n [0, 0, 9, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
262
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[7, -8, -5, 8],\n [-7, -9, 10, -5],\n [2, -10, 12, 12],\n [11, 0, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-5
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-1, -10, -6, -5],\n [0, 2, 11, 11],\n [0, 0, 12, -11],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-1208
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-7, 1, -4, -5],\n [8, -3, -7, -9],\n [10, -2, 0, -1],\n [0, -3, 7, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-43
|
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, -6, 5],\n [0, -5, 3, -1],\n [0, 0, 4, 7],\n [0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
77
|
MATH
|
[
{
"content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[9, -4, 7, -2],\n [-4, 1, 0, 9],\n [7, 0, -3, 10],\n [-2, 9, 10, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, 0, 2, -4],\n [0, -8, -8, 0],\n [2, -8, 3, 4],\n [-4, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
123
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, 10, -2, 11],\n [-11, 9, 8, 11],\n [-2, 7, 4, -10],\n [7, 7, 2, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
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, 0, -10, -4],\n [0, 6, -12, 1],\n [0, 0, -5, -10],\n [0, 0, 0, -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 sum of absolute values of all entries rounded to the nearest integer?\n[[-5, -12, 12, -6],\n [0, 11, 6, -9],\n [0, 0, 7, 5],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
205
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[0, 7, -12, -11],\n [-4, 2, -3, 7],\n [-12, -2, 1, -4],\n [4, 9, -8, -11]]\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[[11, -10, 3, -12],\n [7, -5, -3, -6],\n [-9, 4, 10, -12],\n [-8, -6, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-43
|
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[[2, 3, -4, 7],\n [0, -10, 0, -11],\n [0, 0, -4, -4],\n [0, 0, 0, 6]]\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[8, 4, 3, -12],\n [1, 9, -5, -6],\n [4, -6, 9, -6],\n [7, -2, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
193
|
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, 2, 0, -4],\n [2, -11, -4, 5],\n [0, -4, 9, 2],\n [-4, 5, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-20
|
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, -8, 6, 6],\n [0, -7, -11, 7],\n [0, 0, 11, 11],\n [0, 0, 0, -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 sum of all entries rounded to the nearest integer?\n[[-8, -5, 11, 6],\n [0, 8, -5, 0],\n [0, 0, -2, -6],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-36
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, -2, -6, 5],\n [-2, -6, -2, -10],\n [-6, -2, 3, 4],\n [5, -10, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
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, -8, 0, 4],\n [-8, -1, 1, -5],\n [0, 1, 7, -2],\n [4, -5, -2, 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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, 9, 6, 2],\n [9, 6, 1, 1],\n [-1, -1, -8, -8],\n [-9, -2, 4, -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 sum of all entries rounded to the nearest integer?\n[[12, -4, 12, -4],\n [-4, 8, 3, -5],\n [12, 3, -2, -2],\n [-4, -5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-115
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, -6, -4, -6],\n [-6, -2, 1, 6],\n [-4, 1, -12, 1],\n [-6, 6, 1, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-21
|
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[[-8, 12, 4, 9],\n [0, 7, 9, -12],\n [0, 0, -6, 8],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, 10, -4, -3],\n [10, -9, 6, 6],\n [-4, 6, -3, 4],\n [-3, 6, 4, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
361
|
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, -10, -1, -4],\n [3, -12, -10, -4],\n [12, 7, -6, 9],\n [10, -11, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-23
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-12, -3, 6, -3],\n [5, 7, -12, 0],\n [9, 5, -6, 3],\n [11, -12, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-525
|
MATH
|
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[11, 5, 2, -10],\n [5, -4, -4, 8],\n [2, -4, -5, 4],\n [-10, 8, 4, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[4, -8, -11, -1],\n [0, -6, 9, -6],\n [0, 0, 3, -7],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
59
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 2, -10, 1],\n [2, 9, -1, 4],\n [-10, -1, -4, 1],\n [1, 4, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[12, 2, 0, 3],\n [2, 9, 4, 4],\n [0, 4, 8, 0],\n [3, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-10, -3, 7, 2],\n [0, -5, 1, -7],\n [0, 0, 12, -9],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
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, -6, 12, -6],\n [0, -6, -8, 6],\n [0, 0, -7, 8],\n [0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
104
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[-12, 4, 6, 4],\n [8, 1, -3, -9],\n [-3, 3, -11, -1],\n [-8, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-10
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, 9, -4, -1],\n [0, 11, -3, 9],\n [0, 0, -9, 11],\n [0, 0, 0, 5]]\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[[-1, -2, 6, -2],\n [-2, 9, 9, -4],\n [6, 9, 6, -6],\n [-2, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
614
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[7, -10, 1, 6],\n [0, 5, 8, 9],\n [0, 0, -10, 12],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7
|
MATH
|
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[-4, -12, -4, -12],\n [-4, 0, 0, 12],\n [3, -5, 7, 8],\n [12, -11, 7, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
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, 5, 12],\n [-6, -11, -11, 10],\n [-1, 6, -9, -2],\n [6, 2, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60
|
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, 7, 0, -5],\n [0, -12, 1, 12],\n [0, 0, 6, -10],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
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