messages
listlengths 1
1
| ground_truth
stringlengths 1
6
| dataset
stringclasses 1
value |
|---|---|---|
[
{
"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[[-1, -4, -1, 0],\n [0, 8, 5, 12],\n [0, 0, -6, 12],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -7, -1, -9],\n [0, 2, 3, 5],\n [0, 0, -2, -4],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
72
|
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, -10, -3, 4],\n [0, -7, -2, 7],\n [0, 0, 6, -7],\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": "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, -4, -1, -10],\n [-4, 0, -2, -6],\n [-1, -2, -10, 9],\n [-10, -6, 9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
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, 6, 4, 3],\n [6, -10, 2, -6],\n [4, 2, 10, 0],\n [3, -6, 0, -4]]\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[[-2, -2, 0, 11],\n [-3, -4, -11, -12],\n [-6, -5, 7, -12],\n [9, 9, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-239
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 9, 2, 4],\n [0, 1, 10, -7],\n [0, 0, -8, 0],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
355
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[7, 9, 10, 2],\n [0, 3, 4, 10],\n [0, 0, 6, -4],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
371
|
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, 2, 0, 6],\n [2, -7, -2, 6],\n [0, -2, 11, 2],\n [6, 6, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
94
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 1, -9, -3],\n [4, -1, -9, 8],\n [11, -8, -8, 8],\n [0, -2, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-7
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[2, 12, -2, 10],\n [-6, 12, -1, -11],\n [4, -6, -1, 8],\n [0, 5, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[-1, 3, -5, -7],\n [10, 12, -7, -3],\n [-2, 2, -1, -1],\n [-12, -1, 5, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-1, 0, -8, -2],\n [0, 3, -6, 5],\n [-8, -6, -9, 0],\n [-2, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 5, 6, -6],\n [5, -11, 0, 3],\n [6, 0, 2, 5],\n [-6, 3, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[2, 1, 11, 10],\n [5, 7, -8, -10],\n [10, -2, 12, 4],\n [11, -9, 6, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
130
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 4, 6, 2],\n [-11, 3, 0, 12],\n [8, -2, 6, 10],\n [7, -4, -10, 4]]\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[[-3, 4, -6, 11],\n [0, -3, 3, 9],\n [0, 0, -11, 2],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1273
|
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[[4, -9, 5, 8],\n [9, 9, -3, 2],\n [-2, 2, 11, -10],\n [5, 12, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[-4, 4, -4, -8],\n [4, 9, 0, -4],\n [-4, 0, -12, -10],\n [-8, -4, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-8
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[1, 6, 1, 2],\n [0, 11, -10, 8],\n [0, 0, 10, -3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[1, -6, 8, -5],\n [4, 4, -10, -1],\n [8, 4, -12, 6],\n [-10, -9, 2, -2]]\nRound your answer to the nearest integer.\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 value at position (3, 3) rounded to the nearest integer?\n[[10, 1, -2, 0],\n [1, 3, 0, 1],\n [-2, 0, -4, -9],\n [0, 1, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-4
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[3, -6, 12, 8],\n [7, 10, -7, -10],\n [4, -5, -4, 12],\n [2, 11, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
65
|
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, 1, -3, -8],\n [1, -4, 6, -5],\n [-3, 6, 1, -4],\n [-8, -5, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-59
|
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, -4],\n [-10, -3, 0, 11],\n [3, 0, -11, 0],\n [-4, 11, 0, 1]]\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[[-11, 7, 4, -1],\n [0, 3, 9, -1],\n [0, 0, 4, 12],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/96 * A where A =\n[[-7, 4, -10, -4],\n [4, -8, 8, -7],\n [-10, 8, 8, 8],\n [-4, -7, 8, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33
|
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, 2, 2],\n [-6, 10, 3, 0],\n [2, 3, 0, 2],\n [2, 0, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
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, 11, 4, -8],\n [0, -7, -7, -4],\n [0, 0, -6, 1],\n [0, 0, 0, -10]]\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[[3, -9, 11, -5],\n [0, -9, 11, 7],\n [0, 0, -4, 0],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
220
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, -4, 10, -1],\n [4, 3, -3, 12],\n [11, -7, -6, 3],\n [6, 6, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
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, 9, -12, -7],\n [0, -5, -11, 11],\n [0, 0, 9, -12],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-930
|
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, 6, -6, 3],\n [0, -1, -5, -11],\n [0, 0, 2, -3],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1776
|
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, -4, 1, 8],\n [-4, 8, 4, -4],\n [1, 4, 5, 8],\n [8, -4, 8, -11]]\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, -8, 2, -6],\n [-8, 3, 6, 4],\n [2, 6, 11, -6],\n [-6, 4, -6, -4]]\nRound your answer to the nearest integer.\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 value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -7, -8, -9],\n [-12, 8, 9, 11],\n [-6, 3, -3, -11],\n [8, -3, -6, -9]]\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[[-3, -6, -7, -11],\n [0, 7, 10, 11],\n [0, 0, -10, -12],\n [0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-32
|
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, 0, -6, -1],\n [0, 3, -11, 10],\n [0, 0, -5, -1],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
225
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[2, -11, -4, -12],\n [0, 2, 10, -2],\n [0, 0, 9, 11],\n [0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1528
|
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, -12, -8, 7],\n [-10, 4, -7, -11],\n [0, 12, 12, 1],\n [-7, 11, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
488
|
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[[12, -6, 10, 7],\n [-5, -8, 11, -7],\n [4, -10, -11, 10],\n [-10, 4, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
49
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 7, -10, -1],\n [-2, 10, -4, 1],\n [-8, -1, 10, -3],\n [-2, -9, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
83
|
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, 8, -12, -3],\n [0, 5, -6, 0],\n [0, 0, -8, 12],\n [0, 0, 0, -6]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, -7, 2, 3],\n [10, 0, -3, -11],\n [-12, -9, -6, -10],\n [8, -5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-8, 0, 4, 9],\n [0, 4, -12, -10],\n [0, 0, -5, 7],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-31
|
MATH
|
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[8, 11, 3, -11],\n [3, -1, 8, 8],\n [0, 7, -8, -6],\n [-8, 5, -11, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-17
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, -2, 8, -2],\n [4, -12, 6, -6],\n [-2, 9, -6, 11],\n [-2, 10, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, -8, -11, 10],\n [1, -1, 5, 0],\n [-12, 8, 2, 6],\n [-11, -11, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
69
|
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, -3, 4, 9],\n [-3, 10, -2, 4],\n [4, -2, 1, -5],\n [9, 4, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[7, 9, 4, 12],\n [0, -3, -11, 2],\n [0, 0, 6, -8],\n [0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1141
|
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, 0, -8, -3],\n [5, -9, 0, 7],\n [-10, -12, 3, 8],\n [3, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
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[[3, 1, -12, 12],\n [0, -9, -9, 10],\n [0, 0, -1, -11],\n [0, 0, 0, -9]]\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[[7, 12, 3, 9],\n [0, 9, -12, 11],\n [0, 0, -4, 8],\n [0, 0, 0, -7]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 0, -4, 6],\n [0, 2, -2, 2],\n [-4, -2, -6, -4],\n [6, 2, -4, -4]]\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[[7, -6, 6, 3],\n [-6, -7, -4, -2],\n [6, -4, -8, 7],\n [3, -2, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
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, 3, -1, -1],\n [4, 8, -4, 5],\n [2, 2, 12, 3],\n [3, -9, 8, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
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, -8, 11, 0],\n [0, 2, 5, -1],\n [0, 0, -6, -6],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
187
|
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, -7, -10, 8],\n [-1, 9, 5, 7],\n [-7, 5, 9, 7],\n [-5, 10, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
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, 0, 0, -8],\n [-3, 7, -4, 11],\n [-8, 12, 10, 12],\n [7, -5, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-7, 9, 8, 5],\n [0, -5, -5, 0],\n [0, 0, 5, -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"
}
] |
137
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-12, 11, -1, 4],\n [-6, 8, 11, -4],\n [6, 5, 6, -10],\n [10, -10, -2, 4]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 3, 8, -8],\n [0, 5, -1, 4],\n [0, 0, -8, -10],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
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, 8, -8, -1],\n [0, 2, 10, -10],\n [0, 0, -5, -11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
37
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, 6, 10, -2],\n [6, -7, -6, 6],\n [10, -6, 8, 2],\n [-2, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
170
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -8, 2, -3],\n [0, 9, 3, 3],\n [0, 0, -5, -12],\n [0, 0, 0, -7]]\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[[3, 8, -7, -3],\n [8, -4, -2, 2],\n [-7, -2, 1, -4],\n [-3, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
131
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[-5, -5, -8, -2],\n [0, -9, -12, -2],\n [0, 0, -2, 11],\n [0, 0, 0, -4]]\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 all entries of the inverse. Round your answer to the nearest integer:\n[[-11, -12, 5, 12],\n [0, 7, 10, 1],\n [0, 0, -12, 9],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-128
|
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[[-2, -9, -6, 0],\n [0, -11, 6, 3],\n [0, 0, 11, -6],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -2, -2, -4],\n [-2, 9, -2, -2],\n [-2, -2, 8, -8],\n [-4, -2, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -2, 6, -11],\n [-1, -11, 6, -6],\n [-10, -11, -2, 8],\n [5, 3, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 9, 3, 1],\n [0, 2, -2, -5],\n [0, 0, -10, 2],\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 at position (4, 2) rounded to the nearest integer?\n[[-6, 3, -4, 2],\n [3, -8, -1, -2],\n [-4, -1, 10, -6],\n [2, -2, -6, -8]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 7, 6, -3],\n [0, 5, 7, 1],\n [0, 0, 9, -11],\n [0, 0, 0, 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, -12, 11, 4],\n [-9, 5, 9, 4],\n [-6, -2, 4, 0],\n [-7, -4, 11, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
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[[-10, -8, 5, 4],\n [0, -5, -9, 3],\n [0, 0, -9, 10],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-31
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 0, -2, -5],\n [0, -9, -2, -4],\n [-2, -2, 12, -6],\n [-5, -4, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
135
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-4, -4, 3, -2],\n [-4, 10, -2, 0],\n [3, -2, 3, -2],\n [-2, 0, -2, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
363
|
MATH
|
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[-11, 2, -6, -2],\n [2, 1, 5, 0],\n [-6, 5, -6, -7],\n [-2, 0, -7, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-6
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 4) rounded to the nearest integer?\n[[7, 11, 4, 7],\n [0, 10, -8, 12],\n [0, 0, 9, 3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-10
|
MATH
|
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -4, 4, 0],\n [0, -7, 2, 6],\n [0, 0, -3, -10],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-12, 7, 9, 2],\n [0, -8, -3, -3],\n [0, 0, 11, 8],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-59
|
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, 5, -2, 9],\n [0, -8, 3, -8],\n [0, 0, 12, -1],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-37
|
MATH
|
[
{
"content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[5, -2, -1, -8],\n [-2, 2, 4, -6],\n [-1, 4, 11, -2],\n [-8, -6, -2, -12]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[4, 7, 2, 10],\n [7, -3, -4, -4],\n [2, -4, -11, 2],\n [10, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-8, -8, 6, 2],\n [0, 2, 7, -5],\n [0, 0, -5, -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"
}
] |
95
|
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[[-7, -11, 0, 11],\n [12, 9, 9, -5],\n [1, 4, 11, 1],\n [6, 8, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, -8, 4, 0],\n [-8, 2, 7, 6],\n [4, 7, -4, -4],\n [0, 6, -4, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-3
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -2, 8, 0],\n [-2, 6, -8, 4],\n [8, -8, -7, 2],\n [0, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
122
|
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, 8, 11, 2],\n [-2, -10, 5, 6],\n [8, 8, -5, 1],\n [3, 8, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
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, -5, -9],\n [0, 11, 3, -2],\n [0, 0, -4, -9],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
219
|
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, 4, -11, -2],\n [0, 6, 10, 0],\n [0, 0, 10, 2],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
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, -2, 6],\n [-8, -1, 1, -2],\n [-2, 1, 0, -2],\n [6, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-590
|
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, 7, -4, 9],\n [0, 5, 12, 9],\n [0, 0, 3, 10],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
459
|
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, 4, 5, 0],\n [4, -2, 8, 2],\n [5, 8, 12, -4],\n [0, 2, -4, -12]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 0, 5, 2],\n [0, 11, 1, -2],\n [5, 1, -12, 3],\n [2, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17
|
MATH
|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, 7, -1, -11],\n [0, 3, -12, -11],\n [0, 0, -5, -12],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-117
|
MATH
|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-6, -11, -11, 3],\n [-7, 0, 2, 12],\n [-6, -10, -4, 5],\n [10, 10, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7
|
MATH
|
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/96 * A where A =\n[[11, -5, 12, -3],\n [11, -12, 3, 1],\n [-4, -6, -2, 1],\n [-12, 4, 0, 7]]\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 at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[12, -12, 1, -3],\n [-7, -7, 0, 8],\n [-11, 6, -6, 10],\n [-2, -11, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.