messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -2, -8, 6],\n [-2, 3, -5, -4],\n [-8, -5, 2, 6],\n [6, -4, 6, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -9, -5, 3],\n [0, -2, -4, -9],\n [0, 0, -2, 6],\n [0, 0, 0, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 1, -2, 8],\n [0, 8, 7, -11],\n [0, 0, 8, 1],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
552
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, 2, 3],\n [-2, -8, 10, 9],\n [2, 10, 7, -7],\n [3, 9, -7, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
62
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -2, 3, 6],\n [-2, -2, 1, -10],\n [3, 1, 7, 4],\n [6, -10, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
606
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -5, -12, 2],\n [-1, -4, 2, -7],\n [12, -7, -2, 11],\n [10, 0, 3, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
875
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 8, 7, 10],\n [0, 1, 12, -9],\n [0, 0, -3, 5],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
820
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 2, 0, -3],\n [0, 1, 4, -9],\n [0, 0, 12, 3],\n [0, 0, 0, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
928
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 7, 2, 4],\n [0, -5, -9, -4],\n [0, 0, -10, -5],\n [0, 0, 0, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 1, -11, 5],\n [8, -7, 12, -6],\n [-5, -7, 12, 6],\n [11, 6, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
542
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -11, 10, -11],\n [0, 2, 5, -8],\n [0, 0, -1, -4],\n [0, 0, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
992
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -6, -9, 10],\n [0, -7, 3, -11],\n [0, 0, 5, -6],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
380
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 4, -9, 3],\n [0, -9, -12, -12],\n [0, 0, 6, 6],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
514
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, 3, 3],\n [0, 3, -8, -8],\n [0, 0, 6, 1],\n [0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
838
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 3, 5, 0],\n [-11, 8, 1, -6],\n [-9, -12, 0, -3],\n [-4, -3, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 0, -5, -2],\n [0, -8, 3, -6],\n [-5, 3, 7, 1],\n [-2, -6, 1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 8, 7, 4],\n [8, -9, 6, -5],\n [7, 6, -11, -2],\n [4, -5, -2, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
438
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -10, -12, -9],\n [-12, 9, -8, -7],\n [-8, 5, -10, -6],\n [-5, 8, -6, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
98
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 2, -6, 7],\n [-12, 4, 9, 0],\n [-5, -7, 9, -8],\n [-9, 10, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
110
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 3, -7, -9],\n [-4, -4, -4, -5],\n [12, -12, 4, 9],\n [1, 5, 8, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 4, 8, 8],\n [0, -1, 0, 2],\n [0, 0, -5, -8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
75
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -11, -12, 4],\n [0, 8, -6, 3],\n [0, 0, 7, 6],\n [0, 0, 0, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
952
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 6, -10, 0],\n [6, -9, -5, 7],\n [-10, -5, 1, 0],\n [0, 7, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
872
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -1, 4, -6],\n [-1, -11, 0, 0],\n [4, 0, -1, -4],\n [-6, 0, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
851
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 7, -6, -7],\n [0, 1, 3, -9],\n [0, 0, 7, -3],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 0, -3, -8],\n [0, 9, 1, 8],\n [-3, 1, -10, 0],\n [-8, 8, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
72
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -9, 0, -6],\n [-9, 5, 2, -2],\n [0, 2, -4, 6],\n [-6, -2, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
308
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 9, -4, -6],\n [0, 2, -4, 1],\n [0, 0, 11, 7],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
624
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 11, 1, -3],\n [0, 8, 10, -12],\n [0, 0, 1, 7],\n [0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
192
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -9, -12, 8],\n [7, 4, -5, -9],\n [-11, 6, -6, 4],\n [-1, 0, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
135
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 6, -1, -6],\n [6, 3, 7, -4],\n [-1, 7, -10, 6],\n [-6, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
56
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 5, 0, -3],\n [5, 8, -8, -6],\n [0, -8, -4, -9],\n [-3, -6, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
569
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 3, 1, 10],\n [4, -2, 9, -10],\n [-1, -12, 11, 5],\n [-10, -12, -11, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
206
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 3, 3, -1],\n [3, 11, -6, 0],\n [3, -6, 4, -10],\n [-1, 0, -10, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
405
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, -8, 10],\n [-4, 9, -8, -4],\n [-8, -8, -11, 9],\n [10, -4, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
124
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -1, -7, -5],\n [-3, -2, -12, -2],\n [-11, -9, 6, -2],\n [12, -10, -7, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
237
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 3, 8, -9],\n [0, -9, 1, -9],\n [0, 0, -1, -5],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
352
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -4, -10, 10],\n [-1, 6, 5, -5],\n [8, 3, 10, 6],\n [-9, 10, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
712
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, -6, -5],\n [0, -7, 4, -6],\n [0, 0, -4, -8],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -5, 5, -1],\n [-11, 6, 10, -2],\n [0, -6, -6, -9],\n [5, 9, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
939
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -4, 2, 4],\n [-4, -4, 2, -8],\n [2, 2, 11, -2],\n [4, -8, -2, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
752
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -2, 0, 4],\n [-2, 3, -4, 0],\n [0, -4, 10, -2],\n [4, 0, -2, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
202
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -5, -3, -3],\n [0, 11, 4, 11],\n [0, 0, 6, -9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
660
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -8, -4, 4],\n [-8, 12, 5, 9],\n [-4, 5, -12, -4],\n [4, 9, -4, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
519
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 0, 8, 12],\n [0, -6, 0, -4],\n [8, 0, 5, -8],\n [12, -4, -8, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
872
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 6, 1, 8],\n [0, 5, 10, -9],\n [0, 0, -3, 6],\n [0, 0, 0, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
485
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 4, 0, 10],\n [4, -8, 7, 2],\n [0, 7, -1, -6],\n [10, 2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
744
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -4, -5, 6],\n [6, -5, -12, 6],\n [11, -5, -1, 9],\n [-5, 2, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
996
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 6, 2, -10],\n [0, -7, -12, 8],\n [0, 0, -1, 6],\n [0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
860
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 10, -4, -4],\n [0, -3, 10, 11],\n [0, 0, 5, -3],\n [0, 0, 0, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 0, -2, -3],\n [0, -10, -3, 8],\n [-2, -3, 7, -9],\n [-3, 8, -9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
850
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 12, -2, 2],\n [8, 11, 10, 2],\n [12, 2, 12, -11],\n [8, 10, 0, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
728
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 4, 8, -12],\n [2, -10, 9, 7],\n [2, 7, 3, -1],\n [5, 4, -2, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
308
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -2, 11, -3],\n [0, 4, 3, -6],\n [0, 0, 11, -4],\n [0, 0, 0, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
936
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 9, 12, -1],\n [0, -4, 8, 6],\n [0, 0, -2, 4],\n [0, 0, 0, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -10, -4, 5],\n [-2, -2, 10, -5],\n [11, 6, -11, 1],\n [0, 12, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
472
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 10, 7, -11],\n [0, 12, -8, -10],\n [0, 0, 12, 0],\n [0, 0, 0, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
632
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 3, -12, 12],\n [0, 8, -8, -7],\n [0, 0, 10, -4],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -2, -2, 6],\n [-2, -1, 0, -3],\n [-2, 0, 12, -6],\n [6, -3, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
620
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -7, 4, 10],\n [0, 9, -4, 9],\n [0, 0, -8, 11],\n [0, 0, 0, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 6, 5, 10],\n [0, 10, -10, -8],\n [0, 0, 12, 12],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 8, -4, -4],\n [0, 12, -1, 3],\n [0, 0, 4, -5],\n [0, 0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
992
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 1, -2, -4],\n [1, 4, 6, -4],\n [-2, 6, -6, 5],\n [-4, -4, 5, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
225
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -11, 0, -1],\n [-3, 4, 6, 2],\n [-7, -6, -6, 12],\n [-6, 11, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 6, -8, -6],\n [0, 3, 12, -12],\n [0, 0, -6, -7],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
620
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 1, 0, -7],\n [-9, -2, -1, 4],\n [12, -3, 2, -10],\n [6, -2, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
531
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -12, 2, 6],\n [-3, -3, -1, -6],\n [-2, -5, -1, -4],\n [-3, 6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
980
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -3, -3, -8],\n [-6, 0, 8, -10],\n [-3, -5, -9, -1],\n [-11, 7, -11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 4, 9, 3],\n [0, 8, 11, 8],\n [0, 0, 6, 12],\n [0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
688
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 2, 4, -9],\n [7, -9, -6, -7],\n [8, -7, 4, 8],\n [6, 4, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
472
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -12, -12, -3],\n [0, -12, 3, -2],\n [0, 0, 6, 8],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 4, -10, 0],\n [4, -1, -3, -8],\n [-10, -3, 11, -1],\n [0, -8, -1, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -4, -2, 3],\n [-4, -9, -4, 0],\n [-2, -4, 1, 0],\n [3, 0, 0, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
630
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 4, 0, 4],\n [4, -8, -6, -1],\n [0, -6, 7, -1],\n [4, -1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
993
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 0, 6, 6],\n [0, 5, 8, -9],\n [0, 0, 1, -3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
405
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 6, -10, 0],\n [6, -4, -4, 2],\n [-10, -4, 3, -4],\n [0, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
948
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 6, -6, 5],\n [0, 5, 12, -2],\n [0, 0, -9, -4],\n [0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
215
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 1, 3, -4],\n [5, 1, 2, -3],\n [-6, 7, 10, 4],\n [0, 9, -10, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
495
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -7, 1, -10],\n [-7, -2, -8, 3],\n [1, -8, -7, 4],\n [-10, 3, 4, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
297
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -7, 10, -2],\n [0, -4, -1, 7],\n [0, 0, 12, 8],\n [0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 1, 2, -2],\n [1, 5, 4, -3],\n [2, 4, -1, 5],\n [-2, -3, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
825
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -11, -3, 12],\n [0, 11, -9, -10],\n [0, 0, 11, -3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 8, 0, -12],\n [0, 9, -1, -9],\n [0, 0, 1, 4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
514
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -9, 1, 3],\n [-8, -5, 4, 8],\n [-5, -10, -7, -8],\n [5, 10, -12, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
459
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 1, -3, -9],\n [1, 12, 8, 1],\n [-3, 8, -12, -4],\n [-9, 1, -4, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
381
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -3, 1, 4],\n [-3, 7, -8, 0],\n [1, -8, -4, -4],\n [4, 0, -4, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
570
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -5, -10, 7],\n [-5, 2, 10, 0],\n [-10, 10, -3, 6],\n [7, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
634
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -11, -11, -9],\n [0, -2, -9, 4],\n [0, 0, 7, 10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -5, 8, 1],\n [0, -8, -5, -5],\n [0, 0, 5, 10],\n [0, 0, 0, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -3, -6, 2],\n [0, -7, 6, 5],\n [0, 0, -1, 2],\n [0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
461
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -2, 8, 4],\n [-2, -9, 1, 10],\n [8, 1, 12, 6],\n [4, 10, 6, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
863
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -2, -5, 0],\n [0, -1, -6, -12],\n [0, 0, 3, -1],\n [0, 0, 0, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
192
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, 2, 3],\n [0, 6, 0, 11],\n [2, 0, 2, 3],\n [3, 11, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, 6, -2],\n [-4, 0, -9, 8],\n [6, -9, -12, 4],\n [-2, 8, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
838
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 7, -6, 10],\n [7, 8, 4, 1],\n [-6, 4, 11, 8],\n [10, 1, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
258
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 8, 0, 0],\n [8, 12, 5, -8],\n [0, 5, -12, -5],\n [0, -8, -5, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
256
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -11, -7, 0],\n [0, 11, -5, 3],\n [0, 0, 5, 1],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
155
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -12, 1, 9],\n [3, 10, -5, 6],\n [-11, 11, -3, 8],\n [0, 10, -3, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
119
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 7, -8, 3],\n [12, -10, -2, -9],\n [12, -4, 5, 2],\n [5, 1, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -12, 5, -11],\n [-3, 4, 11, -3],\n [9, 5, -12, -10],\n [12, -2, -8, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
68
|
MATH
|
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