messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 0, 5, 11],\n [-6, -10, 6, 4],\n [7, 12, -8, 4],\n [9, 5, -1, -8]]\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"
}
] |
216
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -5, 9, -3],\n [0, 8, -11, -1],\n [0, 0, -12, -11],\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"
}
] |
968
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 6, 5, 1],\n [6, -3, 10, 11],\n [5, 10, 8, 0],\n [1, 11, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
596
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 10, 12, -8],\n [0, -8, -3, -5],\n [0, 0, -7, -1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
952
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 9, 4, 8],\n [0, -8, 9, 6],\n [0, 0, -11, 6],\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"
}
] |
112
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 12, 8, 12],\n [0, 11, -8, 10],\n [10, -4, 7, -10],\n [-9, 8, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
405
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -4, -10, -8],\n [0, -3, 5, 5],\n [0, 0, 3, -1],\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"
}
] |
28
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -11, 0, 6],\n [-10, 6, 9, 11],\n [7, 8, 4, -12],\n [-4, 3, -4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
177
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -5, 10, -5],\n [0, 7, -7, -8],\n [0, 0, -5, -11],\n [0, 0, 0, 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"
}
] |
50
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 1, 3, 9],\n [0, -2, -6, -10],\n [0, 0, -9, 0],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 2, 8, -12],\n [0, -12, -11, 9],\n [0, 0, -12, -1],\n [0, 0, 0, 4]]\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"
}
] |
760
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -9, -10, -9],\n [0, 4, -7, -9],\n [0, 0, -1, 7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -2, -1, 5],\n [-4, -12, -6, -10],\n [9, -12, -8, 7],\n [1, 12, 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"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 5, -7, 0],\n [-6, 8, 7, 5],\n [6, -9, 1, -9],\n [1, 3, 4, 2]]? 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": "Compute |A| for the matrix A =\n[[5, -11, -2, -7],\n [0, -11, -12, -8],\n [0, 0, -9, 1],\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"
}
] |
535
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -11, 9, -6],\n [-11, -3, 6, -4],\n [9, 6, 7, 4],\n [-6, -4, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 6, 8, -6],\n [6, 4, 4, -6],\n [8, 4, 9, -8],\n [-6, -6, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
188
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -7, -6, -7],\n [0, -3, -11, -4],\n [0, 0, -5, 2],\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"
}
] |
895
|
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, 6, -9, 3],\n [2, -9, 1, -1],\n [6, 3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
310
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 11, 12, -12],\n [0, 7, -8, -2],\n [0, 0, 3, 7],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -3, -12, -1],\n [-1, -6, 8, 0],\n [6, 9, 10, 1],\n [6, -11, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
278
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -11, 2, 0],\n [0, -7, 2, 12],\n [0, 0, 6, 7],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -12, 2, 8],\n [9, 1, 10, -4],\n [-12, -12, 4, -9],\n [-4, 5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
602
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 8, -9, -12],\n [-11, -3, 5, 3],\n [-7, -8, -5, 11],\n [6, -5, -4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
508
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 5, -11, -3],\n [0, -2, 11, -8],\n [0, 0, -11, 5],\n [0, 0, 0, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -5, 12, 8],\n [2, -7, 5, 10],\n [9, -11, 0, 9],\n [8, -5, 9, 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"
}
] |
706
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -4, -2, 0],\n [-4, 3, -2, -4],\n [-2, -2, 4, -8],\n [0, -4, -8, 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": "Compute |A| for the matrix A =\n[[10, 2, 3, -9],\n [0, -7, 2, 7],\n [0, 0, -4, -4],\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"
}
] |
920
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, -9, -2],\n [7, -3, 4, -9],\n [-9, 3, 1, -11],\n [-4, -5, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
972
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -11, -3, 0],\n [0, -2, 10, 7],\n [0, 0, 3, -6],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
126
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 8, 11, 12],\n [0, -2, 1, -7],\n [0, 0, -11, 6],\n [0, 0, 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"
}
] |
822
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -7, -6, 7],\n [0, 5, 3, 5],\n [0, 0, -8, 6],\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"
}
] |
800
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 3, 6, -3],\n [0, 11, -10, 7],\n [0, 0, 11, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
338
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 12, 9, 9],\n [0, 3, -8, 11],\n [0, 0, 9, 5],\n [0, 0, 0, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
271
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -4, 4, -5],\n [-4, 0, -2, 4],\n [4, -2, 8, -4],\n [-5, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
556
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -9, -4, -3],\n [6, -8, -12, -10],\n [-9, 3, -6, 3],\n [2, 8, -4, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 3, -6, 2],\n [0, 5, -8, -11],\n [0, 0, 9, -10],\n [0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 7, 8, 11],\n [-11, -3, 3, 3],\n [-10, 8, -12, -5],\n [6, 3, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
787
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 8, 4, 1],\n [8, -9, 2, 6],\n [4, 2, -8, 2],\n [1, 6, 2, 3]]\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[[10, 2, -1, -9],\n [0, -2, -3, 11],\n [0, 0, -6, -8],\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"
}
] |
960
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -4, 6, -3],\n [-4, -1, 11, 8],\n [6, 11, 10, 3],\n [-3, 8, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
275
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, -10, -8, -8],\n [12, 7, -1, 11],\n [-3, -4, -9, 0],\n [7, -2, 1, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
970
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, -1, 1],\n [0, -3, -3, -7],\n [-1, -3, -1, -2],\n [1, -7, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
147
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -8, -6, 9],\n [-5, -8, -4, 9],\n [-4, -8, 10, -1],\n [4, 0, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 4, 2, 6],\n [4, -6, -1, -2],\n [2, -1, 2, 4],\n [6, -2, 4, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
253
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 11, 5, 6],\n [0, 5, 10, -3],\n [0, 0, 3, 11],\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"
}
] |
900
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -9, -7, 12],\n [0, -2, 0, -12],\n [0, 0, 1, -3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
98
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, -8, -6],\n [0, 12, 0, 2],\n [0, 0, -6, 0],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 5, -8, -3],\n [6, 11, -4, 2],\n [-10, -11, -2, -10],\n [3, -1, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
550
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 3, -2, 9],\n [0, -6, -10, 1],\n [0, 0, 6, -4],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
592
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 1, 3, 1],\n [-12, 6, 10, 9],\n [-6, -11, 6, 11],\n [-12, 4, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
492
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -2, -5, 3],\n [-10, -11, 4, 1],\n [1, -11, 3, 2],\n [-11, -6, 7, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
654
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 8, -7, 3],\n [-4, 9, 3, 10],\n [-11, 8, -12, 1],\n [9, 9, 5, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 7, 12, 2],\n [2, -5, 4, -1],\n [-2, 12, -1, 8],\n [-7, 2, 3, -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"
}
] |
520
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -6, -6, 2],\n [-6, -5, 0, -4],\n [-6, 0, 5, 5],\n [2, -4, 5, 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"
}
] |
96
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 8, 0, 12],\n [-1, -2, -2, 0],\n [10, -12, 2, -7],\n [5, 9, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
680
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -4, 9, 7],\n [-4, -2, 4, 0],\n [9, 4, -11, -8],\n [7, 0, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
282
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 0, 6, -10],\n [12, 6, 2, 3],\n [-4, -1, 0, -8],\n [5, 11, -4, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
458
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 6, 9, 12],\n [-1, -2, 11, -3],\n [-6, -12, -2, -3],\n [11, 1, 9, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
656
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 0, 0, -1],\n [0, -10, -6, -2],\n [0, -6, 5, 4],\n [-1, -2, 4, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
926
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 4, 7, 12],\n [8, -2, -2, -6],\n [-8, 0, 2, 7],\n [-11, -4, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
992
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -6, 10, -2],\n [0, 7, 0, 0],\n [0, 0, -1, 6],\n [0, 0, 0, -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"
}
] |
916
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 2, 0, -9],\n [2, 0, 10, 6],\n [0, 10, -7, 5],\n [-9, 6, 5, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
72
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -10, -2, -1],\n [-10, -7, 2, -9],\n [-2, 2, -4, 3],\n [-1, -9, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, 0, 0],\n [1, 7, -8, 0],\n [0, -8, 0, -1],\n [0, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
807
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, -2, -4],\n [4, 5, 3, -6],\n [-2, 3, 12, -10],\n [-4, -6, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
314
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -11, 6, -8],\n [6, 6, 11, 4],\n [-9, -8, -3, -1],\n [-6, -10, 2, 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"
}
] |
52
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 2, -2, 11],\n [2, -7, 1, 0],\n [-2, 1, 1, 6],\n [11, 0, 6, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 11, 4, 2],\n [11, 2, 4, 6],\n [4, 4, -1, 0],\n [2, 6, 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"
}
] |
902
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -3, 9, -12],\n [1, -1, -1, -4],\n [10, 10, 5, -9],\n [-1, -7, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 2, 0, 9],\n [2, -8, -6, -8],\n [0, -6, 7, 6],\n [9, -8, 6, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
852
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, 12, -5],\n [0, 10, -12, 11],\n [0, 0, -1, -5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 7, -4, -4],\n [7, 10, 0, -2],\n [-4, 0, 4, 1],\n [-4, -2, 1, -4]]\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"
}
] |
553
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -4, 2, 6],\n [-4, -9, 8, -3],\n [2, 8, -6, 2],\n [6, -3, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 7, 6, -12],\n [-6, -4, -3, 3],\n [9, 4, -12, 12],\n [-6, 6, -7, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
540
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -10, -4, -9],\n [6, -11, 7, -10],\n [-2, 4, -11, -12],\n [3, -11, 4, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
639
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 10, -10, -4],\n [0, 3, -7, -4],\n [0, 0, -8, 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"
}
] |
864
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 12, -4, -10],\n [0, 6, 2, -8],\n [0, 0, 9, -6],\n [0, 0, 0, 12]]\nRound to the nearest integer, then take the result modulo 1000.\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[[-6, -11, -7, -1],\n [0, -10, -7, 5],\n [0, 0, 9, 4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -10, 10, -11],\n [3, 12, 5, -1],\n [12, 3, 8, -9],\n [11, 9, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
211
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 6, 2, -2],\n [6, 9, 2, 0],\n [2, 2, -2, -8],\n [-2, 0, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
824
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -4, 2, -7],\n [0, -4, 2, 6],\n [0, 0, 9, -6],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
376
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -4, -8, -6],\n [-4, -5, 5, 4],\n [-8, 5, 12, 6],\n [-6, 4, 6, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
252
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -2, -6, -12],\n [0, -6, 0, -6],\n [0, 0, 1, 10],\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"
}
] |
784
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 12, -4, -2],\n [3, -7, 3, -10],\n [-10, -12, -12, 4],\n [-9, 11, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
428
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 0, -6, 2],\n [0, -6, 2, 4],\n [-6, 2, -6, 4],\n [2, 4, 4, 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"
}
] |
888
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 4, -5, 7],\n [4, 11, -1, 2],\n [-5, -1, -1, 2],\n [7, 2, 2, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
180
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -10, 12, 2],\n [4, -6, -6, -5],\n [-8, -11, -2, -5],\n [9, 1, -11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
678
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, -4, 7],\n [0, -11, -2, 0],\n [-4, -2, 9, -2],\n [7, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
374
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -6, -2, -9],\n [-5, -2, 7, 8],\n [7, -8, 7, 9],\n [-10, 5, -12, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
453
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 0, 5, -4],\n [0, 6, 0, 9],\n [5, 0, 10, 1],\n [-4, 9, 1, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
243
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 10, -12, 8],\n [0, -8, -2, -1],\n [2, -7, 4, 4],\n [12, -4, -11, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
657
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -12, -1, 3],\n [0, 3, -2, 1],\n [-8, -9, 0, 12],\n [0, -9, -8, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
596
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -8, -7, -1],\n [9, 8, -12, 11],\n [6, -6, 0, -9],\n [-8, 2, 4, -8]]\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"
}
] |
182
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, -6, -4],\n [2, 9, -4, 4],\n [-6, -4, -7, -1],\n [-4, 4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
379
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 7, 12, -4],\n [-9, 6, 6, 3],\n [-4, 8, -6, 4],\n [1, 8, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
826
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, -2, 12],\n [0, -10, 7, -3],\n [-2, 7, -8, 1],\n [12, -3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
614
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 0, 12, -4],\n [0, -4, 2, -7],\n [0, 0, 8, -6],\n [0, 0, 0, 11]]\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"
}
] |
352
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -4, -3, -11],\n [-2, 11, -7, 2],\n [6, 9, 7, 3],\n [0, -4, -6, 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"
}
] |
802
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 8, 0, -4],\n [8, 3, 2, -1],\n [0, 2, -11, 0],\n [-4, -1, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
56
|
MATH
|
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