messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 8, 4, 11],\n [-4, -5, -3, 2],\n [-11, -2, -2, 1],\n [2, 7, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
516
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 10, -8, 10],\n [-4, -6, 10, 12],\n [-11, 12, -3, -12],\n [-8, 12, 0, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 12, -2, -7],\n [0, 5, 10, 4],\n [0, 0, -4, 12],\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"
}
] |
680
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -12, -8, -9],\n [0, 3, 10, -8],\n [0, 0, -6, 7],\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"
}
] |
352
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 1, -4, 10],\n [0, -4, 4, 5],\n [0, 0, -5, 2],\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"
}
] |
160
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -9, 3, -2],\n [0, 5, -9, 9],\n [0, 0, 10, -11],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
50
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 1, 12, 5],\n [1, 0, -4, -2],\n [12, -4, 4, -6],\n [5, -2, -6, 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"
}
] |
852
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -2, -7, 2],\n [-2, -12, -6, -5],\n [3, -7, -7, 5],\n [-4, -7, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
373
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 8, 10, 10],\n [0, -8, 10, -7],\n [0, 0, -8, -9],\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"
}
] |
840
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -7, -1, -5],\n [-7, -6, 9, 6],\n [-1, 9, 2, -4],\n [-5, 6, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
949
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -11, 0, 10],\n [-11, -7, -4, 5],\n [0, -4, -8, 1],\n [10, 5, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
496
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -10, -4, -3],\n [-11, 1, -10, -10],\n [2, -3, -10, -3],\n [5, -6, 12, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
344
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -8, -1, -1],\n [10, 3, 8, 3],\n [-1, 1, 0, -4],\n [3, 7, -2, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
672
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -2, -11, 7],\n [0, -12, 0, -5],\n [0, 0, 7, 9],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 1, -4, -2],\n [1, -9, -4, -6],\n [-4, -4, -2, 2],\n [-2, -6, 2, -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"
}
] |
546
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -2, -8, -8],\n [-2, -4, -2, -4],\n [-8, -2, -9, -8],\n [-8, -4, -8, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 2, -4, -12],\n [0, 6, 11, -8],\n [0, 0, 10, 7],\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"
}
] |
600
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 8, 9, 2],\n [0, 10, -7, 10],\n [0, 0, 8, -10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
760
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -10, 7, 5],\n [0, -1, 0, -10],\n [0, 0, 9, -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"
}
] |
28
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -3, -11, 7],\n [1, -8, -8, 7],\n [-3, 0, -9, -11],\n [-6, -8, -5, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
327
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 3, 9, -12],\n [0, -11, 1, 12],\n [0, 0, -7, -2],\n [0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
462
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 1, 0, 0],\n [1, 11, -5, -10],\n [0, -5, -10, -8],\n [0, -10, -8, -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"
}
] |
49
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -2, 5, 10],\n [-2, -3, 6, 2],\n [5, 6, -6, 0],\n [10, 2, 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"
}
] |
75
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 5, -5, 3],\n [-10, 7, 4, 2],\n [3, -3, 5, -10],\n [-4, -5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
993
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 4, 0, -8],\n [4, 8, 2, -4],\n [0, 2, -9, -4],\n [-8, -4, -4, -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"
}
] |
184
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -1, -2, -8],\n [-1, 8, 6, 4],\n [-2, 6, 9, 4],\n [-8, 4, 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"
}
] |
729
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -3, 0, -6],\n [0, -4, 2, 10],\n [0, 0, 5, -5],\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"
}
] |
160
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 8, 6, -2],\n [8, -4, 0, 8],\n [6, 0, -3, -6],\n [-2, 8, -6, 0]]\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"
}
] |
336
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -1, 4, -4],\n [-1, 12, -2, -10],\n [4, -2, 4, -2],\n [-4, -10, -2, 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"
}
] |
932
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -12, -6, 5],\n [0, -8, -6, -4],\n [0, 0, -10, 12],\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"
}
] |
360
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -2, 0, -4],\n [-2, -12, 4, 6],\n [0, 4, 8, -8],\n [-4, 6, -8, -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"
}
] |
312
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 1, 4, 6],\n [1, 2, 6, -1],\n [4, 6, 1, 8],\n [6, -1, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
599
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -8, -2, 4],\n [-8, -5, -5, -4],\n [-2, -5, -2, 2],\n [4, -4, 2, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
216
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 9, 10, 4],\n [-7, -6, 0, -4],\n [7, 8, -5, 3],\n [5, -9, 8, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
593
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -1, 3, 10],\n [0, 9, -2, -5],\n [0, 0, -6, -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"
}
] |
162
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -8, 1, 1],\n [-8, -11, -12, -5],\n [1, -12, -3, -8],\n [1, -5, -8, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -7, 3, -10],\n [0, -7, -8, 8],\n [0, 0, -10, -4],\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"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 3, 10, 8],\n [0, 1, 8, -6],\n [0, 0, 3, 11],\n [0, 0, 0, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
165
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 0, 4, -10],\n [0, -8, -9, -9],\n [0, 0, 12, 4],\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"
}
] |
592
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 7, -9, -11],\n [-12, 9, 7, 5],\n [4, 12, 11, -10],\n [-1, 9, -7, 8]]? Round to the nearest integer, then express your answer 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[[-11, 8, 7, -4],\n [8, -2, -2, 8],\n [7, -2, 0, -6],\n [-4, 8, -6, -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"
}
] |
504
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -8, 0, 4],\n [-8, 5, -6, 2],\n [0, -6, 8, 12],\n [4, 2, 12, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 12, -3, -2],\n [-3, 9, 6, -12],\n [3, 3, 5, -9],\n [-4, 1, -3, 2]]\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": "What is the determinant of the matrix:\n[[-6, 6, 8, 11],\n [0, -8, -9, 10],\n [0, 0, -4, 9],\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"
}
] |
888
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 6, -2, 2],\n [6, 12, 4, -2],\n [-2, 4, -3, -2],\n [2, -2, -2, 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"
}
] |
620
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -2, 6, 2],\n [-2, 10, -6, 3],\n [6, -6, -8, 0],\n [2, 3, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
884
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 12, -12, 3],\n [0, 2, -5, -9],\n [0, 0, -8, 5],\n [0, 0, 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"
}
] |
888
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 2, 5, 9],\n [2, 0, 8, -4],\n [5, 8, -7, 2],\n [9, -4, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 0, -10, -4],\n [0, 5, 0, -6],\n [-10, 0, 1, 2],\n [-4, -6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
982
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -6, 1, -4],\n [-6, 12, -2, -8],\n [1, -2, -10, 0],\n [-4, -8, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
912
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -3, -12, 6],\n [-5, 1, 7, -6],\n [-3, 6, 7, 4],\n [5, 12, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
351
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 9, -10, -4],\n [0, -8, 2, -2],\n [0, 0, 4, 5],\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"
}
] |
776
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -11, -9, -3],\n [0, -12, -2, 0],\n [0, 0, 7, 9],\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"
}
] |
24
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 2, 1, -12],\n [-11, 3, 3, -3],\n [1, 5, -2, -7],\n [8, -6, 2, 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"
}
] |
310
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -2, -5, 1],\n [-2, -3, 5, -2],\n [-5, 5, 4, 6],\n [1, -2, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
852
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -9, 3, -8],\n [0, 8, -11, 12],\n [0, 0, -10, -7],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -12, 9, 12],\n [0, 2, 8, 7],\n [0, 0, -7, 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"
}
] |
224
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -1, -7, 0],\n [-1, -5, 4, 4],\n [-7, 4, -1, 0],\n [0, 4, 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"
}
] |
585
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 6, 2, -2],\n [6, 1, 10, 2],\n [2, 10, -4, -4],\n [-2, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
672
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 2, 2, -3],\n [2, -6, 2, -1],\n [2, 2, 6, 1],\n [-3, -1, 1, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
312
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 6, -3, 4],\n [6, 3, -8, -2],\n [-3, -8, 2, -5],\n [4, -2, -5, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
344
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -5, 4, 2],\n [10, 5, -6, -2],\n [5, 7, -3, -7],\n [-9, -9, -11, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
522
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -8, -2, 5],\n [-4, 3, -7, 8],\n [8, -7, 6, 5],\n [9, -3, 3, -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"
}
] |
409
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -4, -5, -6],\n [2, 6, -6, -8],\n [9, 3, 5, -2],\n [-7, -3, 11, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -2, 11, 3],\n [-9, -12, -7, -2],\n [-3, 12, 10, 4],\n [-1, 12, -7, -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"
}
] |
802
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -10, 6, 9],\n [-12, 11, -10, 6],\n [-7, -4, -2, 2],\n [-6, 5, 9, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
549
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -8, 9, -8],\n [-10, 9, 2, -11],\n [-9, 7, 4, 11],\n [5, 11, 8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
51
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 12, 3, 6],\n [0, 8, 3, 4],\n [0, 0, -11, 9],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
448
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 6, -2, -1],\n [6, 7, -4, -10],\n [-2, -4, -7, 4],\n [-1, -10, 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"
}
] |
409
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, 10, -2],\n [-2, -9, 0, -8],\n [10, 0, -5, -6],\n [-2, -8, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
816
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -5, -12, -8],\n [12, -1, -3, 6],\n [-1, 12, -6, 5],\n [-10, -11, -10, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
910
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -9, -5, 5],\n [0, -5, 12, 6],\n [0, 0, 8, -7],\n [0, 0, 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"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 1, -12, -3],\n [0, -12, -12, 9],\n [0, 0, 2, 11],\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"
}
] |
728
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, -1, -6],\n [0, -5, 4, -8],\n [-1, 4, 7, -5],\n [-6, -8, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
174
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -8, -5, 4],\n [0, -4, 5, -9],\n [0, 0, -9, -3],\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"
}
] |
812
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -3, 8, 4],\n [0, 9, -11, -8],\n [0, 0, -7, -9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
945
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 0, 10, 10],\n [-12, -12, -1, 3],\n [12, -10, 5, 5],\n [6, -10, 3, -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"
}
] |
700
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -10, -5, 2],\n [-10, 7, -4, -8],\n [-5, -4, 5, 12],\n [2, -8, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
171
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, -7, 10],\n [0, 9, 8, -2],\n [-7, 8, 8, 2],\n [10, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
566
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -8, 1, -12],\n [0, -10, 0, 2],\n [0, 0, -4, -1],\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"
}
] |
600
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -2, -2, 1],\n [-2, -11, -6, -3],\n [-2, -6, -5, 0],\n [1, -3, 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"
}
] |
604
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 3, 4, 3],\n [3, -5, 8, 4],\n [4, 8, -9, 2],\n [3, 4, 2, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 4, -4, 0],\n [4, 9, 2, 6],\n [-4, 2, 4, 1],\n [0, 6, 1, -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"
}
] |
433
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -7, 12, -2],\n [12, 3, 7, -2],\n [7, 1, 3, 8],\n [3, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
772
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 1, -4, 8],\n [0, -1, 12, -11],\n [0, 0, -1, -11],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
964
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -8, -8, -8],\n [-8, -7, 5, 6],\n [-8, 5, 6, -4],\n [-8, 6, -4, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
948
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, -3, -8],\n [6, -12, 2, -2],\n [5, 2, -3, 10],\n [10, -1, -10, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
362
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 6, 7, 3],\n [6, -10, 10, 0],\n [7, 10, -11, -8],\n [3, 0, -8, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
932
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 2, -3, 2],\n [0, -1, -3, 11],\n [0, 0, 9, 1],\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"
}
] |
946
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -7, 2, -9],\n [0, 5, 4, -11],\n [0, 0, 2, 4],\n [0, 0, 0, 10]]\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": "Determine the value of det(A) where A =\n[[4, -5, -2, -11],\n [-9, 8, 8, 7],\n [-7, 8, -12, -7],\n [11, -10, -3, -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"
}
] |
280
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 5, -11, -1],\n [0, 2, 1, 6],\n [0, 0, 2, 2],\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"
}
] |
160
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 1, 1, 11],\n [-10, 4, 1, 0],\n [8, 12, 0, 0],\n [-8, 12, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
676
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 6, 0, -4],\n [6, -2, 2, -2],\n [0, 2, 6, 0],\n [-4, -2, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
272
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 2, -9, -4],\n [2, 10, -2, 6],\n [-9, -2, -3, -4],\n [-4, 6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
244
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 5, 9, -1],\n [11, 9, 8, -6],\n [3, 7, -5, -7],\n [-2, -11, -2, -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"
}
] |
0
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 6, -6, 0],\n [6, -3, 12, 1],\n [-6, 12, -3, 2],\n [0, 1, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
428
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -12, -6, -4],\n [-12, 5, -12, 10],\n [12, -8, -10, 9],\n [8, -2, 9, 6]]\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[[-2, 1, 8, -2],\n [1, 0, 4, 8],\n [8, 4, 7, -2],\n [-2, 8, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
73
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -9, -12, -4],\n [9, -9, 11, 11],\n [5, 7, 0, 10],\n [-2, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
394
|
MATH
|
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