messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -12, 2, 1],\n [6, 6, 5, -4],\n [10, -9, -6, -11],\n [-5, -6, -11, -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"
}
] |
9
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 2, -9, 2],\n [2, -9, -8, 2],\n [-9, -8, 9, 4],\n [2, 2, 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"
}
] |
452
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -12, 2, -3],\n [-3, 8, 6, 11],\n [-7, -1, -10, -9],\n [10, 1, 11, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
469
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 2, -5, 12],\n [0, 8, 7, -1],\n [0, 0, -4, 7],\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"
}
] |
776
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 1, -6, 0],\n [0, -2, 3, -10],\n [0, 0, -8, 7],\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"
}
] |
320
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -6, 6, 10],\n [1, -11, -11, -7],\n [-10, 9, -11, 4],\n [-6, 7, 9, -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"
}
] |
470
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -11, -5, -11],\n [-9, 8, 3, -12],\n [-8, 3, 10, 7],\n [12, -4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
860
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 9, -4, -8],\n [0, -2, 1, 1],\n [0, 0, 3, 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"
}
] |
270
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 8, -9, 2],\n [0, -1, 10, 5],\n [0, 0, 11, -7],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
340
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 10, -6, -4],\n [7, 5, 3, 3],\n [2, -12, 10, 12],\n [-1, -9, -11, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
318
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 4, 2, 0],\n [4, 3, 10, -2],\n [2, 10, -5, 9],\n [0, -2, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
874
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, 2, 11],\n [-2, 3, -9, -2],\n [-11, 6, -2, -10],\n [-3, -2, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
161
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 10, -5, 12],\n [-3, 2, 10, -9],\n [-5, -8, -11, -8],\n [-4, 7, -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"
}
] |
796
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 3, 3, -11],\n [0, -2, -10, 6],\n [0, 0, -7, 7],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
294
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 0, 0, 6],\n [0, -8, 10, -3],\n [0, 10, -9, 2],\n [6, -3, 2, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
449
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, -1, 0],\n [-4, -12, 0, 0],\n [-1, 0, 10, -7],\n [0, 0, -7, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
308
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -10, -5, 3],\n [0, -2, 5, 6],\n [0, 0, -5, -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"
}
] |
370
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 2, 8, -7],\n [0, 8, -4, -1],\n [0, 0, 5, 8],\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"
}
] |
320
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -8, -6, 8],\n [-8, -11, 8, 5],\n [-6, 8, -9, -2],\n [8, 5, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -7, -1, -2],\n [-11, -8, -12, 7],\n [-12, -11, -5, -12],\n [6, 1, 4, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
383
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 1, 3, 7],\n [0, 8, 1, -2],\n [0, 0, -4, 8],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
312
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 7, -7, 9],\n [0, 10, -12, 1],\n [0, 0, -4, 7],\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"
}
] |
320
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, 11, 4],\n [7, -8, 5, 0],\n [-9, 10, -3, 0],\n [8, -3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
592
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -8, 6, -4],\n [2, 8, -2, -4],\n [1, 2, -9, -10],\n [-8, 8, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
340
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 12, -8, 12],\n [0, -3, 0, 8],\n [0, 0, 3, -10],\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"
}
] |
9
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -7, -12, -5],\n [0, 1, 7, 8],\n [0, 0, 4, 11],\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"
}
] |
776
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -1, 7, 0],\n [-1, 12, 6, 1],\n [7, 6, -4, -8],\n [0, 1, -8, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
133
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 0, -7, 7],\n [0, -6, 9, 9],\n [0, 0, -11, 2],\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"
}
] |
940
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -12, 11, 12],\n [4, -11, 9, -5],\n [-7, -1, 3, 10],\n [12, 9, 1, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
263
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 4, -10, -1],\n [4, -11, -6, -10],\n [-10, -6, 2, 8],\n [-1, -10, 8, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
74
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -9, 10, -6],\n [12, 8, -5, -2],\n [-5, 10, 9, -12],\n [8, -5, 9, -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"
}
] |
95
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -1, -8, 0],\n [-1, 10, -1, 10],\n [-8, -1, 1, -6],\n [0, 10, -6, -11]]? Round to the nearest integer, then express your answer modulo 1000.\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[[12, -10, -4, 0],\n [-10, -4, 0, -6],\n [-4, 0, -12, 2],\n [0, -6, 2, 9]]\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[[-1, -7, -9, -1],\n [0, -4, 0, 7],\n [0, 0, -6, -5],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
952
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 0, 1, -9],\n [11, -12, -8, -11],\n [-1, 3, 6, -9],\n [3, 5, 2, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
411
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -3, 9, -3],\n [-9, 10, -10, -10],\n [-1, 0, -9, 4],\n [4, -12, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -2, -9, 2],\n [-2, -1, 2, 8],\n [-9, 2, -2, 6],\n [2, 8, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
499
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 10, 12, 0],\n [-7, 0, -5, -1],\n [-5, 3, -8, 10],\n [1, -6, -3, 5]]\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, 2, 0, -2],\n [2, -2, 8, 6],\n [0, 8, -2, 6],\n [-2, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
272
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -4, -10, 3],\n [12, 2, 0, -1],\n [-2, 12, 0, -7],\n [-3, -9, -5, -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"
}
] |
460
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 5, -3, 1],\n [5, -7, -2, -4],\n [-3, -2, -3, -1],\n [1, -4, -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"
}
] |
480
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, 9, 2],\n [0, 11, -2, 1],\n [9, -2, -10, 2],\n [2, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
741
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -7, -6, 3],\n [-7, -12, 6, -4],\n [-6, 6, 5, 4],\n [3, -4, 4, -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"
}
] |
709
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -2, -4, 12],\n [-2, -7, -6, -6],\n [-4, -6, 10, 1],\n [12, -6, 1, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
527
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -11, 12, 1],\n [11, 2, 6, -12],\n [-5, -5, 2, -3],\n [-6, 4, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
208
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -11, -7, -4],\n [0, -6, -9, -9],\n [0, 0, 6, 3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
268
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 7, 5, -11],\n [-1, 3, -1, -2],\n [3, -1, -7, -5],\n [12, -4, -7, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
642
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 11, -5, -5],\n [0, 4, -4, -8],\n [0, 0, -3, -11],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
396
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 3, 2, -4],\n [0, 9, 4, 8],\n [0, 0, 2, 12],\n [0, 0, 0, 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"
}
] |
386
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 12, 6, 2],\n [12, -10, 5, 6],\n [6, 5, -1, 0],\n [2, 6, 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"
}
] |
675
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -2, -2, -9],\n [-3, 0, 7, 11],\n [-8, 1, -5, -3],\n [11, -12, -10, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
687
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, -10, -3],\n [0, 10, -6, -9],\n [0, 0, 6, 4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, -11, -6],\n [0, 8, -2, 10],\n [0, 0, 5, 9],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 7, -7, -11],\n [0, -4, -4, 1],\n [0, 0, -5, 12],\n [0, 0, 0, 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"
}
] |
280
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -6, 2, -1],\n [-8, 10, -6, -2],\n [12, 7, -2, -11],\n [-5, 10, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
886
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, 9, 1],\n [0, 7, 3, 0],\n [0, 0, 12, 7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -3, -8, -3],\n [0, 9, -10, -10],\n [8, 1, -8, -3],\n [7, -10, -7, -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"
}
] |
867
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -7, -12, -5],\n [0, -1, 4, -4],\n [0, 0, 12, 1],\n [0, 0, 0, -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"
}
] |
160
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 6, 0, 6],\n [6, -12, -4, -1],\n [0, -4, -3, -4],\n [6, -1, -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"
}
] |
309
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 11, -12, -10],\n [7, -6, -8, 7],\n [6, 5, 8, -11],\n [-10, 4, 5, 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"
}
] |
92
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -9, 4, -7],\n [-8, 5, 9, -1],\n [5, -5, -2, 9],\n [-7, 1, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
956
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -8, -4, 6],\n [-8, 9, 4, -4],\n [-4, 4, -10, -2],\n [6, -4, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
250
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -4, 7, 8],\n [0, -10, -2, -2],\n [0, 0, 5, -4],\n [0, 0, 0, -6]]\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[[12, 6, 12, 0],\n [0, 8, 1, 8],\n [0, 0, -11, -11],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
608
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -8, 0, 0],\n [-8, 2, 0, 5],\n [0, 0, -12, 0],\n [0, 5, 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"
}
] |
640
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, -5, 12],\n [6, -11, 6, 3],\n [4, 6, 6, 1],\n [-1, 2, 12, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
915
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 8, 9, 12],\n [3, 5, 9, -8],\n [-6, 1, -9, -12],\n [12, -9, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 10, -9, 4],\n [10, -10, -3, 6],\n [-9, -3, 12, 0],\n [4, 6, 0, 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"
}
] |
824
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 4, -5, 6],\n [-11, -12, -1, -4],\n [-4, 11, 12, 10],\n [2, 3, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
532
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -5, -3, -6],\n [2, 8, 2, 9],\n [6, 7, 12, -6],\n [2, 10, -10, -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"
}
] |
416
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 10, 6, 5],\n [0, -8, -7, 12],\n [0, 0, -2, 12],\n [0, 0, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
952
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 1, -1, -4],\n [-6, 9, -2, -10],\n [-6, 0, -7, 11],\n [-4, -7, -6, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
690
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -9, 9, -1],\n [0, -12, 12, -3],\n [0, 0, -8, -1],\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"
}
] |
272
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 7, 2, 9],\n [7, 12, 4, 8],\n [2, 4, 2, 0],\n [9, 8, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
898
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 11, -5, -11],\n [-5, 12, 6, 9],\n [9, -10, -5, 12],\n [-8, -8, -11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
751
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, 0, -3],\n [0, 9, 4, -7],\n [0, 0, 2, -1],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -12, 0, 6],\n [0, -5, -6, -4],\n [0, 0, -4, -8],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
440
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 5, 4, -7],\n [-10, -10, 8, -1],\n [-10, 3, 10, -2],\n [-10, 3, 10, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
420
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -3, -9, 3],\n [0, -11, 8, -5],\n [0, 0, 2, 4],\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"
}
] |
264
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 5, 4, -11],\n [0, -6, 12, -6],\n [0, 0, 12, 1],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
872
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 3, -2, -12],\n [-10, 10, 5, -8],\n [-12, -7, 0, -7],\n [-1, -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"
}
] |
789
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 7, -12, -7],\n [0, 1, -4, 7],\n [0, 0, 5, 2],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 8, 2, 9],\n [0, 10, 6, 2],\n [0, 0, 2, 8],\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"
}
] |
320
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 12, -8, -5],\n [9, -11, 7, -4],\n [-2, -10, 11, -4],\n [-7, -4, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
286
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -6, 2, -4],\n [-6, -11, 6, -9],\n [2, 6, -7, -2],\n [-4, -9, -2, -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"
}
] |
514
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 8, -6, -12],\n [0, 2, 8, 3],\n [0, 0, -6, -10],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
144
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -11, 6, 1],\n [1, -12, -3, -1],\n [-3, 3, -3, 11],\n [-7, -4, -7, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
792
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -1, -2, 9],\n [-2, 5, 11, -5],\n [11, -8, -2, 8],\n [3, 12, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
737
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 1, -6, 5],\n [1, 4, -4, 8],\n [-6, -4, -7, 0],\n [5, 8, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
655
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 2, -6, -2],\n [2, -11, 4, -2],\n [-6, 4, -3, 0],\n [-2, -2, 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"
}
] |
978
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -12, -4, -5],\n [-9, 7, 3, -8],\n [2, -7, 4, -6],\n [4, -5, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
837
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 9, 9, 9],\n [0, 7, -2, -3],\n [0, 0, -5, 3],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
630
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 2, -2, 6],\n [2, -4, 8, 3],\n [-2, 8, 0, 5],\n [6, 3, 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"
}
] |
852
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -2, 3, -2],\n [9, 5, -11, -7],\n [1, 0, -8, 12],\n [1, 12, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
784
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 10, -9, -12],\n [9, -3, -6, -4],\n [-1, 12, 2, -11],\n [-3, -9, -6, -5]]\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": "What is the determinant of the matrix:\n[[5, 2, -7, 8],\n [0, 5, -8, -11],\n [0, 0, -3, -11],\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"
}
] |
475
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, -7, 0],\n [0, 11, 7, -5],\n [0, 0, -7, -9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
149
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -7, -3, 12],\n [0, 1, 9, 0],\n [0, 0, 11, -4],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
660
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 9, 10, 1],\n [0, 4, 8, 4],\n [0, 0, 11, 0],\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"
}
] |
40
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 7, 9, 9],\n [0, 5, -3, -4],\n [0, 0, -1, 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"
}
] |
880
|
MATH
|
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