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[[11, -3, -1, -10],\n [-1, -6, -1, -6],\n [5, 6, -9, -8],\n [9, -7, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
474
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 9, -5, -9],\n [0, 9, -8, -1],\n [0, 0, 9, -5],\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": "Compute |A| for the matrix A =\n[[-5, -9, 8, 12],\n [-10, 0, 3, 0],\n [9, 9, 6, -9],\n [5, -11, 9, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
810
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 3, 6, -5],\n [-8, 4, -11, 2],\n [-8, -7, 5, 12],\n [-7, -6, 11, -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"
}
] |
435
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 9, 6, 11],\n [-10, 7, -5, 12],\n [-4, -7, -5, -12],\n [-3, 4, -3, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
918
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -8, -8, -3],\n [-8, 12, 3, -4],\n [-8, 3, 6, -7],\n [-3, -4, -7, 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"
}
] |
669
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -10, -11, -2],\n [0, -11, -11, 9],\n [0, 0, 9, -7],\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"
}
] |
248
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -3, 5, 2],\n [-3, 4, -6, -9],\n [5, -6, -6, 2],\n [2, -9, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
793
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 6, 2, -10],\n [6, -9, 2, 7],\n [2, 2, -10, 0],\n [-10, 7, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
476
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, 7, 2],\n [-9, 6, -8, -5],\n [7, -8, 5, -7],\n [2, -5, -7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
251
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 1, 5, 11],\n [10, 8, -9, -7],\n [-4, -6, -9, 2],\n [-1, -6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
277
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -9, 8, 2],\n [0, -4, -1, 11],\n [-8, -10, -7, -9],\n [4, 3, -6, -1]]\nRound to the nearest integer, then take the result 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[[4, -4, -1, 1],\n [-8, 12, 4, 3],\n [-3, -10, -1, -12],\n [9, 5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
815
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, 8, -2],\n [0, -3, 8, -8],\n [8, 8, 10, 6],\n [-2, -8, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
692
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -10, -1, 0],\n [-10, -2, 6, -11],\n [-1, 6, 7, -8],\n [0, -11, -8, -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"
}
] |
904
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 6, -11, -9],\n [0, 4, 4, -2],\n [0, 0, -10, -6],\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"
}
] |
440
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -3, 12, 5],\n [-8, -2, -3, -3],\n [8, 6, -11, 5],\n [4, 1, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 0, 2, -9],\n [0, 1, 10, -6],\n [2, 10, 7, 0],\n [-9, -6, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -1, 4, -2],\n [-1, -2, -4, 2],\n [4, -4, -10, -8],\n [-2, 2, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
140
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -3, -3, 3],\n [0, -4, -3, -8],\n [0, 0, -2, 3],\n [0, 0, 0, 3]]\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[[12, 6, 10, -2],\n [-11, 1, -8, 1],\n [-8, -10, -1, 6],\n [1, -11, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
982
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -9, -8, -5],\n [12, -6, -9, 11],\n [4, -11, 5, 7],\n [4, -12, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
669
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -10, -12, -5],\n [-1, 3, 11, 2],\n [-3, 11, 0, 9],\n [-9, -9, -9, -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"
}
] |
217
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 8, -6, 4],\n [8, 4, -10, 2],\n [-10, 9, 0, -7],\n [12, -5, 12, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
766
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -6, -10, -3],\n [-8, 0, 10, -11],\n [0, -6, -5, 12],\n [1, 9, 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"
}
] |
780
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 0, 7, -4],\n [0, -10, -5, 0],\n [7, -5, -11, -2],\n [-4, 0, -2, 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"
}
] |
515
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -7, -3, -4],\n [0, -3, 11, 9],\n [0, 0, 4, -3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
916
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 8, -2, 2],\n [8, 12, -1, 0],\n [-2, -1, -2, -8],\n [2, 0, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
803
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -5, -6, -2],\n [-1, -10, -2, 1],\n [11, 2, -3, -4],\n [-12, 3, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
311
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 4, -7, 1],\n [0, -3, 3, 11],\n [5, 2, -12, -9],\n [7, 2, 3, 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"
}
] |
295
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -2, -9, -7],\n [4, -2, 6, 3],\n [-7, -1, -8, -7],\n [9, -1, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
275
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 0, -3, -2],\n [0, 7, -9, 10],\n [0, 0, -8, 0],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
544
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, 2, -8],\n [4, -1, -2, -4],\n [2, -2, -4, 0],\n [-8, -4, 0, 9]]\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[[7, 6, -11, -4],\n [0, 8, 2, -2],\n [0, 0, -7, 7],\n [0, 0, 0, -2]]\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[[1, -9, 2, -9],\n [0, 10, 8, 9],\n [0, 0, 12, -5],\n [0, 0, 0, -11]]\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[[4, 6, 3, -11],\n [0, -5, 11, -12],\n [0, 0, 8, -1],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -4, -10, -2],\n [-4, 11, -2, 2],\n [-10, -2, -7, 4],\n [-2, 2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -2, 5, 8],\n [-2, -10, 6, 6],\n [5, 6, 1, -5],\n [8, 6, -5, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
862
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 1, -4, 8],\n [1, -2, 7, 0],\n [-4, 7, -8, 4],\n [8, 0, 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"
}
] |
754
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -2, -6, -1],\n [-2, -6, 2, 4],\n [-6, 2, 2, -6],\n [-1, 4, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
936
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 8, -6, 11],\n [0, 1, -3, -4],\n [0, 0, -11, 8],\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"
}
] |
660
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 12, -5, -12],\n [0, -1, -5, 2],\n [0, 0, -5, -9],\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"
}
] |
440
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -10, -6, -3],\n [-10, -10, 0, -2],\n [-6, 0, -7, -6],\n [-3, -2, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
578
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, 7, -10],\n [0, -8, -6, -10],\n [0, 0, -10, 9],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, 11, -7],\n [12, -1, 12, -10],\n [3, 1, 2, -8],\n [-9, 4, -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"
}
] |
614
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -1, 0, -4],\n [-1, 10, 4, 8],\n [0, 4, -9, -3],\n [-4, 8, -3, -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"
}
] |
124
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 8, 0, -8],\n [-3, 1, 7, 4],\n [7, -3, -7, 0],\n [0, 0, -3, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
304
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -9, 3, -5],\n [3, 2, 2, -1],\n [-10, 0, 0, 5],\n [6, -7, -9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
310
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 6, -6, -9],\n [0, -10, 5, -10],\n [0, 0, 10, -7],\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"
}
] |
200
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 6, -12, -7],\n [6, 5, 1, 2],\n [-10, 3, 4, 10],\n [1, -1, 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"
}
] |
793
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -2, 5, -8],\n [-2, -8, -4, -6],\n [5, -4, 5, -6],\n [-8, -6, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
548
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -3, -3, 12],\n [0, 7, 2, 7],\n [0, 0, 8, 7],\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"
}
] |
232
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 6, 0, 3],\n [0, 2, -7, 6],\n [0, 0, -7, -7],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
882
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 12, -2, -6],\n [-5, 0, -2, -10],\n [0, 4, 11, 5],\n [-2, -9, -12, 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"
}
] |
432
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -12, -2, -3],\n [7, 8, -9, -1],\n [10, -4, 10, -2],\n [-6, 3, 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"
}
] |
252
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -8, -6, -4],\n [-8, 2, -4, 6],\n [-6, -4, 1, -6],\n [-4, 6, -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"
}
] |
994
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 9, 4, 0],\n [0, 7, -11, -1],\n [0, 0, -11, -12],\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"
}
] |
71
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -1, 1, 5],\n [-1, -9, -10, 7],\n [1, -10, 1, 2],\n [5, 7, 2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
662
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -6, 1, 4],\n [0, -8, -10, 11],\n [0, 0, 2, 3],\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"
}
] |
176
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 1, 5, -3],\n [6, 6, 11, -10],\n [0, 6, 11, -6],\n [-11, 7, -3, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
340
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -10, 1, -2],\n [-1, 4, -3, 4],\n [8, -12, 1, 11],\n [6, -7, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
190
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, -9, 10],\n [0, 12, 2, 10],\n [0, 0, -12, 8],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
224
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 0, 4, 8],\n [0, 8, 4, -8],\n [4, 4, -4, -4],\n [8, -8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -10, 5, 9],\n [0, 2, -10, 5],\n [0, 0, -11, 0],\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"
}
] |
924
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -2, 12, -2],\n [-12, 11, 0, 5],\n [5, 8, 12, -6],\n [4, -10, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
496
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 3, 2, 6],\n [3, 4, 0, 6],\n [2, 0, 11, 0],\n [6, 6, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
847
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 0, -4, 1],\n [0, 10, -6, -6],\n [-4, -6, -12, 0],\n [1, -6, 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"
}
] |
420
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -11, -11, 1],\n [-3, 2, 7, 8],\n [-5, 3, -10, -11],\n [1, -12, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
434
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 4, -9, -11],\n [0, 12, -8, 11],\n [0, 0, 10, -3],\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"
}
] |
680
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 5, 4, 0],\n [5, -8, 4, -2],\n [4, 4, 6, -4],\n [0, -2, -4, -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"
}
] |
522
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 0, 4, 2],\n [0, -9, 0, 4],\n [4, 0, 5, 1],\n [2, 4, 1, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 4, -9, -8],\n [0, 11, -7, -3],\n [0, 0, -10, 12],\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"
}
] |
680
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -8, 1, -3],\n [0, -2, 9, 2],\n [0, 0, 12, 8],\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"
}
] |
288
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 7, 3, 11],\n [0, -8, 6, -11],\n [0, 0, -9, -4],\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"
}
] |
280
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 4, 4, -8],\n [4, 1, -6, 0],\n [4, -6, 4, 0],\n [-8, 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"
}
] |
176
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 8, 8, 8],\n [2, -2, 11, 0],\n [-4, -7, -2, -7],\n [2, 1, -12, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
161
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 5, -9, -3],\n [-11, -7, -1, 7],\n [5, 7, 3, 5],\n [12, 8, 11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 1, -11, 6],\n [0, -12, -5, 1],\n [0, 0, 2, 2],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 6, -6, 5],\n [8, 2, 10, 0],\n [-8, -7, 5, -5],\n [-6, 11, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
420
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 7, 9, 11],\n [-4, 0, 4, 4],\n [-6, 11, -1, 1],\n [-4, -5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
376
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 5, -5, -3],\n [-5, -2, 0, -8],\n [-5, -4, 5, -9],\n [5, -8, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
813
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 8, -7, 9],\n [3, -4, 7, -6],\n [11, 8, 3, 5],\n [-12, -4, 10, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
244
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 4, -10, -1],\n [4, -4, 2, 0],\n [-10, 2, -7, 5],\n [-1, 0, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
704
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 0, -12, 11],\n [0, 6, 2, 12],\n [0, 0, -10, 10],\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"
}
] |
520
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 8, 10, 12],\n [9, -7, -8, 1],\n [-7, 11, -12, 3],\n [8, -11, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
628
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 6, 11, -1],\n [0, -7, -12, -12],\n [0, 0, 3, -10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
307
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 2, -2, 6],\n [2, -11, 0, 0],\n [-2, 0, 5, 4],\n [6, 0, 4, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
756
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 0, -3, -7],\n [0, -11, -11, -9],\n [0, 0, 8, 2],\n [0, 0, 0, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
816
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 7, 2, -7],\n [-2, -10, 5, 9],\n [8, -3, -8, 8],\n [4, -1, -7, 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"
}
] |
686
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, -1, -2],\n [2, 2, 5, 11],\n [-1, 5, 1, -6],\n [-2, 11, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
514
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 3, 0, -11],\n [0, 7, 10, -8],\n [0, 0, 2, 6],\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"
}
] |
350
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -5, -2, -4],\n [-5, -6, -4, 8],\n [-2, -4, 7, -8],\n [-4, 8, -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"
}
] |
547
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 0, -2, -8],\n [0, 7, -3, -6],\n [-2, -3, 11, -2],\n [-8, -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"
}
] |
684
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, 9, 4],\n [1, -8, 7, -3],\n [-6, 4, -6, 6],\n [-1, 4, 4, 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[[-4, 11, 4, -3],\n [1, -1, -1, 11],\n [9, -9, -12, 9],\n [-3, 9, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
309
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -10, -2, -5],\n [-10, 5, -1, -5],\n [-2, -1, -4, -1],\n [-5, -5, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
915
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 4, 4, -10],\n [0, 6, -4, -4],\n [0, 0, -10, 10],\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"
}
] |
860
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, -8, -4],\n [0, 3, -7, 0],\n [-8, -7, 10, 3],\n [-4, 0, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
787
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -6, 11, 5],\n [-5, -12, -4, 12],\n [8, -6, 12, -2],\n [-9, -4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
222
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, 9, 8],\n [0, -5, 2, 0],\n [0, 0, -12, -6],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
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