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[[-9, -4, 6, -1],\n [-4, 1, 0, -10],\n [6, 0, 1, 4],\n [-1, -10, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
607
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 5, 3, -3],\n [0, -12, 12, -3],\n [0, 0, -12, 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"
}
] |
272
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -2, 2, 0],\n [-2, -10, -4, -9],\n [2, -4, -2, -2],\n [0, -9, -2, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
654
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, -11, -8],\n [2, 4, -1, 4],\n [0, 11, 4, 12],\n [0, 2, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
789
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -2, -2, 6],\n [-2, -8, -12, 6],\n [-2, -12, 5, 6],\n [6, 6, 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"
}
] |
704
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 4, 5, 6],\n [0, 10, -6, -8],\n [0, 0, 8, 5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -9, -1, 8],\n [10, -1, -12, -9],\n [12, 8, 7, -6],\n [7, -11, 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"
}
] |
929
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, -11, 4],\n [0, 8, 4, -3],\n [0, 0, -4, -5],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 1, 1, -7],\n [9, -7, -8, 8],\n [-4, -4, -11, -10],\n [-7, 6, -3, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
147
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -6, 0, -4],\n [-6, -11, -5, 5],\n [0, -5, -8, 8],\n [-4, 5, 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"
}
] |
352
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 10, -7, -9],\n [-3, -5, 1, -8],\n [-11, 6, -12, 3],\n [5, 12, -3, 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"
}
] |
341
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -8, -7, -9],\n [-12, 1, -4, 0],\n [-7, 3, 7, 6],\n [1, 10, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
281
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 5, 8, -4],\n [0, 7, -12, 12],\n [0, 0, 5, 0],\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"
}
] |
20
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 9, 10, -6],\n [-12, -10, 9, 3],\n [-6, -6, -5, -10],\n [9, 0, 5, 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"
}
] |
3
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, 12, -5],\n [0, -6, 5, -8],\n [0, 0, 9, -2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
158
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 4, -6, -8],\n [4, 7, -3, -1],\n [-6, -3, -12, 7],\n [-8, -1, 7, 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"
}
] |
110
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 2, 11, 2],\n [1, -9, 9, 11],\n [5, -6, 6, -12],\n [-5, 8, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
233
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 10, 5, 0],\n [-3, 8, 7, 12],\n [-7, -8, 7, 2],\n [-7, 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"
}
] |
280
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -7, 9, -9],\n [-6, -4, 3, 3],\n [11, 10, -8, -2],\n [9, -7, -8, 0]]\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[[-3, 4, -8, 8],\n [0, -1, -2, -11],\n [0, 0, -3, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 3, 0, 2],\n [9, 1, 3, -5],\n [9, -2, -4, -12],\n [1, -1, 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"
}
] |
246
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -12, 9, -2],\n [8, 8, -12, 10],\n [-2, 12, 3, 11],\n [6, -8, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
832
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -4, 3, 5],\n [0, 10, -10, 10],\n [0, 0, -11, 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"
}
] |
650
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 5, 4, -2],\n [0, 7, 3, 6],\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"
}
] |
176
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -6, -8, 0],\n [-6, -4, -2, -7],\n [-8, -2, 8, -2],\n [0, -7, -2, 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"
}
] |
208
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -10, -7, 5],\n [0, 5, -5, -7],\n [0, 0, -5, -6],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
150
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 0, -6, 4],\n [0, 1, 2, -4],\n [-6, 2, 11, -3],\n [4, -4, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
442
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -11, 9, -5],\n [6, -2, 5, -9],\n [-3, -9, 12, 5],\n [-4, 4, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
496
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 7, 6, -8],\n [-11, 0, 2, 11],\n [-8, 4, -10, -3],\n [7, 12, 9, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
565
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -10, 3, 6],\n [0, -8, -10, -1],\n [0, 0, -4, 2],\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"
}
] |
152
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 2, 6, 1],\n [2, 9, -5, 6],\n [6, -5, -5, 5],\n [1, 6, 5, -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"
}
] |
517
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -2, 2, -6],\n [-2, -4, -3, 2],\n [2, -3, 3, 0],\n [-6, 2, 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"
}
] |
622
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -6, 0, 2],\n [0, -8, 12, 8],\n [0, 0, -11, -1],\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"
}
] |
56
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 10, 9, -6],\n [2, -6, -4, -9],\n [7, -4, 0, -2],\n [5, -8, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
362
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -6, -3, 10],\n [-6, 1, 1, -6],\n [-3, 1, 11, -1],\n [10, -6, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
361
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -5, -5, 6],\n [-8, 5, 4, -5],\n [-3, -11, -12, -6],\n [-5, 4, 3, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
523
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -6, 1, 0],\n [-6, -1, -5, 1],\n [1, -5, 3, -3],\n [0, 1, -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"
}
] |
848
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 10, -7, -5],\n [0, 2, -1, -12],\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"
}
] |
720
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -9, -12, -8],\n [-2, -11, -11, 9],\n [11, -5, -3, -9],\n [-8, 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"
}
] |
575
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 1, 3, 3],\n [-12, -1, -9, -1],\n [4, -9, 10, -10],\n [-1, -2, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
636
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -8, 9, 7],\n [9, -7, -2, 9],\n [7, 12, -8, -8],\n [0, 1, 9, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
418
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -10, 2, 4],\n [0, 11, -12, -3],\n [0, 0, 1, -10],\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"
}
] |
307
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -3, -4, -12],\n [0, 5, 3, 4],\n [0, 0, 4, -10],\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"
}
] |
640
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -4, 3, 11],\n [2, -7, -11, -9],\n [3, -5, 10, -12],\n [4, -1, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 8, 6, 9],\n [0, 1, -11, 11],\n [0, 0, 12, 4],\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"
}
] |
976
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -8, 2, -3],\n [-2, 3, -5, -12],\n [8, 8, -10, 8],\n [10, -2, -7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
920
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -4, 3, 1],\n [-4, 8, -2, 2],\n [3, -2, -1, 8],\n [1, 2, 8, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
928
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 4, -9, 4],\n [4, -12, 0, 0],\n [-9, 0, 3, 0],\n [4, 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"
}
] |
140
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -5, -10, -3],\n [0, 12, -2, 10],\n [0, 0, 2, -7],\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"
}
] |
264
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 2, -4, 7],\n [-12, 2, -12, -8],\n [9, -6, 7, 0],\n [8, 5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
510
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -3, 9, 8],\n [11, -7, -11, 5],\n [10, -12, -5, 10],\n [4, 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"
}
] |
825
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 11, 1, 6],\n [-11, 12, 7, -1],\n [-8, 8, -2, -10],\n [-1, 4, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
478
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 11, 10, 7],\n [0, -5, -11, 7],\n [0, 0, 1, -10],\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"
}
] |
835
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -4, -3, 6],\n [0, -6, 12, 8],\n [0, 0, 9, 0],\n [0, 0, 0, -4]]\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[[-8, 5, 1, 5],\n [0, -9, 7, 11],\n [0, 0, -4, -5],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
576
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 9, -8, 4],\n [12, 4, -8, 11],\n [11, 2, -4, 2],\n [-5, 1, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
103
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -2, 0, -9],\n [0, -11, -1, 11],\n [-5, 9, 11, -8],\n [-12, 8, -9, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
269
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 7, 5, -10],\n [0, -5, -6, 1],\n [0, 0, -2, -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"
}
] |
550
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -1, 10, 9],\n [-7, -2, -6, 4],\n [3, -4, 4, -3],\n [9, 4, -10, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
250
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -4, -4, -4],\n [-4, -12, 8, 10],\n [-4, 8, 9, 6],\n [-4, 10, 6, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
196
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 6, 0, -3],\n [6, -10, 2, -2],\n [0, 2, 7, 0],\n [-3, -2, 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"
}
] |
962
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 12, 2, -1],\n [5, 9, 5, 1],\n [-10, 7, -11, 0],\n [-9, 11, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
298
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -11, -3, -7],\n [0, 12, -4, 2],\n [0, 0, -11, -1],\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"
}
] |
680
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -6, 6, -1],\n [0, -4, 2, 1],\n [0, 0, 6, -4],\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"
}
] |
984
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 6, -6, 2],\n [6, 6, 8, -2],\n [-6, 8, 6, 5],\n [2, -2, 5, 5]]\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[[3, -4, -6, -8],\n [-4, -8, -4, 10],\n [-6, -4, 12, 1],\n [-8, 10, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 0, 1, -7],\n [0, 0, 8, 0],\n [1, 8, 9, -1],\n [-7, 0, -1, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 11, -11, 11],\n [0, -11, -7, 7],\n [0, 0, 3, -3],\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"
}
] |
264
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 0, 1, -2],\n [0, 3, 0, 4],\n [1, 0, 6, 5],\n [-2, 4, 5, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
274
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -1, -4, 1],\n [-1, -5, -6, 2],\n [-4, -6, -11, -6],\n [1, 2, -6, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
211
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 12, -6, 1],\n [-1, 0, 10, -11],\n [1, -1, 10, 7],\n [11, -12, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
716
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 7, 9, -4],\n [7, -10, 4, -8],\n [9, 4, -3, -6],\n [-4, -8, -6, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
534
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -3, 3, -12],\n [5, 2, 5, -6],\n [7, -4, -6, -2],\n [3, 10, 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"
}
] |
548
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -5, 6, 10],\n [-1, -12, 8, 6],\n [5, -3, -6, 0],\n [10, -3, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -11, 4, -1],\n [0, -1, -8, -1],\n [0, 0, -7, 1],\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"
}
] |
230
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 6, 12, -10],\n [0, 3, 1, 1],\n [0, 0, -5, -6],\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"
}
] |
50
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 9, 0, 2],\n [9, 9, 2, 2],\n [0, 2, 8, -9],\n [2, 2, -9, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
574
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -1, 0, 6],\n [-1, 0, 10, -2],\n [0, 10, -2, -7],\n [6, -2, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
385
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 6, 2, -10],\n [6, -7, -2, 4],\n [2, -2, -1, -3],\n [-10, 4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
162
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -10, -3, 4],\n [0, 3, 10, -1],\n [0, 0, -11, 8],\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"
}
] |
79
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 1, 0, -1],\n [1, -8, -2, -3],\n [0, -2, -12, 0],\n [-1, -3, 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"
}
] |
252
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 5, -10, 5],\n [0, 5, -5, 3],\n [0, 0, -9, 1],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
350
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -11, -12, -3],\n [2, 8, 1, -4],\n [10, 11, -7, 11],\n [6, 10, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
52
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -7, -7, 1],\n [0, 2, 0, 4],\n [0, 0, 1, 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"
}
] |
940
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 8, -6, 0],\n [8, -9, 10, -2],\n [-6, 10, -11, 2],\n [0, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
942
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -4, -4, -6],\n [-1, 6, -2, -2],\n [11, -1, 10, 11],\n [-10, 9, -9, -4]]? 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": "Compute |A| for the matrix A =\n[[-12, 0, 6, -2],\n [0, 8, 2, 2],\n [6, 2, 4, 2],\n [-2, 2, 2, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
368
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, -2, -2],\n [2, 4, -4, -6],\n [-2, -4, -9, 6],\n [-2, -6, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
208
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 2, -5, 7],\n [0, 11, 1, 6],\n [0, 0, 11, -3],\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"
}
] |
68
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 3, -3, 0],\n [3, 12, -7, -2],\n [-3, -7, -9, -9],\n [0, -2, -9, 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"
}
] |
571
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 3, -3, -12],\n [-5, -8, 12, 7],\n [-11, -9, -4, -7],\n [10, 2, 9, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
980
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -2, 2, -2],\n [-2, -10, -8, 7],\n [2, -8, 12, -6],\n [-2, 7, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
516
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -10, 2, -3],\n [0, -5, 4, -9],\n [0, 0, -7, -8],\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"
}
] |
260
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 4, 5, -12],\n [0, 9, -4, -6],\n [0, 0, 6, -5],\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"
}
] |
646
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 3, 0, 7],\n [0, 5, -10, 8],\n [-6, 1, 10, 7],\n [-5, 7, 10, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
690
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -12, 8, 8],\n [0, -2, -3, 2],\n [0, 0, -11, 8],\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"
}
] |
306
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 10, 1, 3],\n [0, -11, 4, 11],\n [0, 0, 5, 5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
620
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 0, -8, 2],\n [0, 12, 5, -1],\n [-8, 5, -1, 4],\n [2, -1, 4, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -12, 1, 11],\n [-3, 7, -6, 6],\n [-1, 2, 8, 12],\n [9, -1, 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"
}
] |
559
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -2, 2, 1],\n [-2, 12, 4, 5],\n [2, 4, 4, -10],\n [1, 5, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
580
|
MATH
|
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