messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -3, -7, 3],\n [10, 10, 12, -6],\n [0, 12, -12, -12],\n [-11, -1, 1, 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"
}
] |
352
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 3, -5, 12],\n [0, -11, -8, 12],\n [0, 0, 9, -6],\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"
}
] |
346
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -3, 10, -11],\n [3, 4, -3, 6],\n [0, -2, 4, -4],\n [-5, -1, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
938
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 0, -6, 3],\n [0, 3, 10, 6],\n [-6, 10, -4, -1],\n [3, 6, -1, 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"
}
] |
282
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, 9, 8],\n [0, -1, -4, -1],\n [9, -4, 8, 0],\n [8, -1, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
497
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -4, -1, 4],\n [-4, -7, 0, -2],\n [-1, 0, 3, -3],\n [4, -2, -3, 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"
}
] |
329
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 4, 12, 3],\n [0, 6, -6, 7],\n [0, 0, -5, 3],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
460
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 5, -2, 9],\n [5, 6, -1, 1],\n [-2, -1, 2, 2],\n [9, 1, 2, 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"
}
] |
642
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 3, -1, 7],\n [3, -8, 9, 2],\n [-1, 9, 9, 5],\n [7, 2, 5, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
248
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 4, 8, -5],\n [4, -6, 6, 2],\n [8, 6, -4, 4],\n [-5, 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"
}
] |
924
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -11, 5, 11],\n [-3, -8, 11, 6],\n [-1, -12, -7, 7],\n [-9, 4, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -4, -10, 8],\n [-4, -10, -9, 10],\n [-10, -9, 2, -2],\n [8, 10, -2, -11]]\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[[-10, 4, -4, -8],\n [4, 5, 0, 2],\n [-4, 0, 1, 2],\n [-8, 2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
958
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -9, -10, 12],\n [-9, 0, 7, 9],\n [12, 10, -4, -7],\n [-10, -10, 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"
}
] |
322
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -2, 1, 3],\n [-2, -6, -4, -8],\n [1, -4, -8, -9],\n [3, -8, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
598
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -1, 0, -11],\n [0, 1, 11, 0],\n [0, 0, 12, -12],\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"
}
] |
676
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 3, 0, -5],\n [-3, 1, 12, -3],\n [6, -7, -11, 0],\n [4, 4, 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"
}
] |
277
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 4, 8, 11],\n [10, 2, -6, -1],\n [9, -10, -3, 0],\n [4, -6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
514
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 12, -5, -9],\n [0, -5, -12, 2],\n [0, 0, 3, 12],\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"
}
] |
810
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 12, 12, -5],\n [0, -1, -7, -6],\n [0, 0, 1, 3],\n [0, 0, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 6, 4, -2],\n [0, 12, -7, -8],\n [0, 0, 10, -12],\n [0, 0, 0, 11]]\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, 8, -5, 11],\n [0, -12, 7, 12],\n [0, 0, 11, 2],\n [0, 0, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
340
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 9, -7, 10],\n [4, 8, 2, 11],\n [5, -9, -7, 4],\n [-3, 3, -5, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
574
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -9, 11, -8],\n [0, -11, 1, -5],\n [0, 0, 10, -6],\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"
}
] |
450
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -4, -8, 4],\n [-11, -6, 3, -12],\n [10, -8, -3, 5],\n [-2, -7, 1, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
987
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 12, 12, 9],\n [0, -12, -10, 5],\n [0, 0, -6, 4],\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"
}
] |
464
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 8, 6, 0],\n [8, 10, -7, -5],\n [6, -7, -7, 0],\n [0, -5, 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"
}
] |
24
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -6, -6, 9],\n [-6, -11, 2, -8],\n [-6, 2, 11, -6],\n [9, -8, -6, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
841
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 9, -7, 2],\n [9, -8, -8, -10],\n [4, 6, 5, -11],\n [7, 4, 12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
155
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 6, -1, 12],\n [2, 9, -9, -5],\n [-11, -2, -7, 9],\n [-3, -4, 7, -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"
}
] |
964
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 4, 9, 6],\n [4, -11, 10, 1],\n [9, 10, 12, 5],\n [6, 1, 5, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
372
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, -3, -1],\n [-4, -10, 8, -6],\n [-3, 8, 7, -1],\n [-1, -6, -1, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -3, 4, 9],\n [-10, 6, 12, -10],\n [8, -12, 8, -3],\n [10, 7, 11, -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"
}
] |
54
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -4, 3, -2],\n [0, -12, -10, -6],\n [0, 0, 2, -1],\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"
}
] |
272
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, 1, -1],\n [2, 6, -7, -1],\n [1, -7, 10, 3],\n [-1, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
202
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 2, -5, 2],\n [0, -5, -2, 8],\n [0, 0, -11, 12],\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"
}
] |
380
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 9, 4, 2],\n [0, 9, -9, -1],\n [0, 0, 5, -10],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
700
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -3, 8, 10],\n [0, -5, 11, -4],\n [0, 0, 4, 0],\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"
}
] |
20
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 11, 0, -6],\n [0, -4, 5, 11],\n [-12, 5, 5, -10],\n [9, 6, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
605
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 5, -12, -12],\n [2, 11, -6, -8],\n [5, 0, 2, 4],\n [-9, 4, -9, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -5, 5, 2],\n [-5, 10, 0, 6],\n [5, 0, -6, 8],\n [2, 6, 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"
}
] |
372
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 12, 4, -11],\n [1, 0, -12, -2],\n [10, -10, 7, -10],\n [2, -7, 3, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 5, 2, 12],\n [0, -2, -8, -10],\n [0, 0, 3, 12],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
748
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -6, -7, 2],\n [-6, -11, -2, 5],\n [-7, -2, -12, 0],\n [2, 5, 0, -9]]\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[[9, 2, 4, 1],\n [2, 7, -10, 1],\n [4, -10, -11, 4],\n [1, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
521
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 12, -1, -7],\n [-4, -3, 9, 0],\n [-10, -10, -11, 5],\n [-5, -7, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
328
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 8, 6, 4],\n [0, -6, 9, 3],\n [0, 0, -11, 0],\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"
}
] |
380
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 0, -5, -6],\n [0, 8, 0, 9],\n [0, 0, 10, -5],\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"
}
] |
80
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -6, 8, -3],\n [-6, 4, -3, 2],\n [8, -3, -11, 0],\n [-3, 2, 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"
}
] |
37
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -6, -7, 4],\n [0, 5, 10, -9],\n [0, 0, -12, 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"
}
] |
360
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -8, 4, 9],\n [-7, -9, 8, -6],\n [11, 5, -1, -6],\n [1, -1, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
616
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 0, -8, 8],\n [0, 2, -8, 4],\n [0, 0, 5, -12],\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"
}
] |
930
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -6, 9, 11],\n [9, 4, 9, -4],\n [-4, 1, -6, -11],\n [10, 11, 5, -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"
}
] |
481
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -10, 2, 6],\n [-10, 2, 4, 4],\n [2, 4, -1, 5],\n [6, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -2, 8, 0],\n [-2, -5, -7, 0],\n [8, -7, 7, -8],\n [0, 0, -8, 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"
}
] |
36
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -1, -10, 12],\n [0, -4, -5, -9],\n [0, 0, 4, -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"
}
] |
856
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -3, 4, 9],\n [0, -11, -6, -9],\n [0, 0, -10, 10],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 0, -2, 6],\n [0, -10, -4, -2],\n [-2, -4, -11, -3],\n [6, -2, -3, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
116
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 8, -3, -9],\n [8, 5, -2, 4],\n [-3, -2, -8, -10],\n [-9, 4, -10, -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"
}
] |
181
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -2, -1, 0],\n [-2, 6, 0, -5],\n [-1, 0, 12, 8],\n [0, -5, 8, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
195
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -6, 8, 4],\n [-6, -10, 1, 2],\n [8, 1, -3, 6],\n [4, 2, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
933
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -5, 8, -4],\n [-5, 11, -2, 0],\n [8, -2, -3, -5],\n [-4, 0, -5, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
312
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -11, -2, -12],\n [-9, 5, -6, -12],\n [-9, 1, -10, -12],\n [-6, -10, 11, -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"
}
] |
144
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 6, 8, -4],\n [6, -2, -6, -11],\n [8, -6, -10, -4],\n [-4, -11, -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"
}
] |
348
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 6, 11, -10],\n [0, -11, -1, -8],\n [0, 0, -8, -9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 7, 0, 2],\n [3, 2, -2, -12],\n [11, -12, -12, -1],\n [-4, 9, 2, 6]]\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[[-6, -3, -7, -10],\n [-3, 9, 10, 8],\n [-7, 10, 12, 0],\n [-10, 8, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
681
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 1, 2, -2],\n [1, 9, 4, -4],\n [2, 4, 1, 4],\n [-2, -4, 4, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
946
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -1, 12, 8],\n [0, 5, -6, 3],\n [0, 0, 5, 11],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
500
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 9, 12, 0],\n [9, 8, 2, 2],\n [12, 2, -8, 4],\n [0, 2, 4, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
164
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 12, 0, 5],\n [5, 12, 9, 7],\n [-7, 1, 4, 6],\n [3, -11, -8, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
271
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -2, -4, 0],\n [-2, 3, 0, -6],\n [-4, 0, -4, 6],\n [0, -6, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
688
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 9, 2, 10],\n [5, 5, -5, 0],\n [-2, -12, -4, 4],\n [-9, -11, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -10, -3, -3],\n [0, 1, -11, -4],\n [0, 0, 5, -7],\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"
}
] |
520
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 1, -10, 3],\n [0, 9, -9, 7],\n [0, 0, 3, -9],\n [0, 0, 0, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
704
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -1, 5, 0],\n [-1, -12, -6, 6],\n [5, -6, -10, 6],\n [0, 6, 6, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
496
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 1, 0, 3],\n [-2, -10, 3, -9],\n [12, 4, 0, 10],\n [-2, -9, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
650
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 0, 7, -8],\n [7, 12, -3, -5],\n [0, -11, 3, 10],\n [-4, -8, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
423
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 3, 0, -5],\n [-4, -10, -12, -8],\n [6, -9, -3, 10],\n [10, -8, -4, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
196
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -5, 5, 3],\n [-5, -2, -12, 8],\n [-2, 3, 9, 1],\n [5, 4, 5, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
742
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 10, 2, 4],\n [-9, 10, -8, -12],\n [-2, -8, -11, -11],\n [1, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
888
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 9, 6, -8],\n [9, 1, 2, 1],\n [6, 2, 2, 2],\n [-8, 1, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
536
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 3, -7, 8],\n [0, 12, 9, 7],\n [0, 0, 6, 4],\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"
}
] |
864
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 12, 4, -7],\n [0, 5, 11, -6],\n [0, 0, 11, 1],\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"
}
] |
320
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 10, -6, 4],\n [10, 11, 6, -1],\n [-6, 6, -3, 0],\n [4, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
412
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 3, 6, -4],\n [1, 12, -7, -8],\n [-7, -6, 0, -6],\n [-3, 2, -2, 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"
}
] |
189
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 6, -7, 5],\n [0, -10, -7, -8],\n [0, 0, -3, -12],\n [0, 0, 0, 8]]\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[[0, 8, 9, 3],\n [8, -3, 6, -6],\n [9, 6, -2, 0],\n [3, -6, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
591
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -12, -4, 3],\n [-11, 2, 5, -7],\n [11, -8, -8, -12],\n [8, 9, -6, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
151
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -1, 2, 4],\n [0, -3, -4, 4],\n [0, 0, 3, -11],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
252
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 10, -7, -6],\n [0, -10, 0, -7],\n [0, 0, 8, -3],\n [0, 0, 0, -2]]\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[[-7, 2, 11, 0],\n [0, 3, -4, -11],\n [0, 0, 12, -2],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -1, -5, -1],\n [-1, -5, 10, 0],\n [-5, 10, -10, -1],\n [-1, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
761
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 8, -2, -2],\n [8, 9, 4, 10],\n [-2, 4, 9, 0],\n [-2, 10, 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"
}
] |
115
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 8, 3, 3],\n [8, 3, -4, 4],\n [3, -4, 9, 8],\n [3, 4, 8, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
899
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 1, -2, 0],\n [1, -6, -8, -1],\n [-2, -8, -10, 0],\n [0, -1, 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"
}
] |
384
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 11, 3, 12],\n [0, 5, -8, -6],\n [0, 0, -5, -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"
}
] |
75
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 9, -10, 12],\n [12, -8, -12, 9],\n [-11, 4, 1, 6],\n [9, -11, 1, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
370
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -10, -2, -2],\n [-10, -1, -4, 2],\n [-2, -4, 3, 5],\n [-2, 2, 5, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
584
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 2, 2, -6],\n [-3, -8, 7, 5],\n [-8, -10, -12, 9],\n [8, -1, -6, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
836
|
MATH
|
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