messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -2, -9, 2],\n [-2, -2, -2, -4],\n [-9, -2, -12, 4],\n [2, -4, 4, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
522
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -1, -2, 12],\n [0, -11, 7, 2],\n [0, 0, 9, 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"
}
] |
188
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 4, -1, -6],\n [4, -1, -6, -4],\n [-1, -6, -1, -6],\n [-6, -4, -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"
}
] |
486
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 11, 8, -3],\n [0, -4, -2, -9],\n [0, 0, -8, 11],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
848
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -8, 0, 7],\n [0, -3, -1, 7],\n [0, 0, -3, -12],\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"
}
] |
838
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -10, 9, 2],\n [0, 10, 6, 7],\n [0, 0, 8, -7],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 8, 2, -2],\n [8, 9, 0, 0],\n [2, 0, -6, 2],\n [-2, 0, 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"
}
] |
316
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -6, 2, -4],\n [-6, -12, 4, 0],\n [2, 4, -11, -7],\n [-4, 0, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
948
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 10, -2, 12],\n [6, 11, -3, 1],\n [-1, -2, 12, -10],\n [6, -1, -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"
}
] |
510
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -8, 8, 1],\n [10, -1, 9, -11],\n [-7, 2, 0, 9],\n [11, 9, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
59
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 7, 3, -4],\n [0, 7, 10, 5],\n [0, 0, 7, -9],\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"
}
] |
383
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -8, 2, -7],\n [-8, 10, 3, 2],\n [2, 3, 1, -2],\n [-7, 2, -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"
}
] |
609
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 12, -9, -12],\n [-6, 6, -11, -2],\n [-6, -11, 12, 4],\n [-3, 7, -3, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
897
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -7, -11, -6],\n [3, 4, 5, 5],\n [-8, 11, -10, -4],\n [6, 4, 6, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
430
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 12, -6, 8],\n [8, 4, -12, -10],\n [-1, -10, -9, 7],\n [-1, 4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 8, -4, 11],\n [0, -3, -5, 8],\n [0, 0, -11, 9],\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"
}
] |
320
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -2, 12, -11],\n [-1, -5, -2, -9],\n [6, 6, 10, -1],\n [-3, -4, 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"
}
] |
44
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 0, 0, 12],\n [0, 9, -2, -6],\n [0, -2, 12, -4],\n [12, -6, -4, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
304
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -11, 9, -5],\n [-11, -11, -3, 8],\n [3, -10, 9, 1],\n [11, 5, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
491
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 4, -4, -8],\n [4, 8, 2, 2],\n [-4, 2, 7, -4],\n [-8, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
660
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -9, -8, 0],\n [-9, 10, -6, 10],\n [-8, -6, 4, 7],\n [0, 10, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -11, -10, -7],\n [0, 8, 12, 7],\n [0, 0, 7, 2],\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"
}
] |
696
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 4, -8, 9],\n [0, -4, 1, -2],\n [0, 0, 2, 0],\n [0, 0, 0, 10]]\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[[-11, 8, -2, 3],\n [0, -1, 8, 1],\n [0, 0, -11, 3],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
516
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -8, 12, 0],\n [0, 5, -12, 12],\n [0, 0, -10, -7],\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"
}
] |
500
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, 2, 0],\n [-2, -10, 0, -2],\n [2, 0, 6, 8],\n [0, -2, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
768
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -10, 9, 10],\n [-7, 12, -5, 7],\n [-7, 8, 11, 10],\n [10, -3, -6, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
368
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 0, -10, 1],\n [0, 11, -5, -2],\n [-6, 10, 9, 11],\n [1, -8, 8, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
441
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -3, 2, 0],\n [0, -1, 10, -11],\n [0, 0, -3, -3],\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"
}
] |
976
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -10, 0, 2],\n [-7, -1, 5, -5],\n [-1, -11, -1, -2],\n [-9, 0, -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"
}
] |
162
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 4, 0, -10],\n [4, 10, 4, -2],\n [0, 4, -5, 5],\n [-10, -2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
792
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -4, 4, -7],\n [-9, 10, 9, 1],\n [5, 8, -1, -11],\n [-2, -2, -7, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
554
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 2, -4, 7],\n [2, -2, -2, 12],\n [-4, -2, -10, 0],\n [7, 12, 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"
}
] |
760
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 9, -12, -8],\n [0, 12, 3, -3],\n [0, 0, 1, 2],\n [0, 0, 0, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -10, 2, -7],\n [0, -3, 9, 8],\n [0, 0, 7, 10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
504
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -3, -8, 11],\n [-3, 9, 6, 10],\n [-8, 6, -2, 1],\n [11, 10, 1, 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"
}
] |
388
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -7, -5, 0],\n [-12, -10, 1, -5],\n [-2, -6, 5, -8],\n [5, 6, -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"
}
] |
191
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 1, 1, 12],\n [2, -8, 1, 10],\n [-1, -6, 10, -3],\n [11, -1, -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"
}
] |
139
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 4, -2, 4],\n [4, -5, -3, 2],\n [-2, -3, 1, -4],\n [4, 2, -4, 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"
}
] |
946
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -1, -8, 11],\n [8, -1, 9, 7],\n [-8, 4, 2, 1],\n [-7, 0, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
523
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 0, 8, -6],\n [0, 6, 3, 4],\n [8, 3, 9, -2],\n [-6, 4, -2, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
426
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -2, 9, -6],\n [0, 5, 3, 4],\n [0, 0, 10, 2],\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"
}
] |
700
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 0, -3, 6],\n [9, -2, -10, 9],\n [0, -6, 3, -12],\n [-11, -9, -1, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
832
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -4, -6, -9],\n [-4, 6, -11, 4],\n [11, 9, -7, -6],\n [-8, -11, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
385
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -4, 3, -4],\n [-4, -6, 6, 6],\n [3, 6, -10, 8],\n [-4, 6, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
988
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -2, 12, 8],\n [0, 11, -7, -8],\n [0, 0, -5, -6],\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"
}
] |
845
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 4, -10, -6],\n [5, 7, 8, 4],\n [9, -4, 10, 1],\n [-9, 8, 6, -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"
}
] |
284
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 3, 6, 6],\n [3, 12, -10, 2],\n [6, -10, -6, 5],\n [6, 2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
425
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -5, -6, 5],\n [0, -1, 5, -11],\n [0, 0, -11, 9],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
406
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -11, -7, -10],\n [0, -10, -6, 6],\n [0, 0, 1, -10],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -9, -6, 8],\n [2, 12, -1, 10],\n [-6, 5, 1, -2],\n [-7, 2, 4, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
294
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -2, -10, -6],\n [-2, -4, 4, 2],\n [-10, 4, 10, 8],\n [-6, 2, 8, 8]]\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": "What is the determinant of the matrix:\n[[6, -6, 0, 2],\n [-6, 2, -4, 2],\n [0, -4, 3, -2],\n [2, 2, -2, -11]]? 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[[-4, -3, -4, -6],\n [-3, -12, -4, 8],\n [-4, -4, 9, 3],\n [-6, 8, 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"
}
] |
866
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, 1, 5],\n [7, -3, 6, -3],\n [1, 6, 3, 5],\n [5, -3, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
815
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -4, 10, 11],\n [-2, -2, 8, -1],\n [-12, -5, 12, -7],\n [-1, -10, 1, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
530
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 0, -6, 8],\n [0, -9, 6, 5],\n [-6, 6, -1, -2],\n [8, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
97
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 11, -8, -8],\n [0, -1, 6, 9],\n [0, 0, -4, 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"
}
] |
24
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 12, 7, 8],\n [11, 7, -5, 4],\n [10, -8, 8, -4],\n [-5, 12, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
934
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -8, -12, 5],\n [0, -10, 7, 7],\n [0, 0, 10, 9],\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"
}
] |
400
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -3, 9, -5],\n [-12, 1, -2, -6],\n [-4, 11, 3, -9],\n [-2, 7, -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"
}
] |
724
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 3, 8, 8],\n [6, 5, 2, -12],\n [-9, 10, 9, 6],\n [-5, -12, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
537
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 7, 7, -5],\n [0, 10, -1, -7],\n [0, 0, 12, -4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -11, -10, 4],\n [-12, 3, -9, 4],\n [-4, 4, 9, -9],\n [4, -5, 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"
}
] |
341
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -12, -9, 12],\n [-7, -9, 4, 9],\n [-10, -8, 8, 4],\n [5, -1, 6, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
636
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 0, 2, -2],\n [0, -3, -2, 6],\n [2, -2, 3, -5],\n [-2, 6, -5, 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"
}
] |
88
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 8, -2, 3],\n [0, 12, 8, -5],\n [0, 0, -7, 4],\n [0, 0, 0, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
992
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 0, 0, -7],\n [0, -12, 4, 1],\n [0, 0, -1, -9],\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"
}
] |
756
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -7, 5, -2],\n [0, 9, -8, -12],\n [0, 0, 6, 5],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
536
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 12, 0, -3],\n [12, 8, 4, 0],\n [0, 4, -3, -6],\n [-3, 0, -6, -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"
}
] |
360
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 12, -5, -12],\n [0, -1, 0, -6],\n [0, 0, -9, 5],\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"
}
] |
9
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -3, -6, -2],\n [-12, 6, 10, -8],\n [12, -3, -11, -5],\n [-9, -8, 2, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
958
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -1, 10, 8],\n [-1, -5, 4, 2],\n [10, 4, 9, 1],\n [8, 2, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 11, -10, 7],\n [2, -10, -12, -11],\n [-6, -5, -5, 12],\n [-2, 2, 1, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
461
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 6, -8, -4],\n [6, 2, 2, 7],\n [-8, 2, 10, 4],\n [-4, 7, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 6, 6, 5],\n [6, -11, -8, -2],\n [6, -8, -4, 0],\n [5, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
924
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -3, 7, -3],\n [0, -9, -3, -6],\n [0, 0, -9, -9],\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"
}
] |
252
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -5, 7, 1],\n [0, 12, -7, -5],\n [0, 0, -7, -3],\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[[3, 0, 5, 0],\n [0, 0, -5, -6],\n [5, -5, -1, -2],\n [0, -6, -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"
}
] |
423
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 11, -12, 3],\n [-12, 5, -7, 4],\n [12, -12, 3, -3],\n [-6, 9, -3, 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"
}
] |
228
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -9, -6, -6],\n [12, 1, -3, -10],\n [-6, -1, -11, 11],\n [-11, 1, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
411
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -1, 9, -12],\n [0, -4, -7, -3],\n [0, 0, -2, -7],\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"
}
] |
264
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 7, 8, 2],\n [7, -9, -4, 3],\n [8, -4, -12, -3],\n [2, 3, -3, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
845
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -8, -9, 1],\n [4, 3, -6, -12],\n [1, -2, 11, 6],\n [-12, 4, 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"
}
] |
834
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 2, 2, 4],\n [2, -2, -10, -2],\n [2, -10, 2, -6],\n [4, -2, -6, -1]]? 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": "Compute |A| for the matrix A =\n[[3, -4, 2, -4],\n [-4, 10, -12, 2],\n [2, -12, 2, -6],\n [-4, 2, -6, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
772
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 9, -7, 9],\n [0, 5, 11, 9],\n [0, 0, -4, 8],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -1, -5, -5],\n [0, -12, 6, -1],\n [0, 0, -6, -10],\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"
}
] |
960
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 2, 6, 2],\n [2, -5, -5, 9],\n [6, -5, -6, 2],\n [2, 9, 2, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
639
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 9, 8, 10],\n [0, 9, -9, -7],\n [0, 0, 1, -2],\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"
}
] |
324
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, -2, 8],\n [5, 7, 10, 10],\n [-7, -2, 3, 8],\n [-6, -11, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
777
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -2, 6],\n [-2, -6, -6, -4],\n [-2, -6, -1, 2],\n [6, -4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
554
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 1, 12, 4],\n [0, -2, -12, -7],\n [0, 0, 5, 8],\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"
}
] |
880
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -4, -9, 3],\n [0, 5, 3, 0],\n [0, 0, 9, 11],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
325
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -9, -10, 9],\n [12, -12, -3, 5],\n [5, -8, 7, -1],\n [9, -7, -5, -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"
}
] |
871
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -2, -12, 4],\n [0, -12, 6, -3],\n [0, 0, -2, -4],\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"
}
] |
848
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 2, 3, 0],\n [2, -7, -6, 2],\n [3, -6, -2, 0],\n [0, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
194
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 0, 2, 5],\n [0, -1, -2, 7],\n [2, -2, 1, 2],\n [5, 7, 2, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
450
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 5, 9, 1],\n [0, -11, -3, 4],\n [0, 0, -6, 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"
}
] |
650
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 8, -2, -3],\n [8, 9, 8, -4],\n [-2, 8, -2, 1],\n [-3, -4, 1, 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"
}
] |
34
|
MATH
|
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