messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 9, -2, -4],\n [9, 3, -8, 6],\n [-2, -8, -8, -4],\n [-4, 6, -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"
}
] |
276
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -8, 6, 0],\n [-8, -1, -9, -7],\n [6, -9, -9, 5],\n [0, -7, 5, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
576
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 7, -9, 0],\n [0, 11, -7, 7],\n [0, 0, 12, 10],\n [0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 1, 3, -9],\n [0, -10, -7, -4],\n [0, 0, -3, 0],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
450
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -6, 10, 8],\n [-6, 1, -3, -6],\n [10, -3, 5, -8],\n [8, -6, -8, -7]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 5, -1, 11],\n [5, -8, -5, 7],\n [-12, -11, -9, -10],\n [-8, 6, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 5, 10, -6],\n [11, 10, -4, -12],\n [6, 2, -3, 7],\n [-9, -9, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
580
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, 6, -7],\n [0, 4, 0, -8],\n [6, 0, -2, -2],\n [-7, -8, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
864
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 9, 0, 8],\n [9, 4, 4, -10],\n [0, 4, 2, 0],\n [8, -10, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
448
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -9, 3, 9],\n [0, 5, -12, 6],\n [0, 0, 1, -6],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -2, 5, -11],\n [0, -11, -11, -11],\n [0, 0, 5, -3],\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"
}
] |
320
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 1, -10, 3],\n [1, -10, 1, -2],\n [-10, 1, 1, 5],\n [3, -2, 5, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
396
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -6, 5, 5],\n [-6, 7, 10, 4],\n [5, 10, -8, 4],\n [5, 4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
803
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 3, -12, -8],\n [-4, 1, 4, -9],\n [9, 12, 4, 11],\n [-5, 3, 2, 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"
}
] |
958
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -12, -6, -1],\n [-1, -11, -3, 5],\n [-8, -8, 4, 12],\n [6, 8, -5, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
488
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 4, -10, -10],\n [0, 12, 10, 10],\n [-4, 3, -4, -6],\n [-6, -2, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
336
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 0, -12, 6],\n [-3, -1, -3, -2],\n [-12, -5, -10, 7],\n [8, -3, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
333
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 11, 12, -6],\n [0, -4, -4, -5],\n [0, 0, -7, -10],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
968
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 0, -8, 8],\n [0, -6, 0, 4],\n [-8, 0, -10, -4],\n [8, 4, -4, -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"
}
] |
648
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -8, 12, 5],\n [0, 5, 2, -9],\n [0, 0, -3, -7],\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"
}
] |
865
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -5, 2, 0],\n [-5, 6, -1, 3],\n [2, -1, -3, -3],\n [0, 3, -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"
}
] |
100
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 8, -2, 8],\n [0, 6, 11, -5],\n [0, 0, 9, -8],\n [0, 0, 0, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
700
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -6, 0, -6],\n [11, 11, 6, 11],\n [-8, 12, 11, -5],\n [10, 12, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
913
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 2, 8, -2],\n [2, 9, -4, 4],\n [8, -4, 5, 0],\n [-2, 4, 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"
}
] |
531
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 8, -1, 0],\n [8, -2, 0, -2],\n [-1, 0, -4, -2],\n [0, -2, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
356
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -11, 0, 10],\n [0, 11, 9, -8],\n [0, 0, 10, 6],\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"
}
] |
700
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -4, 8, 9],\n [-8, 6, -3, 9],\n [-9, 10, 1, 0],\n [-10, 12, -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"
}
] |
448
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 3, -12, -7],\n [0, -2, -5, -9],\n [-10, -1, 2, -12],\n [-5, 6, 2, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
865
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -9, -12, -8],\n [10, 11, 2, -10],\n [9, 2, -7, 12],\n [7, -12, -1, 0]]\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": "Determine the value of det(A) where A =\n[[-5, 5, -6, 3],\n [6, -4, -5, 8],\n [7, -3, 4, -6],\n [-4, -12, 7, 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"
}
] |
970
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 9, -10, -1],\n [0, 7, 3, 3],\n [0, 0, -4, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
588
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -3, 8, -12],\n [0, 1, 1, 6],\n [0, 0, -2, 2],\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"
}
] |
100
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 2, 8, -6],\n [2, -11, -2, 8],\n [8, -2, 7, -2],\n [-6, 8, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, -5, -5],\n [-8, 8, 5, 5],\n [-10, -5, -2, -3],\n [5, 6, 6, -12]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 1, 6, -1],\n [12, 0, -10, -2],\n [-4, 5, 4, 8],\n [4, 3, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
192
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -12, 4, -1],\n [-8, 12, -4, -7],\n [7, 12, 11, -8],\n [-6, -12, 11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
336
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -11, -5, 3],\n [0, -3, -6, 12],\n [0, 0, 1, 12],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
243
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 1, 6, 7],\n [1, 0, 4, -4],\n [6, 4, -9, 9],\n [7, -4, 9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
554
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 5, 1, -5],\n [-7, -2, -9, -5],\n [9, 7, -8, 1],\n [10, -9, -8, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
945
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -6, -10, -10],\n [-6, -2, 2, 2],\n [-10, 2, -7, -8],\n [-10, 2, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
304
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -7, -3, -4],\n [11, -1, 10, -11],\n [-12, 12, 5, 2],\n [7, 5, -9, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
825
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 0, -2, -1],\n [0, -4, 8, -8],\n [-2, 8, 6, 7],\n [-1, -8, 7, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
172
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 3, 0, 4],\n [3, 1, -3, 6],\n [0, -3, 5, 4],\n [4, 6, 4, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
460
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 8, 10, -5],\n [11, -4, -10, 7],\n [6, 7, -11, -9],\n [-6, 2, 2, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
954
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 11, -1, 10],\n [0, -4, 11, -4],\n [0, 0, -8, 3],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
712
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -6, 2, 10],\n [9, -11, 3, 1],\n [-9, 10, 10, 4],\n [-10, -6, 9, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
642
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -10, -6, -12],\n [0, 6, -12, -12],\n [0, 0, -11, -12],\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"
}
] |
152
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 2, 4, 2],\n [0, -6, -1, -5],\n [0, 0, 8, 9],\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"
}
] |
184
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -10, -7, 11],\n [-10, -10, -6, 2],\n [-7, -6, -10, -4],\n [11, 2, -4, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
392
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 8, 8, -7],\n [0, -6, 7, 2],\n [0, 0, 5, 8],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 6, 5, -4],\n [6, 11, 0, -3],\n [5, 0, -1, 6],\n [-4, -3, 6, 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"
}
] |
978
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -5, -10, -8],\n [0, -2, 11, 1],\n [0, 0, -12, 1],\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"
}
] |
152
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 0, 4, 4],\n [0, -8, -4, 3],\n [4, -4, 12, 8],\n [4, 3, 8, 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"
}
] |
224
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -2, -4, -2],\n [-2, -7, -2, -4],\n [-4, -2, -8, -2],\n [-2, -4, -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"
}
] |
504
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -2, -2, 11],\n [-2, -8, -2, 6],\n [-2, -2, 1, -8],\n [11, 6, -8, 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"
}
] |
280
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -4, 0, -6],\n [-4, -7, 6, -2],\n [0, 6, -11, 0],\n [-6, -2, 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"
}
] |
791
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 12, 0, -4],\n [0, -9, -9, -10],\n [0, 0, 7, -12],\n [0, 0, 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"
}
] |
488
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 7, 8, -9],\n [0, -12, -3, 6],\n [0, 0, 3, -9],\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"
}
] |
784
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -9, 4, -7],\n [-6, -8, -10, 9],\n [8, 5, -3, 6],\n [5, 3, -9, 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"
}
] |
777
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 8, 0, -7],\n [8, 2, 2, -10],\n [0, 2, 11, -2],\n [-7, -10, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
846
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 1, -10, -2],\n [0, -2, 8, 7],\n [0, 0, 5, -1],\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"
}
] |
300
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -12, -9, -12],\n [0, -8, 12, 9],\n [0, 0, -10, -6],\n [0, 0, 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"
}
] |
40
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 5, -7, 4],\n [4, -4, -12, 3],\n [9, -11, -12, 6],\n [2, -1, 8, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
135
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 7, -12, 12],\n [7, -12, 11, -11],\n [-1, -6, 4, 12],\n [10, -10, 11, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
649
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 2, -6, 0],\n [2, 7, 8, 6],\n [-6, 8, -2, 6],\n [0, 6, 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"
}
] |
6
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -11, -10, 0],\n [-11, 5, 0, -1],\n [-10, 0, -2, -7],\n [0, -1, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
575
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -10, 10, 2],\n [0, 12, -11, 5],\n [0, 0, -2, -2],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
848
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -5, -1, 0],\n [-5, -11, -6, 4],\n [-1, -6, -4, 6],\n [0, 4, 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"
}
] |
819
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 12, 3, 12],\n [-12, -6, 3, -6],\n [-12, 5, -2, -12],\n [-7, -1, 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"
}
] |
616
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 11, -3, -5],\n [-10, 4, 12, 4],\n [-6, -12, -1, 9],\n [11, 1, 11, 8]]\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[[6, 0, -4, 12],\n [0, 11, -6, 9],\n [-4, -6, 9, 3],\n [12, 9, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
344
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 11, 3, 9],\n [-8, -3, 10, -10],\n [-4, 2, -3, -12],\n [-6, 4, -4, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -6, -1, 0],\n [5, 6, 11, -11],\n [4, 0, -3, 4],\n [-3, 7, -3, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
319
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 2, 3, -4],\n [2, -10, 0, 6],\n [3, 0, 10, 6],\n [-4, 6, 6, -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"
}
] |
166
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -9, -5, -11],\n [2, -7, -5, -11],\n [6, -5, 4, -2],\n [5, -4, 5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
380
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -9, 5, -6],\n [2, -3, 12, 1],\n [-9, -10, -9, 7],\n [1, -9, -4, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
491
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 6, 10, -6],\n [6, 1, -2, 2],\n [10, -2, 7, 6],\n [-6, 2, 6, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
860
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -1, 7, -4],\n [-7, -8, -3, -11],\n [-3, 8, 11, -10],\n [-1, -6, -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"
}
] |
192
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 4, 0, 4],\n [4, -7, 2, -6],\n [0, 2, -10, 0],\n [4, -6, 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"
}
] |
24
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -4, 9, 11],\n [0, 4, -9, -2],\n [0, 0, -3, -9],\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"
}
] |
748
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, 2, 0],\n [4, -4, 1, 6],\n [-11, -6, -2, 2],\n [11, -10, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
724
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -4, -11, -2],\n [0, -2, -12, -1],\n [0, 0, -11, -8],\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"
}
] |
452
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -10, -9, 2],\n [0, 6, -12, -1],\n [0, 0, -7, -9],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
772
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 11, -7, -2],\n [0, -12, -3, 1],\n [0, 0, 2, -7],\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"
}
] |
904
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -2, 3, 4],\n [-2, 6, -6, 0],\n [3, -6, 5, 2],\n [4, 0, 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"
}
] |
266
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 9, 0, 5],\n [9, 2, 0, 0],\n [0, 0, 11, 12],\n [5, 0, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
433
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, 5, 4],\n [-4, 11, 8, -3],\n [5, 8, -9, 6],\n [4, -3, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
292
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -1, -1, -2],\n [-1, 8, 2, 3],\n [-1, 2, -4, 2],\n [-2, 3, 2, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
801
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 0, 10, -11],\n [0, -8, 11, 9],\n [0, 0, -4, 10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
488
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 8, 2, -12],\n [5, -9, 6, 7],\n [12, 1, -6, -8],\n [0, -5, 3, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
72
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -7, 2, -9],\n [8, -12, 2, -7],\n [6, 10, -11, 12],\n [-11, -7, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
151
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -2, -8, 0],\n [-2, -2, -8, -2],\n [-8, -8, 9, 12],\n [0, -2, 12, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
650
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -6, 0, -2],\n [0, -12, -4, 9],\n [0, 0, -4, -6],\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"
}
] |
720
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, 12, 9],\n [-1, -7, -11, -4],\n [3, 12, 5, 8],\n [5, 1, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
530
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 8, -2, 7],\n [0, 11, 3, 7],\n [0, 0, -11, 2],\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"
}
] |
306
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 5, 2, -11],\n [0, -8, -3, -10],\n [0, 0, -11, -11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
792
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 10, -9, 2],\n [10, -10, 0, 6],\n [-9, 0, 1, -8],\n [2, 6, -8, 8]]\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[[-12, -5, -10, -9],\n [-5, -7, 2, -12],\n [-6, -5, -10, -9],\n [4, 5, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
762
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -7, -8, -9],\n [11, 8, -1, -5],\n [3, 7, -1, 7],\n [8, -11, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
934
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -10, 11, -6],\n [-10, 2, 0, 5],\n [11, 0, 9, -11],\n [-6, 5, -11, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
228
|
MATH
|
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