messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -2, 2, -4],\n [-2, -5, -2, 1],\n [2, -2, 7, -2],\n [-4, 1, -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"
}
] |
356
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -1, 12, -2],\n [-1, -12, -1, -10],\n [12, -1, -8, 4],\n [-2, -10, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
868
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -6, 0, -4],\n [-6, 5, -1, 8],\n [0, -1, -1, 5],\n [-4, 8, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
229
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -8, 4, -4],\n [-8, 0, -1, -8],\n [4, -1, -12, 1],\n [-4, -8, 1, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
969
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 7, -2, 6],\n [7, -2, -10, 0],\n [-2, -10, 11, 2],\n [6, 0, 2, -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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -9, 4, -1],\n [-9, 12, -2, 0],\n [4, -2, -10, -2],\n [-1, 0, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
390
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 0, -6, 0],\n [0, -8, -2, 3],\n [-6, -2, 12, 2],\n [0, 3, 2, 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"
}
] |
900
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -8, 1, 5],\n [0, -4, -9, -10],\n [0, 0, 12, 1],\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"
}
] |
288
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 9, -1, 8],\n [7, 7, 0, -5],\n [4, 3, -7, -4],\n [-12, 4, 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"
}
] |
801
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -6, 0, 5],\n [-6, 8, -3, -8],\n [0, -3, -11, -10],\n [5, -8, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
864
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -4, 1, 9],\n [-4, 10, -6, 0],\n [1, -6, 8, 6],\n [9, 0, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
358
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 9, 2, 5],\n [0, 2, 5, 5],\n [0, 0, -4, 10],\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"
}
] |
224
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -11, 3, -10],\n [0, -12, -11, -6],\n [0, 0, 4, -11],\n [0, 0, 0, -12]]\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, 7, 6, 9],\n [5, 6, 4, 3],\n [6, -4, 9, 2],\n [0, 0, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -11, -1, -8],\n [-11, -10, -4, 1],\n [-1, -4, 3, 2],\n [-8, 1, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
619
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 1, 1, 6],\n [1, 3, -3, 6],\n [1, -3, -1, -4],\n [6, 6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
964
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -5, 2, 9],\n [0, 2, 3, 4],\n [0, 0, 5, -1],\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"
}
] |
510
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -4, -2, -1],\n [-4, 2, -8, 1],\n [-2, -8, 11, -2],\n [-1, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
748
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -6, -8, -3],\n [-11, -9, -9, -11],\n [0, 4, 5, -8],\n [7, 8, 8, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
405
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 6, -3, 8],\n [0, 1, -6, -8],\n [11, 11, -10, -9],\n [0, -4, 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"
}
] |
384
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 4, 0, 4],\n [4, -6, -7, 5],\n [0, -7, -2, 2],\n [4, 5, 2, 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"
}
] |
720
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -12, -2, -5],\n [0, 10, -4, 10],\n [0, 0, 1, -6],\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"
}
] |
900
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 8, -4, -6],\n [0, 5, -5, 11],\n [0, 0, 6, -5],\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"
}
] |
160
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -3, -5, 1],\n [0, -9, -8, -3],\n [0, 0, -6, 11],\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"
}
] |
140
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 7, 7, 3],\n [-12, -4, 8, -4],\n [4, 5, -6, -6],\n [11, 4, -11, -1]]? Round to the nearest integer, then express your answer modulo 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[[-4, 12, -7, -10],\n [0, -8, -5, 7],\n [0, 0, 11, 1],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
112
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -9, 6, 11],\n [0, -7, 2, 10],\n [0, 0, 8, 12],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
552
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 0, -1, -2],\n [0, 8, -4, 0],\n [-1, -4, 10, 4],\n [-2, 0, 4, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
384
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 9, -8, -8],\n [9, 1, 1, -8],\n [-8, 1, 11, -4],\n [-8, -8, -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"
}
] |
484
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -2, 5, 12],\n [0, 2, 5, 6],\n [0, 0, -6, 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"
}
] |
756
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 10, 5, -7],\n [0, -1, -6, 3],\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"
}
] |
994
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -5, 7, 9],\n [0, 9, -5, 5],\n [0, 0, 6, 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"
}
] |
624
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -7, 3, 12],\n [6, 11, -9, 4],\n [11, -5, -4, 12],\n [-1, -4, 11, -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"
}
] |
430
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 2, -8, 1],\n [2, 4, -2, 2],\n [-8, -2, 3, -6],\n [1, 2, -6, 8]]\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[[12, 5, -9, 11],\n [-9, -8, -6, 5],\n [-10, 5, -10, 9],\n [5, 0, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
571
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 9, -11, -10],\n [-4, -4, -10, -2],\n [11, 10, 11, 12],\n [-4, 4, 12, 7]]\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[[-7, 2, -9, 4],\n [2, -5, -2, -2],\n [-9, -2, -9, 4],\n [4, -2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
778
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -3, -11, -4],\n [6, -2, 11, -7],\n [-7, 8, 7, -6],\n [1, -8, -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"
}
] |
629
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -12, -8, 3],\n [-12, 8, -6, -2],\n [-8, -6, -1, 6],\n [3, -2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
768
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -8, 6, 5],\n [-8, 11, -1, 0],\n [6, -1, -5, 9],\n [5, 0, 9, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
244
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 0, 10, 11],\n [0, 6, 6, -1],\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"
}
] |
280
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 0, -2, 12],\n [2, -1, 9, -1],\n [1, -3, -6, 2],\n [8, -10, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
822
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -11, 4, -4],\n [-6, 3, -10, 1],\n [-5, -2, -9, -7],\n [-1, 8, -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"
}
] |
114
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, -6, 2],\n [2, 6, 0, 9],\n [-6, 0, -9, 1],\n [2, 9, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
354
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, 0, -4],\n [0, 6, -10, -9],\n [0, 0, -12, -3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
136
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 0, -4, -2],\n [0, -9, -3, -2],\n [0, 0, 1, 1],\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"
}
] |
271
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 3, 2, -5],\n [3, 1, 0, -1],\n [2, 0, -2, -4],\n [-5, -1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
992
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -3, 2, -1],\n [2, -5, -3, -5],\n [5, -1, 10, 3],\n [5, -12, -4, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
944
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 0, 1, 10],\n [10, -10, -3, 8],\n [-7, -7, 3, -2],\n [9, 11, -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"
}
] |
483
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -1, -2, 0],\n [-1, 9, 0, 1],\n [-2, 0, -11, 6],\n [0, 1, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
777
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 3, 1, 11],\n [0, -12, -3, -12],\n [0, 0, 2, 8],\n [0, 0, 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"
}
] |
768
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 5, -11, -4],\n [5, 7, 4, 0],\n [-11, 4, 2, -5],\n [-4, 0, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
150
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 8, 2, 2],\n [8, -7, 6, 6],\n [2, 6, -9, 4],\n [2, 6, 4, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 10, -11, 5],\n [-7, -9, -8, -10],\n [-8, 3, -7, 9],\n [-4, -4, 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"
}
] |
618
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, 12, -7],\n [8, 9, 5, -1],\n [-4, -8, 3, -1],\n [8, 12, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
168
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 6, -7, 1],\n [0, -5, 1, -11],\n [0, 0, -12, -3],\n [0, 0, 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"
}
] |
240
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -5, -4, -7],\n [0, -7, 7, -1],\n [0, 0, -7, -6],\n [0, 0, 0, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
688
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -6, -4, 2],\n [-6, 10, -4, -4],\n [-4, -4, 12, 0],\n [2, -4, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
632
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 4, 0, 0],\n [0, -10, 2, -1],\n [0, 0, 9, -11],\n [0, 0, 0, -1]]\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[[-4, 8, 0, -1],\n [8, 0, 1, 8],\n [0, 1, 0, 3],\n [-1, 8, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
437
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 5, 12, -6],\n [0, 6, -5, 5],\n [0, 0, 8, -7],\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"
}
] |
640
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 7, 5, 3],\n [0, 11, -4, 12],\n [-1, -1, 2, 9],\n [1, 12, -3, 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"
}
] |
891
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 1, 7, -12],\n [0, 12, -10, 7],\n [3, 5, -4, 7],\n [3, -12, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
489
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 3, -2, 10],\n [3, 11, -4, 0],\n [-2, -4, -5, 6],\n [10, 0, 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"
}
] |
874
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -2, 5, -1],\n [8, 5, -9, -6],\n [-2, 3, -4, -11],\n [12, 9, 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"
}
] |
664
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -11, 7, 4],\n [0, 3, -12, -4],\n [0, 0, 4, 11],\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"
}
] |
952
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 4, -11, -7],\n [-3, 9, 12, -5],\n [9, -12, 4, 7],\n [9, 2, 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"
}
] |
883
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -10, 2, 12],\n [-5, -4, -2, 6],\n [7, -7, 5, 0],\n [0, -9, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
678
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -9, -6, -6],\n [9, 9, 5, 4],\n [12, 11, -7, 8],\n [8, 6, -11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
647
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 11, 4, 8],\n [0, -10, -4, 7],\n [0, 0, -11, 7],\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"
}
] |
800
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -8, 3, -11],\n [-8, -1, -1, 3],\n [3, -1, -6, 4],\n [-11, 3, 4, -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"
}
] |
719
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 2, -6, 11],\n [2, 9, 10, 0],\n [-6, 10, 9, -2],\n [11, 0, -2, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
723
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 8, 8, 9],\n [-1, 10, -1, 1],\n [3, 0, -11, -6],\n [7, -1, 7, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
767
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -10, 10, 2],\n [0, -5, -5, -5],\n [0, 0, 7, 11],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
155
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 4, 0, 1],\n [4, -9, 2, -6],\n [0, 2, -10, -4],\n [1, -6, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
722
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 11, 1, -11],\n [-12, -9, 10, 4],\n [2, -3, 7, 11],\n [8, -4, 3, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
178
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -9, 5, -9],\n [-2, -7, 2, 8],\n [-3, 0, 11, -8],\n [-12, 4, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
258
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 9, 1, 2],\n [0, -7, -7, -6],\n [0, 0, 8, 9],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
440
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 4, -9, 10],\n [0, 12, 6, 11],\n [0, 0, -5, -10],\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"
}
] |
820
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -7, 9, -1],\n [0, -3, -2, 2],\n [0, 0, -6, -8],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 5, -12, 3],\n [0, -10, -10, -3],\n [0, 0, -4, -3],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 1, -4, 6],\n [-2, 2, 0, -4],\n [7, 0, -10, -1],\n [-2, 4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
802
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 5, 1, 2],\n [0, 2, 4, 7],\n [0, 0, -12, 3],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
432
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -6, 9, 1],\n [8, 12, -11, 1],\n [-9, -1, -11, 9],\n [12, -9, 2, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
356
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -12, 6, 3],\n [7, 11, -3, 5],\n [-3, 6, 2, -6],\n [-11, -7, 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"
}
] |
43
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -5, -8, 4],\n [0, -8, -9, -11],\n [0, 0, -3, 1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
616
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 6, -4, 2],\n [6, -12, -2, 0],\n [-4, -2, 3, 4],\n [2, 0, 4, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
436
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 11, -12, 8],\n [0, -6, 5, -12],\n [0, 0, -12, 7],\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"
}
] |
456
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, 4, -9],\n [0, -7, -9, 8],\n [0, 0, 11, -9],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
769
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -8, 1, -6],\n [4, 4, 4, -2],\n [-1, 5, -2, -11],\n [10, 7, 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"
}
] |
396
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -6, 1, 2],\n [-6, -8, -1, 6],\n [1, -1, -7, -8],\n [2, 6, -8, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
488
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 6, -12, 2],\n [0, 5, 7, 11],\n [0, 0, 1, 2],\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"
}
] |
385
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -7, -8, 0],\n [-7, -12, 4, 8],\n [-8, 4, -7, -5],\n [0, 8, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
666
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -2, 0, 4],\n [0, -11, 7, 2],\n [0, 0, 6, -12],\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"
}
] |
452
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -6, 0, -4],\n [-6, 6, 2, 1],\n [0, 2, -6, -11],\n [-4, 1, -11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
356
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 12, -2, -2],\n [12, -10, -9, 8],\n [-2, -9, -11, 6],\n [-2, 8, 6, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
991
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -8, 8, -11],\n [-1, -11, 4, -7],\n [2, -6, 1, -8],\n [3, -11, -4, -3]]\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[[-3, -8, 7, 9],\n [9, -7, 3, -11],\n [-4, 0, -8, -4],\n [3, 5, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
64
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -10, -10, 0],\n [0, -2, 10, 1],\n [0, 0, 9, 9],\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"
}
] |
892
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -7, -3, -3],\n [-4, 0, -9, -12],\n [9, -7, -2, 4],\n [5, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
788
|
MATH
|
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