messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 8, 4, -6],\n [0, 6, -6, 7],\n [0, 0, -11, 2],\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"
}
] |
152
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 0, 6, -2],\n [2, -5, 2, -9],\n [-6, -11, -1, -12],\n [0, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
719
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 7, -12, -1],\n [5, 9, 1, 7],\n [-1, 6, -12, -12],\n [8, 12, 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"
}
] |
543
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 10, 0, -1],\n [10, -12, 6, -9],\n [0, 6, 6, -2],\n [-1, -9, -2, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
776
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 5, -10, -4],\n [5, 5, -1, 2],\n [-10, -1, -10, -2],\n [-4, 2, -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"
}
] |
318
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -11, 3, -2],\n [9, -6, 9, -3],\n [-11, -1, -1, -6],\n [-10, -2, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
392
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 3, 2, -8],\n [0, 4, -5, -1],\n [0, 0, -5, -9],\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"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -2, -2, 10],\n [-2, 2, -4, 0],\n [-2, -4, -8, 8],\n [10, 0, 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"
}
] |
184
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -1, -12, 8],\n [-7, -1, 9, 6],\n [12, 6, 7, 4],\n [0, 8, -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"
}
] |
612
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 10, 2, -2],\n [10, -2, 6, 8],\n [2, 6, 9, -3],\n [-2, 8, -3, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
906
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -1, -4, -4],\n [0, 7, -4, -6],\n [0, 0, -2, -5],\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"
}
] |
784
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -3, 12, -3],\n [-4, 10, -5, -4],\n [-2, 9, -9, 11],\n [5, 6, -5, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -5, 5, -3],\n [0, 7, -12, 10],\n [0, 0, -5, 9],\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"
}
] |
535
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -10, -4, -2],\n [-10, -7, -6, -6],\n [-4, -6, 9, 4],\n [-2, -6, 4, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
175
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -6, -3, -6],\n [1, 9, 1, -4],\n [-5, -10, 7, -6],\n [-3, 1, -6, 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"
}
] |
681
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -12, -12, -6],\n [0, 11, -1, 6],\n [0, 0, 1, -11],\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"
}
] |
604
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 8, -3, -8],\n [8, 0, -3, 2],\n [-3, -3, 11, 6],\n [-8, 2, 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"
}
] |
788
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 10, -11, -8],\n [0, -4, -3, 4],\n [0, 0, -8, -2],\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"
}
] |
848
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 4, 7, 7],\n [-12, -2, 4, -11],\n [11, 1, -4, 12],\n [1, 10, 7, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
890
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 1, -1, 10],\n [11, 5, 4, -2],\n [-12, 5, -10, 0],\n [-10, 0, -1, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
515
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -4, -3, 10],\n [0, 2, -12, 2],\n [0, 0, 1, 5],\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"
}
] |
16
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 0, -1, -1],\n [0, -12, 0, -6],\n [-1, 0, -12, 9],\n [-1, -6, 9, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
64
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 12, 4, -9],\n [0, -7, 8, -10],\n [0, 0, -1, 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"
}
] |
84
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, -8, 7],\n [7, -6, 2, 0],\n [10, -3, -11, -2],\n [4, 8, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
370
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -1, -2, 11],\n [-8, -9, 6, -11],\n [8, 7, -4, 3],\n [5, -9, 12, 7]]\nRound to the nearest integer, then take the result modulo 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[[-8, 2, 0, -4],\n [2, -6, 6, -8],\n [0, 6, 4, 2],\n [-4, -8, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
824
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 5, -8, -9],\n [0, -11, -1, -11],\n [0, 0, 5, 6],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
670
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -1, 3, 10],\n [4, 10, 8, -4],\n [-5, 1, 9, 3],\n [9, 7, 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"
}
] |
928
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -6, 2, -12],\n [-5, 9, -1, -1],\n [-2, -2, 4, -7],\n [2, -9, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
913
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 7, 12, -7],\n [0, 6, 12, 1],\n [0, 0, -11, 3],\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"
}
] |
848
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -8, -6, -6],\n [-8, -10, 2, -9],\n [-6, 2, -11, 2],\n [-6, -9, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
230
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -11, -10, 4],\n [-3, 3, 0, -12],\n [-4, 5, -5, 12],\n [10, -10, 3, 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"
}
] |
190
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 2, 1, -1],\n [4, 6, -7, -10],\n [6, 12, 0, 12],\n [-2, -11, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
630
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 0, 4, 0],\n [0, 4, 2, 8],\n [0, 0, 1, 10],\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"
}
] |
88
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 5, 3, 6],\n [-10, 2, 5, -11],\n [12, 11, 1, 10],\n [3, 5, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
580
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -1, 8, 10],\n [-1, -6, -4, 2],\n [8, -4, 2, 4],\n [10, 2, 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"
}
] |
710
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 11, 7, 9],\n [1, -4, 9, 2],\n [0, -12, -11, -10],\n [8, -4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
278
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -2, 7, 2],\n [-2, -2, 8, -1],\n [7, 8, -4, -4],\n [2, -1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
217
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 6, -6, 11],\n [-2, -1, 12, 11],\n [-11, 2, 10, 6],\n [2, 11, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
267
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 4, 9, 6],\n [4, 3, -6, 2],\n [9, -6, 12, 0],\n [6, 2, 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"
}
] |
650
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, 6, -6],\n [-6, 8, -11, -4],\n [6, -11, -12, -4],\n [-6, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
566
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -2, 3, 8],\n [5, -5, 4, 2],\n [-1, -5, -10, 2],\n [-3, 4, -10, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
296
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 9, -8, 5],\n [0, 8, -1, 3],\n [11, -7, -5, 2],\n [2, -11, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
558
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 11, -11, 12],\n [0, -1, 1, -7],\n [0, 0, 2, 0],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
216
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 1, 4, -2],\n [1, 6, 6, -8],\n [4, 6, 4, -5],\n [-2, -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"
}
] |
823
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -9, -4, 0],\n [7, 6, 5, -7],\n [8, -1, 7, -12],\n [6, 9, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
466
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 1, 12, 7],\n [0, 10, 9, -8],\n [0, 0, -7, -11],\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"
}
] |
700
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 8, 1, 5],\n [8, -1, -2, 10],\n [1, -2, 7, 0],\n [5, 10, 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"
}
] |
142
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 2, 0, 12],\n [2, -10, -2, 0],\n [0, -2, 3, 4],\n [12, 0, 4, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 6, 7, -7],\n [0, 1, 7, 12],\n [0, 0, -8, 0],\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, -7, 4],\n [0, -3, 11, -6],\n [0, 0, -3, -1],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 0, -2, 4],\n [0, 9, -6, -3],\n [-2, -6, 9, 11],\n [4, -3, 11, 1]]\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": "What is the determinant of the matrix:\n[[-5, -5, -11, -2],\n [6, -10, -4, 1],\n [1, 8, 12, -6],\n [-9, -1, -12, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
441
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -2, 0, 4],\n [6, 1, 4, -10],\n [-1, -5, 2, -11],\n [-1, 11, 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"
}
] |
645
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 0, -4, -9],\n [0, 9, 2, -2],\n [-4, 2, 10, -6],\n [-9, -2, -6, 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"
}
] |
920
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 10, 3, 5],\n [0, 10, -6, -5],\n [0, 0, -12, 8],\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"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -6, 11, -10],\n [5, 2, -12, -3],\n [-12, 7, 12, -12],\n [9, -12, -1, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 0, -7, -10],\n [0, -5, 11, -2],\n [0, 0, 2, -11],\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"
}
] |
450
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -10, 8, -3],\n [0, -2, -7, 5],\n [0, 0, -5, 6],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
700
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 1, 12, -7],\n [9, -2, 12, -1],\n [-1, -9, 7, -9],\n [-7, -1, -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"
}
] |
923
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -4, -3, -4],\n [-4, 12, 4, -4],\n [-3, 4, 7, 0],\n [-4, -4, 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"
}
] |
428
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -2, 12, 4],\n [-2, 12, 8, 0],\n [12, 8, 4, 6],\n [4, 0, 6, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
352
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -9, 3, 12],\n [-10, -10, 0, 10],\n [-5, 11, 7, -8],\n [4, 0, 5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -9, -5, 11],\n [0, 9, 7, 8],\n [0, 0, -1, -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"
}
] |
676
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -4, 0, 4],\n [-4, 10, 0, 8],\n [0, 0, -10, 6],\n [4, 8, 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"
}
] |
996
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 3, 0, 5],\n [3, -5, 6, 2],\n [0, 6, -10, 3],\n [5, 2, 3, -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"
}
] |
786
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 0, 0, 0],\n [0, 10, -2, 0],\n [0, -2, -9, -8],\n [0, 0, -8, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
716
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -9, 4, -12],\n [2, -3, 2, -9],\n [11, 7, -1, 8],\n [0, -5, -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"
}
] |
572
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -1, 0, 9],\n [-1, 8, -10, 0],\n [0, -10, -12, 6],\n [9, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 12, 8, 8],\n [4, -9, 3, 3],\n [1, 12, -1, -6],\n [-12, 0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
888
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 10, 5, -9],\n [0, 10, -4, 2],\n [0, 0, -7, 0],\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"
}
] |
540
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 5, -12, -4],\n [11, 5, 12, 2],\n [11, 8, 1, -3],\n [5, 12, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
654
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -4, 1, 2],\n [-4, 8, -3, -6],\n [1, -3, -8, 4],\n [2, -6, 4, 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"
}
] |
52
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 9, 2, -2],\n [9, 7, -4, -1],\n [2, -4, 4, 2],\n [-2, -1, 2, 8]]\nRound to the nearest integer, then take the result 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[[-8, 7, -6, 6],\n [0, -2, 5, -3],\n [0, 0, -7, 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"
}
] |
344
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -2, -2, -1],\n [-2, -2, 0, -8],\n [-2, 0, 1, 8],\n [-1, -8, 8, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
266
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -1, 3, 8],\n [0, -11, 10, -10],\n [0, 0, -11, 3],\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"
}
] |
288
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, 6, 2],\n [-6, 5, 2, -2],\n [6, 2, 7, 10],\n [2, -2, 10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -4, 6, -7],\n [-8, -4, 4, 4],\n [1, -3, 10, 9],\n [12, -10, 1, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
164
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 3, 5, -11],\n [3, 12, -5, 5],\n [-4, -10, -10, 2],\n [12, -11, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, -7, 5, -4],\n [2, 12, 11, -9],\n [1, -8, -4, 2],\n [10, -2, -11, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
935
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 2, -9, 10],\n [0, 10, 12, -2],\n [0, 0, -5, 10],\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"
}
] |
50
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -10, -10, -6],\n [0, 6, 7, 3],\n [0, 0, -9, -3],\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"
}
] |
464
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 1, 4, 3],\n [0, 5, 11, 5],\n [0, 0, 6, -5],\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"
}
] |
570
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -3, -2, -3],\n [-3, -4, 8, 0],\n [-2, 8, 0, -5],\n [-3, 0, -5, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
117
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 1, -8, -1],\n [1, -12, -4, 4],\n [-8, -4, 3, 8],\n [-1, 4, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
583
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 11, -3, -12],\n [0, -6, -8, -1],\n [-4, 12, 8, 4],\n [1, 10, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
848
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -7, -4, 3],\n [11, -7, -5, 0],\n [6, -5, 2, 4],\n [12, -8, 9, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
159
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 0, 5, 0],\n [0, -3, -4, 4],\n [5, -4, -11, -6],\n [0, 4, -6, 0]]\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[[9, 0, -2, 2],\n [0, -10, 0, 0],\n [-2, 0, 6, 2],\n [2, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
260
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 8, 10, -9],\n [8, 5, 4, 0],\n [10, 4, 11, 0],\n [-9, 0, 0, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
841
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -1, -9, -12],\n [-1, -5, -2, -11],\n [-4, 6, 4, -10],\n [-8, 12, -12, 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"
}
] |
88
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 5, -8, -4],\n [5, -4, -4, -4],\n [-8, -4, -8, -2],\n [-4, -4, -2, 7]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -7, 2, 12],\n [9, -2, -3, -12],\n [5, 5, 11, -10],\n [9, 4, 12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 0, 3, -5],\n [12, 9, 3, 10],\n [3, 6, -4, -3],\n [11, 7, -10, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
655
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -10, -8, -4],\n [0, 6, 6, 0],\n [0, 0, 9, -8],\n [0, 0, 0, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 10, -10, -1],\n [0, -5, -4, -9],\n [0, 0, 1, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
955
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -2, 0, -4],\n [-2, -10, -6, -2],\n [0, -6, -4, 2],\n [-4, -2, 2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
352
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 3, 2, -12],\n [3, 5, 0, 2],\n [2, 0, 2, -2],\n [-12, 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"
}
] |
814
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 10, -4, -1],\n [6, -3, 4, -3],\n [-6, -7, 6, 7],\n [8, 0, -5, -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"
}
] |
564
|
MATH
|
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