messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 3, -5, 6],\n [2, -2, 5, 5],\n [-8, -3, 10, -7],\n [-11, -1, 10, -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"
}
] |
220
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 9, 0, -6],\n [0, 10, -7, 2],\n [0, 0, -7, -1],\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"
}
] |
480
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 1, 5, 7],\n [-3, -3, -1, -2],\n [-4, -3, 5, 9],\n [1, 5, -10, -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"
}
] |
984
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -1, 11, -3],\n [0, 8, 7, 6],\n [0, 0, -5, 3],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, 1, 0],\n [4, -7, 5, -4],\n [1, 5, -5, 4],\n [0, -4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
819
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -7, -1, 1],\n [5, -7, 4, 10],\n [7, -12, 4, -5],\n [-2, -11, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
383
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 2, -6, -10],\n [2, -2, 0, 8],\n [-6, 0, -10, -5],\n [-10, 8, -5, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
758
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -10, -5, 12],\n [0, -10, -7, 0],\n [0, 0, 10, 12],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 3, 2, -10],\n [3, 3, 7, 4],\n [2, 7, -9, 6],\n [-10, 4, 6, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 5, 10, 5],\n [-9, 0, -4, -9],\n [1, -11, 0, 2],\n [12, 6, 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"
}
] |
150
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -8, -4, 6],\n [0, 12, -8, -3],\n [0, 0, 2, -12],\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"
}
] |
80
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -2, 3, -4],\n [-2, 8, 6, 0],\n [3, 6, -1, 0],\n [-4, 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"
}
] |
68
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 12, 10, 10],\n [-10, 11, -1, -7],\n [8, 4, 12, -4],\n [1, 5, 3, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
248
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 12, 4, 3],\n [0, -5, 3, 2],\n [0, 0, 2, -11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
670
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 5, 7, -8],\n [0, -6, -1, 4],\n [0, 0, 7, -2],\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"
}
] |
328
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 4, 10, 7],\n [0, 6, -10, 1],\n [0, 0, -3, -10],\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"
}
] |
260
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -6, 0, -3],\n [0, -9, 8, -11],\n [0, 0, -11, 6],\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"
}
] |
812
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -5, 4, 2],\n [1, 12, 3, 5],\n [-5, 12, 4, 9],\n [6, 10, 2, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
394
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -3, 12, -2],\n [0, -1, -4, 8],\n [0, 0, 6, -6],\n [0, 0, 0, -4]]\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[[-5, -11, 0, 1],\n [0, -8, 1, -6],\n [0, 0, 12, 7],\n [0, 0, 0, 4]]\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, -5, 2, 6],\n [0, 1, 6, -3],\n [0, 0, 12, 11],\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"
}
] |
576
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 6, -5, -2],\n [6, 9, 6, -1],\n [-5, 6, -12, -8],\n [-2, -1, -8, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
866
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -10, -6, 1],\n [0, 2, -9, 7],\n [0, 0, -5, -12],\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"
}
] |
650
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 3, -9, 2],\n [0, 4, 12, 11],\n [0, 0, -9, -12],\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"
}
] |
396
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 9, 2, -7],\n [-12, 5, -10, -3],\n [-7, -8, 10, -12],\n [-10, 11, -11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
168
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, 0, -2],\n [2, 3, 0, 6],\n [0, 0, -6, 3],\n [-2, 6, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
591
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 6, 0, 8],\n [6, 4, 6, 4],\n [0, 6, 2, 4],\n [8, 4, 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"
}
] |
616
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 3, -6, -1],\n [3, 12, -2, -2],\n [-6, -2, 6, 0],\n [-1, -2, 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"
}
] |
378
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -8, 10, -10],\n [0, -5, -6, -11],\n [0, 0, 7, 10],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
420
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 11, -8, 8],\n [0, -8, -1, 10],\n [0, 0, 9, -4],\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"
}
] |
408
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 6, 0, 0],\n [6, 1, 8, 0],\n [0, 8, -2, -8],\n [0, 0, -8, -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"
}
] |
4
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -10, -10, -5],\n [0, 7, -5, -4],\n [7, 10, -8, 0],\n [-8, -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"
}
] |
677
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -6, -2, -5],\n [0, -12, -9, 4],\n [0, 0, 11, -5],\n [0, 0, 0, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
932
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 4, -7, 1],\n [0, -11, -7, 11],\n [0, 0, 11, 6],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
993
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -11, 0, 3],\n [-11, -11, -6, -1],\n [0, -6, -11, -8],\n [3, -1, -8, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
296
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 2, -4, -6],\n [2, 2, -9, -4],\n [-4, -9, 11, 0],\n [-6, -4, 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"
}
] |
190
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 9, 4, 0],\n [9, 7, -10, 3],\n [4, -10, -11, -5],\n [0, 3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
755
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, 0, -2],\n [0, 8, 2, -2],\n [0, 2, 4, 6],\n [-2, -2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
104
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 5, 0, 3],\n [5, -11, 5, -10],\n [0, 5, -8, 2],\n [3, -10, 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"
}
] |
833
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 10, 2, 10],\n [0, 2, 12, 10],\n [0, 0, 8, -8],\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"
}
] |
440
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -9, 11, 6],\n [0, 10, -1, -2],\n [0, 0, -3, 8],\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"
}
] |
920
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 2, 6, -4],\n [0, -5, -3, 2],\n [0, 0, -1, 12],\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"
}
] |
45
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 6, 4, 6],\n [6, -7, -7, 0],\n [4, -7, -4, 6],\n [6, 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"
}
] |
924
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, -12, 1],\n [0, 3, 1, -5],\n [0, 0, -8, 7],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
728
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, -11, 9],\n [0, -6, 8, -7],\n [0, 0, -4, 4],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -5, 8, 12],\n [0, -6, 11, 10],\n [0, 0, 6, 4],\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"
}
] |
288
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 8, -4, 4],\n [8, -10, -8, 6],\n [-4, -8, -4, -8],\n [4, 6, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
920
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 3, 2, 2],\n [3, 11, -2, 6],\n [2, -2, 0, 2],\n [2, 6, 2, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
864
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -8, -1, 5],\n [0, -6, 8, -5],\n [0, 0, -11, -1],\n [0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
614
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 0, 9, 10],\n [-9, -6, 6, 5],\n [3, -8, 5, 5],\n [1, 10, 3, -6]]? 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[[-7, -4, 2, 7],\n [-4, 4, 3, -7],\n [11, 0, 8, -9],\n [-8, 6, 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"
}
] |
160
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 11, 2, -2],\n [11, -12, -2, -4],\n [2, -2, -12, 2],\n [-2, -4, 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"
}
] |
972
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 7, -5, 7],\n [0, -3, -5, 6],\n [0, 0, -6, -1],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
604
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, 4, 7],\n [0, -10, -3, -8],\n [0, 0, -5, 8],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -8, -4, -2],\n [-8, -3, 4, 0],\n [-4, 4, 4, 3],\n [-2, 0, 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"
}
] |
297
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 0, -3, 2],\n [0, 11, -10, -6],\n [-3, -10, -5, 3],\n [2, -6, 3, 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"
}
] |
439
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 0, -4, -1],\n [0, 9, -2, 7],\n [-4, -2, -6, 0],\n [-1, 7, 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"
}
] |
994
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -8, -2, -6],\n [-9, -5, -5, -12],\n [-2, -8, -5, -7],\n [-11, 12, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
573
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -6, -10, 5],\n [0, 2, 10, 3],\n [0, 0, 10, 7],\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"
}
] |
920
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 7, -11, -3],\n [0, -8, -7, 0],\n [0, 0, 8, -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"
}
] |
680
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -2, 6, 4],\n [-2, 12, 3, 8],\n [6, 3, -3, -2],\n [4, 8, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
142
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 3, 4, -12],\n [3, 8, -1, -1],\n [4, -1, 6, -6],\n [-12, -1, -6, -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"
}
] |
379
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 2, 12, -9],\n [0, 6, -10, -5],\n [0, 0, 10, -3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 8, -11, 2],\n [-7, 5, -8, 6],\n [-10, -4, 3, -4],\n [1, -6, 10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
210
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, 2, 0],\n [-4, 9, 0, 2],\n [2, 0, -8, 2],\n [0, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
736
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 8, -4, 4],\n [0, 12, -6, -10],\n [0, 0, 3, 6],\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"
}
] |
620
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 5, 12, -4],\n [0, 5, -6, 10],\n [0, 0, 8, 9],\n [0, 0, 0, -7]]\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[[-5, 7, 8, 0],\n [7, 6, 1, -6],\n [8, 1, -10, -2],\n [0, -6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
494
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, -8, 12],\n [12, -8, 6, -12],\n [6, -11, -2, 6],\n [-1, -3, -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"
}
] |
668
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, -7, -5],\n [0, 6, -4, -10],\n [0, 0, 8, 3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
544
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, -2, 10],\n [-4, 6, 6, -4],\n [-2, 6, 9, -3],\n [10, -4, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
552
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 8, 10, 6],\n [8, 3, 4, 0],\n [10, 4, -4, 6],\n [6, 0, 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"
}
] |
252
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 8, 11, 8],\n [0, -4, 10, 5],\n [0, 0, -7, 6],\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"
}
] |
304
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 2, -6, 11],\n [0, 9, -1, 9],\n [0, 0, 7, 10],\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"
}
] |
992
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 8, 5, -8],\n [-4, 5, 0, 8],\n [12, 9, -2, -11],\n [-3, 9, -4, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
529
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -6, -6, 0],\n [-6, 12, 8, -8],\n [-6, 8, 11, -1],\n [0, -8, -1, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 0, -6, 4],\n [0, 11, 2, -1],\n [-6, 2, -2, -4],\n [4, -1, -4, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
836
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 12, -3, -7],\n [0, 4, -10, -3],\n [0, 0, -11, 2],\n [0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
868
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -4, 4, -2],\n [-4, -11, -3, -10],\n [5, -10, -10, 8],\n [7, -5, -11, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
348
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -2, 12, 3],\n [5, 9, 12, 7],\n [-8, -2, -10, -3],\n [10, -11, 9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
218
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, -1, 1],\n [-2, 0, -4, 12],\n [-1, -8, 9, 3],\n [-10, 1, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
380
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 3, 7, 7],\n [-8, 3, -10, -5],\n [-1, -4, -7, -11],\n [10, 5, -8, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
226
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 0, -9, 1],\n [-1, -10, -3, 5],\n [-7, 10, 7, -3],\n [1, 10, -5, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 8, 4, -6],\n [8, 3, -6, -2],\n [4, -6, 12, -4],\n [-6, -2, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 5, 7, 2],\n [5, -4, -6, 7],\n [7, -6, 4, 3],\n [2, 7, 3, 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"
}
] |
544
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 10, -10, 11],\n [2, 4, 0, -2],\n [-1, -10, -9, -7],\n [3, -2, 11, -9]]\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": "What is the determinant of the matrix:\n[[2, -7, -9, 7],\n [-1, 12, -2, 7],\n [10, -9, 0, -3],\n [-3, -2, -5, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
961
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -6, -1, -6],\n [-6, 9, 6, 0],\n [-1, 6, -12, -4],\n [-6, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
784
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -9, 2, 7],\n [-7, 3, 11, -1],\n [-8, 4, -11, -7],\n [1, -1, -9, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
587
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 0, -4],\n [-2, 3, -8, -2],\n [0, -8, -1, 5],\n [-4, -2, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
308
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -3, -4, -8],\n [-3, 8, -4, 0],\n [-4, -4, -10, 4],\n [-8, 0, 4, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
78
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 4, -6, 1],\n [4, -10, 0, -1],\n [-6, 0, 12, 8],\n [1, -1, 8, -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"
}
] |
420
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -12, -3, -10],\n [0, -7, 12, 6],\n [0, 0, -12, 8],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -9, -1, 2],\n [0, 10, -12, -7],\n [0, 0, 6, 4],\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"
}
] |
560
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -4, -5, -10],\n [9, 12, -8, 9],\n [4, -10, 7, 9],\n [6, 5, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 9, -6, -12],\n [9, -2, 8, -10],\n [9, -9, 11, 7],\n [-3, 9, 1, 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"
}
] |
297
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -6, -5, -7],\n [-6, 0, 0, 3],\n [-5, 0, 11, -8],\n [-7, 3, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
325
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 4, 3, -4],\n [4, -6, -4, 4],\n [3, -4, -4, 2],\n [-4, 4, 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"
}
] |
432
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -4, 5, 12],\n [-1, 10, 9, -12],\n [2, -4, -8, 8],\n [-9, -6, 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"
}
] |
0
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -6, 0, 9],\n [-5, 10, 1, 9],\n [-2, -5, -11, 6],\n [-12, -12, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
966
|
MATH
|
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