messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 4, 0, -4],\n [4, 3, 2, 3],\n [0, 2, 10, -6],\n [-4, 3, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
936
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, 8, 8],\n [0, -11, -5, 5],\n [0, 0, 11, -10],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
616
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 8, -4, -4],\n [8, -9, 4, 6],\n [-4, 4, 3, 4],\n [-4, 6, 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"
}
] |
960
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 0, 2, -6],\n [0, 10, 8, 3],\n [2, 8, 1, -6],\n [-6, 3, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
548
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -2, -4, 9],\n [0, 5, 2, 5],\n [0, 0, -11, 3],\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"
}
] |
210
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 4, 2, -6],\n [4, -4, 0, 4],\n [2, 0, 3, 4],\n [-6, 4, 4, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
232
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, -5, 4],\n [1, -5, 10, 4],\n [-5, 10, 1, 0],\n [4, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
192
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 7, 1, 7],\n [0, -12, 1, -12],\n [0, 0, -4, -5],\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"
}
] |
56
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 8, 7, -1],\n [0, 8, 6, -12],\n [0, 0, 5, 8],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 8, -8, -8],\n [0, 11, -2, 3],\n [0, 0, 4, -7],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
176
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -7, 1, 6],\n [0, 8, 6, -8],\n [0, 0, 10, 6],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -3, 3, 6],\n [12, 8, 8, 0],\n [-10, 6, 5, -6],\n [-12, -6, 5, -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"
}
] |
992
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 8, 2, -8],\n [0, 11, -10, 10],\n [0, 0, -5, 10],\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"
}
] |
980
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 0, 0, -6],\n [0, 5, 1, 2],\n [0, 1, 6, 0],\n [-6, 2, 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"
}
] |
431
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -5, 8, 0],\n [-1, -8, -10, -10],\n [-2, 5, 12, -2],\n [1, -9, 12, 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"
}
] |
458
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 4, 3, -1],\n [7, 3, 12, -10],\n [-6, -5, 4, 4],\n [-9, 11, -10, 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"
}
] |
177
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 5, 11, 1],\n [0, -6, -8, -12],\n [0, 0, -7, -4],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
622
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 3, 2, -12],\n [0, 10, 3, -12],\n [0, 0, 3, -9],\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"
}
] |
360
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -8, -8, 4],\n [-8, -12, -3, 0],\n [-8, -3, 0, 6],\n [4, 0, 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"
}
] |
64
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -2, 4, 3],\n [7, -9, 3, -7],\n [-9, -3, 1, 11],\n [6, 11, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
998
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 9, 5, 6],\n [0, -5, 8, 10],\n [0, 0, -2, -4],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 8, 0, -12],\n [8, 3, 0, -3],\n [0, 0, -11, 1],\n [-12, -3, 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"
}
] |
554
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 10, -3, -4],\n [10, -4, -7, 2],\n [-3, -7, -12, -5],\n [-4, 2, -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"
}
] |
990
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 2, -1, -12],\n [2, 11, 6, -12],\n [-1, 6, 3, 4],\n [-12, -12, 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"
}
] |
952
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 0, 11, -5],\n [0, 11, -5, 6],\n [0, 0, -10, 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"
}
] |
320
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -9, -3, 6],\n [0, 6, -5, -4],\n [0, 0, -11, 8],\n [0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
812
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 3, 7, -6],\n [0, 7, 9, 6],\n [0, 0, -8, 7],\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"
}
] |
656
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 0, -12, 1],\n [0, -7, 0, 6],\n [0, 0, -2, -3],\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"
}
] |
8
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -8, 0, -1],\n [7, -4, -10, 7],\n [6, -4, -9, -11],\n [-11, -9, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
857
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 2, -6, 2],\n [2, 12, 6, 5],\n [-6, 6, -3, 10],\n [2, 5, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
745
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 8, 5, -3],\n [0, -4, 3, -12],\n [0, 0, -9, 1],\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"
}
] |
408
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -5, -8, 5],\n [4, 5, -7, 5],\n [-6, 4, 8, 9],\n [-2, 4, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
552
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -4, 6, 4],\n [-4, 8, -3, -9],\n [6, -3, -7, 2],\n [4, -9, 2, 3]]\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[[-5, -10, 2, -5],\n [-10, 3, -2, 0],\n [2, -2, -6, -8],\n [-5, 0, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
566
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -4, -8, -1],\n [-4, 10, 7, 0],\n [-8, 7, 9, 2],\n [-1, 0, 2, -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"
}
] |
486
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -1, -6, 4],\n [7, -2, 8, 5],\n [-10, -7, 5, -5],\n [-8, 4, -6, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
750
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -1, -2, -2],\n [-1, 1, 0, 4],\n [-2, 0, 4, 8],\n [-2, 4, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
472
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 0, -6, -9],\n [0, -2, -6, -8],\n [0, 0, 12, -7],\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"
}
] |
640
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 5, 5, -11],\n [0, 11, 6, 9],\n [0, 0, 3, -3],\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"
}
] |
670
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 1, -6, -4],\n [1, 3, -8, 10],\n [-6, -8, -11, -2],\n [-4, 10, -2, 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"
}
] |
625
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -6, -7, 3],\n [10, -7, 8, -8],\n [-5, 4, 10, 2],\n [-12, -5, -11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
177
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 1, 4, -4],\n [1, -9, 8, -10],\n [4, 8, -10, 0],\n [-4, -10, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, 0, -12, -1],\n [0, 8, 8, -6],\n [-12, 8, 2, 4],\n [-1, -6, 4, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
936
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 7, -2, 2],\n [7, -3, 6, 8],\n [-2, 6, 0, -5],\n [2, 8, -5, -7]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 4, 8, -3],\n [0, 4, -8, 3],\n [0, 0, 8, 10],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
808
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -1, 2, -2],\n [-1, -10, 10, -3],\n [2, 10, 10, -2],\n [-2, -3, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
924
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -3, 9, 1],\n [0, 5, 6, -4],\n [0, 0, 4, -11],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
680
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 9, 5, -6],\n [0, -6, -6, 0],\n [0, 0, 12, 7],\n [0, 0, 0, 8]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, 12, -1],\n [2, -10, -4, -2],\n [12, -4, -11, -9],\n [-1, -2, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
634
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -2, -5, -11],\n [0, -1, 2, 9],\n [0, 0, 8, 4],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
912
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 10, -5, -11],\n [-9, 8, -5, 6],\n [5, -10, 0, 4],\n [-10, 12, 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"
}
] |
140
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -2, -2, 0],\n [-2, 12, -8, 9],\n [-2, -8, -4, -6],\n [0, 9, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
264
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -10, -4, 4],\n [-10, -12, 2, -6],\n [-4, 2, -7, -5],\n [4, -6, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
836
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 1, 4, 6],\n [1, 9, -3, -4],\n [4, -3, -3, 1],\n [6, -4, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
540
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 0, -2, 11],\n [0, 2, 11, -5],\n [0, 0, 11, 12],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
188
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -2, 2, 0],\n [-2, -6, 3, -2],\n [2, 3, -12, 2],\n [0, -2, 2, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
696
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -1, -1, 4],\n [0, -5, -6, 6],\n [0, 0, 8, -10],\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"
}
] |
0
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -5, -6, 5],\n [-5, 1, -2, 0],\n [-6, -2, -3, -8],\n [5, 0, -8, -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"
}
] |
541
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 8, -10, -5],\n [0, -4, 2, 7],\n [0, 0, -12, -3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
944
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 1, -6, -3],\n [0, 2, 8, -4],\n [0, 0, -12, 4],\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"
}
] |
864
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -4, 0, -8],\n [0, 3, -5, 7],\n [0, 0, 7, -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"
}
] |
895
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 5, 9, -10],\n [-9, 1, -1, 9],\n [-2, 0, -4, 0],\n [3, -1, -9, -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": "Determine the value of det(A) where A =\n[[-10, 6, 2, -6],\n [6, 8, -6, -2],\n [2, -6, 9, 4],\n [-6, -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"
}
] |
996
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -6, -5, -7],\n [-6, 3, -3, 2],\n [-5, -3, 5, 4],\n [-7, 2, 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"
}
] |
783
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 5, -9, 3],\n [0, 12, -3, -2],\n [0, 0, 4, -12],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
616
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 2, 6, -7],\n [2, -3, 0, 10],\n [6, 0, -6, -2],\n [-7, 10, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
466
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 7, 9, -7],\n [4, 1, -12, 7],\n [-4, -9, 2, 9],\n [2, 8, 7, -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"
}
] |
552
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 12, 8, -1],\n [-12, -9, 8, 1],\n [3, -2, -2, 10],\n [-3, -10, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
228
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -10, -2, -1],\n [-6, -12, 9, 12],\n [7, 0, -6, -1],\n [3, 2, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -10, -2, -11],\n [4, -7, 9, -2],\n [-2, -2, -11, 6],\n [5, 11, 9, 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"
}
] |
677
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 11, -8, -5],\n [-10, -10, -6, 8],\n [7, -7, 3, 8],\n [4, -5, -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"
}
] |
696
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, 12, 2],\n [0, 7, 2, 5],\n [0, 0, 7, -10],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
294
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 3, -6, -8],\n [3, 2, 4, -7],\n [-6, 4, -2, -2],\n [-8, -7, -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"
}
] |
786
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 1, -11, -7],\n [0, 7, -6, -7],\n [0, 0, -2, 9],\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"
}
] |
958
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 10, 10, -12],\n [0, -5, 6, 5],\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"
}
] |
630
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 5, -5, 7],\n [3, -3, 2, 4],\n [2, 1, 7, -6],\n [-4, -12, 10, -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"
}
] |
582
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -4, 7, 7],\n [12, 12, -6, -7],\n [7, -12, -7, 6],\n [-12, 8, -11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
668
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -4, 12, 10],\n [2, -11, 11, -7],\n [-7, -2, 9, -8],\n [-1, 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"
}
] |
340
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 6, -4, 0],\n [6, -3, 3, 2],\n [-4, 3, -3, 6],\n [0, 2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
508
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 1, -6, -4],\n [1, -4, -4, 0],\n [-6, -4, 0, 0],\n [-4, 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"
}
] |
136
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -2, 1, -8],\n [-2, -3, -11, 5],\n [1, -11, 9, -8],\n [-8, 5, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
843
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -1, 1, 0],\n [-1, -5, 0, 1],\n [1, 0, 10, 5],\n [0, 1, 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"
}
] |
866
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -3, -10, -12],\n [0, -6, 7, -8],\n [0, 0, -5, -3],\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"
}
] |
580
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 1, -4, 3],\n [-2, -1, -10, 3],\n [-11, 1, 8, 6],\n [0, 5, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
626
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -2, -4, 6],\n [0, -1, 6, -3],\n [0, 0, 3, 5],\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"
}
] |
72
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 7, -1, -1],\n [7, 4, 4, -7],\n [-1, 4, 7, 6],\n [-1, -7, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
279
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -10, -12, 12],\n [0, 11, -4, 11],\n [0, 0, -8, -9],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
64
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -10, 4, -10],\n [0, -5, -8, -10],\n [11, -12, 8, -5],\n [8, -6, -11, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
778
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 5, 7, -7],\n [4, -6, 10, -7],\n [-11, -1, -10, -11],\n [4, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
708
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 4, 7, 2],\n [4, -3, 4, 0],\n [7, 4, -3, 6],\n [2, 0, 6, 12]]\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[[4, 4, 7, 6],\n [11, -1, 0, -4],\n [6, -2, -7, -5],\n [9, -5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
298
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -3, 4, -2],\n [-11, -7, -10, 10],\n [4, -5, 1, 3],\n [-3, -8, -9, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
633
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -6, 10, -12],\n [0, 8, -4, -6],\n [0, 0, -6, -5],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
848
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -3, -1, 0],\n [0, 2, 5, 1],\n [0, 0, -5, 8],\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"
}
] |
900
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 7, 3, -8],\n [7, 8, -2, 0],\n [3, -2, 7, 0],\n [-8, 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"
}
] |
50
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -1, 1, -5],\n [-6, -4, 1, 9],\n [-10, 1, -3, -1],\n [8, 2, 7, 12]]\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[[7, 8, -3, -10],\n [0, -3, 3, -2],\n [0, 0, 10, 1],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
740
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -7, 8, -10],\n [9, 3, -8, 9],\n [1, 12, -8, 7],\n [2, 0, -1, 9]]\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[[3, 6, 2, 4],\n [0, 2, 8, -3],\n [0, 0, -7, 12],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
832
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 11, 11, -4],\n [-11, 7, 11, -1],\n [5, -9, -5, 11],\n [-2, -1, -2, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
384
|
MATH
|
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