messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -2, 3, -2],\n [-8, 10, -9, -6],\n [10, -10, 3, -2],\n [10, 6, 9, 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"
}
] |
680
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -11, 2, 5],\n [-4, 4, 5, 1],\n [2, 0, -2, 7],\n [7, 12, -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"
}
] |
359
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -9, -2, -2],\n [-5, -3, -9, -9],\n [1, 3, -8, -4],\n [6, -7, 3, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
975
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -2, 4, -2],\n [-2, -9, 2, -2],\n [4, 2, -3, 2],\n [-2, -2, 2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
748
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -12, 9, -12],\n [0, 10, 10, 1],\n [0, 0, 1, -10],\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"
}
] |
210
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 0, 7, -11],\n [0, -11, 2, -2],\n [0, 0, 3, 2],\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"
}
] |
485
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 9, 1, 5],\n [0, -11, -4, 4],\n [0, 0, -12, 0],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
416
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -10, 0, 0],\n [0, 1, 0, 7],\n [0, 0, 6, 5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
144
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 0, -6, 4],\n [0, 7, 5, 7],\n [-6, 5, -5, 7],\n [4, 7, 7, 4]]\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[[-11, 9, 9, 12],\n [0, -5, -1, -9],\n [0, 0, 9, 2],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
495
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 6, 3, -5],\n [6, -5, -3, -9],\n [3, -3, 10, 4],\n [-5, -9, 4, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
764
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 4, -2, 12],\n [4, 9, 0, 9],\n [-2, 0, 11, 5],\n [12, 9, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
752
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 11, -12, 6],\n [0, -6, 0, -1],\n [0, 0, -12, 11],\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"
}
] |
16
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -2, 4, 4],\n [-2, 2, -2, -2],\n [4, -2, -10, -5],\n [4, -2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
318
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -10, 4, 5],\n [0, 8, 10, 5],\n [0, 0, -10, 7],\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"
}
] |
320
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -11, -5, 3],\n [-4, 6, -7, -10],\n [8, 5, 6, 0],\n [3, 1, -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"
}
] |
232
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -1, -2, 2],\n [-1, -9, 10, -2],\n [-2, 10, -7, -4],\n [2, -2, -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"
}
] |
264
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -8, -2, -12],\n [10, -5, 7, -8],\n [-3, 4, 7, -1],\n [-10, -7, -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"
}
] |
102
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 12, -4, -5],\n [5, 9, 3, -10],\n [-10, 3, 3, 11],\n [-8, 5, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
810
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 4, 3, 8],\n [4, -10, -3, 4],\n [3, -3, 11, -7],\n [8, 4, -7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
980
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 7, 11, 8],\n [-5, -2, 6, 6],\n [-7, -2, 4, 2],\n [-1, 8, -4, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
150
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, -5, -5],\n [-2, -11, -6, -2],\n [-5, -6, 10, 3],\n [-5, -2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
170
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -7, 1, -2],\n [-7, 1, 2, -6],\n [1, 2, -12, 4],\n [-2, -6, 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"
}
] |
606
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 3, -4, 10],\n [10, -11, 2, 12],\n [-10, 5, 0, 7],\n [-5, 5, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -4, 4, 0],\n [-4, 9, -6, 6],\n [4, -6, -6, 2],\n [0, 6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
116
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 2, -4, 1],\n [2, 10, -8, 1],\n [-4, -8, 1, -4],\n [1, 1, -4, 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"
}
] |
353
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -10, 0, 10],\n [0, -8, 11, -1],\n [0, 0, -8, -9],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
744
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -4, -6, 4],\n [-4, 12, -2, 6],\n [-6, -2, -6, -4],\n [4, 6, -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"
}
] |
376
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 6, 2, 0],\n [6, 1, 0, 4],\n [2, 0, 10, 10],\n [0, 4, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
972
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -4, -5, -9],\n [-11, 12, 8, -12],\n [-12, 11, 9, -4],\n [-12, 9, 9, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
245
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -2, 10, 6],\n [-2, -4, 6, 0],\n [10, 6, -10, -2],\n [6, 0, -2, -9]]\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, 12, 10, -11],\n [4, 10, -11, 6],\n [5, 0, -12, 6],\n [7, -6, 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"
}
] |
268
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -11, -3, -9],\n [-2, 2, -5, -3],\n [10, 4, -3, -2],\n [2, 5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
958
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -7, -2, -5],\n [-7, 12, 0, 10],\n [-2, 0, 6, -5],\n [-5, 10, -5, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
617
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -3, 0, -7],\n [-3, 8, -4, 2],\n [0, -4, -8, 0],\n [-7, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
784
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 6, 8, 6],\n [0, 1, 1, 9],\n [0, 0, 1, 11],\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"
}
] |
976
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 9, -9, 1],\n [0, -4, -3, 8],\n [0, 0, 3, 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"
}
] |
280
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 5, -1, -6],\n [0, -11, -4, -4],\n [0, 0, 1, -6],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -6, -6, -7],\n [-6, -4, -6, 3],\n [-6, -6, -4, -5],\n [-7, 3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
476
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -2, -12, 6],\n [6, 9, 0, -3],\n [6, 9, -3, 0],\n [2, 2, 5, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
415
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 11, 4, -6],\n [0, -12, 7, -8],\n [0, 0, -8, -3],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
408
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -2, 6, 10],\n [-2, 4, -6, 6],\n [6, -6, 11, 4],\n [10, 6, 4, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
308
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 12, -10, -7],\n [0, 1, -4, 10],\n [0, 0, -8, -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"
}
] |
968
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -12, -8, -10],\n [0, -1, -7, 8],\n [0, 0, 3, 8],\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"
}
] |
144
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, -7, 9, -9],\n [11, -4, -12, -1],\n [-7, -4, 8, 5],\n [-4, -1, -8, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
440
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 4, -10, 0],\n [10, -8, -4, 6],\n [-9, 10, 0, -9],\n [9, -3, -5, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
832
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 12, -9, -7],\n [0, -12, 10, -1],\n [0, 0, 5, -8],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -3, 2, 5],\n [-4, -1, -5, 7],\n [-5, -7, 4, 10],\n [8, 0, 10, 9]]\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[[11, -7, 12, -3],\n [0, 11, -8, -10],\n [0, 0, -2, 4],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
420
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -2, -3, 2],\n [-2, -1, -6, -2],\n [-3, -6, -1, -2],\n [2, -2, -2, 4]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 8, -8, -7],\n [8, 2, 8, 2],\n [-8, 8, -7, 4],\n [-7, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
890
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 0, 9, 4],\n [-5, 6, -3, -7],\n [-2, 4, 9, -4],\n [-11, -3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
238
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 3, 3, 3],\n [0, -10, 10, -11],\n [0, 0, -2, -8],\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[[-9, -10, 4, 5],\n [1, -10, 8, -6],\n [-10, -4, 5, -1],\n [5, -4, 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"
}
] |
554
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -6, 10, -2],\n [-3, -11, 7, 6],\n [-9, 9, 6, 4],\n [7, 4, 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"
}
] |
45
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 2, -7, -1],\n [2, -6, -4, 8],\n [-7, -4, 0, 4],\n [-1, 8, 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"
}
] |
298
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 8, 1, 2],\n [8, 5, 0, 6],\n [1, 0, 7, 0],\n [2, 6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
724
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 10, -1, -2],\n [12, 3, 5, 5],\n [-12, 6, -5, 12],\n [2, 3, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
331
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 7, -10, 5],\n [0, -3, -12, 5],\n [0, 0, -8, 7],\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"
}
] |
48
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -9, 10, 7],\n [-3, 0, 9, -1],\n [-6, -8, 7, 4],\n [-8, 1, -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"
}
] |
670
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 10, -6, -8],\n [-6, -2, 2, -8],\n [9, 10, -11, -4],\n [-1, -5, 12, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -7, -1, -1],\n [0, 7, 1, 6],\n [0, 0, 3, -11],\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"
}
] |
328
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 7, -7, -7],\n [-2, 2, -4, -1],\n [-3, 11, 0, 8],\n [-4, -2, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
368
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 1, 1, -4],\n [1, -6, -2, -3],\n [1, -2, 2, -3],\n [-4, -3, -3, 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"
}
] |
104
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 5, -7, -1],\n [0, 2, 1, 8],\n [0, 0, 3, 4],\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"
}
] |
880
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, 4, 6],\n [8, -6, -2, -2],\n [4, -2, -9, 0],\n [6, -2, 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"
}
] |
328
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -4, 0, -6],\n [-4, -11, 1, 3],\n [0, 1, 11, -4],\n [-6, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
489
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 9, -7, 5],\n [0, 2, -3, 11],\n [0, 0, 10, -8],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 10, 6, -2],\n [0, -7, 7, -10],\n [0, 0, -1, -12],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
923
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -12, 4, 5],\n [0, 5, -3, -2],\n [0, 0, -9, 0],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
455
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -1, 6, 4],\n [-1, 7, 6, 2],\n [6, 6, 2, 8],\n [4, 2, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
364
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -6, -11, 4],\n [0, 8, 10, 2],\n [0, 0, 5, 1],\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"
}
] |
440
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -10, -12, -11],\n [-1, -12, -3, -9],\n [3, -1, 0, 7],\n [11, -10, 12, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
545
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -4, -8, 8],\n [-4, -3, 7, 6],\n [-8, 7, -12, 2],\n [8, 6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 5, -2, 7],\n [0, -9, 1, -11],\n [0, 0, -12, 6],\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"
}
] |
108
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 4, -6, 1],\n [4, 1, 0, 3],\n [-6, 0, -11, -4],\n [1, 3, -4, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
599
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -4, 6, 12],\n [11, 8, -3, -10],\n [7, -10, -11, 0],\n [8, 7, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
744
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -4, -10, -6],\n [0, -1, 5, -3],\n [0, 0, -7, -8],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 3, -2, -6],\n [3, -11, 4, -5],\n [-2, 4, -3, 2],\n [-6, -5, 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"
}
] |
527
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 7, 12, -11],\n [7, -6, 7, -5],\n [5, 7, 2, -4],\n [5, 7, 12, -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"
}
] |
567
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 7, -2, -7],\n [6, -9, -6, 4],\n [-12, 5, 6, -11],\n [6, -4, 7, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
265
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 9, 7, -4],\n [0, -9, -11, -10],\n [0, 0, 11, 7],\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"
}
] |
970
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 5, -4, -1],\n [0, 9, -2, 5],\n [0, 0, -6, -1],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
408
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -8, 6, 4],\n [-8, 1, 4, 0],\n [6, 4, 8, -7],\n [4, 0, -7, 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"
}
] |
748
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 6, 3, 10],\n [8, 12, 4, -2],\n [8, 5, 5, 8],\n [5, -9, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
364
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 4, -6, 2],\n [4, 11, 4, -8],\n [-6, 4, 2, -10],\n [2, -8, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
656
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 8, 2, -7],\n [-6, 0, 10, -5],\n [8, -1, -1, -2],\n [5, 8, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
710
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 0, 7, -3],\n [0, 12, 0, -6],\n [7, 0, 12, 5],\n [-3, -6, 5, 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"
}
] |
816
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 11, -9, 9],\n [0, 6, 10, 2],\n [0, 0, -9, -8],\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"
}
] |
728
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 7, 2, 11],\n [5, -5, -9, -2],\n [-2, -10, 9, -3],\n [4, 6, -1, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
908
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 4, 3, 3],\n [-3, -5, 10, -11],\n [2, 12, -3, 1],\n [3, 11, 3, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
507
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 10, -12, -4],\n [-4, -7, -1, 10],\n [-9, 9, 7, -1],\n [-3, -7, 7, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
592
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 2, -3, -2],\n [2, 10, -3, 0],\n [-3, -3, -10, -4],\n [-2, 0, -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"
}
] |
20
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 8, 0, -3],\n [0, -5, -7, 0],\n [0, 0, 8, -10],\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"
}
] |
80
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -3, -10, -4],\n [-3, -6, 8, -2],\n [-10, 8, 12, -1],\n [-4, -2, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
739
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 1, -10, -11],\n [2, -6, 9, 12],\n [-1, -5, 10, -10],\n [-10, -6, -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"
}
] |
188
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 11, -11, -9],\n [0, -2, 1, -5],\n [0, 0, -5, -12],\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"
}
] |
660
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 5, 2, 3],\n [5, -7, 5, 6],\n [2, 5, -8, -2],\n [3, 6, -2, -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"
}
] |
25
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -2, 7, -3],\n [-2, 7, -5, -8],\n [7, -5, -5, -4],\n [-3, -8, -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"
}
] |
844
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -11, 12, 10],\n [-5, -2, -11, 5],\n [-2, 7, -8, -9],\n [-12, -6, 1, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
477
|
MATH
|
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