messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[3, -8, 4, 9],\n [5, -3, -9, -8],\n [6, 0, -11, -7],\n [3, -7, 7, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
551
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 4, -2, 6],\n [4, 2, -4, 5],\n [-2, -4, -12, 4],\n [6, 5, 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"
}
] |
244
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -8, 4, 10],\n [6, 4, 9, -1],\n [9, -10, 0, -4],\n [11, -10, -1, 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"
}
] |
512
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 0, -11, 2],\n [0, 9, 11, 4],\n [0, 0, -2, -12],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 11, 8, 9],\n [0, -3, 7, -3],\n [0, 0, 7, 7],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
538
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, 2, 0],\n [-2, 8, -8, -7],\n [2, -8, -11, 0],\n [0, -7, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
113
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -2, -7, 9],\n [0, -12, 9, 5],\n [0, 0, 12, -5],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -1, 7, 2],\n [0, -9, 0, -11],\n [0, 0, 10, -2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
720
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 12, -11, -12],\n [11, -7, -7, 11],\n [5, 10, 9, 4],\n [-2, 11, -1, -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"
}
] |
566
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 4, -2, 6],\n [0, 5, -10, -4],\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"
}
] |
50
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 0, -12, 0],\n [-9, 0, 5, 2],\n [8, -12, 10, 10],\n [-6, 3, -4, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
806
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -10, 5, -11],\n [2, -9, 6, 8],\n [-5, -11, -8, 1],\n [5, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
966
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -8, 5, -2],\n [-8, 7, 6, 12],\n [5, 6, 3, -3],\n [-2, 12, -3, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
678
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -9, -6, 4],\n [0, 1, -3, -11],\n [0, 0, -12, -11],\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"
}
] |
520
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -11, 7, -7],\n [3, -8, -1, -11],\n [5, 8, 10, -9],\n [6, 2, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
897
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 12, -4, -3],\n [0, -9, 3, -4],\n [0, 0, 11, -12],\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"
}
] |
534
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 3, 11, -6],\n [0, 9, -12, -4],\n [0, 0, -9, 2],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
439
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 4, -2, -6],\n [4, -10, 5, 2],\n [-2, 5, -3, -4],\n [-6, 2, -4, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
608
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 9, -3, -4],\n [6, -1, 4, -4],\n [-10, 1, 12, 10],\n [5, -5, -12, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
798
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 8, -1, -6],\n [1, -1, -6, 11],\n [-9, 0, -10, -10],\n [-10, -6, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
163
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 12, 12, -1],\n [0, 6, -2, -8],\n [0, 0, 1, 10],\n [0, 0, 0, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 11, 1, -11],\n [11, -9, -3, 11],\n [7, -7, 2, 7],\n [-7, 12, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
530
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 0, -3, 8],\n [5, -4, -1, 7],\n [8, -6, -1, 10],\n [5, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
958
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -7, 2, 0],\n [-7, 11, 3, 4],\n [2, 3, 1, 3],\n [0, 4, 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"
}
] |
548
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 0, 0, 2],\n [0, 5, -10, 2],\n [0, -10, 11, -8],\n [2, 2, -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"
}
] |
408
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -6, 4, 2],\n [-6, 4, 9, 9],\n [4, 9, -7, 2],\n [2, 9, 2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
38
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -7, -1, 4],\n [12, 4, 11, -12],\n [8, 12, -6, 11],\n [-8, 5, -7, -11]]\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": "Determine the value of det(A) where A =\n[[-3, 11, 9, 1],\n [0, 10, -11, 6],\n [0, 0, -4, 5],\n [0, 0, 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"
}
] |
400
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 5, 9, -3],\n [0, -7, 11, -10],\n [0, 0, 4, 6],\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"
}
] |
776
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -12, 1, 10],\n [-12, 9, -11, -11],\n [3, -12, 1, 5],\n [11, -3, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -2, -2, 0],\n [-2, 3, 6, -4],\n [-2, 6, 11, -2],\n [0, -4, -2, 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"
}
] |
678
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 3, 6, 6],\n [3, -8, 7, 0],\n [6, 7, -8, 4],\n [6, 0, 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"
}
] |
486
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -2, -2, -6],\n [0, 10, 8, 4],\n [0, 0, -7, 7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -2, 5, 4],\n [-2, -8, -3, 10],\n [5, -3, -4, 7],\n [4, 10, 7, -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"
}
] |
861
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 6, -9, 5],\n [10, -3, 5, -8],\n [-9, 11, 6, 7],\n [3, 10, 1, -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"
}
] |
903
|
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, 0, -4, 0],\n [6, -4, -11, 2],\n [-4, 0, 2, 0]]\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[[9, 6, -4, 8],\n [6, -6, -4, 4],\n [-4, -4, -3, -5],\n [8, 4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
688
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -7, -4, 1],\n [-12, 8, 7, -12],\n [-5, -6, -5, 10],\n [11, 7, 11, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
927
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 6, 1, -4],\n [6, 1, 10, 1],\n [1, 10, -2, -4],\n [-4, 1, -4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
787
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -8, -1, 10],\n [0, -9, -4, -6],\n [0, 0, 3, -7],\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"
}
] |
378
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 4, 6, -8],\n [4, 7, 4, -5],\n [6, 4, 7, -10],\n [-8, -5, -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"
}
] |
848
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, -6, -3],\n [0, -12, 9, 10],\n [0, 0, 10, 4],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -6, -2, 6],\n [0, 3, 4, 9],\n [0, 0, -6, 3],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -5, -3, 2],\n [-1, 9, 6, -2],\n [4, 5, 11, 11],\n [7, 0, 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"
}
] |
870
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -1, -12, 10],\n [12, -1, 4, -8],\n [-5, -8, -8, 5],\n [0, 2, 1, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
242
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -6, 0, 3],\n [-6, 7, 5, 2],\n [0, 5, 10, -10],\n [3, 2, -10, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -2, -4, 3],\n [-2, -9, -8, 4],\n [-4, -8, -12, 8],\n [3, 4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
820
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 7, 8, -8],\n [0, 12, 6, -11],\n [0, 0, -9, -7],\n [0, 0, 0, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 10, 3, -2],\n [0, 5, 9, -1],\n [0, 0, -6, 4],\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"
}
] |
60
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -10, 7, -8],\n [2, -4, 12, 6],\n [10, 8, -2, 1],\n [9, -6, 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"
}
] |
920
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, 5, -10],\n [0, 0, -6, 10],\n [5, -6, -2, 5],\n [-10, 10, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 12, 6, -3],\n [12, -5, 1, 10],\n [6, 1, -7, 8],\n [-3, 10, 8, -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": "What is the determinant of the matrix:\n[[-9, -11, 2, -3],\n [0, 5, 11, -5],\n [0, 0, 8, -4],\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"
}
] |
960
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -3, 0, -3],\n [0, -3, 6, 3],\n [0, 0, 1, 9],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
784
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, -7, -5],\n [0, -5, -4, -4],\n [-7, -4, 4, 2],\n [-5, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
159
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 3, 7, 3],\n [-1, -8, 10, 2],\n [4, 6, -2, 11],\n [-4, 10, 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"
}
] |
755
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -7, 10, -4],\n [-6, -12, -12, 2],\n [0, -3, 6, -11],\n [3, -9, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[0, 2, 10, 5],\n [2, -10, 6, -8],\n [10, 6, -12, 0],\n [5, -8, 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"
}
] |
564
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 1, -4, -12],\n [1, 1, 2, 6],\n [-9, -2, 7, 0],\n [-7, 1, -4, -10]]\nRound to the nearest integer, then take the result 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[[-7, -4, 2, -2],\n [-4, 3, 0, 11],\n [2, 0, -9, -4],\n [-2, 11, -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"
}
] |
838
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 4, -2, 6],\n [4, 8, -2, 8],\n [-2, -2, -5, 11],\n [6, 8, 11, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 1, -8, -2],\n [1, -1, 4, 1],\n [-8, 4, 0, -7],\n [-2, 1, -7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
896
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -1, 0, 8],\n [-1, 9, 1, -4],\n [0, 1, -3, 0],\n [8, -4, 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"
}
] |
622
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 11, -5, -4],\n [0, 11, -6, 2],\n [0, 0, -10, -8],\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"
}
] |
320
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -6, 9, 1],\n [0, -10, 11, 3],\n [0, 0, -3, -3],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
250
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 7, -12, -2],\n [-2, -2, -8, -1],\n [-9, -9, -8, -7],\n [1, -2, -11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
155
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 4, -2, -1],\n [4, -6, 6, -4],\n [-2, 6, 5, -5],\n [-1, -4, -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"
}
] |
386
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, 5, 2],\n [0, 10, 12, 6],\n [0, 0, 9, 6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 4, 4, 3],\n [4, -12, -2, -6],\n [4, -2, -6, -1],\n [3, -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"
}
] |
508
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 4, -1, -8],\n [4, 4, 7, 0],\n [-1, 7, -1, -2],\n [-8, 0, -2, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
470
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -4, -9, 4],\n [0, -10, 9, 9],\n [0, 0, -11, 1],\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"
}
] |
970
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 0, 2, 9],\n [0, -4, -4, 8],\n [2, -4, 2, -2],\n [9, 8, -2, 7]]? 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": "Compute |A| for the matrix A =\n[[-1, 9, -3, 8],\n [5, -5, 6, 4],\n [-11, -6, -6, 1],\n [-9, 11, -5, 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[[-12, 0, 8, 2],\n [0, -5, -10, 2],\n [8, -10, -11, -2],\n [2, 2, -2, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
348
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -5, -4, 0],\n [-5, 12, -8, -2],\n [-4, -8, 8, 0],\n [0, -2, 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"
}
] |
888
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 9, 11, -9],\n [2, -1, -8, -10],\n [10, 10, 2, -3],\n [-2, -4, 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"
}
] |
124
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 1, -5, 4],\n [3, 8, 7, 1],\n [-8, 7, 4, -2],\n [5, 8, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
49
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 4, -6, 1],\n [4, -4, 6, 4],\n [-6, 6, -9, 4],\n [1, 4, 4, 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"
}
] |
400
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -2, -1, -11],\n [-10, -12, -1, 5],\n [10, 0, 4, -9],\n [-8, 9, -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"
}
] |
682
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -8, 2, -10],\n [-4, 11, -11, 0],\n [-3, 9, -10, 10],\n [3, -9, 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"
}
] |
144
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -4, 4, -8],\n [-4, 6, 2, 8],\n [4, 2, -10, 7],\n [-8, 8, 7, -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"
}
] |
980
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -7, 11, -1],\n [0, 9, 11, -9],\n [0, 0, -12, -8],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
440
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 0, 4, 4],\n [0, -12, 0, -3],\n [4, 0, 4, -2],\n [4, -3, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
728
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -9, -3, 3],\n [-7, 6, 12, 4],\n [1, -12, 1, -5],\n [5, -9, 7, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
570
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -10, -1, 9],\n [0, -3, -4, -8],\n [3, -4, 9, 1],\n [9, 1, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
635
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 12, 0, 11],\n [10, 4, -1, 2],\n [10, -10, 9, -7],\n [-9, 11, -11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
987
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 2, 6, 6],\n [2, -11, 4, 0],\n [6, 4, 11, 11],\n [6, 0, 11, -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"
}
] |
703
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -6, -10, 0],\n [-6, -8, 2, 4],\n [-10, 2, 1, 5],\n [0, 4, 5, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
388
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 4, 2, -6],\n [4, 12, 8, 6],\n [2, 8, 2, 4],\n [-6, 6, 4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\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[[2, 6, 4, 8],\n [6, -11, 5, -6],\n [4, 5, 9, -3],\n [8, -6, -3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
730
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 0, 1, 4],\n [0, 11, 6, -2],\n [1, 6, 6, -2],\n [4, -2, -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"
}
] |
363
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 2, 2, 4],\n [0, 2, 0, -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"
}
] |
240
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 4, -5, 12],\n [0, -1, 3, 11],\n [0, 0, 5, -4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
985
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 12, -5, -2],\n [-5, 9, -9, 4],\n [8, -4, 1, 3],\n [11, 5, 3, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
396
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -6, 6, 4],\n [-6, 11, 0, 2],\n [6, 0, -10, -2],\n [4, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
832
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -11, -2, 6],\n [-11, 9, 5, -7],\n [-2, 5, -9, 2],\n [6, -7, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
105
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -5, -3, 12],\n [0, 1, 3, -5],\n [0, 0, 5, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
970
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 11, 11, 12],\n [0, -12, -10, -3],\n [0, 0, 4, 10],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
576
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -11, -5, -3],\n [-2, 6, -7, -8],\n [-7, -7, -6, 4],\n [-12, 7, 10, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 11, 6, 7],\n [0, 2, 7, -6],\n [0, 0, 3, 4],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
802
|
MATH
|
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