messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 6, 0, 2],\n [6, 0, 2, 2],\n [0, 2, 3, 4],\n [2, 2, 4, 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"
}
] |
192
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 0, -2, 2],\n [0, 8, 4, 10],\n [-2, 4, -9, 10],\n [2, 10, 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"
}
] |
20
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -1, 10, -7],\n [11, -6, 6, -11],\n [0, -3, -11, 3],\n [6, -6, 11, 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"
}
] |
806
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 6, -1, -12],\n [0, 9, 4, -4],\n [0, 0, -11, -2],\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"
}
] |
880
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -10, -8, -4],\n [0, 3, 9, -3],\n [0, 0, -3, -8],\n [0, 0, 0, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
136
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 4, -3, 4],\n [0, 8, -2, -8],\n [0, 0, 2, 1],\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"
}
] |
640
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 12, 2, -1],\n [4, 3, -4, -10],\n [1, -11, 5, -11],\n [-10, 0, -2, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
204
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 6, 0, 2],\n [6, -3, 2, 8],\n [0, 2, 10, 1],\n [2, 8, 1, 11]]\nRound to the nearest integer, then take the result 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[[10, 4, 0, -8],\n [6, 11, 10, 8],\n [-10, -2, 8, -5],\n [11, 12, 7, 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"
}
] |
690
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -4, -10],\n [3, -8, -8, -10],\n [6, 8, -1, 6],\n [-4, 4, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
556
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, 3, 3],\n [0, -6, 5, -3],\n [0, 0, 9, 0],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
112
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 10, 2, 0],\n [10, -7, 11, 4],\n [2, 11, -8, -8],\n [0, 4, -8, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
210
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 0, -9, -2],\n [0, 6, -9, 10],\n [0, 0, 12, -5],\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"
}
] |
568
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -8, -5, 3],\n [-8, 10, -7, 3],\n [-5, -7, 0, -2],\n [3, 3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -5, 10, -3],\n [2, 0, 6, -8],\n [-1, 2, 8, 1],\n [3, -5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
610
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 0, 0, 5],\n [0, 7, 4, 2],\n [0, 4, 2, 1],\n [5, 2, 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"
}
] |
37
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 6, 2, 2],\n [6, 3, 2, -8],\n [2, 2, -11, 1],\n [2, -8, 1, 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"
}
] |
456
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -12, 6, -9],\n [0, 3, 5, 7],\n [0, 0, -9, 6],\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"
}
] |
757
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -9, -6, -11],\n [-12, -10, -2, -5],\n [-11, -10, -10, -9],\n [-2, 9, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
622
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 3, -10, 2],\n [0, -5, 4, -5],\n [0, 0, 8, -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"
}
] |
960
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 0, -2, -4],\n [0, 11, 9, -8],\n [0, 0, 9, 0],\n [0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, 5, 8],\n [1, -2, 8, -1],\n [5, 8, 9, 2],\n [8, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
535
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 12, -9, -8],\n [-8, -3, -1, -11],\n [-2, 9, 11, 6],\n [-12, 6, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, -2, -3],\n [2, 11, -4, 10],\n [-2, -4, 9, -1],\n [-3, 10, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
629
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -10, 0, 0],\n [-10, 11, 4, 4],\n [0, 4, 6, 6],\n [0, 4, 6, 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"
}
] |
800
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 11, -11, 8],\n [10, 4, 2, 1],\n [2, 4, -4, 10],\n [-2, 8, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
626
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -1, 5, 4],\n [-1, 11, -3, 0],\n [5, -3, -4, -2],\n [4, 0, -2, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -11, 1, 9],\n [0, -4, 3, 4],\n [0, 0, -4, 3],\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"
}
] |
296
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -2, 3, -9],\n [0, 12, 1, -11],\n [0, 0, -1, 8],\n [0, 0, 0, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 12, 8, -5],\n [0, 11, 7, -3],\n [0, 0, -10, -5],\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"
}
] |
700
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 12, -9, 7],\n [0, -11, -4, -10],\n [0, 0, -5, 8],\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"
}
] |
680
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, -11, -7, -11],\n [2, -6, 1, -7],\n [6, -8, 5, -7],\n [-9, 7, 6, -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"
}
] |
520
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 2, 4, 12],\n [8, -4, 4, -5],\n [-7, 2, 6, -8],\n [-12, -9, -11, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
238
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -2, -8, 2],\n [0, -5, 8, -7],\n [0, 0, -11, -12],\n [0, 0, 0, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 9, 4, -5],\n [9, -10, 5, 6],\n [4, 5, -11, -2],\n [-5, 6, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
695
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, -7, 10, 1],\n [4, 1, -7, 8],\n [-2, -11, -2, 4],\n [-10, -5, -6, 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"
}
] |
556
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -6, 0, 10],\n [-6, 8, 5, -2],\n [0, 5, -4, -3],\n [10, -2, -3, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
632
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -6, 3, 6],\n [-6, 12, 10, -4],\n [3, 10, -5, -2],\n [6, -4, -2, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 4, 0, -2],\n [4, 7, 2, 2],\n [0, 2, 1, 4],\n [-2, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
130
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 9, 11, 5],\n [-3, -4, 5, 8],\n [-5, 5, 10, -6],\n [-5, -10, 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"
}
] |
915
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 10, 12, -1],\n [-2, -10, 4, -9],\n [11, -10, -12, 6],\n [-9, 7, 12, 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"
}
] |
940
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 1, -9, -12],\n [6, 7, -6, -12],\n [11, -11, 9, -2],\n [11, 0, -10, -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"
}
] |
273
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 2, -1, 2],\n [2, -8, -6, -4],\n [-1, -6, -10, -4],\n [2, -4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 7, -5, 2],\n [0, 1, 5, -3],\n [9, -1, -4, 2],\n [7, -7, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
163
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -6, -5, 1],\n [9, 4, -3, -4],\n [2, -7, 0, -5],\n [-9, 7, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
283
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 2, 1, 12],\n [0, -1, -8, -3],\n [0, 0, -11, 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"
}
] |
989
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -12, 11, -1],\n [0, -12, -10, 3],\n [0, -12, -8, 5],\n [12, 10, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
824
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 4, -1, 0],\n [4, 1, 1, 2],\n [-1, 1, -1, 3],\n [0, 2, 3, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
933
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 4, -3, -1],\n [4, -8, 8, 4],\n [-3, 8, -6, 2],\n [-1, 4, 2, -3]]\nRound to the nearest integer, then take the result 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[[-11, 3, -4, -12],\n [-8, 7, -6, 0],\n [-3, -3, 1, 11],\n [10, -9, -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"
}
] |
762
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -6, 0, 6],\n [-6, 12, 2, 8],\n [0, 2, -2, -6],\n [6, 8, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
472
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 4, -4, -2],\n [4, 9, 4, 8],\n [-4, 4, 3, -6],\n [-2, 8, -6, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
566
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -3, -6, -2],\n [-3, 5, 2, 4],\n [-6, 2, 12, 4],\n [-2, 4, 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"
}
] |
976
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, 0, 7],\n [-2, -3, -4, -6],\n [0, -4, -5, 0],\n [7, -6, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 5, 9, 8],\n [0, 6, -4, -3],\n [0, 0, -2, -5],\n [0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -12, 1, -5],\n [0, 10, 9, 11],\n [0, 0, -10, 1],\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"
}
] |
300
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 0, -6, -4],\n [0, -10, -12, -1],\n [0, 0, 12, 5],\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": "What is the determinant of the matrix:\n[[10, -2, -4, 0],\n [0, -11, -10, 7],\n [0, 0, 12, -2],\n [0, 0, 0, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 4, -7, -4],\n [4, 5, 0, 6],\n [-7, 0, -11, -4],\n [-4, 6, -4, 6]]\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": "Determine the value of det(A) where A =\n[[3, -1, 4, -11],\n [0, -9, 4, 5],\n [0, 0, 2, -9],\n [0, 0, 0, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
622
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 1, -11, -2],\n [-8, -12, 8, 12],\n [11, -12, 7, 2],\n [5, 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"
}
] |
352
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 6, 0, 7],\n [6, -9, -7, -8],\n [0, -7, -2, 0],\n [7, -8, 0, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
145
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -11, -9, -11],\n [0, -2, -4, 2],\n [0, 0, -3, 6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
424
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -3, -1, 0],\n [0, 1, 4, -8],\n [0, 0, 10, -11],\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"
}
] |
340
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -9, 4, 5],\n [-7, -1, 4, 2],\n [5, 5, 0, 5],\n [8, -1, -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"
}
] |
250
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, 8, -12, -3],\n [0, 2, 9, -2],\n [0, 0, -1, -2],\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"
}
] |
998
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 6, -8, -2],\n [0, -10, -10, -6],\n [0, 0, 8, 12],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, 0, 4],\n [-2, -2, 7, 2],\n [0, 7, 8, 2],\n [4, 2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
662
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 2, 2, 4],\n [2, -11, -5, -2],\n [2, -5, 6, -7],\n [4, -2, -7, -6]]? 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": "Determine the value of det(A) where A =\n[[-7, -8, 9, 7],\n [0, -10, -6, -1],\n [0, 0, 9, -1],\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"
}
] |
260
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -7, 10, 3],\n [-3, -11, 4, -8],\n [-10, -1, -5, 9],\n [-1, -3, -6, -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"
}
] |
268
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 0, 3, 3],\n [0, 1, -1, -10],\n [0, 0, 2, 2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, 2, 0],\n [-4, -7, -3, -2],\n [2, -3, 3, -5],\n [0, -2, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
614
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 7, 0, 10],\n [-5, 8, 12, 12],\n [-3, 1, 10, 5],\n [5, 5, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
283
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 7, 12, -2],\n [0, -3, 10, -11],\n [0, 0, 2, -5],\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"
}
] |
676
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 11, -7, -8],\n [0, 11, 7, 2],\n [0, 0, -8, -1],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -10, 0, -4],\n [0, -4, -12, -7],\n [0, 0, -8, 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"
}
] |
576
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 7, 2, 1],\n [0, -1, -3, -10],\n [0, 0, 7, -10],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
685
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 8, 3, -4],\n [8, 5, -4, 2],\n [3, -4, -12, 6],\n [-4, 2, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
471
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 8, 0, 0],\n [8, 1, -2, -8],\n [0, -2, 8, -4],\n [0, -8, -4, 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"
}
] |
920
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -1, -8, -8],\n [0, 3, -6, -8],\n [0, 0, 1, -12],\n [0, 0, 0, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
910
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 6, 7, 8],\n [0, 7, 0, -10],\n [0, 0, 6, -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"
}
] |
690
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -9, -2, 8],\n [-1, 2, -12, 8],\n [-1, -4, -11, 9],\n [7, -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"
}
] |
631
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 6, 8, 3],\n [6, -2, 2, -4],\n [8, 2, 7, 8],\n [3, -4, 8, -5]]\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[[-6, 10, 2, 6],\n [-9, -3, 0, 6],\n [-10, -7, -4, -9],\n [-3, 3, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
70
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -7, 2, -5],\n [10, -5, 7, -11],\n [10, -11, 2, -3],\n [10, -3, -7, -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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -1, 1, 6],\n [0, 8, 1, 3],\n [0, 0, 4, -7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
424
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 2, -2, 4],\n [0, -9, -4, 2],\n [0, 0, 4, 0],\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"
}
] |
980
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, 10, 10],\n [1, 8, 0, -10],\n [2, -6, -1, -10],\n [12, -11, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
18
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -4, -4, -11],\n [-4, 2, 9, -9],\n [-9, -7, 11, 10],\n [-4, -2, 3, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
562
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 2, 1, 4],\n [2, 2, 5, -5],\n [1, 5, -1, -2],\n [4, -5, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
126
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 5, 4, 0],\n [10, 3, 2, -10],\n [3, 10, 6, 2],\n [0, -12, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 1, 4, -4],\n [1, -5, 4, 2],\n [4, 4, 11, 0],\n [-4, 2, 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"
}
] |
220
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -11, 3, -10],\n [1, 12, 7, 0],\n [1, 9, -7, 1],\n [6, 4, -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"
}
] |
556
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -2, -2, 2],\n [-2, 10, 0, 0],\n [-2, 0, 1, 10],\n [2, 0, 10, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -5, -11, -7],\n [11, 2, 0, -6],\n [-1, -12, 11, 12],\n [-7, 5, 12, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
977
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -6, -5, -7],\n [-11, 1, 11, -12],\n [-11, -10, -11, 6],\n [2, -3, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
173
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 4, -3, -7],\n [0, 8, 4, 2],\n [0, 0, 7, 5],\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"
}
] |
112
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -6, 3, 3],\n [0, -7, -6, -3],\n [0, 0, -11, 4],\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"
}
] |
688
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -5, 7, 4],\n [-5, -3, 9, 0],\n [7, 9, 4, 6],\n [4, 0, 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"
}
] |
412
|
MATH
|
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