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[[-4, 2, -3, 6],\n [2, -10, -2, -4],\n [-3, -2, 5, -8],\n [6, -4, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 0, 4, 8],\n [0, 10, 9, 9],\n [0, 0, 5, -4],\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" } ]
900
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 7, 4, 11],\n [-7, 10, -2, 2],\n [-1, -3, 1, -6],\n [11, -10, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
322
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -4, -2, -4],\n [0, 7, 1, 3],\n [0, 0, 9, -5],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
780
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -8, -1, 12],\n [0, -8, 4, 0],\n [0, 0, 2, -6],\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" } ]
192
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 10, 2, 0],\n [10, -7, -5, -2],\n [2, -5, -3, 4],\n [0, -2, 4, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 7, 5, -11],\n [0, -6, 7, 12],\n [0, 0, 9, 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" } ]
296
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -2, 7, 3],\n [-2, 0, -2, 0],\n [7, -2, -12, -8],\n [3, 0, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
604
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 6, 2, -4],\n [6, 7, 2, 0],\n [2, 2, 9, 6],\n [-4, 0, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
799
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 12, 4, -6],\n [10, -6, 11, 11],\n [-8, 3, -9, -12],\n [2, -10, -8, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 1, 7, -4],\n [0, -8, 2, -4],\n [0, 0, -1, 3],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -6, -1, -2],\n [0, -12, -4, 2],\n [0, 0, -10, 10],\n [0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, 4, 1],\n [0, 12, 5, 2],\n [4, 5, 0, 8],\n [1, 2, 8, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 1, 8, -6],\n [1, -6, -8, 0],\n [8, -8, 10, 7],\n [-6, 0, 7, -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" } ]
663
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -4, 0, -8],\n [-4, -3, 11, 2],\n [0, 11, 9, 4],\n [-8, 2, 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" } ]
840
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -2, 4, 1],\n [-2, -8, 2, 6],\n [4, 2, 11, 6],\n [1, 6, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -3, 12, -12],\n [2, 11, -6, 5],\n [-3, -1, -12, -9],\n [3, 12, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
353
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -6, -5, 12],\n [-5, 2, 11, -11],\n [-8, 9, -9, 8],\n [-10, 9, 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" } ]
153
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 2, 0, -6],\n [2, 5, 8, -2],\n [0, 8, -5, -4],\n [-6, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 3, -12, -1],\n [-4, -3, 1, 9],\n [7, -2, 10, 8],\n [9, -6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
178
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 1, 2, 5],\n [1, 2, 0, -6],\n [2, 0, -11, -9],\n [5, -6, -9, -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" } ]
271
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -9, -9, 11],\n [0, -12, 7, -7],\n [0, 0, 7, -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" } ]
968
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 8, 9, 10],\n [0, -7, 6, -1],\n [0, 0, 10, -12],\n [0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
230
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -8, 6, 5],\n [0, -11, 11, -11],\n [0, 0, 10, -4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 6, 1, 5],\n [3, 11, 1, 4],\n [-12, -5, -8, 7],\n [-12, -1, -9, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
954
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -12, -11, 12],\n [10, -11, 5, 11],\n [-1, -6, -2, 8],\n [10, 12, 7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
384
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -6, -3, -8],\n [-6, 3, -2, -2],\n [-3, -2, 5, 6],\n [-8, -2, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
368
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -5, 12, 2],\n [-5, -12, -2, 2],\n [12, -2, 2, 0],\n [2, 2, 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" } ]
84
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -8, 8, 7],\n [0, -8, -10, -4],\n [0, 0, 3, 5],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
888
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 2, 4, 0],\n [2, 10, 2, 3],\n [4, 2, -6, 4],\n [0, 3, 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" } ]
594
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 8, 10, -10],\n [0, -7, -6, 12],\n [0, 0, 5, 0],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
370
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -5, -9, -10],\n [-5, 3, 9, -9],\n [-7, -4, -10, 0],\n [-1, 1, 5, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -8, -5, 7],\n [-10, -8, 2, -2],\n [1, -6, 4, -12],\n [-4, -3, -3, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
408
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 1, -4, -5],\n [1, -12, 6, -3],\n [-4, 6, 4, 2],\n [-5, -3, 2, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
852
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 1, -4, 3],\n [0, -9, -6, -5],\n [0, 0, 8, -8],\n [0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 1, -6, -4],\n [1, 7, -8, 8],\n [-6, -8, -11, 4],\n [-4, 8, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
738
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 4, 7, 1],\n [6, -5, -12, 6],\n [3, 6, -10, -10],\n [5, -8, -8, 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" } ]
155
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -12, 2, -8],\n [0, 12, -9, 2],\n [0, 0, 3, -1],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
564
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, -3, 3],\n [0, 1, 9, -1],\n [0, 0, -5, 4],\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" } ]
900
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -12, 4, -2],\n [9, 12, -1, -12],\n [4, 7, 12, -7],\n [11, -12, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
118
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -3, 0, 8],\n [0, 6, 6, -3],\n [0, 0, -1, -4],\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" } ]
300
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 2, -6, 11],\n [2, -10, 0, 6],\n [-6, 0, -8, 8],\n [11, 6, 8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
464
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 6, 0, -4],\n [-11, -12, -12, -8],\n [-4, 11, 7, 8],\n [5, 0, 1, -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" } ]
376
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -4, -5, -5],\n [-4, -5, 0, -6],\n [2, -9, -1, 11],\n [12, -10, 9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
516
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 2, -6, 4],\n [2, -12, 2, 4],\n [-6, 2, 11, -6],\n [4, 4, -6, 6]]\nRound to the nearest integer, then take the result 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[[-11, -1, 0, -12],\n [0, 4, -11, -3],\n [0, 0, 8, -11],\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" } ]
816
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, -2, -11, 11],\n [0, 7, 4, -1],\n [0, 0, 2, -11],\n [0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
78
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 8, -5, 4],\n [8, -2, -7, 10],\n [-5, -7, -11, -2],\n [4, 10, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
878
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 5, 2, 0],\n [5, -8, -2, -8],\n [2, -2, -10, -1],\n [0, -8, -1, -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" } ]
427
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 7, 6, -9],\n [0, -10, 6, -5],\n [0, 0, 1, -3],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
550
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 5, 4, 6],\n [5, 8, 9, 2],\n [4, 9, -8, -2],\n [6, 2, -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" } ]
632
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -7, -2, 11],\n [10, 10, -1, -5],\n [-3, -1, 1, 1],\n [11, -10, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
929
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 3, -2, -7],\n [3, 9, 5, 0],\n [-2, 5, 10, 4],\n [-7, 0, 4, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
302
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -7, -7, -6],\n [-3, -1, -11, 0],\n [-10, -1, -5, -6],\n [1, -10, -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" } ]
618
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 4, 7, 3],\n [0, -2, 12, -6],\n [-8, -1, -5, -6],\n [-7, 3, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
702
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 8, 10, 0],\n [8, 8, -2, 8],\n [10, -2, 3, 2],\n [0, 8, 2, 0]]? 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": "Compute |A| for the matrix A =\n[[-12, -6, -8, -4],\n [-6, 7, 8, 2],\n [-8, 8, -6, -4],\n [-4, 2, -4, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
304
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 0, -11, -9],\n [9, -10, 0, 9],\n [-7, -5, -6, -10],\n [9, -12, 11, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
519
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 8, 0, 9],\n [10, -1, -6, -9],\n [3, -9, -8, 0],\n [5, -11, 1, 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" } ]
68
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 4, -6, 0],\n [4, -10, 1, 6],\n [-6, 1, -3, 4],\n [0, 6, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
516
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -9, -12, -4],\n [3, 4, 4, 10],\n [-1, -8, 12, -9],\n [-8, 9, -10, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
402
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -2, -7, 2],\n [-2, -4, 4, -6],\n [-7, 4, -6, 0],\n [2, -6, 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" } ]
100
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -2, -7, 4],\n [-2, 1, 4, -4],\n [-7, 4, 2, 4],\n [4, -4, 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" } ]
619
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 11, 7, -3],\n [-4, 10, 6, 4],\n [2, 2, -8, 6],\n [-6, -5, -7, 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" } ]
360
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 6, -1, -8],\n [-10, 12, 5, -1],\n [-9, -1, -4, 12],\n [8, -11, -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" } ]
272
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 8, 0, 4],\n [0, 8, -1, 6],\n [0, 0, 6, -7],\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" } ]
960
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 9, 7, -4],\n [0, -4, 11, -10],\n [0, 0, -5, 2],\n [0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -4, 2, -10],\n [-7, 4, -11, 12],\n [0, -11, 1, -6],\n [12, -5, -9, -9]]\nRound to the nearest integer, then take the result modulo 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[[-1, 5, 5, 4],\n [-2, -4, 10, -7],\n [10, -5, -3, -1],\n [3, 2, -10, 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" } ]
530
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 3, 9, -10],\n [0, 11, -4, 8],\n [0, 0, -1, 11],\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[[-12, 0, 1, -1],\n [-8, 2, -7, -2],\n [-2, -7, 2, 5],\n [1, 0, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -4, 12, 0],\n [0, -11, -4, 4],\n [0, 0, 7, -2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
158
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 5, -4, -6],\n [5, 12, -6, -2],\n [-4, -6, -4, 1],\n [-6, -2, 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" } ]
769
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 0, -4, -4],\n [1, -6, 5, 3],\n [2, -5, 11, -6],\n [-6, 10, -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" } ]
674
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -5, 2, 10],\n [0, 3, 8, 0],\n [0, 0, 4, -3],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -7, -5, -4],\n [9, -6, 7, 7],\n [-8, 6, 2, 9],\n [-10, 12, -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" } ]
191
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 5, 3, -12],\n [-2, -3, -4, 12],\n [9, 4, 9, 0],\n [-4, -12, 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" } ]
634
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 1, 11, 0],\n [0, 9, 3, -9],\n [0, 0, 10, -2],\n [0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
110
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -2, 9, 10],\n [0, -8, 1, -4],\n [0, 0, 10, -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" } ]
800
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 2, -7, -2],\n [2, 3, 6, -2],\n [-7, 6, 4, 4],\n [-2, -2, 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" } ]
750
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -7, -1, -4],\n [-9, -3, -8, 8],\n [8, 6, -9, 12],\n [-10, -2, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
916
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -4, 0, 0],\n [-4, 1, 0, -6],\n [0, 0, 5, -2],\n [0, -6, -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" } ]
376
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 10, 0, 3],\n [0, -6, -2, -6],\n [0, 0, -12, 9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -1, -9, 4],\n [5, 3, -5, 12],\n [1, -11, -8, 0],\n [-4, 5, -4, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
578
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 2, -5, -4],\n [2, -1, 2, -5],\n [-5, 2, -4, 2],\n [-4, -5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
693
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, -5, 0],\n [2, 2, 2, -5],\n [-5, 2, 4, -8],\n [0, -5, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
529
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 3, 9, 3],\n [2, 12, -1, 0],\n [1, -8, 6, -1],\n [9, 12, 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" } ]
426
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 0, -2, -7],\n [0, 9, 9, 2],\n [-2, 9, 3, 0],\n [-7, 2, 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" } ]
182
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, -4, 7, 8],\n [0, -6, 9, 4],\n [0, 0, -8, 4],\n [0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
304
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 8, 3, -1],\n [4, -6, 5, -1],\n [-10, -10, -8, 5],\n [1, -10, 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" } ]
250
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 6, -10, 2],\n [0, -8, 3, 12],\n [0, 0, 7, 11],\n [0, 0, 0, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
936
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 6, -1, 4],\n [6, 12, 12, -4],\n [-1, 12, -11, 6],\n [4, -4, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
720
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 7, 7, -5],\n [9, -5, 11, -5],\n [5, -2, 0, 4],\n [10, -10, 1, -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" } ]
736
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -9, 7, 2],\n [10, 8, 4, -7],\n [8, 8, -5, 9],\n [5, -12, 9, 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" } ]
535
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -9, 2, -10],\n [-7, -1, -4, 9],\n [9, 0, -1, -3],\n [8, -5, -5, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
940
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 2, 8, 8],\n [2, 9, -2, -2],\n [8, -2, -2, -10],\n [8, -2, -10, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -1, 2, -5],\n [0, -3, 12, 3],\n [-4, -6, 4, -7],\n [2, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
132
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -4, 12, -1],\n [0, -3, -5, -11],\n [0, 0, -1, -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" } ]
994
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 6, -3, -9],\n [0, 12, 9, -10],\n [0, 0, 8, -8],\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" } ]
184
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -11, -6, 6],\n [0, -6, 8, 7],\n [0, 0, -8, -12],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH