messages
listlengths
1
1
ground_truth
stringclasses
989 values
dataset
stringclasses
1 value
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -6, 5],\n [0, -1, 8],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
993
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 7, -2],\n [-1, 7, -9],\n [5, 3, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
752
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -4, 2],\n [-4, -6, 2],\n [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" } ]
24
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -1, 2],\n [-1, 4, -4],\n [2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
684
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 5, 3],\n [0, 4, -6],\n [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" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 2, -2],\n [2, 9, 0],\n [-2, 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" } ]
284
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -7, -10],\n [-7, -8, 1],\n [3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
361
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 1, -4],\n [-3, 5, -5],\n [-10, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
501
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 6, -6],\n [6, -3, -2],\n [-6, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
380
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -2, -10],\n [-2, 10, 1],\n [-10, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 2, 2],\n [2, 1, 3],\n [2, 3, -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" } ]
6
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 9, 6],\n [0, -4, 1],\n [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" } ]
988
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -4, -8],\n [-9, 2, -3],\n [7, 7, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
266
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 9, -5],\n [10, 6, -3],\n [-7, 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" } ]
41
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -2, 2],\n [-2, 7, -10],\n [2, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
512
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 0, 10],\n [0, -1, 10],\n [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" } ]
18
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -2, 2],\n [-8, 5, 6],\n [8, -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" } ]
855
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -2, 10],\n [0, 6, 8],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -2, 9],\n [-5, -3, -6],\n [7, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
514
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -3, -9],\n [0, -6, -2],\n [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" } ]
210
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 10, 10],\n [4, 4, -9],\n [-1, 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" } ]
77
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -8, 0],\n [-7, 4, 6],\n [-7, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
816
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -7, 4],\n [0, 1, 9],\n [0, 0, -4]]\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[[-2, 0, 4],\n [0, -9, -4],\n [4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 7, 0],\n [0, 6, 4],\n [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" } ]
240
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -1, -5],\n [0, 4, -4],\n [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" } ]
952
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, 10],\n [0, 6, 7],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
460
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -2, 0],\n [-2, 0, 2],\n [0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 8, 4],\n [0, 6, 7],\n [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" } ]
760
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 4, -2],\n [4, -8, 0],\n [-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" } ]
128
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 7, -2],\n [7, 4, 0],\n [-2, 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" } ]
495
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -10, 5],\n [0, -3, 9],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
982
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -4, 1],\n [-9, 6, 9],\n [5, 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" } ]
160
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -4, 9],\n [-7, -6, -6],\n [-10, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
591
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 6, 0],\n [6, -5, 2],\n [0, 2, -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" } ]
96
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 6, 7],\n [7, 9, 0],\n [10, -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" } ]
913
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 10, -4],\n [0, 6, 1],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -10, 4],\n [3, 1, -4],\n [8, -4, 2]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -10, 8],\n [-10, -3, -4],\n [5, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
498
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 10, -7],\n [0, -7, 4],\n [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" } ]
860
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -6, 2],\n [-6, -1, 4],\n [2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
868
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 3, 5],\n [0, -6, -3],\n [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" } ]
904
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 2, 4],\n [2, 8, -2],\n [4, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
572
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -2, 6],\n [-2, 10, 4],\n [6, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
556
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 2, -5],\n [0, -2, 5],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
980
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 1, 5],\n [8, -2, 6],\n [7, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
134
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -5, 4],\n [-5, 6, 6],\n [4, 6, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
249
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 1, 0],\n [3, 5, 0],\n [0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
808
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 1, 9],\n [0, 3, -1],\n [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" } ]
24
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -6, -1],\n [-6, -3, 0],\n [-1, 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" } ]
30
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 4, 6],\n [4, 3, 0],\n [6, 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" } ]
964
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, 0],\n [6, 7, 4],\n [0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -2, -8],\n [-2, 4, 3],\n [-8, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
681
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -2, -5],\n [-2, 0, -2],\n [-5, -2, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 2, 3],\n [0, -6, 8],\n [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" } ]
760
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, 2],\n [0, 2, 3],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
900
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -3, 7],\n [0, 10, -9],\n [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" } ]
900
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -8, 1],\n [0, 6, -9],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
180
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 8, -8],\n [0, -8, -9],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 7, 1],\n [0, 2, 3],\n [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" } ]
984
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 2, 9],\n [-8, -2, 4],\n [9, -5, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
754
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 10, 7],\n [0, -8, 6],\n [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" } ]
560
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -3, 5],\n [-5, 3, 2],\n [-2, -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" } ]
853
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -8, -5],\n [-9, -7, 9],\n [-6, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
623
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 8, -7],\n [-1, -4, -9],\n [6, 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" } ]
400
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -1, -6],\n [10, 0, -2],\n [9, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
138
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -2, -10],\n [-6, -3, 1],\n [5, 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" } ]
98
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -9, 5],\n [10, 2, -5],\n [2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 0, -4],\n [0, 2, -4],\n [-4, -4, -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" } ]
160
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -1, 2],\n [-1, -1, 3],\n [2, 3, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
999
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 8, -10],\n [7, 1, -2],\n [-4, 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" } ]
269
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 3, 10],\n [0, -1, 7],\n [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" } ]
951
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -4, 8],\n [-4, -1, -5],\n [8, -5, -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" } ]
496
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 2, -7],\n [-9, -4, 7],\n [6, 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" } ]
108
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 5, -7],\n [-5, -2, 4],\n [4, 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" } ]
450
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 7, 8],\n [4, 3, 5],\n [-6, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
159
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 1, 9],\n [0, 10, 5],\n [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" } ]
200
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -6, 7],\n [0, -7, -4],\n [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" } ]
916
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -8, 6],\n [-8, 2, 0],\n [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" } ]
192
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 4, -9],\n [-3, 2, 4],\n [-1, 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" } ]
263
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -8, 3],\n [7, 9, -4],\n [-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" } ]
405
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -2, -2],\n [-2, -4, -7],\n [-2, -7, -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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, -6],\n [0, -7, -6],\n [-6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
234
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 1, 3],\n [0, -2, 3],\n [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" } ]
180
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 7, -1],\n [0, 7, -2],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
245
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 0, -6],\n [0, -8, -6],\n [-6, -6, -2]]\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[[3, 2, 10],\n [0, 2, -2],\n [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" } ]
6
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 5, 0],\n [5, -6, -7],\n [0, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
848
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 6, -8],\n [6, -10, -3],\n [-8, -3, -7]]\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[[0, -2, -2],\n [-2, -2, 4],\n [-2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -10, -8],\n [0, -8, -3],\n [0, 0, 5]]\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[[8, 9, -5],\n [0, -1, -2],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -7, -2],\n [-7, -5, 6],\n [-2, 6, 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" } ]
277
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -1, 10],\n [-1, 9, 2],\n [10, 2, -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" } ]
10
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 3, 2],\n [-10, -10, 9],\n [8, 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" } ]
936
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 2, -4],\n [0, 4, 2],\n [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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 8, 4],\n [8, -3, 0],\n [4, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
392
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 7, 7],\n [3, -2, 9],\n [6, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
473
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 1, -1],\n [-9, -9, -5],\n [6, 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" } ]
700
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -6, -7],\n [-1, -10, 3],\n [-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" } ]
726
MATH