messages
listlengths
1
1
ground_truth
stringclasses
989 values
dataset
stringclasses
1 value
[ { "content": "Determine the value of det(A) where A =\n[[0, 0, -4],\n [0, -4, -8],\n [-4, -8, 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" } ]
64
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -9, 0],\n [-5, 4, 3],\n [-1, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
687
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -4, -10],\n [5, -10, 5],\n [0, 9, -7]]? 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[[10, -7, 4],\n [-7, -10, -6],\n [4, -6, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
881
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 8, 6],\n [-2, 0, -8],\n [3, -6, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 0, 9],\n [0, 4, -5],\n [9, -5, -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" } ]
808
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -5, -1],\n [0, -7, 7],\n [0, 0, -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" } ]
210
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 4, -3],\n [0, 3, -5],\n [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" } ]
12
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, -1],\n [0, 6, -2],\n [-1, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
574
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -4, 3],\n [-4, 10, -1],\n [3, -1, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
701
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -5, -10],\n [0, 6, -7],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
622
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -10, 4],\n [0, -1, 5],\n [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" } ]
993
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 9, -6],\n [0, 8, 1],\n [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" } ]
80
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 0, 3],\n [0, -9, 7],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 6, -10],\n [1, 1, 2],\n [10, 9, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -8, 7],\n [2, -8, -10],\n [5, 7, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -10, 10],\n [-1, 5, -9],\n [-3, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
414
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 1, 0],\n [1, -10, 0],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
991
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -2, 1],\n [-3, -3, -3],\n [2, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
718
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 2, 0],\n [2, -1, 0],\n [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" } ]
995
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 8, -5],\n [0, 10, -9],\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" } ]
910
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -4, -1],\n [9, 7, -8],\n [0, 4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
644
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -8, -6],\n [4, 10, 3],\n [10, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
127
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, 6],\n [4, 9, 0],\n [6, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
836
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 7, 10],\n [8, 2, 0],\n [9, 3, -1]]? 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": "Compute |A| for the matrix A =\n[[5, -4, -7],\n [0, 10, 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" } ]
750
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 4, 3],\n [0, -6, 5],\n [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" } ]
958
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 8, -4],\n [1, 5, -9],\n [5, 5, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 3, -1],\n [0, -3, -10],\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" } ]
72
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 2, -4],\n [2, -9, 2],\n [-4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -7, 2],\n [-7, 9, -5],\n [2, -5, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
383
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 0, 5],\n [4, -10, -7],\n [8, 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" } ]
440
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 1, -6],\n [0, 10, -9],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 4, 6],\n [4, -3, -3],\n [6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 2, 4],\n [2, -9, 1],\n [4, 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" } ]
250
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -3, 10],\n [0, 10, 8],\n [0, 0, 10]]\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[[-5, 0, -6],\n [0, -2, -2],\n [-6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
122
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -3, -9],\n [0, 7, -10],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
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 [2, -6, 6],\n [5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
264
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 8, 6],\n [0, 1, -3],\n [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" } ]
10
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -4, 1],\n [9, -1, -7],\n [1, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
344
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 1, 0],\n [1, -1, 1],\n [0, 1, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -6, 1],\n [-7, 6, 7],\n [8, 9, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
973
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 10, 0],\n [0, 7, 8],\n [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" } ]
622
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 8, 1],\n [0, -6, 4],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 6, 6],\n [6, -2, -4],\n [6, -4, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 1, 7],\n [1, -6, -4],\n [7, -4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 6, 3],\n [0, 3, -4],\n [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" } ]
150
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 9, 2],\n [7, 9, 8],\n [4, 6, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -1, 6],\n [0, -10, 9],\n [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" } ]
900
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 8, 10],\n [0, 4, 5],\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" } ]
168
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -3, -4],\n [-6, -10, -8],\n [0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
138
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -9, -5],\n [0, 10, 5],\n [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" } ]
480
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -10, -9],\n [0, -8, 4],\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" } ]
640
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -10, 8],\n [0, 6, -1],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 3, 0],\n [-6, -4, 9],\n [-4, 7, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
756
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -1, 0],\n [-1, -7, -1],\n [0, -1, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
257
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 2, -2],\n [0, -9, 6],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -10, -10],\n [10, 4, -1],\n [0, 1, 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" } ]
763
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -5, -2],\n [-5, -10, 2],\n [-2, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
651
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -2, -1],\n [0, -9, 4],\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" } ]
919
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 9, -2],\n [-4, 10, -7],\n [-4, -9, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
298
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -10, -7],\n [-10, -7, 5],\n [5, 10, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
259
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 8, 2],\n [8, -7, 4],\n [2, 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" } ]
302
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -7, 2],\n [-3, 7, -8],\n [6, -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" } ]
107
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 10, 5],\n [-10, 0, 9],\n [2, -3, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
884
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 6, -2],\n [6, -2, 2],\n [-2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
924
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -4, 5],\n [-2, -10, -1],\n [7, 6, -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" } ]
438
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -2, 6],\n [-2, 3, 0],\n [6, 0, 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" } ]
892
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 1, 2],\n [1, 1, 2],\n [2, 2, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -6, -7],\n [0, 10, -1],\n [0, 0, 6]]\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[[-8, 4, -8],\n [0, 9, 6],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
568
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 3, 4],\n [3, -4, 4],\n [4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
142
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, -10],\n [4, -2, -1],\n [5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
671
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 5, 6],\n [5, -6, -2],\n [6, -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" } ]
192
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 10, 6],\n [0, -1, 9],\n [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" } ]
994
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -2, 9],\n [2, -8, -6],\n [-2, 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" } ]
904
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -9, 10],\n [0, -1, 5],\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" } ]
937
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -10, 6],\n [-10, 9, -4],\n [6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
386
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -5, 1],\n [0, 1, -2],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -2, 2],\n [-2, -1, -4],\n [2, -4, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
890
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 6, 7],\n [0, 2, -10],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 10, -2],\n [-7, -10, 1],\n [4, -6, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
894
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 9, -4],\n [0, 4, -7],\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" } ]
192
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -10, 0],\n [6, 0, -5],\n [1, -8, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 8, 10],\n [4, 8, -3],\n [8, 5, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
449
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -8, -5],\n [-7, 6, 2],\n [8, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
985
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 8, 7],\n [3, -3, -10],\n [1, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
124
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 2, 0],\n [8, 10, -10],\n [-3, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
564
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 6, -1],\n [0, 1, -6],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
946
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 5, 9],\n [-5, -1, 10],\n [7, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
633
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -6, -4],\n [-6, -9, 4],\n [-4, 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" } ]
476
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -1, 3],\n [9, 0, -1],\n [-1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
978
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, -9],\n [9, 0, 3],\n [6, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
706
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -4, 5],\n [-6, 5, -8],\n [-8, -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" } ]
576
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -9, 3],\n [0, 1, 6],\n [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" } ]
955
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 2, -6],\n [3, 1, -9],\n [10, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 0, 5],\n [-4, -2, -4],\n [2, -6, 2]]? Round to the nearest integer, then express your answer 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[[3, -1, 2],\n [-1, -5, -5],\n [2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
933
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -5, -6],\n [-5, -6, -7],\n [-6, -7, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
266
MATH