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[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 0, 10],\n [0, -2, 0],\n [10, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -8, -3],\n [0, -10, -7],\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[[5, 0, 9],\n [0, 2, 1],\n [9, 1, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
903
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 0, 8],\n [0, -9, -8],\n [8, -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" } ]
232
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 8, 3],\n [0, 1, 5],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -2, -4],\n [-2, 2, 8],\n [-4, 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" } ]
598
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 4, 6],\n [0, 6, -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" } ]
892
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -4, -3],\n [10, -2, 7],\n [-8, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
260
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -5, -3],\n [2, -4, 9],\n [-7, -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" } ]
999
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -9, -7],\n [2, 9, -7],\n [5, 4, 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" } ]
700
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -4, 6],\n [-4, -3, 0],\n [6, 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" } ]
238
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 10, -3],\n [7, 6, -8],\n [-6, -7, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
209
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -1, 1],\n [-8, 3, 7],\n [4, 4, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 4, 4],\n [4, -2, -4],\n [4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -9, -1],\n [0, -2, -4],\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" } ]
992
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -1, 1],\n [0, -1, -4],\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" } ]
4
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 2, -9],\n [0, 2, 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" } ]
902
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 4, 5],\n [0, 5, 0],\n [3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
775
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 0, 4],\n [0, 1, 2],\n [4, 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" } ]
924
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 0, 2],\n [0, 6, 6],\n [2, 6, 9]]\nRound to the nearest integer, then take the result modulo 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[[7, -4, -4],\n [0, -4, -6],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 0, 1],\n [0, 1, 4],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 2, 2],\n [0, 10, 5],\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" } ]
400
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 3, -8],\n [-7, 10, 9],\n [-3, -8, 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" } ]
813
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 8, 3],\n [0, -8, 1],\n [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" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -5, -4],\n [-5, 9, -1],\n [-4, -1, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
801
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 0, 1],\n [0, 1, -8],\n [1, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
853
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, -1],\n [0, -10, -4],\n [-1, -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" } ]
666
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -2, -2],\n [-3, 2, -2],\n [8, 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" } ]
902
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 6, 0],\n [-4, -10, 1],\n [-2, 7, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
541
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -6, -10],\n [-4, -8, 7],\n [0, -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" } ]
964
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -9, 4],\n [-9, 0, 4],\n [4, 4, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
535
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 0, -5],\n [-9, -5, -9],\n [4, 7, 10]]\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[[-5, -6, 4],\n [-6, -4, 0],\n [4, 0, -1]]\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, 2, 6],\n [-9, -8, 7],\n [-9, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
102
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -2, 4],\n [-2, 6, -4],\n [4, -4, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
256
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -2, 10],\n [0, 1, -6],\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" } ]
4
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 6, 8],\n [6, -1, 0],\n [8, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -8, -2],\n [-8, 3, -10],\n [-2, -10, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 2, -2],\n [2, -4, 0],\n [-2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
984
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -7, -3],\n [-4, -2, -7],\n [5, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
203
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 1, 7],\n [0, -10, -6],\n [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[[9, -4, -6],\n [-3, -9, -7],\n [8, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
293
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -4, 10],\n [7, 5, 9],\n [-2, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
304
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 8, -5],\n [8, 6, -6],\n [-5, -6, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
912
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -10, 6],\n [1, -4, 6],\n [-4, 5, 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" } ]
214
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -2, 4],\n [0, 8, 0],\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" } ]
808
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 1, 2],\n [-1, -8, 8],\n [0, -3, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
79
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 6, 8],\n [6, 5, 0],\n [8, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
691
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 [9, 4, 6],\n [-5, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
815
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -5, 10],\n [0, -10, 9],\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" } ]
700
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -2, 6],\n [0, 8, -8],\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" } ]
608
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -8, -2],\n [-8, -2, -1],\n [-2, -1, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
502
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -1, 10],\n [-1, 3, 4],\n [1, 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" } ]
102
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -9, -9],\n [0, 1, 0],\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" } ]
936
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -8, 9],\n [8, -2, 8],\n [6, 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" } ]
172
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -7, -10],\n [-7, -7, 6],\n [-10, 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" } ]
775
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 4, -10],\n [5, -2, -9],\n [-9, 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" } ]
391
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, 7],\n [0, -9, 7],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 9, -9],\n [0, -3, 2],\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" } ]
730
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -4, -2],\n [-4, -8, 9],\n [-1, -10, -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" } ]
304
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 0, -3],\n [8, -4, 0],\n [4, 10, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -7, -8],\n [0, -8, -10],\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": "What is the determinant of the matrix:\n[[-9, 10, 7],\n [-5, -2, 4],\n [-4, -8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
368
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 4, -3],\n [-6, -7, -2],\n [2, 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" } ]
92
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 0, 4],\n [0, -10, -3],\n [4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
204
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -1, -1],\n [-1, 6, -3],\n [-1, -3, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
370
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 6, -3],\n [6, -10, -6],\n [-3, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
994
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -10, 1],\n [4, 8, -1],\n [-9, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
926
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 2, 4],\n [2, 1, -6],\n [4, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
149
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 2, 4],\n [2, -7, 4],\n [4, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
824
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 5, 8],\n [0, 5, 9],\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" } ]
925
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 1, 8],\n [8, 2, -10],\n [0, -8, 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" } ]
712
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -6, -2],\n [-6, 5, 4],\n [-2, 4, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
148
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -1, -9],\n [0, -9, -3],\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" } ]
90
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -4, 4],\n [-4, -2, 2],\n [4, 2, 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" } ]
952
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 3, -8],\n [0, 7, 0],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
937
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -1],\n [-2, 5, -6],\n [-1, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
581
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -6, 8],\n [-6, 2, 8],\n [8, 8, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 4, -4],\n [4, 1, -2],\n [-4, -2, -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" } ]
104
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 8, 2],\n [8, 2, 0],\n [2, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
404
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 5, 4],\n [-7, 2, 6],\n [-9, 7, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
720
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 6, 10],\n [1, -5, 0],\n [5, -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" } ]
179
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -1, 0],\n [-1, 10, -5],\n [0, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
135
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -1, 3],\n [0, -4, -6],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 4, -4],\n [4, 0, -1],\n [-4, -1, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
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, 9, -2],\n [2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
980
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 9, -6],\n [1, 10, 4],\n [-10, 10, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
656
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 7, -1],\n [0, 5, 8],\n [-6, 9, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
865
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -1, 5],\n [0, -2, -6],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -2, 1],\n [9, -9, 0],\n [9, 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" } ]
595
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 0, 2],\n [0, 4, -4],\n [2, -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" } ]
8
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -4, 8],\n [0, -9, -8],\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" } ]
54
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 1, -7],\n [1, 6, -6],\n [-7, -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" } ]
374
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 7, 4],\n [0, -1, -1],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, 8],\n [7, -6, 0],\n [8, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
601
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, -3],\n [-6, 3, 7],\n [1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
69
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -5, 10],\n [0, 7, -5],\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" } ]
916
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -5, -1],\n [-6, -1, 6],\n [-2, -1, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
108
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -1, 9],\n [0, 3, -4],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH