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[ { "content": "Determine the value of det(A) where A =\n[[9, -8, 4],\n [0, 1, -4],\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" } ]
45
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -9, 7],\n [0, -3, 10],\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" } ]
964
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -5, 4],\n [6, -4, 10],\n [-9, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
424
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 8, -8],\n [-4, 9, 9],\n [-9, -9, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 5, 7],\n [0, 3, 3],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 4, -6],\n [0, -7, 4],\n [0, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
126
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -3, -8],\n [-3, 4, 2],\n [-8, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
813
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -7, -8],\n [0, 7, 1],\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" } ]
196
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 8, -5],\n [-7, -7, -5],\n [-2, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
212
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -7, -5],\n [0, 1, 7],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
930
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 4, -10],\n [-8, -5, -10],\n [0, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 10, -10],\n [0, -2, 2],\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" } ]
80
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -1, 0],\n [-1, -1, -2],\n [0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
999
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 10, -7],\n [0, 5, 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" } ]
300
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -4, 4],\n [-1, 5, -3],\n [-9, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -4, 10],\n [0, -10, -10],\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" } ]
800
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 10, 5],\n [0, 9, -1],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
270
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -7, 3],\n [4, -7, 7],\n [6, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
324
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, 3],\n [-4, 1, 1],\n [3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
975
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 0, -2],\n [0, 2, 6],\n [-2, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
544
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -2, 4],\n [-2, 2, -4],\n [4, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
992
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 9, 2],\n [0, 5, 4],\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" } ]
940
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, 7],\n [0, -5, -6],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
970
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -10, 2],\n [-8, 6, 4],\n [-2, -6, -1]]\nRound to the nearest integer, then take the result 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[[4, -2, -2],\n [-2, 3, -6],\n [-2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
796
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 6, 10],\n [0, 6, 5],\n [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" } ]
72
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -3, -1],\n [-3, 0, 7],\n [-1, 7, 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" } ]
358
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 4, 2],\n [-2, -10, -8],\n [-4, -7, 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" } ]
940
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -5, 7],\n [9, -3, -9],\n [-7, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
494
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 3, 0],\n [3, -9, -2],\n [0, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
886
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 [-9, -7, 6],\n [2, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
666
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 6, 5],\n [6, 4, 1],\n [5, 1, 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" } ]
957
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 9, -6],\n [0, 3, 4],\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" } ]
820
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 10, -1],\n [0, 1, -7],\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" } ]
16
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -4, 6],\n [-4, 0, 2],\n [6, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 0, 8],\n [3, 9, 8],\n [4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
148
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -2, -5],\n [-1, 0, -8],\n [6, -8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
612
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 0, 6],\n [0, 9, 6],\n [6, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
271
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 7, -4],\n [0, 7, 8],\n [-3, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
697
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 7, 1],\n [0, -9, -1],\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" } ]
640
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 1, -3],\n [8, 2, -9],\n [-7, 7, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 7, 7],\n [4, 6, 5],\n [-5, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
735
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 9, -2],\n [0, 9, 0],\n [0, 0, -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[[3, -8, 6],\n [-6, 0, -9],\n [-10, -9, 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" } ]
929
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -4, -7],\n [-4, 2, -4],\n [-7, -4, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
550
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -3, -1],\n [-3, -4, 1],\n [10, 2, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
843
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 10, 0],\n [7, -7, 7],\n [9, 8, -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" } ]
85
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -3, 1],\n [0, -5, 2],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 4, 9],\n [0, -2, 1],\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" } ]
16
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -10, 5],\n [10, -2, 4],\n [1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
300
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 3, 6],\n [0, -8, 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" } ]
24
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 6, -2],\n [6, 5, -6],\n [1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
870
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 1, -6],\n [-5, -1, -7],\n [-1, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
130
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -6, -3],\n [-4, -8, -3],\n [0, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
643
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, -3],\n [0, -3, -9],\n [-3, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
583
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 8, -4],\n [6, 10, -10],\n [3, 9, 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" } ]
520
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -9, 10],\n [7, -2, 9],\n [-6, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 1, 2],\n [1, 2, -4],\n [2, -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" } ]
986
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -6, 8],\n [0, 8, -5],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
560
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -7, -3],\n [-3, 7, 2],\n [0, 7, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
937
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 2, -6],\n [2, 3, 3],\n [-6, 3, 3]]? 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[[6, -8, -5],\n [-5, -8, 5],\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" } ]
224
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 2, 7],\n [0, 1, -2],\n [0, 0, 3]]\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[[7, -5, -3],\n [8, 9, -5],\n [8, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
791
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -3, 8],\n [0, 3, -2],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
895
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 5, -10],\n [7, 9, 0],\n [7, -3, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
892
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -4, -1],\n [0, -5, 10],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 3, 9],\n [-3, -4, -1],\n [10, -5, 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" } ]
440
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 1, -3],\n [0, -7, -8],\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" } ]
888
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, 0],\n [2, 7, 2],\n [0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
992
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 3, 5],\n [0, -7, 7],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
559
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, -8],\n [-8, 0, -2],\n [-8, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 9, -3],\n [9, 5, -7],\n [7, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
126
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -7, -8],\n [0, -2, 3],\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" } ]
36
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -6, -8],\n [-6, 2, 6],\n [-8, 6, -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" } ]
724
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 2, -2],\n [2, -2, 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" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 10, -6],\n [0, 9, -1],\n [2, -7, -3]]? 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[[10, 6, 9],\n [8, 8, 1],\n [1, -8, -8]]? 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": "Determine the value of det(A) where A =\n[[3, -4, -2],\n [-4, -10, -1],\n [-2, -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" } ]
561
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 2, -2],\n [2, -8, -4],\n [-2, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -1, -8],\n [0, -8, -1],\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" } ]
992
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 1, -4],\n [1, 5, 0],\n [-4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
842
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -9, -5],\n [0, 6, -6],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -6, 4],\n [-6, 0, 4],\n [4, 4, 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" } ]
788
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -9, 2],\n [-7, 2, -1],\n [2, 5, 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" } ]
485
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 5, -6],\n [-2, -5, -8],\n [1, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -5, -1],\n [9, 9, -2],\n [8, -1, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
995
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 1, 10],\n [0, -5, 3],\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" } ]
750
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -2, 5],\n [-2, 6, -6],\n [-10, 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" } ]
960
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -4, 9],\n [0, -3, -5],\n [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" } ]
27
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -2, -3],\n [3, 3, -8],\n [-9, 10, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
917
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 0, -6],\n [0, 2, -6],\n [-6, -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" } ]
946
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 10, -6],\n [0, 2, -2],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, 5],\n [2, -4, 5],\n [5, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
291
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -6, 0],\n [0, -4, 8],\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" } ]
80
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 10, -4],\n [-4, -4, -1],\n [9, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
718
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, -10],\n [0, -4, 1],\n [-10, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
315
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 0, -6],\n [0, 2, 0],\n [-6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
820
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -1, -3],\n [-8, -3, -4],\n [-6, 8, -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" } ]
90
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -6, -6],\n [0, 8, -9],\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" } ]
80
MATH