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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 5, 0, -11, -6],\n [7, 14, 11, 3, 13],\n [-6, -4, -4, 3, -9],\n [10, 3, 9, 0, 3],\n [6, 4, 11, -9, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
684
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 1, 9, 2, 8],\n [-13, 6, 5, 9, -5],\n [9, -6, 0, -9, -3],\n [2, 0, 4, -10, 4],\n [14, -3, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
106
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 6, 0, -8, 2],\n [6, 10, 8, 4, 2],\n [0, 8, -9, 4, -6],\n [-8, 4, 4, -14, 3],\n [2, 2, -6, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
518
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 4, 12, -4, 0],\n [4, -5, 2, -10, 0],\n [12, 2, 8, 8, 12],\n [-4, -10, 8, 15, -7],\n [0, 0, 12, -7, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, -8, -2, -10],\n [-4, 13, 8, -8, -3],\n [-8, 8, 15, -10, 4],\n [-2, -8, -10, -1, -2],\n [-10, -3, 4, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
188
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 14, -4, 13, 4],\n [0, 14, 0, -2, -10],\n [0, 0, -11, -4, -5],\n [0, 0, 0, -4, 5],\n [0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
136
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -15, -1, 11, 13],\n [1, -12, 7, 9, -6],\n [-4, 0, -12, -15, 4],\n [3, -1, 14, -5, 3],\n [-1, -14, -1, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
420
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 0, 6, -4, 2],\n [0, 7, -6, -6, -4],\n [6, -6, 12, -4, 4],\n [-4, -6, -4, -9, 1],\n [2, -4, 4, 1, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
424
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 12, -10, 0, 0],\n [-7, -4, 13, 2, 2],\n [-8, -11, -14, -9, 4],\n [-2, -11, -14, -14, -4],\n [-7, -1, -11, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
968
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -1, 9, -9, 11],\n [0, 4, -4, 10, -14],\n [0, 0, 1, 10, 7],\n [0, 0, 0, 1, 15],\n [0, 0, 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" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 5, -12, 10, 13],\n [5, 13, 2, 5, -1],\n [-12, 2, -1, 2, -8],\n [10, 5, 2, 3, 4],\n [13, -1, -8, 4, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
823
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 11, 3, 11, -6],\n [0, 1, -12, -11, -12],\n [0, 0, -7, -13, 9],\n [0, 0, 0, 13, -15],\n [0, 0, 0, 0, 11]]? 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[[-4, 11, 5, -9, 7],\n [0, 12, 13, -4, 12],\n [0, 0, -6, 2, 6],\n [0, 0, 0, 12, 5],\n [0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
192
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 9, 0, -3, 10],\n [0, 11, -2, 5, 9],\n [4, -9, -12, -15, -12],\n [-4, 6, 5, 11, 7],\n [-12, -3, 13, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
32
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 10, 0, -2, 10],\n [10, -15, -2, -3, -2],\n [0, -2, 12, 6, -5],\n [-2, -3, 6, -3, 0],\n [10, -2, -5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
928
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 3, -5, -5, 10],\n [0, 4, 12, -2, -10],\n [0, 0, -7, 15, 14],\n [0, 0, 0, -7, 3],\n [0, 0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
372
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, 10, -8, -2, -10],\n [0, -8, 2, -7, 11],\n [0, 0, -14, -13, -5],\n [0, 0, 0, 7, 13],\n [0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
344
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 7, 4, 2, 5],\n [7, -5, 13, -2, 2],\n [4, 13, 5, 4, 6],\n [2, -2, 4, 13, 14],\n [5, 2, 6, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
88
MATH
[ { "content": "Compute |A| for the matrix A =\n[[15, 14, -9, -12, 0],\n [0, 11, 2, 11, -8],\n [0, 0, -12, -2, -4],\n [0, 0, 0, -4, -5],\n [0, 0, 0, 0, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, -13, -5, 14, 0],\n [0, -13, -13, 0, 14],\n [0, 0, -6, -1, -9],\n [0, 0, 0, 4, -10],\n [0, 0, 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":...
864
MATH
[ { "content": "Compute |A| for the matrix A =\n[[15, -7, -1, 14, -12],\n [0, -15, 10, -4, -13],\n [0, 0, 11, 4, -6],\n [0, 0, 0, -2, 15],\n [0, 0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
MATH
[ { "content": "What is the determinant of the matrix:\n[[15, -11, 14, -2, -10],\n [8, 7, 6, -7, -6],\n [-11, 6, -8, 3, 2],\n [-1, -15, -4, -3, 5],\n [15, -15, -6, -13, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
580
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 4, 0, -4, 10],\n [4, -11, 0, 4, 0],\n [0, 0, -8, 0, -2],\n [-4, 4, 0, -4, 0],\n [10, 0, -2, 0, -14]]\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[[-3, -12, 4, -11, -6],\n [7, -5, -8, -3, -6],\n [11, -3, 14, -9, 5],\n [-10, -4, -13, 13, -10],\n [3, 15, 8, 15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
374
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -1, 4, 3, 14],\n [2, -10, -15, 1, -2],\n [10, 10, 9, 3, 5],\n [12, -5, -8, 13, 2],\n [-12, 9, 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" } ]
160
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 3, -2, 0, 8],\n [3, 10, 0, 3, 1],\n [-2, 0, 11, 2, 6],\n [0, 3, 2, 5, 8],\n [8, 1, 6, 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" } ]
19
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 14, -14, -3, 5],\n [13, -9, 9, 14, 14],\n [-12, 6, 1, 7, 5],\n [12, -12, -8, -14, -5],\n [-14, -11, 7, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
971
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -12, 10, -14, 2],\n [0, 11, 7, -3, -8],\n [0, 0, 11, 12, 5],\n [0, 0, 0, -13, -11],\n [0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
992
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, 2, 13, -6],\n [0, 4, 8, 8, -12],\n [0, 0, -15, -15, 5],\n [0, 0, 0, -2, -9],\n [0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
680
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 9, -2, 10, -1],\n [15, -6, 1, -14, -10],\n [5, -5, 9, 8, 7],\n [8, -4, 8, 15, 9],\n [4, -10, -12, -7, 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"...
480
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -6, 6, -3, -9],\n [-6, 4, -12, 10, -2],\n [6, -12, -11, 2, 0],\n [-3, 10, 2, 10, -6],\n [-9, -2, 0, -6, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
852
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 4, 0, 1, 3],\n [4, -7, 6, -2, -8],\n [0, 6, -3, -2, -7],\n [1, -2, -2, -10, 9],\n [3, -8, -7, 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": "us...
884
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 12, -11, 2, -4],\n [-8, -5, 6, -3, 13],\n [-8, 11, 3, 2, 8],\n [-2, 8, 15, -4, -14],\n [-5, 15, 14, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
810
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 14, -10, -6, 4],\n [-9, 12, 5, 8, 11],\n [12, -4, 5, -12, -15],\n [3, -2, 10, -2, 1],\n [1, -11, -1, -9, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
4
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-13, -10, 5, -10, -6],\n [-4, -5, 6, -4, -7],\n [10, 15, 8, -1, 8],\n [-11, 9, 15, -6, 8],\n [3, 2, 10, 9, -3]]\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[[-10, 4, 5, 6, -6],\n [4, -3, 4, -1, 4],\n [5, 4, 4, 0, -12],\n [6, -1, 0, -3, -6],\n [-6, 4, -12, -6, -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": "...
828
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 0, -5, 0, 12],\n [-15, 6, -13, -15, 11],\n [10, -15, 13, -3, 2],\n [-2, 6, -8, -5, -6],\n [-7, 1, -1, -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}", "...
644
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 0, 2, -4, 8],\n [0, 6, 0, -2, 1],\n [2, 0, 1, -6, -6],\n [-4, -2, -6, -13, 7],\n [8, 1, -6, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
731
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 9, -5, -5, 7],\n [0, -1, 9, -6, 0],\n [0, 0, -7, 4, -12],\n [0, 0, 0, 3, 5],\n [0, 0, 0, 0, -13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
908
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -4, 1, 0, -4],\n [-4, 2, 0, 6, -12],\n [1, 0, -12, 1, -4],\n [0, 6, 1, 6, -2],\n [-4, -12, -4, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
840
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, -10, -1, -10],\n [0, 5, -15, -8, 13],\n [0, 0, 5, -5, -11],\n [0, 0, 0, -1, 6],\n [0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
100
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 8, -12, 1, 13],\n [0, -6, -7, -12, 7],\n [0, 0, 9, -15, -6],\n [0, 0, 0, 5, 6],\n [0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
240
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 2, -1, 1, -9],\n [-1, 3, 15, 8, 2],\n [-7, 5, -4, 5, 5],\n [8, -1, -6, 9, -12],\n [-2, -13, 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...
959
MATH
[ { "content": "What is the determinant of the matrix:\n[[-14, 13, 1, 6, 6],\n [0, 11, -2, -1, -1],\n [0, 0, 4, 15, -4],\n [0, 0, 0, 15, -9],\n [0, 0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
720
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 1, -11, -8, 12],\n [1, 14, 10, -13, -6],\n [6, 8, -2, -11, -5],\n [10, 14, 8, -3, -6],\n [7, 4, -15, 1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
183
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -1, -3, 8, -8],\n [-10, 11, -2, -6, 0],\n [8, -7, -4, 0, 2],\n [14, -13, 15, 14, -6],\n [-5, 0, 13, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
320
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 14, 13, -15, -11],\n [-12, -12, -11, 2, 6],\n [2, -3, -10, -11, -6],\n [-7, -12, -6, -7, -2],\n [-12, -2, 0, -3, -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}"...
176
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -13, -8, -15, 7],\n [-8, -3, 8, 13, 10],\n [2, -9, -4, -4, -14],\n [5, -6, -5, -4, 7],\n [1, -5, 0, 11, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
499
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 15, -4, 4, 10],\n [0, 14, -11, 5, -5],\n [0, 0, -15, 12, -15],\n [0, 0, 0, 7, 2],\n [0, 0, 0, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
200
MATH
[ { "content": "Compute |A| for the matrix A =\n[[15, -10, 12, -1, -12],\n [0, -11, 2, 5, -12],\n [0, 0, 12, -7, 6],\n [0, 0, 0, -10, 6],\n [0, 0, 0, 0, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Compute |A| for the matrix A =\n[[15, -12, 8, -9, -15],\n [6, -2, 9, -8, 3],\n [-10, 0, -9, -10, 0],\n [-13, 6, -12, 14, 9],\n [-1, 8, -3, 15, -4]]\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": "Compute |A| for the matrix A =\n[[4, -5, -7, 12, -2],\n [-5, 3, 0, 0, 6],\n [-7, 0, 2, -2, -3],\n [12, 0, -2, 0, 6],\n [-2, 6, -3, 6, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
124
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -3, 3, 7, 0],\n [-3, 12, 2, -4, -8],\n [3, 2, -1, 4, 2],\n [7, -4, 4, 9, 2],\n [0, -8, 2, 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" } ]
122
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-15, 6, -4, 3, 12],\n [6, 10, 8, -3, 13],\n [-4, 8, -13, 10, 1],\n [3, -3, 10, -12, 13],\n [12, 13, 1, 13, 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...
819
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 12, -15, 13, 5],\n [6, 2, 7, 9, 8],\n [-3, -2, 3, 7, -8],\n [0, -4, -1, -15, 14],\n [-1, 5, -10, 15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
678
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 12, -8, -4, 5],\n [0, -13, 9, -11, 8],\n [0, 0, 13, -11, 15],\n [0, 0, 0, -3, 13],\n [0, 0, 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" } ]
294
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, 0, 12, -7, 9],\n [15, 6, 11, 9, 7],\n [3, -11, 2, 6, 5],\n [2, -7, 6, 6, -8],\n [-13, -13, -6, -7, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
189
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 5, -7, -4, -5],\n [0, -2, -11, -10, -7],\n [0, 0, -3, -13, 15],\n [0, 0, 0, -13, 5],\n [0, 0, 0, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
994
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -5, 9, -6, -4],\n [0, -1, 6, -15, -13],\n [0, 0, -9, 12, -11],\n [0, 0, 0, 3, -13],\n [0, 0, 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" } ]
216
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -5, 7, -11, 0],\n [-3, -4, -7, -11, 2],\n [6, -2, -5, -14, -7],\n [-9, 12, 3, 5, -7],\n [-15, -7, 8, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
138
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -1, 7, 2, -12],\n [-13, 14, -3, -14, 1],\n [3, 15, 6, 1, 6],\n [-10, -5, -8, 11, -4],\n [-15, -6, 13, 2, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
460
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -8, 5, 7, -7],\n [-11, 5, -8, 9, 12],\n [-3, -6, 5, 2, -4],\n [-6, -2, 3, -2, -10],\n [5, -1, 6, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
551
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 11, -8, -8, 4],\n [0, -1, 10, -4, 15],\n [0, 0, 9, -2, -3],\n [0, 0, 0, 11, -13],\n [0, 0, 0, 0, -14]]? 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": "What is the determinant of the matrix:\n[[9, 3, 8, -4, 5],\n [3, 4, 8, -6, -5],\n [8, 8, -10, 7, 0],\n [-4, -6, 7, 1, 4],\n [5, -5, 0, 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" } ]
398
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -2, 14, 14, 1],\n [0, 1, -7, 11, 11],\n [0, 0, -14, -15, -6],\n [0, 0, 0, -9, 14],\n [0, 0, 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": "...
134
MATH
[ { "content": "What is the determinant of the matrix:\n[[-15, -8, 4, 0, 5],\n [-8, 1, -6, 4, -1],\n [4, -6, 5, -4, -9],\n [0, 4, -4, 8, 13],\n [5, -1, -9, 13, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
575
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 4, -8, -5, 12],\n [0, -10, -11, 0, -14],\n [0, 0, -10, 7, 12],\n [0, 0, 0, -1, 0],\n [0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
0
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, 10, 1, -9],\n [0, -3, 4, 2, -4],\n [10, 4, -4, -6, -8],\n [1, 2, -6, 14, 7],\n [-9, -4, -8, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
436
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -5, -7, 2, -6],\n [0, -1, 3, 10, 5],\n [0, 0, -1, 2, -7],\n [0, 0, 0, -13, -14],\n [0, 0, 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" ...
455
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 5, -3, -9, -12],\n [0, -2, -4, -3, -10],\n [0, 0, 11, -2, -11],\n [0, 0, 0, -7, 1],\n [0, 0, 0, 0, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
842
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, 3, -3, -5],\n [0, -7, 6, -15, 7],\n [0, 0, 5, -1, -3],\n [0, 0, 0, -8, 11],\n [0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 7, -6, 6, 6],\n [1, -10, -12, -14, -5],\n [1, 10, -15, 0, -12],\n [-5, 1, 6, -10, -9],\n [-1, 9, -13, -4, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
34
MATH
[ { "content": "Determine the value of det(A) where A =\n[[14, 1, -9, -11, 8],\n [-11, 8, -2, 10, 1],\n [3, 9, 0, 11, -12],\n [-8, 0, 2, -14, 3],\n [7, -6, 7, 9, -14]]\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":...
595
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 5, 6, -12, -2],\n [0, 3, -12, -8, 8],\n [0, 0, -4, -1, 0],\n [0, 0, 0, 11, 5],\n [0, 0, 0, 0, 13]]\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": "use...
592
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, 14, -11, 15, 8],\n [-5, 6, -6, 1, 0],\n [15, -10, 14, 8, 12],\n [-1, 5, -9, 7, -2],\n [10, 4, 9, -9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
669
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -13, 15, 10, -14],\n [11, -10, -1, 1, 14],\n [7, 6, -10, 10, -1],\n [4, 10, -13, -2, 3],\n [-1, 2, -5, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
762
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -4, 1, -2, -6],\n [-4, -5, 8, 6, 2],\n [1, 8, 9, -3, -2],\n [-2, 6, -3, 4, 8],\n [-6, 2, -2, 8, -9]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, 4, 4, 8],\n [-2, 8, 14, -12, 2],\n [4, 14, 3, -10, 10],\n [4, -12, -10, 10, -2],\n [8, 2, 10, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
336
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -12, -3, -10, -4],\n [10, 6, -3, 4, 11],\n [-1, 15, 3, 8, 5],\n [15, 5, -11, -2, -4],\n [11, 8, 4, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
40
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -10, -14, 12, -4],\n [0, 9, 14, -7, 0],\n [0, 0, 10, -9, -6],\n [0, 0, 0, -15, 11],\n [0, 0, 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" } ]
200
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -6, -4, 5, 9],\n [-6, -13, -14, -6, 2],\n [-4, -14, -8, 6, 4],\n [5, -6, 6, -4, -2],\n [9, 2, 4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
588
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -1, 1, 2, -11],\n [-1, -10, 10, 2, -6],\n [1, 10, -14, 6, 8],\n [2, 2, 6, 1, 0],\n [-11, -6, 8, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
772
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 14, 4, 8, 13],\n [0, -1, -15, -7, -1],\n [0, 0, -3, -9, -8],\n [0, 0, 0, 2, 6],\n [0, 0, 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" } ]
84
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, 7, -4, -2],\n [-4, -13, 0, 4, -1],\n [7, 0, 11, -4, 6],\n [-4, 4, -4, -6, -6],\n [-2, -1, 6, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
296
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 6, 9, -12, -14],\n [-3, 13, -5, 2, -5],\n [4, -2, 1, -6, -7],\n [14, -12, 1, -8, -1],\n [-5, 9, -13, 9, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
876
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -1, 0, 0, 8],\n [-1, 12, 12, -4, 0],\n [0, 12, 6, -9, 3],\n [0, -4, -9, 6, 4],\n [8, 0, 3, 4, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
714
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, 10, -2, -8],\n [-3, -5, 9, -2, 3],\n [-9, 8, 6, -10, -13],\n [9, 11, 8, 7, -5],\n [-14, 12, 4, -15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
607
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 12, 0, 0, 4],\n [12, 14, -2, -2, 0],\n [0, -2, -3, 9, 0],\n [0, -2, 9, -14, 6],\n [4, 0, 0, 6, -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": "use...
960
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -7, 8, 12, -10],\n [-7, -4, -4, 1, -4],\n [8, -4, -2, -1, 4],\n [12, 1, -1, -13, 7],\n [-10, -4, 4, 7, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
657
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -3, 0, 3, 11],\n [0, 10, -2, -5, -6],\n [0, 0, 4, 11, 3],\n [0, 0, 0, 12, -5],\n [0, 0, 0, 0, -15]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 9, -10, -3, -5],\n [0, 9, -1, 4, -14],\n [0, 0, -13, 11, 0],\n [0, 0, 0, 8, -3],\n [0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
792
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -9, 6, 7, -9],\n [0, 6, 5, -1, 8],\n [0, 0, 9, 9, 12],\n [0, 0, 0, -2, -12],\n [0, 0, 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" } ]
380
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 7, 1, 1, -15],\n [-5, 9, -2, 4, -8],\n [-15, 10, 11, -8, 9],\n [-12, -5, 4, -9, 0],\n [-9, 14, -8, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
450
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 7, -11, -2, 13],\n [4, -15, 1, 0, -5],\n [2, 0, -9, -4, -12],\n [6, -11, 6, -13, 0],\n [9, 1, -6, -9, 13]]\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"...
182
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -11, -3, 0, -2],\n [0, 12, 12, -1, -1],\n [0, 0, 6, 0, -9],\n [0, 0, 0, 4, 5],\n [0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
656
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 12, 8, 0, -10],\n [12, 4, 3, -4, -1],\n [8, 3, 0, -11, -8],\n [0, -4, -11, -11, -2],\n [-10, -1, -8, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
780
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, 4, 6, -8, 3],\n [4, -5, 2, -9, 2],\n [6, 2, 4, 0, -4],\n [-8, -9, 0, -4, -2],\n [3, 2, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
548
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, -13, 6, 1],\n [0, 5, 3, 4, 13],\n [0, 0, 6, 4, 13],\n [0, 0, 0, 2, 0],\n [0, 0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, 2, -8, 1],\n [0, 14, -15, 2, 9],\n [2, -15, 1, -3, 2],\n [-8, 2, -3, -12, -1],\n [1, 9, 2, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
386
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 8, 1, 6, 12],\n [0, -8, 0, 2, 13],\n [0, 0, 7, -4, 13],\n [0, 0, 0, 2, 12],\n [0, 0, 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" } ]
896
MATH