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[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-3, -2, 4, 0, 2, 4],\n [-2, 4, 7, -6, -2, 2],\n [4, 7, 6, 0, -12, 2],\n [0, -6, 0, -8, 4, -2],\n [2, -2, -12, 4, -3, 0],\n [4, 2, 2, -2, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
58
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[0, 10, 10, 3, -8, 4],\n [10, -6, 2, 2, -2, 6],\n [10, 2, -5, -4, -2, -6],\n [3, 2, -4, 7, -12, 4],\n [-8, -2, -2, -12, -9, -6],\n [4, 6, -6, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-11, 6, -3, 12, -2, -3],\n [6, -5, -4, -2, 14, -1],\n [-3, -4, -4, 2, 0, 4],\n [12, -2, 2, -6, -5, 4],\n [-2, 14, 0, -5, 11, -8],\n [-3, -1, 4, 4, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-1, 2, -10, 5, -10, 3],\n [2, 6, 4, 4, 14, 2],\n [-10, 4, -7, 0, 5, 6],\n [5, 4, 0, -5, 8, 12],\n [-10, 14, 5, 8, 8, 6],\n [3, 2, 6, 12, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[13, 15, -1, -14, -14, -6],\n [0, 14, -8, 4, -9, -4],\n [0, 0, 10, 12, 14, -1],\n [0, 0, 0, 11, -2, -13],\n [0, 0, 0, 0, -10, 1],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[11, 12, -13, -3, 13, 8],\n [0, -7, -3, -8, 0, 8],\n [0, 0, -3, -12, 2, -14],\n [0, 0, 0, -1, 1, 13],\n [0, 0, 0, 0, -13, 3],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[13, 5, -12, 6, 0, -6],\n [5, -6, -4, -10, -4, -2],\n [-12, -4, -8, 0, -6, 4],\n [6, -10, 0, -13, 0, 4],\n [0, -4, -6, 0, -9, 6],\n [-6, -2, 4, 4, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[7, -4, 1, 4, -8, 14],\n [-4, -14, -10, 4, -8, -4],\n [1, -10, 7, -6, 8, 2],\n [4, 4, -6, -3, -2, 0],\n [-8, -8, 8, -2, -1, 6],\n [14, -4, 2, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[1, 8, -1, -13, -12, -4],\n [0, 1, 15, -10, -6, 6],\n [0, 0, -6, -10, 8, -10],\n [0, 0, 0, 9, 0, 6],\n [0, 0, 0, 0, 10, 1],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-14, 12, -6, -3, 2, 14],\n [0, -5, -3, 3, 13, 8],\n [0, 0, 13, 8, 6, -11],\n [0, 0, 0, -3, -11, -4],\n [0, 0, 0, 0, -7, 1],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[6, 6, 1, -13, 12, -10],\n [0, -1, -2, -5, -5, -7],\n [0, 0, -4, 13, -10, -15],\n [0, 0, 0, -1, -14, 1],\n [0, 0, 0, 0, 7, 13],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[10, 6, 0, 0, 4, 4],\n [6, -5, 9, -4, -5, 2],\n [0, 9, 9, -8, -2, 6],\n [0, -4, -8, 2, -12, 8],\n [4, -5, -2, -12, -14, -4],\n [4, 2, 6, 8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
89
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-6, 2, -5, -10, 3, 10],\n [2, -15, -5, 1, -14, -9],\n [-5, -5, 7, -5, -9, 4],\n [-10, 1, -5, 14, 0, 4],\n [3, -14, -9, 0, 1, 8],\n [10, -9, 4, 4, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-7, 13, 3, -2, -2, 14],\n [0, -14, -8, -11, 11, -9],\n [0, 0, 0, 0, 1, 6],\n [0, 0, 0, -8, -8, 7],\n [0, 0, 0, 0, 6, -4],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
43
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[15, 4, -8, -7, 0, 6],\n [4, -8, -14, 2, -2, 1],\n [-8, -14, -13, 0, -6, 10],\n [-7, 2, 0, 14, 6, 4],\n [0, -2, -6, 6, 8, 4],\n [6, 1, 10, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-12, 12, -3, 14, 13, -10],\n [0, 5, -3, 9, 10, 4],\n [0, 0, -2, -3, -2, -8],\n [0, 0, 0, -1, 3, -15],\n [0, 0, 0, 0, -8, -13],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-8, 1, 7, 7, 8, 0],\n [0, 5, -6, 9, 9, 8],\n [0, 0, 1, 13, 0, -1],\n [0, 0, 0, -12, 14, -14],\n [0, 0, 0, 0, 5, 13],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[14, 10, 8, 3, -14, -7],\n [0, 9, -3, 2, 0, 0],\n [0, 0, -7, -5, 9, 10],\n [0, 0, 0, -6, -13, -10],\n [0, 0, 0, 0, 2, -8],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-8, 2, -2, -12, 4, 7],\n [2, -3, -1, -4, 2, -4],\n [-2, -1, -11, -10, -9, -10],\n [-12, -4, -10, -7, -6, -1],\n [4, 2, -9, -6, 3, -8],\n [7, -4, -10, -1, -8, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-14, -1, 0, 11, -4, 2],\n [-1, 15, -5, 10, 9, -3],\n [0, -5, 2, -2, -8, 6],\n [11, 10, -2, -3, 4, -3],\n [-4, 9, -8, 4, 8, 6],\n [2, -3, 6, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[7, 3, 2, 0, -10, 6],\n [3, 2, 1, -10, 0, 2],\n [2, 1, 7, -6, 0, 12],\n [0, -10, -6, -14, -1, -3],\n [-10, 0, 0, -1, 1, 2],\n [6, 2, 12, -3, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
74
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[5, -12, -10, 4, 10, -6],\n [-12, -15, -5, -4, -8, 6],\n [-10, -5, 1, -1, -10, -12],\n [4, -4, -1, -1, 11, -1],\n [10, -8, -10, 11, -15, 6],\n [-6, 6, -12, -1, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-10, 3, 4, -2, 8, 8],\n [3, -2, -11, 0, -8, -14],\n [4, -11, -11, -12, 3, 8],\n [-2, 0, -12, 10, -6, 7],\n [8, -8, 3, -6, -11, -6],\n [8, -14, 8, 7, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-6, -3, -4, -14, 10, -1],\n [0, 9, -6, 6, -8, 9],\n [0, 0, -8, 5, 5, 6],\n [0, 0, 0, 11, -8, 2],\n [0, 0, 0, 0, -3, -13],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
47
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[14, -5, 0, -5, -2, -6],\n [-5, -1, 3, 6, 4, -8],\n [0, 3, 12, -9, -10, 6],\n [-5, 6, -9, -10, 0, -9],\n [-2, 4, -10, 0, -8, 1],\n [-6, -8, 6, -9, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
89
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[5, -1, 8, 1, 2, -14],\n [0, 0, -12, 9, -14, 12],\n [0, 0, -3, 15, 12, 9],\n [0, 0, 0, -15, 13, 5],\n [0, 0, 0, 0, -10, -14],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[2, -7, 2, -6, -6, -12],\n [-7, 14, 9, 15, 4, 4],\n [2, 9, -7, -8, 0, -6],\n [-6, 15, -8, 5, -6, -10],\n [-6, 4, 0, -6, -10, -6],\n [-12, 4, -6, -10, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[7, -7, -8, 11, -12, -14],\n [0, 13, -14, -14, 14, 11],\n [0, 0, -9, -4, -10, 2],\n [0, 0, 0, -3, 4, 5],\n [0, 0, 0, 0, 11, -14],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[15, -3, 6, 4, 2, 0],\n [-3, -3, -10, -6, -9, 2],\n [6, -10, 3, 10, 4, -4],\n [4, -6, 10, -12, 0, 6],\n [2, -9, 4, 0, 14, -3],\n [0, 2, -4, 6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
85
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, 1, 10, -3, -10, 4],\n [1, -14, -1, -6, 5, 4],\n [10, -1, 4, -6, 6, 9],\n [-3, -6, -6, -13, -6, 8],\n [-10, 5, 6, -6, -15, -6],\n [4, 4, 9, 8, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
95
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-3, 4, 11, 7, 2, -2],\n [4, 9, 0, -6, 8, 0],\n [11, 0, -5, 8, -4, 0],\n [7, -6, 8, 4, -4, 1],\n [2, 8, -4, -4, 7, 12],\n [-2, 0, 0, 1, 12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
82
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-4, 0, -5, -14, -7, 0],\n [0, 0, -5, -4, 4, 6],\n [-5, -5, 4, 3, 4, -1],\n [-14, -4, 3, -14, 0, 4],\n [-7, 4, 4, 0, -10, 6],\n [0, 6, -1, 4, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-15, -10, 8, -2, -6, -9],\n [-10, -12, 2, 6, 4, -2],\n [8, 2, -15, -2, -2, 10],\n [-2, 6, -2, 15, -14, 0],\n [-6, 4, -2, -14, 14, -3],\n [-9, -2, 10, 0, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[3, 11, 2, 5, -4, 12],\n [0, -4, -15, 4, -8, 1],\n [0, 0, 4, 6, -9, -7],\n [0, 0, 0, -12, 6, 10],\n [0, 0, 0, 0, 10, 8],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[6, -4, 1, -2, 2, 14],\n [-4, -1, 4, -8, 2, 14],\n [1, 4, -6, 4, 2, 0],\n [-2, -8, 4, -3, 2, -7],\n [2, 2, 2, 2, -14, 6],\n [14, 14, 0, -7, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
82
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-14, 1, -2, 8, 12, 0],\n [0, -6, 1, -3, 0, -7],\n [0, 0, 8, 13, 12, 13],\n [0, 0, 0, 11, 15, -5],\n [0, 0, 0, 0, -12, -2],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[10, 6, -4, 12, -4, -2],\n [6, -2, -4, 0, 2, -11],\n [-4, -4, 2, 4, -4, 0],\n [12, 0, 4, -3, -4, -5],\n [-4, 2, -4, -4, 1, -12],\n [-2, -11, 0, -5, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
78
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[7, 10, 8, 8, 13, 0],\n [0, -8, 10, -1, 9, -15],\n [0, 0, 14, -1, -2, -2],\n [0, 0, 0, 15, -10, 14],\n [0, 0, 0, 0, -1, -1],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-5, 2, 0, -2, 2, -2],\n [2, -1, 10, 10, -8, 0],\n [0, 10, 0, 4, 4, 4],\n [-2, 10, 4, -7, -2, 6],\n [2, -8, 4, -2, 4, 4],\n [-2, 0, 4, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, 10, -7, -4, 1, 6],\n [10, -11, 4, 6, 10, 3],\n [-7, 4, 8, -2, 0, -8],\n [-4, 6, -2, 1, -4, -6],\n [1, 10, 0, -4, -1, -8],\n [6, 3, -8, -6, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[13, 3, -2, -8, -10, -3],\n [3, -6, 1, 4, 6, -2],\n [-2, 1, -5, -4, -6, 5],\n [-8, 4, -4, -15, 4, -4],\n [-10, 6, -6, 4, 12, -8],\n [-3, -2, 5, -4, -8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-15, 7, 5, -7, -14, 1],\n [0, 8, -6, -10, 15, -11],\n [0, 0, 14, -11, -4, -9],\n [0, 0, 0, -12, 2, -6],\n [0, 0, 0, 0, -5, 2],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-14, -4, -14, -12, -5, 4],\n [-4, 2, 2, 2, 4, -5],\n [-14, 2, 7, 10, -4, 12],\n [-12, 2, 10, 1, 2, 6],\n [-5, 4, -4, 2, -14, 4],\n [4, -5, 12, 6, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[4, -4, -2, 0, -10, -7],\n [-4, -11, 2, 6, 9, 9],\n [-2, 2, 14, -1, 1, 14],\n [0, 6, -1, 0, -2, -8],\n [-10, 9, 1, -2, -13, -7],\n [-7, 9, 14, -8, -7, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[6, 10, 12, -12, -6, 3],\n [0, 2, -1, 14, -12, -7],\n [0, 0, 0, 12, 5, -1],\n [0, 0, 0, 11, -2, -13],\n [0, 0, 0, 0, 14, 15],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[1, -15, -6, 7, 0, 11],\n [0, 3, 8, 9, -13, 12],\n [0, 0, -1, 1, 2, -9],\n [0, 0, 0, 10, -8, 5],\n [0, 0, 0, 0, -1, -9],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[7, 2, -2, -10, 8, -2],\n [2, -13, -10, 11, -12, 4],\n [-2, -10, -11, 13, 12, 7],\n [-10, 11, 13, 7, 1, -6],\n [8, -12, 12, 1, 11, -2],\n [-2, 4, 7, -6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-15, 6, -9, 2, -6, -5],\n [6, 4, -4, 4, 8, -6],\n [-9, -4, -13, 14, 2, 0],\n [2, 4, 14, 7, -6, -6],\n [-6, 8, 2, -6, 1, -6],\n [-5, -6, 0, -6, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[13, -6, 4, 4, 11, -7],\n [-6, -14, 0, -1, 0, 8],\n [4, 0, 10, 6, 6, -2],\n [4, -1, 6, 2, 0, 0],\n [11, 0, 6, 0, -8, -14],\n [-7, 8, -2, 0, -14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
81
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-15, 9, 0, 3, -1, 6],\n [9, 1, -6, 4, -6, -5],\n [0, -6, 14, 2, 4, 10],\n [3, 4, 2, 6, 4, -12],\n [-1, -6, 4, 4, -6, -7],\n [6, -5, 10, -12, -7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
91
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[15, -10, -2, 10, 7, 0],\n [0, -9, -14, -10, -7, -9],\n [0, 0, -8, -5, 9, -12],\n [0, 0, 0, -3, 11, -11],\n [0, 0, 0, 0, -3, 14],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[2, 3, 10, 2, 4, 2],\n [3, 3, 12, 8, -4, -2],\n [10, 12, -8, -11, 4, -2],\n [2, 8, -11, 5, -3, -5],\n [4, -4, 4, -3, 4, -3],\n [2, -2, -2, -5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-12, -1, 3, -10, 11, -11],\n [0, 2, 12, -13, 11, 6],\n [0, 0, -12, 2, -7, 3],\n [0, 0, 0, -1, -15, 13],\n [0, 0, 0, 0, -6, 3],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[7, 9, -9, 3, -9, -1],\n [0, -2, -15, 13, -3, -13],\n [0, 0, -10, 3, -1, -12],\n [0, 0, 0, -12, -11, 2],\n [0, 0, 0, 0, -4, 6],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-8, 8, -6, 6, 11, 8],\n [8, 15, 1, 0, -3, 0],\n [-6, 1, -3, -4, -6, -14],\n [6, 0, -4, -6, -5, -4],\n [11, -3, -6, -5, 15, -1],\n [8, 0, -14, -4, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
95
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-11, 13, 3, 3, -10, 12],\n [0, 13, -6, 7, -2, 1],\n [0, 0, 12, -15, -6, -13],\n [0, 0, 0, -6, 14, 10],\n [0, 0, 0, 0, -7, 12],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-15, 8, -9, 1, 9, 8],\n [8, 11, -5, 14, -8, -6],\n [-9, -5, -10, 2, -7, 2],\n [1, 14, 2, -8, -3, -6],\n [9, -8, -7, -3, -9, 10],\n [8, -6, 2, -6, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
106
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[9, 6, 0, -2, -2, 7],\n [6, 2, 2, 3, 0, 3],\n [0, 2, -3, 9, 8, 4],\n [-2, 3, 9, -15, -4, -4],\n [-2, 0, 8, -4, -1, 4],\n [7, 3, 4, -4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
62
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-7, 0, 4, -4, 8, 3],\n [0, -8, 0, 10, -4, -5],\n [4, 0, 10, -4, -8, 6],\n [-4, 10, -4, -12, 4, -4],\n [8, -4, -8, 4, 8, -2],\n [3, -5, 6, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
73
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[3, -6, -9, -8, -7, -10],\n [-6, 12, -13, -6, -4, 6],\n [-9, -13, -4, 4, -2, -4],\n [-8, -6, 4, -11, 0, -12],\n [-7, -4, -2, 0, 5, 10],\n [-10, 6, -4, -12, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-10, -2, -4, 1, -6, 2],\n [-2, 13, -5, 6, 0, -13],\n [-4, -5, 15, -6, -2, -2],\n [1, 6, -6, 7, -6, -4],\n [-6, 0, -2, -6, -1, -2],\n [2, -13, -2, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-2, -2, -4, -10, -10, 2],\n [-2, 14, 6, 1, 4, 2],\n [-4, 6, 8, -11, -12, -6],\n [-10, 1, -11, 10, 2, 10],\n [-10, 4, -12, 2, 0, 6],\n [2, 2, -6, 10, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[8, 12, -2, 12, 4, -3],\n [12, -7, 5, -4, -10, 9],\n [-2, 5, -1, 2, -6, -10],\n [12, -4, 2, 15, 2, 2],\n [4, -10, -6, 2, 2, 5],\n [-3, 9, -10, 2, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-11, -2, 0, -1, 8, 8],\n [-2, -12, 6, 10, -3, 8],\n [0, 6, 10, 2, -6, -4],\n [-1, 10, 2, 8, -7, 12],\n [8, -3, -6, -7, -8, -10],\n [8, 8, -4, 12, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-12, -4, 9, -11, -7, -1],\n [-4, 1, 0, -6, -1, 3],\n [9, 0, -5, 0, -8, 4],\n [-11, -6, 0, -12, 3, -4],\n [-7, -1, -8, 3, -1, 11],\n [-1, 3, 4, -4, 11, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[10, -2, -4, 2, -12, 11],\n [0, 3, 13, -3, 9, 14],\n [0, 0, -5, 12, -10, -7],\n [0, 0, 0, -1, -5, -10],\n [0, 0, 0, 0, 9, -5],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[1, 8, -10, -4, 5, 1],\n [8, 3, -4, 0, 2, -4],\n [-10, -4, -10, 10, 7, 6],\n [-4, 0, 10, -11, -10, 2],\n [5, 2, 7, -10, -12, -8],\n [1, -4, 6, 2, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-12, -4, -4, -2, 2, 4],\n [-4, -13, -2, 0, -2, 7],\n [-4, -2, 14, -11, -5, 0],\n [-2, 0, -11, 15, 6, 10],\n [2, -2, -5, 6, -1, -7],\n [4, 7, 0, 10, -7, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[8, -2, 6, -6, -1, -4],\n [-2, -5, 8, -4, -1, 2],\n [6, 8, 11, -2, 2, 9],\n [-6, -4, -2, 10, 2, 5],\n [-1, -1, 2, 2, -9, -2],\n [-4, 2, 9, 5, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-5, 8, 10, -7, 1, -12],\n [0, 3, -9, -15, -7, -3],\n [0, 0, -14, 8, 11, 14],\n [0, 0, 0, -9, -7, -4],\n [0, 0, 0, 0, -1, -9],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-6, -2, -2, -8, -2, -4],\n [-2, 5, 6, 2, 6, 1],\n [-2, 6, 0, -11, -8, -2],\n [-8, 2, -11, -5, 4, 4],\n [-2, 6, -8, 4, -4, 4],\n [-4, 1, -2, 4, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[7, 0, 9, -2, 0, -1],\n [0, 10, -4, 6, 2, 12],\n [9, -4, 5, 0, 10, -5],\n [-2, 6, 0, 14, 4, 2],\n [0, 2, 10, 4, 7, 6],\n [-1, 12, -5, 2, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
78
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[15, 4, -12, 3, -12, -11],\n [4, 7, 0, -8, 6, -6],\n [-12, 0, -1, 4, -3, 8],\n [3, -8, 4, 3, 6, -14],\n [-12, 6, -3, 6, 2, -7],\n [-11, -6, 8, -14, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
101
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[2, -8, -2, 10, -6, -5],\n [-8, 8, -10, -10, -2, 8],\n [-2, -10, 5, 3, 4, 8],\n [10, -10, 3, 1, 4, -4],\n [-6, -2, 4, 4, 3, 11],\n [-5, 8, 8, -4, 11, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-11, -5, 8, -11, -9, -10],\n [0, 10, -3, -14, 3, -5],\n [0, 0, -11, -7, -10, 1],\n [0, 0, 0, -9, -11, -1],\n [0, 0, 0, 0, -9, -5],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-8, -3, 6, -6, -4, 8],\n [-3, 4, 0, 5, -14, -4],\n [6, 0, -3, 0, -5, -4],\n [-6, 5, 0, 1, -10, 3],\n [-4, -14, -5, -10, 10, 2],\n [8, -4, -4, 3, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[12, -4, 2, 2, 12, 3],\n [-4, 4, 8, 6, 2, 2],\n [2, 8, 0, -2, -2, 8],\n [2, 6, -2, -6, -6, 3],\n [12, 2, -2, -6, -6, -3],\n [3, 2, 8, 3, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[13, -2, -10, -4, 2, -8],\n [-2, 0, -6, 3, 0, 6],\n [-10, -6, -2, 8, -10, 8],\n [-4, 3, 8, 15, -2, -2],\n [2, 0, -10, -2, 3, 5],\n [-8, 6, 8, -2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-11, -13, 0, 10, -8, 8],\n [0, 3, -2, -1, 1, 5],\n [0, 0, 11, 7, -1, 15],\n [0, 0, 0, -14, -11, -7],\n [0, 0, 0, 0, 15, 6],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[2, 12, -1, 8, -7, 10],\n [12, -1, -1, -8, 8, 6],\n [-1, -1, 3, 0, -3, -2],\n [8, -8, 0, 10, -7, -14],\n [-7, 8, -3, -7, -11, 0],\n [10, 6, -2, -14, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
89
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[4, -2, -10, -10, -8, -4],\n [-2, 9, -5, -2, 4, -6],\n [-10, -5, -2, 8, 5, -5],\n [-10, -2, 8, 11, -2, -10],\n [-8, 4, 5, -2, 14, -5],\n [-4, -6, -5, -10, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[5, 10, -12, -6, 10, 2],\n [10, -8, -6, 4, -12, -11],\n [-12, -6, 1, -8, -6, -8],\n [-6, 4, -8, -7, 8, -4],\n [10, -12, -6, 8, 12, -6],\n [2, -11, -8, -4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
104
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[6, 6, 1, 4, -2, -10],\n [6, -7, -4, 1, 2, -5],\n [1, -4, -3, 8, 10, -6],\n [4, 1, 8, 5, -12, -1],\n [-2, 2, 10, -12, -5, -7],\n [-10, -5, -6, -1, -7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
83
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-7, -2, -6, -6, 0, -8],\n [-2, 14, 2, 4, -6, -6],\n [-6, 2, -11, -2, -4, 4],\n [-6, 4, -2, -13, 2, -4],\n [0, -6, -4, 2, -4, 4],\n [-8, -6, 4, -4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
73
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[7, -1, 11, 0, 3, -2],\n [-1, -6, 12, -4, 5, -4],\n [11, 12, -14, -3, 4, 0],\n [0, -4, -3, 9, -5, -4],\n [3, 5, 4, -5, -12, 14],\n [-2, -4, 0, -4, 14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
83
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[15, -9, 0, 4, 6, 4],\n [-9, 6, 10, -4, -8, 2],\n [0, 10, 6, -2, -2, -1],\n [4, -4, -2, 13, -6, -6],\n [6, -8, -2, -6, -8, -4],\n [4, 2, -1, -6, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
81
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[4, 2, 11, 5, -15, 13],\n [0, 14, -8, -13, -15, 4],\n [0, 0, -7, 15, 1, 11],\n [0, 0, 0, -10, 14, 7],\n [0, 0, 0, 0, -6, -2],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[4, -3, -7, 7, 2, -6],\n [-3, -8, 6, 14, 11, 2],\n [-7, 6, 13, 0, 4, 4],\n [7, 14, 0, -15, -8, 6],\n [2, 11, 4, -8, 5, 4],\n [-6, 2, 4, 6, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-3, 6, 4, 0, 1, 2],\n [6, 2, 3, -2, 0, 6],\n [4, 3, 5, 8, 3, -12],\n [0, -2, 8, -6, 8, -4],\n [1, 0, 3, 8, -3, 0],\n [2, 6, -12, -4, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[6, 2, -2, -10, -4, -12],\n [2, 0, 2, 0, 4, -7],\n [-2, 2, -4, 7, -4, -6],\n [-10, 0, 7, -3, 9, 2],\n [-4, 4, -4, 9, -15, -7],\n [-12, -7, -6, 2, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-6, 6, 6, -2, 4, -4],\n [6, -6, -6, 5, 2, 2],\n [6, -6, 4, -8, -10, -2],\n [-2, 5, -8, 10, -4, -2],\n [4, 2, -10, -4, -2, -10],\n [-4, 2, -2, -2, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[8, 0, -10, -3, -4, -4],\n [0, -9, -6, -6, 15, -8],\n [-10, -6, -2, 6, -7, -12],\n [-3, -6, 6, -8, 2, 2],\n [-4, 15, -7, 2, -10, 14],\n [-4, -8, -12, 2, 14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
101
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[1, 4, 12, -2, -12, -12],\n [4, -5, 4, -1, 5, -4],\n [12, 4, -14, 2, 6, 11],\n [-2, -1, 2, -14, 4, -2],\n [-12, 5, 6, 4, 0, 1],\n [-12, -4, 11, -2, 1, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[4, -8, 11, -4, -2, -7],\n [-8, 14, -2, -3, -8, 5],\n [11, -2, -14, 0, -4, -8],\n [-4, -3, 0, 7, 4, -2],\n [-2, -8, -4, 4, -7, -8],\n [-7, 5, -8, -2, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[11, -8, -1, 5, 14, 7],\n [0, -1, -8, -8, 3, -7],\n [0, 0, 1, -8, -4, 11],\n [0, 0, 0, 14, 13, 0],\n [0, 0, 0, 0, -3, -1],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[6, -11, 3, -9, -13, -3],\n [0, 0, 15, -3, -14, -2],\n [0, 0, -11, -2, -7, -6],\n [0, 0, 0, -2, 9, -2],\n [0, 0, 0, 0, 1, 11],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-11, -14, -3, 0, 3, -10],\n [-14, -15, 5, 2, -4, -8],\n [-3, 5, -5, 0, 8, 6],\n [0, 2, 0, 15, -4, 7],\n [3, -4, 8, -4, 5, 2],\n [-10, -8, 6, 7, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[15, 10, -13, -5, 3, -12],\n [10, 0, 3, 5, 8, -4],\n [-13, 3, -9, -4, -8, 9],\n [-5, 5, -4, 6, 5, -6],\n [3, 8, -8, 5, -8, -2],\n [-12, -4, 9, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[3, 4, 1, 9, -2, 0],\n [4, 0, 4, 7, -6, -8],\n [1, 4, 10, 0, 6, 7],\n [9, 7, 0, -11, 4, 8],\n [-2, -6, 6, 4, -9, 14],\n [0, -8, 7, 8, 14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[15, -2, -11, 12, -2, 1],\n [-2, 8, 0, -1, 0, 4],\n [-11, 0, -11, -7, -8, 0],\n [12, -1, -7, -11, -9, 2],\n [-2, 0, -8, -9, 9, 4],\n [1, 4, 0, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
MATH