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[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-6, 3, -5, -3],\n [3, 12, 2, -4],\n [-5, 2, -2, -2],\n [-3, -4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[4, -8, 0, 5],\n [0, 11, -8, -12],\n [0, 0, -6, -5],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[6, 9, 4, -12],\n [0, -7, 9, 12],\n [0, 0, -2, -1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-11, 5, 6, 0],\n [5, -8, -1, 1],\n [6, -1, -10, -3],\n [0, 1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-11, 8, 0, 2],\n [8, 1, 4, -8],\n [0, 4, -11, 2],\n [2, -8, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[2, 3, -4, -2],\n [3, -7, -4, 8],\n [-4, -4, -10, 1],\n [-2, 8, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[0, -5, -2, 3],\n [-5, 4, 8, 8],\n [-2, 8, -11, 1],\n [3, 8, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[5, 9, -1, -2],\n [9, 7, 0, 10],\n [-1, 0, 8, 0],\n [-2, 10, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-8, -8, -2, 2],\n [0, -2, -4, -8],\n [0, 0, -9, -11],\n [0, 0, 0, -1]]\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[[4, -5, -4, -5],\n [-5, -4, -1, -8],\n [-4, -1, 7, -1],\n [-5, -8, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[6, -2, -4, -2],\n [-2, 10, 6, 8],\n [-4, 6, 5, 2],\n [-2, 8, 2, -5]]\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[[-6, -4, -2, 2],\n [-4, 1, 10, -6],\n [-2, 10, -11, -2],\n [2, -6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
38
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-5, 2, -10, -6],\n [0, 10, 4, -8],\n [0, 0, 4, 10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-6, -10, 4, 2],\n [-10, 0, 2, -8],\n [4, 2, -3, 5],\n [2, -8, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-2, 0, -8, 2],\n [0, -8, -2, -1],\n [-8, -2, -3, -2],\n [2, -1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, 6, 0, 10],\n [6, 11, 6, 10],\n [0, 6, 3, -1],\n [10, 10, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-2, -2, 2, 4],\n [-2, 2, 6, 4],\n [2, 6, -1, -5],\n [4, 4, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[4, 0, 5, -8],\n [0, 4, 4, 3],\n [5, 4, 0, -4],\n [-8, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-4, 2, 7, 4],\n [2, 8, 2, -6],\n [7, 2, 10, -4],\n [4, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-11, 4, -11, 10],\n [4, -5, 1, -4],\n [-11, 1, -2, 10],\n [10, -4, 10, -5]]\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[[12, 4, 3, -9],\n [4, 1, -3, -2],\n [3, -3, -6, 6],\n [-9, -2, 6, -11]]\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, -1, 3],\n [0, 7, -1, 0],\n [0, 0, 11, -12],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-3, -10, -5, 10],\n [-10, -5, 9, -2],\n [-5, 9, -6, 8],\n [10, -2, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
53
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[5, 2, 8, -6],\n [2, 2, 3, 2],\n [8, 3, -10, 10],\n [-6, 2, 10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-12, 2, -10, 6],\n [2, -7, 8, 7],\n [-10, 8, 11, -1],\n [6, 7, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
53
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-1, 0, -4, 0],\n [0, -3, 0, -4],\n [-4, 0, 0, 11],\n [0, -4, 11, -4]]\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[[-11, 10, 8, -6],\n [10, -12, 0, 6],\n [8, 0, -5, 1],\n [-6, 6, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[10, -5, -4, -7],\n [-5, 0, 4, 2],\n [-4, 4, 7, 6],\n [-7, 2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[4, 4, -2, -6],\n [4, -4, -2, 4],\n [-2, -2, -1, 4],\n [-6, 4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-9, 0, -8, 2],\n [0, -2, 6, 2],\n [-8, 6, 9, 3],\n [2, 2, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[2, -4, -2, -3],\n [-4, -5, -11, 10],\n [-2, -11, -2, -8],\n [-3, 10, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[9, 1, -6, 7],\n [0, -12, 6, 12],\n [0, 0, 4, 1],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[11, -5, 9, -8],\n [0, 12, -11, -7],\n [0, 0, -9, -4],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[3, -2, -2, -3],\n [-2, 0, 2, 5],\n [-2, 2, -8, 4],\n [-3, 5, 4, -9]]\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[[0, 0, 1, 0],\n [0, 8, -5, -4],\n [1, -5, -1, 8],\n [0, -4, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-12, 7, 8, -1],\n [0, 7, 6, -10],\n [0, 0, -7, 12],\n [0, 0, 0, 2]]\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[[-8, 6, 3, 5],\n [6, 7, -6, -4],\n [3, -6, -4, -6],\n [5, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[7, -3, -2, 2],\n [-3, 3, -4, 10],\n [-2, -4, 5, -3],\n [2, 10, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-12, 0, -3, -2],\n [0, -7, 6, -5],\n [-3, 6, -3, 2],\n [-2, -5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[6, -6, -6, -2],\n [-6, 3, 6, -8],\n [-6, 6, -8, 0],\n [-2, -8, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-1, -6, 2, -6],\n [0, -2, 7, -1],\n [0, 0, 9, 0],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-4, 0, 7, -10],\n [0, -10, -7, 2],\n [0, 0, -8, 1],\n [0, 0, 0, -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[[-2, 10, 9, -10],\n [0, 2, -6, 3],\n [0, 0, 8, 2],\n [0, 0, 0, 10]]\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[[5, -10, -4, 3],\n [0, 9, 11, -1],\n [0, 0, -5, -7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-10, -2, 2, -7],\n [-2, 3, 0, 5],\n [2, 0, 11, 3],\n [-7, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[10, 6, 5, -12],\n [0, 4, -7, 3],\n [0, 0, -11, -3],\n [0, 0, 0, 1]]\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[[-7, 6, 4, 0],\n [6, 7, 4, 7],\n [4, 4, -3, -10],\n [0, 7, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[9, -4, 2, 2],\n [-4, 11, -2, -7],\n [2, -2, 12, 4],\n [2, -7, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[6, -7, -5, -4],\n [0, -10, 0, 6],\n [0, 0, -2, -4],\n [0, 0, 0, -3]]\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[[-4, 2, 0, -9],\n [2, 5, -6, -9],\n [0, -6, -1, -6],\n [-9, -9, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-1, -1, 4, 9],\n [0, -4, 6, 11],\n [0, 0, 12, 10],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, 10, -5, 0],\n [10, 0, -2, -9],\n [-5, -2, 5, 0],\n [0, -9, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[1, -8, -6, 1],\n [-8, -3, 0, 2],\n [-6, 0, 11, -8],\n [1, 2, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-9, 4, 4, -2],\n [4, 7, 5, -6],\n [4, 5, -7, 2],\n [-2, -6, 2, 4]]\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[[-4, 4, -2, -2],\n [4, 10, 4, -6],\n [-2, 4, 6, 6],\n [-2, -6, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[4, 3, 5, 7],\n [0, 6, 11, 7],\n [0, 0, -11, -12],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[6, 0, -8, -7],\n [0, -9, -8, 2],\n [-8, -8, 3, 1],\n [-7, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-4, 2, -2, 1],\n [2, -7, -2, -8],\n [-2, -2, 12, 2],\n [1, -8, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[5, -1, -7, -2],\n [-1, -9, -3, -2],\n [-7, -3, -1, 0],\n [-2, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[9, 8, 0, 2],\n [8, -10, 2, -6],\n [0, 2, -9, 4],\n [2, -6, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-7, 6, 0, 12],\n [6, -5, -4, -5],\n [0, -4, 0, 2],\n [12, -5, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-1, 12, 0, 3],\n [12, -7, 4, 7],\n [0, 4, 6, 7],\n [3, 7, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-12, -1, -6, 12],\n [0, -11, 4, -10],\n [0, 0, 12, 0],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
44
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[4, -10, 10, 2],\n [-10, 5, 4, -6],\n [10, 4, 4, 0],\n [2, -6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-4, -8, 12, 12],\n [0, -1, -10, 11],\n [0, 0, 0, 8],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[1, -3, -2, 5],\n [-3, 9, -6, 3],\n [-2, -6, 2, 6],\n [5, 3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[9, 2, -3, 6],\n [2, -3, 2, 4],\n [-3, 2, -2, -4],\n [6, 4, -4, 12]]\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, 4, 9, 3],\n [0, 6, 9, 2],\n [0, 0, -1, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[6, 3, -11, 4],\n [0, -8, -3, 1],\n [0, 0, -6, 7],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[6, 5, 12, 1],\n [0, 8, 7, 4],\n [0, 0, -1, -6],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[1, -6, 1, -8],\n [-6, 3, 8, -6],\n [1, 8, -8, -4],\n [-8, -6, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[5, -7, -6, 5],\n [-7, 5, -8, 4],\n [-6, -8, 4, -2],\n [5, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[11, 7, 7, -9],\n [0, -1, 9, 4],\n [0, 0, 10, 10],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-10, 9, 5, -12],\n [0, -1, 4, 10],\n [0, 0, -8, -7],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-1, 12, -5, 3],\n [0, -9, -11, -7],\n [0, 0, -6, -9],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[7, 6, 4, -6],\n [6, 11, 4, 2],\n [4, 4, -4, -2],\n [-6, 2, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[8, -2, -7, -2],\n [-2, 9, 9, 6],\n [-7, 9, -9, 4],\n [-2, 6, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-8, -3, -7, 4],\n [-3, -6, -6, -4],\n [-7, -6, 9, -9],\n [4, -4, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[1, 2, 4, 12],\n [0, 6, -12, 5],\n [0, 0, -4, -1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[8, -2, -1, -7],\n [-2, 0, 4, 6],\n [-1, 4, -3, 2],\n [-7, 6, 2, -8]]\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[[-2, -8, -1, 1],\n [-8, 2, 0, -10],\n [-1, 0, -10, -4],\n [1, -10, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
39
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-9, -9, 4, -9],\n [0, 5, 5, -12],\n [0, 0, -6, 2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-3, -9, 9, -9],\n [0, 6, 10, 6],\n [0, 0, 1, 6],\n [0, 0, 0, -11]]\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[[-7, -8, 2, -3],\n [-8, -3, 9, 6],\n [2, 9, -4, 0],\n [-3, 6, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[12, -9, 7, 6],\n [0, 7, 4, 12],\n [0, 0, -6, -11],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[6, -2, 0, -9],\n [-2, -4, -2, 0],\n [0, -2, -1, -2],\n [-9, 0, -2, -10]]\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[[-5, -7, 8, 0],\n [-7, -8, 0, -4],\n [8, 0, -6, -1],\n [0, -4, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-6, 1, 8, -11],\n [0, -8, 7, 11],\n [0, 0, 8, -11],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[1, 3, 8, 0],\n [3, -10, 8, 2],\n [8, 8, 1, -8],\n [0, 2, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-11, 3, 8, -5],\n [0, -2, -8, 11],\n [0, 0, -7, 8],\n [0, 0, 0, 2]]\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[[-10, -2, -5, 5],\n [-2, 6, 2, -2],\n [-5, 2, 3, 2],\n [5, -2, 2, -5]]\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[[-3, 2, 8, 2],\n [2, 1, 7, -12],\n [8, 7, 1, 7],\n [2, -12, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
49
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[10, 2, -8, -2],\n [2, 2, -6, -6],\n [-8, -6, -10, -4],\n [-2, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-4, 4, 0, 2],\n [4, -12, -2, 0],\n [0, -2, -1, 4],\n [2, 0, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[10, -5, 3, 8],\n [0, 1, -2, 1],\n [0, 0, -9, 6],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-10, -4, 0, -10],\n [-4, 1, -4, 5],\n [0, -4, 1, -2],\n [-10, 5, -2, -12]]\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[[0, 3, -3, -2],\n [3, 7, 0, -2],\n [-3, 0, 0, 1],\n [-2, -2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[12, -4, -12, 6],\n [-4, 11, -6, 2],\n [-12, -6, -8, -6],\n [6, 2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-11, 9, 6, -1],\n [9, -12, 0, -4],\n [6, 0, 9, 3],\n [-1, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[10, 9, -8, -2],\n [9, 2, -2, 4],\n [-8, -2, 6, 4],\n [-2, 4, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
MATH