messages
listlengths 1
1
| ground_truth
stringclasses 65
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-10, 3, -6, -9],\n [0, 6, -6, -5],\n [0, 0, 12, -1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-4, -11, 10, 10],\n [0, -8, 10, 1],\n [0, 0, 4, -4],\n [0, 0, 0, 2]]\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[[-9, -2, -2, 0],\n [-2, 11, 4, -2],\n [-2, 4, -5, -5],\n [0, -2, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[6, -2, -5, -8],\n [-2, 6, 1, -12],\n [-5, 1, -9, -5],\n [-8, -12, -5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
49
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[10, -6, 0, 7],\n [-6, 9, 4, 0],\n [0, 4, 8, 10],\n [7, 0, 10, -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, 10, 0, 1],\n [10, -4, 7, -1],\n [0, 7, 5, -4],\n [1, -1, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
38
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[8, 1, -12, 4],\n [1, 2, -1, 6],\n [-12, -1, 3, -9],\n [4, 6, -9, 8]]\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[[-9, 9, 11, -2],\n [0, -6, 2, -2],\n [0, 0, 11, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[0, 11, 2, 2],\n [11, 10, 9, -5],\n [2, 9, -5, 6],\n [2, -5, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-8, 6, 0, 0],\n [6, 7, -4, 2],\n [0, -4, 9, -2],\n [0, 2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-1, -6, 4, 1],\n [-6, -1, 10, -5],\n [4, 10, -6, -2],\n [1, -5, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
39
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[2, 2, 2, 2],\n [2, -7, -6, -2],\n [2, -6, 1, -6],\n [2, -2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-5, -1, -2, 6],\n [-1, 0, 0, -4],\n [-2, 0, 6, -8],\n [6, -4, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-8, -9, 12, -10],\n [0, -8, -3, 3],\n [0, 0, 6, -12],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-1, -8, 6, -1],\n [-8, 9, 0, 1],\n [6, 0, 0, 6],\n [-1, 1, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-3, -8, 2, -8],\n [-8, 5, 10, 4],\n [2, 10, -5, 8],\n [-8, 4, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, 3, 3, -2],\n [3, -8, 3, 9],\n [3, 3, 0, 2],\n [-2, 9, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-7, 0, 2, 2],\n [0, 5, 4, -5],\n [2, 4, 7, -2],\n [2, -5, -2, -9]]\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[[-2, -8, 3, 5],\n [0, 9, 4, 10],\n [0, 0, -8, -5],\n [0, 0, 0, 6]]\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[[-2, -4, -4, -11],\n [-4, 8, 2, 0],\n [-4, 2, -6, 2],\n [-11, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
39
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[6, 0, 4, 4],\n [0, -2, -4, -4],\n [4, -4, -12, 0],\n [4, -4, 0, 4]]\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[[9, 2, 2, -2],\n [2, -3, 4, -4],\n [2, 4, -6, -8],\n [-2, -4, -8, -6]]\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[[-4, 4, 0, -2],\n [4, -9, -1, 0],\n [0, -1, 4, -2],\n [-2, 0, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-5, -4, -7, -3],\n [-4, -1, -8, -2],\n [-7, -8, -6, 4],\n [-3, -2, 4, 10]]\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[[10, -4, 0, 2],\n [0, -2, -2, 10],\n [0, 0, -7, 0],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-6, -6, -2, -6],\n [-6, -3, 0, -10],\n [-2, 0, 0, 4],\n [-6, -10, 4, -3]]\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[[-11, 6, 0, -2],\n [6, 9, 8, -2],\n [0, 8, -11, -4],\n [-2, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-2, 10, -4, 4],\n [10, -9, -4, -1],\n [-4, -4, -10, -3],\n [4, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
43
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-5, -5, 2, 2],\n [-5, -8, 8, -4],\n [2, 8, 0, 4],\n [2, -4, 4, -2]]\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[[9, -4, 8, -4],\n [-4, -4, 3, -6],\n [8, 3, 11, -10],\n [-4, -6, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-1, 10, -4, -2],\n [10, 8, 5, 4],\n [-4, 5, 3, -4],\n [-2, 4, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
43
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[9, -12, 10, -7],\n [-12, -5, 1, 5],\n [10, 1, 3, 1],\n [-7, 5, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
46
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[12, -4, 10, 3],\n [-4, -2, -2, -7],\n [10, -2, -10, 4],\n [3, -7, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
47
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-8, -8, 4, 4],\n [0, 3, 4, 0],\n [0, 0, -9, -1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-5, -2, 2, -5],\n [-2, 12, 0, 1],\n [2, 0, 4, 4],\n [-5, 1, 4, -12]]\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[[9, 5, 10, 5],\n [0, -11, 6, -11],\n [0, 0, 3, -4],\n [0, 0, 0, -1]]\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[[8, -1, -6, -6],\n [-1, -2, 4, 4],\n [-6, 4, 8, -8],\n [-6, 4, -8, 9]]\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[[-6, -3, -2, -9],\n [-3, -5, 9, 1],\n [-2, 9, 6, -2],\n [-9, 1, -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[[3, -3, 8, -7],\n [0, -11, 12, -2],\n [0, 0, 1, -2],\n [0, 0, 0, 2]]\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[[-10, 9, 9, 9],\n [0, -11, -11, 0],\n [0, 0, 7, -10],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-6, 8, 4, 8],\n [8, -11, 3, 9],\n [4, 3, 4, -4],\n [8, 9, -4, 2]]\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[[-12, 12, 2, 0],\n [12, 1, 4, 0],\n [2, 4, 5, 8],\n [0, 0, 8, -9]]\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[[5, 0, -1, 4],\n [0, 12, -2, 6],\n [-1, -2, -11, 4],\n [4, 6, 4, 1]]\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[[9, 6, -4, -10],\n [6, 3, -6, 1],\n [-4, -6, 6, -6],\n [-10, 1, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-3, 9, 0, -6],\n [0, -12, 10, -6],\n [0, 0, 12, 0],\n [0, 0, 0, 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 largest eigenvalue by absolute value:\n[[-12, -6, -5, 5],\n [0, 11, 4, -9],\n [0, 0, -9, 12],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[0, 0, -4, 1],\n [0, 9, 0, 2],\n [0, 0, 8, 2],\n [0, 0, 0, 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[[5, -5, -3, 9],\n [-5, 12, 3, -2],\n [-3, 3, 9, 8],\n [9, -2, 8, -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[[4, -11, -10, 4],\n [0, -4, 1, -6],\n [0, 0, -2, -6],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[3, -8, 5, -6],\n [-8, -12, 1, -4],\n [5, 1, -6, 2],\n [-6, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[1, -1, 2, 0],\n [-1, -6, 10, -3],\n [2, 10, -12, 0],\n [0, -3, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[1, 8, -3, 10],\n [0, -12, -6, 5],\n [0, 0, -9, 1],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-11, -4, -4, -9],\n [-4, -11, 10, 2],\n [-4, 10, -11, 4],\n [-9, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[1, 10, 10, -8],\n [0, 12, 5, 2],\n [0, 0, -8, -3],\n [0, 0, 0, 6]]\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[[7, -7, 4, 0],\n [-7, -3, 8, -3],\n [4, 8, 9, 4],\n [0, -3, 4, -5]]\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[[-4, 3, -8, 4],\n [3, 3, -6, 8],\n [-8, -6, 8, 6],\n [4, 8, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
43
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[3, 2, 7, -4],\n [2, 9, 10, -8],\n [7, 10, -6, -2],\n [-4, -8, -2, 2]]\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[[8, -3, 0, 6],\n [-3, -7, 3, -1],\n [0, 3, -2, -1],\n [6, -1, -1, -4]]\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[[9, 6, 4, 6],\n [6, 7, -8, -6],\n [4, -8, 11, 2],\n [6, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-1, 0, 2, 8],\n [0, -7, 8, 2],\n [2, 8, -1, 1],\n [8, 2, 1, 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[[-10, -4, 6, -4],\n [-4, -3, 6, 4],\n [6, 6, 7, 6],\n [-4, 4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
37
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[10, -2, 0, 2],\n [-2, 10, 0, -5],\n [0, 0, 2, 10],\n [2, -5, 10, 5]]\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[[4, -8, 0, 11],\n [0, -3, -6, -2],\n [0, 0, 2, -8],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[1, -10, 11, -4],\n [0, 4, 10, 12],\n [0, 0, -10, -6],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-6, 0, -5, 6],\n [0, -4, -2, -4],\n [-5, -2, 10, -4],\n [6, -4, -4, 1]]\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[[-12, -8, 4, -4],\n [-8, 7, 4, 2],\n [4, 4, 1, 0],\n [-4, 2, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-6, 3, 3, -6],\n [3, -1, 0, 7],\n [3, 0, 3, 0],\n [-6, 7, 0, 10]]\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[[-3, -1, 10, -2],\n [-1, 1, 0, 1],\n [10, 0, 10, -4],\n [-2, 1, -4, -6]]\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[[7, 4, 4, -1],\n [4, 12, -6, 5],\n [4, -6, 11, 6],\n [-1, 5, 6, -1]]\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[[7, -6, -2, -5],\n [-6, -12, -8, 1],\n [-2, -8, -1, 2],\n [-5, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[9, 0, -4, 8],\n [0, -3, 3, 0],\n [0, 0, 3, 6],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[5, 1, 1, 7],\n [1, -2, 4, -7],\n [1, 4, -12, -1],\n [7, -7, -1, 0]]\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, 8, 9, -7],\n [8, -3, -4, 4],\n [9, -4, 6, 2],\n [-7, 4, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
38
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-4, -2, 4, 9],\n [0, -8, -8, -10],\n [0, 0, -7, 4],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[12, 9, -2, 4],\n [0, -1, -5, 7],\n [0, 0, 0, -1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-8, -10, -6, -3],\n [-10, 5, 8, 3],\n [-6, 8, -4, -7],\n [-3, 3, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
46
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-6, 12, -4, -3],\n [0, 11, 8, -1],\n [0, 0, 8, 5],\n [0, 0, 0, 5]]\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[[4, -2, -4, 2],\n [-2, -1, 6, 0],\n [-4, 6, -6, 3],\n [2, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[2, 11, 9, 5],\n [0, 12, -10, 6],\n [0, 0, -9, 10],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-10, -1, -3, 6],\n [0, -12, -6, -2],\n [0, 0, -10, 4],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[10, -6, -7, -2],\n [-6, 5, 8, 3],\n [-7, 8, -4, 0],\n [-2, 3, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-5, 1, 0, 7],\n [1, 2, -5, 2],\n [0, -5, -11, 3],\n [7, 2, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-4, 1, -12, 9],\n [0, -3, -4, -9],\n [0, 0, 7, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[2, -6, 2, -8],\n [-6, 12, 1, -2],\n [2, 1, 6, -4],\n [-8, -2, -4, 1]]\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[[8, -1, 2, 4],\n [0, 9, 9, -3],\n [0, 0, 0, 5],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[1, 2, 10, 5],\n [2, -10, 7, 4],\n [10, 7, -10, 0],\n [5, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[12, -9, 5, 4],\n [0, -9, 7, 1],\n [0, 0, -3, -10],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-1, -8, -11, 5],\n [0, 10, -1, -6],\n [0, 0, 5, -11],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[10, -10, -11, 12],\n [0, -4, 1, -5],\n [0, 0, 3, -11],\n [0, 0, 0, -5]]\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[[0, 2, 2, -2],\n [2, -3, 10, 1],\n [2, 10, 7, 0],\n [-2, 1, 0, -10]]\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[[-5, 4, 1, -1],\n [4, -5, -2, 4],\n [1, -2, 6, 2],\n [-1, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-6, -8, 8, -8],\n [-8, -3, 6, 8],\n [8, 6, 6, 4],\n [-8, 8, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
52
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-12, 0, -10, -11],\n [0, -9, 6, -9],\n [0, 0, -6, 12],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-3, -7, -8, -8],\n [-7, 10, -2, 10],\n [-8, -2, -3, 2],\n [-8, 10, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[0, -6, -1, -10],\n [-6, -6, 6, 10],\n [-1, 6, 11, 3],\n [-10, 10, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-6, 2, -2, 4],\n [2, 9, -8, 4],\n [-2, -8, 1, -7],\n [4, 4, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-8, 4, 0, 5],\n [4, 11, -4, -2],\n [0, -4, -7, -1],\n [5, -2, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[2, -5, 2, -4],\n [-5, -3, 1, -8],\n [2, 1, -5, 5],\n [-4, -8, 5, -1]]\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[[-9, 0, 10, 12],\n [0, -1, -8, 8],\n [0, 0, 1, 9],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[12, 1, -9, 8],\n [1, 8, 6, -2],\n [-9, 6, 3, -8],\n [8, -2, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24
|
MATH
|
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