messages listlengths 1 1 | ground_truth stringclasses 65
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-9, -4, -2, 0],\n [-4, 3, -8, 0],\n [-2, -8, -4, 2],\n [0, 0, 2, -7]]\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[[9, 7, -7, 7],\n [0, -12, 4, -6],\n [0, 0, -3, -2],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[10, 6, 7, -7],\n [6, -2, 0, -6],\n [7, 0, 9, 7],\n [-7, -6, 7, 6]]\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[[12, 5, -4, -8],\n [0, 12, -2, -2],\n [0, 0, -7, 7],\n [0, 0, 0, 4]]\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[[1, 2, -4, -1],\n [2, -12, 5, 4],\n [-4, 5, 8, 8],\n [-1, 4, 8, -10]]\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[[-4, 9, -6, 5],\n [9, 10, 8, 0],\n [-6, 8, -2, -8],\n [5, 0, -8, 11]]\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[[0, 2, -4, 10],\n [2, 7, 5, -2],\n [-4, 5, 6, -6],\n [10, -2, -6, -5]]\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[[-9, -7, -2, 8],\n [-7, 8, 0, -7],\n [-2, 0, -9, -8],\n [8, -7, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[7, -11, 7, 7],\n [0, -12, -5, -4],\n [0, 0, -8, 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[[3, -10, -6, 2],\n [-10, 5, 2, -6],\n [-6, 2, -4, 6],\n [2, -6, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[11, 6, 2, -9],\n [0, -12, -10, 2],\n [0, 0, 10, -10],\n [0, 0, 0, -9]]\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[[-11, 10, -1, 0],\n [10, 0, -3, -1],\n [-1, -3, -6, 11],\n [0, -1, 11, -12]]\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[[-6, 4, 6, 8],\n [4, 9, 6, 8],\n [6, 6, 4, -2],\n [8, 8, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[6, -4, 2, 0],\n [-4, -2, -9, -3],\n [2, -9, 3, 5],\n [0, -3, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[11, -2, 0, 2],\n [-2, -3, 6, -3],\n [0, 6, -2, -2],\n [2, -3, -2, -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[[-2, -2, -6, -9],\n [0, 9, 6, 5],\n [0, 0, 7, -5],\n [0, 0, 0, 7]]\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[[-8, -10, 10, 8],\n [-10, -9, 6, -6],\n [10, 6, -12, -4],\n [8, -6, -4, -12]]\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[[-12, 4, 0, -4],\n [0, -5, 1, -11],\n [0, 0, 8, -11],\n [0, 0, 0, 7]]\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, 6, 6, 1],\n [6, -11, -9, 3],\n [6, -9, 10, -9],\n [1, 3, -9, 7]]\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[[-12, 5, 8, -3],\n [0, 7, 11, 3],\n [0, 0, 3, -1],\n [0, 0, 0, 10]]\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[[3, 12, -1, 10],\n [0, -12, -12, -2],\n [0, 0, -2, 6],\n [0, 0, 0, 3]]\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[[8, 1, -6, 11],\n [0, 11, 6, -10],\n [0, 0, 9, 1],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[4, 10, 2, 2],\n [10, 10, 2, -1],\n [2, 2, -7, -6],\n [2, -1, -6, 5]]\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, 5, 5, 7],\n [0, -9, -12, 12],\n [0, 0, -7, 11],\n [0, 0, 0, -3]]\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[[7, 10, -9, -11],\n [0, -5, -10, -9],\n [0, 0, -6, 12],\n [0, 0, 0, 8]]\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[[12, 7, 4, 11],\n [0, 3, 4, -1],\n [0, 0, -3, -6],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-2, 12, -9, 8],\n [0, -8, 0, 9],\n [0, 0, -7, 6],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[6, 7, 11, 9],\n [0, -6, -1, 5],\n [0, 0, -6, -7],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-9, 8, 4, 5],\n [8, -11, -4, -4],\n [4, -4, -4, -8],\n [5, -4, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[11, 4, -1, -2],\n [0, -8, 1, -1],\n [0, 0, 6, -6],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-3, 1, 3, 10],\n [1, 0, 8, -2],\n [3, 8, -2, 0],\n [10, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[5, 10, 4, -12],\n [10, 0, -7, 2],\n [4, -7, -4, 5],\n [-12, 2, 5, 4]]\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[[6, -3, -11, 9],\n [0, -3, 0, -5],\n [0, 0, 8, 1],\n [0, 0, 0, -8]]\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[[-5, 4, 2, 7],\n [4, 1, 8, 0],\n [2, 8, -4, 1],\n [7, 0, 1, -6]]\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[[9, 9, -10, -12],\n [0, -7, -5, -7],\n [0, 0, -12, -3],\n [0, 0, 0, 10]]\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[[-3, -6, -5, 8],\n [-6, 10, -4, -6],\n [-5, -4, -3, 5],\n [8, -6, 5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[3, 4, 11, 3],\n [0, -10, -11, 8],\n [0, 0, 3, -6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[4, 10, 2, -2],\n [10, -11, 10, -8],\n [2, 10, 0, -1],\n [-2, -8, -1, 7]]\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[[-6, -4, -2, -2],\n [-4, 8, 7, -3],\n [-2, 7, 12, -9],\n [-2, -3, -9, -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 largest eigenvalue by absolute value:\n[[-7, 2, 2, 2],\n [2, 1, -8, -10],\n [2, -8, -12, -2],\n [2, -10, -2, 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[[3, -6, -8, -4],\n [-6, -2, 0, -2],\n [-8, 0, -12, 0],\n [-4, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[5, -7, 4, -4],\n [-7, 4, -9, -6],\n [4, -9, -6, 0],\n [-4, -6, 0, 4]]\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[[-1, -8, -2, 2],\n [-8, -2, 1, -6],\n [-2, 1, -1, 4],\n [2, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-1, -2, -4, 0],\n [-2, -10, -7, 8],\n [-4, -7, 9, 2],\n [0, 8, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[9, 2, 4, 0],\n [2, 2, 5, -2],\n [4, 5, 8, 6],\n [0, -2, 6, -5]]\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[[3, -2, -2, 6],\n [-2, -8, 2, 1],\n [-2, 2, 1, 0],\n [6, 1, 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 sum of absolute values of all eigenvalues:\n[[-4, 11, 0, -4],\n [11, -12, -8, 2],\n [0, -8, 3, 8],\n [-4, 2, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, 6, 2, 2],\n [6, 7, -1, 8],\n [2, -1, 11, 4],\n [2, 8, 4, 10]]\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, -4, 8, -3],\n [-4, 11, -8, 2],\n [8, -8, -3, 0],\n [-3, 2, 0, 11]]\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[[-1, 4, -10, -10],\n [0, -8, -11, -6],\n [0, 0, -2, 11],\n [0, 0, 0, 9]]\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[[3, -11, 3, -2],\n [0, 8, -11, 12],\n [0, 0, -10, -12],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[9, 5, -6, -7],\n [5, 10, -3, -4],\n [-6, -3, 0, 6],\n [-7, -4, 6, 7]]\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[[-5, -10, -4, 4],\n [-10, -6, 0, 0],\n [-4, 0, 10, -9],\n [4, 0, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-8, 12, -1, -10],\n [0, -11, 10, -3],\n [0, 0, -2, 9],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[4, -1, 1, -4],\n [-1, 7, 5, -2],\n [1, 5, 11, 2],\n [-4, -2, 2, 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[[0, -5, 10, 8],\n [0, -6, -1, 0],\n [0, 0, -4, 0],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[3, 2, 7, 7],\n [2, 7, -2, 0],\n [7, -2, 1, -6],\n [7, 0, -6, 5]]\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[[-8, -2, -8, -10],\n [-2, -8, 8, -4],\n [-8, 8, -3, -2],\n [-10, -4, -2, -12]]\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[[-3, 4, -10, 0],\n [4, -2, 0, 0],\n [-10, 0, 3, 6],\n [0, 0, 6, 9]]\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[[1, 2, -8, 7],\n [2, 4, -2, 0],\n [-8, -2, -7, -6],\n [7, 0, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-11, 5, 1, 7],\n [0, 0, 11, 4],\n [0, 0, -3, -11],\n [0, 0, 0, -6]]\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[[1, -9, -11, 11],\n [0, -3, -7, -8],\n [0, 0, 7, 11],\n [0, 0, 0, -1]]\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[[-4, 3, 5, -1],\n [0, -9, 4, 6],\n [0, 0, -8, 12],\n [0, 0, 0, -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[[7, 8, 5, 0],\n [8, 1, 2, 3],\n [5, 2, -9, -4],\n [0, 3, -4, 6]]\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, 12, -4, -5],\n [12, -5, 0, 2],\n [-4, 0, 8, -2],\n [-5, 2, -2, -8]]\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[[3, 0, 0, 2],\n [0, 11, 1, 0],\n [0, 1, -9, 2],\n [2, 0, 2, -4]]\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[[-8, 1, -9, -9],\n [0, -3, -6, 6],\n [0, 0, 10, 11],\n [0, 0, 0, -7]]\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[[1, -2, 10, 4],\n [-2, 10, 2, 5],\n [10, 2, 12, -6],\n [4, 5, -6, -6]]\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, 0, 2, -11],\n [0, 7, 3, 8],\n [2, 3, 3, 1],\n [-11, 8, 1, -8]]\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[[-11, 2, 9, -4],\n [0, 6, -10, -12],\n [0, 0, 0, 8],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-4, -9, 3, 0],\n [-9, 11, -8, -7],\n [3, -8, -1, 4],\n [0, -7, 4, 6]]\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[[11, 1, 8, -8],\n [1, 6, -12, 2],\n [8, -12, 8, -6],\n [-8, 2, -6, -9]]\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[[-12, 1, 8, -1],\n [1, 0, 6, 8],\n [8, 6, 7, 1],\n [-1, 8, 1, -2]]\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, -5, -2, 0],\n [-5, 10, 7, -2],\n [-2, 7, -1, 10],\n [0, -2, 10, 5]]\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[[-9, 0, -10, 7],\n [0, 11, -6, -8],\n [0, 0, -7, -4],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-2, -4, -4, 2],\n [-4, 4, 6, -4],\n [-4, 6, 3, 0],\n [2, -4, 0, -9]]\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[[-5, -1, -1, 4],\n [-1, 10, 4, 8],\n [-1, 4, 8, -5],\n [4, 8, -5, -3]]\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[[-5, -5, 9, 9],\n [0, 8, 3, -10],\n [0, 0, 1, -8],\n [0, 0, 0, 8]]\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[[0, 1, -10, 2],\n [1, -1, 2, -7],\n [-10, 2, -8, 0],\n [2, -7, 0, 3]]\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, 2, 0, 0],\n [2, 2, -1, 1],\n [0, -1, 3, 1],\n [0, 1, 1, 11]]\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[[10, 4, 0, -12],\n [4, -11, -7, -8],\n [0, -7, -4, 4],\n [-12, -8, 4, -4]]\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[[-6, -6, 3, 1],\n [-6, -12, -2, 6],\n [3, -2, -8, 6],\n [1, 6, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[5, 8, -12, -1],\n [0, 10, 10, -7],\n [0, 0, -8, -6],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-11, 0, 3, -8],\n [0, -10, -5, -2],\n [3, -5, -9, 7],\n [-8, -2, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[2, 6, 0, -6],\n [6, -9, 4, 1],\n [0, 4, 4, 4],\n [-6, 1, 4, -1]]\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[[0, 0, 0, 6],\n [0, -6, -4, -8],\n [0, -4, -1, -8],\n [6, -8, -8, -7]]\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[[-1, -8, -1, -1],\n [0, -11, -4, -5],\n [0, 0, -5, -10],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[8, 6, 2, -6],\n [6, 11, -3, -1],\n [2, -3, -4, 8],\n [-6, -1, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-2, 3, 1, -4],\n [3, 7, -5, 0],\n [1, -5, 9, -2],\n [-4, 0, -2, 3]]\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[[3, 8, 1, 4],\n [8, 8, 6, -2],\n [1, 6, -1, 2],\n [4, -2, 2, 6]]\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[[11, -1, 0, 4],\n [-1, 4, -6, 0],\n [0, -6, 6, 4],\n [4, 0, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-4, 2, 0, 7],\n [2, -11, -2, 1],\n [0, -2, -6, -9],\n [7, 1, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[11, 4, 8, -8],\n [4, -11, -6, 5],\n [8, -6, -4, -4],\n [-8, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-6, 2, 4, -9],\n [0, 8, 7, 3],\n [0, 0, 8, -3],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[5, 0, 3, -4],\n [0, -9, -2, -3],\n [3, -2, -4, 1],\n [-4, -3, 1, -3]]\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[[-2, 7, 11, 6],\n [0, -8, 0, 10],\n [0, 0, -3, -2],\n [0, 0, 0, 12]]\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, -6, 7, -6],\n [-6, -9, 1, 0],\n [7, 1, 5, 0],\n [-6, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[4, 7, -6, 4],\n [7, -11, 0, 4],\n [-6, 0, -2, -6],\n [4, 4, -6, -11]]\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, -5, -4, -10],\n [0, -2, -4, 0],\n [0, 0, -9, -11],\n [0, 0, 0, 4]]\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[[7, -2, -2, -6],\n [0, 0, 12, -1],\n [0, 0, -7, 3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
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