messages listlengths 1 1 | ground_truth stringclasses 109 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[3, -11, 6, -13, -5],\n [-11, -13, -10, 3, -10],\n [6, -10, 1, 0, 5],\n [-13, 3, 0, 5, 0],\n [-5, -10, 5, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[5, -14, -12, -6, -11],\n [0, -1, 11, -8, -14],\n [0, 0, -6, -8, -4],\n [0, 0, 0, -7, -11],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[3, -8, 1, -15, -14],\n [0, -3, 4, 8, 6],\n [0, 0, -6, 14, 6],\n [0, 0, 0, 3, -13],\n [0, 0, 0, 0, -7]]\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[[-14, 12, 4, 4, 13],\n [12, 0, -6, -8, -2],\n [4, -6, 2, 3, 0],\n [4, -8, 3, -6, 14],\n [13, -2, 0, 14, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[2, -15, -11, 2, 9],\n [0, -14, 13, 9, -3],\n [0, 0, -13, -14, 0],\n [0, 0, 0, -5, 4],\n [0, 0, 0, 0, 15]]\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[[0, 0, 0, -1, -8],\n [0, -14, 6, 5, -4],\n [0, 6, 6, -4, -8],\n [-1, 5, -4, 6, -15],\n [-8, -4, -8, -15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[14, 6, -11, -4, 10],\n [6, 9, 12, 2, 13],\n [-11, 12, 1, 6, -5],\n [-4, 2, 6, 11, -4],\n [10, 13, -5, -4, 14]]\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[[-11, 8, -3, 2, 4],\n [8, -1, -4, 2, -4],\n [-3, -4, 13, -2, 0],\n [2, 2, -2, -14, -9],\n [4, -4, 0, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[6, 15, 11, -8, 3],\n [0, -3, 5, -6, -4],\n [0, 0, 10, 0, -4],\n [0, 0, 0, -6, -7],\n [0, 0, 0, 0, -9]]\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[[-12, 14, 1, -8, 7],\n [0, 7, 1, 15, -9],\n [0, 0, -13, 8, 12],\n [0, 0, 0, -8, 13],\n [0, 0, 0, 0, 3]]\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[[-5, 15, 9, -1, -15],\n [0, 3, -5, 15, 3],\n [0, 0, -6, 2, 5],\n [0, 0, 0, -6, -6],\n [0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-15, -5, 10, 10, 0],\n [-5, 13, -2, -2, -4],\n [10, -2, 8, 4, 12],\n [10, -2, 4, 15, 10],\n [0, -4, 12, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-2, -3, -10, 3, -6],\n [-3, 4, 2, -8, -2],\n [-10, 2, 7, -8, -1],\n [3, -8, -8, 0, -4],\n [-6, -2, -1, -4, 0]]\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[[-10, 9, 8, -6, -6],\n [9, -1, 4, 8, 14],\n [8, 4, -14, 8, -6],\n [-6, 8, 8, 7, 8],\n [-6, 14, -6, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-4, 6, 4, 6, -11],\n [6, -7, 2, 7, 4],\n [4, 2, 8, -4, -14],\n [6, 7, -4, -8, -3],\n [-11, 4, -14, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-12, 7, 3, -2, -11],\n [0, -9, -2, 13, -11],\n [0, 0, -14, -4, 2],\n [0, 0, 0, 7, 5],\n [0, 0, 0, 0, -15]]\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[[-12, 2, -6, 7, 10],\n [2, -8, -2, -3, -6],\n [-6, -2, 10, -6, -5],\n [7, -3, -6, -8, 6],\n [10, -6, -5, 6, -15]]\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[[-11, 11, 8, -12, 4],\n [11, 9, 0, -4, -6],\n [8, 0, 12, 10, 4],\n [-12, -4, 10, 11, 2],\n [4, -6, 4, 2, 5]]\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[[-2, -9, 2, -5, 8],\n [-9, 8, 2, 6, -2],\n [2, 2, 15, -5, -12],\n [-5, 6, -5, -12, 4],\n [8, -2, -12, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-3, -6, 10, 7, 3],\n [-6, 15, -2, -12, -1],\n [10, -2, -6, 5, -10],\n [7, -12, 5, 7, -8],\n [3, -1, -10, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[13, -1, -4, -6, 2],\n [-1, 10, 0, 4, 9],\n [-4, 0, -7, 2, 2],\n [-6, 4, 2, 5, -5],\n [2, 9, 2, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-13, 0, 10, -9, -7],\n [0, 15, 4, -2, -6],\n [0, 0, -3, -4, 9],\n [0, 0, 0, -2, -3],\n [0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[3, -10, -8, 3, 4],\n [-10, 1, -2, -2, 2],\n [-8, -2, 7, 13, 2],\n [3, -2, 13, 0, 0],\n [4, 2, 2, 0, 10]]\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[[-15, 7, -10, 15, -1],\n [0, 2, 2, -7, -4],\n [0, 0, -7, 3, 15],\n [0, 0, 0, 6, -2],\n [0, 0, 0, 0, 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[[7, -3, -1, -6, -4],\n [-3, 7, -6, -4, 7],\n [-1, -6, 1, -8, 6],\n [-6, -4, -8, -11, -11],\n [-4, 7, 6, -11, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-3, 2, -6, 0, -4],\n [2, -1, 2, -6, -1],\n [-6, 2, 2, 12, -6],\n [0, -6, 12, 7, -7],\n [-4, -1, -6, -7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-14, 9, 12, 8, 2],\n [9, -10, -13, 8, -10],\n [12, -13, -11, 12, 2],\n [8, 8, 12, 7, -4],\n [2, -10, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[8, 8, 4, 6, 2],\n [8, 1, -2, 0, 2],\n [4, -2, 6, -10, 2],\n [6, 0, -10, 10, 5],\n [2, 2, 2, 5, 11]]\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[[4, 6, 15, 11, -2],\n [6, 0, 4, -4, -8],\n [15, 4, 0, -13, -9],\n [11, -4, -13, 6, -4],\n [-2, -8, -9, -4, 5]]\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[[-10, -2, 6, 12, 7],\n [-2, -11, -9, -7, 6],\n [6, -9, 5, -2, 5],\n [12, -7, -2, -10, 0],\n [7, 6, 5, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-3, -3, -7, -4, -2],\n [-3, -9, -6, -2, 14],\n [-7, -6, -10, -2, -2],\n [-4, -2, -2, -15, 2],\n [-2, 14, -2, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 64 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[3, -4, 9, -7, -12],\n [-4, -12, -7, 6, -5],\n [9, -7, 10, -10, -2],\n [-7, 6, -10, 6, -8],\n [-12, -5, -2, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[2, -2, -2, 10, 2],\n [-2, 13, 2, 4, -1],\n [-2, 2, -14, 10, 2],\n [10, 4, 10, -12, -10],\n [2, -1, 2, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[2, 5, 13, -9, -13],\n [0, 5, 10, 13, -4],\n [0, 0, 13, 2, -14],\n [0, 0, 0, 15, 15],\n [0, 0, 0, 0, -8]]\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[[1, 8, -2, 6, -4],\n [8, 6, 0, 1, -7],\n [-2, 0, 12, 9, -2],\n [6, 1, 9, 14, -6],\n [-4, -7, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[9, -11, 4, 4, -1],\n [0, 4, 1, 10, -10],\n [0, 0, 12, -2, 9],\n [0, 0, 0, 14, 7],\n [0, 0, 0, 0, 14]]\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, -8, -3, -8, 8],\n [-8, -10, 3, -4, 8],\n [-3, 3, -11, 2, -12],\n [-8, -4, 2, 10, -5],\n [8, 8, -12, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[5, -5, 8, 4, 0],\n [-5, -14, -12, 2, 0],\n [8, -12, -8, -8, -3],\n [4, 2, -8, 0, 6],\n [0, 0, -3, 6, -11]]\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[[10, -6, 10, 8, 2],\n [-6, 7, -2, -3, 13],\n [10, -2, 7, 2, -6],\n [8, -3, 2, -15, -6],\n [2, 13, -6, -6, 1]]\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[[5, 1, 10, 13, 15],\n [0, 7, -4, 15, 0],\n [0, 0, 1, 6, -9],\n [0, 0, 0, -15, 13],\n [0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, -10, 0, -9, 0],\n [-10, 8, -2, 4, -1],\n [0, -2, -14, -2, -3],\n [-9, 4, -2, -11, 5],\n [0, -1, -3, 5, 10]]\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[[15, 4, 7, 6, -2],\n [4, 6, 1, -12, 10],\n [7, 1, 6, -2, -2],\n [6, -12, -2, 12, -10],\n [-2, 10, -2, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-5, -6, 6, -3, -6],\n [-6, -7, 6, 13, 2],\n [6, 6, -14, -8, 11],\n [-3, 13, -8, 9, -6],\n [-6, 2, 11, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-3, 8, 10, 5, 5],\n [8, 3, -6, 14, -1],\n [10, -6, -13, 14, -2],\n [5, 14, 14, 0, 1],\n [5, -1, -2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-2, 0, -9, 8, -4],\n [0, 11, 0, -4, -8],\n [-9, 0, -10, -8, 4],\n [8, -4, -8, 2, 5],\n [-4, -8, 4, 5, 4]]\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[[-2, -12, 2, 5, -4],\n [-12, -1, 5, -4, -8],\n [2, 5, -14, 3, 6],\n [5, -4, 3, 11, 3],\n [-4, -8, 6, 3, -4]]\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[[9, -1, -4, 11, -15],\n [0, 13, -13, 1, 13],\n [0, 0, 13, -14, -11],\n [0, 0, 0, 4, 10],\n [0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[11, 6, 6, -1, -1],\n [6, -14, 6, -8, 3],\n [6, 6, -14, -1, 2],\n [-1, -8, -1, -12, -2],\n [-1, 3, 2, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 70 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[0, 6, -1, 5, -2],\n [6, -13, -4, 0, 1],\n [-1, -4, 7, 0, 12],\n [5, 0, 0, 5, 4],\n [-2, 1, 12, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-15, 11, 3, -2, -2],\n [11, -1, 5, -9, 4],\n [3, 5, 12, 5, 2],\n [-2, -9, 5, 14, 3],\n [-2, 4, 2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[15, -2, -14, 4, -1],\n [0, 3, 10, -4, -12],\n [0, 0, 4, -8, -12],\n [0, 0, 0, 10, -1],\n [0, 0, 0, 0, 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[[-14, -10, -12, -5, -6],\n [-10, -11, 8, -12, 6],\n [-12, 8, -4, -10, -6],\n [-5, -12, -10, -15, -1],\n [-6, 6, -6, -1, -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 sum of absolute values of all eigenvalues:\n[[-7, 14, -6, 1, -8],\n [14, -1, -8, 6, -4],\n [-6, -8, 7, -12, -2],\n [1, 6, -12, 7, 4],\n [-8, -4, -2, 4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-11, 0, -1, 0, 1],\n [0, 6, 0, 0, 2],\n [-1, 0, 13, 11, -3],\n [0, 0, 11, -11, 7],\n [1, 2, -3, 7, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-15, -2, 1, 1, 4],\n [-2, 12, 5, -14, -4],\n [1, 5, 7, 6, 1],\n [1, -14, 6, 14, -14],\n [4, -4, 1, -14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-4, 6, -3, 12, 2],\n [6, 10, 6, 0, 12],\n [-3, 6, 14, 0, 1],\n [12, 0, 0, 7, 2],\n [2, 12, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-9, -7, -6, 7, 10],\n [0, 2, -3, 2, 4],\n [0, 0, 9, -7, -12],\n [0, 0, 0, -1, 12],\n [0, 0, 0, 0, 6]]\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[[-6, 3, -7, -6, -6],\n [3, -6, -1, -11, -2],\n [-7, -1, -12, -3, 2],\n [-6, -11, -3, 13, 2],\n [-6, -2, 2, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, -10, 7, -10, -9],\n [-10, -11, -2, 12, -4],\n [7, -2, -12, 5, 6],\n [-10, 12, 5, -13, 1],\n [-9, -4, 6, 1, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-7, 3, 5, 6, -4],\n [0, 11, -12, 11, 6],\n [0, 0, 10, -1, 14],\n [0, 0, 0, 14, -4],\n [0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-10, -2, 8, 6, -7],\n [-2, -15, -10, -4, 2],\n [8, -10, 11, 4, -9],\n [6, -4, 4, 9, -1],\n [-7, 2, -9, -1, -7]]\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[[14, 9, -7, -1, -14],\n [0, -12, 6, -12, 2],\n [0, 0, -14, -12, -14],\n [0, 0, 0, 13, 3],\n [0, 0, 0, 0, -4]]\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[[-12, 5, -12, 14, -5],\n [0, 7, 0, 13, 4],\n [0, 0, 6, 1, -14],\n [0, 0, 0, 12, -10],\n [0, 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[[2, 2, 4, -2, 9],\n [2, 15, -8, -10, -3],\n [4, -8, -8, 2, 8],\n [-2, -10, 2, 8, 2],\n [9, -3, 8, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-8, -2, 10, 14, 7],\n [-2, 10, -6, 0, -11],\n [10, -6, 14, -4, 6],\n [14, 0, -4, -2, 4],\n [7, -11, 6, 4, 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[[7, -12, -11, -8, 10],\n [0, -9, -5, -11, -6],\n [0, 0, -3, 9, 3],\n [0, 0, 0, -6, -4],\n [0, 0, 0, 0, 4]]\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[[-6, -9, 9, -6, 13],\n [0, 13, -8, -15, -8],\n [0, 0, -5, -3, 9],\n [0, 0, 0, 4, 5],\n [0, 0, 0, 0, -11]]\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[[-12, 10, 2, 1, 0],\n [10, 15, 1, 2, -6],\n [2, 1, -8, 4, 4],\n [1, 2, 4, 11, 4],\n [0, -6, 4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-11, 8, 8, 2, 10],\n [8, 0, -5, 2, -2],\n [8, -5, -13, 8, 7],\n [2, 2, 8, -4, -2],\n [10, -2, 7, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-13, -6, 6, -2, 0],\n [-6, 7, -2, -10, 0],\n [6, -2, -7, -8, -4],\n [-2, -10, -8, 8, 6],\n [0, 0, -4, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-11, 6, -12, -5, 0],\n [6, -7, -8, -3, -3],\n [-12, -8, -8, -3, 4],\n [-5, -3, -3, -4, -2],\n [0, -3, 4, -2, 14]]\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[[-9, -15, -9, 6, -4],\n [0, -2, 7, 8, 2],\n [0, 0, -13, 8, 8],\n [0, 0, 0, 8, 8],\n [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 largest eigenvalue by absolute value:\n[[1, 8, -5, -15, 8],\n [0, -12, 6, -14, 10],\n [0, 0, -14, -2, 9],\n [0, 0, 0, -14, -5],\n [0, 0, 0, 0, 8]]\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[[-1, 3, -1, 8, -6],\n [3, -11, -12, 10, -2],\n [-1, -12, -2, -12, -5],\n [8, 10, -12, 8, -10],\n [-6, -2, -5, -10, -15]]\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[[-13, -6, 4, 10, -8],\n [-6, -15, -8, 6, 10],\n [4, -8, -11, -9, -9],\n [10, 6, -9, 12, 6],\n [-8, 10, -9, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 97 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-9, 10, 6, -2, 1],\n [10, -10, 1, -8, 2],\n [6, 1, 8, 6, -4],\n [-2, -8, 6, 15, -7],\n [1, 2, -4, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, -5, -10, 9, 8],\n [-5, 15, -6, 8, 7],\n [-10, -6, 3, 2, -4],\n [9, 8, 2, -2, 6],\n [8, 7, -4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[2, 0, 9, 4, -13],\n [0, 5, 8, 1, 11],\n [0, 0, -6, -6, -7],\n [0, 0, 0, 4, -14],\n [0, 0, 0, 0, 9]]\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[[4, 7, 6, -2, 0],\n [0, -15, 2, 7, 13],\n [0, 0, 11, 10, -10],\n [0, 0, 0, -1, -12],\n [0, 0, 0, 0, 4]]\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[[3, 10, -9, -5, 4],\n [0, -2, 9, -14, -11],\n [0, 0, -4, 9, 11],\n [0, 0, 0, -8, -10],\n [0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[9, 2, -10, 13, 2],\n [2, 8, -2, -11, 2],\n [-10, -2, -6, -4, 6],\n [13, -11, -4, -9, -1],\n [2, 2, 6, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[8, -5, -12, 0, -4],\n [-5, -6, -4, 2, -10],\n [-12, -4, 5, -2, 2],\n [0, 2, -2, 15, 2],\n [-4, -10, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[0, 2, -2, 5, 0],\n [2, 14, -4, 8, 0],\n [-2, -4, -13, -12, 7],\n [5, 8, -12, -11, 0],\n [0, 0, 7, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[3, 6, -5, -4, 14],\n [6, -9, -6, -2, 2],\n [-5, -6, -1, -7, 8],\n [-4, -2, -7, -14, -8],\n [14, 2, 8, -8, 2]]\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[[6, -7, -12, -2, -12],\n [-7, 11, -8, 1, -4],\n [-12, -8, -14, -3, 2],\n [-2, 1, -3, -1, -4],\n [-12, -4, 2, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[0, 8, 4, 0, 11],\n [8, -2, 8, 5, 2],\n [4, 8, 9, -8, -4],\n [0, 5, -8, 13, -2],\n [11, 2, -4, -2, 15]]\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[[-5, -11, -10, 4, 15],\n [0, -7, -9, 14, -13],\n [0, 0, 1, 6, 3],\n [0, 0, 0, -3, -1],\n [0, 0, 0, 0, -13]]\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[[3, 1, 5, 11, -9],\n [0, -13, 14, -14, -5],\n [0, 0, 0, -2, -3],\n [0, 0, 0, -1, 10],\n [0, 0, 0, 0, 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[[-12, -3, 11, 13, -6],\n [0, 9, 5, 1, 1],\n [0, 0, -3, -7, 11],\n [0, 0, 0, 8, 6],\n [0, 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[[11, 4, 0, -2, -2],\n [4, 11, 4, 0, -10],\n [0, 4, -8, -10, 13],\n [-2, 0, -10, 3, 4],\n [-2, -10, 13, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-4, 13, 0, 2, 12],\n [13, -4, -2, 1, -8],\n [0, -2, 4, -6, 2],\n [2, 1, -6, -3, -8],\n [12, -8, 2, -8, -6]]\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[[14, -10, 8, 0, -12],\n [-10, 12, -6, -2, 2],\n [8, -6, -7, -3, 6],\n [0, -2, -3, -15, -8],\n [-12, 2, 6, -8, -11]]\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[[14, 7, 10, -6, -2],\n [7, -11, 10, 8, 4],\n [10, 10, 5, 0, -6],\n [-6, 8, 0, -9, -13],\n [-2, 4, -6, -13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-8, -12, 2, 2, 4],\n [-12, 6, 4, -1, 6],\n [2, 4, 12, 2, 5],\n [2, -1, 2, 12, 0],\n [4, 6, 5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-10, 2, 6, 9, -1],\n [0, 8, 15, -2, -11],\n [0, 0, -5, -12, 1],\n [0, 0, 0, -1, 10],\n [0, 0, 0, 0, 2]]\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[[11, 4, -12, 3, 9],\n [0, -2, -7, -11, -2],\n [0, 0, -6, -10, 15],\n [0, 0, 0, 4, -15],\n [0, 0, 0, 0, -7]]\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, -14, -4, 13, 6],\n [0, 8, 8, 14, 5],\n [0, 0, 1, 7, 7],\n [0, 0, 0, -12, 1],\n [0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[1, -1, -10, -3, -8],\n [-1, 12, 6, -2, -10],\n [-10, 6, -4, -8, 7],\n [-3, -2, -8, -9, -3],\n [-8, -10, 7, -3, -5]]\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[[8, -10, 4, 12, 6],\n [-10, -9, -5, 0, 2],\n [4, -5, -8, -12, -1],\n [12, 0, -12, -1, 3],\n [6, 2, -1, 3, 11]]\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[[6, 6, -8, 14, -14],\n [6, -5, 11, 4, 8],\n [-8, 11, 12, 12, 4],\n [14, 4, 12, 12, -8],\n [-14, 8, 4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 92 | MATH |
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