messages listlengths 1 1 | ground_truth stringclasses 65
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-2, -11, 10, -9],\n [0, -12, -12, 11],\n [0, 0, 6, 4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[5, -1, -11, 0],\n [0, -8, -12, -5],\n [0, 0, -10, 9],\n [0, 0, 0, 1]]\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[[0, -6, -1, 3],\n [-6, 1, 8, -1],\n [-1, 8, 12, 6],\n [3, -1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-4, 3, -2, -7],\n [0, -9, -5, 5],\n [0, 0, 7, -7],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-2, 0, 2, -4],\n [0, -6, 2, 2],\n [2, 2, 0, 8],\n [-4, 2, 8, -11]]\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, 1, -6, 4],\n [1, 4, 1, 1],\n [-6, 1, -9, -2],\n [4, 1, -2, 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[[-12, -2, -8, 0],\n [-2, 11, 2, -4],\n [-8, 2, 4, -1],\n [0, -4, -1, 10]]\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[[8, -8, -2, 7],\n [0, -2, -3, 11],\n [0, 0, -2, 11],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-11, 10, 4, -2],\n [10, -8, 1, -8],\n [4, 1, 12, 3],\n [-2, -8, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-2, -1, 5, 2],\n [0, 2, -7, 12],\n [0, 0, -7, 3],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[2, -2, 4, 6],\n [-2, -9, -10, 8],\n [4, -10, 6, -9],\n [6, 8, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-3, -9, -8, -1],\n [0, 2, 7, -12],\n [0, 0, -8, 10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[12, -8, -10, -1],\n [0, 0, 10, 6],\n [0, 0, -11, -9],\n [0, 0, 0, -4]]\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[[-12, -6, 5, -3],\n [-6, -3, -6, -1],\n [5, -6, 7, 8],\n [-3, -1, 8, -3]]\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[[6, -4, 8, 0],\n [-4, 12, -6, 1],\n [8, -6, 11, -4],\n [0, 1, -4, 11]]\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[[-8, 0, 8, 4],\n [0, 0, 1, -1],\n [8, 1, 8, -3],\n [4, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[0, -9, 6, -2],\n [0, -2, -8, 4],\n [0, 0, -1, -1],\n [0, 0, 0, 12]]\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[[-1, 4, -1, 2],\n [4, -12, -8, 4],\n [-1, -8, 11, 10],\n [2, 4, 10, -7]]\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[[-6, -1, 0, -4],\n [-1, 9, 6, 0],\n [0, 6, -9, -2],\n [-4, 0, -2, 12]]\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[[-9, -5, 11, -10],\n [0, -5, -8, 10],\n [0, 0, -4, -4],\n [0, 0, 0, 2]]\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[[8, -2, 4, -7],\n [-2, 7, -6, 4],\n [4, -6, -1, -1],\n [-7, 4, -1, 4]]\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[[8, 0, 4, -3],\n [0, -4, 8, -2],\n [4, 8, -9, 0],\n [-3, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-11, -10, 0, -4],\n [-10, 2, 3, 6],\n [0, 3, 7, 2],\n [-4, 6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[9, 0, -6, -9],\n [0, -5, -12, -11],\n [0, 0, -4, -2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[3, -3, 10, 4],\n [-3, 4, 0, -6],\n [10, 0, -7, 0],\n [4, -6, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[1, 10, -3, 1],\n [10, -2, 4, -3],\n [-3, 4, -11, 1],\n [1, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-10, -2, 8, 0],\n [-2, -10, 3, -9],\n [8, 3, 9, -1],\n [0, -9, -1, 0]]\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, 2, 10, 8],\n [2, 3, 2, 1],\n [10, 2, 3, -6],\n [8, 1, -6, 1]]\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[[7, 8, -2, -2],\n [8, 4, -2, -1],\n [-2, -2, -7, 0],\n [-2, -1, 0, -12]]\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[[-12, -2, 0, 0],\n [-2, 3, -3, 7],\n [0, -3, -7, 0],\n [0, 7, 0, -1]]\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[[-5, 2, -8, 4],\n [2, 3, -10, -2],\n [-8, -10, -4, -4],\n [4, -2, -4, -7]]\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[[-9, -7, 8, -7],\n [0, 8, 3, 6],\n [0, 0, -10, 4],\n [0, 0, 0, 5]]\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, 2, -3, -4],\n [2, -3, 2, 1],\n [-3, 2, 11, 0],\n [-4, 1, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-6, -6, -2, -2],\n [-6, 1, -7, -1],\n [-2, -7, -5, 11],\n [-2, -1, 11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-12, 12, -10, 1],\n [0, -2, -6, 0],\n [0, 0, 2, 0],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-12, 2, 2, 2],\n [2, -6, 0, 6],\n [2, 0, 11, 0],\n [2, 6, 0, 3]]\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, 2, 2, -2],\n [2, -7, 8, -4],\n [2, 8, 9, -2],\n [-2, -4, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[11, 9, -3, 0],\n [0, -1, 5, 9],\n [0, 0, 12, 11],\n [0, 0, 0, -1]]\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[[11, 12, 2, -12],\n [0, -7, 10, 7],\n [0, 0, 6, -11],\n [0, 0, 0, 3]]\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[[-9, 2, -9, 2],\n [2, 9, -1, -4],\n [-9, -1, -7, -6],\n [2, -4, -6, -2]]\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, 3, 2, -12],\n [0, -6, -12, 2],\n [0, 0, -3, 3],\n [0, 0, 0, 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[[-9, 11, 4, 9],\n [0, -11, 5, 0],\n [0, 0, 5, -11],\n [0, 0, 0, -9]]\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[[-12, 7, 4, -1],\n [7, -7, -1, -11],\n [4, -1, 5, -2],\n [-1, -11, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-8, 0, -2, 4],\n [0, 9, -2, 8],\n [-2, -2, -7, 0],\n [4, 8, 0, -8]]\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[[-3, 2, 2, 1],\n [2, 0, 5, -4],\n [2, 5, -6, -2],\n [1, -4, -2, 12]]\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[[0, -8, -8, -7],\n [0, -8, -5, 0],\n [0, 0, 8, 3],\n [0, 0, 0, 3]]\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[[-3, 7, -4, 4],\n [7, -4, 0, -4],\n [-4, 0, 8, 2],\n [4, -4, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-2, 4, -5, -2],\n [4, 7, -4, 2],\n [-5, -4, -1, 0],\n [-2, 2, 0, -12]]\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[[8, 6, 1, 0],\n [6, -1, -2, 2],\n [1, -2, -6, -5],\n [0, 2, -5, -1]]\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[[-6, 10, 2, 4],\n [10, -4, 2, -4],\n [2, 2, -5, -6],\n [4, -4, -6, 3]]\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[[-10, -5, -12, -1],\n [0, -3, -3, 2],\n [0, 0, -4, 2],\n [0, 0, 0, 6]]\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[[-7, -6, -1, -6],\n [-6, 6, -4, -8],\n [-1, -4, 3, -6],\n [-6, -8, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-3, 9, 10, 5],\n [0, 9, -12, -10],\n [0, 0, 4, 1],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-2, -5, 9, 1],\n [-5, 2, 8, 4],\n [9, 8, -2, 7],\n [1, 4, 7, 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[[4, 2, -2, 1],\n [2, 0, 9, -4],\n [-2, 9, 12, 4],\n [1, -4, 4, -11]]\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[[-7, 4, -6, 12],\n [0, -5, 0, 5],\n [0, 0, 5, -8],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-6, 11, -12, 3],\n [0, -12, 6, 7],\n [0, 0, -4, -10],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, -6, -9, 5],\n [-6, 8, -7, -6],\n [-9, -7, 1, 0],\n [5, -6, 0, 10]]\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[[5, 4, 0, -6],\n [4, -10, -6, -2],\n [0, -6, 7, -2],\n [-6, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-1, 6, 2, 2],\n [6, 2, 2, -4],\n [2, 2, -12, 4],\n [2, -4, 4, -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[[7, -10, -12, -6],\n [0, 2, 10, 6],\n [0, 0, -7, -3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[1, -4, 1, 0],\n [-4, 4, 8, -4],\n [1, 8, -7, 0],\n [0, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-5, -2, -4, -5],\n [-2, -4, 7, 2],\n [-4, 7, -5, 0],\n [-5, 2, 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[[-8, -2, 4, -2],\n [-2, -5, -7, -4],\n [4, -7, 11, -2],\n [-2, -4, -2, 8]]\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[[-4, 4, 3, -3],\n [4, -12, -2, -4],\n [3, -2, -4, -8],\n [-3, -4, -8, -6]]\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[[10, -1, -2, 0],\n [-1, -10, 4, 2],\n [-2, 4, 12, 2],\n [0, 2, 2, -5]]\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[[1, 4, 7, 1],\n [0, 11, -2, 8],\n [0, 0, -1, 7],\n [0, 0, 0, 8]]\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, 0, 10, -5],\n [0, -9, -10, -1],\n [0, 0, 6, 6],\n [0, 0, 0, 12]]\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[[11, 7, -5, -2],\n [0, 11, -5, 9],\n [0, 0, 10, 6],\n [0, 0, 0, -3]]\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[[2, -2, 0, -2],\n [-2, -7, -3, -2],\n [0, -3, 3, 10],\n [-2, -2, 10, 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[[5, 2, -8, 6],\n [2, -11, 5, -5],\n [-8, 5, 7, 10],\n [6, -5, 10, -7]]\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[[-9, 0, -4, 6],\n [0, 11, 8, -4],\n [-4, 8, 1, -2],\n [6, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[1, 6, 6, -10],\n [6, -11, -6, -10],\n [6, -6, -12, 10],\n [-10, -10, 10, -6]]\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[[9, -6, -6, 6],\n [0, -12, -8, 8],\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": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, -4, 2, -4],\n [0, -10, -1, -7],\n [0, 0, 0, 9],\n [0, 0, 0, -6]]\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[[-7, 6, -11, 2],\n [0, -10, -7, 9],\n [0, 0, -7, 1],\n [0, 0, 0, 0]]\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, -2, 0],\n [0, -11, -2, 2],\n [-2, -2, -9, -4],\n [0, 2, -4, 4]]\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[[-12, 8, -4, 8],\n [8, -1, 2, 4],\n [-4, 2, 0, 3],\n [8, 4, 3, -9]]\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[[12, 0, 8, 6],\n [0, 2, -6, 0],\n [8, -6, 7, 2],\n [6, 0, 2, 8]]\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[[-5, 6, 11, -6],\n [6, 3, -10, -11],\n [11, -10, 0, 6],\n [-6, -11, 6, 4]]\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[[-4, -6, 2, -4],\n [-6, -2, -8, -6],\n [2, -8, 7, -2],\n [-4, -6, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[0, 6, -5, -5],\n [6, 8, -2, -6],\n [-5, -2, 2, -7],\n [-5, -6, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[9, -2, 4, -12],\n [0, -8, 6, -8],\n [0, 0, 11, -6],\n [0, 0, 0, 2]]\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[[-7, -8, -6, 5],\n [-8, 11, -2, 0],\n [-6, -2, -12, 0],\n [5, 0, 0, 11]]\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[[8, -2, -2, 4],\n [-2, 12, -1, -8],\n [-2, -1, -3, -4],\n [4, -8, -4, 9]]\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[[11, -7, 7, 3],\n [0, -12, 6, 2],\n [0, 0, -3, 5],\n [0, 0, 0, -3]]\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[[8, -5, 9, -10],\n [-5, -9, 8, 0],\n [9, 8, 10, 1],\n [-10, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[0, 2, 6, -4],\n [2, -12, 9, 0],\n [6, 9, -7, -2],\n [-4, 0, -2, 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[[-5, 10, 0, -6],\n [10, 1, -10, -6],\n [0, -10, -12, 0],\n [-6, -6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-5, 5, 4, -7],\n [5, 4, 4, 0],\n [4, 4, 5, 4],\n [-7, 0, 4, -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[[-7, -12, 5, 9],\n [-12, 12, 2, -2],\n [5, 2, 1, -2],\n [9, -2, -2, 5]]\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[[11, 9, -10, -1],\n [0, 3, -4, -12],\n [0, 0, -12, -4],\n [0, 0, 0, 12]]\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[[3, 2, 6, 0],\n [2, -9, 1, 8],\n [6, 1, -1, 4],\n [0, 8, 4, 5]]\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, 0, 0],\n [-2, 2, -2, -3],\n [0, -2, -4, 3],\n [0, -3, 3, 9]]\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[[-2, 4, -6, 4],\n [0, 2, -1, 0],\n [0, 0, -7, 5],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[12, 5, 2, -8],\n [5, 6, 2, -8],\n [2, 2, -6, 6],\n [-8, -8, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[3, 6, 12, -5],\n [0, 12, -5, -3],\n [0, 0, 4, 1],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-1, 11, -4, 8],\n [0, 8, -9, 2],\n [0, 0, 1, 3],\n [0, 0, 0, 1]]\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[[12, 2, -10, -1],\n [2, 3, -4, -5],\n [-10, -4, -4, -8],\n [-1, -5, -8, 12]]\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, -6, -2],\n [6, 1, 1, 2],\n [-6, 1, -8, -6],\n [-2, 2, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
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