messages listlengths 1 1 | ground_truth stringclasses 65 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[1, 3, 1, 3],\n [0, 4, 2, 12],\n [0, 0, -2, 1],\n [0, 0, 0, 8]]\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[[12, 2, -8, 5],\n [2, -12, 2, -4],\n [-8, 2, 12, 4],\n [5, -4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[8, 1, -6, 6],\n [1, 2, -6, -4],\n [-6, -6, 9, -2],\n [6, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-7, -4, 0, 0],\n [-4, 6, 7, -3],\n [0, 7, 6, 2],\n [0, -3, 2, 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[[5, 0, 12, -5],\n [0, -4, -2, 1],\n [12, -2, -7, 6],\n [-5, 1, 6, 7]]\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, -4, 2],\n [-2, -2, -4, -11],\n [-4, -4, -1, 3],\n [2, -11, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[3, 6, 6, 4],\n [0, 10, 0, -1],\n [0, 0, -11, 8],\n [0, 0, 0, 2]]\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, 3, 1, -2],\n [3, -11, -6, 5],\n [1, -6, 9, 8],\n [-2, 5, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[10, 8, -11, -2],\n [8, 7, -3, -7],\n [-11, -3, -4, -10],\n [-2, -7, -10, -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[[-2, -9, 2, -6],\n [-9, 9, 2, 4],\n [2, 2, -12, 0],\n [-6, 4, 0, 8]]\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[[10, -8, 4, 4],\n [-8, 10, -7, 0],\n [4, -7, 12, -7],\n [4, 0, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-6, 10, -1, 9],\n [10, 12, -2, 4],\n [-1, -2, -7, -6],\n [9, 4, -6, -12]]\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[[12, 12, 11, -3],\n [0, -11, -9, -9],\n [0, 0, 11, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[7, -3, -8, 12],\n [0, 6, -3, 11],\n [0, 0, -7, 3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[10, -8, -6, 4],\n [-8, 11, -6, 1],\n [-6, -6, 11, 0],\n [4, 1, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-7, -11, -1, 12],\n [0, -6, 2, -3],\n [0, 0, -12, -10],\n [0, 0, 0, 4]]\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[[10, 0, -10, 9],\n [0, -2, -2, 0],\n [-10, -2, -6, 0],\n [9, 0, 0, -6]]\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[[-4, 11, -7, 8],\n [0, 5, 0, -3],\n [0, 0, -7, 11],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-6, -4, 8, 2],\n [-4, -1, 5, 0],\n [8, 5, 4, -7],\n [2, 0, -7, 6]]\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[[-10, 10, -7, -11],\n [0, 0, -8, -6],\n [0, 0, -2, 1],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[10, -2, -5, 4],\n [-2, -2, -4, -3],\n [-5, -4, -4, 5],\n [4, -3, 5, -10]]\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[[-11, 9, 4, -3],\n [0, 4, -1, 10],\n [0, 0, -10, 1],\n [0, 0, 0, -12]]\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[[-7, 12, 0, 0],\n [12, -10, -6, 2],\n [0, -6, -9, -1],\n [0, 2, -1, 7]]\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[[0, 8, 1, 8],\n [8, 1, -8, 0],\n [1, -8, 6, 0],\n [8, 0, 0, -2]]\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[[-7, -5, 8, -9],\n [0, 10, 12, 7],\n [0, 0, 12, 10],\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 largest eigenvalue by absolute value:\n[[-6, 2, 0, -6],\n [2, 1, 0, -10],\n [0, 0, -5, 7],\n [-6, -10, 7, -7]]\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, 5, -11, -11],\n [0, 6, 4, -9],\n [0, 0, -3, -2],\n [0, 0, 0, 6]]\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[[-11, 4, 4, 0],\n [4, -4, 2, -2],\n [4, 2, 7, -2],\n [0, -2, -2, -8]]\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[[12, 10, -10, 0],\n [0, 10, 9, 2],\n [0, 0, -12, 9],\n [0, 0, 0, -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[[-5, 6, -2, -2],\n [6, 5, 4, 6],\n [-2, 4, 0, -6],\n [-2, 6, -6, 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[[1, -4, -9, 5],\n [-4, -9, 6, 6],\n [-9, 6, -10, -6],\n [5, 6, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[2, -3, 0, 0],\n [-3, 9, 5, 10],\n [0, 5, 5, -4],\n [0, 10, -4, -10]]\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[[10, -5, -6, -10],\n [-5, -4, -7, -8],\n [-6, -7, 7, -9],\n [-10, -8, -9, 7]]\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[[6, 6, -1, 4],\n [6, -5, -9, 4],\n [-1, -9, -12, 3],\n [4, 4, 3, 10]]\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, -2, 4, -2],\n [-2, -6, 2, -6],\n [4, 2, 1, -6],\n [-2, -6, -6, 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[[-7, 5, 2, -1],\n [5, 0, -4, 6],\n [2, -4, -3, -5],\n [-1, 6, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[3, 4, 0, -10],\n [4, -6, -2, 11],\n [0, -2, 11, -1],\n [-10, 11, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-10, 0, -1, -2],\n [0, 2, 12, 6],\n [0, 0, 10, 6],\n [0, 0, 0, 2]]\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[[4, 1, 2, 4],\n [1, 6, 2, -2],\n [2, 2, -11, -1],\n [4, -2, -1, 8]]\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[[3, 11, 1, 4],\n [0, -4, 8, -6],\n [0, 0, -3, 1],\n [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[[-1, -11, -12, -6],\n [0, -1, 12, -7],\n [0, 0, 3, -6],\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[[2, -1, 7, 12],\n [0, 12, 10, -6],\n [0, 0, 8, -7],\n [0, 0, 0, 7]]\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[[0, -7, 6, 4],\n [0, -10, 5, -12],\n [0, 0, -5, 11],\n [0, 0, 0, 11]]\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[[6, -6, -8, -10],\n [-6, -6, 0, 6],\n [-8, 0, -12, 1],\n [-10, 6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-4, 9, 4, 6],\n [0, 6, -4, 8],\n [0, 0, 11, 7],\n [0, 0, 0, 11]]\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[[-1, -6, -2, 2],\n [-6, -7, -4, -4],\n [-2, -4, -2, 6],\n [2, -4, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, -4, 10, -3],\n [-4, -7, -6, -4],\n [10, -6, -2, -8],\n [-3, -4, -8, 3]]\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[[12, 1, 2, 2],\n [1, 7, 8, -2],\n [2, 8, 8, 10],\n [2, -2, 10, 8]]\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[[8, -2, -5, 2],\n [-2, 10, 5, -6],\n [-5, 5, -8, 5],\n [2, -6, 5, -4]]\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[[-1, 7, -5, 8],\n [0, 9, 6, -6],\n [0, 0, 1, -7],\n [0, 0, 0, -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, 0, -5, 3],\n [0, 5, 12, 6],\n [0, 0, 7, -4],\n [0, 0, 0, -2]]\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[[6, -9, -4, 1],\n [-9, 5, -4, 2],\n [-4, -4, 4, -6],\n [1, 2, -6, -9]]\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[[4, -10, 0, -7],\n [0, 6, -4, 3],\n [0, 0, 5, 10],\n [0, 0, 0, -11]]\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[[-8, -2, -6, 0],\n [-2, -2, 5, 8],\n [-6, 5, 12, 2],\n [0, 8, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-10, 2, -4, 0],\n [2, 6, 0, 0],\n [-4, 0, 7, 5],\n [0, 0, 5, -4]]\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[[-7, 6, 2, 7],\n [0, 6, -3, -2],\n [0, 0, -5, -7],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[9, 4, -8, 2],\n [4, 0, 2, 8],\n [-8, 2, -8, -6],\n [2, 8, -6, 6]]\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, -2, -8, -2],\n [-2, 10, 6, 6],\n [-8, 6, 8, 2],\n [-2, 6, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[8, 0, -6, -6],\n [0, 9, 2, -1],\n [-6, 2, 10, -2],\n [-6, -1, -2, -8]]\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[[11, 0, 2, -2],\n [0, -9, -2, -8],\n [2, -2, -7, -6],\n [-2, -8, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[1, 9, 10, -12],\n [0, 1, 0, -1],\n [0, 0, -2, 6],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[8, 3, -5, 6],\n [3, -1, 2, -1],\n [-5, 2, -3, -6],\n [6, -1, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, -8, 4, 8],\n [-8, -7, 4, -6],\n [4, 4, -9, -4],\n [8, -6, -4, 8]]\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[[-2, 1, 3, 0],\n [1, 6, 4, 4],\n [3, 4, 7, 0],\n [0, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[8, 2, 4, 0],\n [2, 10, -4, 2],\n [4, -4, 1, 5],\n [0, 2, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-6, 0, -4, 2],\n [0, 2, 3, 2],\n [-4, 3, 3, 4],\n [2, 2, 4, 6]]\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, -1, 8],\n [0, 11, 0, -11],\n [0, 0, -6, 12],\n [0, 0, 0, -12]]\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[[4, 2, 9, -3],\n [2, -5, 0, 0],\n [9, 0, 5, 8],\n [-3, 0, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-10, 11, 7, -1],\n [11, -7, -1, -4],\n [7, -1, -7, 1],\n [-1, -4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-10, -4, -4, 3],\n [-4, 6, -6, 1],\n [-4, -6, -2, 4],\n [3, 1, 4, -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[[10, 6, 12, -1],\n [6, 2, 2, 2],\n [12, 2, -10, 6],\n [-1, 2, 6, -5]]\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[[-10, 0, -11, -6],\n [0, 6, 2, -1],\n [0, 0, -3, 11],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[5, -5, 3, 2],\n [-5, -11, -5, -2],\n [3, -5, -8, -2],\n [2, -2, -2, -9]]\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[[-10, 10, -2, 2],\n [10, 12, 8, 5],\n [-2, 8, 0, 2],\n [2, 5, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, 2, -5, -9],\n [0, 6, 9, -9],\n [0, 0, -10, -3],\n [0, 0, 0, 2]]\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[[-6, 0, 6, -9],\n [0, 3, -1, -6],\n [6, -1, -6, -2],\n [-9, -6, -2, 9]]\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[[-5, -8, -5, 7],\n [0, -11, 12, 9],\n [0, 0, 1, 1],\n [0, 0, 0, 2]]\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[[-12, 2, -8, -3],\n [2, -1, -10, 2],\n [-8, -10, -6, 7],\n [-3, 2, 7, -3]]\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[[10, -8, -1, 2],\n [-8, -9, 1, -6],\n [-1, 1, 12, -4],\n [2, -6, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-10, 5, -2, 5],\n [0, 9, -3, -7],\n [0, 0, -12, -5],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-1, 1, -7, -4],\n [1, -10, -2, -4],\n [-7, -2, 10, 0],\n [-4, -4, 0, 5]]\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[[2, 9, -5, 9],\n [0, -6, -8, -1],\n [0, 0, -3, 12],\n [0, 0, 0, 4]]\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[[4, 2, -2, -8],\n [2, -6, -2, -9],\n [-2, -2, 3, 0],\n [-8, -9, 0, -11]]\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[[-3, 4, -4, 5],\n [4, -7, 10, 0],\n [-4, 10, 4, 0],\n [5, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-4, 2, -9, -4],\n [2, 11, -10, -9],\n [-9, -10, 1, -2],\n [-4, -9, -2, 12]]\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[[7, -1, 3, 5],\n [0, 11, 12, 0],\n [0, 0, 3, 6],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-1, -11, 2, -8],\n [0, 8, -6, 1],\n [0, 0, 11, 3],\n [0, 0, 0, -2]]\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[[-6, -4, -7, 0],\n [-4, -4, 6, -4],\n [-7, 6, -5, 7],\n [0, -4, 7, -11]]\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[[-8, 4, 0, -1],\n [4, 7, 3, -3],\n [0, 3, 3, -2],\n [-1, -3, -2, -6]]\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[[-4, 6, -4, 4],\n [6, -8, 1, 9],\n [-4, 1, -8, 2],\n [4, 9, 2, -1]]\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[[8, -2, 4, 4],\n [-2, -11, 2, 6],\n [4, 2, 7, -3],\n [4, 6, -3, 7]]\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[[-6, 11, -3, 8],\n [0, -3, -5, -1],\n [0, 0, 2, 2],\n [0, 0, 0, 10]]\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[[9, -9, 8, -8],\n [0, -6, -9, -12],\n [0, 0, 10, 5],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[7, 9, 4, 5],\n [0, 5, 3, -11],\n [0, 0, 3, -8],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[12, -3, -9, 3],\n [0, 0, -11, -8],\n [0, 0, -2, -9],\n [0, 0, 0, -11]]\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[[-5, -10, 7, 0],\n [-10, -7, -3, 4],\n [7, -3, -8, 4],\n [0, 4, 4, 6]]\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, -7, 0, -11],\n [0, 4, -6, 9],\n [0, 0, 8, -12],\n [0, 0, 0, 11]]\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[[-4, 12, 6, 9],\n [0, 0, 12, 6],\n [0, 0, -3, 4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-11, -12, 6, -1],\n [-12, 10, 6, 1],\n [6, 6, 10, -8],\n [-1, 1, -8, 11]]\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[[-4, 6, -2, -3],\n [6, -3, -10, 1],\n [-2, -10, 6, 7],\n [-3, 1, 7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
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