messages listlengths 1 1 | ground_truth stringclasses 56 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-9, 5, -4, -1],\n [0, 5, 5, 11],\n [0, 0, 2, -2],\n [0, 0, 0, 3]]\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[[9, 5, -3, -7],\n [5, 12, 0, 0],\n [-3, 0, 5, 8],\n [-7, 0, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[10, -5, -2, 10],\n [-5, -1, 5, 6],\n [-2, 5, -5, 4],\n [10, 6, 4, -7]]\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[[3, -10, 9, 0],\n [0, -8, 9, 4],\n [0, 0, -3, 0],\n [0, 0, 0, -10]]\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[[1, 0, 1, 2],\n [0, -9, 10, 8],\n [1, 10, 10, 2],\n [2, 8, 2, -6]]\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[[0, 6, 3, -11],\n [0, 1, -7, 12],\n [0, 0, 0, 8],\n [0, 0, 0, 4]]\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[[10, 2, -2, 1],\n [2, -2, 6, -1],\n [-2, 6, -2, -2],\n [1, -1, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[0, 3, -4, 0],\n [3, -7, 2, -10],\n [-4, 2, -2, -8],\n [0, -10, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-9, 0, -6, 0],\n [0, -4, -2, 4],\n [-6, -2, -7, -6],\n [0, 4, -6, 8]]\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, 8, -3, 6],\n [8, 0, 2, 9],\n [-3, 2, -8, -10],\n [6, 9, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-8, -6, -2, 4],\n [-6, 11, -6, 4],\n [-2, -6, -1, -10],\n [4, 4, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[11, -6, 6, 8],\n [0, -5, 12, 12],\n [0, 0, -4, 11],\n [0, 0, 0, 1]]\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[[1, 10, -4, -4],\n [10, 4, 4, -3],\n [-4, 4, 6, 0],\n [-4, -3, 0, 3]]\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[[-10, -12, 6, -4],\n [-12, -12, 2, -4],\n [6, 2, 11, 2],\n [-4, -4, 2, -5]]\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[[0, 8, -5, 8],\n [8, -10, -2, -4],\n [-5, -2, 9, -2],\n [8, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-1, 8, 0, -2],\n [8, -12, 2, 2],\n [0, 2, 5, -5],\n [-2, 2, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[2, 3, 1, 8],\n [3, -8, -1, 2],\n [1, -1, -9, 1],\n [8, 2, 1, -11]]\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[[1, 1, 4, -8],\n [1, -12, -2, 6],\n [4, -2, -1, 4],\n [-8, 6, 4, -3]]\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[[0, 10, 1, -11],\n [0, 9, 5, 0],\n [0, 0, 1, 2],\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, 0, 9],\n [0, -8, -5, 9],\n [0, 0, 3, -3],\n [0, 0, 0, 12]]\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[[3, 4, 0, 2],\n [4, -1, 0, 6],\n [0, 0, 9, 0],\n [2, 6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-10, 0, -4, 4],\n [0, -2, -4, -5],\n [-4, -4, -6, -2],\n [4, -5, -2, -4]]\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[[0, 7, 0, -4],\n [7, -9, 0, 4],\n [0, 0, -7, 0],\n [-4, 4, 0, -9]]\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[[6, 9, -4, -3],\n [9, 8, -2, 0],\n [-4, -2, -6, 6],\n [-3, 0, 6, 3]]\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, -8, -4, -2],\n [-8, 4, -6, -4],\n [-4, -6, 2, 6],\n [-2, -4, 6, 10]]\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[[-8, 10, -2, -2],\n [0, -5, 8, -4],\n [0, 0, 8, 3],\n [0, 0, 0, -4]]\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[[-9, 4, 4, -6],\n [4, 7, -8, -1],\n [4, -8, -12, -6],\n [-6, -1, -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 sum of absolute values of all eigenvalues:\n[[-11, 6, 11, 1],\n [0, -11, 5, 2],\n [0, 0, 4, 6],\n [0, 0, 0, 2]]\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[[-2, -8, -6, -2],\n [-8, -9, 6, -2],\n [-6, 6, 1, 0],\n [-2, -2, 0, 3]]\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, -6, 3, 1],\n [-6, 3, 4, 8],\n [3, 4, -12, -4],\n [1, 8, -4, -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[[11, -1, 6, 6],\n [0, -5, 5, 5],\n [0, 0, 6, -8],\n [0, 0, 0, -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 sum of absolute values of all eigenvalues:\n[[-11, 8, 0, -2],\n [8, -3, -4, -1],\n [0, -4, 9, -4],\n [-2, -1, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[1, -1, -4, -1],\n [0, -3, 7, -3],\n [0, 0, -10, 2],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[4, -4, -4, -6],\n [-4, -2, 4, 1],\n [-4, 4, -11, 1],\n [-6, 1, 1, 6]]\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, -6, -11],\n [0, 2, -3, -9],\n [0, 0, -4, -1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-6, 5, 6, 4],\n [5, 3, 4, -5],\n [6, 4, 1, 12],\n [4, -5, 12, -5]]\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[[9, 4, -7, -9],\n [0, 5, 8, 0],\n [0, 0, -8, -5],\n [0, 0, 0, 12]]\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[[6, -1, 2, -6],\n [-1, 10, 4, 2],\n [2, 4, 3, 2],\n [-6, 2, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[5, -2, 0, -5],\n [-2, -12, -6, -3],\n [0, -6, 0, 10],\n [-5, -3, 10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[11, -4, -6, -5],\n [-4, 5, -5, 2],\n [-6, -5, 12, 1],\n [-5, 2, 1, 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, 8, -2, -9],\n [0, 12, -1, -11],\n [0, 0, -7, 4],\n [0, 0, 0, 6]]\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[[3, -2, 0, 5],\n [-2, 8, -8, 4],\n [0, -8, 0, 4],\n [5, 4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-1, -4, 1, 3],\n [0, 12, -11, -6],\n [0, 0, 3, 11],\n [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 largest eigenvalue by absolute value:\n[[8, -6, -10, 3],\n [0, -11, 6, 8],\n [0, 0, -5, -4],\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[[-5, -6, 9, 0],\n [-6, -5, -5, 4],\n [9, -5, 5, -6],\n [0, 4, -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[[7, 0, 4, -2],\n [0, 7, -8, -4],\n [4, -8, 12, 2],\n [-2, -4, 2, 4]]\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[[-10, -5, -2, -1],\n [0, -8, -11, -10],\n [0, 0, 5, 4],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-7, -8, 0, 2],\n [-8, -4, 6, 6],\n [0, 6, 4, -4],\n [2, 6, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[10, 2, 0, 6],\n [2, 1, -2, -8],\n [0, -2, 4, 10],\n [6, -8, 10, -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[[-1, -7, 8, 5],\n [0, 11, 10, -4],\n [0, 0, 11, 1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[0, 4, 10, -8],\n [4, -4, 6, 0],\n [10, 6, 2, 2],\n [-8, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-11, 3, 0, -7],\n [3, -5, 0, 0],\n [0, 0, -9, 0],\n [-7, 0, 0, 9]]\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[[-7, -2, -5, 0],\n [-2, 11, 0, 8],\n [-5, 0, -9, 6],\n [0, 8, 6, -4]]\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[[6, -2, -2, -3],\n [-2, 0, -10, -3],\n [-2, -10, -3, -6],\n [-3, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-3, 0, -2, -3],\n [0, -2, 3, 4],\n [-2, 3, -4, 2],\n [-3, 4, 2, 3]]\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[[12, -4, -1, 10],\n [-4, 11, -4, -1],\n [-1, -4, 1, 2],\n [10, -1, 2, 9]]\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[[-9, 4, 6, -3],\n [4, 10, -6, 0],\n [6, -6, -12, -2],\n [-3, 0, -2, 12]]\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[[10, -8, -2, 0],\n [-8, 0, 6, 3],\n [-2, 6, 8, 5],\n [0, 3, 5, 4]]\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[[11, -11, -6, -8],\n [0, -5, 4, 4],\n [0, 0, -7, -12],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[6, 9, 12, -12],\n [0, 2, 5, 9],\n [0, 0, -10, -12],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[7, -8, -2, 6],\n [-8, -4, 6, 4],\n [-2, 6, -11, -7],\n [6, 4, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-3, 8, -2, 5],\n [0, 3, -8, -1],\n [0, 0, -10, 3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-5, -10, 5, 11],\n [0, -11, 7, 10],\n [0, 0, 11, -3],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, -6, 8, 8],\n [-6, 9, -3, 0],\n [8, -3, 1, 8],\n [8, 0, 8, -3]]\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, -1, -11, -1],\n [0, -5, 0, -11],\n [0, 0, -4, -3],\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[[-5, 6, -2, 2],\n [6, -9, 0, -4],\n [-2, 0, -12, 8],\n [2, -4, 8, -5]]\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[[9, -3, -2, -1],\n [-3, 4, -8, -2],\n [-2, -8, 12, 4],\n [-1, -2, 4, -11]]\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[[3, -8, -4, 7],\n [0, 11, -3, 6],\n [0, 0, 4, 9],\n [0, 0, 0, 11]]\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[[5, -6, 0, -6],\n [-6, -5, -6, 5],\n [0, -6, 7, 6],\n [-6, 5, 6, 5]]\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[[-4, -2, -5, -1],\n [-2, 5, -6, -6],\n [-5, -6, -10, -5],\n [-1, -6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[4, 11, 3, 8],\n [0, -6, 3, 8],\n [0, 0, -1, -1],\n [0, 0, 0, 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[[8, 2, -6, -11],\n [0, -6, -7, 7],\n [0, 0, -4, -2],\n [0, 0, 0, -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[[-5, 5, -4, -11],\n [5, 3, 3, 4],\n [-4, 3, 4, -2],\n [-11, 4, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-12, -10, 2, -8],\n [0, 5, -11, -7],\n [0, 0, 5, 3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-9, -10, -4, 2],\n [-10, -2, 1, 0],\n [-4, 1, 0, 8],\n [2, 0, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[1, -4, -4, -6],\n [-4, -1, 4, 5],\n [-4, 4, 3, -3],\n [-6, 5, -3, 3]]\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[[-4, -2, 0, -9],\n [-2, 6, -4, 10],\n [0, -4, 7, 2],\n [-9, 10, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-3, 11, 5, 7],\n [0, -9, 5, -6],\n [0, 0, -7, -9],\n [0, 0, 0, -7]]\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[[8, 0, 2, -6],\n [0, -4, -8, 5],\n [2, -8, 1, 0],\n [-6, 5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-4, -6, 4, 10],\n [0, -2, -1, -2],\n [0, 0, 1, -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[[-8, -10, 12, 9],\n [-10, 11, -6, 5],\n [12, -6, -8, 2],\n [9, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-6, 6, 12, 2],\n [6, 12, 4, -6],\n [12, 4, 0, 12],\n [2, -6, 12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[12, -6, -2, -4],\n [-6, 5, -5, -6],\n [-2, -5, -3, 4],\n [-4, -6, 4, -6]]\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[[-3, -12, 11, -5],\n [0, 1, 1, 6],\n [0, 0, -10, 6],\n [0, 0, 0, 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[[1, 8, 11, -6],\n [0, -7, -7, -4],\n [0, 0, -8, 3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-1, 0, -6, 10],\n [0, -1, -3, 6],\n [-6, -3, 1, 0],\n [10, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[4, 0, 6, 2],\n [0, -8, -1, 4],\n [0, 0, -8, -11],\n [0, 0, 0, 2]]\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[[-4, 8, -11, -11],\n [0, -8, -6, 10],\n [0, 0, 3, 11],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[2, 0, -5, -4],\n [0, 3, -2, -2],\n [-5, -2, 1, 10],\n [-4, -2, 10, 2]]\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[[4, -8, -4, 2],\n [-8, -3, -8, -4],\n [-4, -8, 12, 0],\n [2, -4, 0, 1]]\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[[7, -2, -5, 4],\n [0, 12, -11, 4],\n [0, 0, 8, -7],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[1, -6, -10, 11],\n [0, 7, 0, 3],\n [0, 0, -6, -4],\n [0, 0, 0, 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[[-1, -5, -7, 4],\n [-5, 9, 5, 2],\n [-7, 5, -4, 0],\n [4, 2, 0, 2]]\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, 2, 4, 0],\n [2, -4, 0, 2],\n [4, 0, 0, 2],\n [0, 2, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[9, -9, 1, 6],\n [0, 12, -4, 0],\n [0, 0, -2, -1],\n [0, 0, 0, 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[[-1, -1, 5, 5],\n [0, 5, 9, -11],\n [0, 0, -2, 9],\n [0, 0, 0, 6]]\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[[-3, -4, 2, 8],\n [-4, -11, -5, -7],\n [2, -5, -7, 11],\n [8, -7, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-8, -2, 5, 7],\n [0, 3, -7, 2],\n [0, 0, 9, -8],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[6, 1, 3, 0],\n [1, 11, 0, -2],\n [3, 0, 9, -3],\n [0, -2, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[9, -11, -2, 10],\n [0, -12, 0, -9],\n [0, 0, -9, -1],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
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