messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[1, -5, 2, -1, 2],\n [2, 1, 4, 3, -2],\n [-3, 5, -2, 5, -5],\n [1, 0, -5, 5, 4],\n [1, 2, 5, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 0, -2, 1, 0],\n [0, 0, -2, 4, 2],\n [-2, -2, -1, 2, -2],\n [1, 4, 2, -1, 4],\n [0, 2, -2, 4, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17811 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -3, -1, 2, 3],\n [0, -1, 0, -4, 2],\n [0, 0, -4, -4, 2],\n [0, 0, 0, 1, 3],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -368 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[0, 0, 2, -2, -4],\n [4, 1, -2, -3, 3],\n [2, 4, -5, 2, -5],\n [-1, -2, -1, 1, 4],\n [-4, 5, -5, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3994 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 2, 1, 5, 5],\n [-4, -2, 5, 0, 0],\n [-1, -1, 5, -1, -2],\n [-4, -1, 3, -1, 3],\n [4, -2, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17826 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, -1, 0, 5, 1],\n [-1, -2, -3, -1, 2],\n [0, -3, -5, -1, 0],\n [5, -1, -1, 4, -2],\n [1, 2, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 168 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-3, -5, 2, 4, 0],\n [-3, -1, 4, 1, -3],\n [1, -2, -3, 4, 3],\n [1, 5, 0, -1, 1],\n [-3, -1, 0, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2699 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, 3, 0, 2, 0],\n [0, 3, 1, 3, 1],\n [0, 0, 2, 2, 1],\n [0, 0, 0, 2, 4],\n [0, 0, 0, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3224 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (1, 1) of the result:\nA =\n[[-4, 0, 3, -3, -2],\n [4, 0, 1, -5, 2],\n [5, 1, -4, -3, -2],\n [-2, -3, -2, 2, 2],\n [5, -5, 5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[1, 2, 0, -2, 0],\n [2, 3, 4, 2, -3],\n [0, 4, -2, -1, 1],\n [-2, 2, -1, -1, 1],\n [0, -3, 1, 1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -475 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, -1, -4, -2, 2],\n [-1, 4, -4, -1, -4],\n [-4, -4, 4, 2, 2],\n [-2, -1, 2, 3, -2],\n [2, -4, 2, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 3, -1, -2, -1],\n [-3, -3, 4, 0, 2],\n [-2, 1, 5, 0, -3],\n [0, 1, -2, -2, -1],\n [-1, -2, 0, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4794 | MATH |
[
{
"content": "Find the value at position (3, 4) of the 2th power of the matrix:\n[[0, 1, 2, -2, 0],\n [1, 0, -2, 2, 0],\n [2, -2, -2, 1, 3],\n [-2, 2, 1, 4, 1],\n [0, 0, 3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 2, 5, -1, -4],\n [-4, 3, -3, 1, 4],\n [3, 4, 4, -3, 1],\n [1, 5, 2, 4, 5],\n [-2, -5, 1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3113 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 4) of the result:\nA =\n[[3, 2, -5, -4, 4],\n [0, 3, 1, -4, -2],\n [5, 0, 1, 5, 5],\n [-3, 2, -4, 3, -2],\n [-5, -4, -1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -112 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 3) of the result:\nA =\n[[-5, -3, -4, -2, 3],\n [4, 5, 1, -2, -1],\n [-3, -3, -2, 1, 4],\n [-4, -3, -4, 5, -2],\n [4, 1, 5, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7863 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-5, 4, 2, -3, 0],\n [-5, -2, 5, 5, 5],\n [-2, -3, -3, -1, -4],\n [0, -2, 1, 4, 3],\n [3, -4, 2, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -109 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 3, -1, 1, -3],\n [-4, 5, 2, -3, -5],\n [5, -1, 2, 3, 4],\n [-2, -2, -2, 2, 3],\n [3, -1, -1, 4, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13031 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[5, -4, 2, 2, -1],\n [5, 0, -2, -4, -3],\n [0, 4, 1, 1, -2],\n [-1, 5, 0, 2, -4],\n [5, -4, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[5, 4, -5, 2, -1],\n [0, 1, 0, -2, -5],\n [0, 0, 1, -5, 0],\n [0, 0, 0, 1, -1],\n [0, 0, 0, 0, -4]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 3th power of the matrix:\n[[2, 2, 0, 1, -2],\n [2, -3, -4, 4, -4],\n [0, -4, -3, 2, 2],\n [1, 4, 2, -5, -2],\n [-2, -4, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -28 | MATH |
[
{
"content": "What is the value at position (5, 1) of the matrix A^4 where A is:\n[[1, 2, 0, 0, 0],\n [2, 0, 0, -2, 2],\n [0, 0, 2, 4, 0],\n [0, -2, 4, 2, -2],\n [0, 2, 0, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (5, 1) of the result:\nA =\n[[-4, 5, -2, 2, -2],\n [5, -5, 1, -1, 0],\n [-2, 1, 0, -1, 2],\n [2, -1, -1, 0, 0],\n [-2, 0, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -92 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[4, 1, -4, -2, 3],\n [0, 2, 5, -5, 4],\n [0, 0, -5, -4, -2],\n [0, 0, 0, -2, -2],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2327 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 4, 0, -5, 0],\n [4, -4, 4, -2, -3],\n [0, 4, -5, -2, -2],\n [-5, -2, -2, -5, 3],\n [0, -3, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 543 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 5, -2, -4, -5],\n [3, 1, 5, -2, 3],\n [0, 4, 1, 2, -3],\n [4, -4, -5, 2, 2],\n [4, -1, -2, 4, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4328 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 1) of the result:\nA =\n[[0, 0, 1, -4, -3],\n [0, -1, 2, 2, 0],\n [0, 0, -5, -5, -5],\n [0, 0, 0, -3, 0],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 3, -4, 3, -2],\n [-2, 3, -2, 4, 5],\n [-4, -4, -3, 4, -3],\n [5, 2, 4, -3, -1],\n [-1, -3, 4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71978 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[0, 1, 2, -2, 0],\n [1, 2, 0, -2, 0],\n [2, 0, 1, 0, -2],\n [-2, -2, 0, 4, -2],\n [0, 0, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, -3, -2, 0, 3],\n [-3, 5, 5, 1, 2],\n [-2, 5, -1, 2, -4],\n [0, 1, 2, -1, -2],\n [3, 2, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7024 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[3, 2, 3, 0, -1],\n [2, 4, 1, 5, 2],\n [3, 1, -4, -2, 0],\n [0, 5, -2, -1, 2],\n [-1, 2, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1173 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^3 where A is:\n[[3, -1, 5, 5, -5],\n [-5, 5, -5, 5, 0],\n [5, 5, -5, -4, 5],\n [3, 5, -3, 5, 0],\n [0, 2, 3, 5, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -335 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-5, -4, 2, -2, -2],\n [-4, 4, 1, 0, 0],\n [2, 1, 1, -4, 3],\n [-2, 0, -4, 0, 4],\n [-2, 0, 3, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, 1, 1, 4, -5],\n [1, 2, 0, -1, -4],\n [-1, 4, 5, -4, 3],\n [-4, 4, 4, 1, -1],\n [3, -1, -3, 2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 85 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -1, -3, -1, 3],\n [-5, -5, -1, 5, 4],\n [3, 4, -5, 1, 2],\n [-5, 2, 1, 5, 5],\n [1, 4, -3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 613 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 3) of the result:\nA =\n[[2, 4, -3, 0, 1],\n [0, 2, 0, 3, -5],\n [0, 0, -5, 3, 0],\n [0, 0, 0, -1, 5],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, 2, -1, -2, -4],\n [2, 3, 2, -2, -4],\n [-1, 2, -1, 0, -2],\n [-2, -2, 0, 0, -3],\n [-4, -4, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2033 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 0, 3, 5, 1],\n [4, 4, -1, -2, 2],\n [-2, -4, 1, 2, -3],\n [-2, 5, -4, 1, 2],\n [-2, -4, 1, 4, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9290 | MATH |
[
{
"content": "What is the value at position (5, 4) of the matrix A^2 where A is:\n[[-4, -5, -2, 3, -3],\n [0, 3, 0, -2, 4],\n [0, 0, -1, -4, 5],\n [0, 0, 0, -5, 1],\n [0, 0, 0, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 4, -1, 2, 4],\n [4, -2, 2, -3, 4],\n [-1, 2, 5, 1, 2],\n [2, -3, 1, 1, 2],\n [4, 4, 2, 2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11356 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[-2, -5, -5, -4, 0],\n [0, -3, -5, 5, -3],\n [0, 0, 0, 4, 1],\n [0, 0, 0, 2, -4],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-1, -1, 2, 5, 5],\n [5, -2, 3, -1, 4],\n [-4, -4, 1, -4, 2],\n [4, -1, 5, -2, -3],\n [4, 5, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 746 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -4, -2, 5, 4],\n [0, 1, 0, -4, -5],\n [0, 0, 1, -2, -1],\n [0, 0, 0, -5, 5],\n [0, 0, 0, 0, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-2, 0, 5, -3, 4],\n [0, -3, -3, 3, 0],\n [5, -3, 1, -2, 0],\n [-3, 3, -2, 1, 3],\n [4, 0, 0, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 5) of the result:\nA =\n[[-1, 2, -2, -2, 4],\n [2, -4, 0, 0, 0],\n [-2, 0, 5, -3, -2],\n [-2, 0, -3, -5, 3],\n [4, 0, -2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -28 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -3, -4, 0, -4],\n [2, 2, -2, -4, -1],\n [4, 5, 5, 2, -5],\n [1, 2, 0, -3, 5],\n [-1, 4, 0, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1435 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -3, -2, -1, -5],\n [0, -3, -5, 0, 2],\n [0, 0, 3, 0, 3],\n [0, 0, 0, 3, 1],\n [0, 0, 0, 0, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 487 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, 1, 0, -4, -2],\n [1, 0, 0, -2, 4],\n [0, 0, -5, 2, 0],\n [-4, -2, 2, 5, 4],\n [-2, 4, 0, 4, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, -4, 2, -1, -2],\n [-4, -3, 0, 1, 2],\n [2, 0, 5, 0, -3],\n [-1, 1, 0, -5, 2],\n [-2, 2, -3, 2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 4) of the result:\nA =\n[[5, -1, 4, -2, 0],\n [0, 3, 5, -4, 0],\n [0, 0, -2, 4, 1],\n [0, 0, 0, 2, -1],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-5, 2, -2, -1, 0],\n [2, -5, -2, 2, 2],\n [-2, -2, 2, 2, 2],\n [-1, 2, 2, -4, -4],\n [0, 2, 2, -4, 2]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, 3, -5, -3, 4],\n [0, 1, -1, 2, -4],\n [0, 0, 5, -3, 4],\n [0, 0, 0, -5, 3],\n [0, 0, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9566 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 3) of the result:\nA =\n[[-2, 5, 3, 0, -4],\n [5, -5, 5, -1, -2],\n [-3, 0, 2, 5, 5],\n [1, -5, 5, -5, 5],\n [5, 1, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2528 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 5, -2, -3, -2],\n [1, -2, -4, 5, -3],\n [-4, -4, 5, 5, 5],\n [-2, -5, -2, -3, -3],\n [-2, -5, -4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4662 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[2, -4, -2, 1, -3],\n [-4, 3, 2, -4, -2],\n [-2, 2, -2, 2, 0],\n [1, -4, 2, 4, 1],\n [-3, -2, 0, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 342 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, 4, -2, -1, 2],\n [5, 4, -3, -4, -2],\n [-2, 0, -3, -4, -1],\n [1, 5, 5, -3, 2],\n [-3, -2, -3, 5, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[5, -4, 3, -1, 5],\n [-4, 5, -5, 2, -1],\n [-5, -1, 5, 5, -2],\n [0, -3, 1, -3, 4],\n [0, -2, -2, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4640 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[5, 3, -2, 4, 1],\n [4, -1, 2, -1, 1],\n [-2, -3, -1, -3, 5],\n [-1, 4, 1, -5, 1],\n [-2, 1, -1, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 490 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[3, 1, -3, 3, 0],\n [1, 0, 4, -3, 1],\n [-3, 4, 2, 0, 0],\n [3, -3, 0, -1, -5],\n [0, 1, 0, -5, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 342 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -3, 2, 2, 2],\n [-3, -2, 1, 0, -1],\n [2, 1, -1, 1, 4],\n [2, 0, 1, 3, 2],\n [2, -1, 4, 2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13848 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, -1, -5, -2, 5],\n [-3, -5, 0, 3, 0],\n [-5, -4, 3, 4, -3],\n [4, -5, 2, 5, 0],\n [1, -4, 0, -1, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 225 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 2, 2, -2, 2],\n [2, 2, -3, 2, 2],\n [2, -3, 1, 0, 2],\n [-2, 2, 0, 5, -2],\n [2, 2, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1278 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 2th power of the matrix:\n[[-4, -4, 0, 5, 4],\n [0, 1, -5, 0, -3],\n [0, 0, -1, -4, -3],\n [0, 0, 0, -3, -4],\n [0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 3th power of the matrix:\n[[-2, 3, -4, 5, 0],\n [0, 5, 5, 5, -4],\n [0, 0, 3, 2, 1],\n [0, 0, 0, 0, -5],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, 2, 2, 4, -3],\n [2, 5, 0, -1, 2],\n [2, 0, -5, -2, -1],\n [4, -1, -2, 5, 1],\n [-3, 2, -1, 1, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 223 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (5, 3) of the result:\nA =\n[[-1, 2, 4, -4, -4],\n [2, -4, 0, 0, -1],\n [4, 0, -2, 2, 0],\n [-4, 0, 2, -1, 3],\n [-4, -1, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, -4, -2, 4, -2],\n [0, 1, 0, -1, 1],\n [1, -5, 3, 2, -3],\n [4, -2, 0, 2, -5],\n [-5, -5, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 114 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[3, 3, -3, -1, 5],\n [0, -1, 4, -2, 4],\n [0, 0, -2, -1, 3],\n [0, 0, 0, -1, 4],\n [0, 0, 0, 0, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 155 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 0, 1, -1, -1],\n [0, -2, -5, -5, -3],\n [0, 0, -5, 4, 3],\n [0, 0, 0, 0, 4],\n [0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -3, 3, -2, -5],\n [0, 1, 4, 1, -1],\n [0, 0, -2, -2, -4],\n [0, 0, 0, -3, -1],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[0, 3, 0, 2, -3],\n [3, 0, 0, -2, -2],\n [0, 0, 4, -3, 1],\n [2, -2, -3, -5, 0],\n [-3, -2, 1, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[2, 0, 1, -3, -3],\n [4, 4, 0, -2, -2],\n [-2, -2, -5, 2, -5],\n [0, 4, 2, 0, -3],\n [5, -4, 1, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 362 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, -5, 2, -4, -2],\n [0, -1, 5, 2, 2],\n [0, 0, -4, -2, -1],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 620 | MATH |
[
{
"content": "Find the value at position (5, 5) of the 2th power of the matrix:\n[[-1, -3, 1, 4, -2],\n [3, -1, -3, -2, -5],\n [2, -1, -5, 4, 5],\n [1, 0, -1, 1, 0],\n [-3, 4, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[1, -3, 4, 0, -1],\n [1, 4, 3, 2, -3],\n [-3, -4, 2, 3, 4],\n [-2, -2, 0, -2, -1],\n [-4, 0, 2, 0, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11 | MATH |
[
{
"content": "Find the value at position (3, 4) of the 4th power of the matrix:\n[[5, 3, 2, -2, -1],\n [2, 2, 3, -2, -1],\n [4, 5, 4, -5, -3],\n [2, -4, -2, -2, -5],\n [-2, 1, -4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3503 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[2, 3, 2, -4, 2],\n [1, 1, -5, 0, 4],\n [3, -4, -1, 5, -5],\n [-2, 0, 4, 5, 5],\n [3, 5, 3, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 328 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, 1, 5, -2, 0],\n [0, 4, -3, 3, 3],\n [0, 0, 2, -5, 3],\n [0, 0, 0, 2, 0],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 262 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 2th power of the matrix:\n[[-5, 2, -1, -2, 2],\n [2, 5, 0, 2, -4],\n [-1, 0, 1, -2, -1],\n [-2, 2, -2, -4, -1],\n [2, -4, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (3, 3) of the result:\nA =\n[[4, 0, 4, 4, 4],\n [0, -5, 1, 5, -1],\n [0, 0, 5, -1, 4],\n [0, 0, 0, -3, 0],\n [0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, 0, 2, -3, -2],\n [0, 1, 2, 4, -2],\n [2, 2, 0, 2, 0],\n [-3, 4, 2, 2, 0],\n [-2, -2, 0, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 299 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 3, 0, 2, -3],\n [0, -3, -4, -3, -5],\n [0, 0, -5, -4, 0],\n [0, 0, 0, -2, 2],\n [0, 0, 0, 0, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8685 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 2, 5, 2, -1],\n [0, 0, -5, 0, 3],\n [0, 0, -4, 5, 4],\n [0, 0, 0, -1, -2],\n [0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2285 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (2, 1) of the result:\nA =\n[[0, 0, 3, 1, -1],\n [0, -3, 4, 0, 0],\n [3, 4, -1, -2, 5],\n [1, 0, -2, -3, -1],\n [-1, 0, 5, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[0, 2, -1, -3, 2],\n [1, -2, 5, 3, -3],\n [2, 4, 3, -2, -3],\n [2, 4, 5, -4, 4],\n [-2, -4, 0, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3436 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 2, -5, 4, 0],\n [1, 3, 3, 5, 2],\n [5, -4, -4, 1, 4],\n [-4, -5, -2, -5, -1],\n [-2, 5, 5, 2, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2108 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 5, 2, 5, 0],\n [0, -2, 2, -2, -5],\n [0, 0, -4, -2, 0],\n [0, 0, 0, 4, 2],\n [0, 0, 0, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1545 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, -2, 0, -2, 1],\n [-2, 3, 0, 5, -4],\n [0, 0, 1, 0, 5],\n [-2, 5, 0, 1, 0],\n [1, -4, 5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 2, 2, 0, 0],\n [2, 0, 0, 1, 1],\n [2, 0, -3, 0, 0],\n [0, 1, 0, 5, -1],\n [0, 1, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3485 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, 4, -1, 3, -1],\n [5, -2, -5, 5, -4],\n [3, 5, -4, -2, -1],\n [1, 1, 2, 0, -5],\n [5, -1, -3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 613 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 3) of the result:\nA =\n[[-2, -1, 1, 0, 0],\n [-1, -2, 2, 0, 2],\n [1, 2, -5, 0, 0],\n [0, 0, 0, 0, -3],\n [0, 2, 0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-5, 0, -2, -2, -2],\n [0, -3, 2, 1, -4],\n [-2, 2, 1, -2, -1],\n [-2, 1, -2, -2, 0],\n [-2, -4, -1, 0, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 279 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, -4, -4, 0, -1],\n [4, -5, -2, 2, -1],\n [1, -2, 1, -1, -5],\n [-1, 4, -1, 4, 1],\n [4, -4, -4, -4, 5]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -4, -2, -1, -2],\n [0, -2, -2, 0, 2],\n [0, 0, -2, -1, 2],\n [0, 0, 0, 4, -3],\n [0, 0, 0, 0, 3]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, 4, 4, 4, -4],\n [4, 2, 0, 0, -2],\n [4, 0, 2, 1, -3],\n [4, 0, 1, 5, 2],\n [-4, -2, -3, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 333 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^3 where A is:\n[[-2, -2, 0, -3, -5],\n [-2, -2, -1, 0, 2],\n [0, -1, 3, 0, 0],\n [-3, 0, 0, 2, 1],\n [-5, 2, 0, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -126 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^4 where A is:\n[[-5, 3, -4, 4, -2],\n [0, -5, -4, 3, -3],\n [0, 0, -3, -2, 2],\n [0, 0, 0, -1, -1],\n [0, 0, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 2, 4, -5, 4],\n [0, 1, 0, -5, 3],\n [0, 0, -3, 2, 2],\n [0, 0, 0, 1, 3],\n [0, 0, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-5, -1, 2, -3, 3],\n [-5, 1, 3, 3, 0],\n [3, 0, 1, -2, -1],\n [-5, 2, -1, -2, 2],\n [2, 0, -3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 70 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, 0, 2, 5, -4],\n [0, 4, 2, 3, -1],\n [2, 2, 3, 4, -2],\n [5, 3, 4, 3, -2],\n [-4, -1, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 116151 | MATH |
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