messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, 0, -2, 2, 4],\n [0, 4, -3, -4, 3],\n [-2, -3, 5, 1, 4],\n [2, -4, 1, -4, 2],\n [4, 3, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8431 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 0, -3, 2, -3],\n [0, 1, -2, 1, 0],\n [-3, -2, 5, -2, -2],\n [2, 1, -2, 4, -2],\n [-3, 0, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2015 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 0, 4, 1, 1],\n [0, -4, -1, 2, 2],\n [4, -1, -3, 4, 4],\n [1, 2, 4, 1, -2],\n [1, 2, 4, -2, 3]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1432 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[3, -1, 0, 2, 0],\n [-1, -5, 2, 0, 4],\n [0, 2, 4, 0, 0],\n [2, 0, 0, 3, -4],\n [0, 4, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "What is the value at position (5, 1) of the matrix A^4 where A is:\n[[-4, 4, 4, 4, 5],\n [0, 1, 2, -5, 2],\n [0, 0, 0, 2, 1],\n [0, 0, 0, 3, -3],\n [0, 0, 0, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 4, 0, 2, 2],\n [4, -5, 0, 0, 0],\n [0, 0, 4, -4, 1],\n [2, 0, -4, -4, 4],\n [2, 0, 1, 4, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 425 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[1, 5, 3, -3, -5],\n [0, 1, 4, 0, 0],\n [0, 0, -2, 4, 4],\n [0, 0, 0, 4, -5],\n [0, 0, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 163 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, 1, 4, -5, 1],\n [3, -2, -2, -2, -1],\n [0, 1, 3, 1, 5],\n [-4, 2, 3, 4, -3],\n [-3, -2, 4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -365 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 4, 2, -5, 3],\n [0, 0, 0, 1, -5],\n [-2, -2, 0, 4, -3],\n [5, 5, 5, 2, 5],\n [-1, -3, 4, 3, -1]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -500 | MATH |
[
{
"content": "What is the value at position (5, 2) of the matrix A^2 where A is:\n[[0, -2, 1, -4, -5],\n [3, -2, 2, -4, -4],\n [2, 4, -5, -2, 5],\n [-1, 0, -2, -5, -4],\n [1, 5, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 4, -4, 4, 5],\n [0, -1, 1, 4, 5],\n [5, 1, 4, 5, 4],\n [-3, -2, -1, 4, -1],\n [5, -3, -1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23847 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, -5, -2, 5, -5],\n [0, -4, 4, -1, -3],\n [0, 0, 3, 1, 2],\n [0, 0, 0, 3, -4],\n [0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 638 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -4, 1, -2, -2],\n [-4, -2, 4, 4, 0],\n [1, 4, -1, 2, 1],\n [-2, 4, 2, -2, -3],\n [-2, 0, 1, -3, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16325 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, -1, -3, -5, 0],\n [3, 2, 0, -2, 5],\n [3, -1, -4, 5, -1],\n [2, 2, -2, -3, 4],\n [-2, -5, -5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21728 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, -4, 4, 3, 1],\n [-4, -2, -1, -3, -2],\n [4, -1, 0, -2, 0],\n [3, -3, -2, -2, 3],\n [1, -2, 0, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -98 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -2, 4, 4, 1],\n [0, -3, -5, 3, -3],\n [0, 0, 4, 1, 0],\n [0, 0, 0, 1, -2],\n [0, 0, 0, 0, 2]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, -5, -2, -3, 4],\n [0, -5, -3, -1, 1],\n [3, -2, -1, -5, -2],\n [3, 4, -2, 5, -3],\n [-1, -2, 4, 0, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[1, 0, -2, 3, 3],\n [0, 4, -4, 0, 4],\n [-2, -4, 2, -1, 2],\n [3, 0, -1, 3, -2],\n [3, 4, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, -1, -3, -4, 3],\n [-3, 4, 5, 4, -4],\n [-4, 5, 2, -1, 5],\n [3, 3, -3, 5, -4],\n [-1, -5, 2, 5, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45336 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[2, -1, 0, 2, 1],\n [0, 4, 0, 3, 2],\n [0, 0, -1, 2, -4],\n [0, 0, 0, 0, 5],\n [0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 0, 1, 2, -4],\n [1, 3, -3, 1, 3],\n [5, -1, 2, 5, -2],\n [4, -4, 1, 5, -5],\n [-4, 1, -5, 5, -1]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1691 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 2, 4, -4, -3],\n [0, 3, 5, 4, 2],\n [0, 0, 3, 3, -4],\n [0, 0, 0, -4, -4],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2662 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, -2, 5, 3, 2],\n [0, 2, -1, -4, 0],\n [0, 0, 4, 2, -2],\n [0, 0, 0, -3, -1],\n [0, 0, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 589 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, 4, -1, 3, 1],\n [-1, 0, 3, -4, -2],\n [2, -5, -3, -4, 4],\n [0, 3, -2, 0, 1],\n [0, -1, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1272 | MATH |
[
{
"content": "Find the value at position (3, 5) of the 3th power of the matrix:\n[[-2, 5, -5, -5, 0],\n [-1, 4, -4, 1, 1],\n [2, 4, 4, -2, 2],\n [0, -5, -3, 2, 5],\n [1, 2, -1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[4, 0, 0, 1, 3],\n [0, -3, 1, 0, -3],\n [0, 1, 5, 0, 0],\n [1, 0, 0, 5, 0],\n [3, -3, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[3, 2, -1, 4, -1],\n [1, -2, -3, 3, 5],\n [4, 4, -5, 2, -3],\n [0, -1, 1, -5, -2],\n [5, 5, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2156 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, -3, 4, 4, -3],\n [-3, -3, -3, -3, 0],\n [2, 4, -3, 3, -5],\n [-1, 5, -2, -1, -2],\n [2, 4, 1, 2, 4]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -42 | MATH |
[
{
"content": "What is the value at position (4, 3) of the matrix A^4 where A is:\n[[2, 0, 0, -3, -1],\n [0, 0, -2, -1, -2],\n [0, -2, 5, 0, 0],\n [-3, -1, 0, 0, 0],\n [-1, -2, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-3, -1, 2, 2, 0],\n [-1, 5, 2, -2, 1],\n [2, 2, 3, -1, 0],\n [2, -2, -1, 4, -1],\n [0, 1, 0, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, -5, 4, 0, -1],\n [0, 3, 5, 5, 0],\n [0, 0, -1, -5, 5],\n [0, 0, 0, 2, 3],\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"
}
] | 270 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, 4, -4, 4, 3],\n [0, 2, -1, 0, -4],\n [0, 0, 0, -5, 0],\n [0, 0, 0, 4, -5],\n [0, 0, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3233 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -4, 1, -2, -5],\n [-4, 5, -1, 0, -3],\n [1, -1, -3, 2, 2],\n [-2, 0, 2, -4, -2],\n [-5, -3, 2, -2, -2]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4530 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[-5, 2, -1, 0, 2],\n [2, -5, 0, 0, 2],\n [-1, 0, 4, 4, -3],\n [0, 0, 4, 5, -2],\n [2, 2, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -225 | MATH |
[
{
"content": "What is the value at position (5, 2) of the matrix A^4 where A is:\n[[2, 5, -3, 2, 5],\n [-5, -4, -2, -4, 5],\n [2, -1, 2, 2, 0],\n [-4, 0, 3, 4, 5],\n [5, 2, 4, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -624 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[3, 3, 4, -2, 4],\n [0, -4, -1, -5, -5],\n [0, 0, -3, -5, -3],\n [0, 0, 0, -5, -1],\n [0, 0, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -614 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, -3, 2, 3, 0],\n [-4, 3, 0, -4, -2],\n [-1, 3, -4, -2, 0],\n [4, -2, 0, 3, -5],\n [-1, 1, -4, 3, -3]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "Find the value at position (5, 4) of the 4th power of the matrix:\n[[2, 5, -2, 1, 4],\n [-1, 3, -1, -4, -5],\n [4, 2, -3, -1, 0],\n [2, 5, -1, -4, -2],\n [-4, -3, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -101 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 1, 0, 1, 1],\n [1, 1, 2, -4, -2],\n [0, 2, 3, 2, 2],\n [1, -4, 2, -3, 2],\n [1, -2, 2, 2, 1]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -140 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (4, 4) of the result:\nA =\n[[-5, -5, 3, 3, 2],\n [3, 0, -1, -2, -4],\n [-4, -1, -2, 3, -2],\n [5, 1, 1, 3, 0],\n [5, 2, 0, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (1, 3) of the result:\nA =\n[[-2, 2, 2, 4, 4],\n [0, -3, 2, 4, 4],\n [0, 0, 4, 5, 1],\n [0, 0, 0, -3, -2],\n [0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[5, -2, 5, -4, 2],\n [-2, 5, -1, -4, -4],\n [5, -1, -2, 0, 0],\n [-4, -4, 0, 2, -2],\n [2, -4, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61432 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-1, 0, -1, 0, 0],\n [0, -1, 1, -4, 3],\n [-1, 1, 3, 0, 0],\n [0, -4, 0, -4, 4],\n [0, 3, 0, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 282 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 4, 5, -3, 4],\n [-2, -3, 1, 0, 0],\n [3, 2, 4, -2, 1],\n [4, 4, -4, 4, 2],\n [5, -1, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[-5, 5, 4, -2, -1],\n [1, 2, -5, 4, -5],\n [-3, -5, 4, 4, 2],\n [-4, -1, -5, 1, 3],\n [-3, -2, -2, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -793 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 5, 0, -2, 4],\n [5, 0, -2, -4, -2],\n [0, -2, -2, 1, -1],\n [-2, -4, 1, -5, 0],\n [4, -2, -1, 0, -2]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3132 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-2, 4, 4, -2, 1],\n [4, 3, 0, 4, 2],\n [4, 0, 2, -4, -2],\n [-2, 4, -4, -4, -2],\n [1, 2, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 350 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[3, -2, 0, -2, 2],\n [-2, -2, -1, 4, 0],\n [0, -1, 5, -2, -2],\n [-2, 4, -2, -1, 3],\n [2, 0, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -306 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 3th power of the matrix:\n[[4, 5, 4, 4, 1],\n [-3, 3, 3, 1, -5],\n [5, 2, 4, -5, -4],\n [1, -4, 4, -5, 3],\n [-5, 0, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 311 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[5, -3, 1, 4, -5],\n [0, -1, 5, -5, -5],\n [0, 0, -4, 4, -1],\n [0, 0, 0, -1, 1],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 139 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, -3, 3, 0, -4],\n [2, -1, -1, -3, 3],\n [2, 3, -1, 3, 2],\n [-1, 2, -5, 2, 5],\n [-1, -4, 3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -337 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, 2, 0, -3, 2],\n [2, 4, 2, 2, -4],\n [0, 2, 1, 0, -4],\n [-3, 2, 0, -1, 0],\n [2, -4, -4, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23434 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, -2, 0, 2, -5],\n [-2, 2, -1, -1, -2],\n [0, -1, 4, -2, 2],\n [2, -1, -2, -5, -2],\n [-5, -2, 2, -2, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3322 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-2, 0, 0, -4, 2],\n [0, -5, 1, 4, 3],\n [0, 1, 2, 0, 0],\n [-4, 4, 0, -3, 2],\n [2, 3, 0, 2, -5]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -3, -4, 4, 3],\n [-2, -5, -2, 3, 2],\n [3, -2, -2, -4, -4],\n [3, -5, -4, 4, -1],\n [-3, -3, 2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2494 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-5, 0, -2, 0, -4],\n [0, 3, -4, -3, 2],\n [-2, -4, -5, 0, -2],\n [0, -3, 0, -5, 2],\n [-4, 2, -2, 2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 366 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 3th power of the matrix:\n[[-4, 4, 2, -1, 5],\n [0, -1, -4, 2, 1],\n [3, -4, -1, 3, -4],\n [4, 4, -5, 2, -2],\n [2, 5, -4, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 218 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[0, -1, 2, 0, 3],\n [0, 3, 0, -4, 2],\n [0, 0, 2, 2, -5],\n [0, 0, 0, -3, 5],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[2, 5, 4, 3, 2],\n [5, -5, -2, 3, 3],\n [4, -2, -4, 0, 0],\n [3, 3, 0, -2, -2],\n [2, 3, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 344 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, -3, -5, 0, 4],\n [0, 5, 5, 5, 2],\n [0, 0, -4, -4, -3],\n [0, 0, 0, -5, -4],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9498 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 2, -2, -4, 2],\n [2, 5, 1, -2, -3],\n [-2, 1, -5, -2, -2],\n [-4, -2, -2, -1, 3],\n [2, -3, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 4050 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (5, 2) of the result:\nA =\n[[3, -1, 0, 1, 2],\n [-1, -1, -1, -2, -4],\n [0, -1, -5, 0, -2],\n [1, -2, 0, -5, 0],\n [2, -4, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -264 | MATH |
[
{
"content": "What is the value at position (2, 5) of the matrix A^3 where A is:\n[[1, -2, 3, -2, -4],\n [-2, -2, -4, -1, -4],\n [3, -4, 2, 3, 2],\n [-2, -1, 3, -4, 2],\n [-4, -4, 2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -290 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -2, -1, -1, -3],\n [-2, 0, -2, -2, -2],\n [-1, -2, -3, 2, -2],\n [-1, -2, 2, -2, -2],\n [-3, -2, -2, -2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8673 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -4, 3, -5, 4],\n [0, 2, -4, 3, 3],\n [0, 0, 4, 5, -5],\n [0, 0, 0, 0, -2],\n [0, 0, 0, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6714 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, -2, -4, -1, -1],\n [-2, 2, 0, 2, 0],\n [-4, 0, -5, -4, 2],\n [-1, 2, -4, 1, -4],\n [-1, 0, 2, -4, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 306 | MATH |
[
{
"content": "What is the value at position (3, 2) of the matrix A^3 where A is:\n[[-4, 1, 0, -5, 2],\n [0, 4, -5, 0, -3],\n [0, 0, 5, -1, -1],\n [0, 0, 0, 0, -2],\n [0, 0, 0, 0, 3]]?\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[[-5, 2, 5, 1, -4],\n [0, 3, 3, 3, 0],\n [0, 0, -2, -5, 4],\n [0, 0, 0, -5, 2],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -104 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 3, 4, -5, 2],\n [-3, 4, -1, -5, -1],\n [3, 5, -1, -1, 4],\n [2, -3, -1, 2, -2],\n [-1, 1, 4, 5, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3881 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-5, 4, 5, 2, 0],\n [4, -4, 4, 2, 0],\n [5, 4, 3, 2, 2],\n [2, 2, 2, -4, 4],\n [0, 0, 2, 4, -1]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 208 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 5, -3, -5, -3],\n [0, 5, 5, -4, 5],\n [0, 2, 2, -5, 2],\n [-3, 5, 0, 2, 4],\n [1, -5, 5, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -25601 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, 3, -5, 4, 5],\n [4, -2, -1, 4, 5],\n [-2, -5, -2, -3, 2],\n [4, 4, -3, 1, 5],\n [-3, 5, -1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51097 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, 5, 4, -5, 4],\n [0, 0, 2, 0, 4],\n [0, 0, 1, 1, -5],\n [0, 0, 0, -2, -1],\n [0, 0, 0, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 532 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 5, 1, 3, -2],\n [5, 4, 2, 2, 3],\n [1, 2, 4, -3, -2],\n [3, 2, -3, 5, 0],\n [-2, 3, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 450 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, 1, 4, -2, 0],\n [2, -3, 2, -1, 4],\n [3, -1, -5, 3, 3],\n [-4, -2, 3, 3, -3],\n [2, 0, 3, -4, -3]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, -2, 1, 2, -2],\n [-2, -4, 2, 2, 4],\n [1, 2, 3, 0, 4],\n [2, 2, 0, -5, 1],\n [-2, 4, 4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 472 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^3 where A is:\n[[3, -5, 2, -4, 2],\n [0, 4, -1, -5, -3],\n [0, 0, -4, 2, 1],\n [0, 0, 0, 1, 0],\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 (4, 1) of the 3th power of the matrix:\n[[4, -1, -3, -4, 0],\n [-1, 5, 0, -5, 1],\n [-3, 0, 5, -2, 0],\n [-4, -5, -2, 3, -1],\n [0, 1, 0, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -239 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, 0, -4, 2, 1],\n [0, -4, 0, 2, -2],\n [-4, 0, -3, -2, 2],\n [2, 2, -2, -1, 0],\n [1, -2, 2, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1360 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[5, -4, 0, -2, 2],\n [1, -2, -3, 3, 4],\n [-5, 2, 3, -2, -4],\n [0, 5, 0, -5, 1],\n [5, 1, -5, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 294 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[-2, 0, -3, -4, -1],\n [0, 2, -3, -1, 1],\n [0, 0, -4, 5, -2],\n [0, 0, 0, 1, 0],\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[[2, -1, 3, 0, -5],\n [0, 0, 5, 1, 1],\n [0, 0, 3, 5, 4],\n [0, 0, 0, 3, -5],\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"
}
] | 237 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 4) of the result:\nA =\n[[-2, 2, -4, 2, 2],\n [-5, 3, 4, 3, 0],\n [3, -3, -4, 3, -4],\n [4, 1, 0, 0, 5],\n [-4, 0, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, -4, -5, 5, 3],\n [0, 2, 2, -3, 1],\n [0, 0, -4, 2, 2],\n [0, 0, 0, 1, -5],\n [0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 758 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[5, 2, 0, -4, -1],\n [2, 2, 0, 0, 0],\n [0, 0, 4, 2, -2],\n [-4, 0, 2, -3, 5],\n [-1, 0, -2, 5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 4th power of the matrix:\n[[-1, -5, -2, -4, -5],\n [0, -3, -4, -1, -3],\n [0, 0, 2, -2, 3],\n [0, 0, 0, 5, 2],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[4, 0, -1, 3, 5],\n [-5, -5, -2, -5, 5],\n [-3, 1, -5, -1, 5],\n [0, 0, 2, 0, 3],\n [-5, -4, 3, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4355 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, -3, -3, 1, -4],\n [5, -4, -3, 5, -3],\n [4, 4, -3, -2, -4],\n [0, 4, 3, -3, 5],\n [4, -5, -1, -5, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5153 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, -3, -2, -4, 1],\n [-2, 0, 0, 0, 2],\n [3, 2, 3, 3, 4],\n [-1, 5, 1, -3, 0],\n [-4, -5, 4, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 963 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 2th power of the matrix:\n[[-2, 3, 2, 4, 0],\n [3, -4, 1, -1, 2],\n [2, 1, 2, 2, 0],\n [4, -1, 2, 3, -2],\n [0, 2, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, 1, 4, -2, 5],\n [0, -1, 3, 2, -2],\n [0, 0, 2, 0, 2],\n [0, 0, 0, 4, -1],\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"
}
] | 105 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -5, -3, 3, 5],\n [0, 0, -5, -4, 3],\n [0, 0, -3, 0, 4],\n [0, 0, 0, -3, -4],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 751 | MATH |
[
{
"content": "What is the value at position (2, 2) of the matrix A^3 where A is:\n[[3, 4, -4, 2, 2],\n [4, -2, 0, 2, 2],\n [-4, 0, -3, -4, 0],\n [2, 2, -4, 5, 2],\n [2, 2, 0, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Find the value at position (5, 1) of the 4th power of the matrix:\n[[4, -1, 4, 2, 2],\n [-1, -1, -4, -2, -3],\n [4, -4, -5, -2, 1],\n [2, -2, -2, 5, 2],\n [2, -3, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2152 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, 3, -2, 1, 2],\n [0, 5, 3, -4, -4],\n [0, 0, 0, -3, 3],\n [0, 0, 0, 2, 1],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -37 | MATH |
[
{
"content": "Find the value at position (1, 2) of the 3th power of the matrix:\n[[3, 2, 3, -3, 3],\n [0, 0, -2, -5, -4],\n [0, 0, 1, -1, -2],\n [0, 0, 0, -5, 3],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[5, -1, 1, 2, -2],\n [-1, 4, 3, 0, 2],\n [1, 3, 2, 3, 1],\n [2, 0, 3, 4, -2],\n [-2, 2, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 351 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, -2, -2, 2],\n [0, 3, 1, 3, -4],\n [-2, 1, 5, -2, 3],\n [-2, 3, -2, 4, -1],\n [2, -4, 3, -1, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5317 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 3, 0, 1, -4],\n [-1, 2, -2, 3, -3],\n [-2, 5, -3, 1, 0],\n [5, -3, 5, 3, 1],\n [-2, -3, 4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12493 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-4, -4, 5, 1, 3],\n [-2, 3, 0, 0, 1],\n [0, 0, -2, 3, -3],\n [2, 2, -2, 0, -4],\n [4, 5, -3, 5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
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