messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, 0, -1, -4, 3],\n [-4, -3, 2, 4, 4],\n [3, -4, -5, 3, 2],\n [5, 5, 0, -1, 1],\n [0, 2, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -318 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, 2, 2, 3, 5],\n [0, -4, 1, 2, -5],\n [0, 0, -2, 4, 1],\n [0, 0, 0, 3, 5],\n [0, 0, 0, 0, -4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-4, 5, -3, 3, -3],\n [-2, 2, -3, -4, 5],\n [-1, -1, -1, -5, 3],\n [2, 2, -4, -4, 3],\n [4, -4, 5, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, 2, -5, 1, -4],\n [0, 3, 1, -5, -1],\n [0, 0, -4, 1, 5],\n [0, 0, 0, -2, -1],\n [0, 0, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 3) of the result:\nA =\n[[5, 1, -2, 3, 0],\n [1, -1, -2, 4, 0],\n [-2, -2, 4, -1, -2],\n [3, 4, -1, 3, -2],\n [0, 0, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -236 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, -5, -2, 3, 3],\n [-2, -5, 2, 1, 0],\n [-3, 1, 5, 0, 2],\n [-1, -3, -5, -2, -2],\n [-5, -2, -5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2510 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 3, 2, -5, 2],\n [2, 3, 2, 1, 2],\n [-1, -1, -2, -2, 2],\n [-2, 4, -1, -2, -2],\n [5, 2, -5, -1, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10389 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 3th power of the matrix:\n[[-1, 5, -4, 4, -1],\n [-2, 5, -5, -3, 1],\n [5, 1, -3, 1, -4],\n [-2, -2, 1, 3, 5],\n [5, 5, -1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 2, -5, -3, 0],\n [0, -5, 4, 3, -1],\n [0, 0, 4, 0, -4],\n [0, 0, 0, 2, 5],\n [0, 0, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -64 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (5, 2) of the result:\nA =\n[[-3, 3, 3, -2, 5],\n [0, -1, -5, -1, -5],\n [0, 0, 5, 0, 5],\n [0, 0, 0, 4, -1],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 3th power of the matrix:\n[[1, -3, 1, 0, -2],\n [2, 2, 0, -1, -2],\n [2, 4, 3, 2, 0],\n [-1, 2, 4, -4, -1],\n [5, 4, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-5, 0, -1, 1, -2],\n [0, 2, 0, -2, 5],\n [0, 0, 2, 1, -4],\n [0, 0, 0, 1, -5],\n [0, 0, 0, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 185 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 2, -4, 2, 0],\n [2, 5, 2, -4, 2],\n [-4, 2, 1, -3, 4],\n [2, -4, -3, -5, 2],\n [0, 2, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4195 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, 0, 4, -3, 3],\n [0, 4, 1, -5, 2],\n [0, 0, -1, -5, 0],\n [0, 0, 0, 2, -5],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 388 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[3, -4, 0, -2, 0],\n [-4, -5, 2, 0, -2],\n [0, 2, 2, -4, 4],\n [-2, 0, -4, 1, 2],\n [0, -2, 4, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2950 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 4, -4, 0, 3],\n [-4, 4, 2, -1, 2],\n [-2, -5, -5, -2, -1],\n [1, 4, 3, 2, -3],\n [5, 5, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2299 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[-5, 2, 3, 4, 4],\n [2, -4, -4, -2, -1],\n [3, -4, -5, 2, -2],\n [4, -2, 2, 2, -5],\n [4, -1, -2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5448 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, -3, -5, -5, 4],\n [0, 3, -3, 1, -3],\n [0, 0, -2, 3, 4],\n [0, 0, 0, -5, -2],\n [0, 0, 0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3696 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, 2, 0, 2, 4],\n [3, -5, 5, -4, 5],\n [2, -2, 1, 1, 0],\n [4, -3, -1, 5, -1],\n [-3, -5, -4, 0, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 462 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 2, 0, -4, -2],\n [-3, 1, 3, 2, 5],\n [3, 1, 2, 4, -1],\n [5, -3, 0, 4, -2],\n [-3, -4, 5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1104 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 1, -3, 2, -5],\n [3, 5, -5, -2, 1],\n [3, 4, 5, -3, 0],\n [2, 1, 2, 3, 0],\n [3, 1, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 510 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, -2, -5, -4, 0],\n [-3, 4, 4, 1, 0],\n [5, -1, 0, 2, -3],\n [-3, 2, -4, 4, 2],\n [2, -3, -4, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2276 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 2th power of the matrix:\n[[-1, 4, 1, 1, 2],\n [-1, 4, 1, -2, -2],\n [5, 3, 3, -3, 3],\n [1, 2, 0, 5, 1],\n [-4, -3, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[5, -2, -2, 2, 5],\n [1, -1, -3, -5, 5],\n [-3, -4, -1, -2, 5],\n [0, 5, 2, -5, -5],\n [2, -1, -2, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 393 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 3th power of the matrix:\n[[-2, -4, -2, -1, 2],\n [-4, 0, 0, 0, 4],\n [-2, 0, 2, 3, -2],\n [-1, 0, 3, 4, 0],\n [2, 4, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -44 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 1) of the result:\nA =\n[[1, -4, -2, 2, 2],\n [-4, -5, -1, 2, -4],\n [-2, -1, 5, 2, -2],\n [2, 2, 2, 2, 2],\n [2, -4, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1798 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-5, 4, 0, 1, 4],\n [4, 5, 0, -2, 0],\n [0, 0, 2, -4, 2],\n [1, -2, -4, -1, -2],\n [4, 0, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 485 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-5, 2, -4, 1, 4],\n [2, 0, 5, 2, 4],\n [-4, 5, -3, 1, 0],\n [1, 2, 1, 3, 4],\n [4, 4, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5033 | MATH |
[
{
"content": "What is the value at position (5, 4) of the matrix A^3 where A is:\n[[-3, 2, 4, 0, 0],\n [2, 1, 3, 0, 0],\n [4, 3, -2, 0, -2],\n [0, 0, 0, 2, -2],\n [0, 0, -2, -2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -54 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, -3, -5, 0, 0],\n [3, -4, -5, 1, 5],\n [-3, 1, 1, -2, -1],\n [4, 1, 0, -2, -2],\n [1, -5, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 523 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, -4, -5, -1, 3],\n [1, 4, 0, -3, 4],\n [3, -3, 4, 3, 3],\n [1, 0, 1, 5, 0],\n [0, -4, 5, -4, -5]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -60 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (5, 1) of the result:\nA =\n[[4, 4, 2, -4, -3],\n [0, -1, 1, -3, -1],\n [0, 0, 3, -5, -2],\n [0, 0, 0, 1, 4],\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^2 where A =\n[[5, -2, -5, 3, -1],\n [3, 0, -2, -3, 1],\n [2, -2, -3, 0, -4],\n [3, 4, -1, 5, -2],\n [5, -2, 2, -3, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 417 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (3, 2) of the result:\nA =\n[[1, -1, -3, 2, -2],\n [1, 2, -5, -5, 3],\n [3, 5, 1, 1, -2],\n [4, -4, -2, 3, -5],\n [-3, -4, 4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "What is the value at position (5, 2) of the matrix A^3 where A is:\n[[-2, 1, 0, 0, -2],\n [1, -4, 2, -2, 4],\n [0, 2, 5, 0, -2],\n [0, -2, 0, -1, -2],\n [-2, 4, -2, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 222 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -2, -1, -2, -1],\n [-2, -5, -2, -1, 4],\n [-1, -2, 1, 2, 0],\n [-2, -1, 2, 3, -3],\n [-1, 4, 0, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2039 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[0, 4, 4, 2, -2],\n [-1, 4, -1, -4, 5],\n [2, 3, -1, 4, -1],\n [-3, 5, 3, -5, 5],\n [4, -1, 3, -5, -5]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, -4, 0, 3, -4],\n [-3, 0, -3, 5, -5],\n [3, -2, 3, 0, -2],\n [1, 3, 3, 3, 2],\n [-3, -3, -5, -5, 5]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 114 | MATH |
[
{
"content": "What is the value at position (4, 1) of the matrix A^4 where A is:\n[[-3, -4, 0, 2, -4],\n [-4, 5, -2, 0, -1],\n [0, -2, 5, -4, -2],\n [2, 0, -4, 2, 0],\n [-4, -1, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -362 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-5, -1, -3, -4, -1],\n [-1, 3, 2, 3, 4],\n [-3, 2, -2, 2, 0],\n [-4, 3, 2, 4, 1],\n [-1, 4, 0, 1, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5002 | MATH |
[
{
"content": "What is the value at position (5, 2) of the matrix A^2 where A is:\n[[3, 4, -2, 4, 2],\n [-1, -1, 1, -4, 5],\n [5, -1, 2, -4, 4],\n [2, -4, 3, -2, -1],\n [4, 0, -3, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -2, -2, -1, 2],\n [-2, 3, -4, 0, -3],\n [-2, -4, -5, -2, 2],\n [-1, 0, -2, 5, -2],\n [2, -3, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34269 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -3, -5, 4, -2],\n [2, -3, 0, 4, 5],\n [-4, 1, 2, 2, 0],\n [1, 3, 4, 4, -3],\n [-3, -2, -2, -2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4025 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, 0, 0, -4, -1],\n [0, 0, -2, 0, -4],\n [0, -2, -4, 1, 2],\n [-4, 0, 1, 5, 2],\n [-1, -4, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -158 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, 4, 0, 4, 3],\n [1, 3, -4, -3, 1],\n [1, -3, -5, 1, 5],\n [5, 2, 4, 1, 3],\n [-2, 1, -5, 4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 564 | 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, 5, 4, -5],\n [-1, -5, 2, -4, 2],\n [0, 4, 2, 2, 1],\n [-4, -1, 2, -1, 4],\n [-4, -2, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 454 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, 0, -4, 1, -4],\n [2, -5, 1, 4, 3],\n [4, 1, 4, -1, -2],\n [-5, 3, -1, 2, 0],\n [2, -3, -4, -5, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 2, 5, 1, -4],\n [2, 2, -2, 0, -2],\n [5, -2, 0, 4, -2],\n [1, 0, 4, -3, 1],\n [-4, -2, -2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11963 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 4, 3, -3, -4],\n [-4, -3, -1, -2, -2],\n [-2, -1, 2, 1, -2],\n [-3, -4, -5, 2, -1],\n [2, -5, -2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 415 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 4th power of the matrix:\n[[1, 0, -2, 4, 1],\n [0, -2, -1, -3, 2],\n [-2, -1, 4, 0, -2],\n [4, -3, 0, 4, 0],\n [1, 2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -502 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, -3, -4, 0, 3],\n [2, -2, -2, -1, -2],\n [-1, 1, 2, 5, 3],\n [-5, 2, -2, 5, 0],\n [2, 0, -5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1835 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, -4, 0, -2, 4],\n [-2, -5, 2, -2, -3],\n [-5, -4, -5, -2, -3],\n [3, -5, 0, 5, 0],\n [2, 4, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -844 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, 2, 1, -3, 2],\n [-4, -4, -3, -2, -2],\n [-3, 2, 2, -3, 4],\n [-3, 2, 3, 3, 3],\n [-4, 1, -4, -2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -122 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[2, 0, 2, -2, 3],\n [0, 2, 2, 4, 2],\n [2, 2, 5, 2, 2],\n [-2, 4, 2, 4, 0],\n [3, 2, 2, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 454 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (4, 1) of the result:\nA =\n[[-5, 2, -3, -2, 2],\n [2, 0, -1, 3, 0],\n [-3, -1, 4, 0, -2],\n [-2, 3, 0, 3, 0],\n [2, 0, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the value at position (1, 5) of the 3th power of the matrix:\n[[-4, -2, -1, -1, 1],\n [-3, 2, 1, -5, 0],\n [-3, 1, 0, 2, -5],\n [-4, -4, -2, -3, 4],\n [-4, -5, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -4, -1, -2, -2],\n [-4, -3, 0, 1, 4],\n [-1, 0, -3, 3, 4],\n [-2, 1, 3, 5, 0],\n [-2, 4, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40267 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[4, -3, -3, 0, 4],\n [4, -5, -4, 4, -5],\n [0, -5, 1, -1, -4],\n [5, -4, -4, 4, 1],\n [3, -2, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 218 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, 1, 0, 0, -2],\n [4, -4, 2, 1, 2],\n [3, -3, -2, -1, 3],\n [-3, -2, 5, 2, 3],\n [-2, 5, 5, 4, 3]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 2, 0, 0, 2],\n [2, 3, 0, -2, 2],\n [0, 0, -5, 0, -2],\n [0, -2, 0, -4, 0],\n [2, 2, -2, 0, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -221 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[1, 0, 0, 0, 2],\n [0, 5, -2, 1, -1],\n [0, -2, -4, -2, 2],\n [0, 1, -2, 5, -2],\n [2, -1, 2, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 294 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, -1, -5, -1, 1],\n [3, -3, 2, -4, 4],\n [-5, -4, 3, 2, -5],\n [-3, -4, 3, -2, -4],\n [-3, 1, 0, 3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, -2, 3, -3, -5],\n [-1, 5, -1, -4, -1],\n [3, -1, -4, 1, -5],\n [4, -4, 3, -1, 0],\n [5, -4, -1, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21868 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-3, 2, 2, 0, -2],\n [2, 2, 2, 0, 4],\n [2, 2, 2, 0, -2],\n [0, 0, 0, -1, -1],\n [-2, 4, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 257 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 3th power of the matrix:\n[[5, -1, 5, -2, -4],\n [2, 0, 5, -5, 3],\n [3, 2, 5, -3, 1],\n [2, 4, 3, -1, 2],\n [5, -2, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-2, -4, 0, -4, 0],\n [5, 0, 4, 5, -4],\n [-2, 5, -2, 5, -4],\n [4, -2, -5, -4, -5],\n [-3, -3, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, 1, -4, -3, 4],\n [3, 5, 5, 4, -2],\n [1, 1, 1, 3, 4],\n [-5, -4, 2, 5, -5],\n [2, 4, 0, -3, 5]], determine the value at position (5, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | 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, 0, 0, 0],\n [-2, 0, 0, 2, -2],\n [0, 0, -2, 0, 0],\n [0, 2, 0, 2, -3],\n [0, -2, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 882 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 4th power of the matrix:\n[[2, -2, -3, 0, 2],\n [-2, -3, -3, 0, -4],\n [-3, -3, 2, -2, 0],\n [0, 0, -2, 3, -4],\n [2, -4, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -123 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[5, -4, 2, 2, 5],\n [-4, 0, -1, -1, 0],\n [2, -1, 5, -3, 0],\n [2, -1, -3, 0, 2],\n [5, 0, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2481 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 1, -3, -2, -2],\n [1, 5, -2, 2, -3],\n [-3, -2, 1, -4, -1],\n [-2, 2, -4, -2, 2],\n [-2, -3, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 21117 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 2, -2, -1, -1],\n [2, 4, -2, 2, 2],\n [-2, -2, 2, 0, -1],\n [-1, 2, 0, 3, 2],\n [-1, 2, -1, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12182 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[5, 3, -3, 5, 4],\n [4, 4, -2, 0, 3],\n [-4, -5, 3, 3, -4],\n [-4, 1, 4, 4, -3],\n [-1, -5, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -552 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 4, 0, 2, -2],\n [4, -2, 2, 3, 4],\n [0, 2, -4, -2, 4],\n [2, 3, -2, -5, -4],\n [-2, 4, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57755 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, -2, 2, -2, -4],\n [-2, 5, 2, -3, 0],\n [2, 2, -4, 2, 0],\n [-2, -3, 2, 2, 2],\n [-4, 0, 0, 2, -3]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1170 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (5, 3) of the result:\nA =\n[[-4, -4, 0, -3, -3],\n [4, -3, 5, -1, 0],\n [-3, -5, 4, -3, -3],\n [-5, -3, -4, -2, -2],\n [-5, -4, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (3, 2) of the result:\nA =\n[[0, -3, 5, -1, 5],\n [-3, 2, -1, 0, 4],\n [-1, 0, -3, 1, -1],\n [3, 0, 4, -5, 2],\n [4, -2, 4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[0, -1, 1, -3, -2],\n [-1, 3, -2, 0, 0],\n [1, -2, 4, 0, -3],\n [-3, 0, 0, 3, 0],\n [-2, 0, -3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[2, 4, 2, 3, 5],\n [-4, 2, -2, 2, 5],\n [-2, -4, -2, 1, 3],\n [-4, 3, 3, -1, 4],\n [-1, -4, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -200 | MATH |
[
{
"content": "What is the value at position (1, 5) of the matrix A^2 where A is:\n[[-1, 0, -2, -5, -4],\n [0, -5, 0, -2, 3],\n [-2, 0, -1, 4, -2],\n [-5, -2, 4, -4, 1],\n [-4, 3, -2, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (2, 2) of the result:\nA =\n[[5, 0, -2, -2, 0],\n [0, -3, 0, 1, -2],\n [-2, 0, 4, -2, 1],\n [-2, 1, -2, 0, 2],\n [0, -2, 1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 1, -2, -2, 0],\n [1, -5, 2, 3, 1],\n [-2, 2, 5, 2, 2],\n [-2, 3, 2, 3, 0],\n [0, 1, 2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14801 | MATH |
[
{
"content": "What is the value at position (4, 5) of the matrix A^3 where A is:\n[[-3, 1, 2, 4, -4],\n [1, 4, 2, -4, 3],\n [2, 2, -2, 2, 0],\n [4, -4, 2, 1, 0],\n [-4, 3, 0, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, -4, 0, 2, 1],\n [5, 1, 3, -5, 4],\n [-2, 1, -1, -1, 3],\n [2, 2, -5, 5, -1],\n [5, -1, 0, -4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1871 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, -4, 2, 0, -4],\n [4, -4, 1, 0, -3],\n [-1, -2, -4, 5, 0],\n [-4, -2, 1, -3, -1],\n [-1, 2, 4, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -92 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, -4, 4, 5, -3],\n [1, -5, -3, -2, -3],\n [5, 2, 4, 4, -2],\n [-2, -5, -4, -2, 2],\n [3, 3, 2, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12808 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[2, -4, -3, 4, 0],\n [0, -2, 1, -2, -3],\n [4, -5, 2, -2, 0],\n [-4, 5, -4, -5, -3],\n [-3, -1, 1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 167 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[3, 1, 2, 2, 0],\n [1, -3, 0, -2, 4],\n [2, 0, 1, 4, 2],\n [2, -2, 4, -3, -4],\n [0, 4, 2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 371 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -3, 0, 4, -1],\n [5, -1, 3, 1, -3],\n [2, -4, 2, 4, 0],\n [-4, -1, 0, 0, -1],\n [4, -3, 2, -3, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -332 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 3) of the result:\nA =\n[[2, 0, -3, 2, 0],\n [0, 2, 2, -1, 4],\n [-3, 2, -5, 0, -2],\n [2, -1, 0, 3, 2],\n [0, 4, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -281 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[1, 1, 2, 4, -4],\n [1, 5, 0, 1, -4],\n [2, 0, -2, 0, 1],\n [4, 1, 0, 2, -2],\n [-4, -4, 1, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 247 | 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, -2, -2, -2],\n [2, 1, 4, 0, 2],\n [-2, 4, -2, 0, 0],\n [-2, 0, 0, -5, -4],\n [-2, 2, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31728 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, -3, -2, -4, 2],\n [3, 3, -1, 3, 2],\n [3, 1, -1, -2, -4],\n [-1, 5, -5, 1, 4],\n [-4, 0, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2806 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 3th power of the matrix:\n[[0, 0, 4, -1, 0],\n [0, -5, 2, 1, 2],\n [4, 2, 5, -2, -3],\n [-1, 1, -2, 3, -1],\n [0, 2, -3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -197 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 0, -2, 1, 1],\n [5, 3, 0, 5, 2],\n [-2, 1, -5, 3, 0],\n [-3, 4, -4, 2, -3],\n [5, 3, 5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4169 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[-4, 0, 1, 4, -3],\n [2, 0, -3, 0, -4],\n [-3, -3, 2, -4, -4],\n [-5, 0, -5, 0, 0],\n [2, -2, 1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 376 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 4, 2, 0, 0],\n [4, 3, -2, 2, 4],\n [2, -2, 1, 0, 2],\n [0, 2, 0, 1, 0],\n [0, 4, 2, 0, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26632 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 0, 4, 0, 2],\n [0, 3, 1, 3, 2],\n [4, 1, 2, 0, 2],\n [0, 3, 0, 1, 0],\n [2, 2, 2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9890 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, 0, 3, 2, -1],\n [2, 5, -2, -3, -4],\n [2, -3, 2, -2, -4],\n [-5, -1, 2, -2, -3],\n [-2, 5, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -97 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -3, -3, 4, -5],\n [2, 3, 5, 3, 5],\n [4, -4, 0, -1, -4],\n [-1, 0, -4, -4, -2],\n [2, 4, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36617 | MATH |
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