messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "For the matrix power A^3 where A =\n[[0, 1, -1, 2, 0],\n [1, -4, 0, -2, -2],\n [-1, 0, -1, 2, -1],\n [2, -2, 2, -1, 1],\n [0, -2, -1, 1, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 950 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 0, -2, -1, 5],\n [5, -3, -3, 4, 1],\n [5, -1, 4, -3, 2],\n [-3, -5, -3, -3, -1],\n [0, 0, -1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10124 | MATH |
[
{
"content": "Find the value at position (5, 5) of the 3th power of the matrix:\n[[-4, 1, 2, 2, -3],\n [1, 3, -3, 1, 2],\n [2, -3, -1, 3, -1],\n [2, 1, 3, 2, -2],\n [-3, 2, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -185 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -2, 3, 2, -2],\n [-2, -5, 4, -1, 0],\n [3, 4, -3, -2, -1],\n [2, -1, -2, 4, -1],\n [-2, 0, -1, -1, 4]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -514 | 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, -4, -3, -1, -3],\n [-2, -3, -2, 2, -3],\n [3, -1, 2, 1, -4],\n [-2, -3, -3, -4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4612 | 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, 5, -2],\n [0, -1, -3, -1, -1],\n [-1, 5, -2, -2, 4],\n [-2, 3, -1, 1, -2],\n [2, 0, -5, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 367 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, -1, -2, -2, 5],\n [-3, 0, -3, -4, 4],\n [1, -5, -1, 5, 1],\n [2, 1, 5, -3, 3],\n [-4, 1, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4573 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[1, 4, -1, 2, 1],\n [4, 2, 5, -2, 3],\n [-5, -2, 5, 3, -1],\n [-2, 5, 5, 2, -4],\n [-5, 2, 2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 167 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[5, 1, -2, -3, 0],\n [1, -4, 2, 3, 1],\n [-2, 2, 3, 2, -3],\n [-3, 3, 2, 1, -1],\n [0, 1, -3, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -79 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[5, 5, -3, 0, -2],\n [2, -3, 5, 3, 5],\n [4, -4, -1, -5, 4],\n [3, 1, -4, -1, 4],\n [-3, 1, -5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[3, 2, 4, 2, -1],\n [2, 5, 2, 2, 0],\n [4, 2, 4, 0, -1],\n [2, 2, 0, 1, 4],\n [-1, 0, -1, 4, 0]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (3, 1) of the result:\nA =\n[[1, -5, -5, -1, 5],\n [2, 4, 5, 3, 4],\n [-2, -2, -1, -5, -5],\n [-5, -5, 1, -1, -5],\n [-1, 5, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 0, 2, -5, -5],\n [0, 0, -2, 2, -5],\n [-1, 1, -1, 4, -2],\n [1, 3, -3, -4, -4],\n [2, -3, 0, -5, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2411 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-5, 0, 0, 0, 2],\n [0, 4, 0, 0, 2],\n [0, 0, 2, -2, -4],\n [0, 0, -2, -3, -3],\n [2, 2, -4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 302 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, 5, 2, -3, 4],\n [1, 0, 5, 3, 2],\n [-2, 4, -4, 3, -3],\n [5, -1, -4, 3, -3],\n [-1, 2, 2, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21007 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[5, 4, 1, -1, -5],\n [-1, -2, -2, 2, 0],\n [1, 5, -3, 1, -4],\n [1, 4, 2, 5, -2],\n [-2, -4, 5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 917 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-5, 2, 3, 4, -2],\n [5, -1, 4, -4, 3],\n [-4, 2, -4, -5, 2],\n [3, 1, -1, -5, 0],\n [-1, 2, 3, 5, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 204 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -3, -2, 1, -4],\n [-3, -3, 1, 5, 4],\n [-5, 1, 1, 4, -1],\n [0, -4, 3, 0, -2],\n [1, 1, 2, -4, 3]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 416 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -2, -2, 0, -1],\n [-2, -3, 2, 0, 0],\n [-2, 2, 2, 4, 0],\n [0, 0, 4, 0, 0],\n [-1, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4882 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[2, 0, -4, -1, -4],\n [0, -3, -4, 3, 1],\n [-4, -4, 0, 0, -4],\n [-1, 3, 0, -2, 2],\n [-4, 1, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1675 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-2, 4, -4, -1, -4],\n [4, 0, 1, 3, -1],\n [3, 2, -2, 1, 4],\n [-4, 0, -3, 1, -4],\n [-4, 2, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -54 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, -2, 3, -3, 5],\n [0, -1, 3, 2, -1],\n [-2, -3, -1, 5, 4],\n [3, -4, 5, -1, -4],\n [-1, -4, 3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1662 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, -4, 0, 4, 0],\n [-4, 4, 4, 4, 1],\n [0, 4, 5, 3, 0],\n [4, 4, 3, 4, 4],\n [0, 1, 0, 4, 1]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-2, 3, 1, -4, -1],\n [3, 1, 2, -1, 0],\n [1, 2, 3, 4, 1],\n [-4, -1, 4, 1, -2],\n [-1, 0, 1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 387 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[2, 0, -2, -1, 3],\n [-3, -5, 3, 0, 1],\n [-1, -2, -5, 2, -3],\n [2, 0, 5, 2, -2],\n [3, 2, 5, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 497 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, -4, -1, -4, 0],\n [-4, 2, 0, 2, -1],\n [-1, 0, 0, 0, 0],\n [-4, 2, 0, 3, -4],\n [0, -1, 0, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3705 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-3, 2, -1, 5, -4],\n [2, 2, 2, -5, 5],\n [-5, -5, -4, -5, -4],\n [2, 5, 2, -1, 1],\n [-4, -4, -2, -3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-1, -1, -4, 1, 0],\n [-1, -2, -2, -2, 1],\n [-4, -2, -1, -1, 0],\n [1, -2, -1, -4, 1],\n [0, 1, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -2, 2, 4, 5],\n [5, -1, 4, 2, -1],\n [3, 1, -3, 1, 3],\n [-2, 0, -1, 5, 5],\n [-2, -4, 1, 5, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15163 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^3 where A is:\n[[1, 3, -4, -5, 2],\n [-4, -2, -1, -2, 1],\n [-3, 4, -1, -3, 4],\n [-3, -5, 5, 5, -4],\n [-5, 2, -4, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, 5, -4, 5, -2],\n [5, 3, -3, -4, -4],\n [-5, 4, 0, -5, -4],\n [4, -5, 3, -3, 3],\n [1, 4, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4259 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 0, -3, -1, -2],\n [0, -5, 0, 4, -2],\n [-3, 0, 0, 1, 2],\n [-1, 4, 1, -3, 0],\n [-2, -2, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1009 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[5, 0, 4, 0, 0],\n [-5, 4, 1, 3, 0],\n [-1, 2, -5, -2, -4],\n [0, -1, -5, -3, 5],\n [1, -4, 4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3332 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[3, -4, -3, 0, 0],\n [-4, -1, -2, -4, 3],\n [-3, -2, -3, -2, -2],\n [0, -4, -2, -1, -2],\n [0, 3, -2, -2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 306 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-2, -2, 5, 0, 2],\n [-3, -3, -1, 2, 1],\n [1, 0, -5, 5, -5],\n [5, -3, -3, 1, -1],\n [-1, -5, -1, -5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -227 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 0, -2, -3, -4],\n [0, 0, 0, -2, 1],\n [-2, 0, -3, -2, 4],\n [-3, -2, -2, -2, 4],\n [-4, 1, 4, 4, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -349 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -2, 0, -2, 3],\n [-2, -4, 0, 0, 1],\n [0, 0, 3, -5, 2],\n [-2, 0, -5, -1, 2],\n [3, 1, 2, 2, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2477 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -4, 0, 0, -3],\n [-4, -4, 1, -4, -4],\n [0, 1, -1, 2, 0],\n [0, -4, 2, -5, 2],\n [-3, -4, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58347 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[5, -5, 1, 1, -3],\n [-2, 2, 3, -4, 5],\n [-1, -5, -5, 4, -2],\n [-4, -5, 0, 3, 3],\n [-5, 4, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -179 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, -4, -1, 5, -1],\n [-4, -5, 5, 0, -5],\n [3, -3, -2, 0, 0],\n [-1, -1, 5, -4, -3],\n [1, -2, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14239 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, 4, -2, -4, 2],\n [-5, 3, -5, -4, 2],\n [5, -3, -3, 1, 0],\n [-2, 3, 0, 0, 3],\n [-1, -3, -2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3228 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 2, -2, 0, -4],\n [2, 5, 2, 0, -1],\n [-2, 2, 2, 2, 4],\n [0, 0, 2, -1, 2],\n [-4, -1, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 326 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-3, 0, -2, 4, 0],\n [0, -3, -2, 0, -1],\n [-2, -2, 5, 2, -2],\n [4, 0, 2, -1, 1],\n [0, -1, -2, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 263 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -1, 2, 1, 2],\n [-1, 4, 0, 0, -2],\n [2, 0, 0, 3, 4],\n [1, 0, 3, -1, 0],\n [2, -2, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2011 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[3, 5, 3, 2, -1],\n [1, 4, 3, 0, -1],\n [5, -3, 3, 0, -3],\n [4, -5, -3, -1, -1],\n [-1, -3, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 2th power of the matrix:\n[[5, -2, 4, 0, -4],\n [-2, 1, -3, 3, 0],\n [4, -3, 3, 0, 1],\n [0, 3, 0, 3, 5],\n [-4, 0, 1, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -26 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -2, 0, -1, 0],\n [-2, 1, 0, 0, 2],\n [0, 0, -2, 1, 1],\n [-1, 0, 1, 5, 2],\n [0, 2, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 195 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-5, 0, 0, -4, -3],\n [0, 4, 0, 1, -1],\n [0, 0, 5, 0, 2],\n [-4, 1, 0, 0, 0],\n [-3, -1, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17267 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -2, -4, -2, 1],\n [-2, -3, -2, 2, 0],\n [-4, -2, -4, 2, 2],\n [-2, 2, 2, -4, -2],\n [1, 0, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 482 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, 2, -2, 5, 4],\n [5, -5, -3, -4, 0],\n [4, 5, 0, 1, 1],\n [3, 4, 3, -4, -2],\n [2, 5, -3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1020 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 4) of the result:\nA =\n[[5, 4, 2, 2, 0],\n [4, -1, 0, -2, 2],\n [2, 0, 2, -2, -2],\n [2, -2, -2, 2, -1],\n [0, 2, -2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 3, -4, 4, 0],\n [-4, -3, -3, 1, -4],\n [-4, 4, 3, 2, -3],\n [3, 2, -5, -3, 5],\n [-4, -1, -5, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 750 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, 0, 1, -1, 5],\n [1, -4, -3, -1, 1],\n [3, -5, 0, -3, 0],\n [5, 0, 5, 5, -5],\n [-2, 0, 3, 5, 1]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (4, 4) of the result:\nA =\n[[-4, -3, -5, -5, -2],\n [5, 5, 3, 2, -2],\n [5, -1, 3, 1, -5],\n [1, -4, -3, 4, -3],\n [4, -5, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, 4, -5, -3, 5],\n [3, -1, 0, -5, -4],\n [2, -5, 3, -4, -4],\n [-5, 3, 4, -2, 4],\n [-5, 1, -2, 3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -58 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-2, -3, 3, 5, 3],\n [-5, -5, -1, 1, -1],\n [4, -5, -1, -3, -4],\n [1, 4, -3, 2, -2],\n [-4, -3, -2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 183 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, -3, -2, 3, -5],\n [1, 5, -1, -2, -3],\n [-5, 3, 0, 2, -2],\n [2, -4, -5, 0, 2],\n [-4, 3, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -810 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, 0, 2, -1, 2],\n [0, -3, -2, 0, -4],\n [2, -2, -5, 0, 2],\n [-1, 0, 0, 3, 1],\n [2, -4, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3724 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 1, 2, -3, 0],\n [1, 1, 2, 3, -4],\n [2, 2, 1, 0, 2],\n [-3, 3, 0, 1, 0],\n [0, -4, 2, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1313 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[1, -1, -4, -3, 0],\n [-2, 3, 0, 1, 4],\n [-3, -3, -5, 3, 2],\n [0, 4, -2, 0, -5],\n [-3, -3, 1, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, -5, 0, 5, 2],\n [-3, 0, 4, 3, 0],\n [3, 2, -5, 1, 5],\n [-1, -2, 4, -4, 2],\n [1, 4, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3648 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 3, 0, -2, 0],\n [3, -5, 0, -1, 0],\n [0, 0, 0, -3, -1],\n [-2, -1, -3, 1, 4],\n [0, 0, -1, 4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1612 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 3, -2, 4, 0],\n [3, -4, 0, 0, -4],\n [-2, 0, -1, -4, -4],\n [4, 0, -4, -3, 2],\n [0, -4, -4, 2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7043 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-3, 5, -4, 3, 1],\n [1, 4, -4, -1, -5],\n [2, -5, -4, -5, -2],\n [1, 5, -4, -5, -4],\n [-4, 2, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 572 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 4, 1, 2, 2],\n [4, 0, 4, 0, 0],\n [1, 4, 4, 2, 0],\n [2, 0, 2, -5, 0],\n [2, 0, 0, 0, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21394 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[4, -5, -5, 2, 5],\n [-1, 4, 4, 0, 0],\n [-1, 4, 2, 4, 1],\n [-4, 5, -5, 0, -5],\n [0, 3, -2, -2, 5]]?\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 absolute values of all entries of the result:\nA =\n[[4, 1, -1, -5, -2],\n [4, -1, -1, 3, 4],\n [1, 1, -4, 5, -1],\n [-1, -4, -1, 4, 3],\n [-4, -5, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31225 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[-2, -1, -4, 2, 0],\n [-5, 0, -3, -1, 1],\n [-4, -2, 4, 3, 5],\n [-1, -3, 5, -4, 1],\n [3, -4, -5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 465 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 4, 4, -1, -2],\n [4, 1, -1, -2, -4],\n [4, -1, -5, 0, 0],\n [-1, -2, 0, -3, 4],\n [-2, -4, 0, 4, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3522 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[5, 5, -1, 5, 4],\n [-5, 2, -2, 4, 3],\n [5, 0, 5, 4, -5],\n [4, -3, -5, -3, 4],\n [0, -4, -3, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5280 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-3, 0, 0, -1, 4],\n [0, 3, 1, 0, -2],\n [0, 1, 0, 0, 0],\n [-1, 0, 0, 5, 0],\n [4, -2, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 131 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 2, -2, 2, 0],\n [2, -4, -2, 4, 3],\n [-2, -2, -1, 2, 0],\n [2, 4, 2, 3, 4],\n [0, 3, 0, 4, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2648 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 5) of the result:\nA =\n[[0, 3, -1, -5, 4],\n [-2, -1, -3, -4, 0],\n [0, 4, 3, 2, 3],\n [3, 4, -2, 1, -1],\n [0, 0, 5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-5, 5, -3, 3, -5],\n [-5, -3, 4, -3, 4],\n [1, -5, 4, -5, 4],\n [3, -4, -3, 4, 5],\n [-2, -4, -1, -2, -5]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -37 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, -2, -4, 0, -4],\n [-3, 3, 0, -5, -4],\n [3, -2, -2, -4, 5],\n [-3, -4, -2, -4, -5],\n [1, -2, -2, 0, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 489 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^3 where A is:\n[[2, 2, -5, 1, -1],\n [-3, -4, -3, 3, 3],\n [-4, -3, -4, -5, -5],\n [1, 0, -4, 3, -2],\n [-4, 4, -1, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 67 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[0, -4, 2, -1, -2],\n [-4, 3, 0, 0, 0],\n [2, 0, 0, -3, 0],\n [-1, 0, -3, -1, 4],\n [-2, 0, 0, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -115 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^3 where A is:\n[[3, 5, -3, -1, 0],\n [4, -3, -5, -5, 4],\n [2, 5, -1, 3, 4],\n [-5, 4, -3, -4, -5],\n [-1, 4, 0, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, 3, 4, -3, -1],\n [3, 5, 2, 2, -2],\n [4, 2, -5, -2, -4],\n [-3, 2, -2, -1, 2],\n [-1, -2, -4, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4607 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 2, -2, -4, 0],\n [2, -4, -1, -2, -2],\n [-2, -1, 1, -2, -1],\n [-4, -2, -2, -3, 2],\n [0, -2, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8111 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, -2, 5, -2, -3],\n [3, -1, -2, -2, -5],\n [4, 3, -1, -1, -2],\n [-1, 4, -1, 3, -2],\n [-3, -2, 3, 4, -1]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[0, -2, 1, 1, 3],\n [-2, -1, 4, -5, 2],\n [1, 4, -4, 0, 1],\n [1, -5, 0, 5, 3],\n [3, 2, 1, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[4, -5, -1, -2, 3],\n [-5, -5, -5, -2, 1],\n [3, -1, -2, -1, 5],\n [-3, -3, 3, 0, 0],\n [-3, 2, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1398 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, 0, 1, 2, 2],\n [0, 1, -1, -2, 3],\n [1, -1, 1, 0, -2],\n [2, -2, 0, -5, -3],\n [2, 3, -2, -3, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 235 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, 0, 5, -5, 1],\n [-5, 3, -2, 1, 4],\n [2, 0, 0, -4, 0],\n [2, 0, 4, 1, 3],\n [-2, 3, 2, -4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12025 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, 3, -3, 3, -5],\n [-4, 1, -4, 1, 1],\n [-5, 0, -1, 5, 3],\n [-5, -1, -3, -5, 3],\n [2, -1, -3, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1470 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^4 where A is:\n[[2, 0, -2, 2, 2],\n [0, -1, -1, 3, 0],\n [-2, -1, -1, -1, 0],\n [2, 3, -1, -2, -2],\n [2, 0, 0, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -264 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -4, -1, -5, -5],\n [5, -3, 1, 3, 0],\n [0, -3, 2, -4, 1],\n [2, 5, -2, -2, -5],\n [-3, -4, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26263 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 0, 2, -2, 1],\n [0, 1, 4, 0, -4],\n [2, 4, -4, 0, 2],\n [-2, 0, 0, 0, 0],\n [1, -4, 2, 0, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1723 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 2th power of the matrix:\n[[-2, -4, -2, -2, 2],\n [-4, -5, 0, -1, 0],\n [-2, 0, 0, -2, -2],\n [-2, -1, -2, 3, 2],\n [2, 0, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, -1, 0, -4],\n [0, 0, -4, -4, 0],\n [-1, -4, 2, 0, 4],\n [0, -4, 0, -2, 2],\n [-4, 0, 4, 2, -5]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 246 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 4th power of the matrix:\n[[-1, 4, 0, 0, 0],\n [4, -1, 3, 1, 3],\n [0, 3, -4, 0, -2],\n [0, 1, 0, 1, 0],\n [0, 3, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 186 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^3 where A is:\n[[1, -4, -4, 5, -3],\n [5, -1, 1, -5, 0],\n [3, -3, 5, -2, 4],\n [3, -2, 5, 4, 0],\n [-4, -4, 4, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -173 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[-3, -2, -5, -4, 1],\n [-5, 2, 0, 3, 5],\n [1, -3, -3, -4, -3],\n [1, 5, 0, 4, -2],\n [4, 3, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1400 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[0, 2, -2, -3, 3],\n [1, 2, 0, -4, -2],\n [1, -5, 1, -1, -1],\n [-3, -1, -2, 2, 1],\n [3, 4, 3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1261 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -3, 3, 2, -1],\n [-3, 0, 0, -1, 2],\n [3, 0, -1, -2, 0],\n [2, -1, -2, -1, -2],\n [-1, 2, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1898 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 1) of the result:\nA =\n[[0, 0, 2, -1, 0],\n [0, -2, -4, -4, -2],\n [2, -4, -4, -2, 2],\n [-1, -4, -2, 4, -3],\n [0, -2, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "What is the value at position (3, 2) of the matrix A^2 where A is:\n[[3, 2, -2, 1, 2],\n [2, -3, -3, -4, 2],\n [-2, -3, 4, 1, -3],\n [1, -4, 1, 1, -4],\n [2, 2, -3, -4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, -2, 0, 0, 2],\n [-2, -3, -2, 4, -4],\n [0, -2, 1, 4, -2],\n [0, 4, 4, 1, 2],\n [2, -4, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11944 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 3th power of the matrix:\n[[-4, 4, -2, -1, -3],\n [0, -2, 2, -3, 0],\n [-4, -5, -2, 4, -3],\n [3, -5, 3, 3, 1],\n [-2, 3, -3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -163 | MATH |
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