messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[2, -4, 2, 4, -4],\n [-4, -2, 0, -4, 3],\n [2, 0, 2, 0, 4],\n [4, -4, 0, 3, 3],\n [-4, 3, 4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 230 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 5, -1, -4, 2],\n [-2, 4, -4, -5, -2],\n [-2, 0, -2, -5, -1],\n [-3, 2, -3, 0, -4],\n [4, 2, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11014 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[4, 4, 4, -5, -4],\n [-5, 1, -3, 5, -3],\n [-3, 4, -4, -4, -4],\n [1, -1, 4, -2, -1],\n [0, 1, 4, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -203 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[3, 2, 2, 0, 2],\n [2, 4, -4, 0, 0],\n [2, -4, -4, 2, 1],\n [0, 0, 2, 1, 5],\n [2, 0, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 207 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 1, -1, -1, -2],\n [3, 2, 3, -4, -2],\n [0, 3, -3, 4, 1],\n [2, -2, 0, -5, 5],\n [3, -4, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4858 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[5, 4, -3, 2, -2],\n [4, 4, 2, 2, -2],\n [-3, 2, 3, 0, -4],\n [2, 2, 0, -3, -2],\n [-2, -2, -4, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 262 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -1, 4, 0, 0],\n [-1, 1, 2, 2, 0],\n [4, 2, 4, -1, -4],\n [0, 2, -1, 0, 1],\n [0, 0, -4, 1, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3000 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, -4, 0, 4, 2],\n [-4, 2, -4, 0, 2],\n [0, -4, 4, 3, -1],\n [4, 0, 3, -2, -2],\n [2, 2, -1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 367 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 2, -1, 2, 2],\n [2, 4, -2, -3, 0],\n [-1, -2, -5, 2, 2],\n [2, -3, 2, -3, -4],\n [2, 0, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3759 | 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, -4, 2, 0],\n [-2, -5, 2, 1, 0],\n [-4, 2, 4, -2, 0],\n [2, 1, -2, -1, -1],\n [0, 0, 0, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 287 | MATH |
[
{
"content": "What is the value at position (2, 5) of the matrix A^2 where A is:\n[[5, 2, 2, 1, 3],\n [2, 3, -3, 0, 1],\n [2, -3, -4, 2, 4],\n [1, 0, 2, 5, -3],\n [3, 1, 4, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-4, -2, -2, 0, 0],\n [-2, -1, 2, -2, 1],\n [-2, 2, 0, -4, -2],\n [0, -2, -4, 2, -3],\n [0, 1, -2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1702 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, -1, 2, 5, -5],\n [-2, -5, 5, 0, 1],\n [-5, 2, -2, 3, 4],\n [-4, 5, 0, 1, -1],\n [0, 2, -4, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -515 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -4, 0, 0, 5],\n [3, 3, -4, 5, 2],\n [5, 2, -1, 5, 1],\n [4, 5, 5, 5, 5],\n [-2, -2, -3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16814 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, -4, -5, 5, -2],\n [-5, -2, 4, 4, -2],\n [2, 3, 0, 5, -1],\n [5, 5, 0, 3, -4],\n [-2, -5, 0, 3, 2]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -19 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[3, -4, 0, -5, 0],\n [-2, 4, 5, 5, 3],\n [5, 1, 3, -4, 1],\n [-1, -4, 4, -4, 4],\n [1, 5, -1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1428 | 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, -4, -2, 1],\n [-1, 4, -2, 3, 4],\n [4, -4, 1, -1, -4],\n [5, 3, 0, -4, -1],\n [-1, 2, -5, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 413 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-5, -5, -4, 0, 5],\n [3, 5, -3, -1, 0],\n [-3, -2, 1, 5, 3],\n [-1, 5, 0, 1, 2],\n [1, 2, -5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 457 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, 0, 1, -2, 0],\n [0, 5, -2, 3, -4],\n [1, -2, 0, 0, 0],\n [-2, 3, 0, 4, -1],\n [0, -4, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[1, -5, 3, -2, 0],\n [0, 3, 1, 2, -5],\n [5, -2, -1, 4, -1],\n [-4, 0, 3, 4, -2],\n [2, 0, 3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3005 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[1, 0, -1, 1, -4],\n [0, -2, 0, -1, -2],\n [-1, 0, 2, 2, -4],\n [1, -1, 2, 4, 2],\n [-4, -2, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[5, 3, 1, 2, 2],\n [3, -4, -2, -2, 4],\n [1, -2, -4, 0, 1],\n [2, -2, 0, 1, 2],\n [2, 4, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 231 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 3, 1, -2, -2],\n [-5, -2, -3, -1, -3],\n [3, 0, 4, 0, 5],\n [1, -5, 0, 3, -3],\n [0, -2, 5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16372 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[1, -1, -1, 4, 3],\n [-3, 1, 0, 3, 4],\n [-4, 4, -4, -5, 3],\n [1, 1, -3, 2, 0],\n [4, 2, -5, 0, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 411 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 4) of the result:\nA =\n[[0, -2, -1, 0, 2],\n [-2, 4, -2, 4, -2],\n [-1, -2, -5, 4, -2],\n [0, 4, 4, 4, 2],\n [2, -2, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1596 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, 5, -5, 4, 4],\n [5, -1, -2, 5, 0],\n [-1, -5, -1, -5, -1],\n [-3, 1, 2, -5, 0],\n [5, 5, 1, -1, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 139 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 3, 3, -5, -4],\n [2, 3, 5, -1, -4],\n [-5, 1, 2, 5, 4],\n [5, 0, -4, 2, -3],\n [4, -5, 4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 632 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, -5, 4, 2, 5],\n [-5, 1, -3, -4, 0],\n [3, 1, -5, -2, -3],\n [4, 2, -1, 5, -5],\n [0, -5, -2, 0, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -313 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, 3, -1, -2, 5],\n [4, 4, 1, -1, 1],\n [-2, -2, -3, -4, 4],\n [3, -3, 2, -3, 1],\n [-2, 0, 0, 3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 127 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[3, 0, -1, -3, -2],\n [0, 1, -1, -1, 1],\n [-1, -1, 4, 1, -2],\n [-3, -1, 1, -5, 0],\n [-2, 1, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 3th power of the matrix:\n[[-2, 0, -1, 0, 0],\n [0, 4, 0, -4, -4],\n [-1, 0, 2, 0, 2],\n [0, -4, 0, -3, -4],\n [0, -4, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -256 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -4, 4, -3, -3],\n [0, -3, 0, 4, -2],\n [2, -3, 2, 5, 4],\n [2, 4, 5, -4, 0],\n [4, 3, 0, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5056 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 0, 3, 4, -1],\n [0, -1, 5, -4, 5],\n [2, -5, 2, 0, -5],\n [-3, -4, 0, 5, 5],\n [-2, -4, 1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3558 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 2) of the result:\nA =\n[[-5, 4, 0, -3, 0],\n [4, -2, -2, 2, -2],\n [0, -2, 1, 2, -3],\n [-3, 2, 2, 2, 2],\n [0, -2, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 742 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, -4, -2, -4, -5],\n [2, -5, -4, 1, 0],\n [5, 2, 3, -1, -4],\n [-5, -4, -4, -2, 5],\n [-5, -1, -1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2633 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -1, 4, 0, 0],\n [-1, 4, -2, -4, 1],\n [4, -2, -5, -4, 1],\n [0, -4, -4, 4, 2],\n [0, 1, 1, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34061 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, -1, -1, 1, 2],\n [1, 3, -3, 4, 4],\n [3, -5, -2, 3, 1],\n [0, -1, 5, -1, 4],\n [-4, -1, 0, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2003 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-4, 0, 5, -1, 0],\n [1, 3, -1, -5, -1],\n [-1, 3, 4, -5, -5],\n [-2, 2, 1, 5, -1],\n [-5, -4, 5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -53 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 4, 3, 1, -2],\n [5, -2, 4, -2, -4],\n [-5, 3, 4, -3, 0],\n [1, 4, 5, -4, 0],\n [-1, -5, 4, -3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1295 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (2, 3) of the result:\nA =\n[[-4, 3, -2, 4, 0],\n [-1, 1, -4, 2, -1],\n [5, 5, 4, -5, -4],\n [-4, 2, -1, 2, -5],\n [-3, 2, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[4, 0, -1, 5, -3],\n [-3, -4, -4, -2, -3],\n [2, 0, 3, 3, 3],\n [-3, 0, 4, 4, 2],\n [-2, -3, -3, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 217 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -3, -4, -2, -1],\n [-3, 3, -2, 0, -2],\n [-4, -2, -4, -2, -3],\n [-2, 0, -2, -2, 4],\n [-1, -2, -3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34769 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 0, 1, 2, 0],\n [0, 4, -2, -2, -2],\n [1, -2, -2, 0, 0],\n [2, -2, 0, -1, -1],\n [0, -2, 0, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 365 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[1, 2, 0, 0, -1],\n [2, 4, -2, 0, -3],\n [0, -2, 0, 0, 0],\n [0, 0, 0, -2, -1],\n [-1, -3, 0, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 242 | MATH |
[
{
"content": "What is the value at position (3, 3) of the matrix A^3 where A is:\n[[-5, -5, -5, -4, 2],\n [-3, -1, -5, 4, -5],\n [3, -1, 2, 2, 2],\n [1, 2, -1, -4, -2],\n [1, -4, -1, 5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, -4, 5, 0, 0],\n [-3, 4, -5, -1, -5],\n [2, -3, -1, 2, 0],\n [-5, 2, 1, 2, 5],\n [2, 3, 4, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5247 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[1, 1, -2, 0, 0],\n [1, -4, -4, -4, 0],\n [-2, -4, 2, 0, 2],\n [0, -4, 0, -5, 0],\n [0, 0, 2, 0, 5]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, -4, 0, 0, 0],\n [-4, -3, -2, 2, -4],\n [0, -2, 2, 4, -2],\n [0, 2, 4, -3, 0],\n [0, -4, -2, 0, 5]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1096 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 0, 0, 0, 2],\n [0, -4, 0, -2, -2],\n [0, 0, -3, 2, -2],\n [0, -2, 2, 4, -3],\n [2, -2, -2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6954 | 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, 2, 5],\n [4, 1, 0, -3, -2],\n [-2, 1, 3, 2, 5],\n [5, -4, 4, 0, 4],\n [2, 3, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2169 | MATH |
[
{
"content": "Find the value at position (5, 1) of the 4th power of the matrix:\n[[0, 3, 2, 5, -4],\n [2, 2, -1, -4, 2],\n [1, -2, 1, 0, -4],\n [1, 0, 4, 0, -1],\n [-4, -4, 3, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -356 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, 3, -2, -5, -4],\n [3, 2, 3, -4, 0],\n [2, 2, 0, -1, 0],\n [3, 4, 2, -3, -2],\n [4, 0, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1979 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, -3, 1, 0, 0],\n [-3, 4, 0, 0, 0],\n [1, 0, -5, 0, 0],\n [0, 0, 0, 1, 0],\n [0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -87 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (4, 1) of the result:\nA =\n[[-3, -2, 0, -1, -2],\n [4, 3, 3, 1, 0],\n [1, 5, 5, 3, -5],\n [-4, -5, 2, -1, -1],\n [-3, 5, 2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | 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, -1, -2, 5],\n [4, -2, 4, 1, -1],\n [-3, 2, -5, -3, 5],\n [3, 4, 0, 2, 1],\n [0, 0, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12768 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, 1, 3, 3, 1],\n [0, -1, 3, 4, -5],\n [1, 4, -4, 0, 3],\n [-4, -2, 5, -1, -3],\n [1, 4, -5, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -970 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, -5, 3, -3, -5],\n [-2, 3, 4, 2, -1],\n [2, 3, 1, -1, -2],\n [3, -3, 0, -3, 2],\n [4, -4, -4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1095 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 0, 2, 1, 0],\n [0, -3, -4, -2, 0],\n [2, -4, 0, 2, -2],\n [1, -2, 2, 3, -1],\n [0, 0, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11120 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, 1, 5, -4, -4],\n [-4, -2, 5, -5, 2],\n [2, 1, 4, 3, -1],\n [3, 2, 1, 0, -4],\n [-4, 0, -3, 5, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7162 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-2, 2, 2, 4, 0],\n [2, 1, 0, 0, 4],\n [2, 0, 2, 0, 1],\n [4, 0, 0, 1, 2],\n [0, 4, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 259 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, 0, 0, -4, 4],\n [-3, 0, -3, -2, -3],\n [-1, -4, 2, 1, -4],\n [2, 0, -2, 2, -3],\n [5, -1, -2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 689 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -1, -3, 3, 5],\n [0, 0, 1, 1, -3],\n [-1, -2, 5, 4, -4],\n [-5, 3, -1, 1, 3],\n [3, -4, 1, 0, 2]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -287 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 1) of the result:\nA =\n[[3, 0, 2, 4, 4],\n [0, -3, 0, 0, 0],\n [2, 0, 1, 1, -2],\n [4, 0, 1, 1, 0],\n [4, 0, -2, 0, 1]]\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 all entries of the result:\nA =\n[[-5, 2, 2, -2, -3],\n [2, 3, 1, 2, -2],\n [2, 1, -4, 0, 0],\n [-2, 2, 0, -4, -2],\n [-3, -2, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1126 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, -2, 0, -1, -1],\n [-2, 0, 0, 3, 2],\n [0, 0, 5, 4, 2],\n [-1, 3, 4, -2, -1],\n [-1, 2, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1333 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, -5, 0, 1, -2],\n [-5, -2, 4, -2, 3],\n [-1, 1, -5, 0, 1],\n [3, -4, 1, 0, 0],\n [3, 5, -5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -189 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[3, 2, -2, -5, 2],\n [2, 4, 0, 1, 2],\n [-2, 0, -4, 0, 4],\n [-5, 1, 0, -3, 0],\n [2, 2, 4, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^2 where A is:\n[[-5, -1, -3, 0, -3],\n [-5, 2, 2, 4, 1],\n [0, 2, -5, -4, -2],\n [-3, -5, 5, 5, -3],\n [-1, 1, 3, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 2) of the result:\nA =\n[[-3, 2, 3, 2, -4],\n [2, -2, 4, 2, -1],\n [3, 4, 0, 1, 5],\n [2, 2, 1, -4, 2],\n [-4, -1, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -59 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^2 where A is:\n[[4, 0, 4, -1, 1],\n [0, -3, 0, 1, 0],\n [4, 0, 4, 2, -2],\n [-1, 1, 2, 0, -4],\n [1, 0, -2, -4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 5) of the result:\nA =\n[[-2, -3, 2, 1, 0],\n [-3, -1, 3, -2, 1],\n [2, 3, -2, 1, 1],\n [1, -2, 1, 4, -2],\n [0, 1, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -83 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -4, 0, -3, -2],\n [-4, 2, 1, 0, -2],\n [0, 1, 1, 0, 2],\n [-3, 0, 0, -2, 0],\n [-2, -2, 2, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1259 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^3 where A is:\n[[-3, 4, -5, 4, 2],\n [1, -2, 0, 4, 1],\n [-5, 2, 4, -5, -4],\n [0, 0, 5, -1, 0],\n [-3, -3, -4, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, -1, 0, -2, 2],\n [-1, 5, 0, -4, -4],\n [0, 0, -5, 2, 0],\n [-2, -4, 2, -5, 2],\n [2, -4, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2351 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -4, -2, 4, -1],\n [4, -1, 3, -3, 3],\n [3, 5, 2, -3, -2],\n [4, -1, 0, -5, -1],\n [0, 0, 0, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13167 | 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, -4],\n [1, 5, -2, -4, 5],\n [-1, 3, 1, 3, 2],\n [2, -2, 0, 3, -4],\n [-5, 1, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3472 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 0, 1, 5, 0],\n [4, -4, -4, -2, 5],\n [2, -1, 0, -2, 2],\n [3, 1, 5, -4, -3],\n [-2, -3, 2, -1, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16311 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[-4, 2, 2, -3, -2],\n [2, 5, 0, 0, 0],\n [2, 0, -5, 0, 0],\n [-3, 0, 0, 0, -5],\n [-2, 0, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1233 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, 0, 2, -5, -4],\n [2, 5, -1, -1, 3],\n [1, 5, -3, 3, -5],\n [4, 3, 4, -4, 2],\n [-3, -3, 1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 416 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 0, -2, 0, -2],\n [0, -1, -5, 2, -1],\n [-2, -5, 2, 3, -2],\n [0, 2, 3, -5, 2],\n [-2, -1, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5842 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[2, -4, -1, 2, -2],\n [-4, -2, -4, -2, -2],\n [-1, -4, -3, -2, -2],\n [2, -2, -2, 1, -2],\n [-2, -2, -2, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 383 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, 3, -5, -4, -1],\n [0, 5, 1, -1, 4],\n [-5, 2, 1, 3, -5],\n [0, 3, -2, -3, 2],\n [4, 3, -1, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1079 | 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, -5, 1],\n [5, -1, 2, 0, 0],\n [2, -3, 3, -5, 4],\n [-2, 1, -4, 2, -4],\n [-5, 4, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4396 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-3, 0, 0, 2, -4],\n [4, 2, 2, 2, 0],\n [2, 3, -4, 4, 3],\n [5, 3, -2, 3, -2],\n [3, 3, 5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-4, 2, 3, 0, 2],\n [2, 3, 2, -1, 1],\n [3, 2, -2, 3, 0],\n [0, -1, 3, -5, -3],\n [2, 1, 0, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2472 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, -2, 0, 5, 2],\n [-2, -1, -2, 2, -5],\n [0, -2, 5, -1, 0],\n [5, 2, -1, 1, -4],\n [2, -5, 0, -4, -5]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -138 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, 0, -2, -2, 3],\n [0, -1, -3, 2, -4],\n [-2, -3, 1, 2, 4],\n [-2, 2, 2, -1, -2],\n [3, -4, 4, -2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 851 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-4, 0, 1, -4, 0],\n [0, 0, 0, -3, 0],\n [1, 0, -2, 5, 0],\n [-4, -3, 5, -5, 0],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 127 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, 0, 0, 2, 2],\n [0, -5, 0, 0, -2],\n [0, 0, 3, -2, -4],\n [2, 0, -2, 3, -4],\n [2, -2, -4, -4, -1]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, -2, -2, -3, -2],\n [-2, -4, 4, 2, 2],\n [-2, 4, -5, 4, -2],\n [-3, 2, 4, 2, -2],\n [-2, 2, -2, -2, 0]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[5, 0, -1, 0, 1],\n [0, -2, -1, -1, -3],\n [-1, -1, 1, 4, -2],\n [0, -1, 4, -2, 3],\n [1, -3, -2, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "What is the value at position (3, 5) of the matrix A^2 where A is:\n[[1, -1, -2, -4, 4],\n [-1, -2, 0, 0, -4],\n [-2, 0, 1, 0, 2],\n [-4, 0, 0, 1, 2],\n [4, -4, 2, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the value at position (1, 5) of the 4th power of the matrix:\n[[5, -2, 2, -3, 2],\n [-2, 4, 0, 1, -2],\n [2, 0, 3, 0, 2],\n [-3, 1, 0, 0, 0],\n [2, -2, 2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3410 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, 0, 0, -1, 2],\n [-3, 1, -5, 5, 5],\n [-4, -4, -1, 3, -1],\n [2, 1, -5, 3, 3],\n [5, 2, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10190 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 3) of the result:\nA =\n[[-1, 1, -4, 0, 0],\n [1, -3, -2, -3, -3],\n [-4, -2, -1, 0, -2],\n [0, -3, 0, 2, -2],\n [0, -3, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -77 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, 1, 0, 2, -4],\n [1, 5, -2, 2, 2],\n [0, -2, -3, 2, 3],\n [2, 2, 2, 5, -4],\n [-4, 2, 3, -4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 491 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -2, -2, 5, 1],\n [0, 0, -4, -2, 5],\n [1, 4, -4, 0, 4],\n [-2, -2, 5, 3, -3],\n [-4, -3, -3, 1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28943 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 2th power of the matrix:\n[[-4, 2, -2, -2, -2],\n [2, 5, 2, 1, -1],\n [-2, 2, 5, -2, -2],\n [-2, 1, -2, 5, 3],\n [-2, -1, -2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[0, -5, -2, -4, 2],\n [-5, -2, 0, 0, -1],\n [-2, 0, 2, 0, 0],\n [-4, 0, 0, -5, 4],\n [2, -1, 0, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 171 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, -2, -2, -1, -2],\n [-2, -5, -2, -2, -3],\n [-2, -2, 3, -1, -1],\n [-1, -2, -1, 3, 2],\n [-2, -3, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1336 | MATH |
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