messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-5, -5, -3, -2, -2],\n [3, 3, 1, -3, 1],\n [2, -3, 5, -5, -3],\n [-4, 0, 3, 1, 1],\n [3, -2, 4, -4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 411 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-4, 1, -3, -4, -2],\n [4, 5, 4, -5, 4],\n [-3, -3, 1, -2, 4],\n [3, -1, -3, -3, -5],\n [0, 3, 5, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 213 | MATH |
[
{
"content": "Find the value at position (2, 5) of the 4th power of the matrix:\n[[-5, -1, 1, 1, -2],\n [-1, -2, 0, 2, -2],\n [1, 0, -2, 0, 4],\n [1, 2, 0, 4, 0],\n [-2, -2, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1582 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-3, -3, 5, 3, -3],\n [0, -4, 2, -4, 4],\n [0, 0, -2, 5, -5],\n [0, 0, 0, -1, 4],\n [0, 0, 0, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -5, 4, 2, 5],\n [-1, 2, 4, 4, -1],\n [-2, -4, 0, -4, -5],\n [-3, -2, -3, 5, 2],\n [0, 5, -1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7784 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-4, -2, 0, -4, -1],\n [-2, 1, 0, 3, -3],\n [0, 0, -5, -3, 1],\n [-4, 3, -3, 5, 2],\n [-1, -3, 1, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 397 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, -4, -1, 3, -3],\n [-1, 5, 4, 1, -2],\n [-2, -1, -5, 0, 1],\n [2, 5, -4, 5, 4],\n [3, 1, -4, 2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1510 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, -4, 0, 0, 5],\n [-4, -3, -2, -5, 1],\n [-1, 5, 4, -5, 0],\n [-4, -1, -4, 1, 0],\n [1, -1, -2, -1, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19146 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[1, -1, 5, 5, -3],\n [0, -4, -3, 1, -4],\n [0, 0, 4, -1, 1],\n [0, 0, 0, 5, -5],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, 2, 0, -2, 2],\n [2, -3, 0, 0, -2],\n [0, 0, -5, -2, 1],\n [-2, 0, -2, 3, -1],\n [2, -2, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "What is the value at position (1, 2) of the matrix A^4 where A is:\n[[2, 0, 0, -4, 2],\n [0, -1, 4, -1, 0],\n [0, 4, -5, 1, -2],\n [-4, -1, 1, 5, 1],\n [2, 0, -2, 1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-5, 5, 1, -2, 1],\n [-5, 1, 3, 1, -5],\n [4, 5, -4, 1, -1],\n [1, -1, -3, 3, 4],\n [-2, 0, 3, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1550 | MATH |
[
{
"content": "Find the value at position (1, 4) of the 4th power of the matrix:\n[[3, 1, -3, 0, 2],\n [1, 5, 0, -2, -2],\n [-3, 0, 5, -3, 4],\n [0, -2, -3, -1, 2],\n [2, -2, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 587 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 4, -1, -2, 4],\n [4, 4, 2, 3, 0],\n [-1, 2, 5, 4, 0],\n [-2, 3, 4, 4, 0],\n [4, 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"
}
] | 42130 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -1, -1, -1, 0],\n [0, 4, 5, -5, -5],\n [0, 0, -4, 1, 4],\n [0, 0, 0, -2, -3],\n [0, 0, 0, 0, -2]], determine the value at position (5, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, 3, -5, 3, 5],\n [3, -2, 4, 2, -1],\n [2, 2, -3, -3, 0],\n [-4, 4, -3, -3, 2],\n [2, 0, 2, 4, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4783 | MATH |
[
{
"content": "What is the value at position (5, 4) of the matrix A^2 where A is:\n[[-2, 1, 5, -5, 4],\n [0, 2, -1, 3, 0],\n [0, 0, -1, -3, 1],\n [0, 0, 0, 0, -2],\n [0, 0, 0, 0, 5]]?\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, -2, -5, -1, -1],\n [-4, -4, -4, 2, 5],\n [-3, 2, 2, 5, -4],\n [2, 2, 0, -4, -3],\n [-1, 2, 1, 4, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2211 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 4, 3, -5, 4],\n [-3, 4, 5, -4, -4],\n [5, -3, 1, -5, -4],\n [3, 0, -2, -4, 0],\n [4, -2, 0, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3070 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (4, 2) of the result:\nA =\n[[0, 2, 1, 5, 2],\n [4, 3, -4, -5, 4],\n [-2, 3, -2, 2, -4],\n [3, 5, 4, -3, 1],\n [-1, 0, 2, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 3) of the result:\nA =\n[[4, 1, -2, 1, -2],\n [1, -5, -2, 0, 1],\n [-2, -2, 5, -1, -4],\n [1, 0, -1, -3, 2],\n [-2, 1, -4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -107 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, 5, -3, 4, -2],\n [2, -2, 4, 0, 4],\n [2, 1, -2, 1, -4],\n [-1, 2, -3, 2, -2],\n [-3, -5, 2, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 784 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 2, -4, 2, -2],\n [2, -1, -2, -3, 2],\n [-4, -2, 0, 0, 4],\n [2, -3, 0, -3, -2],\n [-2, 2, 4, -2, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24373 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 4, -2, 0, -2],\n [4, 2, 0, -3, -4],\n [-2, 0, -4, -2, 4],\n [0, -3, -2, 2, 3],\n [-2, -4, 4, 3, -3]]?\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^4 where A is:\n[[2, -3, 3, 0, 4],\n [-3, -3, 0, 0, -2],\n [3, 0, -4, 2, 1],\n [0, 0, 2, -3, -2],\n [4, -2, 1, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4465 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, 0, -2, 2, 3],\n [3, -3, 4, -1, 0],\n [1, -1, 1, -5, 2],\n [2, -5, -4, 0, 2],\n [-2, -1, -4, -4, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 384 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, -2, 2, 2, 2],\n [-2, 0, -4, 0, 2],\n [2, -4, 5, 2, 1],\n [2, 0, 2, 0, 1],\n [2, 2, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 190 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, 0, 0, -2, 0],\n [0, 3, 2, 0, 0],\n [0, 2, -1, 1, 2],\n [-2, 0, 1, 3, 0],\n [0, 0, 2, 0, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5634 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 3) of the result:\nA =\n[[0, -3, -4, 4, -1],\n [-3, 1, 0, 0, -1],\n [-4, 0, 5, 5, 3],\n [4, 0, 5, 3, 2],\n [-1, -1, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2349 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 3, 2, 3, -1],\n [0, 0, -2, -1, -4],\n [0, 0, -1, 5, 3],\n [0, 0, 0, -4, 1],\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"
}
] | 344 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, -5, -1, 0, -2],\n [3, 5, 5, 4, -2],\n [1, 5, 2, 4, -3],\n [-3, 0, 2, -4, 2],\n [-5, 2, -2, -4, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, -3, -2, -4, -4],\n [0, 2, 4, -5, 5],\n [0, 0, 1, 1, 3],\n [0, 0, 0, 3, -3],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1119 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, -2, 0, 4, -1],\n [-5, 4, -4, -2, -4],\n [3, 0, 4, -3, -5],\n [-5, -3, -1, 4, -1],\n [4, 2, -5, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18655 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[5, 1, 0, -2, -2],\n [1, -3, -2, 0, -1],\n [0, -2, -2, 2, 0],\n [-2, 0, 2, -4, 4],\n [-2, -1, 0, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -139 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 2, -2, 0, 2],\n [2, 4, -5, 4, 0],\n [-2, -5, 2, 0, -4],\n [0, 4, 0, -4, -2],\n [2, 0, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4286 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, -5, 0, 0, 3],\n [0, -2, 2, 3, 3],\n [0, 0, -3, 5, -4],\n [0, 0, 0, -4, 1],\n [0, 0, 0, 0, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 157 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 1) of the result:\nA =\n[[-2, 3, -1, -1, -3],\n [0, 2, 2, -5, 2],\n [2, 5, -1, 3, 2],\n [-5, -4, -3, -1, -1],\n [3, 5, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 204 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 0, -1, -3, 2],\n [0, 5, -1, 1, 4],\n [0, 0, -2, 0, 4],\n [0, 0, 0, 3, 5],\n [0, 0, 0, 0, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 356 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-3, 0, -2, 4, 2],\n [0, -1, 0, -2, 0],\n [-2, 0, -3, -4, 2],\n [4, -2, -4, -4, -2],\n [2, 0, 2, -2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1064 | MATH |
[
{
"content": "What is the value at position (1, 2) of the matrix A^3 where A is:\n[[-4, -1, 3, 1, -4],\n [0, -3, 1, 5, -5],\n [0, 0, 3, -3, 0],\n [0, 0, 0, -5, -4],\n [0, 0, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -37 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-5, 4, -3, 1, 2],\n [3, -4, 3, 2, -4],\n [1, 1, 2, 1, 3],\n [-5, -4, 5, -5, 2],\n [2, 4, 3, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 460 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 3, -3, 5, -3],\n [0, -5, 0, -1, 3],\n [0, 0, -1, -1, 3],\n [0, 0, 0, -1, 4],\n [0, 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"
}
] | 428 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, -2, -3, 5, 3],\n [0, -1, -4, -3, 4],\n [0, 0, 1, 1, 4],\n [0, 0, 0, 0, 3],\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"
}
] | 144 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (5, 4) of the result:\nA =\n[[-5, 2, 4, 4, -2],\n [0, 0, 4, 0, 4],\n [0, 0, 0, -2, -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"
}
] | 0 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -1, -1, 0, 4],\n [-4, 4, -4, -3, 2],\n [-2, -4, -5, 2, 0],\n [3, 1, -5, -4, 5],\n [-5, 4, 1, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9272 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 4, -4, 0, -2],\n [0, -1, 2, -3, -4],\n [0, 0, -3, 5, 2],\n [0, 0, 0, -2, 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"
}
] | 1078 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 2th power of the matrix:\n[[3, -3, -5, 5, -1],\n [0, 1, -4, -4, -4],\n [0, 0, 3, -5, 1],\n [0, 0, 0, 3, -5],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 3, -4, -5, 4],\n [-4, 2, 2, -5, -5],\n [-3, -3, 5, -1, 5],\n [-1, 0, 1, 1, 1],\n [4, -2, 3, 1, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3169 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 0, -4, -4, 1],\n [0, 4, -3, 5, 5],\n [0, 0, 4, 1, -1],\n [0, 0, 0, 3, 5],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1005 | MATH |
[
{
"content": "Find the value at position (5, 4) of the 4th power of the matrix:\n[[3, 3, -1, 3, 1],\n [0, 2, -1, -1, 3],\n [0, 0, -5, 5, -3],\n [0, 0, 0, 4, 2],\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^4 where A =\n[[-5, 0, 0, 1, 4],\n [0, 4, 2, 1, 0],\n [0, 2, 1, 3, -1],\n [1, 1, 3, 1, 0],\n [4, 0, -1, 0, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4445 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 3, 0, 4, 2],\n [3, -1, 0, 3, -2],\n [0, 0, 4, 0, -2],\n [4, 3, 0, 1, -2],\n [2, -2, -2, -2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 539 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, -5, 4, 3, -2],\n [-3, 3, 0, 1, -4],\n [0, -1, 3, -5, -3],\n [0, -4, 0, -3, 2],\n [-5, -3, -4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7723 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[2, -2, 2, 1, 4],\n [-2, 3, -2, -4, -2],\n [2, -2, 2, -2, 1],\n [1, -4, -2, -3, -2],\n [4, -2, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 208 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, -5, -1, 2, -5],\n [3, -3, -4, 2, 1],\n [2, 5, -3, -3, -1],\n [1, -5, -1, 3, -5],\n [-3, -4, -3, -4, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 496 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-3, -5, -5, -1, -2],\n [0, -2, 5, 0, 3],\n [0, 0, 5, 4, 0],\n [0, 0, 0, 5, 2],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 2, 2, -4, 0],\n [2, 4, 0, 0, -1],\n [2, 0, 1, -5, 2],\n [-4, 0, -5, -3, 0],\n [0, -1, 2, 0, 2]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 130 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (5, 3) of the result:\nA =\n[[-3, 1, 3, 0, -2],\n [0, -4, 2, -2, -2],\n [0, 0, -3, -1, 2],\n [0, 0, 0, 1, -1],\n [0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[4, -2, 2, 2, 2],\n [-2, 1, 2, 0, 0],\n [2, 2, -3, 0, -1],\n [2, 0, 0, -4, -3],\n [2, 0, -1, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1752 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-2, 1, -3, 5, 1],\n [0, 5, 2, -2, -1],\n [2, -3, 0, -2, 3],\n [4, 3, 4, -3, -4],\n [2, 4, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 412 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 2, 0, 0, -4],\n [2, 0, -2, 2, -1],\n [0, -2, -4, 2, 3],\n [0, 2, 2, -5, 1],\n [-4, -1, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 406 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, -4, 1, 4, 1],\n [2, 4, -1, 4, -5],\n [-2, -3, 4, 2, -5],\n [0, 0, 3, 2, 5],\n [4, 0, -1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, 2, 2, 0, 2],\n [2, 4, -3, -2, 3],\n [2, -3, -3, 4, 2],\n [0, -2, 4, -4, 2],\n [2, 3, 2, 2, -2]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 898 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 0, -3, 3, -3],\n [0, -1, -2, 0, 0],\n [-3, -2, 2, -1, 2],\n [3, 0, -1, 0, 0],\n [-3, 0, 2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8773 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-2, -1, 2, -5, -2],\n [0, 4, 0, -4, 4],\n [-3, -1, 3, -1, -3],\n [-5, 2, 1, 2, 2],\n [-4, 3, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 114 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 0, 4, 0, -4],\n [0, -2, 4, -1, 2],\n [0, 0, 4, 2, 4],\n [0, 0, 0, -4, -4],\n [0, 0, 0, 0, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5079 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-4, 2, -4, -4, -4],\n [0, -5, -2, 3, 2],\n [0, 0, 5, -1, -4],\n [0, 0, 0, 4, 0],\n [0, 0, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-3, -3, -5, 5, 1],\n [0, 0, -4, 3, 1],\n [0, 0, 0, 2, 3],\n [0, 0, 0, 5, 4],\n [0, 0, 0, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 352 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-3, 4, -5, -1, -5],\n [-1, 2, 5, 1, 4],\n [2, -3, 2, -3, 2],\n [-1, 1, 4, 4, -4],\n [-3, -4, 5, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2567 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, -2, -3, -3, -4],\n [1, 5, 1, -4, -1],\n [5, -2, 4, -2, 4],\n [1, 1, 5, 5, -4],\n [-5, -4, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 130 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -4, 4, 1, 5],\n [0, -4, 5, 5, -3],\n [0, 0, 4, 5, 5],\n [0, 0, 0, 0, 4],\n [0, 0, 0, 0, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9181 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[0, -1, 1, 4, -3],\n [0, 5, -1, -4, 4],\n [0, 0, -2, 1, 5],\n [0, 0, 0, 5, 5],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1088 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[5, -1, 0, -4, -2],\n [-1, -1, 0, 2, 0],\n [0, 0, 4, -4, 1],\n [-4, 2, -4, -1, -2],\n [-2, 0, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2471 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-5, 5, 0, 1, -5],\n [0, 2, -2, 1, -3],\n [0, 0, 4, 5, -4],\n [0, 0, 0, 2, 1],\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"
}
] | -125 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[2, 2, 0, -2, -2],\n [2, 2, -4, 1, 4],\n [0, -4, 0, -2, 0],\n [-2, 1, -2, 4, 0],\n [-2, 4, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[0, 2, 5, 0, 4],\n [4, -3, -1, -3, 3],\n [4, -3, 0, -4, -3],\n [-2, -4, -3, 1, 2],\n [1, -1, 5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -195 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 2th power of the matrix:\n[[2, 0, -2, -1, 0],\n [0, 4, 1, 2, -3],\n [-2, 1, 2, -2, 2],\n [-1, 2, -2, 1, 2],\n [0, -3, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, -1, 0, 0, 4],\n [-1, -4, -2, -1, 0],\n [0, -2, -5, -1, -3],\n [0, -1, -1, -3, -3],\n [4, 0, -3, -3, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3751 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[0, 0, -2, 0, -2],\n [0, -5, 2, -2, -4],\n [-2, 2, 4, -2, 0],\n [0, -2, -2, 0, 0],\n [-2, -4, 0, 0, -3]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 3, -5, -5, -3],\n [0, -5, 1, 1, 1],\n [0, 0, 4, -4, -2],\n [0, 0, 0, -2, 2],\n [0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3047 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[3, 0, -3, -3, -5],\n [4, -2, 5, 5, -3],\n [3, 0, 5, 5, 2],\n [0, -1, 2, -2, 0],\n [0, 3, -5, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 884 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 4, 0, 0, 2],\n [4, 1, 2, 2, 1],\n [0, 2, -1, 4, -2],\n [0, 2, 4, -5, 1],\n [2, 1, -2, 1, -2]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 295 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, 1, 1, 1, 4],\n [-3, -3, -2, 2, -5],\n [0, 2, 1, -3, -2],\n [1, 3, -5, -3, 5],\n [-1, -2, -3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1312 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^3 where A is:\n[[-3, 2, 4, 1, -3],\n [3, 4, 1, -2, -1],\n [-2, -5, 1, -1, 1],\n [2, -2, -4, 2, 3],\n [3, 1, 0, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 0, 0, -2, -4],\n [0, -1, 0, 0, 0],\n [0, 0, 2, 0, -3],\n [-2, 0, 0, 2, 1],\n [-4, 0, -3, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6293 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, -2, 2, -2, 0],\n [-2, -2, 2, -1, 2],\n [2, 2, -5, -3, 2],\n [-2, -1, -3, -2, -2],\n [0, 2, 2, -2, 5]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[0, 0, 2, 0, 0],\n [0, 5, -4, -2, 2],\n [2, -4, 4, -3, 4],\n [0, -2, -3, -5, 1],\n [0, 2, 4, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 159 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[1, -4, -3, 1, 1],\n [-4, -1, 0, 1, 0],\n [-3, 0, 0, 2, 2],\n [1, 1, 2, 2, 0],\n [1, 0, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 193 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 2th power of the matrix:\n[[-4, -4, 2, -3, 5],\n [-4, -5, -4, 0, 0],\n [2, -4, 1, 1, -4],\n [-3, 0, 1, -3, -1],\n [5, 0, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[1, 1, -3, 4, -2],\n [1, 0, 2, -4, -1],\n [-4, -1, 1, 4, -4],\n [-2, 5, 4, -4, 2],\n [-5, 5, -3, -5, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 474 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -3, -4, -3, 2],\n [0, 2, -5, -2, 0],\n [0, 0, 3, -3, -5],\n [0, 0, 0, -5, 2],\n [0, 0, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2106 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -1, 2, 4, -1],\n [3, -5, 3, 3, -3],\n [4, 0, -4, -4, 3],\n [4, -3, -2, -3, -3],\n [-5, 2, 5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42230 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 5, -2, -5, -2],\n [-3, 4, -5, -5, 1],\n [-3, 0, 0, -3, -5],\n [-4, 2, -3, -3, 2],\n [3, 4, -5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 564 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[4, -3, -2, 3, 3],\n [0, 1, -5, -5, 0],\n [0, 0, -2, -2, 4],\n [0, 0, 0, -2, -3],\n [0, 0, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 378 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[1, 4, 5, 4, 5],\n [-3, 3, 5, 3, -5],\n [-3, -5, -1, 3, -1],\n [-5, -1, -5, 4, -3],\n [0, 1, 5, 4, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 730 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, 2, -4, 5, 0],\n [-2, 3, 0, -5, -5],\n [0, -1, 4, 4, 5],\n [-5, -4, -3, -5, 0],\n [-5, 1, -3, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3233 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 4th power of the matrix:\n[[3, -5, 3, -3, -5],\n [0, 3, -2, -5, -1],\n [0, 0, 4, 4, 4],\n [0, 0, 0, -1, 0],\n [0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 256 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -2, 4, 0, 2],\n [-2, 4, -4, 4, -2],\n [4, -4, -4, -2, 4],\n [0, 4, -2, 3, 2],\n [2, -2, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66758 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[1, -3, -4, 2, 1],\n [0, 2, -4, 5, 0],\n [0, 0, -3, 0, -3],\n [0, 0, 0, -5, -2],\n [0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[4, 0, 0, -5, 2],\n [-4, 4, 1, -5, 1],\n [-1, 3, 4, 5, -3],\n [1, 5, 4, 5, 1],\n [1, 3, -5, -5, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 652 | MATH |
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