messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the value at position (5, 1) of the 5th power of the matrix:\n[[-5, 0, -3, -5, -2],\n [0, 3, 4, 4, -1],\n [-3, 4, 3, -5, -2],\n [-5, 4, -5, -1, 2],\n [-2, -1, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17060 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, 4, -3, -5, -3],\n [5, -4, -4, 3, 2],\n [-5, -2, -5, -5, -2],\n [-4, -3, 5, 3, -4],\n [-2, -5, -4, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 329217 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 4, 2, -2, 2],\n [4, 0, 0, 0, 2],\n [2, 0, 0, -2, 4],\n [-2, 0, -2, 4, 0],\n [2, 2, 4, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3534 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 4, 1, -2, 5],\n [-2, 1, 3, 5, -2],\n [-2, 0, 0, 1, -5],\n [5, -3, 3, 0, 0],\n [-1, 5, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2806 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 5th power of the matrix:\n[[-5, 0, 1, -3, 0],\n [0, -2, -2, 1, -2],\n [1, -2, 1, 4, 1],\n [-3, 1, 4, -1, -2],\n [0, -2, 1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3735 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[5, 5, -1, 4, -1],\n [5, 4, 0, -4, 1],\n [-1, 0, -2, -2, -2],\n [4, -4, -2, 2, -2],\n [-1, 1, -2, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 135753 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[5, -3, 4, -4, 0],\n [-3, 5, -2, -5, 5],\n [4, -2, 5, -2, 0],\n [-4, -5, -2, 0, 2],\n [0, 5, 0, 2, -2]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2570 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 0, -2, -2, 4],\n [0, 1, 2, 2, 2],\n [-2, 2, -3, -2, -2],\n [-2, 2, -2, -3, -4],\n [4, 2, -2, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -54404 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -4, -1, 2, -2],\n [-4, -3, 0, 4, 0],\n [-1, 0, -5, -4, 1],\n [2, 4, -4, -3, -4],\n [-2, 0, 1, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51596 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 4, -2, -5, -4],\n [5, -5, 0, -3, 1],\n [-1, 3, 1, -2, -1],\n [-1, 5, -1, 4, 3],\n [4, -3, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 161384 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 1, -3, -5, -2],\n [0, -3, -5, 0, -5],\n [3, 5, -5, 0, -5],\n [1, -3, 0, 1, -5],\n [-5, -1, 0, 3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2203 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 4, 2, 4, 3],\n [-3, 5, -4, -2, -4],\n [-5, -3, 1, -5, -4],\n [-5, 2, -1, 2, -3],\n [1, 2, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7270 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, -1, 1, -5, -1],\n [-5, 2, -2, -2, -4],\n [-1, -5, 3, -1, 0],\n [-4, 4, 4, -5, -2],\n [1, 0, 4, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26701 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 1, -3, 2, -1],\n [1, 1, 0, 0, 0],\n [-3, 0, 3, 0, -4],\n [2, 0, 0, -3, -2],\n [-1, 0, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9293 | MATH |
[
{
"content": "Find the value at position (1, 2) of the 5th power of the matrix:\n[[2, 0, -2, 0, -2],\n [0, 3, 0, 4, -4],\n [-2, 0, -2, 2, 1],\n [0, 4, 2, 3, 0],\n [-2, -4, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5192 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 5th power of the matrix:\n[[4, -1, -4, -1, -1],\n [-1, -2, 0, 0, -2],\n [-4, 0, 2, 0, 3],\n [-1, 0, 0, -5, 4],\n [-1, -2, 3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4389 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, 2, -4, -2, 5],\n [2, 2, 0, 2, -1],\n [-4, 0, -2, -2, -2],\n [-2, 2, -2, 5, 1],\n [5, -1, -2, 1, -1]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2732 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 3, 3, 3, 5],\n [-5, 3, 2, -4, 5],\n [-5, -5, 0, 3, 1],\n [-1, 5, -4, -5, -4],\n [-5, -3, 0, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48385 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 3, 4, -1, 1],\n [2, -3, -4, -4, -1],\n [-5, -4, 3, 1, 0],\n [3, 1, 5, -1, 3],\n [0, 0, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48316 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, 2, 3, 2, 0],\n [2, 3, -2, -4, -5],\n [3, -2, -4, -1, 2],\n [2, -4, -1, 1, 0],\n [0, -5, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 191086 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, -1, 2, -2, 0],\n [-1, 5, -2, 2, 0],\n [2, -2, 1, 0, -2],\n [-2, 2, 0, -2, -2],\n [0, 0, -2, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13471 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-1, 5, 2, 2, 2],\n [5, -5, 0, -2, -2],\n [2, 0, 1, -2, 0],\n [2, -2, -2, 3, -2],\n [2, -2, 0, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -62548 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, 2, 5, -4, 2],\n [-2, 4, 4, -5, -1],\n [-5, 1, 2, -3, -3],\n [1, -2, -3, 2, -3],\n [1, -4, 5, 5, -5]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3651 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 0, -1, 0, 4],\n [0, -3, 2, 2, -2],\n [-1, 2, -3, 0, 0],\n [0, 2, 0, -1, -2],\n [4, -2, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1590 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 0, 0, -3, 0],\n [0, -1, 1, -2, 2],\n [0, 1, 5, -2, 0],\n [-3, -2, -2, -3, -2],\n [0, 2, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24111 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 5, -5, 1, -3],\n [5, 2, 0, -2, 5],\n [2, 3, 4, -4, 0],\n [-1, -1, 4, 5, -3],\n [2, 2, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4970 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -3, -4, 3, -4],\n [3, -2, -4, 4, -5],\n [-2, 3, 3, -2, 3],\n [0, -5, 4, 0, 3],\n [-4, 0, -4, -2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1625 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 0, 2, 2, -3],\n [0, 0, 0, -3, 2],\n [2, 0, 0, -2, -2],\n [2, -3, -2, 4, 0],\n [-3, 2, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3981 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 2, -2, 3, 2],\n [1, 1, -3, 0, -1],\n [-5, 5, -3, -5, -2],\n [4, -3, 5, -2, 3],\n [-3, 0, 0, 1, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5585 | 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, 1],\n [0, -1, 2, -4, 5],\n [0, 2, 3, -2, -4],\n [-2, -4, -2, 3, -2],\n [1, 5, -4, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25189 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, 3, -4, -1, -2],\n [3, 1, 0, -1, -1],\n [-4, 0, 5, 0, -4],\n [-1, -1, 0, -2, -2],\n [-2, -1, -4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5024 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -5, 3, -3, 4],\n [-3, 5, -4, 2, -3],\n [0, -4, 1, -2, 3],\n [4, 3, 1, 2, -3],\n [5, -1, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45187 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, 3, 5, 5, 1],\n [4, 4, 2, 3, 0],\n [4, -4, -4, -2, 3],\n [1, -4, 2, 5, 1],\n [3, 2, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118984 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -2, 2, -2, 3],\n [-2, 0, -2, 4, 5],\n [2, -2, 2, -4, 0],\n [-2, 4, -4, -1, -4],\n [3, 5, 0, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3141 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, -3, 1, 0, 3],\n [-1, -2, -3, 4, -5],\n [-3, -3, 1, 1, -5],\n [-3, 2, 3, 1, 1],\n [5, 2, 0, 5, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 142487 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 4th power of the matrix:\n[[-5, 2, -5, -4, 0],\n [2, 1, 3, -4, 2],\n [-5, 3, 0, -2, 0],\n [-4, -4, -2, -3, -2],\n [0, 2, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2614 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, -2, -1, 1, 2],\n [0, -5, 1, -3, 0],\n [2, 1, 4, 0, 3],\n [3, -5, -5, -5, 2],\n [4, 1, -3, -4, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -72836 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -1, 4, 2, -2],\n [-1, 0, -2, 0, 4],\n [4, -2, -2, 0, -2],\n [2, 0, 0, 1, 4],\n [-2, 4, -2, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1283 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, -1, 4, 4, 1],\n [-1, -5, 4, 4, 0],\n [4, 4, 0, 0, 0],\n [4, 4, 0, -2, 4],\n [1, 0, 0, 4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12450 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, 0, -2, -4, 2],\n [0, -4, 0, 0, 0],\n [-2, 0, -4, 2, 2],\n [-4, 0, 2, -5, 3],\n [2, 0, 2, 3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -51382 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -4, 2, 5, -4],\n [3, -2, -5, -2, -3],\n [0, 1, 2, -4, 0],\n [0, 4, -1, 4, 4],\n [1, -3, -2, 4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1599 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 0, -4, -2, 2],\n [0, 1, 2, 0, -2],\n [-4, 2, 3, 2, -3],\n [-2, 0, 2, 0, 0],\n [2, -2, -3, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 970 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 0, 0, -4, 1],\n [0, -5, 0, 2, 0],\n [0, 0, 3, 2, -2],\n [-4, 2, 2, -2, 0],\n [1, 0, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15972 | MATH |
[
{
"content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[-2, 0, 0, -2, -2],\n [0, 3, -4, 5, 1],\n [0, -4, -2, 0, 2],\n [-2, 5, 0, -5, 2],\n [-2, 1, 2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2252 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 4, 4, 2, 0],\n [4, -5, 0, 0, -1],\n [4, 0, -3, -4, 2],\n [2, 0, -4, 0, 2],\n [0, -1, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4282 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-3, 2, 4, -1, -2],\n [2, 4, 1, 4, -1],\n [4, 1, 1, 1, 0],\n [-1, 4, 1, -4, 2],\n [-2, -1, 0, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30509 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 4th power of the matrix:\n[[4, -4, 2, 2, 1],\n [-4, 1, 0, -1, 2],\n [2, 0, 1, 1, 1],\n [2, -1, 1, -2, 0],\n [1, 2, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 276 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 3, -4, 0, -1],\n [-1, -2, 0, -1, 5],\n [-2, 3, 0, 5, 4],\n [4, 4, -3, 4, 0],\n [-5, -1, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21086 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, 0, 0, 2, -3],\n [0, -2, 0, 2, -1],\n [0, 0, -3, 4, 0],\n [2, 2, 4, 5, -3],\n [-3, -1, 0, -3, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 367049 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 1, 0, 1, -3],\n [-3, 5, -5, -2, -4],\n [4, 2, -3, 1, 1],\n [3, 0, -5, 2, -5],\n [-3, 5, -1, 2, 3]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 749 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[1, 4, 0, -4, 0],\n [4, 2, 0, 0, 2],\n [0, 0, 4, -2, -2],\n [-4, 0, -2, 4, -2],\n [0, 2, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1953 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 5, -3, -5, -4],\n [-1, 4, -1, 4, -5],\n [-5, 3, -4, 1, 4],\n [-2, 1, 2, -1, -5],\n [-2, 4, -3, 4, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13459 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[4, 4, 0, -4, 1],\n [-3, -5, 4, -3, 3],\n [4, 5, 5, 0, 5],\n [0, -2, 2, -1, 1],\n [3, -1, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -4, -2, -4, 0],\n [-4, 2, 0, -4, -1],\n [-2, 0, -1, -2, -2],\n [-4, -4, -2, 1, -4],\n [0, -1, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31496 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, -2, 0, 2, 4],\n [-2, -1, 3, 3, 2],\n [0, 3, 1, -2, 2],\n [2, 3, -2, 0, 4],\n [4, 2, 2, 4, -2]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8296 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, -4, 0, 0, 0],\n [-4, -4, 2, 4, -2],\n [0, 2, 0, 0, -2],\n [0, 4, 0, -1, 3],\n [0, -2, -2, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26144 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 4, -3, 2, 0],\n [-4, -4, 3, 1, 4],\n [3, 0, -1, -5, 0],\n [0, -3, -3, -3, -3],\n [1, 4, 5, -4, 4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -334 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -4, 1, 3, 0],\n [-4, 1, 0, 4, 3],\n [1, 0, 1, 1, 0],\n [3, 4, 1, -1, -2],\n [0, 3, 0, -2, 2]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2252 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 0, -1, -1, 4],\n [-4, -2, 2, 2, 5],\n [-5, -4, -1, 3, 4],\n [5, 5, 1, 4, -1],\n [-5, 0, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61622 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, 5, -2, 3, 4],\n [-5, 0, -3, 5, 3],\n [-1, 0, 5, 3, 3],\n [2, 3, -2, 0, -1],\n [-1, -2, -4, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28525 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 0, -2, -3, -2],\n [0, 3, 0, -1, -4],\n [-2, 0, 5, 4, 2],\n [-3, -1, 4, -3, -4],\n [-2, -4, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 407992 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, -3, 1, 0, 2],\n [-3, -3, -2, -3, 3],\n [5, -2, 0, 2, 5],\n [2, -1, -1, 0, 4],\n [1, 4, 1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7328 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[1, 0, -2, -1, 0],\n [0, 5, -2, 2, 0],\n [-2, -2, 5, 4, -1],\n [-1, 2, 4, -3, 2],\n [0, 0, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 294 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, -2, 0, 5, 1],\n [-2, 0, 4, -2, 3],\n [0, 4, 2, 1, -4],\n [5, -2, 1, -1, 2],\n [1, 3, -4, 2, -5]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21542 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 1, 2, -5, -3],\n [1, 3, 2, 2, 3],\n [4, -3, 2, -5, 2],\n [1, 2, -5, 0, 1],\n [5, -1, -1, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14344 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 0, 1, -5, -4],\n [-2, 2, 5, 4, 0],\n [-5, 4, -1, 1, 0],\n [3, 2, -2, 5, -1],\n [1, 2, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22933 | MATH |
[
{
"content": "Find the value at position (1, 2) of the 5th power of the matrix:\n[[-2, -2, 2, -5, 2],\n [-1, 5, -5, -2, -4],\n [-2, 2, -1, -5, 1],\n [-5, 3, -3, -3, 0],\n [4, 0, 5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3036 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 4) of the result:\nA =\n[[-5, -1, 0, 2, -5],\n [-1, -3, -4, 5, 2],\n [1, 4, 1, -1, 3],\n [-1, -4, -3, -2, -1],\n [-3, 1, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -123 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 4, 4, 2, 3],\n [5, -2, -1, -1, 2],\n [3, 1, -1, -3, -5],\n [5, 3, -1, 3, 4],\n [-2, -1, -2, -4, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16799 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -2, -1, 0, 2],\n [5, 2, 1, -2, 0],\n [-2, 1, 5, -5, -1],\n [4, 4, -2, 5, 1],\n [3, -1, -2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 723 | MATH |
[
{
"content": "What is the value at position (5, 3) of the matrix A^4 where A is:\n[[3, 2, -2, 2, 2],\n [2, -1, 4, -3, 2],\n [-2, 4, 3, 0, 0],\n [2, -3, 0, -4, -2],\n [2, 2, 0, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, -2, 4, -4, -3],\n [-3, 3, -2, -5, -5],\n [1, 1, -4, 3, 3],\n [-1, -3, -3, -3, 0],\n [-2, 2, 5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10400 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -5, 2, 0, -1],\n [-5, -3, 4, 1, 4],\n [2, 4, 2, 2, 0],\n [0, 1, 2, 3, 2],\n [-1, 4, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 326312 | MATH |
[
{
"content": "What is the value at position (4, 1) of the matrix A^5 where A is:\n[[-5, -4, 4, -3, 2],\n [0, 4, 5, -1, -5],\n [5, 3, -3, -3, -4],\n [-2, -4, 3, 4, 1],\n [2, -3, 0, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -25959 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-5, -2, 1, 4, -1],\n [-2, 4, 4, 0, 0],\n [1, 4, -1, -3, 4],\n [4, 0, -3, 2, -1],\n [-1, 0, 4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2968 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-3, 1, -4, 0, 4],\n [1, -2, -1, 2, 0],\n [-4, -1, -3, -1, -2],\n [0, 2, -1, -3, 2],\n [4, 0, -2, 2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -26031 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -3, 4, 4, -2],\n [1, -4, -3, 1, 1],\n [4, -3, -5, -3, -1],\n [1, -2, 5, 5, -5],\n [0, -4, -3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26584 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[0, -2, 2, -1, -4],\n [-2, 4, 3, -2, 0],\n [2, 3, 0, -2, 4],\n [-1, -2, -2, -2, -2],\n [-4, 0, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 597 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, -2, -2, -2, 4],\n [-2, 5, 3, 0, -3],\n [-2, 3, -1, -1, 0],\n [-2, 0, -1, -5, 0],\n [4, -3, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35627 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, -4, 1, 2, 0],\n [-4, 2, 2, 4, 4],\n [1, 2, 4, 2, -2],\n [2, 4, 2, -4, 0],\n [0, 4, -2, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32351 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -3, 3, -2, -2],\n [-3, -1, -3, 3, -3],\n [-4, -1, 0, -5, 5],\n [0, 4, -3, -2, 0],\n [2, 3, 0, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -344 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, -2, 0, 2, 0],\n [-2, -5, -1, 0, 3],\n [0, -1, 1, 2, 1],\n [2, 0, 2, -1, 4],\n [0, 3, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3886 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, 4, -1, -3, 2],\n [1, -1, 4, -3, -1],\n [-3, 4, -1, -5, 0],\n [4, -2, -2, 2, -4],\n [-2, -4, -5, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12278 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 1, 2, 0, -1],\n [1, 2, 0, -2, 0],\n [2, 0, -4, -2, -1],\n [0, -2, -2, -2, 0],\n [-1, 0, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2326 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 0, 2, 2, 1],\n [0, 0, 4, 5, 0],\n [2, -5, -1, -3, 2],\n [5, 0, -4, 1, 1],\n [-1, 2, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11023 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -3, -3, -1, -1],\n [-3, -4, 1, -2, 3],\n [-3, 1, -1, 2, 0],\n [-1, -2, 2, -5, 1],\n [-1, 3, 0, 1, -3]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 426 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 2, 1, 2, 4],\n [2, 0, 3, 0, 4],\n [1, 3, -4, 1, 0],\n [2, 0, 1, 4, 0],\n [4, 4, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 417721 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -2, -4, 1, 2],\n [-2, 0, 0, 0, 0],\n [-4, 0, 5, 2, 1],\n [1, 0, 2, 2, -1],\n [2, 0, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 134300 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[5, 2, -3, -2, -4],\n [2, 2, 0, 2, 0],\n [-3, 0, 1, 2, 2],\n [-2, 2, 2, -5, 4],\n [-4, 0, 2, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5766 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, 4, 2, 2, -2],\n [4, 1, -1, 0, 2],\n [2, -1, 1, -3, -2],\n [2, 0, -3, 2, -1],\n [-2, 2, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31951 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -3, 0, 1, 2],\n [1, -3, 0, -1, 4],\n [-2, -5, 1, 2, -4],\n [1, 0, -1, -2, -4],\n [4, 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"
}
] | 14237 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 2, 2, 4, 2],\n [2, -1, 3, 2, -4],\n [2, 3, 1, -2, -2],\n [4, 2, -2, -2, -1],\n [2, -4, -2, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7911 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^5 where A is:\n[[0, 1, 2, 5, 3],\n [3, 2, 4, 5, -3],\n [-4, -1, -5, -3, -5],\n [-3, -2, 1, -1, -1],\n [-5, 2, -2, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8416 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-4, -5, 4, -1, -2],\n [-5, -5, 1, -4, 4],\n [4, 1, 1, -1, 0],\n [-1, -4, -1, -3, 0],\n [-2, 4, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32001 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, -3, -1, 1, -4],\n [-3, -3, 2, 0, -2],\n [-1, 2, 5, 2, 0],\n [1, 0, 2, 1, 2],\n [-4, -2, 0, 2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22440 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[-3, 3, -2, 4, -4],\n [0, -5, 0, 4, -5],\n [2, -1, 0, -4, -4],\n [3, -3, 0, 4, -1],\n [-2, 4, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -555 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 5, -4, 0, 2],\n [1, -5, -1, -4, 0],\n [1, 1, -3, 1, -1],\n [2, 2, 1, 0, -4],\n [0, 5, 3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54517 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, -1, 5, 0, -3],\n [2, 1, -4, 1, -5],\n [3, 1, 0, -4, -3],\n [-5, 4, -1, 3, 0],\n [-1, -3, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7080 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, 0, 2, 1, 1],\n [0, 3, -1, 0, 0],\n [2, -1, -2, -2, 2],\n [1, 0, -2, 4, -2],\n [1, 0, 2, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2314 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 0, 0, -2, 0],\n [0, -3, 0, 3, 4],\n [0, 0, 2, -2, 0],\n [-2, 3, -2, 0, 4],\n [0, 4, 0, 4, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5234 | MATH |
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