messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the matrix power A^2 and find the value at position (4, 1) of the result:\nA =\n[[0, 0, 0, -2],\n [0, -1, -1, -1],\n [0, -1, -2, 0],\n [-2, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[3, 2, 0, 4],\n [2, -2, 1, 0],\n [0, 1, -1, 2],\n [4, 0, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1276 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-4, -1, -2, 0],\n [-1, 2, -3, -2],\n [-2, -3, 0, -4],\n [0, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 179 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -2, 3, -3],\n [1, 1, -3, 2],\n [-2, 0, -4, -1],\n [-1, -2, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1056 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 1) of the result:\nA =\n[[-1, -2, 2, 1],\n [-2, -1, -1, -1],\n [4, 0, -1, 3],\n [4, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 1, -1, 4],\n [-4, 4, -1, -1],\n [-3, 0, 4, -3],\n [-3, 0, 4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1983 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^3 where A is:\n[[-4, -3, -4, -3],\n [-1, 2, 0, 4],\n [-1, 3, -3, -4],\n [-4, -3, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -42 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[4, 0, 3, 0],\n [0, -1, -1, -2],\n [3, -1, -4, 1],\n [0, -2, 1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, -4, -2, -3],\n [-4, 2, 1, 0],\n [-2, 1, -4, 3],\n [-3, 0, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[0, -2, 1, 2],\n [-1, -3, 2, 0],\n [3, -4, 0, 3],\n [-1, 4, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^3 where A is:\n[[-2, 2, -3, 1],\n [-2, -3, -4, 0],\n [-4, 4, 3, 2],\n [-4, -3, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, 1, 2, -1],\n [1, -1, 1, 0],\n [2, 1, 0, 3],\n [-1, 0, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1987 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 0, 4, -3],\n [0, -3, -1, 2],\n [4, -1, -2, -2],\n [-3, 2, -2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 222 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 2) of the result:\nA =\n[[0, 3, -3, -4],\n [4, 2, 4, -2],\n [-3, 1, 3, 1],\n [4, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-2, 2, -1, -1],\n [1, 2, -4, 4],\n [2, 3, 4, -1],\n [-1, 0, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^2 where A is:\n[[1, -4, -4, -2],\n [0, -1, 0, 3],\n [4, -4, 2, 1],\n [3, -1, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[-2, 2, -3, -3],\n [-2, 2, -1, 2],\n [-1, 2, 3, -4],\n [3, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, -2, 0, 2],\n [-2, -3, -1, -2],\n [0, -1, -3, -1],\n [2, -2, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, -2, -2, 1],\n [-2, -1, -2, 0],\n [-2, -2, -2, -2],\n [1, 0, -2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -181 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[1, -2, 0, -1],\n [-2, 4, 2, 2],\n [0, 2, -2, -2],\n [-1, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[4, 1, -2, 1],\n [2, -1, 3, 2],\n [-3, -3, -1, -4],\n [-3, -3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-3, 0, -2, 0],\n [0, -1, -2, 0],\n [-2, -2, 2, 2],\n [0, 0, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-3, 0, 3, 4],\n [0, 1, 2, -2],\n [3, 2, -4, 1],\n [4, -2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, 2, -2, 2],\n [2, 3, -1, 1],\n [-2, -1, 4, 3],\n [2, 1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1511 | 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, -4, -4],\n [0, 0, 0, -1],\n [4, 2, 4, 0],\n [-1, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1133 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 1, -2, 0],\n [1, -4, 0, 0],\n [-2, 0, -4, 2],\n [0, 0, 2, 4]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 0, 3, 2],\n [0, 3, 3, -2],\n [3, 3, 0, -2],\n [2, -2, -2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5290 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, 3, -1, 2],\n [-4, -3, 2, 1],\n [-2, 3, 3, 1],\n [0, 2, -4, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -41 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[4, -2, 0, 2],\n [-2, -2, 0, 2],\n [0, 0, 1, 0],\n [2, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, 0, 0, 4],\n [0, 4, -2, 2],\n [0, -2, 2, 4],\n [4, 2, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1175 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-2, -2, -2, -2],\n [-2, 1, 2, 0],\n [-2, 2, -1, 3],\n [-2, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "Find the value at position (2, 2) of the 2th power of the matrix:\n[[2, 1, 0, -1],\n [1, 1, 0, 2],\n [0, 0, 1, 0],\n [-1, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^2 where A is:\n[[4, 2, -1, 0],\n [2, -4, 1, -1],\n [-1, 1, 3, 3],\n [0, -1, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-2, 0, 0, 2],\n [0, 3, 3, 2],\n [0, 3, -3, 2],\n [2, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 369 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, 0, 0, 0],\n [0, 4, 1, 0],\n [0, 1, -2, 0],\n [0, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, -3, -2, -1],\n [-1, 2, 3, -2],\n [2, 1, -2, -3],\n [1, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 3th power of the matrix:\n[[0, 3, 0, 2],\n [-4, -3, 1, -3],\n [4, 1, 0, 2],\n [4, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[4, 2, 1, 2],\n [2, 1, 2, 4],\n [1, 2, 2, 0],\n [2, 4, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 268 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, -3, -2, -2],\n [-3, -1, 2, 0],\n [-2, 2, -4, -2],\n [-2, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -307 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[3, 2, 1, 2],\n [-2, 2, -4, 4],\n [4, 1, 0, -1],\n [-3, 0, -1, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 176 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 3th power of the matrix:\n[[0, -1, 0, -2],\n [-1, -3, 2, 0],\n [0, 2, 2, 2],\n [-2, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 3th power of the matrix:\n[[-3, 0, 2, 0],\n [0, -2, 1, 0],\n [2, 1, 2, 0],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "What is the value at position (4, 1) of the matrix A^4 where A is:\n[[-4, -3, 1, -4],\n [-2, -3, -3, 0],\n [3, 2, 3, 3],\n [-4, -3, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 283 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -2, 4, 0],\n [-3, -3, -4, -3],\n [0, 2, 0, -2],\n [3, 3, 1, -1]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -267 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[3, 0, 1, 0],\n [0, -3, 0, 4],\n [1, 0, 2, -2],\n [0, 4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -272 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 3th power of the matrix:\n[[3, -3, 1, 2],\n [-3, -2, -4, 0],\n [1, -4, 0, -1],\n [2, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[0, 0, 0, 3],\n [0, 2, 0, 0],\n [0, 0, -2, -4],\n [3, 0, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, 0, -2, -2],\n [0, 3, 0, -1],\n [-2, 0, 4, 2],\n [-2, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -144 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 2) of the result:\nA =\n[[-1, 4, 2, -3],\n [1, 0, 0, -4],\n [0, 2, 3, -1],\n [4, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 688 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, 0, 0, -4],\n [-2, 2, 3, -4],\n [-4, -3, -2, 4],\n [2, 3, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 2th power of the matrix:\n[[1, -2, 2, -3],\n [-1, -3, 3, 2],\n [2, -3, 3, -4],\n [-2, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^2 where A is:\n[[-2, -4, 0, 1],\n [-4, 2, 0, 0],\n [0, 0, 1, -2],\n [1, 0, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 4, -4, -2],\n [2, 2, -2, 3],\n [1, 4, 1, 1],\n [0, 1, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1250 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^2 where A is:\n[[-4, 2, -2, 1],\n [2, 1, 0, 2],\n [-2, 0, 0, 1],\n [1, 2, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -2, -1, 1],\n [-3, -3, 4, 4],\n [4, 1, 3, 1],\n [-3, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3495 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 2) of the result:\nA =\n[[2, -3, -2, 1],\n [4, 1, -1, -4],\n [4, 2, -2, 3],\n [-1, -2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[-4, 0, 2, -3],\n [0, -1, 0, 0],\n [2, 0, 4, -1],\n [-3, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -1, -4, 0],\n [-1, -4, -2, -2],\n [-3, 1, 0, 3],\n [1, -4, -4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1118 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 1) of the result:\nA =\n[[1, -1, 2, 0],\n [3, 1, -4, 3],\n [1, 2, 0, -3],\n [4, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, -4, -2, -3],\n [-4, 0, 0, -2],\n [-2, 0, 3, -2],\n [-3, -2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -769 | MATH |
[
{
"content": "Find the value at position (2, 4) of the 3th power of the matrix:\n[[3, 1, -4, 1],\n [-3, 3, -4, 2],\n [2, 1, -1, 1],\n [3, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, -1, 2, 2],\n [-4, 4, 3, 1],\n [-1, 4, 2, 0],\n [-1, -3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 790 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, 2, 0, 0],\n [2, 1, 2, -2],\n [0, 2, -4, -3],\n [0, -2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -196 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 0, 2, -2],\n [0, -2, 0, -2],\n [2, 0, -1, -1],\n [-2, -2, -1, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 827 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, 4, -3, 0],\n [4, 4, 0, -4],\n [-3, 0, 3, 0],\n [0, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1673 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 3, 0, -1],\n [3, -1, 1, 4],\n [-2, -1, 4, 3],\n [1, 1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 176 | 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, 2, 0],\n [-4, -2, 1, 0],\n [2, 1, 4, 0],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3091 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, -4, 3, 1],\n [0, 1, 3, -3],\n [-2, -1, 1, 4],\n [-3, 2, 0, -1]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -68 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[0, 4, -3, 0],\n [2, -3, -2, -1],\n [4, -4, 1, -1],\n [-3, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -158 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, -2, 1, 2],\n [-2, 3, -2, -2],\n [1, -2, -2, 1],\n [2, -2, 1, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 691 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[0, 0, 0, -2],\n [0, -4, 0, 2],\n [0, 0, -1, 0],\n [-2, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 273 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 0, 0, 2],\n [0, -3, -2, 2],\n [0, -2, 4, 1],\n [2, 2, 1, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^3 where A is:\n[[-2, 4, 4, -3],\n [-3, 4, -1, 0],\n [3, -1, 1, -1],\n [-3, 3, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 2th power of the matrix:\n[[-4, 0, 4, 0],\n [0, 3, 3, -2],\n [4, 3, 1, -2],\n [0, -2, -2, -4]]\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[[3, 1, -3, 0],\n [2, -4, -2, -3],\n [-2, 0, -3, -4],\n [-3, 1, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2211 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[4, -4, -3, 1],\n [-3, 4, -1, -3],\n [4, 0, 3, -4],\n [-3, -3, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -29 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[1, 0, 0, 0],\n [0, 3, -2, 0],\n [0, -2, -4, 0],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[1, 0, 3, 0],\n [0, 1, -2, 0],\n [3, -2, -2, 3],\n [0, 0, 3, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, -1, 4, -1],\n [3, 0, -3, 1],\n [4, -4, -2, -1],\n [1, -1, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1524 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, -4, -3, 3],\n [-3, -2, 2, -4],\n [-2, 3, 4, 0],\n [-3, -2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4936 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, -1, -4, 3],\n [-1, 3, 3, 2],\n [-3, -3, -1, 3],\n [3, 0, -3, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[0, 4, -4, 0],\n [1, -1, 0, -4],\n [4, 2, 0, -2],\n [1, -4, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 930 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, -3, -4, 1],\n [-2, 3, -4, 3],\n [-2, 4, -1, -1],\n [2, 1, -2, 3]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-1, -2, 0, -3],\n [4, -3, -1, -3],\n [-4, -4, 1, 1],\n [4, -3, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, 3, 4, -4],\n [-4, -3, 4, -2],\n [-4, 2, 1, 0],\n [0, 4, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5004 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[2, 3, -2, 0],\n [3, 3, -3, 0],\n [-2, -3, -3, 0],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-3, 4, 2, 1],\n [3, -2, 3, 3],\n [2, -1, -1, -2],\n [3, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -4, -4, -1],\n [-3, 0, -4, -4],\n [-2, 2, -2, -2],\n [-4, -4, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29764 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, 2, 1, -1],\n [-1, 4, 0, 2],\n [-4, -4, -4, 4],\n [-2, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 2, 0, 0],\n [2, -4, 2, 0],\n [0, 2, -3, 0],\n [0, 0, 0, 2]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -4, 1, -2],\n [2, -2, 1, -2],\n [4, -3, 3, -4],\n [-1, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2908 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 1, -2, 4],\n [1, -3, -1, 0],\n [-2, -1, 0, 2],\n [4, 0, 2, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4975 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-1, -1, -1, 1],\n [4, -2, 0, 2],\n [-4, 0, -2, 0],\n [3, 1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[3, 2, 1, -3],\n [1, -2, 4, 3],\n [1, -4, 0, -1],\n [3, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -28 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-1, 3, -3, -3],\n [0, -4, -4, -3],\n [-2, 3, -4, 1],\n [4, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 1, -2, 0],\n [1, 1, -4, -3],\n [4, -4, -3, -2],\n [-4, -1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2032 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-3, -2, 0, -4],\n [-2, -1, 2, -1],\n [0, 2, 4, 2],\n [-4, -1, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 206 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 2, 1, 4],\n [1, 0, 1, 3],\n [-2, 0, -4, -4],\n [3, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3688 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 2, -4, 0],\n [2, 3, -2, 2],\n [-4, -2, 0, 2],\n [0, 2, 2, -1]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 797 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 3th power of the matrix:\n[[0, 4, -2, 2],\n [-1, 2, -4, 1],\n [-1, -2, 1, 0],\n [-3, -1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
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