messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "For the matrix power A^3 where A =\n[[2, -2, -3, 0],\n [-2, -3, 0, -2],\n [-3, 0, -1, -2],\n [0, -2, -2, 0]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -68 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 3) of the result:\nA =\n[[0, 4, -2, 3],\n [3, -3, -1, 3],\n [-4, 0, 1, 3],\n [3, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -52 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, 3, 1, -4],\n [2, 0, -2, -3],\n [3, 4, 0, 1],\n [-3, -1, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10242 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, 0, 4, 3],\n [0, -4, -2, 0],\n [4, -2, 1, 0],\n [3, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7781 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 3, -2, -4],\n [1, -3, 3, -4],\n [-4, 3, 2, 4],\n [-4, 1, -2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1192 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 3th power of the matrix:\n[[-2, -2, -1, -2],\n [-2, -1, 1, 2],\n [-1, 1, 3, -2],\n [-2, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -4, -3, 0],\n [-4, -4, -1, 1],\n [-3, -1, -1, -2],\n [0, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1805 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 3, 0, 2],\n [3, -3, 1, 0],\n [0, 1, 2, 0],\n [2, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 485 | 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, -1, 0],\n [1, 2, 4, -4],\n [-4, 4, -1, 0],\n [0, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1094 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 1) of the result:\nA =\n[[0, 0, -1, 1],\n [0, 3, -2, -2],\n [-1, -2, -1, 4],\n [1, -2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 2, 0, -2],\n [2, -4, -3, 3],\n [0, -3, -3, 2],\n [-2, 3, 2, 2]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[2, -3, 0, 0],\n [-3, 4, -2, 1],\n [0, -2, 4, -2],\n [0, 1, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 696 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 0, 2, 4],\n [0, 2, 2, -3],\n [2, 2, -1, -2],\n [4, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3250 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[-2, -2, 0, 3],\n [-4, -4, -4, 1],\n [-4, 2, 2, 0],\n [-1, -3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -331 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, -1, 0, 0],\n [-1, -1, 0, -1],\n [0, 0, -4, 2],\n [0, -1, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 333 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, -2, -2, 1],\n [-2, 1, 2, 2],\n [-2, 2, 0, -2],\n [1, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1314 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, -2, 0, 0],\n [-2, -3, 2, -3],\n [0, 2, -3, 0],\n [0, -3, 0, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 997 | MATH |
[
{
"content": "What is the value at position (3, 3) of the matrix A^4 where A is:\n[[-3, 3, -1, 0],\n [3, 3, -2, 0],\n [-1, -2, -2, -2],\n [0, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 199 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 1) of the result:\nA =\n[[-4, 2, -2, -2],\n [2, 0, -2, -1],\n [-2, -2, 2, 0],\n [-2, -1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -112 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^3 where A is:\n[[-3, 0, -1, 2],\n [0, -3, 0, -2],\n [-1, 0, -1, -1],\n [2, -2, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -54 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[4, 0, -2, 1],\n [0, -2, 3, 0],\n [-2, 3, 2, 2],\n [1, 0, 2, -4]]\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^4 where A is:\n[[1, -4, -1, 3],\n [-4, 2, 3, -3],\n [-4, -2, 4, 1],\n [2, 0, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | 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, 0, -1],\n [0, 4, -2, 2],\n [0, -2, 4, -2],\n [-1, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 964 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 2, -4, -4],\n [2, -4, 0, -4],\n [-4, 1, 3, 2],\n [0, 3, -1, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4615 | 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, 4, -1],\n [0, 3, 0, -4],\n [4, 0, -1, 0],\n [-1, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1288 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 4th power of the matrix:\n[[2, 2, 2, 4],\n [2, 0, -2, 2],\n [2, -2, -4, 1],\n [4, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -96 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 3, 1, -3],\n [-3, -1, 2, 1],\n [-3, 0, 4, -1],\n [1, 4, 4, -4]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 4, 2, 1],\n [-2, -4, -1, -2],\n [1, 3, -2, -3],\n [-2, 0, -3, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3562 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 4th power of the matrix:\n[[-3, 2, 1, 2],\n [4, -2, 2, 3],\n [1, 4, 0, 4],\n [-2, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 110 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 4, -1, -1],\n [0, -1, 0, 0],\n [0, 0, -3, -2],\n [4, -4, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 757 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, -2, -2, 2],\n [-2, 0, -2, 0],\n [-2, -2, -2, 0],\n [2, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 957 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[4, -2, 4, -3],\n [3, 4, -1, -1],\n [0, -2, 4, -3],\n [-2, 4, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1440 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, 2, -1, 4],\n [2, -4, -2, 0],\n [-1, -2, -3, 0],\n [4, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4913 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-3, -1, -2, 4],\n [1, 0, 2, -2],\n [-2, 2, -4, 0],\n [4, 2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -158 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 1, 0, 1],\n [-4, 4, -4, 2],\n [-1, -4, 0, 2],\n [-4, -2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5680 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 0, 0, 4],\n [0, 3, 4, 2],\n [0, 4, 4, 0],\n [4, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10454 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 3th power of the matrix:\n[[0, 2, 0, -1],\n [-2, -4, 3, 1],\n [0, -2, 3, 3],\n [4, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, -2, 2, 2],\n [-2, 1, 0, 0],\n [2, 0, 1, 0],\n [2, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, 2, -3, -3],\n [-2, 0, 4, -1],\n [1, 4, -4, 2],\n [-1, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -578 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -2, 0, 2],\n [-2, 1, 4, 3],\n [0, 4, 3, -4],\n [2, 3, -4, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1451 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[1, 3, 0, -1],\n [3, -2, -1, 2],\n [0, -1, 4, 2],\n [-1, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 633 | 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, 1, 0],\n [-4, -4, -2, -2],\n [1, -2, 1, 0],\n [0, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10101 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[4, 1, -1, 4],\n [1, -1, 3, 4],\n [-1, 3, 1, 1],\n [4, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -38 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 1, 0, 4],\n [3, 4, -1, 1],\n [-3, -1, 4, -1],\n [4, -4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -249 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-2, -4, -4, 1],\n [-1, 2, -4, 3],\n [-1, 4, 0, -2],\n [1, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 319 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 4, 4, 0],\n [4, -2, 4, -3],\n [0, 4, 1, 0],\n [1, -2, -4, -1]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[0, 1, -4, -4],\n [4, 1, -2, -1],\n [2, 4, -1, -4],\n [3, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 207 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, -3, -1, 0],\n [-4, -4, -3, 1],\n [-4, -2, 0, 4],\n [-2, -4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14982 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 1, 4, 3],\n [0, -4, 1, -2],\n [-4, 1, -4, 0],\n [-3, 3, 3, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 4, 0, 0],\n [-4, 2, -2, -4],\n [1, 1, -4, 4],\n [-1, -4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2208 | MATH |
[
{
"content": "Find the value at position (3, 4) of the 3th power of the matrix:\n[[-3, -1, 3, 2],\n [0, 1, 4, 1],\n [-2, 2, -2, 0],\n [4, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, 0, 0, -4],\n [0, 1, -2, 1],\n [0, -2, 1, 0],\n [-4, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4158 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^4 where A is:\n[[-1, 0, 2, 0],\n [0, 2, 0, -1],\n [2, 0, -1, -4],\n [0, -1, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -72 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, -2, 2, 2],\n [-2, -3, -1, -2],\n [2, -1, -4, 3],\n [2, -2, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 1) of the result:\nA =\n[[-4, 2, -2, 0],\n [2, -1, 1, 0],\n [-2, 1, 4, -2],\n [0, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, -2, 0, 2],\n [-2, -1, 0, -2],\n [0, 0, 1, 2],\n [2, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 979 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[-3, 1, 4, 4],\n [-2, -4, -4, -1],\n [0, -4, 1, -3],\n [-3, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -194 | 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, 0, 2],\n [0, 1, 4, -1],\n [0, 4, -4, 0],\n [2, -1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 575 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 1) of the result:\nA =\n[[-2, 0, -3, 2],\n [-4, -2, 1, 4],\n [2, 1, 3, 2],\n [-4, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -72 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 3, -3, 0],\n [-1, 3, 0, -2],\n [4, 0, -3, -2],\n [3, 2, 4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 722 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^4 where A is:\n[[3, -2, -3, -3],\n [-3, 2, -2, 2],\n [-4, 0, 1, -4],\n [-4, -1, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 3) of the result:\nA =\n[[1, 3, 4, -1],\n [4, 2, 3, -3],\n [-3, 3, -2, 1],\n [4, 3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | 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],\n [2, 2, -3, 2],\n [-2, -3, 3, -2],\n [2, 2, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2514 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 4, -2, -2],\n [4, -2, 0, 2],\n [-2, 0, -1, 0],\n [-2, 2, 0, 2]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 3th power of the matrix:\n[[3, -1, -3, 2],\n [-1, 0, 4, -2],\n [-3, 4, -4, 0],\n [2, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -141 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 0, 3, -4],\n [0, 2, 0, -1],\n [3, 0, -1, -2],\n [-4, -1, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6153 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 1) of the result:\nA =\n[[-3, 3, 2, 0],\n [3, 1, -1, 1],\n [3, 2, -3, -3],\n [-3, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 3, -4, 2],\n [-3, 1, -4, 1],\n [1, 4, -3, 1],\n [-2, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9890 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^4 where A is:\n[[3, -1, 3, -4],\n [1, -1, -3, 1],\n [-1, 2, -3, -3],\n [1, 3, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -147 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 0, 1, 2],\n [0, -3, -2, -2],\n [1, -2, 0, 0],\n [2, -2, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -64 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 0, -2, 0],\n [0, 4, 2, 2],\n [-2, 2, 0, -2],\n [0, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4169 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[-4, 2, -1, -3],\n [3, -3, 3, -3],\n [-3, -3, 1, -1],\n [-1, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 145 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -4, 3, -2],\n [0, 0, 3, 4],\n [4, -4, 3, 2],\n [1, 2, 1, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3992 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 0, -2, 0],\n [0, -2, 4, 1],\n [-2, 4, 2, 4],\n [0, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18415 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 0, 0, 0],\n [0, -4, 2, 4],\n [0, 2, 0, 0],\n [0, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 0, -2, 4],\n [0, 3, -1, 2],\n [-2, -1, 2, 0],\n [4, 2, 0, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4102 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, -1, 3, -1],\n [0, -1, 2, 0],\n [2, 0, -1, -3],\n [0, 3, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 519 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 0, -4, 0],\n [-2, 3, 4, 1],\n [0, 2, -4, 2],\n [4, -4, -3, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1087 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, 1, 0, -2],\n [1, -1, 0, -2],\n [0, 0, 2, -1],\n [-2, -2, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 532 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 2, 0, 0],\n [-3, -4, 4, -4],\n [1, 1, -4, -3],\n [0, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6528 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 4, -3, -1],\n [-2, 2, -4, -2],\n [0, -4, -1, -1],\n [3, 1, 2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 396 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-1, -2, 3, 3],\n [-2, 1, -2, 2],\n [-4, 3, -1, 2],\n [1, 3, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 319 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[-2, 0, 0, -2],\n [0, -2, 2, 1],\n [0, 2, 0, 0],\n [-2, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -64 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -2, 2, 2],\n [-2, -3, 2, -2],\n [2, 2, 0, 0],\n [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"
}
] | 739 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -1, -2, -2],\n [-1, -1, 2, 1],\n [-2, 2, 1, 0],\n [-2, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1180 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -4, 2, 4],\n [-1, -3, -1, -1],\n [3, 3, 0, 2],\n [-4, -3, 3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1030 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, -2, 0, -1],\n [-2, 1, 2, -2],\n [0, 2, -1, 3],\n [-1, -2, 3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -107 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 1, -4, -1],\n [2, -2, -3, 3],\n [-3, 1, -2, 0],\n [-4, 4, 3, -2]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -432 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[3, -1, 2, 0],\n [-1, 0, -1, 0],\n [2, -3, -2, 3],\n [-4, -1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 253 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[3, -2, -4, -2],\n [-2, 1, -1, 2],\n [-4, -1, -1, 0],\n [-2, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 843 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, 0, 1, -3],\n [-1, -2, 0, 2],\n [4, 3, 1, -2],\n [-3, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -102 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, -1, 4, 4],\n [0, 3, 0, -1],\n [-2, -1, -2, -4],\n [-4, 4, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -114 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 0, -3, -4],\n [3, 1, 2, -3],\n [2, 2, -4, 0],\n [1, 2, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -147 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, -2, -2, 1],\n [-2, 2, -2, -1],\n [-2, -2, 1, 0],\n [1, -1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 1, -4, 2],\n [1, -3, 0, 2],\n [-4, 0, 2, -1],\n [2, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8633 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 1) of the result:\nA =\n[[0, 0, -4, -2],\n [1, 0, -3, 1],\n [0, -3, 3, 2],\n [1, -1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^3 where A is:\n[[0, 2, 0, -3],\n [-1, 3, -1, 4],\n [4, 0, 0, 2],\n [2, 0, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -56 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -1, 2, -2],\n [3, -2, 4, 2],\n [-4, 1, -4, -2],\n [2, 3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1400 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 0, 3, 1],\n [0, 1, -3, 0],\n [3, -3, -4, 2],\n [1, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2496 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-4, -2, -1, 4],\n [3, 0, -2, -1],\n [-4, 2, -4, -4],\n [-4, 4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2070 | MATH |
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