Solve the Matrix

12 -3 8
01 2 4
00 1 2

you can't "solve" a matrix, any more than you can solve a number. What is it you want to do with the matrix?

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To solve a matrix, we need to understand what you mean by "solve." There are several operations and techniques that can be applied to matrices, depending on the specific goal you have in mind.

If you are looking to find the determinant of the matrix, you can use the following formula:

det(A) = (12 * 2 * 2) + (-3 * 4 * 0) + (8 * 0 * 1) - (8 * 2 * 0) - (12 * 0 * 1) - (-3 * 4 * 2)

det(A) = 48 + 0 + 0 - 0 - 0 - 24
det(A) = 24

Therefore, the determinant of the given matrix is 24.

If you are looking to find the inverse of the matrix, you can use the formula:

A^-1 = (1/det(A)) * adj(A)

Where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A.

To find the adjugate of matrix A, you need to find the cofactor matrix of A and then take its transpose.

Cofactor matrix of A:
12 2 4
-3 1 2
0 1 2

Taking the transpose of the cofactor matrix gives us the adjugate of A:
12 -3 0
2 1 1
4 2 2

Finally, we can find the inverse of A by dividing the adjugate of A by the determinant of A:
A^-1 = (1/det(A)) * adj(A)

A^-1 = (1/24) * [12 -3 0]
[2 1 1]
[4 2 2]

Simplifying the expression gives us the inverse matrix:

A^-1 = [0.5 -0.125 0]
[0.0833 0.0417 0.0417]
[0.1667 0.0833 0.0833]

Therefore, the inverse of the given matrix is:
0.5 -0.125 0
0.0833 0.0417 0.0417
0.1667 0.0833 0.0833