So I'm trying to find A^-1 (inverse) matrix. The theorem I'm supposed to use for this is of a matrix using its Adjoint.
A^-1 = [1 / det(A)] * [adj(A)]
The matrix used is A =
2 0 0
8 1 0
-5 3 6
I expanded the matrix using cofactors and obtained
c11=6, c12=48, c13=29
c21=0, c22=12, c23=6
c31=0, c32=0, c33=2
so the matrix cofactor is
6 48 29
0 12 6
0 0 2
and the adjoint of A is
6 0 0
48 12 0
29 6 2
now what do I do? I'm stuck here.
No, the inverse of a matrix is not a value, like it's determinant.
The inverse of a matrix A = adjoint(A)/det(A).
It's not det(adj(A))*(adj(A)) [which is what I think you are suggesting]
Anyway, I don't see how the determinant of adj(A)=6. It's 144 . (12²)
The answer dedust posted is the inverse of A.
Okay so I understand my mistake. The answer is 1/det(A) * ajd(A) (where ads(A) is the matrix starting with line 6 0 0).
However, nahduma really confused me. Just so I can correct my mistake of trying to find the det of such a matrix:
6 0 0
48 12 0
29 6 2
I originally ended up with
(-1)^1+1 6det
12 0
6 2
+ (-1)^1+2 0 det (matrix doesn't matter here is mult by zero).
+ (-1)^1+3 0 det (matrix doesn't matter here it's mult by zero).
So with this I ended up with 6 multiplied by ad-bc which is 12x2 - 6x0. We get 6x24 = 144.
Originally I forgot to count the ad-bc part and ended up with just 6.
Now back to nahduma's post, did you just get 12^2 by simplifying 144 or did you use a method which gave you 12^2?