Diagonalizing a 3x3 Matrix: Troubleshooting the P-1AP = D Expression

[F1fan]

I have to diagonalize this matrix and I've found the eigenvalues and vectors and they're linearly independent but I can't get the expression P-1AP = D to work.

It's a 3x3 matrix, (-11,-46,-3),(0,12,0),(-1,-2,-9) with eigenvalues of 12,-12 and [STRIKE]8[/STRIKE] -8.
The eigenvectors are (-2,1,0), (3,0,1) and (-1,0,1).

The (P) I made was using the vectors but D is never a diagonal matrix am I missing something?

Edited to correct typo.

 

[vela]

Did you make the columns of P (not the rows) out of the eigenvectors? What did you get for P^-1?

 

[F1fan]

Did you make the columns of P (not the rows) out of the eigenvectors? What did you get for P^-1?

My matrix P was (-2,3,-1), (1,0,0), (0,1,1)

 

[vela]

P^-1AP comes out diagonal here with that matrix.

 

[F1fan]

IF you say it's diagonal than my matrix multiplication skills must be in need of help... I'll try again and see. Thanks for your help!

 

[Mark44]

I get the third eigenvalue to be -8, not 8 as you showed. That wouldn't have made a difference in your calculation of P and P^-1 though.