# Thread: Finding invertible and diagonal matrix

1. ## Finding invertible and diagonal matrix

Let A be a 3x3 Matrix (Im not sure how to make a matrix)

A=
-1 0 1
5 3 2
6 0 4

Compute: An invertible Matrix P and diagonal matrix D such that AP=PD
I am not sure what to do here, any help will be appreciated.
Thanks!

2. ## Re: Finding invertible and diagonal matrix

Originally Posted by farmeruser1
Let A be a 3x3 Matrix (Im not sure how to make a matrix)

A=
-1 0 1
5 3 2
6 0 4
[TEX]A=\left(\begin{matrix} -1 &0 &1\\5 &3 &2\\6 &0 4\end{matrix}\right)[/TEX] gives $A=\left(\begin{matrix} -1 &0 &1\\5 &3 &2\\6 &0 &4\end{matrix}\right)$

3. ## Re: Finding invertible and diagonal matrix

An n by n matrix is "diagonalizable" if and only if it has n independent eigenvectors. If that is true then "D" is the diagonal matrix having A's eigenvalues on its diagonal and "P" is the matrix whose columns are the corresponding eigenvectors (if eigenvalue [tex]\lambda[/itex] is at the first row, the first column of D is the eigenvector corresponding to $\lambda$, etc.