# Eigne values

1. Nov 2, 2005

Hi, I need help for this problem:
Find the eignevalues and eingenvectors for the matrix below. DO NOT compute them directly by computing the matrix:
A-1

We need to find some kind of demonstration to see if the eignevalues of A-1 are the same, opposite or inverse (or whatever) as those of matrix A
Suppose that the eignvalues are 1,2,3 and the eignvectors are [1,1,0], [0,1,0],[ 3,-1,2] ( in columns
Thank you
B

2. Nov 2, 2005

### HallsofIvy

Staff Emeritus
If $$Ax= \lambda x$$ Then $$A^{-1}Ax= A^{-1}\lambda x= \lambda A^{-1}x$$.

What does that tell you?

3. Nov 2, 2005