# Computing eigenvalues and eigenvectors

1. Jul 27, 2010

### jinksys

Find the characteristic polynomial, eigenvectors, and eigenvalues of the matrix.

Code (Text):

[
2 -2 3
0 3 -2
0 -1 2
]
My characteristic poly is x^3 - 7x^2 + 14x - 8

The roots are 1, 2, and 4.

When solving the system, (2I - A)x = 0 I get:
Code (Text):

[
0 1 0 0
0 0 1 0
0 0 0 0
]

Can someone tell me how this relates to a solution?

It looks like x2 and x3 would be zero, but what about x1?

2. Jul 27, 2010

### hgfalling

This means that (t 0 0) is an eigenvector for any t. Since constant multiples of eigenvectors are also eigenvectors, typically we would say that (1 0 0) is the eigenvector (associated with the eigenvalue 2).

3. Jul 27, 2010

### jinksys

Thanks, that makes sense.