- #1

Dassinia

- 144

- 0

I'm really having a problem to calculate the eigenvectors of a specific matrix, I'm used to do this but i don't know why I'm stuck at this one

## Homework Statement

A=

2 1 0 1

0 3 -1 0

0 1 1 0

0 -1 0 3

λ

_{1}=2 multiplicity 3

λ

_{2}=3 multiplicity 1

A-2I=

0 1 0 1

0 1 -1 0

0 1 -1 0

0 -1 0 1

The eigenvectors are given

[-1 -1 -1 -1]

[0 1 2 0]

[1 0 0 0]

If I solve

(A-2I)xi=0

I have

x1=0

x2+x4=0

x2-x3=0

-x2+x4=0

I have to use this for differential equations, and my linear algebra course is far behind, I don't remember what I'm supposed to do when we get the first eigenvector =0, because when the multiplicity of the eigenvalue is > 0 we use the first one to find the following eigenvectors

Thanks!