# Homework Help: Eigenvalues of a 3x3 Matrix

1. Nov 8, 2012

### Jalo

1. The problem statement, all variables and given/known data
Given the matrix A=

1 -1 -1
-1 1 -1
-1 -1 1

Find the eigenvalues.

2. Relevant equations

I = identity matrix

3. The attempt at a solution

det(A-xI) = (1-x)3 - 2 - 3*(1-x) = 0 ⇔
⇔(1-x)3 - 3*(1-x) - 2 = 0

I can't find a way to solve this equation...
Any help would be appreciated!4

Daniel

Last edited by a moderator: Nov 8, 2012
2. Nov 8, 2012

### Mentallic

If you let y=1-x, then the cubic $y^3-3y-2$ has a zero at y=2.