# Thread: solving for these eigenvalues

1. ## solving for these eigenvalues

Hi there, i want to find the eigenvalues for the given matrix

2 0 -2
0 -1 0
-2 0 -1

so doing the basic steps. det(A - lamda i)

after finding the determinant i get

-L^3 + 7L + 6

L = lambda

cant figure out a way to factor that cubic.

2. ## Re: solving for these eigenvalues

What happens when $\lambda = -1$ ?

3. ## Re: solving for these eigenvalues

oh, so that makes it 0, but couldn't there be other solutions as well?

4. ## Re: solving for these eigenvalues

Yep, you can find them as follows

$\displaystyle \frac{-\lambda^3 + 7\lambda + 6}{\lambda+1} = \cdots$