# Math Help - Final today at 6 - Eigen Values in 3x3 matrix

1. ## Final today at 6 - Eigen Values in 3x3 matrix

| 1 2 0 |
A = | 3 2 0 |
| 0 0 3 |

Find the eigen values and corresponding eigenspace. I know generally how to find eigenvalues but in a 3x3 matrix I get a cubic function that I cannot find the roots for. Thanks so much for the help!

2. solve $det(A - Ix)=0$

I got $det(A - Ix)=(3-x)[(1-x)(2-x)-2*3]=(3-x)[2-3x+x^2-6]=(3-x)(x-4)(x+1)$

so eigenvalues are 3,4,-1

Can you take it from here? You just gotta solve:
$(A-I\lambda_i)v_i=0$
and these will give the the associated eigenvector to the eigenvalues.