Finding Eigenvectors with Close Eigenvalues

[cookiesyum]

Homework Statement

Given the characteristic polynomial -2+x-2x^2-x^3, find the eigenvalues and eigenvectors of the matrix [-1, -1, 0] [1, 1, 1] [3, 1, -2]

Homework Equations

The Attempt at a Solution

The eigenvalues are -2.659, 0.329-.802i, and 0.329+.802i. Next you plug each eigenvalue into the matrix A-xI to solve the system (A-xI)v=0 and find the eigenvectors. Then you solve the system by reducing the matrix to row echelon form. However, when I do that I get the identity matrix. So then what are the eigenvectors?

 

[lurflurf]

That occurs often when the eigenvalues are not close enough. You either need to switch to a less sensitive method, or find closer approximations to the eigenvalues.