Finding eigenvectors?

1. The problem statement, all variables and given/known data

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]

2. Relevant equations



3. 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

Homework Helper
2,410
116
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.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top