Understanding Eigenvectors: Troubleshooting and Verification

[awl2k]

Hello people!

I am having a bit trouble with verifying my result when i compute the eigenvectors for the following matrix:

A=[[3,4],[3,2]]

I know for sure that the eigenvalues is respectively -1 and 6, so i start finding a solution for the following null spaces:

1) N(A--1I)=[[4,4|0],[3,3|0]]~[[1,1|0],[0,0|0]] => x1 = x2 so the the vector x2[1,-1] will be a solution and therefor the first eigenvector is [1,-1]

2) N(A-6I)=[[-3,4|0],[3,-4|0]]~[[1,-4/3|0],[0,0|0]] => x1=4/3 so this indicate that x2[-4/3,1] will be a solution to the null space, and therefor the second eigen vector i [-4/3,1].

However the result should be [1,-1] [4,3] respectively. What am i doing wrong?

 

[GaussGreyjoy]

[-4/3,1] is not an eigenvector of 6. The correct eigenvector is [4/3,1] because the equation you get is 3x-4y=0.

 

[phyzguy]

Eigenvectors are always undermined up to a multiplicative factor, since if A*x = λ*x, then
A*(nx) = λ*(nx). So (4/3,1) and (4,3) are the same eigenvector.