Help in Finding Eigenvectors Associated with Complet Eigenvalue

[tehipwn]

The last matrix at the bottom of the second page is the Eigenvector found using Matlab.

I'm trying to find it by hand. I found the Real Eigenvector associated with L=76.2348. But I've tried to find the Eigenvector's for the complex Eigenvalues for a while and can't get the answer given by Matlab. I might be doing the row operations and solving for x1,x2,x3 correctly but then using the wrong norm to get the Matlab answer?

Any help would be much appreciated.

The Attempt at a Solution

The attempt is in the attachments.

Note:
On the second page, the equation:

(-3.5476+j316.915)*x2 - 83.33*x3 = 0

should have been:
(-3.5476+j316.915)*x2 + 83.33*x3 = 0

But I tried working it from that and it still didn't work out. So I must be doing something fundamentally wrong.

 

[tehipwn]

My question only pertains to the second page of the pdf. The first page consists of simply finding the Eigenvalues, and then the Eigenvector for the real Eigenvalue.

To refine my question, is the method of performing Gauss Elimination the correct method for finding the complex Eigenvector?

If so, what norm should be used to get the Eigenvector given by Matlab as shown in the final matrix of the second page of the pdf?

I hope this clarifies things.

Thank you.