Linear Algebra Eigenvectors -- question on x1+x2+x3 = 0 and more

Hello.

Okay, I'm struggling with eigenvectors -- I have already searched the forum and found a thread here (http://www.mathhelpforum.com/math-he...n-problem.html) which is more or less about the subject I'm interested in. But I still need to know how the answer was found.

Let A = [1 1 1]

----- = [0 0 0]

----- = [0 0 0]

This is a RREF matrix, which I want to 'extract' an eigenvector from...

TD! posted that the eigenvectors are e.g. (1,0,-1) and (1,-1,0). What I want to know is how they are found?

Also - I would like to know more about eigenvectors of this matrix...

B = [0 1 0]

- = [0 0 1]

- = [0 0 0]

I see x2 = x3 = 0, so I guess the eigenvector is [? 0 0], but what is x1? I think x1 is supposed to be x1 = 1, but why? I don't get why..?

Thanks in advance!

Simon DK.