Good morning guys,

I've got a matrix with multiplicity 3, where all of the eigenvalues must be 0. (Ie: |sI-A| = s^3)

I understand that in order to get the Q to put this in JCF I need to chain generalized Eigenvectors, but I'm having issues. The way the professor explained it I start with:

(A-sI)^2v=0, and solve that. (I did, and I get [0 -4 5]' (col vector))

Then solve (A-sI)v=0 (which gives [-1 0 0]' (col vector))

and then his instructions get blurry, and the book also does not explain what happens at this point. It glosses over it and says the final v is [...]' where they give a col vector that is a solution to their problem.

My A matrix is [0 4 3; 0 20 16; 0 -25 -20].

So my question is what do I do to get this last eigenvector?

Thanks in advance,