Let x and y be eigenvectors of a matrix A such that http://s3.amazonaws.com/answer-board...3637509032.gifis also an eigenvector of A. Is http://s3.amazonaws.com/answer-board...7075006798.gif an eigenvector of A? Prove or disprove.

I know that http://s3.amazonaws.com/answer-board...2075003085.gif and http://s3.amazonaws.com/answer-board...2075002173.gif and http://s3.amazonaws.com/answer-board...1450003583.gif but I'm not sure where I can go from there without being given that x and y correspond to the same eigenvalue... I started with:http://s3.amazonaws.com/answer-board...5825002257.gif but I don't know how to proceed. Please help!!

OP edit after getting help:Thank you--I didn't think of the 2 cases, it becomes easy! :)