Hello,

the task is following:

Let's assume that vector is eigenvector corresponding to eigenvalue of matrix . Also corresponds to eigenvalue of matrix . Now the questions:

I Is the eigenvector of matrix ?

II Is the eigenvector of matrix ?

If answer is yes to atleast one question, it must be shown, to which eigenvalue vector corresponds.

I think I should use following theorem:

"If is eigenvector corresponding to eigenvalue of matrix , then is is eigenvector corresponding to 's ".

But somehow, I can't get anywhere, though I inspected eigenvalues and -vectors definitions closely. Also it's no problem to me calculate those vectors and values in normal cases. So, any help is appreciated. Thank you!