Hey so I am studying for a test and am working on a practice and came across these questions, the first one is (a), second (b), third (c):



I was able to get part (a) but I'm not sure how to use that to get part (b), can anyone help?

from a) u showed all espaces for every eigenvalue is an invariant subspace.
so if A had more than 1 eingenvalue than V and 0 wuldnt be the only invariant subspaces

good luck on test

This post was edited by 2wo1ne on Mar 12 2015 09:01pm

Thank you!!

And for (c) if there is only one eigenvalue then clearly A = (lambda)*I correct?

ya, since theres only 1 eigenvalue, Av = lambda v
so lambda has same transformation as A, and A = lambda