1. The problem statement, all variables and given/known data Let T: V [tex]\rightarrow[/tex] W be a linear trans. Prove: a) N(T) = N(-T) b) N(Tk) = N((-T)k) c) If V = W and [tex]\lambda[/tex] is an eigenvalue of T, then for any positive integer k: N((T - [tex]\lambda[/tex]Iv)k) = N(([tex]\lambda[/tex]Iv - T)k) 2. Relevant equations 3. The attempt at a solution Im not sure how to start on a. I know if I can get started on that one, I can handle the rest. I like this: -T(v) = -0 -T(v) = 0 -T(v) = T(v) therefore N(T) = N(-T) ? Im not sure if that's even remotely on the right track, but this question is in the first Jordan Conanical form section, and Im not sure how that concept can be applie to this very first question. I can see it needing to be applied in the other two, but not this one.