Homework Statement
Let V be an n-dimensional vector space over R, and let S and T be linear transformations from V to V.
(i) Show that im(S+T) \subseteq im(S) + im(T)
(ii) Show that r(ST) \leq min(r(S),r(T)), and that n(ST) \leq n(S) + n(T)
Homework Equations
none that i can think...