Linear Transformations: im(S+T) subset of im(S) + im(T)

[csMajor9]

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 of

The Attempt at a Solution

I'm pretty much stuck at the start and could really use and hints or guidance to get me on the right track

 

[lanedance]

i'd start with the definetion of the image as the column space of a matrix