Hey there,

If anyone could give me a hint that would be awesome.

All I have is:Let V be a finite-dimensional vector space and let $\displaystyle S,T \in \mathcal{L}(V)$.

prove rank(S+T)<= rankS+rankT

Take any x from V.

Rank (S+T) implies dim((S+T)(x)) = dim(S(x)+T(x))

But I have no clue what to do from here. I know it's really trivial, but I'm stuck.

Hints?