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 .
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.