Let V be the space of all linear transformations from c(R) to C(R). Then Vis a vector space of dimension 3 Vis a vector space of dimension 6 Vis a vector space of dimension 12 VIs not a vector space
I assume that you know the dimensions of C^3(R) and C(R). so I am not going to prove them.
thm.#. if V(F) and V'(F) are finite dimensions vector space over F, then hom(V , V') is ...