For vector spaces V,W, let L(V,W) be the set of linear transformations from V to W. Define addition on L(V,W) by (L₁+L₂)(v):=L₁(v)+L₂(v). Also define scalar multiplication on L(V,W) by L(v):=(L(v)). Show that under these operations, L(V,W) is a vector space (verify the two closure axioms and the eight vector space axioms).