1. The problem statement, all variables and given/known data Let S be a set and let V be a vector space over the field F. LetV^S denote the set of all maps from S to V . We define an addition on V^S and a scalar multiplication of F on V^S as follows: (f+g)(s):=f(s)+g(s) and (af)(s):=a(f(s)) for any s belongs to S show that V^S is a vector space over F 2. Relevant equations 3. The attempt at a solution how to show it is a vector space , do i need to show all the axioms exist ? or ,is there any specific way to use ?