Question: 3. Let V be a vector space and S a set. Let Vs = {f: S+V} be the set of all functions from S

. Let V be a vector space and S a set. Let V$ = {f S V} on VS by be the set of all functions from S to V. Define addition and

3. Let V be a vector space and S a set. Let Vs = {f: S+V} be the set of all functions from S to V. Define addition and scalar multiplication on VS by (f+g)(s) = f(s) + g(s) and (af)(s) = af(s) for all a F, f.g VS, and s S. Show that VS is a vector space.

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