Suppose that V is a vector space and S is a finite subset of

Suppose that V is a vector space and S is a finite subset of V such that span(S) = Prove that V has finite dimension.

Solution

V is finite dimensional when V is spanned by a finite set of vectors, now since S is a finite subset of V that means that V is spanned by a finite set of vector ie. S . hence we can definitely tell that V has finite dimensions.