Hi can anyone tell me if this true of false and why If S v1

Hi, can anyone tell me if this true of false and why?

If S = {v_1. v_2,..., V_n} is a basis for R^n and W is a subspace of R^n, then S W = {proj w(v_i) 1 lessthanorequalto i lessthanorequalto n} is a spanning set for W.

Solution

true because S is a basis for R^n and W is a subspace of R^n by the principal of spanning set S intersection W is a spanning set for W.