For each vector space V and subset S, find the smallest subspace of V that containsS. (Be sure to briefly justify your answer.) (a) V =R2 andS={(x,y)...

For each vector space V and subset S, find the smallest subspace of V that containsS. (Be sure to briefly justify your answer.)

(a) V =R2 andS={(x,y) : x+y=1}

(b) V =R3 andS={(x,y,z) : x≥0,y≥0,z≥0}

(c) V = {polynomials p(x)} and S is the set of polynomials of degree exactly

(d) V = {all 2 × 2 matrices} and S is the set of invertible 2 × 2 matrices.

(e) V = {all n × n matrices} and S is the set of symmetric n × n matrices.