3. [10] In each of the following cases, determine whether the given set S is a subspace of R3 (if it is a subspace, give a proof; if not, show by example that one of the defining conditions fails to hold in general): (a) S=x1x2x3R3x1x2=x1x3; (b) S=x1x2x3R3x12x2+x3=0 and x23x3=0}