[10 points] Determine if the set U is a subspace of a vector space V where : (a) U is the intersection of the plane y = 2z with the plane x + 2y + 3z = 0 and V = R 3 ; (b) U is the set of all (x, y, z) with x = 2z − 3y + 1 and V = R 3 ; (c) U is the set of all polynomials of degree exactly 3 and V is the set of all polynomials. (d) U is the set of all polynomials of degree not greater than 3 and V is the set of all polynomials. (e) U is the set of all symmetric (3 × 3) matrices (i. e. AT = A) and V = M3,3 is the space of all matrices (3 × 3).