Determine whether the given set S is a subspace of the vector space V.

A) V = Mn( R ), and S is the subset of all upper triangular matrices.

B) V = C2(I), and S is the subset of V consisting of those functions satisfying the differential equation y′′′ - 4 y′ + 3 y = 0.

C) V is the vector space of all real-valued functions defined on the interval [ a , b ] and S is the subset of V consisting of those functions satisfying f(a)=f(b).

D) V = C3(I), and S is the subset of V consisting of those functions satisfying the differential equation y ′′′ + 4y = x^{2}.

E) V = R4, and S is the set of vectors of the form (0, x^{2}, 5, x^{4} ).

F) V = P3, and S is the subset of P3 consisting of all polynomials of the form p(x) = ax^{3} + bx.

G) V = P5, and S is the subset of P5 consisting of those polynomials satisfying p(1) > p(0).