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

A. V={\mathbb R}^2 , and S consists of all vectors (x_1, x_2) satisfyingx_1^2 - x_2^2 = 0.

B. V=M_n({\mathbb R}) , and S is the subset of all symmetric matrices
C. V=P_n , and S is the subset of P_n consisting of those polynomials satisfying p(0) = 0.
D. V=C^2(I) , and S is the subset of V consisting of those functions satisfying the differential equation y''-4y'+3y=0.
E. V is the vector space of all real-valued functions defined on the interval(-\infty, \infty), and S is the subset of V consisting of those functions satisfyingf(0)=0.
F. 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)=4.
G. V=C^3(I) , and S is the subset of V consisting of those functions satisfying the differential equation y'''+3 y=x^2.