Determine whether the given set S is a subspace of the vector space V.
A. V=${P}_{5}$, and S is the subset of ${P}_{5}$ consisting of those polynomials satisfying p(1)>p(0).
B. $V={R}_{3}$, and S is the set of vectors $({x}_{1},{x}_{2},{x}_{3})$ in V satisfying ${x}_{1}-6{x}_{2}+{x}_{3}=5$.
C. $V={R}^{n}$, and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.
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 [a,b], and S is the subset of V consisting of those functions satisfying f(a)=5.
F. V=${P}_{n}$, and S is the subset of ${P}_{n}$ consisting of those polynomials satisfying p(0)=0.
G. $V={M}_{n}(R)$, and S is the subset of all symmetric matrices