Determine whether the given set S is a subspace of the vector space V.
A. V=, and S is the subset of consisting of those polynomials satisfying p(1)>p(0).
B. , and S is the set of vectors in V satisfying .
C. , and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.
D. V=, 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=, and S is the subset of consisting of those polynomials satisfying p(0)=0.
G. , and S is the subset of all symmetric matrices