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

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

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

B. V=?³, and S is the set of vectors (x₁,x₂,x₃) in V satisfying x₁−6x₂+x₃=5.

C. V=?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=C²(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(?), and S is the subset of all symmetric matrices