Question

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

A. V=C²(ℝ) (twice continuously differentiable functions), and S is the subset of VV consisting of those functions satisfying the differential equation y″=0. 
B. V=ℙ₅, and SS is the subset of ℙ5 consisting of those polynomials satisfying p(1)>p(0)
C. V=ℙ₄, and SS is the subset of ℙ4 consisting of all polynomials of the form p(x)=ax3+bx.
D. V=M_n×n(ℝ), and SS is the subset of all symmetric matrices.
E. V=ℝ², and S consists of all vectors (x1,x2) satisfying x₁²−x₂²=0.
F. V=M_n×n(ℝ), and S is the subset of all nonsingular matrices.
G. V is the vector space of all real-valued functions defined on the interval [a,b], and SS is the subset of V consisting of those functions satisfying f(a)=f(b).

Answer 1