Determine whether the given set s is a subspace of the vector space v.


a. v=mn(r), and s is the subset of all upper triangular matrices.


b. v is the vector space of all real-valued functions defined on the interval (−∞,∞), and s is the subset of v consisting of those functions satisfying f(0)=0.


c. v=c2(i), and s is the subset of v consisting of those functions satisfying the differential equation y′′−4y′+3y=0.


d. v=c1(r), and s is the subset of v consisting of those functions satisfying f′(0)≥0.


e. v=r2, and s is the set of all vectors (x1,x2) in v satisfying 5x1+6x2=0. f. v=p5, and s is the subset of p5 consisting of those polynomials satisfying p(1)>p(0). g. v=mn(r), and s is the subset of all nonsingular matrices.