Linear Algebra

Question 1. Let (Fun(R, R), +, .) be the real vector space of all functions from R to R. Recall that the addition of two functions f, g E Fun(R, R) and the multiplication of a function f E Fun(R, R) with a real scalar A E R are explained by (f + g) (t) = f(t) + g(t) and (Af) (t) = Af (t) for all te R. a) Pick any real number q E R. Let V(q, 0) = {f E Fun(R, R) : f(q) = 0} be the set of all functions f : R - R with the property that their value at q is equal to zero, i.e. f(q) = 0. Explain why V(q, 0) is a subspace of Fun (R, R). b) Pick any real number q E R. Let V(q, 7) = {f E Fun(R, R) : f(q) =