Problem 4 Let V = {z R, x > 0} be the set of positive real numbers and let us define the following operations on V: +v: VXV = V (fa = xy and v RxV V \\z) - 2 we use when we see x in the abstract vector space V and x for its \"actual\" value (as a positive real number) We have seen in Homework 2 that (V,+y,-v) is a vector space. (1) Show that V = Span(3) (with the operations defined for V). (2) Let us consider exp R V a e Show that exp is a linear map from (R, +,-) to (V, +v, v)