Problem 1 Let V = {r E R. x > 0} be the set of positive real numbers and let us define the following operations on V: tv : V xV V (I, y) H xcy and V R XV V ( 1, I ) H we use a when we see x in the abstract vector space V and x for its "actual" value (as a positive real number) Show that (V, +v. .v) is a vector space (i.e. the 10 axioms are satisfied by (V. tv, v)). Hint: Ov = 1 and -