4. Let V be a vector space over R. We can define the norm . as a function that satisfies the following three conditions for all x, y V, and a R : 1. x 0, and x = 0 if and only if x = 0, 2. ax = |a|x, 3. x + y x + y. Let . be a norm over a real vector space V that satisfies the parallelogram law, and define x, y := 1 4 [x + y2 x y2]. Prove that this , defines an inner product on V such that x2 = x, x for all x V