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Question 1 [15 marks] This question investigates a nonstandard inner product on R- that arises in quantum mechanics (and other areas of mathematics), which comes from looking at reflections of a triangle. The goal of this problem is to show that (v, w) = ((01, 02), (21, W2)) = [v v2] w1 2 W2 is an inner product on R2 and to compute an orthogonal basis. a. (5 marks) Show that (v, w) = (w, v). b. (7 marks) Show that (v, v) 2 0 and that (v, v) = 0 if and only if v = 0. c. (3 marks) Find a vector orthogonal to e, = (1,0) with respect to this inner product