(a) Let $u = (u_1, u_2)$ and v = (v1, v2). Prove that $\langle u, v \rangle = 3u_1v_1 + 5u_2v_2$ defines an inner product on R2 by showing that the inner product axioms hold.
(b) What conditions must k1 and k2 satisfy for = k1u1v1 + k2u2v2 to define an inner product on R2?
For part a, how do I prove that the inner product axioms hold with the coefficient values of 3 and 5?
For part b, how would I find the values k1 and k2, when I don't know the initial vector values of ?