linear algebra vector space

16. [12] Recall that an inner product on a vector space V is a function that, to each pair of vectors u, v E V, associates a real number (u, v) satisfying the following axioms: (a) (7, B) = (0, u) (b) ( 2 + 3, W) = (u, w)+ (3, w) (c) (cu, v) = c(u, B) (d) (7, u) 2 0 Show that, for all vectors u = u , u = , the product given by (u, v) = 641 01 - 3U2 12 satisfies axioms (b) and (c)