1.4 a) Show that the sum of two semiscalar products is a semiscalar product. b) Show that if (u, v) is a semiscalar product on a vector space W and if T is a linear transformation from a vector space V to W, then [, "] = (Tu, Tv) is a semiscalar product on V. C) Deduce from (a) and (b) that b (f, g) = flag(a) + ( f'(t)g'(t) at is a semiscalar product on V = C'([a, b]). Prove that it is a scalar product