Exercise 2, § 7

With the notation of II, p. 74, exerc. 3, let G be the vector subspace of E generated by $K \cup \{ \lambda \}$. Show that, in G, the point $\lambda$ is an extremal point of the closed convex envelope of K, but that $\lambda$ does not belong to K (cf. II, p. 25, corollary).