Let A n be a convex set. LetMbe an nn matrix and define,B:B is the set of all points in n that can be obtained by selecting a point xAand applying...

Let A⊆ ℜn be a convex set. LetMbe an n×n matrix and define,B:={Mx:x∈A}i.e.B is the set of all points in ℜn that can be obtained by selecting a point x∈Aand applying the transformationx→Mx.(a) Show that B is convex.(b) Suppose thatMis invertible and considerz∈A, hence Mz∈B.Show thatzis an extreme point ofAif and only if Mz is an extreme point of B