Let A Rn be a set. Let M be an nxn matrix and define, B := {Mx : x A} i. B is the set of all points inRn that can be obtained by selecting a point x...

Let A ∈Rn be a set. Let M be an nxn matrix and define, B := {Mx : x ∈A} i.e. B is the set of all points inRn that can be obtained by selecting a point x ∈ A and applying the

transformation x → Mx.

a) Show that if A is convex then so is B.

b) Show that if B is convex and M is non-singular then A is convex.

c) Can you omit the "non-singular" condition in (b)?