(a) Where ,  ∈ Rn, by definition the line segment connecting them is the set ℓ = {t ∙  + (1 - t) ∙  | t ∈ [0..1]}. Show that the image, under a homomorphism h, of the segment between  and  is the segment between h() and h().
(b) A subset of Rn is convex if, for any two points in that set, the line segment joining them lies entirely in that set. (The inside of a sphere is convex while the skin of a sphere is not.) Prove that linear maps from Rn to Rm preserve the property of set convexity.