Prove that the vector spaces Rmn (m by n matrices with real entries) and Rmn (column vectors of length m times n) are isomorphic as vector spaces. :

mn mn (a) First define a map (function) from R to R .

Show that your map is injective. (c) Show that your map is surjective.

(d) Show that your map is a homomorphism.

(If the general case proves too difficult, let m = 3 and n = 2 and prove this case.)