Let f: Rn Rm be a matrix transformation defined by f(u) = Au, where A is

Question:

Let f: Rn → Rm be a matrix transformation defined by f(u) = Au, where A is an m x n matrix.
(a) Show that f(u + v) = f(u) + f(v) for any u and v in Rn.
(b) Show that f(cu) = cf(u) for any u in Rn and any real number c.
(c) Show that f(cu + df) = cf(u) + df(f) for any u and v in Rn and any real numbers c and d.