Let A € Mmxn (C) and B ¤ Mnxp (℃). (a) Using the rank-nullity theorem, prove that rank(A) = rank(AT). (b) Prove that rank(AB) < min{rank(A), rank(B)}.

Let (a,m) = 1 with m>1 and let f = expm(a). Then expm (ak): expm (a) (k, f)

let f(x)={x^2+2, x >-1 AND -x^2-x, x less than for equal to -1} compute f(0), f(-1)and f(-2) a. 0, 2, 6 b. 2, 0, 6 c. 2, 2, 6 d. 2, 0, -2 e. 0, 1, -2