Let A = [aij ] be the I! x /I matrix defined by (Iii = k and(lij =Oifi i=- j. Show that if B is any n x /I matrix. then AB = kB.

Lecture 8: Evaluating Limits (Sections 2.3 and 2.5) Basic Limit Laws Suppose x→c f(x)adml x→c g(x)xtnd k is a constant. We have the following limit laws: 1. x→c [f(x) ± g(x)]= 2. lim kf (x)= x→c 3. lim f(x)g(x)= x→c 4. If lim g(x) ,l0 f(x) = x→c x→c g(x) 5. If p, q are integers, with q enl,t [f(x)]p/q= x→c Assume that lim f(x) ≥ 0fi q is even, and that x→c lim f(x) ▯=if p/q < 0. x→c In particular, for a positive integer n: n ▯n lim [f(x)] = , lim f(x)= x→c x→c