Let A be an n n matrix such that ||A|| < 1, where the norm is

Question:

Let A be an n × n matrix such that ||A|| < 1, where the norm is either the sum norm or the max norm.
(a) Prove that An → O as n → ∞.
(b) Deduce from (a) that I - A is invertible and (I - A)-1 = I + A + A2 + A3 + · · ·
(c) Show that (b) can be used to prove Corollaries 3.35 and 3.36.