Q2. A Fall 2022 MATH 135 assignment introduced the recursive sequence (ao, a1, . . .) defined by an =7, a1 = 26 and an = 7an-1 - 10an-2 for n > 2. [26 Let A = 30 ] and (a) Using the convention that A = 12, prove that A" d = an+1 for all integers n 2 0. an (b) Determine an invertible matrix P and diagonal matrix D such that A = PDP-1. (c) Using parts (a) and (b), prove that an explicit formula for the nth term of this recursive sequence is an = 3 . 2" + 4 . 5". Note: This explicit formula was given on the MATH 135 assignment. In this problem, you must use parts (a) and (b) in order for your proof to earn any marks