Question: (a) Consider the following recursion formula 1 an : (n1+Gn2), n :3 0 withagz 1, and a1 =0. (i) [3 marks] Find the recurrence matrix

(a) Consider the following recursion formula 1 an : (n1+Gn2), n :3 0 withagz 1, and a1 =0. (i) [3 marks] Find the recurrence matrix A and use it to find a5. Give your answers in fraction form. (ii) [3 marks] By diagonalizing A, nd the general formula for on. Show all your workings clearly, however, you do not need to show your ele mentar}r row operations. [13) [3 marks] Suppose A = PEP1 where P is an invertible matrix and A; U - - - l] U A2 - - - G D = _ _ _ is a diagonal matrix such that [Ail

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