Question: Exercise 3. (Application of matrices to recursive sequences) (30 points) Consider the following matrices A = 3 1. (15 points) (a) Compute the following products

Exercise 3. (Application of matrices to recursive sequences) (30 points) Consider the following matrices A = 3 1. (15 points) (a) Compute the following products PD and AP. (b) Explain, without any computation, why P is invertible. (c) Deduce from the questions above that A = PDP-1 (1) (d) Deduce that A? = PD-P-' and more generally that, for every n E N. A" = PDP-1. (2)

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