1. Write the matrix A in the form A = PDP-' where D is a diagonal matrix in the following two cases: (a) (5 marks) A = 2 (b) (5 marks) 6 A = 5 2. (**) Consider the dynamical system In+1 = 3in - 2yn; 1 Un+1 = 5Un (a) (2 marks) Write the dynamical system in the form On+1 = Aun where Un = (In: yn) , and A is a matrix which you should specify. (b) (9 marks) Determine matrices P and D such that D is diagonal, and A = PDP-1. (c) (3 marks) Show that Un = PD"P-vo. Note that you don't need to use the explicit form of the matrices for this. (d) (6 marks) Find explicit expressions for T, and y, in terms of ro, yo and n