Let A = 0 0 0 4 2 Find the eigenvalues of A. Is A diagonalizable?...

 

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Let A = 0 0 0 4 2 Find the eigenvalues of A. Is A diagonalizable? 1 1 [3] Fibonnaci numbers are defined recursively by Fo= 0, F = 1 and Fn+1 Fn + Fn-1 for all n. a) Find Fg. [1] ( . b) Let A = Show that A" = [2] c) Find the eigenvalues of A and an invertible matrix Q such that Q-AQ is diagonal. [4] [XT c) Show that A" Q = Fatl F F F-1 Q- where A, A2 are the two eigen- 0 X values of A and find an explicit formula for Fn (i.e. a formula 2 which could be plugged into your calculator, for n = 52, say). Let A = 0 0 0 4 2 Find the eigenvalues of A. Is A diagonalizable? 1 1 [3] Fibonnaci numbers are defined recursively by Fo= 0, F = 1 and Fn+1 Fn + Fn-1 for all n. a) Find Fg. [1] ( . b) Let A = Show that A" = [2] c) Find the eigenvalues of A and an invertible matrix Q such that Q-AQ is diagonal. [4] [XT c) Show that A" Q = Fatl F F F-1 Q- where A, A2 are the two eigen- 0 X values of A and find an explicit formula for Fn (i.e. a formula 2 which could be plugged into your calculator, for n = 52, say).