A 4 Show by means of complete induction that the Fibonacci numbers as entries of

the Powers of the matrix A'-appear. To do this, show that

(0) = (1 for all n n.

fn

Where the (n + 1)-th Fibonacci number fn + 1 is given by the recursive law of education

In+1 = fn + fn-1 for n € N with the initial values fo = 0, fi = f2 = 1.

(2 Points)