Se rezolva cu inductie matematica.
A^2 = (1 2) A^3 =( 1 3)
(0 1) (0 1)
Etapa verificarii:
A^2 = (1 2)
(0 1)
Demonstram:
Presupunem P(k) adevarata si demonstram P(k+1).
P(k): A^k= (1 k)
(0 1)
P(k+1): A^(k+1)= (1 k+1)
(0 1 )
dar A^(k+1)= A^k * A = (1 k) * (1 1) = ( 1 k+1)
(0 1) (0 1) (0 1 )
=> Presupunerea este adevarata deci A^n = (1 n)
(0 1)
