Question

Se considera matricea A=(4 3 -4 -3) si multimea H={X(a)|X(a)=I2+aA,a>-1}....a)sa se calculeze A la puterea 2015;b)sa se arate ca X(a)•X(b)=X(a+b+ab);c)sa se calculeze X(1)•X(2)•...•X(2016).

Answer 1

a)
Calculezi A^2 : ( 4 3 * (4 3 = (4 3=
-4 -3) -4 -3) -4 -3)
=A

A^3= A^2 *A = A^2= A
...
...
Presupunem ca A^n=A si
Demonstrezi ca A^(n+1)=A

A^(n+1)= A^n * A =A*A= A^2=A

Deci A^2015= A