All problems below refer to a** dynamical system** of the form

** x(k+1) = Ax(k) x(0) given**

which we know has solutions of the form

**x(k) = A ^{k}x(0)**

In each case below, what can you say about the* long term behavior* of the system, given the information provided?

(The **Principal Axis Theorem ** and **Diagonalization** help here!)

(-1,1,0), (0,-1,2) and ( 1,3,2)

(-2.3, 1.7, 0), (.5,.3,.2) (-.5,0, 1.7)

(-1, 3, .65, .33), (-3,1,2,0), ( 1,2,1,7) and (2,1,1, .5)

(1, 3,2,1), ( -8,1,4,-4) ( 0,0, 1 , 3) and (7,1,1,5)