+2354 Hello 
,
Let A be a 2 x 2 matrix with multiple eigenvalues r and only 1 independent eigenvector v1. Consider the system zn+1=Azn with it's general solution given by zn=(c0rn+nc1rn−1)v1+c1rnv2 where v2 is a generalized eigenvector corresponding to v1 and r.
Prove that zn=0 for all n is an asymptiotically stable steady state of the system zn+1=Aznprovided that|r|<1
Reinout 
+11912 u r questioning and answering urself ! is all this for our knowledge or what ! 
+2354 Hey Rosala,
I'm not, the question is to give a 'proof' that zn = 0 is an asymptotically stable steady state of the system for all n given that abs[r] < 1
Even though it seems obvious that zn+1=Azn⇒0=A0. I don't know the conditions which must be checked before I can formally prove it to be an asymptotically stable steady state of the system
