+2353 Hello 
,
Let A be a 2 x 2 matrix with multiple eigenvalues r and only 1 independent eigenvector v1. Consider the system $$z_{n+1} = Az_n$$ with it's general solution given by $$z_n = (c_0r^n+nc_1r^{n-1})v_1 + c_1r^nv_2$$ where v2 is a generalized eigenvector corresponding to v1 and r.
Prove that $$z_n = 0$$ for all n is an asymptiotically stable steady state of the system $$z_{n+1} = Az_n\\
\mbox{provided that}\\
|r| < 1$$
Reinout 
+11912 u r questioning and answering urself ! is all this for our knowledge or what ! 
+2353 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 $$z_{n+1} = Az_n \Rightarrow 0 = A 0$$. 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
