Continue from Uo = (1,0) to U7, and also from Vo = (0,1) to V7. What do you notice about

Chapter 2, Problem 30

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Continue from Uo = (1,0) to U7, and also from Vo = (0,1) to V7. What do you notice about U7 and V7? Here are two MATLAB codes, with while and for. They plot Uo to U7 and Vo to V7. You can use other languages: u = [1 ; 0]; A = [.8 .3 ; .2 .7]; x = u; k = [0 : 7]; while size(x,2) <= 7 u = A*u; x = [x u]; , end plot(k, x) v = [0; 1]; A = [.8.3;.2.7]; x = v; k = [0 : 7]; for j = 1 : 7 v = A*v; x = [x v]; end plot(k, x) The u's and v's are approaching a steady state vector s. Guess that vector and check that As = s. If you start with s, you stay with s.