1. The problem statement, all variables and given/known data Find the long-term behavior of the Markov system described by the following matrix with initial conditions below: (i.e. find T^infinity) Find x_infinity 2. Relevant equations x_0 = [.3 .3 .4]^T T = [.5 .4 .1] [.4 .3 .3] [.1 .3 .6] 3. The attempt at a solution So in my attempt to find x_infinity I know that x_n = ( T^n)(x_0) This means: [.5^n .4^n .1^n] * [.3 .3 .4]^T [.4^n .3^n .3^n] [.1^n .3^n .6^n] Which I solved to be [ .3*.5^n .3*.4^n .4*.1^n] [ .3*.4^n .3*.3^n .4*.3^n] [ .3*.1^n .3*.3^n .4*.6^n] But as n approaches infinity all the terms get smaller and all go to zero. Does this seem correct so far? That would mean: x_infinity = ( 0 0 0 )^T ??? I tried this on my webassign, but it is not correct. Any tips or help in pointing out my mistakes would be great, thanks!