Question: Consider the following stochastic matrix: and the dynamical system given by A 1 0.5 0 01 0 .5 0 0.50 000 .5 x(k+ 1)

Consider the following stochastic matrix: and the dynamical system given by A

Consider the following stochastic matrix: and the dynamical system given by A 1 0.5 0 01 0 .5 0 0.50 000 .5 x(k+ 1) = Ax(k) (a) What are the steady state solutions of the system? Answer using set notation or as a span of vectors. (b) Is the matrix A regular? Explain. (c) Give two different probability vectors p and p2 that when used as initial conditions end up giving convergence to the same steady state solution in the long run.

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