Question: Consider the 2 Ã 2 stochastic matrix where 0 (a) Show that is the steady-state vector for P. (b) Show that PM converges to the

Consider the 2 Ã— 2 stochastic matrix

where 0 (a) Show that

is the steady-state vector for P.
(b) Show that PM converges to the matrix

by first verifying inductively that

for m = 1, 2,... (It can be shown that the sequence of powers P, P2, P3,... of any regular transition matrix converges to the matrix each of whose columns equals the steady-state vector for P.)

P+ L-P

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