   Chapter 9.2, Problem 14E

Chapter
Section
Textbook Problem

In Exercise 9-16, find the steady state vector for the transition matrix. [ 0.6 0.3 0.1 0.4 0.4 0.4 0 0.3 0.5 ]

To determine

The steady state vector of the matrix [0.60.30.10.40.40.400.30.5].

Explanation

Approach:

If T is a regular stochastic matrix, then the Steady state distribution vector X can be found by solving the vector equation,

TX=X

together with the condition that the sum of the elements of the vector X should be equal to 1.

Calculation:

Consider the matrix,

[0.60.30.10.40.40.400.30.5]

Let,

X=[xyz]

Be a steady state vector associated with the Markov process, where x and y are to be determined. The condition TX=X translates into the matrix equation,

[0.60.30.10.40.40.400.30.5][xyz]=[xyz]

Solve the above matrix equation,

[0.6x+0.3y+0.1z0.4x+0.4y+0.4z0.3y+0.5z]=[xyz]

Equivalently, the linear system of equation for above matrix equation is,

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