Explanation Approach: If T is a regular stochastic matrix, then the Steady state distribution vector X can be found by solving the vector equation, T X = X together with the condition that the sum of the elements of the vector X should be equal to 1. Calculation: Consider the matrix, T = [ 0.2 0.2 0.3 0.2 0.1 0.1 0.2 0.1 0.2 0.1 0.3 0.4 0.1 0.3 0.3 0.2 0.1 0.2 0.2 0.2 0.2 0.1 0.3 0.1 0.3 ] Let, X = [ x y z u v ] Be a steady state vector associated with the Markov process, the condition T X = X translates into the matrix equation, [ 0.2 0.2 0.3 0.2 0.1 0.1 0.2 0.1 0.2 0.1 0.3 0.4 0.1 0.3 0.3 0.2 0.1 0.2 0.2 0.2 0.2 0.1 0.3 0.1 0.3 ] [ x y z u v ] = [ x y z u v ] Solve the above matrix equation, [ 0.2 x + 0.2 y + 0.3 z + 0.2 u + 0.1 v 0.1 x + 0.2 y + 0.1 z + 0.2 u + 0.1 v 0.3 x + 0.4 y + 0.1 z + 0.3 u + 0.3 v 0.2 x + 0.1 y + 0.2 z + 0.2 u + 0.2 v 0.2 x + 0.1 y + 0.3 z + 0.1 u + 0.3 v ] = [ x y z u v ] Equivalently, the linear system of equation for above matrix equation is, 0.2 x + 0.2 y + 0.3 z + 0.2 u + 0.1 v = x 0.1 x + 0.2 y + 0.1 z + 0.2 u + 0.1 v = y 0.3 x + 0.4 y + 0.1 z + 0.3 u + 0.3 v = z 0.2 x + 0.1 y + 0.2 z + 0.2 u + 0.2 v = u 0.2 x + 0.1 y + 0.3 z + 0.1 u + 0.3 v = v The condition is that sum of X is 1 so, 0.8 x − 0.2 y − 0.3 z − 0.2 u − 0.1 v = 0 0

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

11th Edition

ISBN: 9781305283831

Author: Tan

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 9.2, Problem 1TE

To determine

The steady state vector of the matrix T=[0.20.20.30.20.10.10.20.10.20.10.30.40.10.30.30.20.10.20.20.20.20.10.30.10.3].

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.2, Problem 29E

Chapter 9.2, Problem 2TE

Students have asked these similar questions

Express (...) e as a 2 x 2 matrix; a is a positive constant.

if matrix A= [[a,1-b],[1-a,b]] Assume A does not equal the idenituty . what is the steady state vector for matrix A

Given A 0.5 0.3 0 0.5 find the changes in production required to meet an increase in demand of 70 units of Sector 1 products and 50 units of Sector 2 products. x= 41

Chapter 9 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

Knowledge Booster

$Advanced Math$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

The steady state vector of the matrix T = [ 0.2 0.2 0.3 0.2 0.1 0.1 0.2 0.1 0.2 0.1 0.3 0.4 0.1 0.3 0.3 0.2 0.1 0.2 0.2 0.2 0.2 0.1 0.3 0.1 0.3 ] .

Solution Summary: The author explains that the steady state vector of the matrix T=left is X=X.

Videos

The steady state vector of the matrix T=[0.20.20.30.20.10.10.20.10.20.10.30.40.10.30.30.20.10.20.20.20.20.10.30.10.3].

Want to see the full answer?

Chapter 9 Solutions