Explanation Given Information: The absorbing stochastic matrix is standard form [ 1 0 0 0.1 0.2 0 1 0 0.3 0 0 0 1 0 0.2 0 0 0 0.5 0 0 0 0 0.1 0.6 ] . Formula used: Matrix subtraction rule is, When the two matrices are subtracted, their corresponding elements are subtracted. That is, [ a b c d ] − [ e f g h ] = [ a − e b − f c − g d − h ] Matrix multiplication rule is, When the two matrices are multiplied then the elements of the first row of first matrix and the elements of the first column of the second matrix are multiplied. [ a b c d ] [ e f g h ] = [ a e + b g a f + b h c e + d g c f + d h ] . Determinant of a matrix [ a b c d ] is, △ = a d − b c . Calculation: Consider the absorbing stochastic matrix is standard form [ 1 0 0 0.1 0.2 0 1 0 0.3 0 0 0 1 0 0.2 0 0 0 0.5 0 0 0 0 0.1 0.6 ] . Suppose the above matrix partition an absorbing stochastic matrix into sub-matrices such that, A = [ I S 0 R ] where I denote the identity matrix, and 0 denotes a matrix having all entries 0 the matrices S and R are the two pieces corresponding to the non-absorbing states. I = [ 1 0 0 0 1 0 0 0 1 ] , S = [ 0.1 0.2 0.3 0 0 0.2 ] and R = [ 0.5 0 0.1 0.6 ] . Now, find the fundamental matrix, Apply the matrix subtraction rule, I − R = [ 1 0 0 1 ] − [ 0.5 0 0

MyLab Math plus Pearson eText -- Standalone Access Card -- for Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134765723

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 8.3, Problem 17E

To determine

To calculate: The fundamental matrix and the stable matrix in each identity R and S in the given absorbing stochastic matrix.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.3, Problem 16E

Chapter 8.3, Problem 18E

Students have asked these similar questions

26.1. Locate and determine the order of zeros of the following functions: (a). e2z – e*, (b). z2sinhz, (c). z*cos2z, (d). z3 cosz2.

Write 7. √49 using rational exponents. ○ A. 57 47 B. 7 O C. 47 ○ D. 74

Q/ show that: The function feal = Se²²²+d+ is analytic

Chapter 8 Solutions

MyLab Math plus Pearson eText -- Standalone Access Card -- for Finite Mathematics & Its Applications (12th Edition)

Ch. 8.1 - 1. Is a stochastic matrix? Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E

Knowledge Booster

Learn more about

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

The fundamental matrix and the stable matrix in each identity R and S in the given absorbing stochastic matrix.

Solution Summary: The author calculates the fundamental matrix and the stable matrix in the given absorbing stochastic matrix.

Videos

To calculate: The fundamental matrix and the stable matrix in each identity R and S in the given absorbing stochastic matrix.

Want to see the full answer?

Chapter 8 Solutions