Explanation Given Information: The absorbing stochastic matrix is standard form [ 1 0 1 4 1 6 0 1 1 6 0 0 0 1 4 1 2 0 0 1 3 1 3 ] . 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 ] . Calculation: Consider the absorbing stochastic matrix is standard form [ 1 0 1 4 1 6 0 1 1 6 0 0 0 1 4 1 2 0 0 1 3 1 3 ] . 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 1 ] , S = [ 1 4 1 6 1 6 0 ] and R = [ 1 4 1 2 1 3 1 3 ]

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134507125

Author: Goldstein

Publisher: PEARSON

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Chapter 8.3, Problem 15E

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

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Chapter 8.3, Problem 14E

Chapter 8.3, Problem 16E

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Chapter 8 Solutions

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

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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.

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

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