Explanation Given: The provided absorbing chain: [ 0.4 0.2 0.3 0 0.1 0 1 0 0 0 0 0 1 0 0 0.1 0.5 0.1 0.1 0.2 0 0 0 0 1 ] Explanation: The matrix is rearranged based on a different order of occurrence of stages as follows: 2 3 5 1 4 2 3 5 1 4 [ 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0.2 0.3 0.1 0.4 0 0.5 0.1 0.2 0.1 0.1 ] Any absorbing chain is of the form of the following sub-matrices, [ I m 0 R Q ] Comparing this with the provided absorbing chain, I m = [ 1 0 0 0 1 0 0 0 1 ] R = [ 0.2 0.3 0.1 0.5 0.1 0.2 ] Q = [ 0.4 0 0.1 0.1 ] The fundamental matrix is defined as, F = ( I n − Q ) − 1 where the matrix Q has order n × n . I n − Q = [ 1 0 0 1 ] − [ 0.4 0 0.1 0.1 ] = [ 0.6 0 − 0.1 0.9 ] The inverse of this matrix can be found using the Gauss Jordan method

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ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10.3, Problem 14E

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The fundamental matrix, F, for the provided absorbing Markov chain and the product FR.

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Chapter 10.3, Problem 13E

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