Explanation Given: The provided absorbing chain: [ 0.3 0.5 0.1 0.1 0.4 0.1 0.3 0.2 0 0 1 0 0 0 0 1 ] Explanation: The matrix is rearranged based on a different order of occurrence of stages as follows: 3 4 1 2 3 4 1 2 [ 1 0 0 0 0 1 0 0 0.1 0.1 0.3 0.5 0.3 0.2 0.4 0.1 ] Any absorbing chain is of the form of the following submatrices: [ I m 0 R Q ] Comparing this with the provided absorbing chain: I m = [ 1 0 0 1 ] R = [ 0.1 0.1 0.3 0.2 ] Q = [ 0.3 0.5 0.4 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 ] − [ 0.3 0.5 0.4 0.1 ] = [ 0.7 − 0.5 − 0.4 0.9 ] The inverse of this matrix can be found using the Gauss Jordan method. The augmented matrix is: [ 0.7 − 0.5 1 0 − 0.4 0.9 0 1 ] 1 0.7 R 1 → R 1 gives, [ 1 − 5 7 10 7 0 − 0

11th Edition

ISBN: 9780321979438

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

Publisher: PEARSON

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Chapter 10, Problem 42RE

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Chapter 10, Problem 41RE

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