Explanation Given: The matrix is [ 1 2 0 1 3 0 1 2 1 0 0 0 0 2 3 0 0 0 0 1 ] . Approach: Consider the formula to compute the steady-state matrix for an absorbing stochastic matrix An absorbing stochastic matrix A has been partitioned into submatrices. A = [ I 0 | S R ] … (1) Then, the steady-state matrix of A is given by A = [ I 0 | S ( I - R ) - 1 0 ] … (2) Here, I is an identity matrix, 0 is the zero matrix and the order of the identity matrix appearing in the expression ( I − R ) − 1 is chosen to have the same order as R . The absorbing stochastic matrix, it is always possible by suitably reordering the states if necessary, to rewrite it so that the absorbing states appear first. Then the resulting matrix can be partitioned into four sub-matrices. A = [ I 0 | S R ] absorbing Nonabsorbing where, I is an identity matrix whose order is determined by the number of absorbing states and 0 is a zero matrix. The sub-matrices R and S correspond to the non absorbing states. Calculation: Rewrite the given matrix in the form of that the absorbing states appear first, partition the resulting matrix and identify the sub-matrices R and S . [ 1 0 1 2 0 0 1 0 0 0 0 1 2 1 3 0 0 0 2 3 ] Comparing the matrix element from the equation (1). Here, the place of I is 1 , the place of zero matrix is 0 , the place of S is [ 1 2 0 0 0 ] and the place of R is [ 1 2 1 3 0 2 3 ] . Calculate the matrix of S ( I − R ) − 1 . S ( I − R ) − 1 = ( [ 1 2 0 0 0 ] ) ( [ 1 0 0 1 ] − [ 1 2 1 3 0 2 3 ] ) − 1 = ( [ 1 2 0 0 0 ] ) ( [ 1 2 − 1 3 0 1 3 ] ) − 1 = ( [ 1 2 0 0 0 ] ) { 1 ( ( 1 3 ) × ( 1 2 ) − ( 0 ) ( − 1 3 ) ) [ 1 3 1 3 0 1 2 ] } Further solve

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

11th Edition

ISBN: 9781285464657

Author: Soo T. Tan

Publisher: Brooks Cole

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Chapter 9.3, Problem 19E

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The steady-state matrix of the given stochastic matrix [12013012100002300001]

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Chapter 9.3, Problem 18E

Chapter 9.3, Problem 20E

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Chapter 9 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th 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

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The steady-state matrix of the given stochastic matrix [ 1 2 0 1 3 0 1 2 1 0 0 0 0 2 3 0 0 0 0 1 ]

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To compute: The steady-state matrix of the given stochastic matrix [12013012100002300001]

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Chapter 9 Solutions

To compute:

The steady-state matrix of the given stochastic matrix [12013012100002300001]