Explanation Given: The matrix is [ 1 .2 .3 0 .4 .2 0 .4 .5 ] . Approach: Consider the formula to compute the steady-state matrix for an absorbing stochastic matrix An absorbing stochastic matrix A has been partitioned into sub-matrices. 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 .2 .3 0 .4 .2 0 .4 .5 ] 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 [ .2 .3 ] and the place of R is [ .4 .2 .4 .5 ] . Calculate the matrix of S ( I − R ) − 1 . S ( I − R ) − 1 = ( [ .2 .3 ] ) ( [ 1 0 0 1 ] − [ .4 .2 .4 .5 ] ) − 1 = ( [ .2 .3 ] ) ( [ .6 − .2 − .4

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Chapter 9.3, Problem 17E

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The steady-state matrix of the given stochastic matrix [1.2.30.4.20.4.5].

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Chapter 9.3, Problem 16E

Chapter 9.3, Problem 18E

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The steady-state matrix of the given stochastic matrix [ 1 .2 .3 0 .4 .2 0 .4 .5 ] .

Solution Summary: The author explains the formula to compute the steady-state matrix for an absorbing stochastic matrix.

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To compute:

The steady-state matrix of the given stochastic matrix [1.2.30.4.20.4.5].

Want to see the full answer?

Chapter 9 Solutions

The steady-state matrix of the given stochastic matrix [ 1 .2 .3 0 .4 .2 0 .4 .5 ] .

Solution Summary: The author explains the formula to compute the steady-state matrix for an absorbing stochastic matrix.

Videos

To compute: The steady-state matrix of the given stochastic matrix [1.2.30.4.20.4.5].

Want to see the full answer?

Chapter 9 Solutions

To compute:

The steady-state matrix of the given stochastic matrix [1.2.30.4.20.4.5].