Explanation Given Information: The absorbing stochastic matrix is, [ 1 0 1 6 1 2 2 5 0 1 0 0 2 5 0 0 0 0 0 0 0 2 3 1 2 0 0 0 1 6 0 1 5 ] Formula used: The absorbing stochastic matrix of the form [ I S 0 R ] has the stable matrix [ I S ( I − R ) − 1 0 0 ] . Here, ( I − R ) − 1 is the fundamental matrix. Also, the Gauss Jordan method of finding inverse is as follows: Step 1: Write the provided matrix and combine identity matrix in the right of it. Step 2: Transform left hand matrix into identity matrix by using row operations, do the same operations for the matrix on the right as well. Step 3: After the matrix on the left transforms into an identity matrix, the matrix on the right will be the desired inverse. Calculation: Here, the absorbing stochastic matrix is, [ 1 0 1 6 1 2 2 5 0 1 0 0 2 5 0 0 0 0 0 0 0 2 3 1 2 0 0 0 1 6 0 1 5 ] Now, convert above absorbing stochastic matrix into standard form as, [ I S 0 R ] = [ 1 0 1 6 1 2 2 5 0 1 0 0 2 5 0 0 0 0 0 0 0 2 3 1 2 0 0 0 1 6 0 1 5 ] Compare left and right side of the above equation, the value of R and S is, R = [ 0 0 0 2 3 1 2 0 1 6 0 1 5 ] and S = [ 1 6 1 2 2 5 0 0 2 5 ] Now, to find the stable matrix, calculate ( I − R ) , where I is an identity matrix. I − R = [ 1 0 0 0 1 0 0 0 1 ] − [ 0 0 0 2 3 1 2 0 1 6 0 1 5 ] = [ 1 0 0 − 2 3 1 2 0 − 1 6 0 4 5 ] Now, find the inverse of ( I − R ) that is ( I − R

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Author: Larry Goldstein, David Schneider

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Chapter 8, Problem 11RE

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To calculate: The stable matrix for the absorbing stochastic matrix,

[101612250100250000000231200016015]

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Chapter 8, Problem 10RE

Chapter 8, Problem 12RE

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Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)

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 stable matrix for the absorbing stochastic matrix, [ 1 0 1 6 1 2 2 5 0 1 0 0 2 5 0 0 0 0 0 0 0 2 3 1 2 0 0 0 1 6 0 1 5 ]

Solution Summary: The author explains the formula used to calculate the absorbing stochastic matrix.

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To calculate: The stable matrix for the absorbing stochastic matrix,

[101612250100250000000231200016015]

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Chapter 8 Solutions

The stable matrix for the absorbing stochastic matrix, [ 1 0 1 6 1 2 2 5 0 1 0 0 2 5 0 0 0 0 0 0 0 2 3 1 2 0 0 0 1 6 0 1 5 ]

Solution Summary: The author explains the formula used to calculate the absorbing stochastic matrix.

Videos

To calculate: The stable matrix for the absorbing stochastic matrix, [101612250100250000000231200016015]

Want to see the full answer?

Chapter 8 Solutions

To calculate: The stable matrix for the absorbing stochastic matrix,

[101612250100250000000231200016015]