Explanation Given Information: The stochastic matrix and initial distribution matrix is given [ 0.3 0.9 0.7 0.1 ] , [ 0.5 0.5 ] 0 . Formula used: The product of two matrixes of order m × n and p × q is possible only if the internal dimensions, that is, n and p are equal. The order of the resultant matrix will be m × q which means, it is determined by the external dimensions of the two matrices. Calculation: Consider the initial distribution matrix [ 0.3 0.9 0.7 0.1 ] , [ 0.5 0.5 ] 0 . Suppose matrix A = [ 0.3 0.9 0.7 0.1 ] . Now, calculate the value of A 2 , A 3 a n d A 4 . Compute the product of matrix A and its self-matrix A as follows. The product of the matrices of order 2 × 2 and 2 × 2 is possible as the internal dimensions, n and p are equal, that is n = p = 2 . The order of the resultant matrix will be 2 × 2 , as these are the external dimensions of the two matrices. Now, compute the multiplication of the two matrices by multiplying each element present in the first row of the first matrix with each corresponding element present in the first column of the second matrix and add them up, continue this way. A 2 = A ⋅ A = [ 0.3 0.9 0.7 0.1 ] [ 0.3 0.9 0.7 0.1 ] = [ 0.72 0.36 0.28 0.64 ] A 3 = A 2 ⋅ A = [ 0.72 0.36 0.28 0.64 ] [ 0

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134507125

Author: Goldstein

Publisher: PEARSON

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Chapter 8.1, Problem 38E

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To calculate: The third and fourth distribution matrices for the provided stochastic matrix and initial distribution A=(0.30.90.70.1),[0.50.5]0

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Chapter 8.1, Problem 37E

Chapter 8.1, Problem 39E

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Chapter 8 Solutions

Finite Mathematics & Its Applications (12th Edition)

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 third and fourth distribution matrices for the provided stochastic matrix and initial distribution A = ( 0.3 0.9 0.7 0.1 ) , [ 0.5 0.5 ] 0

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To calculate: The third and fourth distribution matrices for the provided stochastic matrix and initial distribution A=(0.30.90.70.1),[0.50.5]0

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