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

MyLab Math plus Pearson eText -- Standalone Access Card -- for Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134765723

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 8.1, Problem 38E

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.1, Problem 37E

Chapter 8.1, Problem 39E

Students have asked these similar questions

A biologist is investigating the effect of potential plant hormones by treating 20 stem segments. At the end of the observation period he computes the following length averages: Compound X = 1.18 Compound Y = 1.17 Based on these mean values he concludes that there are no treatment differences. 1) Are you satisfied with his conclusion? Why or why not? 2) If he asked you for help in analyzing these data, what statistical method would you suggest that he use to come to a meaningful conclusion about his data and why? 3) Are there any other questions you would ask him regarding his experiment, data collection, and analysis methods?

Business

Answer first question

Chapter 8 Solutions

MyLab Math plus Pearson eText -- Standalone Access Card -- for 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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

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

Videos

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

Want to see the full answer?

Chapter 8 Solutions