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A = [3] mal matrix D at P-¹AP = D, for some invertible matrix P. You do not need to find the chain is being used to model the weekly behaviour of 8000 employees. It has two states works from home = works in the office tion matrix is P = 0.8 0.3] 0.2 0.7 00 employees work in the office initially (week 0), how many of these switch to working from week 1?

A = [3] mal matrix D at P-¹AP = D, for some invertible matrix P. You do not need to find the chain is being used to model the weekly behaviour of 8000 employees. It has two states works from home = works in the office tion matrix is P = 0.8 0.3] 0.2 0.7 00 employees work in the office initially (week 0), how many of these switch to working from week 1?

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...
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Extended Answer Question 3 (a) Let A = = [21] at P-¹ AP = D, for some invertible matrix P. You do not need to find the Find a diagonal matrix D matrix P. (b) A Markov chain is being used to model the weekly behaviour of 8000 employees. It has two states State 1: works from home State 2: works in the office and its transition matrix is P = 0.8 0.3] 0.2 0.7 (i) If 2000 employees work in the office initially (week 0), how many of these switch to working from home in week 1? 0.6 (ii) Let x = Show that x is a steady-state probability vector (SSPV), and explain why x is the 0.4 unique SSPV. (iii) In the long run, how many employees work from home? (c) Let V1, V2, V3 be any three linearly independent vectors in R³. Determine whether the vectors V1 V2, V2 V3 and V3 - V1 are linearly independent, and justify your answer.
Transcribed Image Text:Extended Answer Question 3 (a) Let A = = [21] at P-¹ AP = D, for some invertible matrix P. You do not need to find the Find a diagonal matrix D matrix P. (b) A Markov chain is being used to model the weekly behaviour of 8000 employees. It has two states State 1: works from home State 2: works in the office and its transition matrix is P = 0.8 0.3] 0.2 0.7 (i) If 2000 employees work in the office initially (week 0), how many of these switch to working from home in week 1? 0.6 (ii) Let x = Show that x is a steady-state probability vector (SSPV), and explain why x is the 0.4 unique SSPV. (iii) In the long run, how many employees work from home? (c) Let V1, V2, V3 be any three linearly independent vectors in R³. Determine whether the vectors V1 V2, V2 V3 and V3 - V1 are linearly independent, and justify your answer.
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