This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Tutorial #10  MAT 1332A  Fall 2009 November 23, 2009 Find the eigenvalues and eigenvectors of A = 1 8 4 . Solution: 1 = 2 + 2 i , v 1 = 1 2 + 2 i ; 2 = 2 2 i , v 2 = 1 2 2 i On any given day, a student is either healthy or ill. Of the students who are healthy today, 95% will be healthy tomorrow. Of the students who are ill today, 55% will still be ill tomorrow. (a) What is the transition matrix for this situation? (b) Suppose 20% of the students are ill on Monday. What fraction of per centage of the students are likely to be ill on Tuesday? On Wednes day? (c) If a student is well today, what is the probability that he or she will be well two days from now? (d) Find the steadystate vector for the Markov chain. Solution : (a) From : H I To : P = . 95 . 45 . 05 . 55 Healthy Ill Note that the sum of the entries in each column is 1. (b) Recall that the sum of the entries of a state vector is always 1. Let x (0) be the state vector on Monday. So x (0) = . 80 . 20 . Then....
View
Full
Document
 Fall '09
 ARIANEMASUDA
 Eigenvectors, Vectors

Click to edit the document details