One of the main differences, between difference equations and differential equation is that differenceequations model discreet changes ( that is month to month or year to year) whereas differential equationsmodel continuous changes.Suppose Un+1= A Un is a matrix difference equation which describes discreet populationchanges from year to year.A. Suppose matrix A has eigenvalues X1 and Xz with corresponding eigenvectors V and W.What is the general solution of this difference equation ?B. Let UN =where x represents the number of individuals in the first stage of lifeand y represents the number of individuals in the second stage of life in this population .In the long run, how do you find the fraction of the population that will be in stage one and thefraction of the population that will be in stage two ?

Given: The equation of difference matrix is Un+1=AUn. To find: (a) The general solution of the…

Suppose Un+1= A U₁ is a matrix difference equation which describes discreet population changes from year to year. A. Suppose matrix A has eigenvalues X₁ and X2 with corresponding eigenvectors V and W. What is the general solution of this difference equation? B. Let UN = (Y) where x represents the number of individuals in the first stage of life and y represents the number of individuals in the second stage of life in this population. In the long run, how do you find the fraction of the population that will be in stage one and the fraction of the population that will be in stage two ?

Suppose Un+1= A U₁ is a matrix difference equation which describes discreet population changes from year to year. A. Suppose matrix A has eigenvalues X₁ and X2 with corresponding eigenvectors V and W. What is the general solution of this difference equation? B. Let UN = (Y) where x represents the number of individuals in the first stage of life and y represents the number of individuals in the second stage of life in this population. In the long run, how do you find the fraction of the population that will be in stage one and the fraction of the population that will be in stage two ?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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