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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 ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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One of the main differences, between difference equations and differential equation is that difference equations model discreet changes ( that is month to month or year to year) whereas differential equations model continuous changes. Suppose Un+1= A Un is a matrix difference equation which describes discreet population changes 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 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 ?
Transcribed Image Text:One of the main differences, between difference equations and differential equation is that difference equations model discreet changes ( that is month to month or year to year) whereas differential equations model continuous changes. Suppose Un+1= A Un is a matrix difference equation which describes discreet population changes 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 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 ?
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