By observing a certain colony of mice. reearchcrs found

Chapter , Problem 10

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By observing a certain colony of mice. reearchcrs found that all animals die within 3 year>. or thoe off,pring that are females, 601! live for at least I year. Of these. 20% reach their second birthday. The females who are under Elementary Linear Algebra: A Matrix Approach, 2nd Edition, page: 118 No part of any book may be reproduced or transmitted by any means without the publishers prior permission. Use (other than qualified fair use) in violation of the law or Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law. User: Thomas McVaney Page 1 of 10 118 CHAPTER 2 Matrices and Li near Transformations I year of :~ge ha\e, on average. three female offspring. Those females between I and 2 years of age have, on average. two female off:.pring while they are in this age group. None of the females of age 2 give birth. (a) Construct the Lc.he matrix that describes this situation. (b) Suppose that the current population distribution for females h given b) the \ector [I~J Find the population dbtribution for next year. Also. find the population distribution 4 years from now. (c) Show th:u there is no nonzero stable population distribution for the colony of mice. Him: Let A be the Leslie matrix. and suppose that z is a stable population distribution. Then Az = z. This is equivalent to (A - /3)7. = 0 . Solve this homogeneous system of linear equations.