Let vk = Yk () Consider the difference equation vk+1 = Avk with initial condition vo = where A is a 2 x 2 matrix with eigenvalues A1 = -2/5, X2 = 1/2 and corresponding eigenvectors ¤1 2 and #2 = -2 (:) Then, lim Vk = 2 ()

Let vk = Yk () Consider the difference equation vk+1 = Avk with initial condition vo = where A is a 2 x 2 matrix with eigenvalues A1 = -2/5, X2 = 1/2 and corresponding eigenvectors ¤1 2 and #2 = -2 (:) Then, lim Vk = 2 ()

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter10: Matrices

Section10.CR: Chapter 10 Review

Problem 62CR

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Concept explainers

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.

Question

Please solve

Consider the difference equation vk+1 =
Let vk =
Yk
Avk with initial condition vo =
where A is a 2 x 2 matrix with eigenvalues A1 = -2/5, X2 = 1/2 and corresponding eigenvectors x1
-()
and x2 =
Then, limk→∞ Vk =
2
(9)
()
()

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