Questions A and B please!!! Each year, 5% of the population in Antapolis immigrate to Bumbleton, and 3% of the population inBumbleton immigrate to Antapolis. Let ci, r; be the population of Antapolis and Bumbleton in the thyear. In the following your mission is to find the distribution of the population.a) Find a 2 x 2 matrix M =such that for all natural numbers n ≥ 2a b(d)( ₂ ) = M (²n-1).Tnb) Find the eigenvalues of M.c) Find the eigenvectors associated with each eigenvalue of M.d) Diagonalize M, i.e., write M in the form M = NDN-1, where N and D are 2 x 2 matrices and Dis diagonal.e) Let c₁ = r₁=0.5 (where we count population in units of millions). Derive a formula for Cn, Tnfrom (d), and find the equilibrium distribution, namely find limno Cn, limn→∞0 Tn.

Note:As per asked by the student, solving only part a and b of the question.To solve this problem,we…

Each year, 5% of the population in Antapolis immigrate to Bumbleton, and 3% of the population in Bumbleton immigrate to Antapolis. Let ci, r; be the population of Antapolis and Bumbleton in the th year. In the following your mission is to find the distribution of the population. a) Find a 2 x 2 matrix M = such that for all natural numbers n ≥ 2 a b (d) b) Find the eigenvalues of M. (₂) - M (C-1). = Tn-1

Each year, 5% of the population in Antapolis immigrate to Bumbleton, and 3% of the population in Bumbleton immigrate to Antapolis. Let ci, r; be the population of Antapolis and Bumbleton in the th year. In the following your mission is to find the distribution of the population. a) Find a 2 x 2 matrix M = such that for all natural numbers n ≥ 2 a b (d) b) Find the eigenvalues of M. (₂) - M (C-1). = Tn-1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 2DE

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