1. Two species are said to be symbiotes if they help each other to survive. For instance,elown fish and sea anemones are symbiotes (they protect each other from differenttypes of predators).Say in some region, without sea anemones to shelter them, the clown fish populationis stable (that is, the clown fish population in the k + 1-th season is the same as thepopulation in the k-th season). However, for each sea anemone present, an extra 0.2clown fish are present in the next season.Similarly, in the absence of clown fish, the sea anemone population in the k + 1-thseason is only 70% of the population in the k-th season. However, for each clown fishpresent, an extra 0.2 anemones are present the next season.(a) Write down difference equations for the number of clown fish and sea anemonesin the k + 1-th season in terms of the clown fish c& and sea anemones ar in thek-th season.(b) Write the system of difference equations above as a matrix equation, then diago-nalize the matrix.

Given: ck=The population of clown fish in kth seasonak=The population of sea anemones in kth…

Answered: 1. Two species are said to be symbiotes…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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