3.9 .65 .68 .75 .7 A .6 .55 .4 .35 0 0 0 0 0.2 0 A is called a Leslie matrix. 1. What does the “.65" in the second row mean? Why are so many elements of this matrix zero? 2. Suppose that the initial population vector is [1 0 0 0 0 0 0 0 0 o] (measured in hundreds of thousands of individuals). Determine the population after 10, 20, 50, 80, and 100 years. 3. Is the long-term population stable? (i.e. does x; stabilize to some fixed numbers?) If so, compute them and say how you know the population is stable. If not, what can you say about the long-term age distribution? 4. Suppose that pollution lowers all the birth rates by 10%. How do your answers change? What about if it lowers survival rates by 10%? Or both? 5. Let's start fishing. Write f for the fishing rate: a number between 0 and 1 so that 100f% of fish in each age group are harvested each year. Write down a matrix B so that x41 = Bx. Answer problems 2 and 3 again for f = .2. 6. Suppose now that fish under three years of age are never harvested. Write down a matrix C so that x+1= Answer problems 2 and 3 again for f = .2. = Cx.

3.9 .65 .68 .75 .7 A .6 .55 .4 .35 0 0 0 0 0.2 0 A is called a Leslie matrix. 1. What does the “.65" in the second row mean? Why are so many elements of this matrix zero? 2. Suppose that the initial population vector is [1 0 0 0 0 0 0 0 0 o] (measured in hundreds of thousands of individuals). Determine the population after 10, 20, 50, 80, and 100 years. 3. Is the long-term population stable? (i.e. does x; stabilize to some fixed numbers?) If so, compute them and say how you know the population is stable. If not, what can you say about the long-term age distribution? 4. Suppose that pollution lowers all the birth rates by 10%. How do your answers change? What about if it lowers survival rates by 10%? Or both? 5. Let's start fishing. Write f for the fishing rate: a number between 0 and 1 so that 100f% of fish in each age group are harvested each year. Write down a matrix B so that x41 = Bx. Answer problems 2 and 3 again for f = .2. 6. Suppose now that fish under three years of age are never harvested. Write down a matrix C so that x+1= Answer problems 2 and 3 again for f = .2. = Cx.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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