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4. After exposure to certain live pathogens, the body develops long-term immunity. The evolution over time of the associated disease can be modeled as a dynamical system whose state vector at time t consists of the number of people who have not been exposed and are therefore susceptible, the number who are currently sick with the disease, and the number who have recovered and are now immune. Suppose that the associated 3 × 3 yearly transition matrix A has eigenvalues λ = 1,1,0, and that the eigenvectors corresponding to the first two eigenvalues are x1 = (60, 20, 30) and x₂ = (-60, -30, 90), respectively. The initial state vector for the population is given by = Vo = 500x₁+200x2 + 100x3 where the third eigenvector x3 is not given here. How many people will be sick with the disease 2 years later? (a) 15450 (b) 27000 (c) 8500 (d) 9700 (e) 4000

4. After exposure to certain live pathogens, the body develops long-term immunity. The evolution over time of the associated disease can be modeled as a dynamical system whose state vector at time t consists of the number of people who have not been exposed and are therefore susceptible, the number who are currently sick with the disease, and the number who have recovered and are now immune. Suppose that the associated 3 × 3 yearly transition matrix A has eigenvalues λ = 1,1,0, and that the eigenvectors corresponding to the first two eigenvalues are x1 = (60, 20, 30) and x₂ = (-60, -30, 90), respectively. The initial state vector for the population is given by = Vo = 500x₁+200x2 + 100x3 where the third eigenvector x3 is not given here. How many people will be sick with the disease 2 years later? (a) 15450 (b) 27000 (c) 8500 (d) 9700 (e) 4000

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 23EQ
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4. After exposure to certain live pathogens, the body develops long-term immunity. The evolution over time of the associated disease can be modeled as a dynamical system whose state vector at time t consists of the number of people who have not been exposed and are therefore susceptible, the number who are currently sick with the disease, and the number who have recovered and are now immune. Suppose that the associated 3 × 3 yearly transition matrix A has eigenvalues λ = 1, 2, 0, and that the eigenvectors corresponding to > the first two eigenvalues are x₁ = (60, 20, 30) and x₂ = (-60, -30, 90), respectively. The initial state vector for the population is given by Vo = 500x1 + 200x2 + 100x3 where the third eigenvector x3 is not given here. How many people will be sick with the disease 2 years later? (a) 15450 (b) 27000 (c) 8500 (d) 9700 (e) 4000
Transcribed Image Text:4. After exposure to certain live pathogens, the body develops long-term immunity. The evolution over time of the associated disease can be modeled as a dynamical system whose state vector at time t consists of the number of people who have not been exposed and are therefore susceptible, the number who are currently sick with the disease, and the number who have recovered and are now immune. Suppose that the associated 3 × 3 yearly transition matrix A has eigenvalues λ = 1, 2, 0, and that the eigenvectors corresponding to > the first two eigenvalues are x₁ = (60, 20, 30) and x₂ = (-60, -30, 90), respectively. The initial state vector for the population is given by Vo = 500x1 + 200x2 + 100x3 where the third eigenvector x3 is not given here. How many people will be sick with the disease 2 years later? (a) 15450 (b) 27000 (c) 8500 (d) 9700 (e) 4000
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