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9. Consider a linear model for the progression of a contagious Vll'llE through a population, described by: 3i+1 = Si TIL Jir:'+1 = If. +012 - fe Ri+1 = R: 'l' 4'31: In this model 3,- describes the number of people that have never been infected, 1,- describes the number of people who are currentlyr infected, and R,- describes the number for people that have recovered from infection, with i representing time counted in days. o: is a parameter that describes the infec'ti1l.."1|:j,l..r of the Tvirus, and is a parameter that describes hOW long it takes to recover from an infection. {a} Write a matrix expression EH1 = Air} for this model, with it = [LII] and ,5 = .5. {b} Find the eigenvalue decomposition of A, A = XX'l; you ma},r wish to use a calculator for the arithmetic. {c} Use the result of (h) to nd the number of people that are currently infected and the number that have recovered from an infection after 1012}, E and 300 days, if we begin with lllllllll susceptible people and 1G people that are infected. Use a calculator [or other computational aid) for the arithmetic. {d} Discuss whether the results you obtain in [c] make sense