Question: (a) Let A be the matrix 1 2 1 01-2 0 1 4, Calculate the eigenvalues of A. (b) In Smalltown, there are only

$(a) Let A be the matrix 1 2 1\ 01-2 0 1$

(a) Let A be the matrix 1 2 1\ 01-2 0 1 4, Calculate the eigenvalues of A. (b) In Smalltown, there are only two restaurants, a Fish and chips shop and an Indian curry restaurant. Every day, the people in Smalltown eat either at one of the two restaurants, or they eat at Home. We assume that their choice only depends on where they had dinner the previous day. The transition matrix T for this situation is as follows: H H F I 0 3 We will assume that T is regular. (i) What proportion of inhabitants of Smalltown who eat at the Indian curry restau- rant on a given Monday will eat at home on Tuesday? (ii) Find the steady-state vector of T. Felle 10-13 113 12113 113 O

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