In an office complex of 1020 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 80% chance that she will be at work tomorrow, and if the employee is absent today, there is a 65% chance that she will be absent tomorrow. Suppose that today there are 785 employees at work.

(a) Find the transition matrix for this scenario. (Assume the components of the state vector are listed in this order: [number at work, number absent]).

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(b) Predict the number that will be at work five days from now. (Your answer should be an integer.)

(c) Find the steady-state vector. (The components need not be integers.)

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