The Car has offices in NYC and LA. Customers can create local rentals or 1-way rentals to other location. Every month: 3/4 of cars which start month in NYC end in LA and 3/5 of cars which begin month in LA end up in NYC. At begin of operation Rusty has 700 cars in LA and 300 in NYC.
(i) Determine transition matrix A.
(ii) Compute initial state or distribution matrix X0.
(iii) Compute state or distribution matrix X3 after three months.
(iv) How many cars are in every city at the end of three months?
(v) Compute X stable state or distribution and A stable stable matrix.