During any given year, 10% of all rural residents move to the city, and 20% of all city re...

During any given year, 10% of all rural residents move to the city, and 20% of all city residents move to a rural area (all other people stay put!). Let Rt be the number of rural residents at the beginning of year t, and Ct be the number of city residents at the beginning of year t. Use matrix multiplication to relate the vector  to the vector .