Suppose that a particular region with a constant population is divided into three areas: the city, suburbs, and country. the probability that a person living in the city moves to the suburbs (in one year) is .10, and the probability that someone moves to the country is .50. the probability is .20 that a person living in the suburbs moves to the city and is .10 for a move to the country. the probability is .20 that a person living in the country moves to the city and is .20 for a move to the suburbs. suppose initially that 50% of the people live in the city, 30% live in the suburbs, and 20% live in the country.

a. determine the transition matrix for the three states.

b. determine the percentage of people living in each area after 1, 2, and 3 years.

c. find the percentage of people living in each area after 5 and 8 years.

d. determine the eventual percentages of people in each area.