Question 3 (5 points): In a certain region each person is understood to live either in the city or the suburbs. Each year 6% of the city population moves to the suburb (and the rest stays in the city). Also each year 4% of the suburb population moves to the city (and the rest stay in the suburbs). Suppose that x1 is the number of people who live the city in a certain year, and x2 is the number of people who live in the suburb in that same year. Let y1 be the number of people who live in the city the year after, and similarly y2 be the number who live in the suburbs. (a) Write down a formula for y1 in terms of x1 and x2. Then write down a formula for y2 in terms of x1 and x2. (b) Let x = x1 x2 and y = y1 y2 . Use your answer in part (a) to find a matrix A such that y = Ax (c) Suppose that in 2020 there are 10,000,000 people in the city and 800,000 in the suburbs. What is the population in the city and in the suburb in the year 2021? (d) What is the population in the city and in the suburb in the year 2022? (Calculators are allowed)