A nature reserve on an island contains a population of endangered turtles. The reserve is not fenced, so the turtles are free to cross the boundary coming in or going out. Every year, 10% of the turtles leave the reserve, while 1% of the turtles from outside the reserve (but on the island) make their way in. Suppose the island has a total of 2,200 turtles. Is there a population of turtles inside and outside the reserve that will stay constant over time?

The solution needs to be done by matrix.