Definitions and Examples
Suppose that each year 6% of the population of Delhi migrate to Mumbai and 4% of the population of Mumbai migrate to Delhi. Let the population of Delhi be x0 and that of Mumbai be y0. We are interested in knowing the population after 1, 2, 3 years.
Initial population vector X0 = [x0 y0]t if x1, y1 are the populations of Delhi and Mumbai after 1 year.
In the matrix form, we get
If X1 = [x1 y1]t is the population vector after 1 year
If X2 = [x2, y2]t is the population vector after 2 years, then we will get