**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 x_{0} and that of Mumbai be y_{0}. We are interested in knowing the population after 1, 2, 3 years.

Initial population vector X_{0} = [x_{0} y_{0}]^{t} if x_{1}, y_{1} are the populations of Delhi and Mumbai after 1 year.

∴

In the matrix form, we get

If *X*_{1} = [x_{1} y_{1}]t is the population vector after 1 year

where

If *X*_{2} = [*x*_{2}, *y*_{2}]^{t} is the population vector after 2 years, then we will get

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