Village/Nightlife/Movements/Eigendistribution/Exercise

The nightlife in the village Kleineisenstein consists in the following three opportunities: to stay in bed (at home), the pub "Nightowl“ and the dancing club "Pirouette“. In a night, one can observe within an hour the following movements:

a) ${}1/10$ of the people in bed go to the Nightowl, ${}1/12$ go to the Pirouette and the rest stays in bed.

b) ${}1/3$ of the people in the Nightowl go to the Pirouette, ${}1/5$ go to bed and the rest stays in the Nightowl.

c) ${}3/5$ of the people in the Pirouette stay in the Pirouette, a percentage of ${}8$ go to the Nightowl, the rest goes to bed.

1. Establish a matrix, which describes the movements within an hour.
2. Kleineisenstein has ${}500$ inhabitants. Determine a distribution of the inhabitants (on the three locations) which does not change within an hour.

Create a solution