Problem 2, p. 20
Only three brands of beer are availablefor sale in Metropolis.
From time to time, people try one or another of these brands.
Suppose that at the beginning of the month people change the beer they drink
according to the following rules:
30% of people who prefer brand 1 switch to 2
20% of people who prefer brand 1 switch to 3
30% of people who prefer brand 2 switch to 3
30% of people who prefer brand 3 switch to 2
10% of people who prefer brand 3 switch to 1
xi = # people who prefer brand i at the beginning of the month
yi = # people who prefer brand i at the end of the month
Matrix formulation:
A x = y