Only three brands of beer (beer 1, beer 2, and beer 3) are available for sale in Metropoli...

Only three brands of beer (beer 1, beer 2, and beer 3) are available for sale in Metropolis. From time to time, people try one or another of these brands. Suppose that at the beginning of each month, people change the beer they are drinking according to the following rules:

30% of the people who prefer beer 1 switch to beer 2.

20% of the people who prefer beer 1 switch to beer 3.

30% of the people who prefer beer 2 switch to beer 3.

30% of the people who prefer beer 3 switch to beer 2.

10% of the people who prefer beer 3 switch to beer 1.

For i = 1, 2, 3, let xi be the number who prefer beer i at the beginning of this month and y, be the number who prefer beer i at the beginning of next month. Use matrix multiplication to relate the following: