2 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 x, be the number who prefer beer i at the beginning of this month and y, be the number who pre- fer beer i at the beginning of next month. Use matrix mul- tiplication to relate the following: E A X2

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ISBN:9780470458365
Author:Erwin Kreyszig
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2 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 x, be the number who prefer beer i at
the beginning of this month and y, be the number who pre-
fer beer i at the beginning of next month. Use matrix mul-
tiplication to relate the following:
E A
X2
Transcribed Image Text:2 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 x, be the number who prefer beer i at the beginning of this month and y, be the number who pre- fer beer i at the beginning of next month. Use matrix mul- tiplication to relate the following: E A X2
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