A country is divided into three regions: regions A, B, and C. It's found that each year, one tenth of the people in region A move to region B and 1 tenths of the people in region A move to region C. Similarly, 5 tenths of the people in region B move to region A and two tenths of the the people in region B move to region C. Finally, one tenth of the people in region C move to region A and 1 tenths of them move to region B. What percentage of the population lives in each of the three regions after a long period of time? % live in region A, % live in region B, and ☐ % live in region C, Hint: if you're trying to solve Ax: = and the matrix A has fractions that you wish weren't there, you can multiply both sides of the matrix equation by a well-chosen number to make the problem simpler. (Note: you may still get fractions when doing Gaussian elimination but that's a different situation.)
A country is divided into three regions: regions A, B, and C. It's found that each year, one tenth of the people in region A move to region B and 1 tenths of the people in region A move to region C. Similarly, 5 tenths of the people in region B move to region A and two tenths of the the people in region B move to region C. Finally, one tenth of the people in region C move to region A and 1 tenths of them move to region B. What percentage of the population lives in each of the three regions after a long period of time? % live in region A, % live in region B, and ☐ % live in region C, Hint: if you're trying to solve Ax: = and the matrix A has fractions that you wish weren't there, you can multiply both sides of the matrix equation by a well-chosen number to make the problem simpler. (Note: you may still get fractions when doing Gaussian elimination but that's a different situation.)
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
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Transcribed Image Text:A country is divided into three regions: regions A, B, and C.
It's found that each year, one tenth of the people in region A move to region B and 1 tenths of the people in region A move to region C.
Similarly, 5 tenths of the people in region B move to region A and two tenths of the the people in region B move to region C. Finally, one tenth
of the people in region C move to region A and 1 tenths of them move to region B.
What percentage of the population lives in each of the three regions after a long period of time?
% live in region A,
% live in region B,
and
☐ % live in region C,
Hint: if you're trying to solve Ax:
=
and the matrix A has fractions that you wish weren't there, you can multiply both sides of the matrix
equation by a well-chosen number to make the problem simpler. (Note: you may still get fractions when doing Gaussian elimination but that's
a different situation.)
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