Science:Math Exam Resources/Courses/MATH221/December 2008/Question 06 (a)
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Question 06 (a) 

Suppose that each year 10% people living in Alberta move to BC, while 15% of people living in BC move to Alberta. Write a transition matrix that represents the change in population each year. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Science:Math Exam Resources/Courses/MATH221/December 2008/Question 06 (a)/Hint 1 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. To begin with, we assume that people live in either Alberta or BC. We represent a transition matrix as T=[]. Then, , , and finally . Thus, we have . 