Science:Math Exam Resources/Courses/MATH221/April 2009/Question 06
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Question 06 

If and , ﬁnd the limiting values of as 
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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/April 2009/Question 06/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Set up Markov System
Find the eigenvalues, and get which yields the eigenvectors and The solution can now be written as As we have Using initial conditions to find At k = 0, Solving for and , we get
and thus our steady state solution is and our limiting values would be 