Science:Math Exam Resources/Courses/MATH307/December 2006/Question 03 (b)
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Question 03 (b) 

Consider the discrete dynamical system
which describes the evolution of the vector Find a fixed vector for this discrete dynamical system, i.e., a vector such that
holds for all n. 
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/MATH307/December 2006/Question 03 (b)/Hint 1 
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Solution 

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as n approaches infinity. If the solution starts as a steady state solution then it will not change with n. ie. we need to find a steady state solution. One solution is:
