Science:Math Exam Resources/Courses/MATH307/December 2010/Question 07 (b)
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Question 07 (b) 

Suppose that A is a symmetric 4x4 matrix with eigenvalues 0, 1, 4, 5. Define a sequence of vectors by choosing x_{0} at random, and then settings for n = 1, 2, .... You then observe that x_{n} converges to as . (b) What is the value of the inner (dot) product ? 
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 

Recall that from part (a) that . 
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. From part (a), we recall that was the eigenvalue associated to the eigenvector . We can use these to find the solution:
