MATH307 December 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q6 (e) • Q6 (f) • Q7 (a) • Q7 (b) • Q7 (c) •
Question 07 (b)
Suppose that A is a symmetric 4x4 matrix with eigenvalues 0, 1, 4, 5. Define a sequence of vectors by choosing x0 at random, and then settings
for n = 1, 2, .... You then observe that xn converges to
(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?
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Recall that from part (a) that .
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From part (a), we recall that was the eigenvalue associated to the eigenvector . We can use these to find the solution:
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MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Eigenvalues and eigenvectors, MER Tag Power iteration, Pages using DynamicPageList parser function, Pages using DynamicPageList parser tag