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Unformatted text preview: Homework 6 Math 471, Fall 2007 Assigned: Friday, October 19, 2006 Due: Friday, October 26, 2006 Include a cover page Clearly label all plots using title , xlabel , ylabel , legend Use the subplot command to compare multiple plots Include printouts of all Matlab code, labeled with your name, date, section, etc. (1) (Condition Numbers, P. 187 #1, 2) 1. Let A and B be n n matrices, and be a nonzero real number. (a) Show that ( AB ) ( A ) ( B ); (b) Show that ( A ) = ( A ). 2. Let A be an n n matrix, and suppose that A x = y for some vectors x and y . Show that ( A ) k A kk x k k y k . (2) (Error Estimates, P. 188 #7c, 8c) 7c. Compute for A = 1- 1- 1 1- 1 1 8c. Compute the error e = x- x and the residual r = A x- b and then compare the relative error to the condition number times the relative residual with l norm....
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