Fall2011-HW7-soln - Homework 7 solution sketches Math 371,...

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Unformatted text preview: Homework 7 solution sketches Math 371, Fall 2011 Assigned: Saturday, October 28, 2011 Due: Thursday, November 3, 2011 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, and section. Add 12 for page numbers in the international edition. (1) (Condition numbers) For two n n matrices A and B , prove that ( AB )- 1 = B- 1 A- 1 , and ( A )- 1 = 1 A- 1 . Now do P. 187 #1, 2. ( AB )( B- 1 A- 1 ) = A ( BB- 1 ) A- 1 = AIA- 1 = AA- 1 = I . Alternatively, you can verify that B- 1 A- 1 AB = I . ( A ) ( A- 1 / ) = 1 / AA- 1 = I . Therefore ( A )- 1 = A- 1 / . ( AB ) = || AB || || B- 1 A- 1 || || A || || A- 1 || || B || || B- 1 || = ( A ) ( B ). ( A ) = || A || || 1 A- 1 || = | | | | || A || || A- 1 || = ( A )....
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Fall2011-HW7-soln - Homework 7 solution sketches Math 371,...

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