Fall2011-HW7-soln

# 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 ( αA )- 1 = 1 α 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 . • ( αA ) ( A- 1 /α ) = α × 1 /α × AA- 1 = I . Therefore ( αA )- 1 = A- 1 /α . • κ ( AB ) = || AB || · || B- 1 A- 1 || ≤ || A || · || A- 1 || · || B || · || B- 1 || = κ ( A ) κ ( B ). • κ ( αA ) = || αA || · || 1 α A- 1 || = | α | | α | || A || · || A- 1 || = κ ( A )....
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## This note was uploaded on 12/16/2011 for the course MATH 371 taught by Professor Krasny during the Fall '08 term at University of Michigan.

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

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