Fall2011-HW6-soln - Homework 6 Solution Sketches Math 371,...

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Homework 6 Solution Sketches Math 371, Fall 2011 Assigned: Thursday, October 20, 2011 Due: Thursday, October 26, 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, section, etc. (1) (Norms) (a) Do problems #3(a), (b) from page 180 (b) Consider the matrix A = 2 0 0 0 3 4 0 2 - 1 . Compute the spectrum of A T A . What is the ü 2 matrix norm of A ? (c) Compute the ü matrix norm of A . Find a vector x such that ë A ë = ë Ax ë / ë x ë . (d) Verify your calculations in (b) and (c) using Matlab. We prove that || · || 1 is a vector norm as follows. It is clear that ë x ë 1 0. If ë x ë 1 = 0, then | x i | = 0 for each i . So x = 0. • ë λx ë = | λ || x i | = | λ | | x i | . • ë x + y ë 1 | x i | + | y i | = ë x ë 1 + ë y ë 1 . #3(b). The following
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Fall2011-HW6-soln - Homework 6 Solution Sketches Math 371,...

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