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Unformatted text preview: 18.03 Problem Set 9b Spring 2009 Due with 9a in Room 2106 at 12:55 pm, Friday, May 1 Part A (16 points for 9a and 9b combined) 1. L32 Mon April 27: Linear systems; Matrix notation. Read EP 5.15.3, LS.1 Work: 4A1 (do not hand in); Write down the matrix products bracketleftbigg 2 3 bracketrightbigg [ x, y ] and [2 , 3] bracketleftbigg x y bracketrightbigg 4A4, 6; 4B1, 2, 3, 7 2. L33 Wed April 29: Eigenvalues and Eigenvectors. Read LS.2, EP 5.4 (not including complex roots) Work: 4C1b, 2, 6ab Part B (50 points for 9a and 9b combined) 0. (at due date) Write the names of any person, web site, or materials you consulted. Write No C (no consultation) on your paper if you consulted no outside materials/people. 1. On 9a: 6 pts = 3 + 3 2. On 9a: 14 pts = 2 + 2 + 2 + 2 + 1 + 2 + 3 3. Mon April 27 Phase plane portraits. 14 pts = 3 + 1 + 3 + 3 + 4 a) Find the general solution to each of the equations i) x + 4 x + 3 x = 0; ii) x + 2 x + 3 x = 0 b) Find the companion matrix to each of (i) and (ii) in the form bracketleftbigg 1...
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