springps09b

# springps09b - 18.03 Problem Set 9b Spring 2009 Due with 9a...

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Unformatted text preview: 18.03 Problem Set 9b Spring 2009 Due with 9a in Room 2-106 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 5.1–5.3, LS.1 Work: 4A-1 (do not hand in); Write down the matrix products bracketleftbigg 2 3 bracketrightbigg [ x, y ] and [2 , 3] bracketleftbigg x y bracketrightbigg 4A-4, 6; 4B-1, 2, 3, 7 2. L33 Wed April 29: Eigenvalues and Eigenvectors. Read LS.2, EP 5.4 (not including complex roots) Work: 4C-1b, 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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springps09b - 18.03 Problem Set 9b Spring 2009 Due with 9a...

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