GSW Problem Set 5

GSW Problem Set 5 - 3 Consider the forced system ~x = A~x ~...

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Engineering Analysis 4 Workshop questions - week of 11/09/08 1. Give an example of a matrix which has repeated eigenvalues, but which is not defective. 2. Consider the forced system ~x 0 = A~x + te 2 t ~ f , (1) where ~ f a constant vector and A is a matrix. (a) Set up the equations to Fnd a particular solution using undetermined coefFcients. (b) When will this procedure breakdown? (c) If A is 10 × 10 then how large is the system of equations that you have to solve?
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Unformatted text preview: 3. Consider the forced system ~x = A~x + ~ f, where ~ f = ± 1 ² , A = ± 1 k 1 1 ² . (a) Set up the system of equations to Fnd ~x p . (b) Determine all values of k such that this procedure works. (c) Determine ~x p for all values of k that you can. 4. Consider the forced system ~x = A~x + cos t ~ f , where ~ f = ± 1 ² , A = ± 1 1 1 ² . ±ind ~x p ....
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This note was uploaded on 09/08/2010 for the course GEN_ENG 205 taught by Professor Taflove during the Spring '08 term at Northwestern.

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