# Quiz4 - -- = - Let 1 1 1 2 2 1 1 3 3 1 2 2 1 1 1 1 2 2 t t...

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EGM 4313 – Spring 2009 NAME:____________________________________ Quiz 4 25 minute time limit. Closed notes – Open book – No calculators Find a particular solution to the system of first order differential equations 1 1 2 2 1 2 1 2 1 1 t y y e y y - ÷ = + ÷ ÷ ÷ ÷ - by the diagonalization method . The matrix 1 2 2 1 A = ÷ has eigenvalues 3, 1 λ = - with eigenvectors 1 1    ÷   and 1 1 ÷ - . Solution: 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 2 2 2 2 1 1 1 1 0 1 0 2 1 1 0 2 0 1 1 1 1 1 2 2 1 1 2 2 1 1 2 2 X X - ÷ ÷ = →  ÷ ÷ ÷ ÷ ÷ - - - - -
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Unformatted text preview: -- = - Let 1 1 1 2 2 1 1 3 3 1 2 2 1 1 1 1 2 2 t t u u u X y u u e u u e--- = = = + -- = -+- A solution is 1 2 0, t u u te-= = Hence ( 29 1 1 1 1 1 1 t p t y Xu te te-- = = = --...
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## This note was uploaded on 12/15/2011 for the course EGM 4313 taught by Professor Mei during the Fall '08 term at University of Florida.

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