ENME361 Quiz 9 Solution

# ENME361 Quiz 9 Solution - ENME 361 Fall 2008 Solution for...

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ENME 361 Fall 2008 Solution for Quiz #9 (November 20, 2008; Duration: 10 minutes) 1) Consider the following system of algebraic equations: 2 11 11 1 11 12 2 21 21 22 1 22 0 X km k X kk m λ ⎡⎤ −− ⎧⎫ = ⎨⎬ ⎢⎥ ⎩⎭ ⎣⎦ i) Define eigenvalues. Solution : Eigenvalues are the special values of 2 , for which X 11 and X 21 are non-zero or not trivial. ii) Determine the characteristic equation for this system. Solution : The characteristic equation is given by 2 11 11 12 2 21 22 22 det 0 k m = which when expanded leads to 22 11 11 22 22 12 21 () ( ) 0 k k λλ = . ii) Say, the determined eigenvalues are λ 1 and
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## This note was uploaded on 02/13/2011 for the course ENME 361 taught by Professor Yoo during the Spring '11 term at Maryland.

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