0-11 - CHAP 0 Mathematical Preliminaries 11. Find the eigen...

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CHAP 0 Mathematical Preliminaries 11 11. Find the eigen values and eigen vectors of the following matrices: (a) 5 2 0 [ ] 2 2 0 0 0 1    A (b) 2 0 2 [ ] 0 1 0 2 0 5 B Solution: (a) The eigen value problem is defined as: [ ]{ } 0  A I x 1 2 3 5 2 0 0 2 2 0 0 0 0 1 0 x x x                            From the condition of zero determinant, the characteristic equation becomes: ( 1 ) ((5 ) (2 ) (2 2)) ( 1 ) (1 ) ( 6 )         The roots of the equation work out to be: 1 2 3 6 1 1   Substituting 1 into the characteristic equation gives: 11 22 33 5 6 2 0 1 2 0 0 2 2 6 0 2 4 0 0 0 0 1 6 0 0 7 0 xx                                 Solving for x (1) gives: 1
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This note was uploaded on 08/22/2011 for the course EML 4500 taught by Professor Staff during the Fall '08 term at University of Florida.

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0-11 - CHAP 0 Mathematical Preliminaries 11. Find the eigen...

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