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hw3.6 - Math 43 Fall 2007 B Dodson Week 9 Monday Finish...

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Unformatted text preview: Math 43, Fall 2007 B. Dodson Week 9: Monday: Finish Suggested Hw8; start on Hw9 material 1. Determinants 2. Properties of Dets 3. Eigenvalues and Eigenvectors 2 We compute det 2 1 5 4 2 3 9 5 1 using the (first) row expansion (by minors): det ( A ) = 2 fl fl fl fl 2 3 5 1 fl fl fl fl- 1 fl fl fl fl 4 3 9 1 fl fl fl fl + 5 fl fl fl fl 4 2 9 5 fl fl fl fl = 2(2- 15)- (4- 27) + 5(20- 18) = 2(- 13)- (- 23) + 5(2) =- 26 + 33 = 7 . ———– Problem Reduce A = 2 1 3 5 3 1 2 4 1 4 3 5 2 5 3 to an upper triagular matrix and use the reduction to find det ( A ) . Solution: A → - 1 1 2 3 3 1 2 4 1 4 3 5 2 5 3 ( r 1- r 2 ) → - 1 1 2 3 3 7 11 5 12 15 7 15 18 ( r 2 + 3 r 1 , r 3 + 4 r 1 , r 4 + 5 r 1 ) → - 1 1 2 3 3 7 11 5 12 15 1 1- 4 ( r 4- 2 r 2 ) → - 1 1 2 3 1 1- 4 5 12 15 3 7 11 ( r 2 ↔ r 4 ) → - 1 1 2 3 1 1- 4 7 35 4 23 ( r 3-...
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hw3.6 - Math 43 Fall 2007 B Dodson Week 9 Monday Finish...

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