Quiz8-Solutions

Quiz8-Solutions - Name Math 331 Quiz 9 Solutions Thursday...

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Unformatted text preview: Name:.......................................................................................... Math 331 - Quiz 9 - Solutions Thursday, November 17 1. Let 30 21 A= Find a basis of the eigenspace corresponding to the eigenvalue Î» = 3. Solution: A âˆ’ 3I = 00 . 2 âˆ’2 0 0 |0 2 âˆ’2 | 0 âˆ¼ 1 âˆ’1 | 0 0 0 |0 So we have x2 is a free variable and Nul(A âˆ’ 3I ) = So a basis for the eigenspace is x2 1 1 1 . 1 Check: 30 21 1 1 = 3 3 =3 1 1 . 2. Find the characteristic polynomial and real eigenvalues of the matrix 82 33 Solution: 8âˆ’Î» 2 3 3âˆ’Î» (8 âˆ’ Î»)(3 âˆ’ Î») âˆ’ 6 24 âˆ’ 11Î» + Î»2 âˆ’ 6 Î»2 âˆ’ 11Î» + 18 (Î» âˆ’ 9)(Î» âˆ’ 2) det(A âˆ’ Î»I ) = det = = = = So the real eigenvalues are Î» = 2 and Î» = 9. ...
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This document was uploaded on 04/02/2012.

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