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 λ = 3. Solution: A − 3I = 00 . 2 −2 0 0 |0 2 −2 | 0 ∼ 1 −1 | 0 0 0 |0 So we have x2 is a free variable and Nul(A − 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: 8−λ 2 3 3−λ (8 − λ)(3 − λ) − 6 24 − 11λ + λ2 − 6 λ2 − 11λ + 18 (λ − 9)(λ − 2) det(A − λI ) = det = = = = So the real eigenvalues are λ = 2 and λ = 9. ...
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This document was uploaded on 04/02/2012.

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