Hw4Attachment

Hw4Attachment - are   -1 1    ,  ...

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Question 2 (a) Prove that A and A T have the same eigenvalues. What, if anything, can we say about the associated eigenvectors of A and A T . (b) Let A = 2 2 3 4 0 2 3 2 0 0 1 1 0 0 0 1 . (1) Find a basis for the eigenspace associated with the eigenvalue λ 1 = 1. (2) Find a basis for the eigenspace associated with the eigenvalue λ 2 = 2. (c) Let A be a 3 × 3 matrix whose eigenvalues are - 3 , 4 and 4, and the associated eigenvectors
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Unformatted text preview: are   -1 1    ,    1    , and    1 1    . Without computation, find a diagonal matrix D that is similar to A , and a nonsingular matrix P such that P-1 AP = D . • (d) Diagonalize the given matrix A =   -1 2 2 2-1 2 2 2-1    and find an orthogonal matrix P such that P-1 AP is diagonal. 1...
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This note was uploaded on 11/13/2010 for the course SEEM SEEM2018 taught by Professor Chan during the Spring '10 term at CUHK.

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