Problem 11.3 Let -4 2 A = -4 1 -2 2 -2 -2 Find the eigenvalues of A and for each eigenvalue find an orthonormal basis for the corresponding eigenspace. Hence find an orthogonal matrix P such that p™ AP = P¯'AP = D.

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Chapter2: Second-order Linear Odes
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Problem 11.3 Let
-4
A =
-4 1
-2
2
-2 -2,
Find the eigenvalues of A and for each eigenvalue find an orthonormal
basis for the corresponding eigenspace.
Hence find an orthogonal matrix P such that
p™ AP = P¯'AP = D.
Write down D and check that PTAP = D.
Transcribed Image Text:Problem 11.3 Let -4 A = -4 1 -2 2 -2 -2, Find the eigenvalues of A and for each eigenvalue find an orthonormal basis for the corresponding eigenspace. Hence find an orthogonal matrix P such that p™ AP = P¯'AP = D. Write down D and check that PTAP = D.
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