-2] -4 2 Given: A = 2 -7 4 -7 has eigenvalues –3 and –12. -2 4 a) Explain why we know that A is orthogonally diagonalisable.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 65E
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a
-4
2
-27
Given: A =
2
-7
4
has eigenvalues -3 and – 12.
-7
-2
4
a) Explain why we know that A is orthogonally diagonalisable.
b) Find an orthogonal matrix P and a diagonal matrix D such that D = P" AP. Show all
calculations.
Transcribed Image Text:-4 2 -27 Given: A = 2 -7 4 has eigenvalues -3 and – 12. -7 -2 4 a) Explain why we know that A is orthogonally diagonalisable. b) Find an orthogonal matrix P and a diagonal matrix D such that D = P" AP. Show all calculations.
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