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-4 2 Given: A = 2 -7 4 has eigenvalues -3 and – 12. [-2 4 -7 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.

-4 2 Given: A = 2 -7 4 has eigenvalues -3 and – 12. [-2 4 -7 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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-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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