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(b) State the eigenvalues of ATA and find the eigenspace associated with each eigenvalue. Hence determine if AT A is diagonalisable.

(b) State the eigenvalues of ATA and find the eigenspace associated with each eigenvalue. Hence determine if AT A is diagonalisable.

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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part b)

 

For parts (a) to (c) of this question, we consider the 2 x 3 matrix A = (619) (a) Compute AT A and show that its characteristic polynomial can be factored as: XATA(X) = X(X - 1)(A-3) (b) State the eigenvalues of ATA and find the eigenspace associated with each eigenvalue. Hence determine if AT A is diagonalisable.
Transcribed Image Text:For parts (a) to (c) of this question, we consider the 2 x 3 matrix A = (619) (a) Compute AT A and show that its characteristic polynomial can be factored as: XATA(X) = X(X - 1)(A-3) (b) State the eigenvalues of ATA and find the eigenspace associated with each eigenvalue. Hence determine if AT A is diagonalisable.
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