Answered: Find a matrix P that orthogonally…

Find a matrix P that orthogonally diagonalizes A, and determine P-'AP. A = 1 4 P = P = 2 V3 V3 2 P = 3 2/2 3 P = 3 O p-'AP = 0 1 4 P-'AP = 0 -4 3 0 P-'AP = 0 5 O p--AP = 3 0 0 6 -1 0 P-'AP = 05 +/5

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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Question

100%

Find a matrix P that orthogonally diagonalizes A, and determine P-'AP.
A =
1 4
P =
P =
2
V3
V3
2
P =
3
2/2
3
P =
3
O
p-'AP =
0 1
4
P-'AP =
0 -4
3 0
P-'AP =
0 5
O p--AP =
3 0
0 6
-1 0
P-'AP =
05
+/5

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