5. Prove that an orthogonal 2 × 2 matrix must have the form or -a. Note: From this, we can conclude that every 2×2 orthogonal matrix is of the form cos 0 sin -sin 0 cos
5. Prove that an orthogonal 2 × 2 matrix must have the form or -a. Note: From this, we can conclude that every 2×2 orthogonal matrix is of the form cos 0 sin -sin 0 cos
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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![5. Prove that an orthogonal 2 x 2 matrix must have the form
[a -b]
a
b]
or
cos 0 sin 0]
- sin 0 cos 0
Note: From this, we can conclude that every 2x2 orthogonal matrix is of the form](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66929a91-06e2-4d75-91bc-646df1edc40f%2F2f17c750-92b4-46dd-ae77-4633dcfa8cc4%2F0b5m7i_processed.png&w=3840&q=75)
Transcribed Image Text:5. Prove that an orthogonal 2 x 2 matrix must have the form
[a -b]
a
b]
or
cos 0 sin 0]
- sin 0 cos 0
Note: From this, we can conclude that every 2x2 orthogonal matrix is of the form
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