Let T: R2 R² be such that cos 0 - sin 0 cos e sin 0 How that T is an orthogonal linear transformation.
Let T: R2 R² be such that cos 0 - sin 0 cos e sin 0 How that T is an orthogonal linear transformation.
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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![Let \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) be such that
\[
T \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}
\]
Show that \( T \) is an orthogonal linear transformation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb7f1ce8-2552-49b5-ba1d-534a58de11ae%2F7b2223d9-1a03-4c61-9dc3-0ceb9dea1a69%2F3jq8w1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) be such that
\[
T \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}
\]
Show that \( T \) is an orthogonal linear transformation.
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