5) Let T : R2 → R² be the linear operator given by the formula T(< x,y >) =< x + ky, –y > Show for any value of k that T is one-to-one and that T is its own inverse.
5) Let T : R2 → R² be the linear operator given by the formula T(< x,y >) =< x + ky, –y > Show for any value of k that T is one-to-one and that T is its own inverse.
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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![### Problem 5
Let \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) be the linear operator given by the formula
\[ T(<x, y>) = <x + ky, -y> \]
Show for **any** value of \( k \) that \( T \) is one-to-one and that \( T \) is its own inverse.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcecab317-fab7-42bc-8c65-e82787a88e59%2Fd92e654a-8eb8-4f76-936b-3dfc6f6caf07%2Fc7xub4_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 5
Let \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) be the linear operator given by the formula
\[ T(<x, y>) = <x + ky, -y> \]
Show for **any** value of \( k \) that \( T \) is one-to-one and that \( T \) is its own inverse.
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