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1. Show the function T : R² → R³ given by T(x – y, 3x + 2y, 0) is linear.

1. Show the function T : R² → R³ given by T(x – y, 3x + 2y, 0) is linear.

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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1. Show the function \( T : \mathbb{R}^2 \rightarrow \mathbb{R}^3 \) given by \( T(x - y, 3x + 2y, 0) \) is linear. 2. Find the matrix \( A \) of \( T \) so that \( T \left( \begin{bmatrix} x \\ y \end{bmatrix} \right) = A \begin{bmatrix} x \\ y \end{bmatrix} \).
Transcribed Image Text:1. Show the function \( T : \mathbb{R}^2 \rightarrow \mathbb{R}^3 \) given by \( T(x - y, 3x + 2y, 0) \) is linear. 2. Find the matrix \( A \) of \( T \) so that \( T \left( \begin{bmatrix} x \\ y \end{bmatrix} \right) = A \begin{bmatrix} x \\ y \end{bmatrix} \).
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