Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
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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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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