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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Question 8** (8 pts)
Consider the mapping \( T: \mathbb{R}^2 \longrightarrow \mathbb{R}^3 \) defined by
\[
T \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} x_1 + x_2 \\ x_1 - x_2 \\ x_1 - 5 \end{bmatrix} \quad \text{(4 pts each)}
\]
a. Find \( T \begin{bmatrix} 5 \\ 1 \end{bmatrix} \).
b. Show that \( T \) is not a linear transformation. Justify.](https://content.bartleby.com/qna-images/question/7803273c-2063-4cef-bfbb-565e22329fee/639e14fd-e516-454e-bedf-f332bb70bf5d/v3vuo1p_thumbnail.png)
Transcribed Image Text:**Question 8** (8 pts)
Consider the mapping \( T: \mathbb{R}^2 \longrightarrow \mathbb{R}^3 \) defined by
\[
T \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} x_1 + x_2 \\ x_1 - x_2 \\ x_1 - 5 \end{bmatrix} \quad \text{(4 pts each)}
\]
a. Find \( T \begin{bmatrix} 5 \\ 1 \end{bmatrix} \).
b. Show that \( T \) is not a linear transformation. Justify.
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