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Expert-verified Found in: Page 107 ### Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974 # The function ${\mathbit{T}}\left[\begin{array}{c}x\\ y\end{array}\right]{\mathbf{=}}\left[\begin{array}{c}x-y\\ y-x\end{array}\right]$is a linear transformation?

The given statement is true.

See the step by step solution

## Step 1: Definition of linear Transformation

Therefore, from Definition- A function T from ${R}^{m}$ to ${R}^{n}$is called a linear transformation if there exists an$n×m$ matrix A such that $T\left(\stackrel{\to }{x}\right)=A\stackrel{\to }{x}$ for all x in the vector space ${R}^{m}$ .

## Step 2: Check for the given statement

Notice that the given function can be representing as follows:

$T\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{cc}1& -1\\ -1& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]$

Hence, T is a linear transformation. ### Want to see more solutions like these? 