Short Answer

The function $T [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} x - y \\ y - x \end{matrix}]$ is a linear transformation?

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Step by Step Solution

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TABLE OF CONTENTS

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 $n \times m$ matrix A such that $T (\vec{x}) = A \vec{x}$ 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:

$T [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 1 & - 1 \\ - 1 & 1 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}]$

Hence, T is a linear transformation.

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Linear Algebra With Applications

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Short Answer

The function $T [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} x - y \\ y - x \end{matrix}]$ is a linear transformation?

Step by Step Solution

Step 1: Definition of linear Transformation

Step 2: Check for the given statement

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Linear Algebra With Applications

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The function T[xy]=[x-yy-x]is a linear transformation?

Step by Step Solution

Step 1: Definition of linear Transformation

Step 2: Check for the given statement

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The function $T [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} x - y \\ y - x \end{matrix}]$ is a linear transformation?