Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.8 Exercises - Page 69: 16

Answer

Vectors are reflected across the line y=x. $T(u)=\begin{bmatrix} 2\\ 5\\ \end{bmatrix}$ $T(v)=\begin{bmatrix} 4\\ -2\\ \end{bmatrix}$

Work Step by Step

$T(u)=\begin{bmatrix} 0 & 1\\ 1 & 0\\ \end{bmatrix}\begin{bmatrix} 5\\ 2\\ \end{bmatrix}=\begin{bmatrix} 2\\ 5\\ \end{bmatrix}$ $T(v)=\begin{bmatrix} 0 & 1\\ 1 & 0\\ \end{bmatrix}\begin{bmatrix} -2\\ 4\\ \end{bmatrix}=\begin{bmatrix} 4\\ -2\\ \end{bmatrix}$ Vectors are graphed using Geogebra
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