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

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

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