Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 725: 64

Av = $\begin{bmatrix} -2\\ -4\\ \end{bmatrix}$ The transformation is a reflection across y = -x.

First rewrite the vector as a matrix: v = $\begin{bmatrix} 4\\ 2\\ \end{bmatrix}$ Then multiply the two matrices to find Av: Av = $\begin{bmatrix} 0(4) + (-1)(2)\\ (-1)(4) + 0(2)\\ \end{bmatrix}$ = $\begin{bmatrix} -2\\ -4\\ \end{bmatrix}$ The transformation is a reflection across y = -x.