# Chapter 8 - Section 8.3 - Matrix Operations and Their Applications - Exercise Set - Page 918: 49

$BZ=\left[ \begin{matrix} x \\ -y \\ \end{matrix} \right]$ and the $x$ coordinate is the same but the $y$ coordinate is changed by $-y$. Thus, its graphic reflection is about the $x-\text{axis}$.

#### Work Step by Step

Perform matrix multiplication in order to find $BZ$ as below. \begin{align} & BZ=\text{ }\left[ \begin{matrix} 1 & 0 \\ 0 & -1 \\ \end{matrix} \right]\text{ }\left[ \begin{matrix} x \\ y \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 1\cdot x+0\cdot y \\ 0\cdot x-1\cdot y \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} x \\ -y \\ \end{matrix} \right] \end{align} It can be observed that in $BZ$, the $x$ coordinate is the same but the $y$ coordinate is changed by $-y$. Thus, its graphic reflection is about the $x-\text{axis}$.

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