## Precalculus (6th Edition) Blitzer

The matrix is, $AB=\left[ \begin{array}{*{35}{r}} 0 & 2 & 2 \\ 0 & 0 & 4 \\ \end{array} \right]$; reflection about the x-axis.
The matrix representing the triangle is $B=\left[ \begin{array}{*{35}{r}} 0 & 2 & 2 \\ 0 & 0 & -4 \\ \end{array} \right]$ The multiplication matrix is $A=\left[ \begin{array}{*{35}{r}} 1 & 0 \\ 0 & -1 \\ \end{array} \right]$ Consider the given matrices, \begin{align} & AB=\left[ \begin{array}{*{35}{r}} 1 & 0 \\ 0 & -1 \\ \end{array} \right]\left[ \begin{array}{*{35}{r}} 0 & 2 & 2 \\ 0 & 0 & -4 \\ \end{array} \right] \\ & =\left[ \begin{array}{*{35}{r}} 0 & 2 & 2 \\ 0 & 0 & 4 \\ \end{array} \right] \end{align} That is, the transformed graph is a triangle with vertices $\left( 0,0 \right),\left( 2,0 \right),\left( 2,4 \right)$ Therefore, the transformed triangle will be reflection about the x-axis. The required matrix is, $AB=\left[ \begin{array}{*{35}{r}} 0 & 2 & 2 \\ 0 & 0 & 4 \\ \end{array} \right]$ and the transformed triangle will be reflection about the x-axis.