# Chapter 8 - Review Exercises - Page 950: 34

The required matrix, $AB=\left[ \begin{array}{*{35}{r}} 0 & -2 & -2 \\ 0 & 0 & -4 \\ \end{array} \right]$; reflection about the y-axis.

#### Work Step by Step

The matrix representing the matrix 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 the reflection about the y-axis. The matrix $AB=\left[ \begin{array}{*{35}{r}} 0 & -2 & -2 \\ 0 & 0 & -4 \\ \end{array} \right]$ and the transformed triangle will be the reflection about the y-axis.

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