Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 8 - Review Exercises - Page 950: 33

Answer

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

Work Step by Step

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.
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