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: 34

Answer

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.