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: 35

Answer

The required matrix is, $ AB=\left[ \begin{array}{*{35}{r}} 0 & 0 & 4 \\ 0 & 2 & 2 \\ \end{array} \right]$, 90° counterclockwise rotation about the origin.

Work Step by Step

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}} 0 & -1 \\ 1 & 0 \\ \end{array} \right]$ Consider the given matrices, $\begin{align} & AB=\left[ \begin{array}{*{35}{r}} 0 & -1 \\ 1 & 0 \\ \end{array} \right]\left[ \begin{array}{*{35}{r}} 0 & 2 & 2 \\ 0 & 0 & -4 \\ \end{array} \right] \\ & =\left[ \begin{array}{*{35}{r}} 0 & 0 & 4 \\ 0 & 2 & 2 \\ \end{array} \right] \end{align}$ That is, the transformed graph is a triangle with vertices $\left( 0,0 \right),\left( 0,2 \right),\left( 4,2 \right)$ Therefore, the transformed triangle will be based on a 90° counterclockwise rotation about the origin. The matrix $ AB=\left[ \begin{array}{*{35}{r}} 0 & 0 & 4 \\ 0 & 2 & 2 \\ \end{array} \right]$ and the transformed triangle will be based on a 90° counterclockwise rotation about the origin.
Small 1570430283
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.