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: 36

Answer

The required matrix is, $ AB=\left[ \begin{array}{*{35}{r}} 0 & 4 & 4 \\ 0 & 0 & -4 \\ \end{array} \right]$, horizontal stretch by a factor of 2.

Work Step by Step

The original 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}} 2 & 0 \\ 0 & 1 \\ \end{array} \right]$ Consider the given matrices to find $\begin{align} & AB=\left[ \begin{array}{*{35}{r}} 2 & 0 \\ 0 & 1 \\ \end{array} \right]\left[ \begin{array}{*{35}{r}} 0 & 2 & 2 \\ 0 & 0 & -4 \\ \end{array} \right] \\ & =\left[ \begin{array}{*{35}{r}} 0 & 4 & 4 \\ 0 & 0 & -4 \\ \end{array} \right] \end{align}$ That is, the transformed graph is a triangle with vertices $\left( 0,0 \right),\left( 4,0 \right),\left( 4,-4 \right)$ Thus, the matrix $ AB=\left[ \begin{array}{*{35}{r}} 0 & 4 & 4 \\ 0 & 0 & -4 \\ \end{array} \right]$ and the transformed triangle will be horizontally stretched by a factor of 2.
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