Precalculus (6th Edition) Blitzer

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

Chapter 8 - Section 8.3 - Matrix Operations and Their Applications - Exercise Set - Page 919: 60

Answer

a) $AB=\left[ \begin{matrix} 0 & 6 & 6 & 2 & 2 & 0 \\ 0 & 0 & 1 & 1 & 5 & 5 \\ \end{matrix} \right]$
1570416614

Work Step by Step

(a) $\begin{align} & AB=\left[ \begin{matrix} 2 & 0 \\ 0 & 1 \\ \end{matrix} \right]\left[ \begin{matrix} 0 & 3 & 3 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 5 & 5 \\ \end{matrix} \right] \\ & AB=\left[ \begin{matrix} 2\left( 0 \right)+\left( 0 \right)\left( 0 \right) & 2\left( 3 \right)+\left( 0 \right)\left( 0 \right) & 2\left( 3 \right)+\left( 0 \right)\left( 1 \right) & 2\left( 1 \right)+\left( 0 \right)\left( 1 \right) & 2\left( 1 \right)+\left( 0 \right)\left( 5 \right) & 2\left( 0 \right)+\left( 0 \right)\left( 5 \right) \\ 0\left( 0 \right)+1\left( 0 \right) & 0\left( 3 \right)+1\left( 0 \right) & 0\left( 3 \right)+1\left( 1 \right) & 0\left( 1 \right)+1\left( 1 \right) & 0\left( 1 \right)+1\left( 5 \right) & 0\left( 0 \right)+1\left( 5 \right) \\ \end{matrix} \right] \\ & AB=\left[ \begin{matrix} 0+0 & 6+0 & 6+0 & 2+0 & 2+0 & 0+0 \\ 0+0 & 0+0 & 0+1 & 0+1 & 0+5 & 0+5 \\ \end{matrix} \right] \\ & AB=\left[ \begin{matrix} 0 & 6 & 6 & 2 & 2 & 0 \\ 0 & 0 & 1 & 1 & 5 & 5 \\ \end{matrix} \right] \\ \end{align}$ (b) The graph for matrix A and AB is drawn as shown above. From the graph, it can be inferred that the shape of letter “L” has been changed because of matrix multiplication. The length and width of the letter “L” has increased.
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