Precalculus (6th Edition) Blitzer

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

Chapter 11 - Cumulative Review Exercises - Page 1181: 25

Answer

The product of matrix B and matrix A is $\left[ \begin{matrix} 2 & 1 & 3 \\ 8 & 1 & 9 \\ 5 & 1 & 6 \\ \end{matrix} \right]$.

Work Step by Step

Considered the matrices, $A=\left[ \begin{matrix} 2 & 1 & 3 \\ 1 & -1 & 0 \\ \end{matrix} \right]$ And $B=\left[ \begin{matrix} 1 & 0 \\ 3 & 2 \\ 2 & 1 \\ \end{matrix} \right]$ Now, use the product rule of matrices, $\begin{align} & \text{BA}=\left[ \begin{matrix} 1 & 0 \\ 3 & 2 \\ 2 & 1 \\ \end{matrix} \right]\left[ \begin{matrix} 2 & 1 & 3 \\ 1 & -1 & 0 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 1\cdot 2+0\cdot 1 & 1\cdot 1+0\cdot -1 & 1\cdot 3+0\cdot 0 \\ 3\cdot 2+2\cdot 1 & 3\cdot 1+2\cdot -1 & 3\cdot 3+2\cdot 0 \\ 2\cdot 2+1\cdot 1 & 2\cdot 1+1\cdot -1 & 2\cdot 3+1\cdot 0 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 2 & 1 & 3 \\ 8 & 1 & 9 \\ 5 & 1 & 6 \\ \end{matrix} \right] \end{align}$ Hence, the product of matrix B and matrix A is $\left[ \begin{matrix} 2 & 1 & 3 \\ 8 & 1 & 9 \\ 5 & 1 & 6 \\ \end{matrix} \right]$.
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