Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 9 - Systems and Matrices - 9.7 Properties of Matrices - 9.7 Exercises - Page 930: 68

Answer

$\begin{bmatrix} -2 & 5 & 0 \\ 6 & 6 & 5 \\ 12 & 2 & 5 \end{bmatrix} $

Work Step by Step

Consider $A=\begin{bmatrix} -1 & 2 & 0\\ 0&3&2\\0 &1&4 \end{bmatrix} $ and $B=\begin{bmatrix} 2 & -1 & 2 \\ 0 & 2 & 1\\ 3& 0& -1\end{bmatrix} $ Since, the dimensions of both matrix $A$ and $B$ is $3 \times 3$ .This follows that the number of columns of matrix-$A$ will be same as the number of rows of the matrix-$B$ and so, we can take their product $AB$. $AB=\begin{bmatrix} -1 & 2 & 0\\ 0&3&2\\0 &1&4 \end{bmatrix} \begin{bmatrix} 2 & -1 & 2 \\ 0 & 2 & 1\\ 3& 0& -1\end{bmatrix}\\=\begin{bmatrix} -2&1+4& -2+2+0 \\ 0+0+6 & 0+6+0 &0+3+2\\0+0+12&0+2+0&0+1+4 \end{bmatrix}$ $ \\ =\begin{bmatrix} -2 & 5 & 0 \\ 6 & 6 & 5 \\ 12 & 2 & 5 \end{bmatrix} $
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.