Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 4 - Section 4.2 - Matrix Multiplication - Exercises - Page 252: 26

Answer

$\left[\begin{array}{c} {-16}\\ {7}\\ {-4}\\ {7}\end{array}\right]$

Work Step by Step

If $A$ is an $m\times\boxed{n }$ matrix and $B$ is an $\boxed{n }\times k$ matrix, then the product $AB$ is the $m\times k$ matrix whose $ij-$th entry is the product $(AB)_{ij}=[a_{i1}\ a_{i2}\ a_{i3}\ \ldots\ a_{in}]\left[\begin{array}{l} b_{1j}\\ b_{2j}\\ b_{3j}\\ \vdots\\ b_{nj} \end{array}\right]$ $=a_{i1}b_{1j}+a_{i2}b_{2j}+a_{i3}b_{3j}+\cdots+a_{in}b_{nj}$. ------- Here, A is a $4\times 4$ matrix, B is a $4\times 1$ matrix AB is defined, and is a $4\times 1$ matrix. $AB=\left[\begin{array}{c} {1 \cdot 1+1 \cdot(-3)+(-7) \cdot 2+0 \cdot 1}\\ {(-1)\cdot 1+0\cdot(-3)+2\cdot 2+4\cdot 1}\\ {(-1)\cdot 1+0\cdot(-3)+(-2)\cdot 2+1\cdot 1}\\ {1\cdot 1+(-1)(-3)+1\cdot 2+1\cdot 1}\end{array}\right]=$$\left[\begin{array}{c} {-16}\\ {7}\\ {-4}\\ {7}\end{array}\right]$
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.