Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 2 - Matrices - 2.1 Operations with Matrices - 2.1 Exercises - Page 49: 30

Answer

(a) $AB$ not defined. (b)\begin{align*} BA&=\left[ \begin {array}{ccccc} 37&78&51&-104&124\\ 16& 26&28&-42&56\end {array} \right] . \end{align*}

Work Step by Step

Given $$ A=\left[\begin{array}{ccccc}{1} & {0} & {3} & {-2} & {4} \\ {6} & {13} & {8} & {-17} & {20}\end{array}\right], \quad B=\left[\begin{array}{ll}{1} & {6} \\ {4} & {2}\end{array}\right]. $$ We have (a) $AB$ not defined. (b)\begin{align*} BA&=\left[\begin{array}{ll}{1} & {6} \\ {4} & {2}\end{array}\right]\left[\begin{array}{ccccc}{1} & {0} & {3} & {-2} & {4} \\ {6} & {13} & {8} & {-17} & {20}\end{array}\right] \\ &=\left[ \begin {array}{ccccc} 37&78&51&-104&124\\ 16& 26&28&-42&56\end {array} \right] . \end{align*}
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