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 48: 13

Answer

(a) $C_{21}=-6$. (b) $C_{13}=29$.

Work Step by Step

Given $$ A=\left[\begin{array}{rrr}{5} & {4} & {4} \\ {-3} & {1} & {2}\end{array}\right], \quad \text { and } \quad B=\left[\begin{array}{rrr}{1} & {2} & {-7} \\ {0} & {-5} & {1}\end{array}\right]. $$ We have \begin{align*} C=2A-3B&=2\left[\begin{array}{rrr}{5} & {4} & {4} \\ {-3} & {1} & {2}\end{array}\right]-3\left[\begin{array}{rrr}{1} & {2} & {-7} \\ {0} & {-5} & {1}\end{array}\right]\\ &=\left[\begin{array}{rrr}{10} & {8} & {8} \\ {-6} & {2} & {4}\end{array}\right]-\left[\begin{array}{rrr}{3} & {6} & {-21} \\ {0} & {-15} & {3}\end{array}\right]\\ &=\left[\begin{array}{rrr}{7} & {2} & {29} \\ {-6} & {17} & {1} \end{array}\right]. \end{align*} Then, (a) $C_{21}=-6$. (b) $C_{13}=29$.
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