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: 14

Answer

(a) $C_{23}=32$. (b) $C_{32}=13$.

Work Step by Step

Given $$ A=\left[\begin{array}{rrr}{4} & {11} & {-9} \\ {0} & {3} & {2}\\ {-3} & {1} & {1}\end{array}\right], \quad \text { and } \quad B=\left[\begin{array}{rrr}{1} & {0} & {5} \\ {-4} & {6} & {11}\\ {-6} & {4} & {9} \end{array}\right]. $$ We have \begin{align*} C=5A+2B&=5\left[\begin{array}{rrr}{4} & {11} & {-9} \\ {0} & {3} & {2}\\ {-3} & {1} & {1}\end{array}\right]+2\left[\begin{array}{rrr}{1} & {0} & {5} \\ {-4} & {6} & {11}\\ {-6} & {4} & {9} \end{array}\right]\\ &=\left[\begin{array}{rrr}{20} & {55} & {-45} \\ {0} & {15} & {10}\\ {-15} & {5} & {5}\end{array}\right]+\left[\begin{array}{rrr}{2} & {0} & {10} \\ {-8} & {12} & {22}\\ {-12} & {8} & {18} \end{array}\right]\\ &=\left[\begin{array}{rrr}{22} & {55} & {-55} \\ {-8} & {27} & {32}\\ {-27} & {13} & {23} \end{array}\right]. \end{align*} (a) $C_{23}=32$. (b) $C_{32}=13$.
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