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 - Review Exercises - Page 98: 19

Answer

$$x=1,\quad y=-5.$$

Work Step by Step

We have the system $$\left[\begin{array}{rrr}{5} & {4} \\{-1}& {1} \end{array}\right]\left[\begin{array}{rrr}{x}\\ {y} \end{array}\right]=\left[\begin{array}{rrr}{-15} \\ {-6} \end{array}\right].$$ The coefficients matrix $A=\left[\begin{array}{rrr}{5} & {4} \\{-1}& {1} \end{array}\right]$ has the inverse $$A^{-1}=\left[ \begin {array}{cc} \frac{1}{9}&-\frac{4}{9}\\ \frac{1}{9}&\frac{5}{9} \end {array} \right]. $$ The system has the solution $$\left[\begin{array}{rrr}{x}\\ {y} \end{array}\right]=\left[ \begin {array}{cc} \frac{1}{9}&-\frac{4}{9}\\ \frac{1}{9}&\frac{5}{9} \end {array} \right]\left[\begin{array}{rrr}{-15} \\ {-6} \end{array}\right]=\left[ \begin {array}{c} 1\\ -5\end {array} \right] .$$ That is $$x=1,\quad y=-5.$$
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