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: 7


$x_1=-4$ and $x_2=0$.

Work Step by Step

The system can written on the form $Ax=b$ as follows $$\left[ \begin {array}{cc} {2}& {1}\\{1}&{4} \end {array} \right]\left[ \begin {array}{cc} {x_1}\\ {x_2} \end {array} \right]=\left[ \begin {array}{cc} {-8}\\ {-4} \end {array} \right].$$ To solve system using Gaussian elimination, we form the augmented matrix as follows $$\left[ \begin {array}{ccc} 2&1&-8\\ 1&4&-4 \end {array} \right]. $$ The reduced row echelon form is given by $$\left[ \begin {array}{ccc} 1&0&-4\\ 0&1&0 \end {array} \right]. $$ From which, we have $x_1=-4$ and $x_2=0$.
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