Elementary Linear Algebra 7th Edition

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

Chapter 1 - Systems of Linear Equations - Review Exercises - Page 35: 34


$$x=-\frac{3}{4}, \quad y=0 , \quad z=-\frac{5}{4}.$$

Work Step by Step

The augmented matrix is given by $$ \left[ \begin {array}{cccc} 2&0&6&-9\\ 3&-2&11&-16 \\ 3&-1&7&-11\end {array} \right] . $$ Using Gauss-Jordan elimination, we get the row-reduced echelon form as follows $$\left[ \begin {array}{cccc} 1&0&0&-\frac{3}{4}\\ 0&1&0&0 \\ 0&0&1&-\frac{5}{4}\end {array} \right] .$$ From which the solution is $$x=-\frac{3}{4}, \quad y=0 , \quad z=-\frac{5}{4}.$$
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