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: 36


$$x=2-3t, \quad y=6+5t , \quad z=t.$$

Work Step by Step

The augmented matrix is given by $$ \left[ \begin {array}{cccc} 2&5&-19&34\\ 3&8&-31&54 \end {array} \right] . $$ Using Gauss-Jordan elimination, we get the row-reduced echelon form as follows $$\left[ \begin {array}{cccc} 1&0&3&2\\ 0&1&-5&6 \end {array} \right] .$$ Putting, $z=t$ and by the back substitution we get the solution $$x=2-3t, \quad y=6+5t , \quad z=t.$$
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