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: 37


$x_1=1, \quad x_2=4 , \quad x_3=-3, \quad x_4=-2.$$

Work Step by Step

The augmented matrix is given by $$ \left[ \begin {array}{ccccc} 2&1&1&2&-1\\ 5&-2&1&-3 &0\\ -1&3&2&2&1\\ 3&2&3&-5&12 \end {array} \right] . $$ Using Gauss-Jordan elimination, we get the row-reduced echelon form as follows $$\left[ \begin {array}{ccccc} 1&0&0&0&1\\ 0&1&0&0&4 \\ 0&0&1&0&-3\\ 0&0&0&1&-2 \end {array} \right] .$$ From which we get the solution $$x_1=1, \quad x_2=4 , \quad x_3=-3, \quad x_4=-2.$$
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