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 - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises - Page 23: 36


The system is inconsistent and has no solutions.

Work Step by Step

The augmented matrix is given by $$\left[ \begin {array}{cccc} 1&2&1&8\\ -3&-6&-3&-21 \end {array} \right] . $$ Multiply the first row by $3$ and adding it the second row , we get $$\left[ \begin {array}{ccccc} 1&2&1&8\\ 0&0&0&3\end {array} \right]. $$ Now, the crossposting system is given by $$ \begin{array}{l} x+2y+z&=8 \\ 0 z&=3. \end{array} $$ The above system is inconsistent and has no solutions.
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