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 24: 54

Answer

the reduced echelon form is $$\left[ \begin {array}{ccc} 1&0 &-1\\ 0&1&2 \\ 0&0&0\end {array} \right]. $$

Work Step by Step

Given the matrix $$\left[ \begin {array}{ccc} 1&2&3\\ 4&5&6 \\ 7&8&9\end {array} \right] $$ Multiply the first row by $-4$ and adding it to the second row, we get $$\left[ \begin {array}{ccc} 1&2&3\\ 0&-3&-6 \\ 0&-6&-12\end {array} \right] $$ Multiply the second row by $-2$ and adding it to the third row, we have $$\left[ \begin {array}{ccc} 1&2&3\\ 0&-3&-6 \\ 0&0&0\end {array} \right] $$ Multiply the second row by $-\frac{1}{3}$, we have $$\left[ \begin {array}{ccc} 1&2&3\\ 0&1&2 \\ 0&0&0\end {array} \right] $$ Multiply the second row by $-2$ and adding it to the first row, we get the reduced echelon form $$\left[ \begin {array}{ccc} 1&0&-1\\ 0&1&2 \\ 0&0&0\end {array} \right]. $$
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