## Elementary Linear Algebra 7th Edition

Published by Cengage Learning

# Chapter 1 - Systems of Linear Equations - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises: 31

#### Answer

$x=4$ $y=-3$ $z=2$

#### Work Step by Step

Write the augmented matrix of the system of linear equations. $\begin{bmatrix} 1 &0 & -3 & -2\\ 3 & 1 & -2 & 5\\ 2 & 2 &1 & 4 \end{bmatrix}$ Add -3 times the 1st row to the 2nd row to produce a new 2nd row. Add -2 times the 1st row to the 3rd row to produce a new 3rd row. $\begin{bmatrix} 1 &0 & -3 & -2\\ 0 & 1 & 7 & 11\\ 0 & 2 &7 &8 \end{bmatrix}$ Add -2 times the 2nd row to the 3rd row to produce a new 3rd row. $\begin{bmatrix} 1 &0 & -3 & -2\\ 0 & 1 & 7 & 11\\ 0 & 0 &-7 & -14 \end{bmatrix}$ Divide the third row by -7. $\begin{bmatrix} 1 &0 & -3 & -2\\ 0 & 1 & 7 & 11\\ 0 & 0 &1 & 2 \end{bmatrix}$ Use back-substitution to find the solution. $z=2$ $y+7z=11 \rightarrow y=-3$ $x-3z=-2 \rightarrow x=4$

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