Answer
$\begin{bmatrix}1&-3&4&|&3\\0&4&-6&|&-3\\0&-12&24&|&21\end{bmatrix}$
Work Step by Step
We are given the augmented matrix:
$\begin{bmatrix}1&-3&4&|&3\\3&-5&6&|&6\\-5&3&4&|&6\end{bmatrix}$
Write the system of equations corresponding to the given augmented matrix:
$\begin{cases}
x-3y+4z=3\\
3x-5y+6z=6\\
-5x+3x+4z=6
\end{cases}$
Perform the row operation:
$R_2=-3r_1+r_2$
$\begin{bmatrix}1&-3&4&|&3\\-3(1)+3&-3(-3)-5&-3(4)+6&|&-3(3)+6\\-5&3&4&|&6\end{bmatrix}$
$=\begin{bmatrix}1&-3&4&|&3\\0&4&-6&|&-3\\-5&3&4&|&6\end{bmatrix}$
$R_3=5r_1+r_3$
$\begin{bmatrix}1&-3&4&|&3\\0&4&-6&|&-3\\5(1)-5&5(-3)+3&5(4)+4&|&5(3)+6\end{bmatrix}$
$=\begin{bmatrix}1&-3&4&|&3\\0&4&-6&|&-3\\0&-12&24&|&21\end{bmatrix}$
