RREF of $$$\left[\begin{array}{ccc}-1 & 3 & 0\\2 & -1 & 1\\0 & 2 & 2\end{array}\right]$$$

Find the reduced row echelon form of $$$\left[\begin{array}{ccc}-1 & 3 & 0\\2 & -1 & 1\\0 & 2 & 2\end{array}\right]$$$.

Multiply row $$$1$$$ by $$$-1$$$: $$$R_{1} = - R_{1}$$$.

$$$\left[\begin{array}{ccc}1 & -3 & 0\\2 & -1 & 1\\0 & 2 & 2\end{array}\right]$$$

Subtract row $$$1$$$ multiplied by $$$2$$$ from row $$$2$$$: $$$R_{2} = R_{2} - 2 R_{1}$$$.

$$$\left[\begin{array}{ccc}1 & -3 & 0\\0 & 5 & 1\\0 & 2 & 2\end{array}\right]$$$

Divide row $$$2$$$ by $$$5$$$: $$$R_{2} = \frac{R_{2}}{5}$$$.

$$$\left[\begin{array}{ccc}1 & -3 & 0\\0 & 1 & \frac{1}{5}\\0 & 2 & 2\end{array}\right]$$$

Add row $$$2$$$ multiplied by $$$3$$$ to row $$$1$$$: $$$R_{1} = R_{1} + 3 R_{2}$$$.

$$$\left[\begin{array}{ccc}1 & 0 & \frac{3}{5}\\0 & 1 & \frac{1}{5}\\0 & 2 & 2\end{array}\right]$$$

Subtract row $$$2$$$ multiplied by $$$2$$$ from row $$$3$$$: $$$R_{3} = R_{3} - 2 R_{2}$$$.

$$$\left[\begin{array}{ccc}1 & 0 & \frac{3}{5}\\0 & 1 & \frac{1}{5}\\0 & 0 & \frac{8}{5}\end{array}\right]$$$

Multiply row $$$3$$$ by $$$\frac{5}{8}$$$: $$$R_{3} = \frac{5 R_{3}}{8}$$$.

$$$\left[\begin{array}{ccc}1 & 0 & \frac{3}{5}\\0 & 1 & \frac{1}{5}\\0 & 0 & 1\end{array}\right]$$$

Subtract row $$$3$$$ multiplied by $$$\frac{3}{5}$$$ from row $$$1$$$: $$$R_{1} = R_{1} - \frac{3 R_{3}}{5}$$$.

$$$\left[\begin{array}{ccc}1 & 0 & 0\\0 & 1 & \frac{1}{5}\\0 & 0 & 1\end{array}\right]$$$

Subtract row $$$3$$$ multiplied by $$$\frac{1}{5}$$$ from row $$$2$$$: $$$R_{2} = R_{2} - \frac{R_{3}}{5}$$$.

$$$\left[\begin{array}{ccc}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{array}\right]$$$

The reduced row echelon form is $$$\left[\begin{array}{ccc}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{array}\right]$$$A.