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RREF of $$$\left[\begin{array}{ccc}3 & -4 & 2\\1 & 6 & 8\\2 & 7 & 9\end{array}\right]$$$

The calculator will find the reduced row echelon form of the $$$3$$$x$$$3$$$ matrix $$$\left[\begin{array}{ccc}3 & -4 & 2\\1 & 6 & 8\\2 & 7 & 9\end{array}\right]$$$, with steps shown.

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Your Input

Find the reduced row echelon form of $$$\left[\begin{array}{ccc}3 & -4 & 2\\1 & 6 & 8\\2 & 7 & 9\end{array}\right]$$$.

Solution

Divide row $$$1$$$ by $$$3$$$: $$$R_{1} = \frac{R_{1}}{3}$$$.

$$$\left[\begin{array}{ccc}1 & - \frac{4}{3} & \frac{2}{3}\\1 & 6 & 8\\2 & 7 & 9\end{array}\right]$$$

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

$$$\left[\begin{array}{ccc}1 & - \frac{4}{3} & \frac{2}{3}\\0 & \frac{22}{3} & \frac{22}{3}\\2 & 7 & 9\end{array}\right]$$$

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

$$$\left[\begin{array}{ccc}1 & - \frac{4}{3} & \frac{2}{3}\\0 & \frac{22}{3} & \frac{22}{3}\\0 & \frac{29}{3} & \frac{23}{3}\end{array}\right]$$$

Multiply row $$$2$$$ by $$$\frac{3}{22}$$$: $$$R_{2} = \frac{3 R_{2}}{22}$$$.

$$$\left[\begin{array}{ccc}1 & - \frac{4}{3} & \frac{2}{3}\\0 & 1 & 1\\0 & \frac{29}{3} & \frac{23}{3}\end{array}\right]$$$

Add row $$$2$$$ multiplied by $$$\frac{4}{3}$$$ to row $$$1$$$: $$$R_{1} = R_{1} + \frac{4 R_{2}}{3}$$$.

$$$\left[\begin{array}{ccc}1 & 0 & 2\\0 & 1 & 1\\0 & \frac{29}{3} & \frac{23}{3}\end{array}\right]$$$

Subtract row $$$2$$$ multiplied by $$$\frac{29}{3}$$$ from row $$$3$$$: $$$R_{3} = R_{3} - \frac{29 R_{2}}{3}$$$.

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

Divide row $$$3$$$ by $$$-2$$$: $$$R_{3} = - \frac{R_{3}}{2}$$$.

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

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

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

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

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

Answer

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