Reduced Row Echelon Form (RREF) Caclulator

The calculator will find the row echelon form (simple or reduced – RREF) of the given (augmented) matrix (with variables if needed), with steps shown.

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Your Input

Find the reduced row echelon form of $$$\left[\begin{array}{ccc}1 & 5 & 1\\2 & 11 & 5\end{array}\right]$$$.

Solution

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

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

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

$$$\left[\begin{array}{ccc}1 & 0 & -14\\0 & 1 & 3\end{array}\right]$$$

Answer

The reduced row echelon form is $$$\left[\begin{array}{ccc}1 & 0 & -14\\0 & 1 & 3\end{array}\right]$$$A.