# Reduced Row Echelon Form (RREF) Calculator

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

Related calculators: Gauss-Jordan Elimination Calculator, Matrix Inverse Calculator

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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 $1$: $R_{1} = R_{1} - 5 R_{2}$.

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

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