# Gauss-Jordan Elimination Calculator

The calculator will perform the Gaussian elimination on the given augmented matrix, with steps shown. Complete reduction is available optionally.

Related calculator: Inverse of Matrix Calculator

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Perform the Gauss-Jordan elimination (reduce completely) of $\left[\begin{array}{cc|c}1 & 3 & 14\\7 & -1 & 10\end{array}\right]$.

## Solution

Subtract row $1$ multiplied by $7$ from row $2$: $R_{2} = R_{2} - 7 R_{1}$.

$\left[\begin{array}{cc|c}1 & 3 & 14\\0 & -22 & -88\end{array}\right]$

Divide row $2$ by $-22$: $R_{2} = - \frac{R_{2}}{22}$.

$\left[\begin{array}{cc|c}1 & 3 & 14\\0 & 1 & 4\end{array}\right]$

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

$\left[\begin{array}{cc|c}1 & 0 & 2\\0 & 1 & 4\end{array}\right]$

The reduced matrix is $\left[\begin{array}{cc|c}1 & 0 & 2\\0 & 1 & 4\end{array}\right]$A.