# 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 calculators: Reduced Row Echelon Form (RREF) Calculator, Matrix Inverse Calculator

## Your Input

**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 $$$1$$$: $$$R_{1} = R_{1} - 3 R_{2}$$$.

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

## Answer

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