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