Gauss-Jordan elimination on [[[1,1,1],[0,-1,1],[-1,0,0]],[4,0,-2]']

The calculator will perform the Gaussian elimination on the $$$3$$$x$$$4$$$ matrix $$$\left[\begin{array}{ccc|c}1 & 1 & 1 & 4\\0 & -1 & 1 & 0\\-1 & 0 & 0 & -2\end{array}\right]$$$, with steps shown.

Size of the matrix:

$$$\times$$$

Matrix:

Reduce completely?

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Your Input

Perform the Gauss-Jordan elimination on $$$\left[\begin{array}{ccc|c}1 & 1 & 1 & 4\\0 & -1 & 1 & 0\\-1 & 0 & 0 & -2\end{array}\right]$$$.

Solution

Add row $$$1$$$ to row $$$3$$$: $$$R_{3} = R_{3} + R_{1}$$$.

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

Add row $$$2$$$ to row $$$3$$$: $$$R_{3} = R_{3} + R_{2}$$$.

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

Answer

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