Gauss-Jordan elimination on [[[1,1,1],[4,2,1],[1,-1,1]],[4,9,6]']

The calculator will perform the Gaussian elimination on the $$$3$$$x$$$4$$$ matrix $$$\left[\begin{array}{ccc|c}1 & 1 & 1 & 4\\4 & 2 & 1 & 9\\1 & -1 & 1 & 6\end{array}\right]$$$, with steps shown.

Size of the matrix:

$$$\times$$$

Matrix:

Reduce completely?

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Your Input

Perform the Gauss-Jordan elimination on $$$\left[\begin{array}{ccc|c}1 & 1 & 1 & 4\\4 & 2 & 1 & 9\\1 & -1 & 1 & 6\end{array}\right]$$$.

Solution

Subtract row $$$1$$$ multiplied by $$$4$$$ from row $$$2$$$: $$$R_{2} = R_{2} - 4 R_{1}$$$.

$$$\left[\begin{array}{ccc|c}1 & 1 & 1 & 4\\0 & -2 & -3 & -7\\1 & -1 & 1 & 6\end{array}\right]$$$

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

$$$\left[\begin{array}{ccc|c}1 & 1 & 1 & 4\\0 & -2 & -3 & -7\\0 & -2 & 0 & 2\end{array}\right]$$$

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

$$$\left[\begin{array}{ccc|c}1 & 1 & 1 & 4\\0 & -2 & -3 & -7\\0 & 0 & 3 & 9\end{array}\right]$$$

Answer

The reduced matrix is $$$\left[\begin{array}{ccc|c}1 & 1 & 1 & 4\\0 & -2 & -3 & -7\\0 & 0 & 3 & 9\end{array}\right]$$$A.