Gauss-Jordan elimination on [[[-23/4,-5/4],[-5/2,-1/2]],[5,2]']

The calculator will perform the Gaussian elimination on the $$$2$$$x$$$3$$$ matrix $$$\left[\begin{array}{cc|c}- \frac{23}{4} & - \frac{5}{4} & 5\\- \frac{5}{2} & - \frac{1}{2} & 2\end{array}\right]$$$, with steps shown.

Size of the matrix:

$$$\times$$$

Matrix:

Reduce completely?

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Your Input

Perform the Gauss-Jordan elimination (reduce completely) on $$$\left[\begin{array}{cc|c}- \frac{23}{4} & - \frac{5}{4} & 5\\- \frac{5}{2} & - \frac{1}{2} & 2\end{array}\right]$$$.

Solution

Multiply row $$$1$$$ by $$$- \frac{4}{23}$$$: $$$R_{1} = - \frac{4 R_{1}}{23}$$$.

$$$\left[\begin{array}{cc|c}1 & \frac{5}{23} & - \frac{20}{23}\\- \frac{5}{2} & - \frac{1}{2} & 2\end{array}\right]$$$

Add row $$$1$$$ multiplied by $$$\frac{5}{2}$$$ to row $$$2$$$: $$$R_{2} = R_{2} + \frac{5 R_{1}}{2}$$$.

$$$\left[\begin{array}{cc|c}1 & \frac{5}{23} & - \frac{20}{23}\\0 & \frac{1}{23} & - \frac{4}{23}\end{array}\right]$$$

Multiply row $$$2$$$ by $$$23$$$: $$$R_{2} = 23 R_{2}$$$.

$$$\left[\begin{array}{cc|c}1 & \frac{5}{23} & - \frac{20}{23}\\0 & 1 & -4\end{array}\right]$$$

Subtract row $$$2$$$ multiplied by $$$\frac{5}{23}$$$ from row $$$1$$$: $$$R_{1} = R_{1} - \frac{5 R_{2}}{23}$$$.

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

Answer

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

Gauss-Jordan elimination on $$$\left[\begin{array}{cc|c}- \frac{23}{4} & - \frac{5}{4} & 5\\- \frac{5}{2} & - \frac{1}{2} & 2\end{array}\right]$$$

Your Input

Solution

Answer