Gauss-Jordan elimination on [[a,b]',[-1,1]']

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

Size of the matrix:

$$$\times$$$

Matrix:

A

Reduce completely?

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Your Input

Perform the Gauss-Jordan elimination (reduce completely) on $$$\left[\begin{array}{cc}a & -1\\b & 1\end{array}\right]$$$.

Solution

Divide row $$$1$$$ by $$$a$$$: $$$R_{1} = \frac{R_{1}}{a}$$$.

$$$\left[\begin{array}{c|c}1 & - \frac{1}{a}\\b & 1\end{array}\right]$$$

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

$$$\left[\begin{array}{c|c}1 & - \frac{1}{a}\\0 & \frac{a + b}{a}\end{array}\right]$$$

Answer

The reduced matrix is $$$\left[\begin{array}{cc}1 & - \frac{1}{a}\\0 & \frac{a + b}{a}\end{array}\right]$$$A.

Gauss-Jordan elimination on $$$\left[\begin{array}{c|c}a & -1\\b & 1\end{array}\right]$$$

Your Input

Solution

Answer