$\"\"$

\

Guass-jordan elimination method :

\

The system of equations are

\

$\"\"$

\

Write the equations into matrix form $\"\"$ .

\

Where $\"\"$ is coefficient matrix, $\"\"$ is variable matrix and $\"\"$ is constant matrix.

\

Solve the equations in Gauss-Jordan method.

\

$\"\"$

\

The augmented matrix is $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

The augmented matrix is $\"\"$ .

\

Apply elementary row operations to obtain a reduce the row-echelon form.

\

Here $\"\"$ are represents first row, second row and third row .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Write the corresponding system of the linear equations for the reduced row-echelon form of the augmented matrix is

\

$\"\"$ .

\

The matrix equation is $\"\"$ .

\

$\"\"$

\

The matrix equation is $\"\"$ .