Gauss - Jordan Elimination:

The system of linear equations are .

The system of linear equations can be written as the form of augmented matrix or [A : B], where A is coefficient matrix and B is constant matrix.

.

are represent the first row, second row and third row respectively.

The first column has already leading 1 in upper left corner.

Perform the operations on so first column has zeros below its leading 1.

Now the matrix is in reduced row-echelon form, and converting back to a system of linear equations is .

The resultant equations 2 and 3 have no variables. The statement is true, so the system of equations has infinitely many solutions.