Gauss-Jordan Reduction in Matrix Form

The Gauss-Jordan algorithm reduces a nonsingular matrix A to the identity matrix I by the following series of matrix multiplications  

The matrix operation of Eq. (2.133), when applied to the augmented matrix [A I c], yields the unique solution 

3 Gauss-Jordan Reduction with Matrix inversion 

This simply states that the inverse of A is equal to L. This has veiy important implications in numerical method.s because it shows that the Gauss-Jordan reduction method is essentially a matrix inversion algorithm Eq. (2.136), when rearranged, clearly shows that the application of the reduction operation L on the identity matrix yields the inverse of A  

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