Matrix Inverse Using Gauss Jordan Method Pseudocode


Earlier in Matrix Inverse Using Gauss Jordan Method Algorithm, we discussed about an algorithm for finding inverse of matrix of order n. In this tutorial we are going to develop pseudocode for this method so that it will be easy while implementing using programming language.

Complete Pseudocode for Finding Inverse of Matrix Using Gauss Jordan Method

1. Start 

2. Read Order of Matrix (n).

3. Read Matrix (A):

	For i = 1 to n
	  For j = 1 to n
	    Read Ai,j
	  Next j
	Next i

4. Augment Identity Matrix of Order n to Matrix A:

	For i = 1 to n
	  For j = 1 to n
	    
	    If i = j
	      Ai,j+n = 1
	    Else
	      Ai,j+n = 0
	    End If
	  
	  Next j
	Next i

5. Apply Gauss Jordan Elimination on Augmented Matrix (A):
	For i = 1 to n
	  If Ai,i = 0
	    Print "Mathematical Error!"
	    Stop
	  End If
	  
	  For j = 1 to n
	    If i ≠ j
	      Ratio = Aj,i/Ai,i
	      
	      For k = 1 to 2*n
	        Aj,k = Aj,k - Ratio * Ai,k
	      Next k
	    
	    End If
	  Next j
	Next i
	
6. Row Operation to Convert Principal Diagonal to 1.
	
	For i = 1 to n
	  For j = n+1 to 2*n
	    Ai,j = Ai,j/Ai,i
	  Next j
	Next i
	
7. Display Inverse Matrix:

	For i = 1 to n
	  For j = n+1 to 2*n
	    Print Ai,j
	  Next j
	Next i

8. Stop

---------------
Note: All array indexes are assumed to start from 1.

Recommended Readings

  1. Matrix Inverse Using Gauss Jordan Method Algorithm
  2. Matrix Inverse Using Gauss Jordan Method Pseudocode
  3. Matrix Inverse Using Gauss Jordan C Program
  4. Matrix Inverse Using Gauss Jordan C++ Program