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Gauss Jordan is a variant of the Gauss elimination method in which row reduction operations are done to find out the inverse of the matrix. Here also the row reduced echelon form of the matrix is formed. 

DERIVATION

Then we write the augmented matrix as

Then the first step will be,

 Where

And

The second step will be

The third and ultimate step:

INPUT: 

A matrix 

OUTPUT: 

The inverse of the given matrix

PROCESS:

Step 1: [taking the inputs from the user]

Read n [the order of the matrix]

for i = 1 to n repeat
for j = 1 to n repeat
Read a[i][j]
[End of ‘for’ loop]
[End of ‘for’ loop]

Step 2: [Gauss Jordan Inverse]
Set c ← n + 1
		for i = 1 to n repeat
			for j = n + 1 to 2n repeat
				If c = j then
					Set a[i][j] ← 1.0
				else
					Set a[i][j] ← 0.0
[End of ‘if’]
			[End of ‘for’ loop]
		Set c ← c + 1
		[End of ‘for’ loop]

	for i = 1 to n repeat
			for j = 1 to 2n repeat
				Print a[i][j]
[End of ‘for’ loop]
			Move to next line
		[End of ‘for’ loop]

    for k = 1 to n repeat
			for j = 1 to 2n repeat
		Set a[k][j] ← a[k][j]/a[k][k]
[End of ‘for’ loop]
			for i = 1 to n repeat
				If i = k then 
					Continue
[End of ‘if’]
				Set r ← a[i][k]
			
			for j = 1 to 2n repeat
					Set a[i][j] ← a[i][j] - (a[k][j] * r)
				[End of ‘for’ loop]
			[End of ‘for’ loop]
		for i = 1 to n repeat
				for j = 1 to 2n repeat
					Print a[i][j]
[End of ‘for’ loop]
				Move to the next line
			[End of ‘for’ loop]
		[End of ‘for’ loop]
	[Printing the matrix after inversion]
		for i = 1 to n repeat
			for j = n + 1 to 2n repeat
				Print a[i][j]
			[End of ‘fot’ loop]
		Move to the next line
[End of ‘for’ loop]
	
[End of Gauss Jordan Inverse Method]