Program to calculate the Inverse of a Matrix using Gauss Jordon Method, a simple yet complete algorithm follows below.

Gauss Jordon Method can be employed to solve a system of linear equations having solutions. Unlink in Gauss Elimination method (in which triangular matrix is formed), in Gauss Jordon Method all off diagonal elements are eliminated producing a diagonal matrix. Finally, inverse of the matrix formed by system of equations is computed.

[A:I]?[I:A-1]
where

[A]= matrix to be solved for

[A-1]= required inverse matrix

[I]= identity matrix

/** To compute the inverse of matric [A] using Gauss Jordon Method

Simple but complete algorithm

1. start

2. n ie size of sq matrix

3.matrix reading

i= 1 to n

j= 1 to n

read a[i][j]
2.identity matrix

i= 1 to n

j= 1 to n

{

if(i==j)

b[i][j]=1

else

b[i][j]=0

}

3.elimination

k= 1 to n

{

i= 1 to n

{

if(i==k) goto LABEL;

pivot= a[i][k]/a[k][k]
j= 1 to n

{

a[i][j]= a[i][j]-pivot*a[k][j]
b[i][j]= b[i][j]-pivot*b[k][j]
}

LABEL

}

}

4.identity matrix

i= 1 to n

j= 1 to n

b[i][j]= b[i][j]/a[i][i]
5.display inverse matrix

i= 1 to n

j= 1 to n

cout “b[“< <

*************************************/

#include

#include

#include

void main()

{

int n;

clrscr();

cout< }

}

getch();

}

To calculate the Inverse of a Matrix using Gauss Jordon Method in C++ Programming Language for Numerical Methods for Engineering Students