Program : Finding Inverse of a 3 X 3 Matrix

#include<stdio.h>
#include<conio.h>
//                   a         3        i          i
void reduction(float a[][6],int size,int pivot ,int col)
{
int i,j;
float factor;
  factor=a[pivot][col];
  for(i=0;i<2*size;i++)
       a[pivot][i]/=factor;
  for(i=0;i<size;i++)
      if(i!=pivot)
      {
      factor=a[i][col];
           for(j=0;j<2*size;j++)
                a[i][j]=a[i][j]-a[pivot][j]*factor;
      }
}
//--------------------------------------------------
void main()
{
float a[3][6];
int i,j;
clrscr();
for(i=0;i<3;i++)    // Append Unit Matrix
  for(j=0;j<6;j++)
    {
    if(j==i+3)
       a[i][j]=1;
    else
       a[i][j]=0;
    }
printf("\n Enter a 3 X 3 Matrix");
for(i=0;i<3;i++)
  for(j=0;j<3;j++)
    scanf("%f",&a[i][j]);
for(i=0;i<3;i++)
    reduction(a,3,i,i);
printf("\nInvers Matrix");
 for(i=0;i<3;i++)
 {
 printf("\n");
   for(j=0;j<3;j++)
    printf("%8.3f",a[i][j+3]);
 }
}
Output :

Enter a 3 X 3 Matrix
1 3 1
1 1 2
2 3 4
Invers Matrix
   2.000   9.000  -5.000
   0.000  -2.000   1.000
  -1.000  -3.000   2.000
Explanation :
Suppose we have to find Inverse of -

1 3 1
1 1 2
2 3 4

Step 1 :

  1. Create One Matrix of Size 3 x 6
  2. i.e Create 3 x 3 Matrix and Append 3 x 3 Unit Matrix

Step 2 :

  1. Factor = a[0][0]
  2. Now For First Row : Divide all Elements by Factor Itself

Step 3 :

  1. Now Factor = a[1][0] and Apply Following Formula to 2nd Row
Row Element = Row Element - (Corresponding Master * (Factor)
                                    Row Element)

Step 4 :

  1. Now Factor = a[2][0] and Apply Following Formula to 3rd Row
Row Element = Row Element - (Corresponding Master * (Factor)
                                    Row Element)

Step 5 :

  • Now Call Reduction Function Again
  • So In 2nd Call 2nd Row will be Master Row
for(i=0;i<3;i++)
    reduction(a,3,i,i);

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