C Program to Find Inverse Of 3 x 3 Matrix in 10 Lines

Program : Finding Inverse of a 3 X 3 Matrix

#include<stdio.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 matrix[3][6];
   int i, j;
   for (i = 0; i < 3; i++) {
      for (j = 0; j < 6; j++) {
         if (j == i + 3) {
            matrix[i][j] = 1;
         } else {
            matrix[i][j] = 0;
         }
      }
   }
   printf("\nEnter a 3 X 3 Matrix :");
   for (i = 0; i < 3; i++) {
      for (j = 0; j < 3; j++) {
         scanf("%f", &matrix[i][j]);
      }
   }
   for (i = 0; i < 3; i++) {
      reduction(matrix, 3, i, i);
   }
   printf("\nInvers Matrix");
   for (i = 0; i < 3; i++) {
      printf("\n");
      for (j = 0; j < 3; j++) {
         printf("%8.3f", matrix[i][j + 3]);
      }
   }
}

#include<stdio.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 matrix[3][6];

int i, j;

for (i = 0; i < 3; i++) {

for (j = 0; j < 6; j++) {

if (j == i + 3) {

matrix[i][j] = 1;

} else {

matrix[i][j] = 0;

}

printf("\nEnter a 3 X 3 Matrix :");

for (i = 0; i < 3; i++) {

for (j = 0; j < 3; j++) {

scanf("%f", &matrix[i][j]);

}

for (i = 0; i < 3; i++) {

reduction(matrix, 3, i, i);

}

printf("\nInvers Matrix");

for (i = 0; i < 3; i++) {

printf("\n");

for (j = 0; j < 3; j++) {

printf("%8.3f", matrix[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

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

1 3 1

1 1 2

2 3 4

Step 1 :

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

Step 2 :

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

Step 3 :

Now Factor = a[1][0] and Apply Following Formula to 2nd Row

Row Element = Row Element - (Corresponding Master * (Factor)
                                    Row Element)

1 2	Row Element = Row Element - (Corresponding Master * (Factor) Row Element)

Step 4 :

Now Factor = a[2][0] and Apply Following Formula to 3rd Row

Row Element = Row Element - (Corresponding Master * (Factor)
                                    Row Element)

1 2	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);
}

for(i=0;i<3;i++) {

reduction(a,3,i,i);

}

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C Program to Find Inverse Of 3 x 3 Matrix in 10 Lines

Explanation :