Oct 19, 2011

C Program to find the Inverse of the Matrix.

C Program to find the Inverse of a Matrix. To find the Matrix Inverse, matrix should be a square matrix and Matrix Determinant is should not Equal to Zero. if A is a Square matrix and |A|!=0, then AA'=I (I Means Identity Matrix). Read more about C Programming Language .

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#include<stdio.h> 
#include<math.h> 
float detrminant(float[][], float);
void cofactors(float[][], float);
void trans(float[][], float[][], float);
main() {
 float a[25][25], n, d;
 int i, j;
 printf("Enter the order of the matrix:\n");
 scanf("%f", &n);
 printf("Enter the elemnts into the matrix:\n");
 for (i = 0; i < n; i++) {
  for (j = 0; j < n; j++) {
   scanf("%f", &a[i][j]);
  }
 }
 d = detrminant(a, n);
 printf("\nTHE DETERMINANT IS=%2f", d);
 if (d == 0)
  printf("\nMATRIX IS NOT INVERSIBLE\n");
 else
  cofactors(a, n);
}

float detrminant(float a[25][25], float k) {
 float s = 1, det = 0, b[25][25];
 int i, j, m, n, c;
 if (k == 1) {
  return (a[0][0]);
 } else {
  det = 0;
  for (c = 0; c < k; c++) {
   m = 0;
   n = 0;
   for (i = 0; i < k; i++) {
    for (j = 0; j < k; j++) {
     b[i][j] = 0;
     if (i != 0 && j != c) {
      b[m][n] = a[i][j];
      if (n < (k - 2))
       n++;
      else {
       n = 0;
       m++;
      }
     }
    }
   }
   det = det + s * (a[0][c] * detrminant(b, k - 1));
   s = -1 * s;
  }
 }
 return (det);
}

void cofactors(float num[25][25], float f) {
 float b[25][25], fac[25][25];
 int p, q, m, n, i, j;
 for (q = 0; q < f; q++) {
  for (p = 0; p < f; p++) {
   m = 0;
   n = 0;
   for (i = 0; i < f; i++) {
    for (j = 0; j < f; j++) {
     b[i][j] = 0;
     if (i != q && j != p) {
      b[m][n] = num[i][j];
      if (n < (f - 2))
       n++;
      else {
       n = 0;
       m++;
      }
     }
    }
   }
   fac[q][p] = pow(-1, q + p) * detrminant(b, f - 1);
  }
 }
 trans(num, fac, f);
}

void trans(float num[25][25], float fac[25][25], float r)

{
 int i, j;
 float b[25][25], inv[25][25], d;
 for (i = 0; i < r; i++) {
  for (j = 0; j < r; j++) {
   b[i][j] = fac[j][i];
  }
 }

 d = detrminant(num, r);
 inv[i][j] = 0;
 for (i = 0; i < r; i++) {
  for (j = 0; j < r; j++) {
   inv[i][j] = b[i][j] / d;
  }
 }

 printf("\nTHE INVERSE OF THE MATRIX:\n");
 for (i = 0; i < r; i++) {
  for (j = 0; j < r; j++) {
   printf("\t%2f", inv[i][j]);
  }
  printf("\n");
 }
}
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