C Program to Find the Rank of the given Matrix of any order

In this Article we will see a C program to find the rank of the matrix in step by step process.

Rank of a Matrix

The rank of the matrix r is defined if –
1) It has at least one non-zero mirror of order r.
2) Every minor of A of order higher than r is zero.
To find the rank of matrix reduce the given matrix to upper triangular form. Rank of the matrix is equal to the number of non-zero rows.

Rank of a Matrix C Program

/* C Program:Rank of Matrix */
#include<stdio.h>
#include<conio.h>

int a[10][10],i,j,m,n;
int rank(int, int);
void swap(int,int,int);
void read(int, int);
void display(int, int);
int main()
{
   int rnk;
   printf("enter the order of matrix (row and col size):\n");
   scanf("%d%d",&m,&n);
   read(m,n);
   display(m,n);
   rnk= rank(m,n);
   printf("\n\nThe rank of above matrix is: %d\n", rnk);
   return 0;
}
/** Function reading the matrix row by row **/
void read(int r,int c)
{
   printf("Enter %d x %d order matrix values(Row by Row) :\n",r,c);
   for(i=0;i<r;i++)
      for(j=0;j<c;j++)
       scanf("%d",&a[i][j]);
}

/** function display matrix **/
void display(int r, int c)
{
   printf("Matrix is : \n");
   for(i=0;i<r;i++)
   {
      for(j=0;j<c;j++)
       printf("%4d",a[i][j]);
      printf("\n");
   }
}
/** This function exchange two rows of a matrix **/
void swap(int r1, int r2, int c)
{
   int t;
   for(i=0;i<c;i++)
   {
      t= a[r1][i];
      a[r1][i] = a[r2][i];
      a[r2][i]=t;
   }
}
/**This function find rank of matrix **/
int rank(int r1, int c1)
{
    int i,j,k;
    float ratio;
    for(i=0;i<c1;i++)
    {
       printf("\nSTEP = %d\n",i+1);
       display(m,n);
       if(a[i][i]!=0)    /* Diagonal element is not zero */
     for(j=0;j<r1;j++)
       if (j!=i)
       {
          /* Make all the element above and nelow the current principal
         diagonal element zero */
          ratio = a[j][i]/a[i][i];
          for(k=0;k<c1;k++)
         a[j][k]-=ratio*a[i][k];
       }
       else
         printf("\n");
         /* principal Diagonal element is zero */
       else
       {
       for(j=i+1;j<r1;j++)
          if(a[j][i]!=0)
          {   /* Find non zero elements in the same column */
          swap(i,j,c1);
          break;
          }
          if(j==r1)
          {
          c1--;
          for(j=0;j<r1;j++)
             a[j][i] = a[j][c1];
          }
          i--;
     	}
     }
   return  c1;
}

OUTPUT

enter the order of matrix (row and col size):
3 4
Enter 3 x 4 order matrix values(Row by Row) :
1 2 -1 3
3 4 0 -1
-1 0 -2 7
Matrix is :
   1   2  -1   3
   3   4   0  -1
  -1   0  -2   7

STEP = 1
Matrix is :
   1   2  -1   3
   3   4   0  -1
  -1   0  -2   7


STEP = 2
Matrix is :
   1   2  -1   3
   0  -2   3 -10
   0   2  -3  10


STEP = 3
Matrix is :
   1   0   2  -7
   0  -2   3 -10
   0   0   0   0

STEP = 3
Matrix is :
   1   0  -7  -7
   0  -2 -10 -10
   0   0   0   0


The rank of above matrix is: 2

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