gauss elimination with back substitution code in c

Question

can anyone provide some help with it . i am totally unable to do this one.i tried to do some coding but it didn't work at all. Anyways i have included the code.It is incomplete and wrong anyways.

#include<stdio.h>
#include<math.h>
main()
{
  int rows, columns, iter, i,j,k;
  printf("enter the number of rows and columns:");
  scanf("%d, %d",&rows, &columns);
  double a[rows][columns], b[rows][1],x[rows][1];
  printf("enter the elements of A matrix:");
   for(i=0;i<rows;i++)
  {
    for(j=0;j<columns;j++)
    scanf("%lf",&a[i][j]);
  }
   printf("\n enter the elements of B matrix:");
  for(i=0,i<rows;i++)
  scanf("%lf",&b[i][0]);

  printf("\n");
  for (iter=1; iter<rows; iter++)
  {
    for(i=iter;i<rows;i++)

      b[i][0] = b[i][0]- a[k][iter-1]*(b[i-1][0]/a[iter-1][iter-1]);


      for(j=iter-1,k=iter;j<columns;j++)

        a[i][j] = a[i][j]-a[i-1][j]*(a[k][iter-1]/a[iter-1][iter-1]);

    }


  printf("the elements of the matrix A are now:");

  for(i=0;i<rows; i++)
  { 
    for(j=0; j<columns; j++)  
      printf("%lf",a[i][j]);
  }
  return(0);
}

After this back substitution has to be done . The equation is [a][x] = [b] and we have to find the values of x for given [a] and [b] matrices.

Answer 1

Nobody uses code like this, it has serious numerical stability issues. Using LU-decomp is a good approach, many libraries available for it. Numerical Recipes, if you have to.

Answer 2

int rows, columns, iter, i,j,k;
printf("enter the number of rows and columns:");
scanf("%d, %d",&rows, &columns);
double a[i][j], b[i],x[i];

Using i, and j to specify array sizes is a very questionable activity, as i and j have not been initialized.

Answer 3

The first thig that I notice is this loop

for(i=0;i<=columns-1;i++) 
{ 
  for(j=0;j<=columns-1;j++) 
  {  
    scanf("%lf",&a[i][j]); 
  } 
}

I'm guessing that one of these columns should be rows instead, porbably the one used in i<=columns-1.

Also, just out of interest why i<=columns-1 instead of i < columns, they should be equivalent in all cases that matter.