Write a report in which you discuss and compare your Gauss elimination and Gauss-Jordan programs. Gauss elimination #include int main ( ) { int i, j, k, n; float A[20] [20], c, x [10], sum=0.0; printf("\Enter the order of matrix: "); Sacnf("%d,&n); prinf("\n Enter the elements of augmented matrix row-wise: \n\n"); for(i =1; i<=n; i++) { for(j=1; j<(n+1); j++) { printf("A[%d][%d] : ", i, j); scanf("%f", [i][j]); } } for(j=1; jj) { c=A[i][j]/A[j][j]; for(k=1; k<=n+!; k++) { A[i][k] = A[i][k]-c*A[j][k]; } } } } x[n]= A[n] [n+1]/A[n][n]; for(i=n-1; i>=1; i--) { sum=0; for(j=i+1; j<=n; j++) { sum=sum+A[i][j]*x[j]; } x[i]=A[i][n+1]-sum)/A[i][I]; } printf("\n The solution is : \n"); for(i=1; i<=n; i++) { printf("\nx%d=%f\t", i, x[i]; } return(0); } Gauss-Jordan method #include int main() { int i,j,k,n; float A[20][20],c,x[10],sum=0.0; printf("\nEnter the order of matrix: "); scanf("%d",&n); printf("\nEnter the elements of augmented matrix row-wise:\n\n"); for(i=1; i<=n; i++) { for(j=1; j<=(n+1); j++) { printf("A[%d][%d] : ", i,j); scanf("%f",&A[i][j]); } } for(j=1; j<=n; j++) /* loop for the generation of upper triangular matrix*/ { for(i=1; i<=n; i++) { if(i>j) { c=A[i][j]/A[j][j]; for(k=1; k<=n+1; k++) { A[i][k]=A[i][k]-c*A[j][k]; } } } } x[n]=A[n][n+1]/A[n][n]; /* this loop is for backward substitution*/ for(i=n-1; i>=1; i--) { sum=0; for(j=i+1; j<=n; j++) { sum=sum+A[i][j]*x[j]; } x[i]=(A[i][n+1]-sum)/A[i][i]; } printf("\nThe solution is: \n"); for(i=1; i<=n; i++) { printf("\nx%d=%f\t",i,x[i]); /* x1, x2, x3 are the required solutions*/ } return(0); }
Write a report in which you discuss and compare your Gauss elimination and Gauss-Jordan programs.
Gauss elimination
#include<stdio.h>
int main ( )
{
int i, j, k, n;
float A[20] [20], c, x [10], sum=0.0;
printf("\Enter the order of matrix: ");
Sacnf("%d,&n);
prinf("\n Enter the elements of augmented matrix row-wise: \n\n");
for(i =1; i<=n; i++)
{
for(j=1; j<(n+1); j++)
{
printf("A[%d][%d] : ", i, j);
scanf("%f", [i][j]);
}
}
for(j=1; j<n; j++)
{
for(i=1; j<n; i++)
{
if(i>j)
{
c=A[i][j]/A[j][j];
for(k=1; k<=n+!; k++)
{
A[i][k] = A[i][k]-c*A[j][k];
}
}
}
}
x[n]= A[n] [n+1]/A[n][n];
for(i=n-1; i>=1; i--)
{
sum=0;
for(j=i+1; j<=n; j++)
{
sum=sum+A[i][j]*x[j];
}
x[i]=A[i][n+1]-sum)/A[i][I];
}
printf("\n The solution is : \n");
for(i=1; i<=n; i++)
{
printf("\nx%d=%f\t", i, x[i];
}
return(0);
}
Gauss-Jordan method
#include<stdio.h>
int main()
{
int i,j,k,n;
float A[20][20],c,x[10],sum=0.0;
printf("\nEnter the order of matrix: ");
scanf("%d",&n);
printf("\nEnter the elements of augmented matrix row-wise:\n\n");
for(i=1; i<=n; i++)
{
for(j=1; j<=(n+1); j++)
{
printf("A[%d][%d] : ", i,j);
scanf("%f",&A[i][j]);
}
}
for(j=1; j<=n; j++) /* loop for the generation of upper triangular matrix*/
{
for(i=1; i<=n; i++)
{
if(i>j)
{
c=A[i][j]/A[j][j];
for(k=1; k<=n+1; k++)
{
A[i][k]=A[i][k]-c*A[j][k];
}
}
}
}
x[n]=A[n][n+1]/A[n][n];
/* this loop is for backward substitution*/
for(i=n-1; i>=1; i--)
{
sum=0;
for(j=i+1; j<=n; j++)
{
sum=sum+A[i][j]*x[j];
}
x[i]=(A[i][n+1]-sum)/A[i][i];
}
printf("\nThe solution is: \n");
for(i=1; i<=n; i++)
{
printf("\nx%d=%f\t",i,x[i]); /* x1, x2, x3 are the required solutions*/
}
return(0);
}
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