Unit 2.2 Gauss Jordan

// AFTER CHANGES

// Algorithm
start
declare the variables and read the order of the matrix n
take the cofficients of the linear equation as

Do for i=1 to n
    Do for j=1 to n+1
        read a[i][j]
    end for j
end for i

Do for i to n
    Do for j=i+1 to n+1
        a[i][j] = a[i][j]/a[i][i]
    End for j

    set a[i][i] to 1

    Do for k=1 to n
        if(k not equal to i) then
            Do for l=i+1 to n+1
                a[k][l] = a[k][l] - (a[i][l] * a[k][i])
            End for l
    End for k
End for i

Do for m=1 to n
    x[m] = a[m][n+1]
    Display x[m]
End for m

Stop


// Program
#include <stdio.h>
int main()
{
    int n,i,j,k,l;
    float sum=0,a[5][5],x[10];

    printf("Enter the value of n\n");
    scanf("%d",&n);
    for(i=1 ; i<=n ; i++){
        for(j=1 ; j<=n+1 ; j++){
            scanf("%f",&a[i][j]);
        }
    }

    for(i=1 ; i<=n ; i++){
        for(j=i+1 ; j<=n+1 ; j++){
            a[i][j] = a[i][j]/a[i][i];
        }
        a[i][i] = 1;
        for(k=1 ; k<=n ; k++){
            if(k!=i){
                for(l=i+1 ; l<=n+1 ; l++){
                    a[k][l] = a[k][l] - (a[i][l] * a[k][i]);
                }
            }
        }
    }


    for (int m =1 ; m<=n ; m++){
        x[m] = a[m][n+1];
        printf("x[%d]=%f\n",m,x[m]);
    }

    return 0;
}


//BEFORE CHANGES

start
Read the order of the matrix 'n' and read the cofficients of the linear equations


Do for k=1 to n
    Do for l=k+1 to n+1
        a[k][l] = a[k][l]/a[k][k]
    end for l
    set a[k][k] = 1

    Do for i=1 to n
        if(i not equal to k) then,
            Do for j=k+1 to n+1
                a[i][j] = a[i][j] - (a[k][j] * a[i][k])
            End for j
    End for i
End for k

Do for m=1 to n
    x[m] = a[m][n+1]
    Display x[m]
End for m

Stop










#include <stdio.h>
int main()
{
    int n,i,j,k,l;
    float sum=0,a[5][5],x[10];

    printf("Enter the value of n\n");
    scanf("%d",&n);
    for(k=1 ; k<=n ; k++){
        for(j=1 ; j<=n+1 ; j++){
            scanf("%f",&a[k][j]);
        }
    }

    for(k=1 ; k<=n ; k++){
        for(l=k+1 ; l<=n+1 ; l++){
            a[k][l] = a[k][l]/a[k][k];
        }
        a[k][k] = 1;
        for(i=1 ; i<=n ; i++){
            if(i!=k){
                for(j=k+1 ; j<=n+1 ; j++){
                    a[i][j] = a[i][j] - (a[k][j] * a[i][k]);
                }
            }
        }
    }


    for (int m =1 ; m<=n ; m++){
        x[m] = a[m][n+1];
        printf("x[%d]=%f\n",m,x[m]);
    }

    return 0;
}
/*
Enter the value of n
3
2 1 4 12
8 -3 2 23
4 11 -1 33
x[1]=3.357143
x[2]=1.857143
x[3]=0.857143
*/