GAUSS JORDAN METHOD lab report

TITLE: 

TO  SOLVE THE SYSTEM OF LINEAR EQUATIONS USING GAUSS JORDAN METHOD

 OBJECTIVES:

• To be able to follow the algorithm of Gauss Jordan method of solving linear equation.

• To build some programming concepts by solving practical problems.

 TOOLS REQUIRED:

• Computer workstation

• Program software (as necessary)

 THEORY:

Gauss Jordan Method is a procedure for solving systems of linear equation which is in fact the modification of gauss elimination method . It is also known as Row Reduction Technique. In this method, the problem of systems of linear equation having n unknown variables is converted into a matrix having rows n and columns n+1. This matrix is also known as Augmented Matrix. After forming n x n+1 matrix, matrix is transformed to diagonal matrix by row oper.... Show More

TITLE: 

TO  SOLVE THE SYSTEM OF LINEAR EQUATIONS USING GAUSS JORDAN METHOD

 OBJECTIVES:

• To be able to follow the algorithm of Gauss Jordan method of solving linear equation.

• To build some programming concepts by solving practical problems.

 TOOLS REQUIRED:

• Computer workstation

• Program software (as necessary)

 THEORY:

Gauss Jordan Method is a procedure for solving systems of linear equation which is in fact the modification of gauss elimination method . It is also known as Row Reduction Technique. In this method, the problem of systems of linear equation having n unknown variables is converted into a matrix having rows n and columns n+1. This matrix is also known as Augmented Matrix. After forming n x n+1 matrix, matrix is transformed to diagonal matrix by row operations. Finally result is obtained by making all diagonal element to 1 i.e. identity matrix.

 ALGORITHM:

1. Start

2. Read Number of Unknowns: n

3. Read Augmented Matrix (A) of n by n+1 Size

4. Transform Augmented Matrix (A)   to Diagonal Matrix by Row Operations.

5. Obtain Solution by Making All Diagonal Elements to 1.

6. Display Result.

7.  Stop

 C-PROGRAM: 

#include
#include
#include
#define SIZE 10
Void main()
{
		 float a[SIZE][SIZE], x[SIZE], ratio;
		 int i,j,k,n;
		 clrscr();
		 printf("Enter number of unknowns: ");
		 scanf("%d", &n);
		 /* 2. Reading Augmented Matrix */
		 printf("Enter coefficients of Augmented Matrix:\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]);
			  }
		 }
		 /* Applying Gauss Jordan Elimination */
		 for(i=1;i<=n;i++)
		 {
			  if(a[i][i] == 0.0)
			  {
				   printf("Mathematical Error!");
				   exit(0);
			  }
			  for(j=1;j<=n;j++)
			  {
				   if(i!=j)
				   {
					    ratio = a[j][i]/a[i][i];
					    for(k=1;k<=n+1;k++)
					    {
					     	a[j][k] = a[j][k] - ratio*a[i][k];
					    }
				   }
			  }
		 }
		 /* Obtaining Solution */
		 for(i=1;i<=n;i++)
		 {
		  	x[i] = a[i][n+1]/a[i][i];
		 }
		 /* Displaying Solution */
		 printf("\nSolution:\n");
		 for(i=1;i<=n;i++)
		 {
		  	printf("x[%d] = %0.3f\n",i, x[i]);
		 }
		 getch();
	}

CONCLUSION:

Thus the given linear equations were solved using Gauss Jordan Elimination Method.