Gauss Elimination method || C programming Gauss Elimination || C programming

 Question ( 1 ) = Write a computer program in C++ to find solution of the following systems of equations using Gauss

Elimination Method.

1. 2x+y+z=10,

3x+2y+3z=18,

X+4y+9z=16

(Answer: x=7, y = -9, z=5)

Ans :

/*

Program: Gauss Elimination Method

All array indexes are assumed to start from 1

*/

#include<iostream>

#include<iomanip>

#include<math.h>

#include<stdlib.h>

#define   SIZE   10

using namespace std;

int main()

{

float a[SIZE][SIZE], x[SIZE], ratio;

int i,j,k,n;

     /* Setting precision and writing floating point values in fixed-point notation. */

     cout<< setprecision(3)<< fixed;

/* Inputs */

/* 1. Reading number of unknowns */

cout<<"Deepak Shriwastav ,Regestration no:";cin>>n;

 

/* 1. Reading number of unknowns */

cout<<"Enter number of unknowns: ";

cin>>n;

/* 2. Reading Augmented Matrix */

cout<<"Enter Coefficients of Augmented Matrix: "<< endl;

for(i=1;i<=n;i++)

{

  for(j=1;j<=n+1;j++)

  {

   cout<<"a["<< i<<"]"<< j<<"]= ";

   cin>>a[i][j];

  }

}

/* Applying Gauss Elimination */

for(i=1;i<=n-1;i++)

{

  if(a[i][i] == 0.0)

  {

   cout<<"Mathematical Error!";

   exit(0);

  }

  for(j=i+1;j<=n;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 by Back Substitution Method */

x[n] = a[n][n+1]/a[n][n];

for(i=n-1;i>=1;i--)

{

  x[i] = a[i][n+1];

  for(j=i+1;j<=n;j++)

  {

  x[i] = x[i] - a[i][j]*x[j];

  }

  x[i] = x[i]/a[i][i];

}

/* Displaying Solution */

cout<< endl<<"Solution: "<< endl;

for(i=1;i<=n;i++)

{

  cout<<"x["<< i<<"] = "<< x[i]<< endl;

}

return(0);

}

Question ( 2 ) : Write a computer program in C++ to find solution of the following systems of equations using Gauss

Elimination Method

 2x+2y+z=12

 3x+2y+2z=8,

 5x+10y-8z=10.

 (Answer: x= -12.75, y=14.375, z=8.75)

Ans :

/*

Program: Gauss Elimination Method

All array indexes are assumed to start from 1

*/

#include<iostream>

#include<iomanip>

#include<math.h>

#include<stdlib.h>

#define   SIZE   10

using namespace std;

int main()

{

float a[SIZE][SIZE], x[SIZE], ratio;

int i,j,k,n;

     /* Setting precision and writing floating point values in fixed-point notation. */

     cout<< setprecision(3)<< fixed;

/* Inputs */

/* 1. Reading number of unknowns */

cout<<"Deepak Shriwastav ,Regestration no:";cin>>n;

 

/* 1. Reading number of unknowns */

cout<<"Enter number of unknowns: ";

cin>>n;

/* 2. Reading Augmented Matrix */

cout<<"Enter Coefficients of Augmented Matrix: "<< endl;

for(i=1;i<=n;i++)

{

  for(j=1;j<=n+1;j++)

  {

   cout<<"a["<< i<<"]"<< j<<"]= ";

   cin>>a[i][j];

  }

}

/* Applying Gauss Elimination */

for(i=1;i<=n-1;i++)

{

  if(a[i][i] == 0.0)

  {

   cout<<"Mathematical Error!";

   exit(0);

  }

  for(j=i+1;j<=n;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 by Back Substitution Method */

x[n] = a[n][n+1]/a[n][n];

for(i=n-1;i>=1;i--)

{

  x[i] = a[i][n+1];

  for(j=i+1;j<=n;j++)

  {

  x[i] = x[i] - a[i][j]*x[j];

  }

  x[i] = x[i]/a[i][i];

}

/* Displaying Solution */

cout<< endl<<"Solution: "<< endl;

for(i=1;i<=n;i++)

{

  cout<<"x["<< i<<"] = "<< x[i]<< endl;

}

return(0);

}

  

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