C++ Metode Eliminasi Gauss & Gauss Jordan

Soal

 

 

 

 

 

 

 

Jawaban Menggunakan C++

Metode Gauss

Syntak :

#include <iostream.h>

#include <conio.h>

#include <stdio.h>

float a[6][6]={{4,3,5,-6,8,-2},{-9,-2,-3,10,4,-3},{2,4,6,-3,-2,2},{5,-7,8,3,9,3},{0,5,-2,10,6,-7},{-10,2,8,5,9,2}};

float k[6][6];

float b[6]={30,50,-32,-24,28,60};

float l[6];

float temp,x[6];

int n,i,j;

void TampilPersamaanK(int i);

void TampilPersamaanA(int i);

void main(){

cout<<"==================================================================\n";

cout<<"             PENYELESAIAN SISTEM PERSAMAAN LINIER\n";

cout<<"                        METODE GAUSS\n";

cout<<"==================================================================\n";

cout<<endl;

cout<<"Dik. persamaan Liniernya sebagai berikut : \n";

cout<<"==================================================================\n";

for (i=0;i<6;i++){

cout<<(i+1)<<".) ";

TampilPersamaanA(i);

}

for (n=0;n<(6-1);n++){

temp = a[n][n];

//penormalan

for (j=0;j<6;j++){

k[n][j]=a[n][j];

a[n][j]=a[n][j]/temp;

}

l[n]=b[n];

b[n]=b[n]/temp;

//proses penghilangan variabel

for (i=(n+1);i<6;i++){

temp = a[i][n];

for (j=n;j<6;j++){

a[i][j]=a[i][j]-(a[n][j]*temp);

}

b[i]=b[i]-(b[n]*temp);

}

}

cout<<"==================================================================\n";

cout<<"\nSetelah dilakukan penormalan dan penghilangan variabel,\n";

cout<<"maka didapat persamaan baru yaitu \n";

for (i=0;i<6;i++){

cout<<(i+1)<<".) ";

if (i<(6-1))

TampilPersamaanK(i);

else

TampilPersamaanA(i);

}

//penghitungan x

temp=a[5][5];

x[5]=b[5]/temp;

for (i=(6-2);i>=0;i--){

temp=k[i][i];

for (j=i+1;j<6;j++){

l[i]=l[i]-(k[i][j]*x[j]);

}

x[i]=l[i]/temp;

}

cout<<"\nSetelah dilakukan eliminasi dan substitusi pada persamaan diatas,\n";

cout<<"maka didapat nilai masing-masing x yaitu \n";

cout<<"*********************************\n";

for (i=0;i<6;i++){

printf("X%d = %3.4f \n",(i+1),x[i]);

cout<<"=================================\n";

}

getch();

}

void TampilPersamaanA(int i){

for (j=0;j<6;j++){

if (j==0){

cout<<(a[i][j])<<"x"<<(j+1)<<" ";

}else{

if (a[i][j]<0){

cout<<"- "<<(a[i][j]*-1)<<"x"<<(j+1)<<" ";

}else if (a[i][j]>=0){

cout<<"+ "<<(a[i][j])<<"x"<<(j+1)<<" ";

}

}

}

cout<<"\t = "<<b[i];

cout<<endl;

}

void TampilPersamaanK(int i){

for (j=0;j<6;j++){

if (j==0){

cout<<(k[i][j])<<"x"<<(j+1)<<" ";

}else{

if (k[i][j]<0){

cout<<"- "<<(k[i][j]*-1)<<"x"<<(j+1)<<" ";

}else if (k[i][j]>=0){

cout<<"+ "<<(k[i][j])<<"x"<<(j+1)<<" ";

}

}

}

cout<<"\t = "<<l[i];

cout<<endl;

}

Metode Gauss-Jordan

 

Syntak :

#include <iostream.h>

#include <conio.h>

#include <stdio.h>

float a[6][6]={{4,3,5,-6,8,-2},{-9,-2,-3,10,4,-3},{2,4,6,-3,-2,2},{5,-7,8,3,9,3},{0,5,-2,10,6,-7},{-10,2,8,5,9,2}};

float b[6]={30,50,-32,-24,28,60};

float temp;

int n,i,j;

void TampilMatriks();

void main(){

cout<<"==================================================================\n";

cout<<"             PENYELESAIAN SISTEM PERSAMAAN LINIER\n";

cout<<"                    METODE GAUSS-JORDAN\n";

cout<<"==================================================================\n";

cout<<endl;

cout<<"Dik. Persamaan Liniernya   : \n";

cout<<"==================================================================\n";

for (i=0;i<6;i++){

cout<<(i+1)<<".) ";

for (j=0;j<6;j++){

if (j==0){

cout<<(a[i][j])<<"x"<<(j+1)<<" ";

}else{

if (a[i][j]<0){

cout<<"- "<<(a[i][j]*-1)<<"x"<<(j+1)<<" ";

}else if (a[i][j]>=0){

cout<<"+ "<<(a[i][j])<<"x"<<(j+1)<<" ";

}

}

}

cout<<"\t = "<<b[i];

cout<<endl;

}

cout<<"==================================================================\n";

cout<<"\nMaka Bentuk Matriksnya : \n";

TampilMatriks();

//tahap2 penyelesaian menggunakan metode Gauss-Jordan

cout<<"\nPENYELESAIAN : \n";

cout<<"--------------------------------------------------------\n";

for (n=0;n<6;n++) {

cout<<"\nTahap "<<(n+1)<<endl;

temp=a[n][n];

for (j=0;j<6;j++){

a[n][j]=a[n][j]/temp;

}

b[n]=b[n]/temp;

for (i=0;i<6;i++){

if (i!=n){

temp=a[i][n];

for (j=n;j<6;j++){

a[i][j]=a[i][j]-(temp*a[n][j]);

}

b[i]=b[i]-(temp*b[n]);

}

}

//menampilkan matriks

TampilMatriks();

}

//tahap pembuktian

cout<<"\nDari penyelesaian diatas diperoleh nilai x1 sampai x6 yaitu : \n";

for (i=0;i<6;i++){

printf("X%d = %3.4f \n",(i+1),b[i]);

}

getch();

}

void TampilMatriks(){

for (i=0;i<6;i++){

cout<<" |  ";

for (j=0;j<6;j++){

if (a[i][j]>=0)

printf(" %3.4f ",a[i][j]);

else

printf("%3.4f ",a[i][j]);

}

cout<<"|  |x"<<(i+1)<<"|";

if (i==3)

cout<<" = ";

else

cout<<"   ";

printf("| %3.4f |",b[i]);

cout<<endl;

}

}