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## Matrix-Method of solving simultaneous linear equations

After the implementation of crammer's rule came up with something new again. Matrix method of solving simultaneous linear equations.

```import java.io.*;
public class matrix_method
{
public static void main(String args[])throws Exception
{
System.out.println("No of variables to be dealt with ::");
int v[][]=new int[n][n];
int R[]=new int[n];
int i,j;
for(i=0;i<n;i++)
{
System.out.println("Equation ::"+(i+1)+"\n");
for(j=0;j<n;j++)
{
System.out.println("Enter the coefficient of variable ::"+(j+1));
}
System.out.println("\nEnter the value of the right hand side of equation ::"+(i+1));
}
process(v,R,n);
}
public static double[][] transpose(double det[][],int n)
{
int i=0,j=0;
double temp=0;
for(i=0;i<n;i++)
{
for(j=i+1;j<n;j++)
{
temp=det[i][j];
det[i][j]=det[j][i];
det[j][i]=temp;
}
}
return det;
}
public static void process(int v[][],int R[],int n)
{
int i=0,j=0;
double res=0;
double D[][]=new double[n][n];
res=(double)det(v,n);
if(res==0.0)
{
System.out.println("The above system of equations is inconsistent");
return;
}
res=(1.0)/(res);
for(i=0;i<n;i++)
for(j=0;j<n;j++)
{
D[i][j]=(Math.pow((-1),(i+j+2)))*res*calculate(v,n,i,j);
}
D=transpose(D,n);
System.out.println();
for(i=0;i<n;i++)
{
res=0.0;
for(j=0;j<n;j++)
{
res=res+((double)(D[i][j]*R[j]));
}
System.out.println("The value of term "+(i+1)+" is "+res);
}
}
public static double calculate(int D[][],int n,int r,int c)
{
int i=0,j=0,x=0,y=0;
double res=0.0;
if(n==2)
{
if(r==0 && c==0)
res=(double)D[1][1];
else if(r==0 && c==1)
res=(double)D[1][0];
else if(r==1 && c==0)
res=(double)D[0][1];
else if(r==1 && c==1)
res=(double)D[0][0];
}
else
{
int t[][]=new int[n-1][n-1];
for(i=0;i<n;i++)
{
if(i==r)
x--;
else
{
y=0;
for(j=0;j<n;j++)
{
if(j==c)
{
y--;
}
else
{
t[x][y]=D[i][j];
}
y++;
}
}
x++;
}
res=(double)det(t,n-1);
}
return res;
}

public static int det(int v[][],int n)
{
int i=0,t=0,sign=1,sum=0;
if(n==2){
t=(v[0][0]*v[1][1])-(v[0][1]*v[1][0]);
return t;
}
else
{
for(i=0;i<n;i++)
{
sum+=v[0][i]*sign*matrix(v,i,n);
sign=sign*(-1);
}
}
return sum;
}
public static int matrix(int v[][],int c,int n)
{
int i=0,j=0,a=0,b=0;
int t[][]=new int[n-1][n-1];
for(i=1;i<n;i++)
{
b=0;j=0;
while(j<n)
{
if(j==c)
j++;
if(j<n)
t[a][b]=v[i][j];
j++;
b++;
}
a++;
}
return det(t,n-1);
}
}
```

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