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Inverse Matrix

Finds the determinant of 3x3 matrix, then the transpose, then the adjunct of the transpose, then the inverse

Submitted By: PennyBoki

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Views: 7,714

Language: C++

Last Modified: August 5, 2007

Instructions: Copy/Paste/Compile/Run

Snippet

//PennyBoki @ </dream.in.code>
#include <iostream.h>
int main()
{
float A[3][3];// the matrix that is entered by user
float B[3][3];//the transpose of a matrix A
float C[3][3];//the adjunct matrix of transpose of a matrix A not adjunct of A
double X[3][3];//the inverse
int i,j;
float x,n=0;//n is the determinant of A
cout<<"========== Enter matrix A =============================================\n";
for(i=0;i<3;i++)
{ cout<<endl;
for(j=0;j<3;j++)
{
cout<<" A["<<i<<"]["<<j<<"]= ";
cin>>A[i][j];
B[i][j]=0;
C[i][j]=0;
}
}
for(i=0,j=0;j<3;j++)
{
if(j==2)
n+=A[i][j]*A[i+1][0]*A[i+2][1];
else if(j==1)
n+=A[i][j]*A[i+1][j+1]*A[i+2][0];
else
n+=A[i][j]*A[i+1][j+1]*A[i+2][j+2];
}
for(i=2,j=0;j<3;j++)
{
if(j==2)
n-=A[i][j]*A[i-1][0]*A[i-2][1];
else if(j==1)
n-=A[i][j]*A[i-1][j+1]*A[i-2][0];
else
n-=A[i][j]*A[i-1][j+1]*A[i-2][j+2];
}
cout<<"\n========== The matrix A is ==========================================\n";
for(i=0;i<3;i++)
{
cout<<endl;
for(j=0;j<3;j++)
{
cout<<" A["<<i<<"]["<<j<<"]= "<<A[i][j];
}
}
cout<<endl<<endl;
cout<<"=====================================================================\n"<<endl;
cout<<"The determinant of matrix A is "<<n<<endl<<endl;
cout<<"====================================================================="<<endl;
if(n!=0) x=1.0/n;
else
{
cout<<"Division by 0, not good!\n";
cout<<"=====================================================================\n"<<endl;
return 0;
}
cout<<"\n========== The transpose of a matrix A ==============================\n";
for(i=0;i<3;i++)
{
cout<<endl;
for(j=0;j<3;j++)
{
B[i][j]=A[j][i];
cout<<" B["<<i<<"]["<<j<<"]= "<<B[i][j];
}
}
cout<<endl<<endl;
C[0][0]=B[1][1]*B[2][2]-(B[2][1]*B[1][2]);
C[0][1]=(-1)*(B[1][0]*B[2][2]-(B[2][0]*B[1][2]));
C[0][2]=B[1][0]*B[2][1]-(B[2][0]*B[1][1]);
C[1][0]=(-1)*(B[0][1]*B[2][2]-B[2][1]*B[0][2]);
C[1][1]=B[0][0]*B[2][2]-B[2][0]*B[0][2];
C[1][2]=(-1)*(B[0][0]*B[2][1]-B[2][0]*B[0][1]);
C[2][0]=B[0][1]*B[1][2]-B[1][1]*B[0][2];
C[2][1]=(-1)*(B[0][0]*B[1][2]-B[1][0]*B[0][2]);
C[2][2]=B[0][0]*B[1][1]-B[1][0]*B[0][1];
cout<<"\n========== The adjunct matrix of transpose of the matrix A ==========\n";
for(i=0;i<3;i++)
{
cout<<endl;
for(j=0;j<3;j++)
{
cout<<" C["<<i<<"]["<<j<<"]= "<<C[i][j];
}
}
cout<<endl<<endl;
for(i=0;i<3;i++)
{
for(j=0;j<3;j++)
{
X[i][j]=C[i][j]*x;
}
}
cout<<"\n========== The inverse matrix of the matrix you entered!!! ==========\n";
for(i=0;i<3;i++)
{ cout<<endl;
for(j=0;j<3;j++)
{
cout<<" X["<<i<<"]["<<j<<"]= "<<X[i][j];
}
}
cout<<endl<<endl;
return 0;
}

Copy & Paste

//PennyBoki @ </dream.in.code>
#include <iostream.h>

int main()
{
     float A[3][3];// the matrix that is entered by user
     float B[3][3];//the transpose of a matrix A 
     float C[3][3];//the adjunct matrix of transpose of a matrix A not adjunct of A
     double X[3][3];//the inverse
     int i,j;
     float x,n=0;//n is the determinant of A
     
     cout<<"========== Enter matrix A =============================================\n";
     for(i=0;i<3;i++)
     {     cout<<endl;
          for(j=0;j<3;j++)
          {     
               cout<<" A["<<i<<"]["<<j<<"]= ";
               cin>>A[i][j];
               B[i][j]=0;
               C[i][j]=0;
          }
     }
     
     
          for(i=0,j=0;j<3;j++)
          {     
               if(j==2) 
               n+=A[i][j]*A[i+1][0]*A[i+2][1];
               else if(j==1)
               n+=A[i][j]*A[i+1][j+1]*A[i+2][0];
               else 
               n+=A[i][j]*A[i+1][j+1]*A[i+2][j+2];
          }
          for(i=2,j=0;j<3;j++)
          {     
               if(j==2) 
               n-=A[i][j]*A[i-1][0]*A[i-2][1];
               else if(j==1)
               n-=A[i][j]*A[i-1][j+1]*A[i-2][0];
               else
               n-=A[i][j]*A[i-1][j+1]*A[i-2][j+2];
          }

cout<<"\n========== The matrix A is ==========================================\n";     
     for(i=0;i<3;i++)
     {
          cout<<endl;
          for(j=0;j<3;j++)
          {     
               cout<<" A["<<i<<"]["<<j<<"]= "<<A[i][j];
          }
     }
     cout<<endl<<endl;
     
     cout<<"=====================================================================\n"<<endl;
     cout<<"The determinant of matrix A is "<<n<<endl<<endl;
     cout<<"====================================================================="<<endl;
     
     if(n!=0) x=1.0/n;
     else 
     {
          cout<<"Division by 0, not good!\n";
          cout<<"=====================================================================\n"<<endl;
          return 0;
     }
     cout<<"\n========== The transpose of a matrix A ==============================\n";     
     for(i=0;i<3;i++)
     {
          cout<<endl;
          for(j=0;j<3;j++)
          {     
                    
               B[i][j]=A[j][i];
               cout<<" B["<<i<<"]["<<j<<"]= "<<B[i][j];
               
          }
     }
     cout<<endl<<endl;

C[0][0]=B[1][1]*B[2][2]-(B[2][1]*B[1][2]);
     C[0][1]=(-1)*(B[1][0]*B[2][2]-(B[2][0]*B[1][2]));
     C[0][2]=B[1][0]*B[2][1]-(B[2][0]*B[1][1]);
     
     C[1][0]=(-1)*(B[0][1]*B[2][2]-B[2][1]*B[0][2]);
     C[1][1]=B[0][0]*B[2][2]-B[2][0]*B[0][2];
     C[1][2]=(-1)*(B[0][0]*B[2][1]-B[2][0]*B[0][1]);

C[2][0]=B[0][1]*B[1][2]-B[1][1]*B[0][2];
     C[2][1]=(-1)*(B[0][0]*B[1][2]-B[1][0]*B[0][2]);
     C[2][2]=B[0][0]*B[1][1]-B[1][0]*B[0][1];

cout<<"\n========== The adjunct matrix of transpose of the matrix A ==========\n";     
     for(i=0;i<3;i++)
     {
          cout<<endl;
          for(j=0;j<3;j++)
          {     
               cout<<" C["<<i<<"]["<<j<<"]= "<<C[i][j];
               
          }
     }
     cout<<endl<<endl;

for(i=0;i<3;i++)
     {
          for(j=0;j<3;j++)
          {     
               X[i][j]=C[i][j]*x;
               
          }
     }

cout<<"\n========== The inverse matrix of the matrix you entered!!! ==========\n";
     for(i=0;i<3;i++)
     {     cout<<endl;
          for(j=0;j<3;j++)
          {     
               cout<<" X["<<i<<"]["<<j<<"]= "<<X[i][j];
          
          }
     }
     cout<<endl<<endl;

return 0;
}