inverse of a matrix

[jackman05]

hi, i hv to do the inverse of a matrix by row elimination

plz
help

[jonsca]

This has a step by step method:
http://www.ehow.com/how_5079317_calculate-inverse-matrix.html

[rahul8590]

This has a step by step method:
http://www.ehow.com/how_5079317_calculate-inverse-matrix.html

That was a nice link enlightening the procedure.

I would like to add more on it by saying that u could use matrix template library
http://www.osl.iu.edu/research/mtl/intro.php3

It might be helpful to you.

[jonsca]

I'm going to go out on a limb and say that it's probably a school assignment so the OP probably can't incorporate it but he/she can get some good ideas from it.

[StuXYZ]

If you do write your own Gauss-Jorden elimination procedure, be very careful to deal with the huge numerical rounding errors. Re- stabalization of matrix after most steps is essential. Also please not
the obvious test matrix [1,2,3][4,5,6][7,8,9] has zero determinate so has no inverse.

Simple approaches in books like numerical recipeshttp://www.nr.com/, e.g. pivoting are a start but much better methods exist (e.g. partial row summation).

Note the NR book is freely viewable.

[KASHIF JAMAL]

//PennyBoki @ </dream.in.code>
#include <stdio.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

     printf("========== Enter matrix A =============================================\n");
     for(i=0;i<3;i++)
     {     printf("\n");
          for(j=0;j<3;j++)
          {     
               printf(" A[%d][%d]= ",i,j);
               scanf("%f", &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];
          }


     printf("\n========== The matrix A is ==========================================\n");     
     for(i=0;i<3;i++)
     {
          printf("\n");
          for(j=0;j<3;j++)
          {     
               printf(" A[%d][%d]= %.2f  ",i,j,A[i][j]);
          }
     }
     printf("\n \n");

     printf("=====================================================================\n\n");
     printf("The determinant of matrix A is %.2f ",n);
     printf("\n\n=====================================================================\n");

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

               B[i][j]=A[j][i];
               printf(" B[%d][%d]= %.2f  ",i,j,B[i][j]);

          }
     }
     printf("\n\n");


     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];


     printf("\n========== The adjunct matrix of transpose of the matrix A ==========\n");     
     for(i=0;i<3;i++)
     {
          printf("\n");
          for(j=0;j<3;j++)
          {     
               printf("C[%d][%d]= %.2f",i,j,C[i][j]);

          }
     }
     printf("\n\n");


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

          }
     }



     printf("\n========== The inverse matrix of the matrix you entered!!! ==========\n");
     for(i=0;i<3;i++)
     {     printf("\n");
          for(j=0;j<3;j++)
          {     
               printf(" X[%d][%d]= %.2f",i,j,X[i][j]);

          }
     }
     printf("\n\n");


return 0;
}

[mrnutty]

Note there are explicit formulas for 2x2 and 3x3 matrix, see here