C Program to Find Inverse of Matrix of any given order
Inverse of Matrix for a matrix A is A-1.
The inverse of A is A-1 only when: A × A-1 = A-1 × A = I
We can find the Inverse of the matrix with the help of adjoin matrix that is :-
C-Program to read any order of Square Matrix and find its inverse.
/* C-Program: Inverse Matrix of any Order of Square Matrix */
#include<stdio.h>
#include<conio.h>
/* Function Prototype declaration */
float detr(float [][10],int);
void cofactor(float [][10],int);
void transpose(float [][10],float [][10],int);
void display(float [][10], int);
int main()
{
float a[10][10],d;
int i,j,k;
printf("Enter the order of the Matrix : ");
scanf("%d", &k);
printf("Enter the row by row values of %dX%d Matrix:\n",k,k);
for (i = 0;i < k; i++)
for (j = 0;j < k; j++)
scanf("%f", &a[i][j]);
printf("The given matrix is:\n");
display(a, k);
d=detr(a,k);
printf("The determinant of matrix is: %.2f \n",d);
if(d==0)
printf("Inverse of Matrix is not possible\n");
else
cofactor(a,k);
return 0;
}
/* for calculate Deterrminant of the Matrix function definition*/
float detr(float a1[10][10],int k)
{
float d=0,b[10][10];
int i,j,m,n,c,s=1;
if(k==1)
return (a1[0][0]);
for(c=0;c<k;c++)
{
m=0; n=0;
for(i=0;i<k;i++)
for(j=0;j<k;j++)
{
if(i!=0 && j!=c)
{
b[m][n]=a1[i][j];
n++;
if(n == k-1)
{
n=0; m++;
}
}
}
d=d+s*(a1[0]*detr(b,k-1));
s = -s;
}
return(d);
}
/* function define find co-factor */
void cofactor(float x[10][10],int k)
{
float b[10][10], y[10][10];
int p,q,m,n,i,j,s=1;
for(q=0;q<k;q++)
for(p=0;p<k;p++)
{
m=0; n=0;
for(i=0;i<k;i++)
for(j=0;j<k;j++)
if(i!=q && j!=p)
{
b[m][n]=x[i][j];
if(n<(k-2))
n++;
else
{
n=0; m++;
}
}
y[q][p]=s*detr(b,k-1);
s=-1*s;
}
transpose(x,y,k);
}
/*Finding transpose of matrix*/
void transpose(float x[10][10],float y[10][10],int r)
{
int i,j;
float b[10][10],inv[10][10],d;
printf("The cofactor of matrix is:\n");
display(y,r);
/* transpose of cofactor matrix */
for(i=0;i<r;i++)
for(j=0;j<r;j++)
b[i][j]=y[j][i];
d=detr(x,r);
printf("The adjoint matrix is:\n");
display(b,r);
/* calculate inverse matrix */
for(i=0;i<r;i++)
for(j=0;j<r;j++)
inv[i][j]=b[i][j]/d;
printf("The inverse of matrix is:\n");
display(inv,r);
}
/* display function definition */
void display(float m[][10], int o)
{ int i,j;
for(i=0;i<o;i++)
{
for(j=0;j<o;j++)
printf("%8.2f", m[i][j]);
printf("\n");
}
}
OUTPUT :-
EXAMPLE 1
Enter the order of the Matrix : 3
Enter the row by row values of 3X3 Matrix:
0 1 3
1 2 1
2 3 1
The given matrix is:
0.00 1.00 3.00
1.00 2.00 1.00
2.00 3.00 1.00
The determinant of matrix is: -2.00
The cofactor of matrix is:
-1.00 1.00 -1.00
8.00 -6.00 2.00
-5.00 3.00 -1.00
The adjoint matrix is:
-1.00 8.00 -5.00
1.00 -6.00 3.00
-1.00 2.00 -1.00
The inverse of matrix is:
0.50 -4.00 2.50
-0.50 3.00 -1.50
0.50 -1.00 0.50
EXAMPLE 2
Enter the order of the Matrix : 3
Enter the row by row values of 3X3 Matrix:
1 2 3
1 2 3
2 3 4
The given matrix is:
1.00 2.00 3.00
1.00 2.00 3.00
2.00 3.00 4.00
The determinant of matrix is: 0.00
Inverse of Matrix is not possible
EXAMPLE 3
Enter the order of the Matrix : 4
Enter the row by row values of 4X4 Matrix:
1 1 1 1
0 2 1 3
4 2 1 0
3 2 1 5
The given matrix is:
1.00 1.00 1.00 1.00
0.00 2.00 1.00 3.00
4.00 2.00 1.00 0.00
3.00 2.00 1.00 5.00
The determinant of matrix is: -17.00
The cofactor of matrix is:
0.00 17.00 -34.00 -0.00
-5.00 14.00 -8.00 -1.00
-2.00 -8.00 7.00 3.00
3.00 -5.00 -2.00 4.00
The adjoint matrix is:
0.00 -5.00 -2.00 3.00
17.00 14.00 -8.00 -5.00
-34.00 -8.00 7.00 -2.00
-0.00 -1.00 3.00 4.00
The inverse of matrix is:
-0.00 0.29 0.12 -0.18
-1.00 -0.82 0.47 0.29
2.00 0.47 -0.41 0.12
0.00 0.06 -0.18 -0.24