Matrix : Inverse always null - c

Question

The inverse of my matrix shows always 0 and I don't understand why. Thank you for advance.
4 fonctions :
-main : user enters the matrix, and the results (of matrix, determinant, LU factorisation and inverse) are display.
#include<stdio.h>
#include<conio.h>
#include<math.h>
float determinant(float[20][20],float);
void cofactor(float[20][20],float);
void transpose(float[20][20],float[20][20],float);
void main()
{
float A[20][20]= {0},L[20][20]= {0}, U[20][20];
float B[20]= {0}, X[20]= {0},Y[20]= {0};
int i,j,k,n;
printf("Enter the order of square matrix: ");
scanf("%d",&n);
printf("\nEntrer les elements de la matrice A:\n");
for(i=0; i<n; i++)
{
for(j=0; j<n; j++)
{
printf("Entrer l'element A[%d][%d] : ", i,j);
scanf("%f",&A[i][j]);
}
}
printf("\nEntrer les termes de la matrice B\n");
for(i=0; i<n; i++)
{
printf("B[%d]",i);
scanf("%f",&B[i]);
}
for(j=0; j<n; j++)
{
for(i=0; i<n; i++)
{
if(i<=j)
{
U[i][j]=A[i][j];
for(k=0; k<i-1; k++)
U[i][j]-=L[i][k]*U[k][j];
if(i==j)
L[i][j]=1;
else
L[i][j]=0;
}
else
{
L[i][j]=A[i][j];
for(k=0; k<=j-1; k++)
L[i][j]-=L[i][k]*U[k][j];
L[i][j]/=U[j][j];
U[i][j]=0;
}
}
}
printf("[L]: \n");
for(i=0; i<n; i++)
{
for(j=0; j<n; j++)
printf("%9.3f",L[i][j]);
printf("\n");
}
printf("\n\n[U]: \n");
for(i=0; i<n; i++)
{
for(j=0; j<n; j++)
printf("%9.3f",U[i][j]);
printf("\n");
}
//Y pour calculer X
for(i=0; i<n; i++)
{
Y[i]=B[i];
for(j=0; j<i; j++)
{
Y[i]-=L[i][j]*Y[j];
}
}
for(i=0; i<n; i++)
{
printf("%9.3f",Y[i]);
}
for(i=n-1; i>=0; i--)
{
X[i]= Y[i];
for(j=i+1; j<n; j++)
{
X[i]-=U[i][j]*X[j];
}
X[i]/=U[i][i];
}
printf("\n\n[X]: \n");
for(i=0; i<n; i++)
{
printf("%9.3f",X[i]);
}
printf("\n\nLe determinant de la matrice A est = %f",n);
if (n==0)
printf("\nCette matrice n'a pas d'inverse!\n");
else {
cofactor(A,k);
}
getch();
}
float determinant(float a[20][20],float k)
{
float s=1,det=0,b[20][20];
int i,j,m,n,c;
if (k==1)
{
return (a[0][0]);
}
else
{
det=0;
for (c=0;c<k;c++)
{
m=0;
n=0;
for (i=0;i<k;i++)
{
for (j=0;j<k;j++)
{
b[i][j]=0;
if (i != 0 && j != c)
{
b[m][n]=a[i][j];
if (n<(k-2))
n++;
else
{
n=0;
m++;
}
}
}
}
det=det + s * (a[0][c] * determinant(b,k-1));
s=-1 * s;
}
}
return (det);
}
void cofactor(float num[20][20],float f) //fonction which will calculate the cofactof of matrix
{
float b[20][20],fac[20][20];
int p,q,m,n,i,j;
for (q=0;q<f;q++)
{
for (p=0;p<f;p++)
{
m=0;
n=0;
for (i=0;i<f;i++)
{
for (j=0;j<f;j++)
{
if (i != q && j != p)
{
b[m][n]=num[i][j];
if (n<(f-2))
n++;
else
{
n=0;
m++;
}
}
}
}
fac[q][p]=pow(-1,q + p) * determinant(b,f-1);
}
}
transpose(num,fac,f);
}
/*Finding transpose of matrix*/
void transpose(float num[20][20],float fac[20][20],float r)
{
int i,j;
float b[20][20],inverse[20][20],n;
for (i=0;i<r;i++)
{
for (j=0;j<r;j++)
{
b[i][j]=fac[j][i];
}
}
n=determinant(num,r);
for (i=0;i<r;i++)
{
for (j=0;j<r;j++)
{
inverse[i][j]=b[i][j] / n;
}
}
printf("\n\n\nThe inverse of matrix is : \n");
for (i=0;i<r;i++)
{
for (j=0;j<r;j++)
{
printf("\t%f",inverse[i][j]); //show inverse of the matrix
}
printf("\n");
}
}

Answer 1

There are several issues with your code, but the principal error is that you pass a wrong parameter to
cofactor(A,k);
Here, k is a loop variable that has the value it had after it was used in the code that does the triangular decomposition. (You can see that this value is 1, because only one entry of the matrix is printed.)
You should use the order of the matrices, n:
cofactor(A, n);
In general, you should use a more consistent nomenclature. In main, the order of the matrices is n, in determinant it's k, in cofactor you use the floating-point variable f and in transpose, you use the floating-point variable r. To add to the confusion, n is a float here that represents the determinant. I suggest you use the integer n for the order, local integers i, j and k as loop variables – C99 allows you to define them only for the scope of the loop, e.g. for (int i = 0; ...) – and more or less meaningful names for the floating-point numbers; det for the determinant is good.
Further suggestions:
Don't write explicit loops to print matrices every time; write a function to print a matrix and a function to print a vector instead and call them.
Separate calculating from printing. For example, the code to print the inverse should not be part of (the badly named?) transpose. Instead, transpose should fill a matrix passed in from main, and main should then print that matrix.
Ideally, triangular decomposition and solving the equation should be functions, too. Experience the joys of nicely organised code. :)