Create an m-file mydet.m to compute the determinant of a square matrix using rec

ID: 3109286 • Letter: C

Question

Create an m-file mydet.m to compute the determinant of a square matrix using recursion. The function should take as input a matrix A and return its determinant d. Test your code on the following matrix and use det (middot) to check your answer. B = [-7 4 -2 -8 6 8 7 2 3 -1 6 -6 6 0 -7 -6 2 -9 2 0 -9 6 7 5 0] Approach: Computing the determinant using recursion: The determinant of an n times n square matrix A can be calculated in the following way: det(A) = a_11 C_11 + a_12 + ... + a_1n C_1n where C_1j = (-1)^1 + j det(M_1j) and the (n - 1) times (n - 1) submatrix M_1j of A throws out row 1 and column j.

Explanation / Answer

#include<iostream.h>
#include<conio.h>
#include<math.h>
#include<process.h>

void main()
{
int determinant(int[5][5],int);// FUNCTIONS
void read(int[5][5],int);
void print(int[5][5],int); // PROTOYPES
int a[5][5],l,n;
int result;
l1:clrscr();
cout<<"

ENTER ORDER OF MATRIX(MAX. OF 4X4):";
cin>>l>>n;
if(l!=n)
{ //TESTING CONDITION
cout<<"

SORRY!!!!! ONLY SQUARE MATRIX";
goto l1;
}
read(a,n);
result = determinant(a,n);
print(a,n);
cout<<"

THE DETERMINANT OF THE ABOVE MATRIX IS:"<<result;
getch();
}

void read(int b[5][5],int m) //FUNCTION FOR READING MATRIX
{
cout<<"

ENTER "<<m*m<<" ELEMENTS OF MATRIX(ROW-WISE):";
for(int i=0;i<m;i++)
for(int j=0;j<m;j++)
cin>>b[i][j];
}

void print(int b[5][5],int m)
{
clrscr(); //FUNCTION FOR PRINTING MATRIX
cout<<"

MATRIX IS :-

";
for(int i=0;i<m;i++)
{
cout<<"
";
for(int j=0;j<m;j++)
cout<<" "<<b[i][j];
}
}

int determinant(int b[5][5],int m) //FUNCTION TO CALCULATE
DETERMINANT
{
int i,j,sum = 0,c[5][5];
if(m==2)
{ //BASE CONDITION
   sum = b[0][0]*b[1][1] - b[0][1]*b[1][0];
   return sum;
}
for(int p=0;p<m;p++)
{
int h = 0,k = 0;
for(i=1;i<m;i++)
{
   for( j=0;j<m;j++)
   {
   if(j==p)
   continue;
   c[h][k] = b[i][j];
   k++;
   if(k == m-1)
   {
       h++;
       k = 0;
   }

}
}

sum = sum + b[0][p]*pow(-1,p)*determinant(c,m-1);
}
return sum;
}

using the code written above we can check the det of the given matrix is -77871

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Create an m-file mydet.m to compute the determinant of a square matrix using rec

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