Here is the MATLAB program to find the determinant of a nxn matrix by the cofactor method. I had to develop a separate function for each size of the matrix. I may be wrong about having to do that – is there a single function that can be written to find the determinant of any nxn matrix using the cofactor method?

## Contents

## Finding the determinant of a matrix using the cofactor method

and comparing the CPU time with MATLAB det function

clc
clear all
format long
n=6;
A=rand(n,n);
tbegin=cputime;
detval=det6(A);
TimeCrammer=cputime-tbegin;
tbegin=cputime;
MatlabDet=det(A);
TimeMatlab=vpa(cputime-tbegin,32);
fprintf('Size of matrix is %gx%g \n',n,n)
fprintf('Determinant by cofactor method = %g \n', detval)
fprintf('Determinant by Matlab function = %g \n', MatlabDet)
fprintf('Approximate CPU time taken by cofactor method = %g seconds\n',TimeCrammer)
fprintf('Approximate CPU time taken by MATLAB function = %e seconds\n',TimeMatlab)

## Individual functions for determinant of a nxn matrix

function detvalue=det2(A)
detvalue=A(1,1)*A(2,2)-A(1,2)*A(2,1);
end
function detvalue=det3(A)
n=3;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det2(A(2:n,[1:j-1 j+1:n]));
end
end
function detvalue=det4(A)
n=4;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det3(A(2:n,[1:j-1 j+1:n]));
end
end
function detvalue=det5(A)
n=5;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det4(A(2:n,[1:j-1 j+1:n]));
end
end
function detvalue=det6(A)
n=6;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det5(A(2:n,[1:j-1 j+1:n]));
end
end
function detvalue=det7(A)
n=7;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det6(A(2:n,[1:j-1 j+1:n]));
end
end
function detvalue=det8(A)
n=8;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det7(A(2:n,[1:j-1 j+1:n]));
end
end
function detvalue=det9(A)
n=9;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det8(A(2:n,[1:j-1 j+1:n]));
end
end
function detvalue=det10(A)
n=10;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det9(A(2:n,[1:j-1 j+1:n]));
end
end
function detvalue=det11(A)
n=11;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det10(A(2:n,[1:j-1 j+1:n]));
end
end
function detvalue=det12(A)
n=12;
detvalue=0;
for j=1:1:n
detvalue=detvalue+(-1)^(j+1)*A(1,j)*det11(A(2:n,[1:j-1 j+1:n]));
end
end

Size of matrix is 6x6
Determinant by cofactor method = -0.0431
Determinant by Matlab function = -0.0431
Approximate CPU time taken by cofactor method = 0.140625 seconds
Approximate CPU time taken by MATLAB function = 1.562500e-02 seconds

The above mfile can be downloaded here.