Matlab code for finding determinant and inverse of a matrix without using in built function?

Answer 1

To find the determinant of a matrix in MATLAB without using built-in functions, you can implement a recursive function that utilizes cofactor expansion. For the inverse, you can use the adjugate method, which involves calculating the matrix of minors, cofactors, and then transposing it before dividing by the determinant. Here’s a simple illustration:

function detA = myDet(A)
    n = size(A,1);
    if n == 1
        detA = A(1,1);
    elseif n == 2
        detA = A(1,1)*A(2,2) - A(1,2)*A(2,1);
    else
        detA = 0;
        for j = 1:n
            detA = detA + ((-1)^(1+j)) * A(1,j) * myDet(A(2:end,[1:j-1,j+1:end]));
        end
    end
end

function invA = myInverse(A)
    detA = myDet(A);
    if detA == 0
        error('Matrix is singular, cannot compute inverse');
    end
    adjA = zeros(size(A));
    for i = 1:size(A,1)
        for j = 1:size(A,2)
            minor = A; minor(i,:) = []; minor(:,j) = [];
            adjA(j,i) = ((-1)^(i+j)) * myDet(minor); % Cofactor
        end
    end
    invA = adjA / detA; % Divide by determinant
end

Make sure to call myInverse(A) to get the inverse and myDet(A) for the determinant of matrix A.