correctly (at the end of code). Correct it please.
###CODE
%A=rand(n) , B= rand(n,1)
L = zeros(n,n);
U = zeros(n,n);
%Substituting 1's im the diagonal of U
for i=1:n
U(i,i)=1;
end
%Calculating the 1st column of L
%the first column of L in Crout's factorization is always equal
to the
%first column of A
for i=1:n
L(i,1) = A(i,1);
end
%Calculating the elements in the first row of U(Except U11 which
already
%was already calculated
for i=2:n
U(1,i) = A(1,i) / L(1,1);
end
%calculating the remaining elements row after row.The
elements of L are calculated first
%because they are used for calculating the elements of U
for i = 2:n
for j = 2:i
L(i, j) = A(i, j) - L(i, 1:j - 1) *
U(1:j - 1, j);%%%formula
end
for j = i + 1:n
U(i, j) = (A(i, j) - L(i, 1:i - 1) *
U(1:i - 1, j)) / L(i, i);%%%formula
end
end
L
U
%det(A)=det(L)*det(U).
% As we know, det(U)=1.
%Calculate det(L), which is
%the product of diagonal elements
detA=1;
for i=1:n
detA=detA*L(i,i);
end
detA
% AX=B
% let A=LU => LUX=B
% let UX=Y => LY=B
%forward substitution
Y = zeros(n,1); %Intializing Y
Y(1) = B(1)/L(1,1);
for k=2:n
Y(k) = (B(k) -
L(k,1:k-1)*Y(1:k-1))/L(k,k);
end
Y
%backward substitution
% X = zeros(n,1);
% X(n) = Y(n)/U(n,n);
% for k=n-1
1% x(k) = (Y(k) - U(k,k+1:n)*X(k+1:n))/U(k,k);
%
% end
X