variables not being saved?

Hi @Olivia,

I have updated both functions. The updated provided code consists of two functions: lumine and lusolver.The lumine function performs the LU decomposition of a given coefficient matrix A and returns the lower matrix L and upper matrix U. It follows the following steps:Checks if the matrix A is square. If not, it throws an error and also if the matrix A is singular. If yes, it throws an error.Then, it initializes L as an identity matrix and U as A.Performs the LU decomposition using nested loops.Updates the rows of U and store the factors in L and sets the diagonal elements of L to 1.The lusolver function takes the lower matrix L, upper matrix U, and a vector B as inputs and solves the system of linear equations using LU decomposition. It follows the following steps:Initializes vectors y and x with zeros., performs forward substitution to solve Ly = B and backward substitution to solve Ux = y. Afterwards, returns the solution vector x.

Lumine Function

    function [L,U] = lumine(A)

    % lumine: LU decomposition

    % input:

    % A = coefficient matrix

    % output:

    % L = lower matrix

    % U = upper matrix

    [m,n] = size(A); % defines m and n

    if m ~= n  % checks if the matrix is square

        error('Matrix A must be square');

    end 

    if det(A) == 0 % checks if the matrix is singular

        error('Matrix cannot be singular');

    end

    % Initialize L as an identity matrix and U as A

    L = eye(n); 

    U = A;

    for k = 1:n % starts at position 1, goes to the last column
        for i = k+1:n % starts at row after k, 
         goes to second to last row

            factor = U(i,k)/U(k,k); % defines factor

            U(i,k:n) = U(i,k:n) - factor * U(k,k:n); 
            % update row i of U

            L(i,k) = factor; % store factor in L

        end

     end

    % The diagonal of L should be set to 1 (identity property)
    for i = 1:n

        L(i,i) = 1; 

     end

     end

     q = [2 1 -1; 4 0 2; 8 1 0];

     [L,U] = lumine(q); 
     % Now both L and U will be defined correctly.

     disp('Matrix L:');

     disp(L); % Display the lower matrix L

     disp('Matrix U:');

     disp(U); % Display the upper matrix U

Lusolver function

    function solution = lusolver(L, U, B)

    n = length(B);

    y = zeros(n, 1);

    x = zeros(n, 1);

    % Forward Substitution (Ly = B)

    for i = 1:n

        y(i) = B(i) - L(i,1:i-1)*y(1:i-1);

    end

    % Backward Substitution (Ux = y)

    for i = n:-1:1

        x(i) = (y(i) - U(i,i+1:n)*x(i+1:n)) / U(i,i);

    end

    solution = x;

    end

    B = [-1;-2;-3];

    solution = lusolver(L,U,B);

    disp(solution);

Please see attached.

Hope, after this detailed explanation and provided two updated functions, your problem is resolved. Please let me know if you still have any further questions.