function X_rec = recoverData(Z, U, K)
    %% RECOVERDATA Recovers an approximation of the original data when using the 
    %projected data
    %   X_rec = RECOVERDATA(Z, U, K) recovers an approximation the 
    %   original data that has been reduced to K dimensions. It returns the
    %   approximate reconstruction in X_rec.
    %

    % You need to return the following variables correctly.
    X_rec = zeros(size(Z, 1), size(U, 1));

    % ====================== YOUR CODE HERE ======================
    % Instructions: Compute the approximation of the data by projecting back
    %               onto the original space using the top K eigenvectors in U.
    %
    %               For the i-th example Z(i,:), the (approximate)
    %               recovered data for dimension j is given as follows:
    %                    v = Z(i, :)';
    %                    recovered_j = v' * U(j, 1:K)';
    %
    %               Notice that U(j, 1:K) is a row vector.
    %               
    X_rec = U(:, 1:K) * Z';
    X_rec = X_rec';
end
