 0 2 -13]
b = [ 4; 9; 29; 40 ]
%% 
% It has a perfectly good solution, obtainable through LU factorization.
%%
[L,U] = lufact(A);
x = backsub( U, forwardsub(L,b) )
%% 
% If we swap the second and fourth equations, nothing essential is changed, 
% and MATLAB still finds the solution.
%%
A([2 4],:) = A([4 2],:);  
b([2 4]) = b([4 2]); 
x = A\b
%% 
% However, LU factorization fails.
%%
[L,U] = lufact(A);
L
##### SOURCE END #####
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