  A = [1 2 3;4 6 5;7 8 9]; b = [1;1;2;]; % Initialize matrix and vector
  x = A\b, % solve linear system of equations \texttt{A*x=b}
  x = linsolve(A,b); % An alternative way to write the backslash
  r = A*x-b, % Test, whether a solution was found
  A = [1 2 3;4 5 6;7 8 9] % $3\times 3$-matrix with rank 2 (\textbf{not regular}!)
  z = A\b, % In exact arithmetic this linear system has \textbf{no solution}
  % However. MATLAB computes a solution, because the tiny perturbations 
  % introduced by \emph{roundoff} make it believe that the linear system 
  % has a unique solution.
  r = A*z-b, % test pseudo-solution: not quite a solution