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% Aufgabe 1
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 A = [ 0  1  0  0;
       0 -1  0  0;
       1  0  2 -2;
      10 11 12 13]

 % (a) Rang(A) = 3 <=> mindestens ein Eigenwert ist
 %     gleich Null => System ist grenzstabil oder 
 %     instabil. Unendlich viele Ruhelagen.
 rank(A)

 % (b) System ist instabil (EW: {-1, 0, 5, 10}, siehe auch (a))
 [ReEV,EW]=eig(A)
 LiEV = inv(ReEV)

 % (c) EW sind paarweise verschieden => diagonalaehnlich <=> n lin. unabh. EV
 T=LiEV*A*ReEV

 % (d)
 expm(A*2)*[1 1 1 1]'