Lösungen/Solutions/F1S2Ue/Ex3

L=Lektion/Leçon-- Sprechstunde/heures de consultation
W=Work/Arbeit/Travail
A  =Anhang/  Annexe / Appendice

Remove["Global`"]

Aufgabe/ Problème 1

g1 =  (λ x  -  5 y  +  6 z  +  7 w  ==  
            8 );
g2 =  (4 x  -  8 y  +  9 z  +  1 w  ==  
            1 );
 g3 =  (1 x  +  1 y  -  1  z  +  1 w  ==  
            0 );

a

Solve[{g1, g2, g3}, {x, y, z}] /. λ -> 3    //  
      Flatten

w  ist Parameter!  /  w est paramètre!

b

Solve[{g1, g2, g3}, {x, y, z}]  //  Flatten

Solve[{g1, g2, g3}, {x, y, z}]  /. λ -> 7  //  
      Flatten

λ = 7  !

c

Clear[λ]; λ

Ord=4, Dim = 2 -> Rang = 2     
->  λ so wählen, dass g1= μ1 g2 +μ2 g3 :  /  ->  Choisir λ de façon que  g1= μ1 g2 +μ2 g3 :

Solve[{λ, -5, 6, 7, 
          8} ==  μ1 {4, -8, 9, 1, 1} +  μ2 {1, 1, -1, 1, 
              0}, {λ, μ1, μ2}]

Keine Lösung /  Pas de solution

Aufgabe 2

Identische Abbildung / Application identique

Remove["Global`*"];    
Remove["Global`@*"];

w[s_, t_] := s + I t;

a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -10, 
                10}]], {s, -10, 10}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -10, 
                10}]], {s, -10, 10}];
Show[a, b];

Remove["Global`*"];    
Remove["Global`@*"];

w[s_, t_] := (s + I t)^2;

a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -5, 5}]], {s, -20, 
            20}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -5, 5}]], {s, -20, 
            20}];
Show[a, b];

Remove["Global`*"];    
Remove["Global`@*"];

w[s_, t_] := (1/(1 + s + I t));
a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -5, 5}]], {s, -20, 
            20}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -5, 5}]], {s, -20, 
            20}];
Show[a, b];