Lösungen/Solutions/E1S2AlUe/Ex3a

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

Remove["Global`"]

Aufgabe 1

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

a

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

b

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

λ = 7  !

c

Clear[λ]; λ

λ so wählen, dass g1= μ1 g2 +μ2 g3 :

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

Keine Lösung

Aufgabe 2

g11 = {1  x + 1  y + 1  z == 1};
g21 = {1  x + 2  y + 3  z == 2};
g31 = {1  x + 4  y + 9  z == 3};
g41 = {3  x + 7  y + 13  z == 6};
{g11, g21, g31, g41} //  MatrixForm

Solve[Flatten[{g11, g21, g31, g41}], {x, y, z}]

Aufgabe 3

Clear[x, y, z, g1, g2, g3, g4]

g12 = (1 x  +  1 y  +  1 z  ==  
            1);
g22 = (1 x  +  2 y  +  3 z  ==  
            2);
g32 = (2  x  +  3 y  +  4 z  ==  
            3);
g42 = (0  x  +  1 y  +  2 z  ==  1);

Solve[{g12, g22, g32, g42}, {x, y, z}] // Flatten

Aufgabe 4

a = {5, -1, 2};  b = {5, -1, 3};  
    c = {-1, 2, 5};
V = Det[{a, b, c}]

{a, b, c} //  MatrixForm

Transpose[{a, b, c}] //  MatrixForm

Aufgabe 5

vLen[v_] := Sqrt[v . v]

r01 = {5, -1, 2};  a1 = {5, -1, 3};
r02 = {-1, 2, 5};  b1 = {4, -1, 4};
d = Abs[Det[{a1, b1, r02 - r01}]/vLen[Cross[a1, b1]]]

d // N