Lösungen/Solutions/
B1S2Ue/Ex3

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

vecLen[a_] := Sqrt[a . a]

Ueb/Ex 1      W

a

g1 = (3 x  +  4 y  ==  
            7);
g2 =  (α x  +  9 y  ==  6);

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

Solve[{g1, g2}, {x, y}] /.  α -> 27/4  //  
      Flatten

Solve[{g1, g2 /.  α -> 27/4}, {x, y}]  //  
      Flatten

b

Solve[{g1, g2}, {x, y}] /.  α -> 2  //  
      Flatten

c

s = Flatten[Solve[{g1, g2}, {x, y}]][[1]]

x[α_] := x /. s;   x[α]

Ueb/Ex 2      W

a = {5, 2};  b = {3, 4};
m = Transpose[{a, b}];  MatrixForm[m]

m1 = Transpose[{a, -b}];  MatrixForm[m1]

A1 = Det[m]

A2 = Det[m1]

A3 = 1/2 Det[m]

Ueb/Ex 3      W

a0 = {10, 0};  a1 = {10 Cos[Pi/10],  10 Sin[Pi/10] }

N[a1]

m3 = Transpose[{a0, a1}];  MatrixForm[m3]

A1 = 1/2 Det[m3]

N[A1]

s = 20 A1

N[s]

A = 10^2 Pi  // N

Ueb/Ex 4      W

b = {1, 4}; 
a1 = {3, 3};  a2 = {4, 1};  a3 = {4, 0};  a4 = {3, -2};  
    a5 = {1, -2};

a = a1 + a2 + a3 + a4 + a5

m = Transpose[{a, b}];  MatrixForm[m]

A = Det[m]

A = A1+A2+A3+A4+A5 = 60