Lösungen/Solutions/E1S2AlUe/Ex5

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

Remove["Global`"]

Aufgabe 1

a

g = {1 x  + 2  y + 0  z + 4  w == 0, 
          0  x + 1  y + 0  z + 0  w == 1, 
          1  x + 0  y + 3  z + 6  w == 2,  
          0  x + 1  y + 5  z + 1  w == 
            3}; 
Solve[g, {x, y, z, w}]

b

Remove[a]

Ma = {{1, 2, 0, a}, {0, 1, 0, 0}, {1, 0, 3, 6}, {0, 1, 5, 1}};  
    MatrixForm[Ma]

Aufgabe 2

a

M4 = {{1, 2, 0, 4}, {0, 1, 0, 0}, {1, 0, 3, 6}, {0, 1, 5, 1}};  
    MatrixForm[M4]

Det[M4]

b

Remove[a]

Ma = {{1, 2, 0, a}, {0, 1, 0, 0}, {1, 0, 3, 6}, {0, 1, 5, 1}};  
    MatrixForm[Ma]

Aufgabe 3

a = {1, -2, 3};  b = {1, 1, 2};  
    c = {3, y, 4};
M = Transpose[{a, b, c}]; MatrixForm[M]

Det[M]

Solve[Det[M] == 0, {y}] // Flatten

Aufgabe 4

M1 = {{1, 2, 1, 3, 5}, {-1, 4, 1, 2, 4}, {1, 8, 1, 1, 6}, {0, 16, 
          1, 0, 11}, {-1, 32, 1, -1, 8}};  MatrixForm[M1]

M2 = {{-1, 2, 1, 3, 5}, {1, 4, 1, 2, 4}, {-1, 8, 1, 1, 6}, {0, 
          16, 1, 0, 11}, {1, 32, 1, -1, 8}};  MatrixForm[M2]

Det[M1 + M2]

MatrixForm[M1 + M2]