Lösungen

0. Materialbereitstellung

Di1 = {{1,0},{0,-2}}; 
Dr21 = {{3,5},{0,1}}; 
Dr22 = {{4,0},{12,6}};
Map[MatrixForm,{Di1,Dr21,Dr22}]

A2 = {{1,2},{1,-1}}; 
B2 = {{3,5},{4,7}}; 
C2 = {{4,1},{5,6}};
Map[MatrixForm,{A2,B2,C2}]

A3 = {{1,2,3},{1,-1,0},{-2,1,5}}; 
B3 = {{3,5,1},{4,7,9},{3,2,6}}; 
C3 = {{4,1,3},{5,6,5},{5,8,8}};
Map[MatrixForm,{A3,B3,C3}]

A4 = {{1,2,3,4},{1,-1,0,1},{-2,1,5,2},{-2,2,1,5}}; 
B4 = {{3,5,1,1},{4,7,9,5},{3,2,6,8},{5,6,5,1}}; 
Map[MatrixForm,{A4,B4}]

C4 = {{3,5,1,1},{3,5,2,1},{3,4,1,1},{4,7,9,5}}; 
D3 = {{1,2,2},{1,-1,-1},{-2,1,1}};  
Map[MatrixForm,{C4,D3}]

VdM4 = {{1,2,3,4},{2,3,4,5},{-3,-2,-1,0},{3,4,5,6}}; 
NVdM5 = {{1,2,3,4,5},{2,3,4,5,6},{-3,-2,-1,0,1},{3,4,5,6,7},{3,3,3,3,3}};
Map[MatrixForm,{VdM4,NVdM5}]

Programme für unten:

detOut[M_]:=Print[Det[ToExpression[M]], " = ", "det(", M, ");"];
invOut[M_]:=Print[MatrixForm[Inverse[ToExpression[M]]], " = ", "Inverse(", M, ");"];
invNOut[M_]:=Print[MatrixForm[N[Inverse[ToExpression[M]]]], " = ", "Inverse(", M, ");"];
detInvOut[M_]:=Print[Det[Inverse[ToExpression[M]]] Det[ToExpression[M]], " = ", "det(", "Inv(", M, "))", ";" ];
detInvKontrOut[M_]:=Print[Det[Inverse[ToExpression[M]]] Det[ToExpression[M]], " = ", "det(", "Inv(", M, "))", "*",  "det(", M, ")", ";" ];

1. Determinanten von A4, B4, C4

Selbststudium nach Uebungsblatt

2. Determinanten von A4, B4, C4

Map[detOut,{"A4","B4","C4"}];

3. Inverse von Di2, Dr21, Dr22, A2, B2, C2, A3, B3, C3, A4, B4, C4

Map[detOut,{"Di1", "Dr21", "Dr22", "A2", "B2", "C2", "A3", "B3", "C3", "A4", "B4", "C4"}];

Map[invOut,{"Di1", "Dr21", "Dr22", "A2", "B2", "C2", "A3", "B3", "C3", "A4", "B4", "C4"}];

Map[invNOut,{"Di1", "Dr21", "Dr22", "A2", "B2", "C2", "A3", "B3", "C3", "A4", "B4", "C4"}];

Map[detInvKontrOut,{"Di1", "Dr21", "Dr22", "A2", "B2", "C2", "A3", "B3", "C3", "A4", "B4", "C4"}];

4. Inverse von D3, VdM4, NVdM5

Map[detOut,{"D3", "VdM4", "NVdM5"}];

Map[invOut,{"D3", "VdM4", "NVdM5"}];

Keine der Inversen existiert!

5. Matlabanwendung

Arbeit mit MATLAB - führt zu obigen Resultaten.

6. Jacobi

A={{1,0.1,0,0,0,0},{0.2,1,0.1,0,0,0},{0,0.2,1,0.1,0,0},{0,0,0.2,1,0.1,0},{0,0,0,0.2,1,0.1},{0,0,0,0,0.2,1}};
A//MatrixForm

X[1]={{1,0.1,0.1,0.1,0.1,0.1},{0.2,1,0.1,0.1,0.1,0.1},{0.1,0.2,1,0.1,0.1,0.1},{0.1,0.1,0.2,1,0.1,0.1},{0.1,0.1,0.1,0.2,1,0.1},{0.1,0.1,0.1,0.1,0.2,1}}; X[1]//MatrixForm

X[n_]:=IdentityMatrix[6]-(A-IdentityMatrix[6]).X[n-1]

X[2]//MatrixForm

X[3]//MatrixForm

X[4]//MatrixForm

X[5]//MatrixForm

X[6]//MatrixForm

X[7]//MatrixForm

Inverse[A]//MatrixForm

Fehler nach 7 Schritten (Beachte die nachstehende Differenz):

Round[(Inverse[A]-X[7]) 100000] / 100000.//MatrixForm