Lösungen

1

x={{x1,x2,x3,x4}};
y=Transpose[{{x1,x2,x3,x4}}];
a1={1,0,1,2};
a2={2,2,2,3};
a3={3,2,1,-1};
a4={-1,-2,1,1};
m={a1,a2,a3,a4};
Print[{a1,a2,a3,a4}//MatrixForm];
b=Transpose[{{-1,2,3,3}}];
Print[Inverse[m].b//MatrixForm];
Solve[m.y==b,x[[1]]]

Inverse[m]//MatrixForm

x={{x1,x2,x3,x4,x5}};
y=Transpose[{{x1,x2,x3,x4,x5}}];
a1={1,0,1,2,5};
a2={2,2,2,3,5};
a3={3,2,1,-1,5};
a4={-1,-2,1,1,5};
m={a1,a2,a3,a4};
Print[{a1,a2,a3,a4}//MatrixForm];
b=Transpose[{{-1,2,3,3}}];
Solve[m.y==b,x[[1]]]

x={{x1,x2,x3,x4}};
y=Transpose[{{x1,x2,x3,x4}}];
a1={1,0,1,2};
a2={2,2,2,3};
a3={3,2,1,-1};
a4={5,2,5,9};
a5={-1,-2,1,1};
m={a1,a2,a3,a4,a5};
Print[{a1,a2,a3,a4,a5}//MatrixForm];
b=Transpose[{{-1,2,3,3,10}}];
Solve[m.y==b,x[[1]]]

2

a={{1,0,1},{2,α,2},{2,2,3}}; Inverse[a]

y={x1,x2,x3};
b1={-1,β,3};
Solve[a.y==b1,y]

α=2 keine Lösung. Unendlich viele Lösungen kommt nicht vor, da Zähler und Nenner nie alle gleichzeitig 0.

2

a={{1,0,1},{2,α,2},{2,2,3}}; Inverse[a]

y={x1,x2,x3};
b2={-1,2,γ};
Solve[a.y==b2,y]

α=2 keine Lösung. Unendlich viele Lösungen kommt nicht vor, da Zähler und Nenner nie alle gleichzeitig 0.

3

a={1,1,0,4}; 
b={0,0,0,-1+u}; 
c={1,2,3,6};
d={0,0,4,1};
M=
Transpose[{a,b,c,d}]; M//MatrixForm

Det[M]

Det[M]/.u->1

4

M1= {{2,-1,6},{4,4,1},{-1,5,3}};
D1= {{1,0,0},{0,2,0},{0,0,3}};

A= Transpose[M1].D1.Inverse[Transpose[M1]];
A//MatrixForm

A//N//MatrixForm

A//Transpose//MatrixForm

A//Transpose//N//MatrixForm

Inverse[A]//MatrixForm

Inverse[A]//N//MatrixForm

Solve[A.{x1,x2,x3}=={1,0,0},{x1,x2,x3}]

Solve[A.{x1,x2,x3}=={1,0,0},{x1,x2,x3}]//N

5

Remove[x,y,z]

g[t_]:={5,8,11}+t{2,-3,5};

g[t].{2,-3,5}==4

Solve[g[t].{2,-3,5}==4,{t}]//Flatten

g[-37/38]

v={5,8,11}-g[-37/38];
v1=v/Norm[v]

v1//N

p1=g[-37/38]+10v1

p1//N