Beispiel 6.2

A={{1,I,1},{1,1,I},{0,1,-1}}

MatrixRank[A]

Beispiel 6.3

A={{0,2},{1,-2},{2,3}}

MatrixRank[A]

Basiswechsel

Inverse[{{1,0,0},{0,1,1},{0,0,2}}]

Inverse[{{1,0,0},{0,1,1},{0,0,2}}].{{2,0},{0,1},{1,1}}.{{2,0},{3,1}}

Verkettung

f[{x_,y_,z_}]:={3x+2y,4x-y-z}

A={{3,2,0},{4,-1,-1}}

g[{u_,v_}]:={3u+2v,4u-v,u+v,u-v}

B={{3,2},{4,-1},{1,1},{1,-1}}

Expand[g[f[x,y,z]]]

B.A

Übung 6.4

M={{3+I,1,0},{0,1-I,1}}

Solve[M.{{x},{y},{z}}==0,{x,y,z}]

NullSpace[M]

Übung 6.5

M={{1,I},{2,0},{0,I}}

f[{x_,y_}]:=Module[{j,a1,a2,b,res},
a1={1,0};a2={1,-1};sol=Solve[{x,y}==λ a1+μ a2,{λ,μ}];
M={{1,I},{2,0},{0,I}};
b[1]={1,0,0};
b[2]={0,I,1};
b[3]={0,0,1};
res=M.{λ,μ}/.sol[[1]];Sum[res[[j]]*b[j],{j,1,3}]
]

f[{-1,2}]

M={{-3,-3I},{2I,-2},{4,1+4I}}

f[{x_,y_}]:=Module[{j,a1,a2,b,res},
a1={1,0};a2={0,I};sol=Solve[{x,y}==λ a1+μ a2,{λ,μ}];
M={{-3,-3I},{2I,-2},{4,1+4I}};
b[1]={1,0,0};
b[2]={0,1,I};
b[3]={1,0,1};
res=M.{λ,μ}/.sol[[1]];Sum[res[[j]]*b[j],{j,1,3}]
]

f[{-1,2}]

Beispiel 6.14

M={{3,2,1,0},{1,2,-1,1}}

Solve[M.{{(Subscript[x, 1])},{(Subscript[x, 2])},{(Subscript[x, 3])},{(Subscript[x, 4])}}==0,{(Subscript[x, 1]),(Subscript[x, 2]),(Subscript[x, 3]),(Subscript[x, 4])}]

NullSpace[M]

Beispiel 6.14

Solve[{2(Subscript[x, 2])+(Subscript[x, 3])==2,(1/2)(Subscript[x, 1])+3(Subscript[x, 2])==2,5(Subscript[x, 1])+2(Subscript[x, 3])==1},{(Subscript[x, 1]),(Subscript[x, 2]),(Subscript[x, 3])}]

A={{0,2,1},{(1/2),3,0},{5,0,2}}

NullSpace[A]

LinearSolve[A,{2,2,1}]