Matrizen

A=Array[a,{4,6}]

Transpose[A]

3A

X={{(Subscript[x, 1])},{(Subscript[x, 2])},{(Subscript[x, 3])},{(Subscript[x, 4])},{(Subscript[x, 5])},{(Subscript[x, 6])}}

A.X

B=Array[b,{4,6}]

A+B

A.B

Transpose[A].B

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

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

A.B

B.A

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

B={{5,9,2},{0,0,1},{1,-1,-2},{-2,3,4}}

A.B

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

B={{1},{I},{-1}}

A.B

B.A

A={{a,1},{3,0}}

Inerse Matrizen

Inverse[A]

Inverse[A].A

A.Inverse[A]

X={{(Subscript[x, 1])},{(Subscript[x, 2])}}

B={{(Subscript[b, 1])},{(Subscript[b, 2])}}

Solve[A.X==B,{(Subscript[x, 1]),(Subscript[x, 2])}]

Inverse[A].B

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

Inverse[A]

Aerw=Transpose[Join[Transpose[A],IdentityMatrix[3]]]

RowReduce[Aerw]

A={{Cos[ϕ],-Sin[ϕ]},{Sin[ϕ],Cos[ϕ]}}

Inverse[A]

Inverse[A]//Simplify

Aerw=Transpose[Join[Transpose[A],IdentityMatrix[2]]]

RowReduce[Aerw]

RowReduce[Aerw]//Simplify

A={{a,1},{3,0}}

Inverse[A]

Lösen von Gleichungssystemen mit Matrizen

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

b={{2},{2},{1}}

Aerw=Transpose[Join[Transpose[A],Transpose[b]]]

RowReduce[Aerw]

Inverse[A].b

A={{2,3,3},{1,5,(5/2)},{7,21,(27/2)}}

b={{-5},{0},{-10}}

Aerw=Transpose[Join[Transpose[A],Transpose[b]]]

RowReduce[Aerw]

Inverse[A].b

A={{(2/3),4,-(3/2)},{(1/2),-2,3},{(7/6),(26/3),-4}}

b={{5},{-3},{-1}}

Aerw=Transpose[Join[Transpose[A],Transpose[b]]]

RowReduce[Aerw]

Inverse[A].b