Kern und Bild einer linearen Abbildung

Kurz Programm Bestimmung Bild/Kern R^4

---Kern der Abbildung Ax=0 A:={{1,1,-2,-6},{1,-1,-4,2},{2,1,-5,-8},{3,2,-7,-14}} nc:=Element( Dimension(A),1) nr:=Element( Dimension(A),2) n:=MatrixRank(A) X:=Take({{x1},{x2},{x3},{x4},{x5},{x6},{x7},{x8},{x9}},1,nr); A_{Gauss}:=ReducedRowEchelonForm(A) ker_A:=Solutions(Flatten(A_{Gauss} X),Flatten(X)) Basis_{Kern}:=Transpose(Sequence(Flatten(Substitute(ker_f,Flatten(X) = Flatten(Take(Identity(nr),k,k)))),k,1,nr) \ {Sequence(0,k,1,nr)}) Pivots:=RemoveUndefined(Sequence(IndexOf(Flatten(Element(Identity(nc),j)), Transpose(A_{Gauss})),j,1,nc)) Basis_{img}:=Transpose(Sequence(Element(Transpose(A), Pivots( j)),j,1,Length(Pivots) )) --- Anpassen A: Copy to https://www.geogebra.org/classic#cas

Darstellende Matrix der Abbildung.