Lösungen/Solutions/F1S2Ue/Ex10

L=Lektion/Leçon-- Sprechstunde/heures de consultation
W=Work/Arbeit/Travail
A  =Anhang/  Annexe / Appendice

Remove["Global`"]

m[x_] := MatrixForm[x]

Aufgabe/ Problème 1

A = {{1, 1, 1}, {0, 1, 1}, {0, 0, 1}};  m[A]

At = Transpose[A]; m[At]

A2 = A . A; m[A2]

Ai = Inverse[A];  m[Ai]

A2i = Inverse[A2];  m[A2i]

Ai2 = Ai . Ai; m[Ai2]

A2Ai = Inverse[A2 + A];  m[A2Ai]

Aufgabe/ Problème 2

X = 
      Inverse[Transpose[
            A]] . (Inverse[A] . (A . A - A + Transpose[A]));  
    m[X]

Aufgabe/ Problème 3

a = {1, 2};  b = {2, -3};  
    B = {{1, 0}, {2, 2}};
v = 2 a  -  b

v2 = a + b

Ba = B . a

Bb = B . b

Bv = B . v

Bv2 = B . v2

p[z_] := Point[{z[[1]], z[[2]]}];  p[b]

<< Graphics`Arrow`

ar[z_] := Arrow[{0, 0}, z]

Show[
        Graphics[
{PointSize[0.03], 
p[
              a], p[b], p[v], p[Ba], p[Bb], p[Bv], p[v2], 
            p[Bv2], 
ar[a], ar[b], ar[v], ar[Ba], ar[Bb], 
            ar[Bv], ar[v2], 
            ar[Bv2], 
Line[{{-1, 0}, {5, 0}}], 
            Line[{{0, -1}, {0, 5}}]
}], 
        AspectRatio -> 01];