Lösungen/Solutions/E1S2AlUe/Ex12

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

Remove["Global`"]

m[x_] := MatrixForm[x]

vecLen[u_] := 
        Sqrt[Flatten[u] . Flatten[u]];
vecLen[{{u1}, {u2}, {u3}}]

Aufgabe 1

Matrix

mD = {{1, 0}, {0, -2}};  m[mD]

mX = Transpose[{{2, -1}, {3, 2}}];  m[mX]

A = mX . mD . Inverse[mX];  m[A]

Punkte abbilden, Rechnung

v[p_] := Transpose[{p}]

P[1] = {1, 2};
P[2] = {2, -4};
P[3] = {-2, -1};

Table[m[ v[P[k]]], {k, 1, 3}]

Table[m[A .  v[P[k]]], {k, 1, 3}]

B[k_] := Flatten[ A . v[P[k]]];  B[1]

Punkte abbilden, Zeichnung

Show[
        Graphics[
{PointSize[
              0.03], 
Point[P[1]], Point[P[2]], 
            Point[P[3]], 
Line[{P[1], P[2]}], 
            Line[{P[1], P[3]}], 
            Line[{P[3], P[2]}], 
Point[B[1]], Point[B[2]], 
            Point[B[3]], 
Line[{B[1], B[2]}], 
            Line[{B[1], B[3]}], 
            Line[{B[3], 
                B[2]}], 
Line[{{-2, 0}, {2, 0}}], 
            Line[{{0, -2}, {0, 2}}], 
Line[{{0, 
                  0}, {2, -1}}], 
Line[{{0, 0}, {3, 
                  2}}]
}], 
        AspectRatio -> 0.5];

<< Graphics`Arrow`

Show[
        Graphics[
{PointSize[
              0.03], 
Point[P[1]], Point[P[2]], 
            Point[P[3]], 
Line[{P[1], P[2]}], 
            Line[{P[1], P[3]}], 
            Line[{P[3], P[2]}], 
Point[B[1]], Point[B[2]], 
            Point[B[3]], 
Line[{B[1], B[2]}], 
            Line[{B[1], B[3]}], 
            Line[{B[3], 
                B[2]}], 
Line[{{-2, 0}, {2, 0}}], 
            Line[{{0, -2}, {0, 2}}], 
Line[{{0, 
                  0}, {2, -1}}], 
Line[{{0, 0}, {3, 
                  2}}], 
Arrow[P[1], B[1]], 
            Arrow[P[2], B[2]], Arrow[P[3], B[3]]
}], 
        AspectRatio -> 0.5];