Lösungen/Solutions/F1S2Ue/Ex12

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

Remove["Global`"]

m[x_] := MatrixForm[x]

Aufgabe/ Problème 1

A1 = {{1, -1}, {1, 1}};  m[A1]

a

ew1 = Eigenvalues[A1]

Keine reellen Eigenwerte/ Pas de valeurs propres réelles!

b

ev1 = Eigenvectors[A1]

m[Transpose[ev1]]

Aufgabe/ Problème 2

A2 = {{1, 2, 3, 4}, {0, 5, 6, 7}, {0, 0, 8, 9}, {0, 0, 0, 10}};  
    m[A2]

a

ew2 = Eigenvalues[A2]

b

ev2 = Eigenvectors[A2]

m[Transpose[ev2]]

Aufgabe/ Problème 3

A3 = {{1, 0, 0}, {4, 2, 0}, {6, 4, 4}};  m[A3]

a

ew3 = Eigenvalues[A3]

b

ev3 = Eigenvectors[A3]

m[Transpose[ev3]]

Aufgabe/ Problème 4

A4 = {{1, 1}, {1, 0}};  m[A4]

a

ew4 = Eigenvalues[A4]

N[%]

b

ev4 = Eigenvectors[A4]

N[%]

m[Transpose[ev4]]

m[Transpose[ev4]] // N

Aufgabe/ Problème 5

A5 = {{1, 0}, {0, 1}};  m[A5]

a

ew5 = Eigenvalues[A5]

b

ev5 = Eigenvectors[A5]

m[Transpose[ev5]]