Protokoll GaussJordan 1:

>ClrScr<
Anzahl der zu lösenden Gleichungen:4
>ClrScr<
>Koeffizienteneingabe<


Sollen die Rechenschritte angezeigt werden (J/N):j
>ClrScr<
  Start-Gleichungen:
| (1) 1*x1 +  2*x2 +  3*x3 +  4*x4 =  30
| (2) 2*x1 +  1*x2 +  4*x3 +  3*x4 =  28
| (3) 3*x1 +  4*x2 +  1*x3 +  2*x4 =  24
| (4) 4*x1 +  3*x2 +  2*x3 +  1*x4 =  20
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I. Vorwärtselimination

(1) mit (4) vertauscht:
| (1) 4*x1 +  3*x2 +  2*x3 +  1*x4 =  20
| (2) 2*x1 +  1*x2 +  4*x3 +  3*x4 =  28
| (3) 3*x1 +  4*x2 +  1*x3 +  2*x4 =  24
| (4) 1*x1 +  2*x2 +  3*x3 +  4*x4 =  30
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(2) -  0.5*(1):
| (1) 4*x1 +  3*x2 +  2*x3 +  1*x4 =  20
| (2) 0*x1 + -0.5*x2 +  3*x3 +  2.5*x4 =  18
| (3) 3*x1 +  4*x2 +  1*x3 +  2*x4 =  24
| (4) 1*x1 +  2*x2 +  3*x3 +  4*x4 =  30
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(3) -  0.75*(1):
| (1) 4*x1 +  3*x2 +  2*x3 +  1*x4 =  20
| (2) 0*x1 + -0.5*x2 +  3*x3 +  2.5*x4 =  18
| (3) 0*x1 +  1.75*x2 + -0.5*x3 +  1.25*x4 =  9
| (4) 1*x1 +  2*x2 +  3*x3 +  4*x4 =  30
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(4) -  0.25*(1):
| (1) 4*x1 +  3*x2 +  2*x3 +  1*x4 =  20
| (2) 0*x1 + -0.5*x2 +  3*x3 +  2.5*x4 =  18
| (3) 0*x1 +  1.75*x2 + -0.5*x3 +  1.25*x4 =  9
| (4) 0*x1 +  1.25*x2 +  2.5*x3 +  3.75*x4 =  25
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(2) mit (3) vertauscht:
| (1) 4*x1 +  3*x2 +  2*x3 +  1*x4 =  20
| (2) 0*x1 +  1.75*x2 + -0.5*x3 +  1.25*x4 =  9
| (3) 0*x1 + -0.5*x2 +  3*x3 +  2.5*x4 =  18
| (4) 0*x1 +  1.25*x2 +  2.5*x3 +  3.75*x4 =  25
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(3) - -0.285714*(2):
| (1) 4*x1 +  3*x2 +  2*x3 +  1*x4 =  20
| (2) 0*x1 +  1.75*x2 + -0.5*x3 +  1.25*x4 =  9
| (3) 0*x1 +  0*x2 +  2.85714*x3 +  2.85714*x4 =  20.5714
| (4) 0*x1 +  1.25*x2 +  2.5*x3 +  3.75*x4 =  25
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(4) -  0.714286*(2):
| (1) 4*x1 +  3*x2 +  2*x3 +  1*x4 =  20
| (2) 0*x1 +  1.75*x2 + -0.5*x3 +  1.25*x4 =  9
| (3) 0*x1 +  0*x2 +  2.85714*x3 +  2.85714*x4 =  20.5714
| (4) 0*x1 +  0*x2 +  2.85714*x3 +  2.85714*x4 =  18.5714
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(4) -  1*(3):
| (1) 4*x1 +  3*x2 +  2*x3 +  1*x4 =  20
| (2) 0*x1 +  1.75*x2 + -0.5*x3 +  1.25*x4 =  9
| (3) 0*x1 +  0*x2 +  2.85714*x3 +  2.85714*x4 =  20.5714
| (4) 0*x1 +  0*x2 +  0*x3 +  0*x4 = -2
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II. Gauß-Jordan-Reduktion

Die Determinante ist 0     =>    es existiert keine eindeutige Lösung





Protokoll GaussJordan 2:

>ClrScr<
Anzahl der zu lösenden Gleichungen:4
>ClrScr<
>Koeffizienteneingabe<


Sollen die Rechenschritte angezeigt werden (J/N):n
>ClrScr<
  Start-Gleichungen:
| (1) 2*x1 +  3*x2 +  5*x3 +  7*x4 =  95
| (2) 3*x1 +  4*x2 +  10*x3 +  1*x4 =  132
| (3) 4*x1 +  2*x2 +  3*x3 +  10*x4 =  79
| (4) 7*x1 +  3*x2 +  2*x3 +  10*x4 =  82
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I. Vorwärtselimination


II. Gauß-Jordan-Reduktion

| (1) x1 =  1
| (2) x2 =  9
| (3) x3 =  9
| (4) x4 =  3
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