Protokoll Gauss 2:

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


Sollen die Rechenschritte angezeigt werden (J/N):j
>ClrScr<

Start-Gleichungen:

| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) 3*x1 +  5*x2 +  8*x3 +  2*x4 = 4
| (3) 3*x1 +  5*x2 +  9*x3 +  2*x4 =  8
| (4) 3*x1 +  10*x2 +  13*x3 +  12*x4 =  25
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I. Vorwärtselimination

(2) -  0.15*(1):
| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) 0*x1 +  3.5*x2 +  7.55*x3 +  1.4*x4 =  3.25
| (3) 3*x1 +  5*x2 +  9*x3 +  2*x4 =  8
| (4) 3*x1 +  10*x2 +  13*x3 +  12*x4 =  25
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(3) -  0.15*(1):
| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) 0*x1 +  3.5*x2 +  7.55*x3 +  1.4*x4 =  3.25
| (3) 0*x1 +  3.5*x2 +  8.55*x3 +  1.4*x4 =  7.25
| (4) 3*x1 +  10*x2 +  13*x3 +  12*x4 =  25
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(4) -  0.15*(1):
| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) 0*x1 +  3.5*x2 +  7.55*x3 +  1.4*x4 =  3.25
| (3) 0*x1 +  3.5*x2 +  8.55*x3 +  1.4*x4 =  7.25
| (4) 0*x1 +  8.5*x2 +  12.55*x3 +  11.4*x4=  24.25
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(2) mit (4) vertauscht:
| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 + =  5
| (2) 0*x1 +  8.5*x2 +  12.55*x3 +  11.4*x4 =  24.25
| (3) 0*x1 +  3.5*x2 +  8.55*x3 +  1.4*x4 =  7.25
| (4) 0*x1 +  3.5*x2 +  7.55*x3 +  1.4*x4 =  3.25
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(3) -  0.411765*(2):
| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) 0*x1 +  8.5*x2 +  12.55*x3 +  11.4*x4 =  24.25
| (3) 0*x1 +  0*x2 +  3.38235*x3 + -3.29412*x4 = -2.73529
| (4) 0*x1 +  3.5*x2 +  7.55*x3 +  1.4*x4 =  3.25
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(4) -  0.411765*(2):
| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) 0*x1 +  8.5*x2 +  12.55*x3 +  11.4*x4 =  24.25
| (3) 0*x1 +  0*x2 +  3.38235*x3 + -3.29412*x4 = -2.73529
| (4) 0*x1 +  0*x2 +  2.38235*x3 + -3.29412*x4 = -6.73529
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(4) -  0.704348*(3):
| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) 0*x1 +  8.5*x2 +  12.55*x3 +  11.4*x4 =  24.25
| (3) 0*x1 +  0*x2 +  3.38235*x3 + -3.29412*x4 = -2.73529
| (4) 0*x1 +  0*x2 +  0*x3 + -0.973913*x4 = -4.8087
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II. Rückwärtseinsetzen

| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) 0*x1 +  8.5*x2 +  12.55*x3 +  11.4*x4 =  24.25
| (3) 0*x1 +  0*x2 +  3.38235*x3 + -3.29412*x4 = -2.73529
| (4) x4 = (-4.80870) : -0.973913
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| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) 0*x1 +  8.5*x2 +  12.55*x3 +  11.4*x4 =  24.25
| (3) x3 = (-2.73529 - -3.29412* 4.9375) :  3.38235
| (4) x4 =  4.9375
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| (1) 20*x1 +  10*x2 +  3*x3 +  4*x4 =  5
| (2) x2 = ( 24.25 -  12.55* 4 -  11.4* 4.9375) :  8.5
| (3) x3 =  4
| (4) x4 =  4.9375
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| (1) x1 = ( 5 -  10*-9.675 -  3* 4 -  4* 4.9375) :  20
| (2) x2 = -9.675
| (3) x3 =  4
| (4) x4 =  4.9375
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| (1) x1 =  3.5
| (2) x2 = -9.675
| (3) x3 =  4
| (4) x4 =  4.9375
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Protokoll Gauss 3:

>ClrScr<
Anzahl der zu lösenden Gleichungen:3
>ClrScr
>Koeffizienteingabe<


Sollen die Rechenschritte angezeigt werden (J/N):j
>ClrScr<
Start-Gleichungen:

| (1) 5*x1 +  8*x2 +  10*x3 =  7
| (2) 3*x1 +  5*x2 +  8*x3 =  2
| (3) 10*x1 +  16*x2 +  20*x3 =  4
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I. Vorwärtselimination


II. Rückwärtseinsetzen

Die Determinante ist 0     =>    es existiert keine eindeutige Lösung