Método gauss jordan

UNIVERSIDAD NACIONAL DE CHIMBORAZO

FACULTAD DE CIENCIAS POLÍTICAS Y ADMINISTRATIVAS

CARRERA DE CONTABILIDAD Y AUDITORÍA CPA

INVESTIGACIÓN OPERATIVA I

Dr. Marlón Villa

Deber 08

Nombre: Diana Curicama

Curso: 5to Semestre

Paralelo: “A”

Fecha: 2 de junio 2015

-Tema: Desarrollar 3 ejercicios de Sistema 4x4 por el método de Gauss-Jordán

MÉTODO DE GAUSS-JORDÁN

EJERCICIO 1

1

5A - 4B + 6C - 2D =-37

-2A + 3B - 4C + 5D= 26

6A - 2B + 3C - 4D = -32

-A + 5B - 8C - 2D = 26

5 - 4 + 6 – 2 = -37

-2 + 3 – 4 + 5= 26

6 – 2 +3 - 4 = -32

-1 +5 – 8 – 2 = 26

2 -8/5 12/5 -4/5 =-74/5

-2 3 -4 5 = 26

0 -14/5 +16/5 -42/5 – 112/5

0 +14/5 -51/5 -8/5 +62/5

-1 +5 -8 -2 = 26

1 -4/5 6/5 -2/5 = -37/5

-6 + 24/5 - 36/5 + 12/5 = 222/5

6 - 2 +3 -4 = -32

COMPROBACIÓN

5A-4B+6C-2D=-37

5(-3)-4(5)+6(0)-2(1)

=-37


DIANA CURICAMA, QUINTO SEMESTRE “A”

A= -3

B= 5

C= 0

D= 1

1 – 4/5 + 6/5 – 2/5 = -37/5

0 + 7/5 - 8/5 + 21/5= 56/5

0 + 14/5 – 51/5 – 8/5= 62/5

0 + 21/5 – 34/5 – 12/5=93/5

2

1 + 0 + 2/7 + 2 = -1

0 + 1 – 8/7 + 3 = 8

0 – 0 – 7 - 10 =-10

0 0 - 2 - 15= -15

0 +4/5 -32/35 +12/5 + 32/5

1 -4/5 -6/5 -2/5 - 37/5

0 -21/5 +24/5 -63/5 – 168/5

0 21/5 -34/5 -12/5 + 93/5

1 – 0 + 0 – 78/49 = -69/49

0 + 1 + 0 + 227/49= 472/49

0 + 0 – 1 – 10/7= 10/7

0 + 0 – 0 – 85/7= -85/7

0 +0 2 +20/7 + 20/7

1 0 -2 -15 - 15

1 – 0 + 0 – 0 = -3

0 – 1 + 0 – 0 = 5

0 – 0 + 1 – 0 = 0

0 – 0 + 0 – 1 = 1

0 +0 8/7 +80/49 + 80/49

0 1 -8/7 3 + 8

0 +0 0 -10/7 - 10/7

0 0 1 10/7 10/7



EJERCICIO 2

3

2X1 + X2 + 3X3 + 2X4= 3

3X1 + 2X2 -4X3 - X4= 4

4X1 - 3X2 +2X3 +3X4= 2

2X1 +2X2 +2X3 -4X4= 5

1 + 1/2 + 3/2 + 1 =3/2

0 + 1/2 – 17/2- 4=-1/2

0 – 5 – 4 -1 = -4

0 + 1 - 1 -6 = 2

2 – 1 + 3 + 2 = 3

3 + 2 - 4 - 1 = 4

4 – 3 + 2 + 3= 2

2 + 2 + 2 -4= 5

X1= 521/478

X2= 373/478

X3= 105/478

X4= -123/478

3 -3/2 -9/2 -3 = -9/2

3 2 -4 -1 = 4

-4 - 2 - 6 - 4 = -6

4 -3 2 3 = 2

-2 - 1 - 3 - 2 = -3

2 2 2 -4 = 5

0 - 1 17 8 = 1

0 1 -1 -6 = 2

0 0 -16 -656/89 =– 144/89

0 0 16 +2 = 3

0 0 17 697/89 = 153/89

0 0 -17 -8 = -1

0 0 0 -41/89 =5043/42542

0 0 1 41/89 = 9/89

0 0 0 15/89 = -1845/42542

0 1 0 -15/89 = 64/89

0 0 0 -35/89 =4305/42542

1 0 0 35/89 = 88/89

1 + 0 + 10 + 5 = 2

0 + 1 – 17 – 8 =-1

0 + 0 –89 -41 =-9

0 + 0 +16 2 = 3

1 + 0 + 0 + 35/89 =88/89

0 + 1 +0 –15/89 =64/89

0 + 0 +1 +41/89 = 9/89

0 + 0 +0 -478/89 =123/89

1 + 0 + 0 + 0 =521/478

0 + 1 +0 + 0 =323/478

0 + 0 +1 +0 =105/478

0 + 0 +0 +1=-123/478



COMPROBACIÓN

2X1 + X2 + 3X3 + 2X4= 3

2(521/478) + (373/478)+3 (105/478) + 2(-123/478)

= 3

EJERCICIO 3

4

3X1 - 2X2 + 4X3 - X4= 4

2X1 + X2 - 3X3 - 2X4= 3

5X1 +2X2 +2X3 +3X4= 5

2X1 -3X2 - X3 + 2X4= 2

1 - 2/3 + 4/3 – 1/3 =4/3

0 +7/3 –17/3- 4/3= 1/3

0 – 16/3 –14/3+ 14/3 =-5/3

0 – 5/3 - 11/3 + 8/3 =-2/3

3 – 2 + 4 + -1 = 4

2 + 1 - 3 - 2 = 3

5 + 2 + 2 + 3= 5

2 - 3 - 1 + 2= 2

-2 4/3 -8/3 2/3 = -8/3

2 1 -3 -2 = 3

-5 + 10/2 -20/3 5/3 = -20/3

5 + 2 + 2 + 3 = +5

-2 +4/3 - 8/3 2/3 = -8/3

2 -3 -1 2 = 2

0 - 16/3 272/21 + 64/21 = -16/21

0 16/3 -14/3 +14/3 = -5/3

0 2/3 -34/21 -8/21 = 2/21

0 -2/3 4/3 -1/3 = 4/3

0 0 17/7 459/203 =-289/406

0 1 -17/7 -4/7 = 1/7

1 + 0 -2/7 - 5/7 = 10/7

0 + 1 –17/7 –4/7 = 1/7

0 + 0 +58/7 +54/7=-17/7

0 + 0 -54/7 +12/7 =-3/7

1 + 0 + 0 - 13/29 =39/29

0 + 1 +0 +49/29 =-33/58

0 + 0 +1 +27/29 = -17/58

0 + 0 +0 +252/29 =-78/29



COMPROBACIÓN

3X1 - 2X2 + 4X3 - X4= 4

3(52/43) - 2(-5/86)+4 (-1/86) - (-13/43)

= 4

5

X1= 52/43

X2= -5/86

X3= -1/86

X4= -13/43

0 0 0 -27/29 = 351/1247

0 0 1 27/29 = -17/58

0 0 0 -49/29 = 637/1247

0 1 0 49/29 = -33/58

0 0 0 13/29 = -169/1247

1 0 0 -13/29 = 39/29

1 + 0 + 0 + 0 =52/43

0 + 1 +0 + 0 =-5/86

0 + 0 +1 +0 =-1/86

0 + 0 +0 +1=-13/43

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