The document provides three examples of solving systems of linear equations using Gauss-Jordan elimination. The first example solves a system of 4 equations with 4 unknowns. The second example solves another system of 4 equations with 4 unknowns. The third example solves a final system of 4 equations with 4 unknowns. Each example shows the row operations used to put the system in reduced row echelon form and identifies the values of the unknowns that satisfy all the equations.

1. INVESTIGACIÓN OPERATIVA I DR. MARLON VILLA
1
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
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

2. INVESTIGACIÓN OPERATIVA I
DIANA CURICAMA, QUINTO SEMESTRE “A”
2
COMPROBACIÓN
5A-4B+6C-2D=-37
5(-3)-4(5)+6(0)-2(1)
=-37
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
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

3. INVESTIGACIÓN OPERATIVA I
DIANA CURICAMA, QUINTO SEMESTRE “A”
3
EJERCICIO 2
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
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

4. INVESTIGACIÓN OPERATIVA I
DIANA CURICAMA, QUINTO SEMESTRE “A”
4
COMPROBACIÓN
2X1 + X2 + 3X3 + 2X4= 3
2(521/478) + (373/478)+3 (105/478) + 2(-123/478)
= 3
EJERCICIO 3
X1= 521/478
X2= 373/478
X3= 105/478
X4= -123/478
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 = 4/31 + 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
-

5. INVESTIGACIÓN OPERATIVA I
DIANA CURICAMA, QUINTO SEMESTRE “A”
5
COMPROBACIÓN
3X1 - 2X2 + 4X3 - X4= 4
3(52/43) - 2(-5/86)+4 (-1/86) - (-13/43)
= 4
X1= 52/43
X2= -5/86
X3= -1/86
X4= -13/43
0 0 17/7 459/203 =-289/406
0 1 -17/7 -4/7 = 1/7
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 - 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
-
1 + 0 + 0 + 0 =52/43
0 + 1 +0 + 0 =-5/86
0 + 0 +1 +0 =-1/86
0 + 0 +0 +1=-13/43