Método de Gauss-Jordán

1. DIANA CURICAMA UNACH. QUINTO SEMESTRE “A”
INVESTIGACIÓN OPERATIVA I Dr. Marlon Villa1
COMPROBACIÓN
2x1+3X2+4X3=5
2(283/149)+3(-3/149)+4(47/149)
5 = 5
MÉTODO DE GAUSS-JORDÁN
EJERCICIO 1
X= 283/149
Y= -3/149
Z= 47/149
2x1+3X2+4X3=5
2x1+X2-5X3= 6
3x1-2X2+4X3=1
1 + 0 - 19/10 = 13/10
0 + 1 + 13/5 = 4/5
0 + 0 – 149/10 =47/10
1 - 3/2 + 2= 5/2
0 – 5 – 13 = -4
0- 13/2 -2 = -1/2
1 + 0 + 0 = 283/149
0 + 1 + 0 = -3/149
0 + 0 + 1 = 47/149
-4 -6 -8 = -10
4 +1 -5 = 6
0 - 3/2 -39/2 =-6/5
1 +3/2 +2 = 5 /2
-3 -9/2 -6 = -15/2
3 -2 4 7
0 0 -13/5 =-611/745
0 1 13/5 = 4/5
0 - 13/2 -169/10 =26/5
1 +13/2 +2 =-1 /2
0 0 19/10 = +893/1490
1 0 -19/10 = 13/10

2. DIANA CURICAMA UNACH. QUINTO SEMESTRE “A”
INVESTIGACIÓN OPERATIVA I Dr. Marlon Villa2
COMPROBACIÓN
2x+5y-2z= 10
2(693/284)+3(32/71)+4(-407/284)
10 =10
EJERCICIO 2
X= 693/284
Y= 32/71
Z=-407/284
2x+5y-2z= 10
5x-2y+3z= 7
4x+6y+8z=1
1 + 0 + 11/29 = 55/29
0 + 1 + 16/29 = 36/29
0 + 0 – 284/29 =-407/29
1 + 5/2 - 1= 5
0 – 29/2 – 8 = -18
0 - 4 12 = -19
1 + 0 + 0 = 693/149
0 + 1 + 0 = 32/71
0 + 0 + 1 = -407/284
-5 -25/2 5 = -25
5 -2 3 = 7
0 - 5/2 40/29 =-20/29
1 5/2 -1 = 5
-4 -10 4 = -20
4 6 8 = 1
0 0 -11/29 = 4477/8236
1 0 11/29 = 55/29
0 4 -64/29 =144/29
1 -4 12 = -19
0 0 16/29 = -1628/2059
1 0 -16/29 = 36/29