INVESTIGACIÓN OPERATIVA I
Dr. Marlón Villa
MÉTODO DE GAUSS-JORDÁN EJERCICIO 1 2x1+3X2+4X3=5 2x1+X2-5X3= 6
-4 -6 -8 = -10
3x1-2X2+4X3=1
4 +1 -5 = 6
-3 -9/2 -6 = -15/2 3 -2 1 - 3/2 + 2= 5/2
4
7
0 - 3/2 -39/2 =-6/5
0 – 5 – 13 = -4
1 +3/2 +2
= 5 /2
0- 13/2 -2 = -1/2
00 - 13/2 -169/10 =26/5 0 19/10 = +893/1490
1 + 0 - 19/10 = 13/10
11 +13/2 +2 = 13/10 =-1 /2 0 -19/10
0 + 1 + 13/5 = 4/5 0 + 0 – 149/10 =47/10
0
0
-13/5 =-611/745
0
1
13/5 = 4/5
1 + 0 + 0 = 283/149 0 + 1 + 0 = -3/149 0 + 0 + 1 = 47/149
X= 283/149
COMPROBACIÓN
Y= -3/149
2x1+3X2+4X3=5
Z= 47/149
2(283/149)+3(-3/149)+4(47/149) 5=5
pág. 2
Srta. Paola Meza
INVESTIGACIÓN OPERATIVA I
Dr. Marlón Villa
EJERCICIO 2 2x+5y-2z= 10 5x-2y+3z= 7
-5 -25/2 5 = -25
4x+6y+8z=1
5
-4 4 1 + 5/2 - 1= 5
-2
3= 7
-10 4 = -20 6
8
= 1
0 - 5/2 40/29 =-20/29
0 – 29/2 – 8 = -18
1 5/2 -1
= 5
0 - 4 12 = -19
1 + 0 + 11/29 = 55/29 0 + 1 + 16/29 = 36/29
0
4
1
-4
-64/29 =144/29 12
=
-19
0 0 16/29 = -1628/2059
0 + 0 – 284/29 =-407/29
1 0 -16/29 = 36/29
1 + 0 + 0 = 693/149
0
0
-11/29 = 4477/8236
1
0
11/29 = 55/29
0 + 1 + 0 = 32/71 0 + 0 + 1 = -407/284
X= 693/284
COMPROBACIÓN
Y= 32/71
2x+5y-2z= 10
Z=-407/284
2(693/284)+3(32/71)+4(-407/284) 10 =10
pág. 3
Srta. Paola Meza