Colegio Universitario Francisco de Miranda Alexander Osorio C.I. V- 8.872.421Ingeniera en Informtica Secin I06P-302INVESTIGACIN DE OPERACIONES EVALUACIN 4 (25%) 03DIC2014

1) RESOLVER EL DETERMINANTE: [2 x 4x 3 x ] = 2Solucin:

2) RESOLVER APLICANDO DETERMINANTE

a) { 3 x + 2 y = 54 x 6 y = 8 Solucin:

A B C

[ 3 24 6] 58 = |AB| = (36)[(24 )] = 18 8 = 26 = 26

[ 5 28 6] x = |CB| = (56)[(28)] = 30 +16 = 14 x = 14

[3 54 8 ] y = |AC| = (38)[(54)] = 24 20 = 44 y = 44x = x =

1426 =

713 x =

713 ; y =

y =

4426 =

2213 y =

2213

= (2 x3x )[(4x )] = 2 6x 4 x = 2 3x 2x = 1 3 x 2 x 1 = 0

aplicar resolvente ax + bx + c = 0 ; para a0

x = b(b 4 ac)2a

=(2)((2) 431)

23= 216

6= 24

6

x1 =66

= 1 ; x2 = 26

= 13

Colegio Universitario Francisco de Miranda Alexander Osorio C.I. V- 8.872.421Ingeniera en Informtica Secin I06P-302INVESTIGACIN DE OPERACIONES EVALUACIN 4 (25%) 03DIC2014

b) { 3 x 2 y + z = 32x + 3 y 2 z = 4x 4 y + 3 y = 5 Solucin:

Se replantea el sistema :

{ 3 x 2 y + z = 32 x + 3 y 2 z = 4x 4 y + 3 y =5 {3 x 2 y + z = 32 x + 3 y 2 z = 4

x y =5A B C D

[ 3 2 12 3 21 1 0] 345 = |ABC| = (330)+(221)+(121)[(131)+(220)+(321)] = 3[3 2 14 3 25 1 0 ] x = |DBC| = (330)+(225)+(141)[(135)+(240)+(321)] x = 3[ 3 3 12 4 21 5 0 ] y = |ADC| = (340)+(321)+(125)[(141)+(320)+(325)] y = 18[ 3 2 32 3 41 1 5 ] z = |ABD| = (335)+(241)+(321)[(331)+(225)+(341)] z = 18

x = x =33

= 1 x = 1 ; y = y =183

= 6 y = 6 ; z = z =183

= 6 z = 6

c) { 2 x 3 y z = 33 x + y + 2 z = 4x + 4 y 3 z = 1Solucin:

A B C D

[ 2 3 13 1 21 4 3] 341 = |ABC| = (213)+(321)+(134)[(111)+(333)+(224)] = 12[ 3 3 14 1 21 4 3] x = |DBC| = (313)+(321)+(144 )[(111)+(343)+(324)] x = 24[ 2 3 13 4 21 1 3 ] y = |ADC| = (243)+(321)+(131)[(141)+(333)+(221)] y = 0[ 2 3 33 1 41 4 1] z = |ABD| = (211)+(341)+(334)[(311)+(331)+(244 )] z = 12

x = x =2412

= 2 x = 2 ; y = y =0

12= 0 y = 0 ; z = z =

1212

= 1 z = 1