Question

5x+Y-3Z=-62x+3y+Z=5-3x-2y+4z=3. Resolve sustenance de tres equação a tres variav

Answer 1

Resposta:

5x+y-3z=-6 ==>vezes 4==> 20x+4y-12z=24  (i)

2x+3y+z=5  ==>vezes 12 ==>24x+36y+12z=60  (ii)

-3x-2y+4z=3 ==>vezes 3 ==> -9x-6y+12z=9  (iii)

A=[5    1   -3; 2    3    1; -3   -2   4]

B=[6   ; 5 ;3]

(i)+(ii)

44x+40y=84      (iv)  

(ii)-(iii)

33x+42y=51    ==> x= (51-42y)/33   (v)

(v)  em (iv)

44* (51-42y)/33  +40y=84  

44*51-42*44y+40*33y=84*33

44*51 -84*33= 42*44y-40*33y

y= (44*51 -84*33)/(42*44-40*33) = -1

usando (v)  x= (51-42*(-1))/33=2,8182

usando (i)   20*2,8182+4*(-1)-12z=24  

z= (20*2,8182+4*(-1)-24)/12 = 2,3636

x=2,8182     ==> 279/99

y=-1

z=2,3636  ==> 234/99