Odpowiedzi

2010-02-23T22:42:01+01:00
Rozwiąż układ równań:
-8a+4b-2c+d=0
a+b+c+d=0
8a+4b+2c+d=0
-a+b-c+d=0

z ostatniego równania wyznaczam d i wstawiam do 1,2 i3 równania
-8a+4b-2c+d=0
a+b+c+d=0
8a+4b+2c+d=0
d = a -b +c

-8a+4b-2c + a -b +c = 0
a+b+c + a -b +c = 0
8a+4b+2c+a -b +c = 0
d = a -b +c

-7a +3b -c = 0
2a +2c = 0 /:2
9a +3b +3c = 0 /:3
d = a -b +c

-7a +3b -c = 0
a + c = 0
3a +b +c = 0
d = a -b +c
teraz z drugiego równania obliczam c i wstawiam do 1 i 3 równania

-7a +3b -c = 0
3a +b +c = 0
c = -a
d = a -b +c

-7a + 3b - (-a) = 0
3a +b -a = 0
c = -a
d = a -b -a

-7a + 3b +a = 0
2a +b = 0
c = -a
d = -b

-6a + 3b = 0 /:3
2a + b = 0
c = -a
d = -b

-2a + b = 0
2a +b = 0
c = -a
d = -b

Wyznaczam b z i równania i wstawiam do drugiego
b = 2a
2a + 2a = 0
c = -a
d = -b

b = 2a
4a = 0 /:4
c = -a
d = -b

b = 2a
a = 0
c = - 0 = 0
d = -b

b = 2*0 = 0
a = 0
c = 0
d = 0

a = 0
b = 0
c = 0
d = 0

1 5 1