Sistemas Lineares

  • June 2020
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sistemas lineares escalonamento exercicio resolvido 2x+y-z=-2 x-3y+3z=-1 -x+y+2z=7

c a b

2�passo reorganizar x menor coeficiente na 1� incognita a b c

x-3y+3z=-1 -x+y+2z=7 2x+y-z=-2

3� passo montar a matrix 1 -3 3 -1 1 2 2 1 -1

-1 7 -2

a (manter ate o final) b c

1 0 0

-3 3 -2 5 7 -7

-1 a 6 a+b=d 0 -2a+c=e

1 0 0

-3 3 -2 5 0 21

-1 6 42

a d 7d+2e

x-3+3=-1 -2y+5z=6 21z=42 z=2 substitui na de cima -2y+5.(2)=6 -2y=-4 .(-1) 2y=4 y=2 substitui na de cima x-3y+3z=-1 x=-1 spd

s={(-1,2,2)}

sistemas homogeneos possuem todos os termos independente iguais a zero se o determinante da matriz incompleta (di)for diferente de zero a solucao e unica e sera s={0,0,0}chamada solucao trivial se o (di)for igual a zero (di=0)o sistema admite infinitas solucoes

2x-y+2z=0 di =-2x+y-z=0 x+y-3z=0 2 -1 di=-2 1 1 1

2 2 -1 -1 -2 1 -3 1 1

-6+1-4-2+2+6=-3 s={(0,0,0,)} spd

solucao dos sistemas lineares por chamer 2x-y+2z=1 -2+y-z=2 x+y-3z=-10 montar matrix incompleta 2 -1 2 2 -1 di=-2 1 -1 -2 1 1 1 -3 1 1 di = -3 dx=determonante da variavel x 1 -1 2 dx=2 1 -1 -10 1 -3

1 -1 2 1 -10 1

dx=6 dy=determonante da variavel y 2 1 2 2 1 dy=-2 2 -1 -2 2 1 -10 -3 1 -10 dy=-3 dz=determonante da variavel z 2 -1 1 2 -1 dz=-2 1 2 -2 1 1 1 -10 1 1 dz=-9

spd s={(6,-3,-9)}

resolva e classifique utilizando a regra de chamer os sitemas abaixo a)3x-4y=2 -4x+7y=-1 di=3 -4 -4 7

= 5

dx=2 -4 -1 7

= 10

dy=3 -4

2 1

= 5

x= dx / di = 10/5 =2 y= dy / di = 5/5 =1] spd s{(2,1)}

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