Seja A = [[[1,0,5],[1,1,1],[0,1,-,4]]]

  1. Encontre a solução geral do sistema (A+4 I_3 ) X = 0

Passo 1

Inicialmente:

I_3 = [[[1,0,0],[0,1,0],[0,0,1]]]

4 I_3 = [[[4,0,0],[0,4,0],[0,0,4]]]

A+4 I_3 = [[[1,+,4,0,+,0,5,+,0],[1,+,0,1,+,4,1,+,0],[0,+,0,1,+,0,-,4,+,4]]]

A+4 I_3 = [[[5,0,5],[1,5,1],[0,1,0]]]

Passo 2

Montando um sistema em forma de matriz e resolvendo:

[[[5,0,5],[1,5,1],[0,1,0]],[[0],[0],[0]]]

[[[5,0,5],[1,5,1],[0,1,0]],[[0],[0],[0]]] , L_1 // 5 -> L_1 :

[[[1,0,1],[1,5,1],[0,1,0]],[[0],[0],[0]]] , L_2 - 1 L_1 -> L_2 :

[[[1,0,1],[0,5,0],[0,1,0]],[[0],[0],[0]]] , L_2 // ( 5 ) -> L_2 :

[[[1,0,1],[0,1,0],[0,1,0]],[[0],[0],[0]]] , L_3 - L_2 -> L_3 :

[[[1,0,1],[0,1,0],[0,0,0]],[[0],[0],[0]]]

Passo 3

{[[x_1 + x_3 = 0],[x_2 = 0],[]])

Resposta

X = ([[-,a],[0],[a]])

Exercícios de Livros Relacionados