In exercises 9-16, find the basis for the eigenspace corresponding to each listed eigenvalue.

15)

A = 4 2 3 - 1 1 - 3 2 4 9 ,   λ = 3

Passo 1

Faaaaaala, galera... Tranquileba??

A - λ I = 0

A - 3 I = 0

Passo 2

Assim:

4 2 3 - 1 1 - 3 2 4 9 - 3 0 0 0 3 0 0 0 3 = 1 2 3 - 1 - 2 - 3 2 4 6

Que nos dá o sistema:

x = - 2 y - 3 z

Passo 3

Desse modo:

v 1 = - 2 y - 3 z y z = y - 2 1 0 + z - 3 0 1

Assim temos a base:

B = - 2 1 0 , - 3 0 1

Resposta

B = - 2 1 0 , - 3 0 1