Sejam

A = [[[1,2,3],[6,-,2,3],[5,2,4]]] e I_3 = [[[1,0,0],[0,1,0],[0,0,1]]] .

Se λ é um número real, calcule λI3 – A.

Passo 1

E aí pessoal, belezinha. Vamos agora trabalhar em algumas questões de matrizes.

A partir das operações com matrizes vamos calcular:

lambda I_3 - A = lambda [[[1,0,0],[0,1,0],[0,0,1]]] - [[[1,2,3],[6,-,2,3],[5,2,4]]] = [[[lambda,*,1,lambda,*,0,lambda,*,0],[lambda,*,0,lambda,*,1,lambda,*,0],[lambda,*,0,lambda,*,0,lambda,*,1]]] - [[[1,2,3],[6,-,2,3],[5,2,4]]] =

= [[[lambda,0,0],[0,lambda,0],[0,0,lambda]]] - [[[1,2,3],[6,-,2,3],[5,2,4]]] = [[[lambda,-,1,0,-,2,0,-,3],[0,-,6,lambda,-,(- 2),0,-,3],[0,-,5,0,-,2,lambda,-,4]]] = [[[lambda,-,1,-,2,-,3],[-,6,lambda,+,2,-,3],[-,5,-,2,lambda,-,4]]]

Resposta

Ver passo a passo.