Inverta

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

Passo 1

E aí, pessoal, beleza? Vamos fazer mais um!!!

Para encontrar a inversa de uma matriz A de ordem n , devemos fazer sobre a matriz identidade I as mesmas operações feitas para escalonar a matriz A , de modo que a matriz resultante das operações feitas sobre a matriz I será a inversa de A .

Sabendo disso, vamos para o exercício!!!

Passo 2

Vamos escalonar a matriz:

[[[0,1,0,1,|,1,0,0,0],[1,0,0,0,|,0,1,0,0],[0,1,0,0,|,0,0,1,0],[0,0,1,0,|,0,0,0,1]]] overset(l_1 harr l_2)(->) [[[1,0,0,0,|,0,1,0,0],[0,1,0,1,|,1,0,0,0],[0,1,0,0,|,0,0,1,0],[0,0,1,0,|,0,0,0,1]]] overset(l_3 = l_3 - l_2)(->)

[[[1,0,0,0,|,0,1,0,0],[0,1,0,1,|,1,0,0,0],[0,0,0,-,1,|,-,1,0,1,0],[0,0,1,0,|,0,0,0,1]]] overset(l_3 harr l_4)(->) [[[1,0,0,0,|,0,1,0,0],[0,1,0,1,|,1,0,0,0],[0,0,1,0,|,0,0,0,1],[0,0,0,-,1,|,-,1,0,1,0]]] overset(l_4 = - l_4)(->)

[[[1,0,0,0,|,0,1,0,0],[0,1,0,1,|,1,0,0,0],[0,0,1,0,|,0,0,0,1],[0,0,0,1,|,1,0,-,1,0]]] overset(l_2 = l_2 - l_4)(->) [[[1,0,0,0,|,0,1,0,0],[0,1,0,0,|,0,0,1,0],[0,0,1,0,|,0,0,0,1],[0,0,0,1,|,1,0,-,1,0]]]

Portanto, a inversa da matriz A dada no enunciado é a matriz A^(- 1) , dada por:

A^(- 1) = [[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,-,1,0]]]

Resposta

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