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Aula: Encontrando o Inverso de uma Matriz Quatro por Quatro

Atividade • 2 Questões

Q1:

Determine 𝐴   , sendo 𝐴 = ⎑ ⎒ ⎒ ⎣ 1 2 0 2 1 1 2 0 2 1 βˆ’ 3 2 1 2 1 2 ⎀ βŽ₯ βŽ₯ ⎦ .

  • A ⎑ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎣ βˆ’ 1 1 2 1 2 1 2 3 1 2 βˆ’ 1 2 βˆ’ 5 2 βˆ’ 1 0 0 1 βˆ’ 2 βˆ’ 3 4 1 4 9 4 ⎀ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ ⎦
  • B ⎑ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎣ βˆ’ 1 1 2 1 2 1 2 3 1 2 βˆ’ 1 2 βˆ’ 5 2 βˆ’ 1 0 0 1 βˆ’ 2 βˆ’ 3 2 1 2 9 2 ⎀ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ ⎦
  • C ⎑ ⎒ ⎒ ⎣ βˆ’ 1 1 1 1 3 1 βˆ’ 1 βˆ’ 5 βˆ’ 1 0 0 1 βˆ’ 2 βˆ’ 3 1 9 ⎀ βŽ₯ βŽ₯ ⎦
  • D ⎑ ⎒ ⎒ ⎣ 1 0 0 0 0 1 βˆ’ 2 0 3 βˆ’ 1 3 βˆ’ 3 1 0 0 βˆ’ 1 ⎀ βŽ₯ βŽ₯ ⎦
  • E ⎑ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎣ 0 0 1 0 1 0 βˆ’ 1 2 0 βˆ’ 1 3 1 βˆ’ 1 3 0 βˆ’ 8 9 βˆ’ 1 3 1 9 1 ⎀ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ ⎦

Q2:

Utilizando operaçáes elementares nas linhas, determine 𝐴   para a matriz dada, se possΓ­vel. 𝐴 = ⎑ ⎒ ⎒ ⎣ 3 5 8 5 1 2 3 1 2 4 7 2 1 3 5 3 ⎀ βŽ₯ βŽ₯ ⎦

  • A 𝐴 = 1 4 ⎑ ⎒ ⎒ ⎣ 3 βˆ’ 2 1 βˆ’ 5 βˆ’ 2 1 6 βˆ’ 6 2 0 βˆ’ 8 4 0 1 βˆ’ 2 βˆ’ 1 1 ⎀ βŽ₯ βŽ₯ ⎦  
  • B A matriz nΓ£o admite inversa.
  • C 𝐴 = ⎑ ⎒ ⎒ ⎣ βˆ’ 2 5 βˆ’ 2 3 3 βˆ’ 2 1 βˆ’ 5 0 βˆ’ 2 1 0 1 βˆ’ 1 0 βˆ’ 1 ⎀ βŽ₯ βŽ₯ ⎦  
  • D 𝐴 = ⎑ ⎒ ⎒ ⎣ 3 βˆ’ 2 1 βˆ’ 5 βˆ’ 2 5 βˆ’ 2 3 0 βˆ’ 2 1 0 βˆ’ 1 1 0 1 ⎀ βŽ₯ βŽ₯ ⎦  
  • E 𝐴 = 1 4 ⎑ ⎒ ⎒ ⎣ 3 βˆ’ 2 1 βˆ’ 5 βˆ’ 2 5 βˆ’ 2 3 0 2 βˆ’ 1 0 1 βˆ’ 1 0 βˆ’ 1 ⎀ βŽ₯ βŽ₯ ⎦  
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