Atividade: Propriedades da Matriz Inversa

Nesta atividade, nós vamos praticar a utilizar algumas propriedades da matriz inversa.

Q1:

Dado que 𝐴 =  βˆ’ 2 βˆ’ 9 8 7  , encontre ο€Ή 𝐴     .

  • A  βˆ’ 2 8 βˆ’ 9 7 
  • B  7 βˆ’ 8 9 βˆ’ 2 
  • C ⎑ ⎒ ⎒ ⎣ βˆ’ 1 2 9 4 2 9 βˆ’ 9 5 8 7 5 8 ⎀ βŽ₯ βŽ₯ ⎦
  • D ⎑ ⎒ ⎒ ⎣ 7 5 8 βˆ’ 4 2 9 9 5 8 βˆ’ 1 2 9 ⎀ βŽ₯ βŽ₯ ⎦
  • E ⎑ ⎒ ⎒ ⎣ 7 5 8 9 5 8 βˆ’ 4 2 9 βˆ’ 1 2 9 ⎀ βŽ₯ βŽ₯ ⎦

Q2:

Se 𝐴 Γ© uma matriz, qual das seguintes opçáes Γ© igual a ο€Ή 𝐴     ?

  • A ο€Ή 𝐴     
  • B 𝐴 
  • C 𝐴  
  • D ο€Ή 𝐴    

Q3:

Considere a matriz apresentada 𝐴 . Determine ο€Ή 𝐴      . 𝐴 =  βˆ’ 3 1 βˆ’ 2 5 

  • A ⎑ ⎒ ⎒ ⎣ βˆ’ 3 1 3 2 1 3 βˆ’ 1 1 3 5 1 3 ⎀ βŽ₯ βŽ₯ ⎦
  • B ⎑ ⎒ ⎒ ⎣ βˆ’ 5 1 3 1 1 3 βˆ’ 2 1 3 3 1 3 ⎀ βŽ₯ βŽ₯ ⎦
  • C  3 βˆ’ 1 2 βˆ’ 5 
  • D  βˆ’ 3 1 βˆ’ 2 5 
  • E  βˆ’ 5 2 βˆ’ 1 3 

Q4:

Se 𝐴 e 𝐡 sΓ£o matrizes nΓ£o-singulares, entΓ£o qual Γ© o valor de ( 𝐴 𝐡 ) βˆ’ 1 ?

  • A 𝐴 𝐡 βˆ’ 1 βˆ’ 1
  • B βˆ’ 𝐴 𝐡
  • C ( 𝐡 𝐴 ) βˆ’ 1
  • D 𝐡 𝐴 βˆ’ 1 βˆ’ 1

Q5:

Se 𝐼 Γ© a matriz identidade, qual das seguintes opçáes Γ© igual a 𝐼 βˆ’ 1 ?

  • A  0 1 1 0 
  • B βˆ’ 𝐼
  • C  1 1 1 1 
  • D 𝐼

Q6:

Sendo 𝐴 =  βˆ’ 6 βˆ’ 2 1 βˆ’ 3  , determine ο€Ή 𝐴      .

  • A  βˆ’ 3 βˆ’ 1 2 βˆ’ 6 
  • B  βˆ’ 3 1 βˆ’ 2 βˆ’ 6 
  • C  βˆ’ 6 2 βˆ’ 1 βˆ’ 3 
  • D  βˆ’ 6 βˆ’ 2 1 βˆ’ 3 

Q7:

Dado que ( 𝐴 𝐡 ) = 1 6  5 βˆ’ 3 βˆ’ 3 3 2 1  𝐴 =  βˆ’ 2 βˆ’ 1 βˆ’ 3 βˆ’ 2  ,   , determine 𝐡   .

  • A  βˆ’ 1 1 3 βˆ’ 9 
  • B  βˆ’ 9 βˆ’ 1 βˆ’ 3 βˆ’ 1 
  • C  2 1 3 3 3 5 
  • D ⎑ ⎒ ⎒ ⎣ βˆ’ 1 6 1 6 1 2 βˆ’ 3 2 ⎀ βŽ₯ βŽ₯ ⎦

Q8:

Dado que 𝐴 =  5 2 βˆ’ 6 βˆ’ 5  𝐡 =  βˆ’ 2 2 βˆ’ 4 2  , , encontre 𝐡 𝐴     .

  • A ⎑ ⎒ ⎒ ⎣ βˆ’ 1 1 2 6 βˆ’ 7 2 6 βˆ’ 8 1 3 βˆ’ 9 2 6 ⎀ βŽ₯ βŽ₯ ⎦
  • B ⎑ ⎒ ⎒ ⎣ βˆ’ 9 2 6 βˆ’ 7 2 6 βˆ’ 8 1 3 βˆ’ 1 1 2 6 ⎀ βŽ₯ βŽ₯ ⎦
  • C ⎑ ⎒ ⎒ ⎣ 9 2 6 7 2 6 8 1 3 1 1 2 6 ⎀ βŽ₯ βŽ₯ ⎦
  • D ⎑ ⎒ ⎒ ⎣ 1 1 2 6 7 2 6 8 1 3 9 2 6 ⎀ βŽ₯ βŽ₯ ⎦

Q9:

Se 𝐴 Γ© uma matriz, qual das seguintes opçáes Γ© igual a ο€Ή 𝐴     ?

  • A ο€Ή 𝐴     
  • B 𝐴 
  • C 𝐴  
  • D ο€Ή 𝐴    
  • E 𝐴  

Q10:

Suponha que 𝐴 , 𝐡 , e 𝐢 sΓ£o matrizes invertΓ­veis 𝑛 Γ— 𝑛 . Qual das seguintes afirmaçáes Γ© falsa?

  • A 𝐴 𝐢 𝐡   Γ© invertΓ­vel.
  • B ( 𝐴 𝐡 𝐢 ) = 𝐢 𝐡 𝐴        
  • C d e t ( 𝐢 𝐴 𝐡 ) β‰  0
  • D 𝐴 𝐡 𝐢   nΓ£o tem caracterΓ­stica completa.

Q11:

Considere a matriz apresentada 𝐴 . Determine ο€Ή 𝐴      . 𝐴 =  βˆ’ 6 βˆ’ 1 2 0 

  • A  3 1 βˆ’ 1 2 0 ο₯
  • B  0 1 2 βˆ’ 1 βˆ’ 3 ο₯
  • C  6 1 βˆ’ 2 0 
  • D  βˆ’ 6 βˆ’ 1 2 0 
  • E  0 βˆ’ 2 1 6 

Q12:

Considere a matriz apresentada 𝐴 . Determine ο€Ή 𝐴      . 𝐴 =  βˆ’ 5 βˆ’ 4 6 2 

  • A ⎑ ⎒ ⎒ ⎣ 5 1 4 3 7 βˆ’ 2 7 βˆ’ 1 7 ⎀ βŽ₯ βŽ₯ ⎦
  • B ⎑ ⎒ ⎒ ⎣ 1 7 2 7 βˆ’ 3 7 βˆ’ 5 1 4 ⎀ βŽ₯ βŽ₯ ⎦
  • C  5 4 βˆ’ 6 βˆ’ 2 
  • D  βˆ’ 5 βˆ’ 4 6 2 
  • E  βˆ’ 2 βˆ’ 6 4 5 

Q13:

Considere a matriz apresentada 𝐴 . Determine ο€Ή 𝐴      . 𝐴 =  βˆ’ 5 βˆ’ 1 3 βˆ’ 2 

  • A ⎑ ⎒ ⎒ ⎣ 5 1 3 3 1 3 βˆ’ 1 1 3 2 1 3 ⎀ βŽ₯ βŽ₯ ⎦
  • B ⎑ ⎒ ⎒ ⎣ βˆ’ 2 1 3 1 1 3 βˆ’ 3 1 3 βˆ’ 5 1 3 ⎀ βŽ₯ βŽ₯ ⎦
  • C  5 1 βˆ’ 3 2 
  • D  βˆ’ 5 βˆ’ 1 3 βˆ’ 2 
  • E  2 βˆ’ 3 1 5 

Q14:

Sendo 𝐴 =  βˆ’ 7 βˆ’ 2 βˆ’ 1 6  , determine ο€Ή 𝐴      .

  • A  6 1 2 βˆ’ 7 
  • B  6 βˆ’ 1 βˆ’ 2 βˆ’ 7 
  • C  βˆ’ 7 2 1 6 
  • D  βˆ’ 7 βˆ’ 2 βˆ’ 1 6 

Q15:

Sendo 𝐴 =  βˆ’ 2 βˆ’ 5 4 βˆ’ 1  , determine ο€Ή 𝐴      .

  • A  βˆ’ 1 βˆ’ 4 5 βˆ’ 2 
  • B  βˆ’ 1 4 βˆ’ 5 βˆ’ 2 
  • C  βˆ’ 2 5 βˆ’ 4 βˆ’ 1 
  • D  βˆ’ 2 βˆ’ 5 4 βˆ’ 1 

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