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Aula: Multiplicando Matrizes

Nesta aula, nós vamos aprender como multiplicar matrizes.

Atividade • 22 Questões

Q1:

Sabendo que 𝐴 =  βˆ’ 5 βˆ’ 5 βˆ’ 6 6  𝐡 =  4 6 βˆ’ 3 5  , , determine ( 𝐴 + 𝐡 ) 𝐴 .

  • A  βˆ’ 1 1 1 βˆ’ 2 1 1 1 1 
  • B  5 9 βˆ’ 7 1 βˆ’ 4 9 6 1 
  • C  βˆ’ 6 βˆ’ 4 βˆ’ 1 5 1 7 
  • D  βˆ’ 1 βˆ’ 2 1 1 1 1 1 1 

Q2:

Sabendo que 𝐴 =  6 βˆ’ 4 2 6  𝐡 =  3 4 0 βˆ’ 3  , , determine ( 𝐴 + 𝐡 ) 𝐴 .

  • A  5 4 βˆ’ 3 6 1 8 1 0 
  • B  5 8 6 βˆ’ 2 4 1 8 
  • C  1 5 βˆ’ 4 4 9 
  • D  5 4 1 8 βˆ’ 3 6 1 0 

Q3:

Considere as matrizes 𝐴 =  βˆ’ 3 βˆ’ 4 4 βˆ’ 4 4 4 5 βˆ’ 1 βˆ’ 1  , 𝐡 =  βˆ’ 2 βˆ’ 3 2 6 0 2 3 5 βˆ’ 4  .

Encontre 𝐴 𝐡 se possível.

  • A  βˆ’ 6 2 9 βˆ’ 3 0 4 4 3 2 βˆ’ 1 6 βˆ’ 1 9 βˆ’ 2 0 1 2 
  • B  βˆ’ 6 4 4 βˆ’ 1 9 2 9 3 2 βˆ’ 2 0 βˆ’ 3 0 βˆ’ 1 6 1 2 
  • C  2 6 βˆ’ 1 0 βˆ’ 4 5 4 βˆ’ 1 6 βˆ’ 8 βˆ’ 9 2 8 1 4 
  • D  2 6 4 βˆ’ 9 βˆ’ 1 0 βˆ’ 1 6 2 8 βˆ’ 4 5 βˆ’ 8 1 4 

Q4:

Considere as matrizes 𝐴 =  0 1  , 𝐡 =  βˆ’ 4 1 βˆ’ 6 6  , 𝐢 = [ 5 3 ] . Encontre 𝐴 𝐢 𝐡 e 𝐡 𝐴 𝐢 se possΓ­vel.

  • A 𝐴 𝐢 𝐡 =  0 0 βˆ’ 3 8 2 3  , 𝐡 𝐴 𝐢 =  5 3 3 0 1 8 
  • BNΓ£o Γ© possΓ­vel.
  • C 𝐴 𝐢 𝐡 =  βˆ’ 3 0 3 0 βˆ’ 1 8 1 8  , 𝐡 𝐴 𝐢 =  5 3 0 3 1 8 
  • D 𝐴 𝐢 𝐡 =  0 βˆ’ 3 8 0 2 3  , 𝐡 𝐴 𝐢 =  βˆ’ 3 0 3 0 βˆ’ 1 8 1 8 
  • E 𝐴 𝐢 𝐡 =  βˆ’ 3 0 βˆ’ 1 8 3 0 1 8  , 𝐡 𝐴 𝐢 =  βˆ’ 3 0 βˆ’ 1 8 3 0 1 8 

Q5:

Considere as matrizes

Encontre 𝐴 𝐡 .

  • A 𝐴 𝐡 =  π‘Ž 𝑏 𝑐 π‘Ž 𝑏 𝑐 π‘Ž 𝑏 𝑐 ο₯
  • B 𝐴 𝐡 =  π‘Ž π‘Ž π‘Ž 𝑏 𝑏 𝑏 𝑐 𝑐 𝑐 
  • C 𝐴 𝐡 =  π‘Ž π‘Ž π‘Ž 𝑏 𝑏 𝑏 𝑐 𝑐 𝑐 
  • D 𝐴 𝐡 =  π‘Ž 𝑏 𝑐 π‘Ž 𝑏 𝑐 π‘Ž 𝑏 𝑐 ο₯
  • E 𝐴 𝐡 =  π‘Ž 𝑏 𝑏 𝑐 π‘Ž 𝑏 𝑐 𝑐 π‘Ž 

Encontre 𝐡 β€² 𝐴 β€² .

  • A 𝐡 β€² 𝐴 β€² =  π‘Ž π‘Ž π‘Ž 𝑏 𝑏 𝑏 𝑐 𝑐 𝑐 
  • B 𝐡 β€² 𝐴 β€² =  π‘Ž π‘Ž π‘Ž 𝑏 𝑏 𝑏 𝑐 𝑐 𝑐 
  • C 𝐡 β€² 𝐴 β€² =  π‘Ž 𝑏 𝑐 π‘Ž 𝑏 𝑐 π‘Ž 𝑏 𝑐 ο₯
  • D 𝐡 β€² 𝐴 β€² =  π‘Ž 𝑏 𝑐 π‘Ž 𝑏 𝑐 π‘Ž 𝑏 𝑐 ο₯
  • E 𝐡 β€² 𝐴 β€² =  π‘Ž 𝑐 𝑐 𝑏 π‘Ž 𝑐 𝑏 𝑏 π‘Ž 

Q6:

Dados 𝐴 =  βˆ’ 7 7  𝐡 = [ 0 βˆ’ 5 ] , , determine 𝐴 𝐡 , se possΓ­vel.

  • A  0 3 5 0 βˆ’ 3 5 
  • B  0 0 3 5 βˆ’ 3 5 
  • C [ 0 βˆ’ 3 5 ]
  • D  0 βˆ’ 3 5 

Q7:

Dados 𝐴 =  2 βˆ’ 5 7 5  𝐡 =  βˆ’ 1 0  , , determine 𝐴 𝐡 , se possΓ­vel.

  • A  βˆ’ 2 βˆ’ 7 
  • B [ βˆ’ 2 βˆ’ 7 ]
  • C [ βˆ’ 2 5 ]
  • D  βˆ’ 2 5 

Q8:

Dados 𝐴 =  7 6  𝐡 = [ βˆ’ 3 βˆ’ 6 ] , , determine 𝐴 𝐡 , se possΓ­vel.

  • A  βˆ’ 2 1 βˆ’ 4 2 βˆ’ 1 8 βˆ’ 3 6 
  • B  βˆ’ 2 1 βˆ’ 1 8 βˆ’ 4 2 βˆ’ 3 6 
  • C [ βˆ’ 2 1 βˆ’ 3 6 ]
  • D  βˆ’ 2 1 βˆ’ 3 6 

Q9:

Dados 𝐴 =  βˆ’ 5 2 0 βˆ’ 1  𝐡 =  βˆ’ 7 βˆ’ 3 5 βˆ’ 6 4 βˆ’ 5  , , determine 𝐴 𝐡 , se possΓ­vel.

  • A  2 3 2 3 βˆ’ 3 5 6 βˆ’ 4 5 
  • B  2 3 6 2 3 βˆ’ 4 βˆ’ 3 5 5 
  • C  3 5 βˆ’ 8 1 5 βˆ’ 1 0 βˆ’ 2 5 1 5 
  • D  3 5 1 5 βˆ’ 2 5 βˆ’ 8 βˆ’ 1 0 1 5 

Q10:

Calcule o produto das matrizes  8 1 1 βˆ’ 3 7   1 0 βˆ’ 1 3 1  .

  • A  1 1 3 3 βˆ’ 9 1 0 
  • B  4 7 βˆ’ 1 9 βˆ’ 5 1 βˆ’ 4 
  • C  8 0 βˆ’ 1 1 βˆ’ 9 7 
  • D  1 1 0 βˆ’ 8 2 1 βˆ’ 3 
  • E  8 3 8 9 2 1 βˆ’ 4 

Q11:

Considere o produto da matriz

O que vocΓͺ pode concluir sobre isso?

  • APara uma dada matriz 2 Γ— 3 , 𝐴 , pode haver uma matriz 𝐡 que nΓ£o Γ© a matriz de identidade 2 Γ— 2 para a qual 𝐡 𝐴 = 𝐴 .
  • BPara uma dada matriz 2 Γ— 3 , 𝐴 , pode haver uma matriz 𝐡 que nΓ£o Γ© a matriz de identidade 3 Γ— 3 para a qual 𝐴 𝐡 = 𝐴 .
  • CPara uma dada matriz 2 Γ— 3 , 𝐴 , nΓ£o pode haver matriz 𝐡 exceto a matriz identidade 2 Γ— 2 para a qual 𝐡 𝐴 = 𝐴 .
  • DPara uma dada matriz 2 Γ— 3 , 𝐴 , pode haver uma matriz 𝐡 que nΓ£o Γ© a matriz de identidade 3 Γ— 3 para a qual 𝐴 𝐡 = 𝐡 .

Γ‰ possΓ­vel encontrar uma matriz 𝐡 com a propriedade acima para cada matriz 2 Γ— 3 , 𝐴 ?

  • Asim
  • BnΓ£o

Q12:

Considere as matrizes 𝐴 =  βˆ’ 4 2 βˆ’ 6 βˆ’ 6  , 𝐡 =  βˆ’ 5 βˆ’ 1 1 0  .

Encontre 𝐴 𝐡  e 𝐴 𝐡  .

  • A 𝐴 𝐡 =  1 4 4 βˆ’ 1 6 βˆ’ 2   , 𝐴 𝐡 =  1 8 βˆ’ 4 3 6 βˆ’ 6  
  • B 𝐴 𝐡 =  1 4 βˆ’ 1 6 4 βˆ’ 2   , 𝐴 𝐡 =  1 8 3 6 βˆ’ 4 βˆ’ 6  
  • C 𝐴 𝐡 =  1 4 4 βˆ’ 1 6 βˆ’ 2   , 𝐴 𝐡 =  1 4 4 βˆ’ 1 6 βˆ’ 2  
  • D 𝐴 𝐡 =  2 6 βˆ’ 4 βˆ’ 4 2   , 𝐴 𝐡 =  2 6 βˆ’ 4 βˆ’ 4 2  

Q13:

Considere as matrizes 𝐴 =  1 2 0 βˆ’ 3  , 𝐡 =  4 βˆ’ 5 βˆ’ 5 6  , 𝐢 =  3 6 3 0  . Determine 𝐴 𝐡 𝐢 , se possΓ­vel.

  • A  3 βˆ’ 3 6 βˆ’ 9 9 0 
  • B  3 βˆ’ 9 βˆ’ 3 6 9 0 
  • C  2 7 βˆ’ 3 3 βˆ’ 3 6 4 2 
  • D  2 7 βˆ’ 3 6 βˆ’ 3 3 4 2 

Q14:

Sabendo que 𝐴 =  βˆ’ 1 5 0 5  𝐡 =  5 βˆ’ 5 0 βˆ’ 1  , , e 𝐼 Γ© a matriz identidade da mesma ordem, determine a matriz 𝑋 para a qual 𝐴 𝐡 = 𝑋 Γ— 𝐼 .

Q15:

Dada a equação 𝐴 =  πœƒ πœƒ πœƒ βˆ’ πœƒ  𝐡 =  πœƒ πœƒ βˆ’ πœƒ βˆ’ πœƒ  , c o s s e n s e n c o s , s e n s e n c o s c o s determine 𝐴 𝐡 , se possΓ­vel.

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

Q16:

Sendo 𝐴 =  𝑖 𝑖 0 0  𝐡 =  𝑖 𝑖 0 0  ,   , e 𝑖 = βˆ’ 1  , determine 𝐴 𝐡 se possΓ­vel.

  • A  βˆ’ 1 1 0 0 
  • B  1 βˆ’ 1 0 0 
  • C  2 0 0 0 
  • D  βˆ’ 2 0 0 0 

Q17:

Dados 𝐴 =  βˆ’ 3 βˆ’ 7 βˆ’ 1 3 4 1  𝐡 =  6 βˆ’ 4 3  , , determine 𝐴 𝐡 se possΓ­vel.

  • A  7 5 
  • B [ 7 5 ]
  • C  βˆ’ 1 8 2 8 βˆ’ 3 1 8 βˆ’ 1 6 3 
  • D  βˆ’ 1 8 1 8 2 8 βˆ’ 1 6 βˆ’ 3 3 

Q18:

Dados 𝐴 =  βˆ’ 2 βˆ’ 4 5 βˆ’ 3 6 βˆ’ 4  𝐡 =  4 1 0 βˆ’ 7 6 βˆ’ 3  , , determine 𝐴 𝐡 se possΓ­vel.

  • A  2 2 1 1 βˆ’ 3 6 βˆ’ 3 3 
  • B  2 2 βˆ’ 3 6 1 1 βˆ’ 3 3 
  • C  βˆ’ 8 βˆ’ 3 0 βˆ’ 4 2 3 0 1 2 
  • D  βˆ’ 8 0 3 0 βˆ’ 3 βˆ’ 4 2 1 2 

Q19:

Considere as matrizes dadas 𝐴 e 𝐡 . Encontre 𝐴 𝐡 se possível.

  • A  βˆ’ 8 0 βˆ’ 1 1 5 4 8 1 6 6 8 1 2 βˆ’ 8 4 βˆ’ 7 1 0 5 
  • B  βˆ’ 8 0 1 6 βˆ’ 8 4 βˆ’ 1 1 5 6 8 βˆ’ 7 4 8 1 2 1 0 5 
  • C  βˆ’ 8 8 3 6 4 2 8 3 2 6 3 
  • D  βˆ’ 8 8 8 3 6 3 2 4 2 6 3 

Q20:

Considere as matrizes dadas 𝐴 e 𝐡 . Encontre 𝐴 𝐡 se possível.

  • A  βˆ’ 2 βˆ’ 1 4 βˆ’ 1 8 βˆ’ 5 0 6 8 7 8 2 9 βˆ’ 6 βˆ’ 3 
  • B  βˆ’ 2 βˆ’ 5 0 2 9 βˆ’ 1 4 6 8 βˆ’ 6 βˆ’ 1 8 7 8 βˆ’ 3 
  • C  8 5 0 1 8 βˆ’ 1 0 1 8 βˆ’ 2 1 
  • D  8 βˆ’ 1 0 5 0 1 8 1 8 βˆ’ 2 1 

Q21:

Considere as matrizes 𝐴 = [ 1 2 βˆ’ 7 ] , 𝐡 =  βˆ’ 4 6 βˆ’ 2  . Encontre 𝐴 𝐡 , se possΓ­vel.

  • A [ 2 2 ]
  • B [ 3 0 ]
  • C  βˆ’ 4 1 2 1 4 
  • D [ βˆ’ 4 1 2 1 4 ]

Q22:

Dado que 𝐴 =  βˆ’ 5 βˆ’ 6 2 5  𝐡 =  3 βˆ’ 7 5  , , determine 𝐴 𝐡 se possΓ­vel.

  • Aindefinida
  • B  βˆ’ 1 5 4 2 2 5 
  • C  βˆ’ 1 5 4 2 1 0 5 
  • D  βˆ’ 1 5 βˆ’ 6 βˆ’ 1 4 5 
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