Atividade: Igualdade de Matrizes

Nesta atividade, nós vamos praticar a verificar a igualdade de matrizes e como determinar valores de variáveis desconhecidas representadas como elementos em duas matrizes iguais.

Q1:

Dadas 𝐴=333333 e 𝐡=3333, serΓ‘ verdade que 𝐴=𝐡?

  • AnΓ£o
  • Bsim

Q2:

Se 𝐴=ο”βˆ’53βˆ’7βˆ’3,𝐡=ο”βˆ’5βˆ’3βˆ’73, Γ© verdade que 𝐴=𝐡?

  • AnΓ£o
  • Bsim

Q3:

Para qual das seguintes matrizes se tem 𝐴𝐡=𝐴𝐢?

  • A 𝐴 =  1 βˆ’ 1 βˆ’ 1 1  , 𝐡 =  1 1 1 1  , 𝐢 =  2 2 2 2 
  • B 𝐴 =  1 βˆ’ 1 βˆ’ 1 1  , 𝐡 =  1 1 1 1  , 𝐢 =  2 1 1 2 
  • C 𝐴 =  1 1 1 1  , 𝐡 =  βˆ’ 1 βˆ’ 1 βˆ’ 1 βˆ’ 1  , 𝐢 =  2 2 2 2 
  • D 𝐴 =  1 βˆ’ 1 βˆ’ 1 1  , 𝐡 =  βˆ’ 1 1 1 βˆ’ 1  , 𝐢 =  2 2 2 2 
  • E 𝐴 =  1 1 1 1  , 𝐡 =  βˆ’ 1 βˆ’ 1 βˆ’ 1 βˆ’ 1  , 𝐢 =  βˆ’ 1 1 1 βˆ’ 1 

Q4:

Dado que 99π‘₯+3𝑦2π‘₯βˆ’6𝑦9=32π‘π‘Ž2,ο—ο˜ encontrar o valor de π‘π‘Ž.

  • A 1 9
  • B2
  • C9
  • D 1 2
  • E12

Q5:

Sendo ο”π‘Ž+π‘π‘Žβˆ’π‘π‘Ž+𝑏+π‘π‘Žβˆ’7π‘βˆ’π‘‘ο =ο”βˆ’3βˆ’17βˆ’5βˆ’64, determine os valores de π‘Ž, 𝑏, 𝑐 e 𝑑.

  • A π‘Ž = βˆ’ 1 0 , 𝑏 = 7 , 𝑐 = 1 2 , 𝑑 = 5
  • B π‘Ž = βˆ’ 1 0 , 𝑏 = 7 , 𝑐 = βˆ’ 2 , 𝑑 = βˆ’ 2 0
  • C π‘Ž = βˆ’ 1 0 , 𝑏 = 4 , 𝑐 = βˆ’ 2 , 𝑑 = 5
  • D π‘Ž = βˆ’ 1 0 , 𝑏 = 7 , 𝑐 = βˆ’ 2 , 𝑑 = 5

Q6:

Sendo 3π‘₯βˆ’3βˆ’3βˆ’10π‘¦βˆ’1=0βˆ’3βˆ’105π‘¦βˆ’5, determine os valores de π‘₯ e 𝑦.

  • A π‘₯ = 1 , 𝑦 = 1
  • B π‘₯ = 0 , 𝑦 = βˆ’ 9
  • C π‘₯ = 1 , 𝑦 = βˆ’ 1
  • D π‘₯ = βˆ’ 1 , 𝑦 = βˆ’ 1
  • E π‘₯ = 3 , 𝑦 = βˆ’ 1

Q7:

Dado que 0βˆ’22π‘Ž+42𝑏+9=0βˆ’22βˆ’5, determinar os valores de π‘Ž e 𝑏.

  • A π‘Ž = 3 , 𝑏 = 2
  • B π‘Ž = βˆ’ 1 , 𝑏 = 2
  • C π‘Ž = βˆ’ 2 , 𝑏 = βˆ’ 1 4
  • D π‘Ž = 2 , 𝑏 = βˆ’ 5
  • E π‘Ž = βˆ’ 1 , 𝑏 = βˆ’ 7

Q8:

Dado que ο•βˆ’21630βˆ’6𝑧+𝑦=𝑙π‘₯+2βˆ’9𝑦60, encontre os valores de π‘₯, 𝑦, 𝑧, e 𝑙.

  • A π‘₯ = Β± 1 , 𝑦 = 0 , 𝑧 = βˆ’ 1 0 , 𝑙 = βˆ’ 6 .
  • B π‘₯ = Β± 1 , 𝑦 = 0 , 𝑧 = βˆ’ 1 0 , 𝑙 = 6 0 .
  • C π‘₯ = 1 , 𝑦 = 0 , 𝑧 = βˆ’ 1 0 , 𝑙 = 6 0 .
  • D π‘₯ = √ 3 , 𝑦 = 0 , 𝑧 = 6 0 , 𝑙 = βˆ’ 6 .

Q9:

Dado ο•βˆ’43π‘₯βˆ’7=ο•βˆ’438π‘¦βˆ’6, determine os valores de π‘₯ e 𝑦.

  • A π‘₯ = 1 4 , 𝑦 = βˆ’ 1
  • B π‘₯ = βˆ’ 7 , 𝑦 = βˆ’ 6
  • C π‘₯ = 8 , 𝑦 = 6
  • D π‘₯ = 8 , 𝑦 = βˆ’ 7
  • E π‘₯ = 8 , 𝑦 = βˆ’ 1

Q10:

Considere que a matriz 𝐴=[βˆ’10π‘₯π‘₯+3𝑦2π‘₯βˆ’π‘§] e a matriz 𝐡=[βˆ’302710]. Dado que 𝐴=𝐡, determine os valores de π‘₯, 𝑦, e 𝑧.

  • A π‘₯ = βˆ’ 3 0 , 𝑦 = 8 , 𝑧 = βˆ’ 4
  • B π‘₯ = 3 , 𝑦 = 8 , 𝑧 = 4
  • C π‘₯ = 3 , 𝑦 = 8 , 𝑧 = βˆ’ 4
  • D π‘₯ = 3 , 𝑦 = 2 4 , 𝑧 = βˆ’ 4
  • E π‘₯ = 3 , 𝑦 = 8 , 𝑧 = βˆ’ 1 6

Q11:

Dado o seguinte, encontre os valores de π‘₯ e 𝑦. 10π‘₯+102βˆ’39=2022𝑦+99

  • A π‘₯ = Β± 1 , 𝑦 = 3
  • B π‘₯ = 1 , 𝑦 = 0
  • C π‘₯ = βˆ’ 1 , 𝑦 = 3
  • D π‘₯ = Β± 1 , 𝑦 = βˆ’ 6
  • E π‘₯ = 2 0 , 𝑦 = βˆ’ 1 2

Q12:

Dadas as matrizes 𝐴=βŽ‘βŽ’βŽ’βŽ£βˆ’0,6βˆ’12βˆ’7101⎀βŽ₯βŽ₯⎦𝐡=ο™βˆ’35βˆ’0,5βˆ’0,71ο₯,, Γ© verdade que 𝐴=𝐡?

  • Asim
  • BnΓ£o

Q13:

Dadas 𝐴=777777 e 𝐡=7777, serΓ‘ verdade que 𝐴≠𝐡?

  • AnΓ£o
  • Bsim

Q14:

Dadas 𝐴=222222 e 𝐡=2222, serΓ‘ verdade que 𝐴≠𝐡?

  • Asim
  • BnΓ£o

Q15:

Dadas 𝐴=181818181818 e 𝐡=18181818, serΓ‘ verdade que 𝐴≠𝐡?

  • Asim
  • BnΓ£o

Q16:

Dado que 66π‘₯βˆ’3𝑦3π‘₯βˆ’8𝑦6=27π‘π‘Ž3,ο—ο˜ encontrar o valor de π‘π‘Ž.

  • A6
  • B 1 3
  • C15
  • D3
  • E 1 6

Q17:

Se 𝐴=3321,𝐡=3123, Γ© verdade que 𝐴=𝐡?

  • Asim
  • BnΓ£o

Q18:

Se 𝐴=𝐡, onde 𝐴=2βˆ’105βˆ’8,𝐡=ο”βˆ’π‘‘52π‘’βˆ’8, quais sΓ£o os valores de 𝑑 e 𝑒?

  • A 𝑑 = βˆ’ 2 , 𝑒 = βˆ’ 4
  • B 𝑑 = βˆ’ 2 , 𝑒 = βˆ’ 8
  • C 𝑑 = βˆ’ 2 , 𝑒 = βˆ’ 5
  • D 𝑑 = βˆ’ 5 , 𝑒 = βˆ’ 5
  • E 𝑑 = 5 , 𝑒 = βˆ’ 5

Q19:

Dado que π‘₯βˆ’5βˆ’9βˆ’3𝑧1+55π‘₯βˆ’6βˆ’π‘§7=ο•βˆ’3π‘₯+24π‘¦βˆ’22π‘˜ο‘+4π‘₯3π‘¦βˆ’24π‘˜ο‘, encontre os valores de π‘₯, 𝑦, 𝑧, e π‘˜.

  • A π‘₯ = 7 2 5 , 𝑦 = βˆ’ 3 9 1 6 , 𝑧 = 5 4 , π‘˜ = 2
  • B π‘₯ = 7 8 , 𝑦 = βˆ’ 1 5 7 , 𝑧 = 5 8 , π‘˜ = 2
  • C π‘₯ = βˆ’ 7 2 5 , 𝑦 = βˆ’ 3 9 1 6 , 𝑧 = 5 4 , π‘˜ = 4 3
  • D π‘₯ = 7 8 , 𝑦 = βˆ’ 1 5 7 , 𝑧 = 1 , π‘˜ = 4 3

Q20:

Dado que π‘₯ο˜βˆ’3βˆ’8βˆ’8+π‘¦ο˜007ο€βˆ’π‘§ο˜04βˆ’1=ο˜βˆ’12βˆ’28βˆ’19, encontre os valores de π‘₯, 𝑦, e 𝑧.

  • A π‘₯ = 4 , 𝑦 = βˆ’ 2 , 𝑧 = 1
  • B π‘₯ = βˆ’ 1 2 , 𝑦 = βˆ’ 2 8 , 𝑧 = βˆ’ 1 9
  • C π‘₯ = 4 , 𝑦 = 2 , 𝑧 = βˆ’ 1 9
  • D π‘₯ = βˆ’ 9 , 𝑦 = βˆ’ 2 8 , 𝑧 = βˆ’ 1
  • E π‘₯ = 4 , 𝑦 = 2 , 𝑧 = βˆ’ 1

Q21:

Seja 𝐴=[βˆ’23], e 𝐡=[12]. Encontre 𝑠 e 𝑑 que satisfaz 𝑠+𝑑=1 de tal modo que 𝑠𝐴+𝑑𝐡=[π‘žπ‘ž] por algum nΓΊmero π‘ž. TambΓ©m dΓͺ o nΓΊmero π‘ž.

  • A 𝑠 = βˆ’ 5 2 , 𝑑 = 1 2 , π‘ž = βˆ’ 9 4
  • B 𝑠 = βˆ’ 1 4 , 𝑑 = 5 4 , π‘ž = 7 4
  • C 𝑠 = βˆ’ 1 4 , 𝑑 = 5 4 , π‘ž = 5 4
  • D 𝑠 = βˆ’ 1 4 , 𝑑 = βˆ’ 5 4 , π‘ž = βˆ’ 3 4
  • E 𝑠 = 5 2 , 𝑑 = 1 2 , π‘ž = 7 4

Q22:

Dada a equação 5π‘₯1𝑦=5𝑧6βˆ’5, determine π‘₯, 𝑦 e 𝑧.

  • A π‘₯ = 6 , 𝑦 = βˆ’ 5 , 𝑧 = 5
  • B π‘₯ = 1 , 𝑦 = 1 , 𝑧 = βˆ’ 5
  • C π‘₯ = 6 , 𝑦 = βˆ’ 5 , 𝑧 = 1
  • D π‘₯ = 6 , 𝑦 = 1 , 𝑧 = βˆ’ 5
  • E π‘₯ = 5 , 𝑦 = 5 , 𝑧 = 6

Q23:

Determine os valores de π‘₯, 𝑦, π‘˜ e 𝑙 que satisfazem a equação π‘₯ο”βˆ’4610π‘˜ο +π‘¦ο”βˆ’7𝑙0βˆ’5+43βˆ’110βˆ’2=𝑂, em que 𝑂 Γ© a matriz nula 2Γ—2.

  • A π‘₯ = βˆ’ 4 , 𝑦 = βˆ’ 1 4 , π‘˜ = βˆ’ 1 6 , 𝑙 = βˆ’ 1 6
  • B π‘₯ = βˆ’ 2 4 , 𝑦 = βˆ’ 2 0 , π‘˜ = 3 , 𝑙 = 1
  • C π‘₯ = βˆ’ 4 , 𝑦 = 4 , π‘˜ = βˆ’ 1 6 , 𝑙 = βˆ’ 1 6
  • D π‘₯ = βˆ’ 4 , 𝑦 = 4 , π‘˜ = βˆ’ 7 , 𝑙 = 7

Q24:

Dada a equação 451356090180180=⎑⎒⎒⎒⎒⎒⎣11√22π‘₯12𝑦2√33π‘§βŽ€βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯⎦,cotgsenseccosseccostg∘∘∘∘∘∘ quais sΓ£o os valores de π‘₯, 𝑦 e 𝑧?

  • A π‘₯ = βˆ’ 2 , 𝑦 = βˆ’ 1 , 𝑧 = 0
  • B π‘₯ = 1 , 𝑦 = βˆ’ 2 , 𝑧 = 0
  • C π‘₯ = βˆ’ 1 , 𝑦 = βˆ’ 2 , 𝑧 = 0
  • D π‘₯ = βˆ’ 2 , 𝑦 = 1 , 𝑧 = 0

Q25:

Escreva a matriz 3βˆ’8βˆ’1βˆ’9 na forma π‘Žο”1000+𝑏0100+𝑐0010+𝑑0001, onde π‘Ž, 𝑏, 𝑐, e 𝑑 sΓ£o nΓΊmeros reais que vocΓͺ deve encontrar.

  • A 3  1 0 0 0  βˆ’ 8  0 1 0 0  βˆ’  0 0 1 0  βˆ’ 9  0 0 0 1 
  • B βˆ’ 8  1 0 0 0  βˆ’ 9  0 1 0 0  + 3  0 0 1 0  βˆ’  0 0 0 1 
  • C βˆ’ 8  1 0 0 0  + 3  0 1 0 0  βˆ’ 9  0 0 1 0  βˆ’  0 0 0 1 
  • D βˆ’ 8  1 0 0 0  + 3  0 1 0 0  βˆ’  0 0 1 0  βˆ’ 9  0 0 0 1 

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