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Lesson: Finding an Unknown Matrix

Worksheet • 20 Questions

Q1:

Consider the matrices Find the matrix 𝑋 that satisfies the equation 𝑋 = 𝐴 + 𝐡 𝑇 𝑇 𝑇 .

  • A ο€Ό βˆ’ 5 1 5 βˆ’ 3 βˆ’ 7 4 1 
  • B  βˆ’ 5 βˆ’ 7 1 5 4 βˆ’ 3 1 
  • C ο€Ό 9 7 1 1 0 3 βˆ’ 9 
  • D  9 1 3 7 1 0 βˆ’ 9 

Q2:

Consider the matrices Find the matrix 𝑋 that satisfies the equation 𝑋 = 𝐴 βˆ’ 𝐡 𝑇 𝑇 𝑇 .

  • A ο€Ό 1 2 0 0 7 βˆ’ 3 0 
  • B  1 2 7 0 βˆ’ 3 0 0 
  • C ο€Ό βˆ’ 4 7 βˆ’ 1 0 9 2 0 8 
  • D  βˆ’ 4 βˆ’ 1 0 2 0 7 9 8 

Q3:

Consider the matrices Find the matrix 𝑋 that satisfies the equation 𝑋 = 𝐴 + 𝐡 𝑇 𝑇 𝑇 .

  • A ο€Ό 5 βˆ’ 3 βˆ’ 3 6 βˆ’ 1 βˆ’ 9 
  • B  5 6 βˆ’ 3 βˆ’ 1 βˆ’ 3 βˆ’ 9 
  • C ο€Ό 1 3 2 βˆ’ 7 βˆ’ 1 5 1 3 9 
  • D  1 3 βˆ’ 7 1 3 2 βˆ’ 1 5 9 

Q4:

Given that what are 𝑋 and π‘Œ ?

  • A 𝑋 = ο€Ό βˆ’ 3 βˆ’ 1 2 3 1 1  , π‘Œ = ο€Ό 3 4 3 βˆ’ 8 
  • B 𝑋 = ο€Ό βˆ’ 6 βˆ’ 2 4 6 2 2  , π‘Œ = ο€Ό 0 8 βˆ’ 6 βˆ’ 3 
  • C 𝑋 = ο€Ό βˆ’ 6 βˆ’ 8 βˆ’ 6 1 6  , π‘Œ = ο€Ό 0 βˆ’ 8 6 3 
  • D 𝑋 = ο€Ό βˆ’ 6 βˆ’ 2 4 6 2 2  , π‘Œ = ο€Ό 1 2 1 βˆ’ 4 

Q5:

Given that what are 𝑋 and π‘Œ ?

  • A 𝑋 = ο€Ό 3 1 1 9 βˆ’ 8  , π‘Œ = ο€Ό βˆ’ 1 4 βˆ’ 7 1 2 
  • B 𝑋 = ο€Ό 3 3 4 βˆ’ 3 2 0  , π‘Œ = ο€Ό βˆ’ 1 βˆ’ 1 9 5 βˆ’ 1 6 
  • C 𝑋 = ο€Ό 1 βˆ’ 4 7 βˆ’ 1 2  , π‘Œ = ο€Ό 1 1 9 βˆ’ 5 1 6 
  • D 𝑋 = ο€Ό 6 2 2 1 8 βˆ’ 1 6  , π‘Œ = ο€Ό 0 2 βˆ’ 3 6 

Q6:

Find the matrix 𝐴 that satisfies the equation 𝐴 βˆ’ 2 𝐴 = ο€Ό 5 βˆ’ 9 9 1  𝑇 .

  • A ο€Ό βˆ’ 5 3 βˆ’ 3 βˆ’ 1 
  • B ο€Ό βˆ’ 5 βˆ’ 3 3 βˆ’ 1 
  • C βŽ› ⎜ ⎜ ⎝ βˆ’ 5 βˆ’ 3 2 3 2 βˆ’ 1 ⎞ ⎟ ⎟ ⎠
  • D βŽ› ⎜ ⎜ ⎝ βˆ’ 5 3 2 βˆ’ 3 2 βˆ’ 1 ⎞ ⎟ ⎟ ⎠

Q7:

Given that find the matrix 𝐴 .

  • A ο€Ό βˆ’ 6 βˆ’ 3 3 4 
  • B ο€Ό βˆ’ 3 3 1 4 
  • C ο€Ό βˆ’ 3 βˆ’ 2 4 7 
  • D ο€Ό 0 3 5 4 

Q8:

Given that find the matrix 𝐴 .

  • A ο€Ό βˆ’ 3 2 2 2 
  • B βŽ› ⎜ ⎜ ⎝ βˆ’ 2 9 5 βˆ’ 7 4 7 1 ⎞ ⎟ ⎟ ⎠
  • C ο€Ό βˆ’ 3 4 8 3 0 
  • D βŽ› ⎜ ⎜ ⎝ βˆ’ 5 2 9 βˆ’ 1 7 7 4 1 ⎞ ⎟ ⎟ ⎠

Q9:

Given that solve the equation

  • A  7 2 5 βˆ’ 1 5 2 
  • B ο€Ό 7 5 5 2 βˆ’ 1 2 
  • C  βˆ’ 1 βˆ’ 7 βˆ’ 3 1 2 6 βˆ’ 5 1 9 
  • D ο€Ό βˆ’ 1 βˆ’ 3 1 βˆ’ 5 βˆ’ 7 2 6 1 9 

Q10:

Determine 𝑋 , given that

  • A ο€Ό 1 0 0 1 
  • B ο€Ό 1 1 1 1 
  • C  1 1 1 1 1 1 1 1 1 
  • D  1 0 0 0 1 0 0 0 1 

Q11:

Given that find the matrix 𝑋 .

  • A ο€Ό βˆ’ 6 βˆ’ 2 5 5 
  • B ο€Ό 2 4 8 βˆ’ 2 0 βˆ’ 2 0 
  • C ο€Ό 2 8 1 2 βˆ’ 1 6 βˆ’ 1 6 
  • D ο€Ό βˆ’ 6 βˆ’ 2 9 9 
  • E ο€Ό βˆ’ 2 2 9 9 

Q12:

Consider the matrices Determine the matrix 𝑋 that satisfies βˆ’ 𝑋 = 𝐴 + ( 𝐡 𝐢 ) 𝑇 2 𝑇 .

  • A ο€Ό 2 2 βˆ’ 9 βˆ’ 4 5 βˆ’ 4 8 
  • B ο€Ό 2 2 βˆ’ 4 5 βˆ’ 9 βˆ’ 4 8 
  • C ο€Ό 2 2 βˆ’ 5 1 βˆ’ 3 βˆ’ 4 8 
  • D ο€Ό 2 2 βˆ’ 3 βˆ’ 5 1 βˆ’ 4 8 

Q13:

Consider the matrices 𝐴 and 𝐡 : Find 𝐴 + 𝐡 βˆ’ 1 2 .

  • A βŽ› ⎜ ⎜ ⎝ βˆ’ 5 1 3 2 βˆ’ 2 5 6 1 2 ⎞ ⎟ ⎟ ⎠
  • B ο€Ό βˆ’ 6 8 βˆ’ 2 5 3 0 
  • C  βˆ’ 9 2 1 3 2 βˆ’ 2 5 3 0 
  • D βŽ› ⎜ ⎜ ⎝ 1 2 5 2 1 1 1 2 1 2 ⎞ ⎟ ⎟ ⎠

Q14:

Given that determine the matrix 𝑋 that satisfies the relation 𝑋 = ( 𝐴 𝐡 + 𝐴 𝐢 ) 𝑇 .

  • A ο€Ό βˆ’ 1 2 βˆ’ 4 βˆ’ 4 3 3 
  • B ο€Ό βˆ’ 1 6 0 βˆ’ 4 0 1 3 
  • C ο€Ό βˆ’ 1 6 βˆ’ 4 0 0 1 3 
  • D ο€Ό βˆ’ 1 2 βˆ’ 4 3 βˆ’ 4 3 

Q15:

Solve the matrix equation βˆ’ 3  𝑋 + ο€Ό 3 6 5 7   = βˆ’ 𝑋 + ο€Ό βˆ’ 5 4 1 7  .

  • A ο€Ό βˆ’ 2 βˆ’ 1 1 βˆ’ 8 βˆ’ 1 4 
  • B ο€Ό βˆ’ 2 2 2 7 1 4 
  • C ο€Ό 4 2 2 1 6 2 8 
  • D ο€Ό 7 7 7 7 
  • E ο€Ό 4 1 2 0 

Q16:

Given that find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 1 , 𝑦 = βˆ’ 9
  • B π‘₯ = 8 , 𝑦 = βˆ’ 1 0
  • C π‘₯ = 5 , 𝑦 = βˆ’ 3 0
  • D π‘₯ = 7 , 𝑦 = βˆ’ 2 6

Q17:

Given that find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 9 , 𝑦 = βˆ’ 2
  • B π‘₯ = 3 2 , 𝑦 = 8
  • C π‘₯ = 2 1 , 𝑦 = 2 3
  • D π‘₯ = βˆ’ 1 , 𝑦 = 1

Q18:

Given that 𝑀 =  5 6 βˆ’ 5 βˆ’ 4  , find the values of π‘₯ and 𝑦 that satisfy 𝑀 + π‘₯ 𝑀 + 𝑦 𝐼 = 𝑂  , where 𝑂 is the zero matrix of order 2 Γ— 2 and 𝐼 is the unit matrix of order 2 Γ— 2 .

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

Q19:

Adam guesses that any matrix , where , must be a combination of and . In other words, it must be for some numbers and . Ramy wants to challenge this, since he see that produces the same product when multiplied on either side. Help Adam by finding and so that

  • A
  • B
  • C
  • D
  • E

Q20:

Given that

solve the following matrix equation for :

  • A
  • B
  • C
  • D
  • E
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