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Lesson: Finding an Unknown Variable in a Matrix

Worksheet • 13 Questions

Q1:

If 𝐴 = 𝐡 𝑇 , where what are the values of 𝑑 and 𝑒 ?

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

Q2:

Given that find the values of π‘₯ , 𝑦 , 𝑧 , and 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 = 1 , π‘˜ = 4 3
  • 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 = 5 8 , π‘˜ = 2

Q3:

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

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

Q4:

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

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

Q5:

Let 𝐴 = ( βˆ’ 2 3 ) , and 𝐡 = ( 1 2 ) . Find 𝑠 and 𝑑 satisfying 𝑠 + 𝑑 = 1 such that 𝑠 𝐴 + 𝑑 𝐡 = ( π‘ž π‘ž ) for some number π‘ž . Also give the number π‘ž .

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

Q6:

Given that find π‘₯ , 𝑦 , and 𝑧 .

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

Q7:

Determine the values of π‘₯ , 𝑦 , π‘˜ , and 𝑙 that satisfy the given equation where 𝑂 is the zero matrix of order 2 Γ— 2 .

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

Q8:

Given that what are the values of π‘₯ , 𝑦 , and 𝑧 ?

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

Q9:

Write the matrix ο€Ό 3 βˆ’ 8 βˆ’ 1 βˆ’ 9  in the form π‘Ž ο€Ό 1 0 0 0  + 𝑏 ο€Ό 0 1 0 0  + 𝑐 ο€Ό 0 0 1 0  + 𝑑 ο€Ό 0 0 0 1  , where π‘Ž , 𝑏 , 𝑐 , and 𝑑 are real numbers that you should find.

  • A 3 ο€Ό 1 0 0 0  βˆ’ 8 ο€Ό 0 1 0 0  βˆ’ ο€Ό 0 0 1 0  βˆ’ 9 ο€Ό 0 0 0 1 
  • B βˆ’ 8 ο€Ό 1 0 0 0  + 3 ο€Ό 0 1 0 0  βˆ’ 9 ο€Ό 0 0 1 0  βˆ’ ο€Ό 0 0 0 1 
  • C βˆ’ 8 ο€Ό 1 0 0 0  βˆ’ 9 ο€Ό 0 1 0 0  + 3 ο€Ό 0 0 1 0  βˆ’ ο€Ό 0 0 0 1 
  • D βˆ’ 8 ο€Ό 1 0 0 0  + 3 ο€Ό 0 1 0 0  βˆ’ ο€Ό 0 0 1 0  βˆ’ 9 ο€Ό 0 0 0 1 

Q10:

Let 𝐴 = ο€Ό 1 2 3 4  and 𝐡 = ο€Ό 1 2 1 π‘˜  . Is it possible to choose a value for π‘˜ so that 𝐴 𝐡 = 𝐡 𝐴 ? If so, what is this value?

  • AThere is no possible choice for π‘˜ .
  • BThere is a possible choice for π‘˜ . π‘˜ = 3 .
  • CThere is a possible choice for π‘˜ . π‘˜ = 4 .
  • DThere is a possible choice for π‘˜ . π‘˜ = 7 .
  • EThere is a possible choice for π‘˜ . π‘˜ = 1 0 .

Q11:

Consider the shown matrices Is it possible to choose π‘˜ such that 𝐴 𝐡 = 𝐡 𝐴 ? If so, what should π‘˜ be equal to?

  • A yes, π‘˜ = 4
  • B yes, π‘˜ = 5
  • C no, there is no possible choice for π‘˜
  • D yes, π‘˜ = 1 5
  • E yes, π‘˜ = 1 0

Q12:

Consider the matrices If 𝐴 𝐡 = 𝐡 𝐴 , what are the values of π‘₯ and 𝑦 ?

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

Q13:

Given that where 𝐼 is the unit matrix, determine the value of π‘₯ .

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