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Worksheet: Finding an Unknown Variable in a Matrix

Q1:

If , where what are the values of and ?

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q2:

Given that find the values of , , , and .

  • A , , ,
  • B , , ,
  • C , , ,
  • D , , ,

Q3:

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

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

Q4:

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

  • A π‘₯ = βˆ’ 1 , 𝑦 = βˆ’ 1 4 , 𝑧 = 1 0
  • B π‘₯ = βˆ’ 1 , 𝑦 = 2 , 𝑧 = 4
  • C π‘₯ = βˆ’ 2 , 𝑦 = βˆ’ 1 4 , 𝑧 = βˆ’ 4
  • D π‘₯ = βˆ’ 1 , 𝑦 = βˆ’ 2 , 𝑧 = βˆ’ 4
  • E π‘₯ = βˆ’ 1 , 𝑦 = βˆ’ 2 , 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’ 5 2 , 𝑑 = 1 2 , π‘ž = βˆ’ 9 4
  • B 𝑠 = βˆ’ 1 4 , 𝑑 = βˆ’ 5 4 , π‘ž = βˆ’ 3 4
  • C 𝑠 = 5 2 , 𝑑 = 1 2 , π‘ž = 7 4
  • D 𝑠 = βˆ’ 1 4 , 𝑑 = 5 4 , π‘ž = 7 4
  • E 𝑠 = βˆ’ 1 4 , 𝑑 = 5 4 , π‘ž = 5 4

Q6:

Given that find , , and .

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q7:

Determine the values of , , , and that satisfy the given equation where is the zero matrix of order .

  • A , , ,
  • B , , ,
  • C , , ,
  • D , , ,

Q8:

Given that what are the values of , , and ?

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q9:

Write the matrix in the form , where , , , and are real numbers that you should find.

  • A
  • B
  • C
  • D

Q10:

Let 𝐴 =  1 2 3 4  and 𝐡 =  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 a possible choice for π‘˜ . π‘˜ = 1 0 .
  • BThere is a possible choice for π‘˜ . π‘˜ = 4 .
  • CThere is a possible choice for π‘˜ . π‘˜ = 7 .
  • DThere is no possible choice for π‘˜ .
  • EThere is a possible choice for π‘˜ . π‘˜ = 3 .

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

Q12:

Consider the shown matrices and . If , what are the values of and ?

  • A ,
  • B ,
  • C ,
  • D ,

Q13:

Given that where is the unit matrix, determine the value of .