Worksheet: Equality of Matrices

In this worksheet, we will practice checking the equality of matrices and finding values of unknown variables represented as elements in two equal matrices.

Q1:

Given that 𝐴 = 3 3 3 3 3 3 and that 𝐵 = 3 3 3 3 , is it true that 𝐴 = 𝐵 ?

  • Ano
  • Byes

Q2:

If is it true that 𝐴 = 𝐵 ?

  • Ano
  • Byes

Q3:

For which of the following matrices is ?

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

Q4:

Given that find the value of 𝑏 𝑎 .

  • A 1 9
  • B9
  • C2
  • D12
  • E 1 2

Q5:

Given that determine the values of 𝑎 , 𝑏 , 𝑐 , and 𝑑 .

  • A 𝑎 = 1 0 , 𝑏 = 7 , 𝑐 = 1 2 , 𝑑 = 5
  • B 𝑎 = 1 0 , 𝑏 = 7 , 𝑐 = 2 , 𝑑 = 2 0
  • C 𝑎 = 1 0 , 𝑏 = 4 , 𝑐 = 2 , 𝑑 = 5
  • D 𝑎 = 1 0 , 𝑏 = 7 , 𝑐 = 2 , 𝑑 = 5

Q6:

Given that find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 1 , 𝑦 = 1
  • B 𝑥 = 3 , 𝑦 = 1
  • C 𝑥 = 0 , 𝑦 = 9
  • D 𝑥 = 1 , 𝑦 = 1
  • E 𝑥 = 1 , 𝑦 = 1

Q7:

Given that determine the values of 𝑎 and 𝑏 .

  • A 𝑎 = 3 , 𝑏 = 2
  • B 𝑎 = 2 , 𝑏 = 1 4
  • C 𝑎 = 2 , 𝑏 = 5
  • D 𝑎 = 1 , 𝑏 = 7
  • E 𝑎 = 1 , 𝑏 = 2

Q8:

Given that find the values of 𝑥 , 𝑦 , 𝑧 , and 𝑙 .

  • A 𝑥 = 1 , 𝑦 = 0 , 𝑧 = 1 0 , 𝑙 = 6 0 .
  • B 𝑥 = 3 , 𝑦 = 0 , 𝑧 = 6 0 , 𝑙 = 6 .
  • C 𝑥 = ± 1 , 𝑦 = 0 , 𝑧 = 1 0 , 𝑙 = 6 0 .
  • D 𝑥 = ± 1 , 𝑦 = 0 , 𝑧 = 1 0 , 𝑙 = 6 .

Q9:

Given that find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 8 , 𝑦 = 6
  • B 𝑥 = 8 , 𝑦 = 7
  • C 𝑥 = 7 , 𝑦 = 6
  • D 𝑥 = 8 , 𝑦 = 1
  • E 𝑥 = 1 4 , 𝑦 = 1

Q10:

Consider the matrices 𝐴 and 𝐵 . Given that 𝐴 = 𝐵 , determine the values of 𝑥 , 𝑦 , and 𝑧 .

  • A 𝑥 = 3 , 𝑦 = 2 4 , 𝑧 = 4
  • B 𝑥 = 3 , 𝑦 = 8 , 𝑧 = 4
  • C 𝑥 = 3 0 , 𝑦 = 8 , 𝑧 = 4
  • D 𝑥 = 3 , 𝑦 = 8 , 𝑧 = 4
  • E 𝑥 = 3 , 𝑦 = 8 , 𝑧 = 1 6

Q11:

Find the values of 𝑥 and 𝑦 , given that

  • A 𝑥 = 1 , 𝑦 = 3
  • B 𝑥 = 1 , 𝑦 = 0
  • C 𝑥 = 2 0 , 𝑦 = 1 2
  • D 𝑥 = ± 1 , 𝑦 = 6
  • E 𝑥 = ± 1 , 𝑦 = 3

Q12:

Consider the linear transformation , where rotates each vector 90 degrees about the positive -axis. Find the matrix representation of in the standard basis.

  • A
  • B
  • C
  • D

Q13:

Given that is it true that 𝐴 = 𝐵 ?

  • Ayes
  • Bno

Q14:

Given that 𝐴 = 7 7 7 7 7 7 and that 𝐵 = 7 7 7 7 , is it true that 𝐴 𝐵 ?

  • Ayes
  • Bno

Q15:

Given that 𝐴 = 2 2 2 2 2 2 and that 𝐵 = 2 2 2 2 , is it true that 𝐴 𝐵 ?

  • Ayes
  • Bno

Q16:

Given that 𝐴 = 3 3 3 3 3 3 and that 𝐵 = 3 3 3 3 , is it true that 𝐴 = 𝐵 ?

  • Ano
  • Byes

Q17:

Given that find the value of 𝑏 𝑎 .

  • A 1 7
  • B7
  • C2
  • D 2 7 1 4
  • E 1 2

Q18:

If is it true that 𝐴 = 𝐵 ?

  • Ano
  • Byes

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