Worksheet: Equal Matrices

In this worksheet, we will practice identifying the conditions for two matrices to be equal.

Q1:

Given that 𝐴=333333 and that 𝐵=3333, is it true that 𝐴=𝐵?

  • Ayes
  • Bno

Q2:

If 𝐴=5373,𝐵=5373, is it true that 𝐴=𝐵?

  • Ano
  • Byes

Q3:

For which of the following matrices is 𝐴𝐵=𝐴𝐶?

  • A𝐴=1111, 𝐵=1111, 𝐶=2112
  • B𝐴=1111, 𝐵=1111, 𝐶=2222
  • C𝐴=1111, 𝐵=1111, 𝐶=2222
  • D𝐴=1111, 𝐵=1111, 𝐶=2222
  • E𝐴=1111, 𝐵=1111, 𝐶=1111

Q4:

Given that 99𝑥+3𝑦2𝑥6𝑦9=32𝑏𝑎2, find the value of 𝑏𝑎.

Q5:

Given that 𝑎+𝑏𝑎𝑏𝑎+𝑏+𝑐𝑎7𝑏𝑑=317564, determine the values of 𝑎, 𝑏, 𝑐, and 𝑑.

  • A𝑎=10, 𝑏=7, 𝑐=12, 𝑑=5
  • B𝑎=10, 𝑏=7, 𝑐=2, 𝑑=5
  • C𝑎=10, 𝑏=4, 𝑐=2, 𝑑=5
  • D𝑎=10, 𝑏=7, 𝑐=2, 𝑑=20

Q6:

Given that 3𝑥3310𝑦1=03105𝑦5, find the values of 𝑥 and 𝑦.

  • A𝑥=1, 𝑦=1
  • B𝑥=0, 𝑦=9
  • C𝑥=1, 𝑦=1
  • D𝑥=3, 𝑦=1
  • E𝑥=1, 𝑦=1

Q7:

Given that 022𝑎+42𝑏+9=0225, determine the values of 𝑎 and 𝑏.

  • A𝑎=1, 𝑏=2
  • B𝑎=2, 𝑏=14
  • C𝑎=3, 𝑏=2
  • D𝑎=1, 𝑏=7
  • E𝑎=2, 𝑏=5

Q8:

Given that 216306𝑧+𝑦=𝑙𝑥+29𝑦60, find the values of 𝑥, 𝑦, 𝑧, and 𝑙.

  • A𝑥=3, 𝑦=0, 𝑧=60, 𝑙=6.
  • B𝑥=1, 𝑦=0, 𝑧=10, 𝑙=60.
  • C𝑥=±1, 𝑦=0, 𝑧=10, 𝑙=60.
  • D𝑥=±1, 𝑦=0, 𝑧=10, 𝑙=6.

Q9:

Given that 43𝑥7=438𝑦6, find the values of 𝑥 and 𝑦.

  • A𝑥=14, 𝑦=1
  • B𝑥=8, 𝑦=6
  • C𝑥=7, 𝑦=6
  • D𝑥=8, 𝑦=7
  • E𝑥=8, 𝑦=1

Q10:

Consider the matrix 𝐴=[10𝑥𝑥+3𝑦2𝑥𝑧] and the matrix 𝐵=[302710]. Given that 𝐴=𝐵, determine the values of 𝑥, 𝑦, and 𝑧.

  • A𝑥=30, 𝑦=8, 𝑧=4
  • B𝑥=3, 𝑦=8, 𝑧=4
  • C𝑥=3, 𝑦=8, 𝑧=4
  • D𝑥=3, 𝑦=8, 𝑧=16
  • E𝑥=3, 𝑦=24, 𝑧=4

Q11:

Find the values of 𝑥 and 𝑦, given that 10𝑥+10239=2022𝑦+99.

  • A𝑥=20, 𝑦=12
  • B𝑥=±1, 𝑦=3
  • C𝑥=1, 𝑦=3
  • D𝑥=1, 𝑦=0
  • E𝑥=±1, 𝑦=6

Q12:

Given that 𝐴=0.6127101𝐵=350.50.71,, is it true that 𝐴=𝐵?

  • Ayes
  • Bno

Q13:

Given that 𝐴=777777 and that 𝐵=7777, is it true that 𝐴𝐵?

  • Ano
  • Byes

Q14:

Given that 𝐴=222222 and that 𝐵=2222, is it true that 𝐴𝐵?

  • Ano
  • Byes

Q15:

Given that 𝐴=181818181818 and that 𝐵=18181818, is it true that 𝐴𝐵?

  • Ano
  • Byes

Q16:

Given that 66𝑥3𝑦3𝑥8𝑦6=27𝑏𝑎3, find the value of 𝑏𝑎.

Q17:

If 𝐴=3321,𝐵=3123, is it true that 𝐴=𝐵?

  • Ano
  • Byes

Q18:

If 𝐴=𝐵, where 𝐴=21058,𝐵=𝑑52𝑒8, what are the values of 𝑑 and 𝑒?

  • A𝑑=2, 𝑒=5
  • B𝑑=5, 𝑒=5
  • C𝑑=5, 𝑒=5
  • D𝑑=2, 𝑒=8
  • E𝑑=2, 𝑒=4

Q19:

Given that 𝑥593𝑧1+55𝑥6𝑧7=3𝑥+24𝑦22𝑘+4𝑥3𝑦24𝑘, find the values of 𝑥, 𝑦, 𝑧, and 𝑘.

  • A𝑥=78, 𝑦=157, 𝑧=1, 𝑘=43
  • B𝑥=725, 𝑦=3916, 𝑧=54, 𝑘=2
  • C𝑥=78, 𝑦=157, 𝑧=58, 𝑘=2
  • D𝑥=725, 𝑦=3916, 𝑧=54, 𝑘=43

Q20:

Given that 𝑥388+𝑦007𝑧041=122819, find the values of 𝑥, 𝑦, and 𝑧.

  • A𝑥=12, 𝑦=28, 𝑧=19
  • B𝑥=4, 𝑦=2, 𝑧=1
  • C𝑥=9, 𝑦=28, 𝑧=1
  • D𝑥=4, 𝑦=2, 𝑧=19
  • E𝑥=4, 𝑦=2, 𝑧=1

Q21:

Let 𝐴=[23], and 𝐵=[12]. Find 𝑠 and 𝑡 satisfying 𝑠+𝑡=1 such that 𝑠𝐴+𝑡𝐵=[𝑞𝑞] for some number 𝑞. Also give the number 𝑞.

  • A𝑠=14, 𝑡=54, 𝑞=34
  • B𝑠=14, 𝑡=54, 𝑞=74
  • C𝑠=52, 𝑡=12, 𝑞=74
  • D𝑠=52, 𝑡=12, 𝑞=94
  • E𝑠=14, 𝑡=54, 𝑞=54

Q22:

Given that 5𝑥1𝑦=5𝑧65, find 𝑥, 𝑦, and 𝑧.

  • A𝑥=6, 𝑦=1, 𝑧=5
  • B𝑥=5, 𝑦=5, 𝑧=6
  • C𝑥=6, 𝑦=5, 𝑧=5
  • D𝑥=6, 𝑦=5, 𝑧=1
  • E𝑥=1, 𝑦=1, 𝑧=5

Q23:

Determine the values of 𝑥, 𝑦, 𝑘, and 𝑙 that satisfy the given equation 𝑥4610𝑘+𝑦7𝑙05+431102=𝑂, where 𝑂 is the zero matrix of order 2×2.

  • A𝑥=4, 𝑦=4, 𝑘=7, 𝑙=7
  • B𝑥=4, 𝑦=4, 𝑘=16, 𝑙=16
  • C𝑥=24, 𝑦=20, 𝑘=3, 𝑙=1
  • D𝑥=4, 𝑦=14, 𝑘=16, 𝑙=16

Q24:

Given that 451356090180180=1122𝑥12𝑦233𝑧,cotsinseccsccostan what are the values of 𝑥, 𝑦, and 𝑧?

  • A𝑥=2, 𝑦=1, 𝑧=0
  • B𝑥=2, 𝑦=1, 𝑧=0
  • C𝑥=1, 𝑦=2, 𝑧=0
  • D𝑥=1, 𝑦=2, 𝑧=0

Q25:

Write the matrix 3819 in the form 𝑎1000+𝑏0100+𝑐0010+𝑑0001, where 𝑎, 𝑏, 𝑐, and 𝑑 are real numbers that you should find.

  • A3100080100001090001
  • B8100090100+300100001
  • C81000+30100900100001
  • D81000+30100001090001

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