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?

  • A 𝐴 = 1 1 1 1 , 𝐵 = 1 1 1 1 , 𝐶 = 2 1 1 2
  • B 𝐴 = 1 1 1 1 , 𝐵 = 1 1 1 1 , 𝐶 = 2 2 2 2
  • C 𝐴 = 1 1 1 1 , 𝐵 = 1 1 1 1 , 𝐶 = 2 2 2 2
  • D 𝐴 = 1 1 1 1 , 𝐵 = 1 1 1 1 , 𝐶 = 2 2 2 2
  • E 𝐴 = 1 1 1 1 , 𝐵 = 1 1 1 1 , 𝐶 = 1 1 1 1

Q4:

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

  • A12
  • B 1 9
  • C 1 2
  • D2
  • E9

Q5:

Given that 𝑎+𝑏𝑎𝑏𝑎+𝑏+𝑐𝑎7𝑏𝑑=317564, 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 = 5
  • C 𝑎 = 1 0 , 𝑏 = 4 , 𝑐 = 2 , 𝑑 = 5
  • D 𝑎 = 1 0 , 𝑏 = 7 , 𝑐 = 2 , 𝑑 = 2 0

Q6:

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

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

Q7:

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

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

Q8:

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

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

Q9:

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

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

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

Q11:

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

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

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.

  • A15
  • B 1 6
  • C 1 3
  • D3
  • E6

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?

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

Q19:

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

  • A 𝑥 = 7 8 , 𝑦 = 1 5 7 , 𝑧 = 1 , 𝑘 = 4 3
  • B 𝑥 = 7 2 5 , 𝑦 = 3 9 1 6 , 𝑧 = 5 4 , 𝑘 = 2
  • C 𝑥 = 7 8 , 𝑦 = 1 5 7 , 𝑧 = 5 8 , 𝑘 = 2
  • D 𝑥 = 7 2 5 , 𝑦 = 3 9 1 6 , 𝑧 = 5 4 , 𝑘 = 4 3

Q20:

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

  • A 𝑥 = 1 2 , 𝑦 = 2 8 , 𝑧 = 1 9
  • B 𝑥 = 4 , 𝑦 = 2 , 𝑧 = 1
  • C 𝑥 = 9 , 𝑦 = 2 8 , 𝑧 = 1
  • D 𝑥 = 4 , 𝑦 = 2 , 𝑧 = 1 9
  • E 𝑥 = 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.

  • A 𝑠 = 1 4 , 𝑡 = 5 4 , 𝑞 = 3 4
  • B 𝑠 = 1 4 , 𝑡 = 5 4 , 𝑞 = 7 4
  • C 𝑠 = 5 2 , 𝑡 = 1 2 , 𝑞 = 7 4
  • D 𝑠 = 5 2 , 𝑡 = 1 2 , 𝑞 = 9 4
  • E 𝑠 = 1 4 , 𝑡 = 5 4 , 𝑞 = 5 4

Q22:

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

  • A 𝑥 = 6 , 𝑦 = 1 , 𝑧 = 5
  • B 𝑥 = 5 , 𝑦 = 5 , 𝑧 = 6
  • C 𝑥 = 6 , 𝑦 = 5 , 𝑧 = 5
  • D 𝑥 = 6 , 𝑦 = 5 , 𝑧 = 1
  • E 𝑥 = 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.

  • A 𝑥 = 4 , 𝑦 = 4 , 𝑘 = 7 , 𝑙 = 7
  • B 𝑥 = 4 , 𝑦 = 4 , 𝑘 = 1 6 , 𝑙 = 1 6
  • C 𝑥 = 2 4 , 𝑦 = 2 0 , 𝑘 = 3 , 𝑙 = 1
  • D 𝑥 = 4 , 𝑦 = 1 4 , 𝑘 = 1 6 , 𝑙 = 1 6

Q24:

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

  • A 𝑥 = 2 , 𝑦 = 1 , 𝑧 = 0
  • B 𝑥 = 2 , 𝑦 = 1 , 𝑧 = 0
  • C 𝑥 = 1 , 𝑦 = 2 , 𝑧 = 0
  • D 𝑥 = 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.

  • A 3 1 0 0 0 8 0 1 0 0 0 0 1 0 9 0 0 0 1
  • B 8 1 0 0 0 9 0 1 0 0 + 3 0 0 1 0 0 0 0 1
  • C 8 1 0 0 0 + 3 0 1 0 0 9 0 0 1 0 0 0 0 1
  • D 8 1 0 0 0 + 3 0 1 0 0 0 0 1 0 9 0 0 0 1

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.