Worksheet: Two-by-Two Determinants

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In this worksheet, we will practice finding the value of a two-by-two determinant.

Q1:

Find all the values of 𝑥 for which | | 𝑥 − 2 − 2 𝑥 | | + | | 6 3 1 8 | | = 4 5 .

  • A1 or − 1
  • B4
  • C1
  • D2 or − 2
  • E4 or − 4

Q2:

Solve

  • A 𝑥 = 3 6
  • B 𝑥 = 4 9
  • C 𝑥 = − 2 0 9
  • D 𝑥 = − 4

Q3:

Solve

  • A2 or 1
  • B2 or 3
  • C − 1 or 3
  • D − 2 or − 3
  • E − 5 or − 2

Q4:

Find the value of

  • A − 7 𝑏 𝑥 − 1 2 𝑎 𝑏
  • B − 7 𝑏 𝑥 − 3 5 𝑎 𝑦
  • C − 7 𝑏 𝑥 + 3 5 𝑎 𝑦 − 2 𝑎 𝑏
  • D − 7 𝑏 𝑥 − 3 5 𝑎 𝑦 − 1 2 𝑎 𝑏
  • E − 7 𝑏 𝑥 − 3 5 𝑎 𝑦 − 2 𝑎 𝑏

Q5:

Find the value of the determinant | | | 𝜃 𝜃 − 𝜃 𝜃 | | | c o t t a n c o t t a n .

Q6:

Find the value of | | | − 3 𝑥 + 3 4 𝑥 + 4 − 3 𝑦 + 4 − 𝑦 + 3 | | | 2 2 .

  • A 1 5 𝑥 𝑦 − 9 𝑥 − 3 𝑦 − 1 6 𝑥 + 1 2 𝑦 − 7 2 2 2
  • B 3 𝑥 𝑦 − 2 5 𝑥 + 9 𝑦 + 1 2 𝑥 𝑦 − 7 2 2 2
  • C 3 𝑥 𝑦 − 3 𝑥 − 𝑦 + 1 2 𝑥 𝑦 − 4 𝑥 + 3 𝑦 2 2 2 2
  • D 3 𝑥 𝑦 − 9 𝑥 − 3 𝑦 + 1 2 𝑥 𝑦 − 1 6 𝑥 + 1 2 𝑦 − 7 2 2 2 2
  • E 1 5 𝑥 𝑦 − 2 5 𝑥 + 9 𝑦 + 1 2 𝑥 𝑦 − 7 2 2 2

Q7:

Evaluate

Q8:

Find all the values of 𝑥 for which | | 𝑥 8 8 𝑥 | | + | | 6 − 2 − 8 4 | | = 8 8 .

  • A10 or − 1 0
  • B144
  • C100
  • D12 or − 1 2
  • E144 or − 1 4 4

Q9:

Solve

  • A − 3 or 1
  • B − 3 or 6
  • C − 1 or 6
  • D3 or − 6
  • E3 or − 4

Q10:

Solve

  • A 𝑥 = − 4 8
  • B 𝑥 = 1 0
  • C 𝑥 = 6 0
  • D 𝑥 = − 8
  • E 𝑥 = − 9

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