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Worksheet: Two-by-Two Determinants

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

Q1:

Find all the values of π‘₯ for which | | π‘₯ βˆ’ 2 βˆ’ 2 π‘₯ | | + | | 6 3 1 8 | | = 4 5 .

  • A1 or βˆ’ 1
  • B4
  • C1
  • D2 or βˆ’ 2
  • E4 or βˆ’ 4

Q2:

Find all the values of π‘₯ for which | | π‘₯ 8 8 π‘₯ | | + | | 6 βˆ’ 2 βˆ’ 8 4 | | = 8 8 .

  • A10 or βˆ’ 1 0
  • B144
  • C100
  • D12 or βˆ’ 1 2
  • E144 or βˆ’ 1 4 4

Q3:

Find the value of

  • A βˆ’ 7 𝑏 π‘₯ βˆ’ 1 2 π‘Ž 𝑏
  • B βˆ’ 7 𝑏 π‘₯ βˆ’ 3 5 π‘Ž 𝑦
  • C βˆ’ 7 𝑏 π‘₯ + 3 5 π‘Ž 𝑦 βˆ’ 2 π‘Ž 𝑏
  • D βˆ’ 7 𝑏 π‘₯ βˆ’ 3 5 π‘Ž 𝑦 βˆ’ 1 2 π‘Ž 𝑏
  • E βˆ’ 7 𝑏 π‘₯ βˆ’ 3 5 π‘Ž 𝑦 βˆ’ 2 π‘Ž 𝑏

Q4:

Solve

  • A2 or 1
  • B2 or 3
  • C βˆ’ 1 or 3
  • D βˆ’ 2 or βˆ’ 3
  • E βˆ’ 5 or βˆ’ 2

Q5:

Solve

  • A βˆ’ 3 or 1
  • B βˆ’ 3 or 6
  • C βˆ’ 1 or 6
  • D3 or βˆ’ 6
  • E3 or βˆ’ 4

Q6:

Find the value of the determinant | | | πœƒ πœƒ βˆ’ πœƒ πœƒ | | | c o t t a n c o t t a n .

Q7:

Solve

  • A π‘₯ = 3 6
  • B π‘₯ = 4 9
  • C π‘₯ = βˆ’ 2 0 9
  • D π‘₯ = βˆ’ 4

Q8:

Solve

  • A π‘₯ = βˆ’ 4 8
  • B π‘₯ = 1 0
  • C π‘₯ = 6 0
  • D π‘₯ = βˆ’ 8
  • E π‘₯ = βˆ’ 9

Q9:

Evaluate

Q10:

Find the value of | | | βˆ’ 3 π‘₯ + 3 4 π‘₯ + 4 βˆ’ 3 𝑦 + 4 βˆ’ 𝑦 + 3 | | | 2 2 .

  • A 1 5 π‘₯ 𝑦 βˆ’ 9 π‘₯ βˆ’ 3 𝑦 βˆ’ 1 6 π‘₯ + 1 2 𝑦 βˆ’ 7 2 2 2
  • B 3 π‘₯ 𝑦 βˆ’ 2 5 π‘₯ + 9 𝑦 + 1 2 π‘₯ 𝑦 βˆ’ 7 2 2 2
  • C 3 π‘₯ 𝑦 βˆ’ 3 π‘₯ βˆ’ 𝑦 + 1 2 π‘₯ 𝑦 βˆ’ 4 π‘₯ + 3 𝑦 2 2 2 2
  • D 3 π‘₯ 𝑦 βˆ’ 9 π‘₯ βˆ’ 3 𝑦 + 1 2 π‘₯ 𝑦 βˆ’ 1 6 π‘₯ + 1 2 𝑦 βˆ’ 7 2 2 2 2
  • E 1 5 π‘₯ 𝑦 βˆ’ 2 5 π‘₯ + 9 𝑦 + 1 2 π‘₯ 𝑦 βˆ’ 7 2 2 2

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