Lesson Worksheet: Two-by-Two Determinants Mathematics

In this worksheet, we will practice identifying determinants and evaluating 2x2 determinants.

Q1:

Find all the values of 𝑥 for which ||𝑥22𝑥||+||6318||=45.

  • A2 or 2
  • B1 or 1
  • C1
  • D4 or 4
  • E4

Q2:

Solve ||𝑥549||=16.

  • A𝑥=36
  • B𝑥=49
  • C𝑥=209
  • D𝑥=4

Q3:

Solve||𝑥25𝑥||||523𝑥||=10.

  • A2 or 3
  • B2 or 3
  • C2 or 1
  • D5 or 2
  • E1 or 3

Q4:

Expand |||𝑎+𝑥5𝑎𝑏+7𝑦7𝑏|||.

  • A7𝑏𝑥35𝑎𝑦
  • B7𝑏𝑥+35𝑎𝑦2𝑎𝑏
  • C7𝑏𝑥35𝑎𝑦12𝑎𝑏
  • D7𝑏𝑥12𝑎𝑏
  • E7𝑏𝑥35𝑎𝑦2𝑎𝑏

Q5:

Find the value of the determinant |||𝜃𝜃𝜃𝜃|||cottancottan.

Q6:

Find the value of |||3𝑥+34𝑥+43𝑦+4𝑦+3|||.

  • A15𝑥𝑦9𝑥3𝑦16𝑥+12𝑦7
  • B15𝑥𝑦25𝑥+9𝑦+12𝑥𝑦7
  • C3𝑥𝑦3𝑥𝑦+12𝑥𝑦4𝑥+3𝑦
  • D3𝑥𝑦25𝑥+9𝑦+12𝑥𝑦7
  • E3𝑥𝑦9𝑥3𝑦+12𝑥𝑦16𝑥+12𝑦7

Q7:

Evaluate |||48𝜃𝜃2𝜃|||.secsectan

Q8:

Find all the values of 𝑥 for which ||𝑥55𝑥||+||1248||=40.

  • A7 or 7
  • B8 or 8
  • C64
  • D49 or 49
  • E49

Q9:

Solve||𝑥34𝑥||+||624𝑥||=12.

  • A4 or 2
  • B4 or 2
  • C4 or 1
  • D4 or 3
  • E1 or 2

Q10:

Solve ||𝑥3105||=40.

  • A𝑥=70
  • B𝑥=10
  • C𝑥=14
  • D𝑥=6
  • E𝑥=2

Q11:

Find the value of the determinant 𝐴=||𝑥11𝑥1||.

  • A10𝑥
  • B10𝑥
  • C𝑥
  • D12𝑥
  • E12𝑥

Q12:

Find the value of 𝑥 which satisfies ||340250340250||=5𝑥4sinsincoscos.

  • A1
  • B35
  • C45
  • D1

Q13:

Evaluate||3415||.

Q14:

Find the value of ||2977||.

Q15:

Find the determinant of the matrix 5005.

Q16:

Evaluate |||10𝑥2𝑥10𝑥2𝑥|||cossinsincos.

Q17:

Find the determinant of the following matrix. 5115

Q18:

Find the value of |||||1𝜃11+𝜃1𝜃|||||.sincotsin

Q19:

Given that the determinant of the matrix 𝑎2𝑏5 is zero, what is 𝑏 in terms of 𝑎?

  • A𝑏=2𝑎5
  • B𝑏=2𝑎5
  • C𝑏=25𝑎
  • D𝑏=5𝑎2
  • E𝑏=5𝑎2

Q20:

Which of the following is equal to |||68𝜃3𝜃2|||.sinsin

  • A|||8𝜃623𝜃|||sinsin
  • B|||12𝜃432𝜃|||coscos
  • C|||412𝜃2𝜃3|||coscos
  • D|||1242𝜃3𝜃2|||sinsin
  • E|||6𝜃432𝜃|||coscos

Q21:

Find the determinant of the matrix 5105.

Q22:

Solve the equation |||𝜃𝜃𝜃𝜃|||=2cossincsccsc given that 0<𝜃<90.

Q23:

Find all the possible values of 𝑥: ||1𝑥66𝑥+1||=1.

  • A7,7
  • B17,17
  • C16,16
  • D16
  • E6,6

Q24:

Solve for 𝑥||6𝑥10𝑥5𝑥7||=||4𝑥10182𝑥||.

  • A87,16
  • B43,17
  • C17,43
  • D16,87

Q25:

Solve for 𝑥: |||3𝑥1𝑥+1𝑥+13𝑥1|||=0.

  • A𝑥=0, 𝑥=3, or 𝑥=23
  • B𝑥=1, or 𝑥=32
  • C𝑥=0, 𝑥=13, 𝑥=1, or 𝑥=23
  • D𝑥=1, 𝑥=32, 𝑥=3, or 𝑥=23
  • E𝑥=0, 𝑥=3, 𝑥=13, or 𝑥=32

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