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 ||𝑥−2−2𝑥||+||6318||=45.

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

Q2:

Solve ||𝑥54−9||=16.

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

Q3:

Solve||𝑥2−5𝑥||−||−523𝑥||=10.

  • A2 or 3
  • B−2 or −3
  • C2 or 1
  • D−5 or −2
  • E−1 or 3

Q4:

Expand |||𝑎+𝑥5𝑎𝑏+7𝑦−7𝑏|||.

  • A−7𝑏𝑥−35𝑎𝑦
  • B−7𝑏𝑥+35𝑎𝑦−2𝑎𝑏
  • C−7𝑏𝑥−35𝑎𝑦−12𝑎𝑏
  • D−7𝑏𝑥−12𝑎𝑏
  • E−7𝑏𝑥−35𝑎𝑦−2𝑎𝑏

Q5:

Find the value of the determinant |||𝜃𝜃−𝜃𝜃|||cottancottan.

Q6:

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

  • A15𝑥𝑦−9𝑥−3𝑦−16𝑥+12𝑦−7
  • B15𝑥𝑦−25𝑥+9𝑦+12𝑥𝑦−7
  • C3𝑥𝑦−3𝑥−𝑦+12𝑥𝑦−4𝑥+3𝑦
  • D3𝑥𝑦−25𝑥+9𝑦+12𝑥𝑦−7
  • E3𝑥𝑦−9𝑥−3𝑦+12𝑥𝑦−16𝑥+12𝑦−7

Q7:

Evaluate |||−48𝜃−𝜃2𝜃|||.secsectan

Q8:

Find all the values of 𝑥 for which ||𝑥−5−5𝑥||+||1−248||=40.

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

Q9:

Solve||𝑥3−4𝑥||+||62−4𝑥||=12.

  • A4 or 2
  • B−4 or −2
  • C4 or 1
  • D−4 or −3
  • E−1 or 2

Q10:

Solve ||𝑥310−5||=−40.

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

Q11:

Find the value of the determinant 𝐴=||𝑥−11𝑥−1||.

  • A10𝑥
  • B−10𝑥
  • C−𝑥
  • D−12𝑥
  • E12𝑥

Q12:

Find the value of 𝑥 which satisfies ||340−250−340250||=5𝑥−4sinsincoscos∘∘∘∘.

  • A1
  • B35
  • C−45
  • D−1

Q13:

Evaluate||3−415||.

Q14:

Find the value of ||−2−977||.

Q15:

Find the determinant of the matrix 5005.

Q16:

Evaluate |||10𝑥−2𝑥10𝑥2𝑥|||cossinsincos.

Q17:

Find the determinant of the following matrix. 51−15

Q18:

Find the value of |||||−1𝜃11+𝜃−1𝜃|||||.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 |||−6−8𝜃3𝜃2|||.sinsin

  • A|||−8𝜃−623𝜃|||sinsin
  • B|||−12𝜃−432𝜃|||coscos
  • C|||−4−12𝜃2𝜃3|||coscos
  • D|||−12−42𝜃3𝜃2|||sinsin
  • E|||−6𝜃−432𝜃|||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: ||1−𝑥6−6𝑥+1||=1.

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

Q24:

Solve for 𝑥||6𝑥−10𝑥5𝑥7||=||4𝑥−10182𝑥||.

  • A−87,−16
  • B−43,−17
  • C17,43
  • D16,87

Q25:

Solve for 𝑥: |||3𝑥−1𝑥+1𝑥+13𝑥−1|||=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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