Worksheet: Finding the Value of the Unknown Variable by Evaluating the Determinant

In this worksheet, we will practice using the evaluation of the determinants of 2x2 and 3x3 matrices to solve equations and find its unknown variables.

Q1:

Solve the equation

  • A 1 8
  • B { 8 }
  • C 1 8
  • D { 8 }

Q2:

Solve the equation

  • A 7 3
  • B 7 𝑖 3 , 7 𝑖 3
  • C 7 𝑖 3
  • D 7 3 , 7 3

Q3:

Find the solution set of

  • A 1 4 , 1 4
  • B 0 , 1 4 , 1 4
  • C { 4 , 4 }
  • D { 0 , 4 , 4 }
  • E { 0 , 4 }

Q4:

Find the solution set of the equation | | | 𝑥 8 1 𝑥 + 9 𝑥 + 9 𝑥 8 1 | | | = 0 . 2 2

  • A { 8 , 9 , 1 0 }
  • B { 1 0 , 8 , 9 }
  • C { 1 0 , 9 , 8 }
  • D { 9 , 8 , 1 0 }
  • E { 9 , 9 }

Q5:

Solve

  • A
  • B
  • C
  • D
  • E

Q6:

Solve the determinant given that 0 < 𝜃 < 9 0 .

Q7:

Find the solution set of the equation

  • A { 3 , 1 }
  • B { 3 , 1 , 0 }
  • C 1 3 , 1 , 0
  • D { 3 , 1 , 0 }

Q8:

Solve the equation

  • A { 0 , 8 𝑎 + 𝑏 4 𝑐 }
  • B ± 8 𝑎 + 4 𝑐 , 8 𝑎 𝑏 4 𝑐
  • C ± 8 𝑎 + 4 𝑐 , 8 𝑎 + 𝑏 4 𝑐
  • D { 0 , 8 𝑎 𝑏 4 𝑐 }

Q9:

Solve for 𝑥 :

  • A 𝑥 = 9 or 𝑥 = 2 0
  • B 𝑥 = 9 or 𝑥 = 4
  • C 𝑥 = 9 or 𝑥 = 2 0
  • D 𝑥 = 9 or 𝑥 = 4

Q10:

Find all the possible values of 𝑥 :

  • A 7 , 7
  • B 1 6 , 1 6
  • C 1 7 , 1 7
  • D 6 , 6
  • E 1 6

Q11:

Find the solution set of the equation

  • A { 3 , 2 }
  • B { 0 , 2 , 3 }
  • C { 2 , 3 }
  • D { 0 , 3 , 2 }

Q12:

Solve for 𝑥

  • A 1 6 , 8 7
  • B 1 7 , 4 3
  • C 8 7 , 1 6
  • D 4 3 , 1 7

Q13:

Solve for 𝑥 :

  • A 𝑥 = 0 , 𝑥 = 3 , or 𝑥 = 2 3
  • B 𝑥 = 1 , or 𝑥 = 3 2
  • C 𝑥 = 1 , 𝑥 = 3 2 , 𝑥 = 3 , or 𝑥 = 2 3
  • D 𝑥 = 0 , 𝑥 = 1 3 , 𝑥 = 1 , or 𝑥 = 2 3
  • E 𝑥 = 0 , 𝑥 = 3 , 𝑥 = 1 3 , or 𝑥 = 3 2

Q14:

Find the solution set of in .

  • A { 1 }
  • B { 2 }
  • C { 3 }
  • D { 2 }

Q15:

Given that 𝑏 and 𝑐 are the roots of the equation 𝑥 1 2 𝑥 + 2 5 6 = 0 2 , determine the value of

Q16:

Solve the equation

  • A { 3 , 6 }
  • B { 2 , 9 }
  • C { 6 , 3 }
  • D { 9 , 2 }
  • E 5 3 3 , 4 6

Q17:

Consider the equation

How many distinct solutions does it have in the set of complex numbers?

Q18:

Determine the value of 𝑘 that makes 𝑥 = 4 a root of the equation

  • A 1 5
  • B5
  • C 3 2
  • D 1 2

Q19:

Solve

  • A 𝑥 = 0 or 𝑥 = 1 5
  • B 𝑥 = 0 , 𝑥 = 4 , or 𝑥 = 5
  • C 𝑥 = 0 or 𝑥 = 1 5
  • D 𝑥 = 0 , 𝑥 = 4 , or 𝑥 = 5

Q20:

Find the solution set of the equation

  • A { 2 , 3 }
  • B { 3 , 2 , 3 }
  • C { 3 , 2 }
  • D { 3 , 2 }
  • E { 2 , 3 }

Q21:

Given that 𝑎 is a fixed constant, find solution set of the equation

  • A { 𝑎 }
  • B { 0 , 9 𝑎 }
  • C { 9 𝑎 }
  • D { 0 , 𝑎 }

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