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In this lesson, we will learn how to use the evaluation of the determinants of 2x2 and 3x3 matrices to solve equations and find its unknown variables.

Q1:

Solve the equation

Q2:

Q3:

Find the solution set of

Q4:

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

Q5:

Solve

Q6:

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

Q7:

Find the solution set of the equation

Q8:

Q9:

Solve for 𝑥 :

Q10:

Find all the possible values of 𝑥 :

Q11:

Q12:

Solve for 𝑥

Q13:

Q14:

Find the solution set of in ℝ .

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:

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

Q19:

Q20:

Q21:

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

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