# Worksheet: Three-by-Three Determinants

In this worksheet, we will practice evaluating 3x3 determinants using the cofactors (Laplace expansion) or the Sarrus method.

**Q3: **

Which of the following is equal to the determinant

- A
- B
- C
- D

**Q5: **

Given that is a complex cube root of unity, evaluate

**Q9: **

Find, in its simplest form, an expression for the determinant

- A
- B
- C
- D

**Q11: **

Consider

Write the determinant whose value is equal to the minor of the element .

- A
- B
- C
- D

**Q12: **

Find the solution set of

- A
- B
- C
- D
- E

**Q13: **

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

- A
- B
- C
- D

**Q15: **

Solve

- A
- B
- C
- D
- E

**Q16: **

Find the solution set of in .

- A
- B
- C
- D

**Q17: **

Solve the equation

- A
- B
- C
- D

**Q18: **

Determine the value of that makes a root of the equation

- A
- B
- C5
- D

**Q19: **

Find the solution set of the equation

- A
- B
- C
- D

**Q20: **

Solve

- A, , or
- B, , or
- C or
- D or

**Q21: **

Find the solution set of the equation

- A
- B
- C
- D
- E

**Q22: **

Find the solution set of the equation

- A
- B
- C
- D

**Q24: **

Which of the following pairs of points does the straight line represented by the equation pass through?

- A,
- B,
- C,
- D,

**Q25: **

Given that equals two times , determine the value of .