# Worksheet: Properties of Determinants

In this worksheet, we will practice identifying the properties of determinants and using them to simplify problems.

**Q1: **

Find the value of

**Q2: **

Using the properties of determinants, find the value of

**Q3: **

Use the properties of determinants to evaluate

**Q4: **

Without expanding, find the value of the determinant

**Q5: **

Using the properties of determinants, find the value of

**Q6: **

Evaluate

**Q7: **

Evaluate

**Q8: **

Which of the following is equal to the determinant

- A
- B
- C
- D

**Q9: **

Consider the equation

Evaluate

**Q10: **

Consider the equation

Determine all the possible values of given that .

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

**Q11: **

Use the properties of determinants to find the value of which makes a factor of the determinant

- A
- B36
- C
- D4

**Q12: **

Consider the equation Given that , find its solution set.

- A
- B
- C
- D
- E

**Q13: **

Find, without expanding, the value of the determinant

**Q14: **

Given that and , find a relation between and without expanding either determinant.

- A
- B
- C
- D

**Q15: **

Select the determinant that is equal to

- A
- B
- C
- D
- E

**Q18: **

Consider the equation

Find, without expanding, the value of the determinant

**Q19: **

Put the determinant in upper triangular form, and find its value.

- A ,
- B , 504
- C ,
- D , 5,544

**Q20: **

Use the properties of determinants to find

**Q21: **

Consider

Find the value of

**Q22: **

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

- A
- B
- C
- D
- E

**Q23: **

Use the properties of determinants to find the values of

Then, determine which of the following has the value of but not in triangular form.

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

**Q24: **

Use the properties of determinants to evaluate

**Q25: **

Using the properties of determinants, find the value of