In this worksheet, we will practice using the properties of determinants to solve problems.

**Q1: **

Find the value of

**Q2: **

Find the value of .

**Q3: **

Using the properties of determinants, find the value of

**Q4: **

Use the properties of determinants to evaluate

**Q5: **

Without expanding, find the value of the determinant

**Q6: **

Using the properties of determinants, find the value of

**Q7: **

Evaluate

**Q8: **

Evaluate

**Q9: **

Which of the following is equal to the determinant

- A
- B
- C
- D

**Q10: **

Consider the equation

Evaluate

**Q11: **

Consider the equation

Determine all the possible values of given that .

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

**Q12: **

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

- A36
- B
- C
- D4

**Q13: **

Consider the equation Given that , find its solution set.

- A
- B
- C
- D
- E

**Q14: **

Find, without expanding, the value of the determinant

**Q15: **

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

- A
- B
- C
- D

**Q16: **

Select the determinant that is equal to

- A
- B
- C
- D
- E

**Q19: **

Consider the equation

Find, without expanding, the value of the determinant

**Q20: **

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

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

**Q21: **

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

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

**Q22: **

Use the properties of determinants to find

**Q23: **

Consider

Find the value of

**Q24: **

Find the solution set of the equation

- A
- B
- C
- D
- E

**Q25: **

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

- A
- B
- C
- D
- E