# 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

Q16:

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

• A
• B
• C
• D
• E

Q17:

Select a factor of the determinant

• A
• B
• C
• D

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