# Worksheet: Three-by-Three Determinants

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

Q1:

Find the value of

Q2:

Consider the determinant Given that and , determine the determinant’s numerical value.

Q3:

Which of the following is equal to the determinant

• A
• B
• C
• D

Q4:

Evaluate

Q5:

Given that is a complex cube root of unity, evaluate

Q6:

Evaluate the shown determinant where .

Q7:

Evaluate

Q8:

Find the value of

Q9:

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

• A
• B
• C
• D

Q10:

Calculate when

Q11:

Find the determinant of the matrix

Q12:

Find the determinant of the matrix

Q13:

Calculate when

Q14:

Find the determinant of the matrix

Q15:

Consider

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

• A
• B
• C
• D

Q16:

Find the determinant of the matrix

Q17:

Calculate the determinant of

Q18:

Find the solution set of

• A
• B
• C
• D
• E

Q19:

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

• A
• B
• C
• D

Q20:

Solve for :

• A or
• B or
• C or
• D or

Q21:

Solve

• A
• B
• C
• D
• E

Q22:

Find the solution set of in .

• A
• B
• C
• D

Q23:

Solve the equation

• A
• B
• C
• D

Q24:

Determine the value of that makes a root of the equation

• A
• B
• C5
• D

Q25:

Find the solution set of the equation

• A
• B
• C
• D