# 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:

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

Q14:

Solve for :

• A or
• B or
• C or
• D or

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

Q23:

Find the value of .

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 .