Worksheet: Solving by Using Properties of Determinants

For large values of n, evaluating a determinant of order n is not very practical, since the number of terms is n! (for example, a determinant of order 10 contains 3,628,800 terms). This worksheet assesses your ability to use 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:

Use the properties of determinants to evaluate

Q8:

Using the properties of determinants, find the value of

Q9:

Evaluate

Q10:

Evaluate

Q11:

Which of the following is equal to the determinant

Q12:

Find the solution set of

Q13:

Consider the equation

Evaluate

Q14:

Consider the equation

Determine all the possible values of given that .

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

Q15:

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

Q16:

Consider the equation Given that , find its solution set.

Q17:

Find, without expanding, the value of the determinant