# Worksheet: Matrix Operations

Q1:

Suppose that , , and .

Find .

• A
• B
• C
• D
• E

Find .

• A
• B
• C
• D
• E

Find .

• A
• B
• C
• D
• E

Express in terms of and .

• A
• B
• C
• D
• E

Q2:

If and then which of the following cannot exist?

• A
• B
• C
• D

Q3:

Given that find .

• A
• B
• C
• D

Q4:

Given that determine .

• A
• B
• C
• D

Q5:

Given that determine the matrix .

• A
• B
• C
• D

Q6:

Given that the order of the matrix is , and that of the matrix is , which of the following operations can be performed?

• A
• B
• C
• D

Q7:

and are two matrices with the property that for any matrix , and . Are and equal?

• A No, they are different matrices of the same dimensions.
• B No, they have different dimensions.
• C Yes, they are both the identity matrix.

Q8:

Consider the matrices and . Find .

• A
• B
• C
• D
• E

Q9:

and are two matrices with the property that for any matrix , and . Are and equal?

• A No, they are different matrices of the same dimensions.
• B Yes, they are both the identity matrix.
• C No, they have different dimensions.

Q10:

Evaluate

• A
• B
• C
• D
• E

Q11:

Suppose that and . Solve the equations from to find conditions on and for this equality to be true.

• A
• B
• C
• D
• E

Q12:

Given that find the result of , if possible.

• A
• BIt is not possible.
• C
• D
• E

Q13:

Consider the matrix We wish to find the matrix for which , where is the identity matrix. Suppose that

Find in terms of . Hence, by comparing this to , find the value of .

• A
• B
• C
• D
• E

By considering suitable entries of , find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Using your answers to the previous parts of the question, find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Find the values of , , , and .

• A , , ,
• B , , ,
• C , , ,
• D , , ,
• E , , ,

Q14:

If and , is ?

• Ayes
• Bno