# Worksheet: Matrix Multiplication Dimensions

Q1:

Is it possible to have a matrix and a matrix such that If so, give an example.

• Ayes, ;
• Byes, ;
• Cno

Q2:

Given that is a matrix of order and is a matrix of order , find the order of the matrix , if possible.

• A
• B
• C
• D
• Eundefined

Q3:

Suppose the matrix product makes sense. We also know that has 2 rows, has 3 columns, and has 4 entries. Is it possible to determine the possible sizes of these matrices? If so, what are the possible sizes of , , and ?

• A yes, , , ; , , ; , ,
• Bno
• C yes, , , ; , , ; , ,
• D yes, , , ; , , ; , ,
• E yes, , , ; , , ; , ,

Q4:

Find the matrices and such that, for any matrix , and . Explain why and are not the same.

• A , , and have different dimensions.
• B , , and have different dimensions.
• C , , and have different dimensions.
• D , , and have different dimensions.
• E , , and have different dimensions.

Q5:

Suppose Which of the following products is defined?

• A
• B
• C
• D
• E

Q6:

Suppose is a matrix, is a matrix, and is a matrix. What are the sizes of the product matrices , and ?

• A
• B
• C
• D
• E

Q7:

If is a matrix of order and is a matrix of order , then what is the order of ?

• A
• B
• C
• D

Q8:

Find a matrix such that for all matrices .

• A
• B
• C
• D
• E

Q9:

Given that is a matrix of order , and is a matrix of order , determine the condition under which AB is defined.

• A
• B
• C
• D
• E

Q10:

Given that is a matrix of order and is a matrix of order , find the order of the matrix , if possible.

• A
• B
• C
• Dundefined
• E

Q11:

Given that is a matrix of order and is a matrix of order , find the order of the matrix , if possible.

• A
• B
• C
• D
• Eundefined

Q12:

If is a matrix of order and is a matrix of order , then what is the order of ?

• A
• B
• C
• D

Q13:

If is a matrix of order and is a matrix of order , then what is the order of ?

• A
• B
• C
• D