# Worksheet: Matrix Multiplication

In this worksheet, we will practice identifying the conditions for matrix multiplication and evaluating the product of two matrices if possible.

**Q3: **

Given that , find .

- A
- B
- C
- D

**Q5: **

Consider the matrices Find , if possible.

- A
- B
- C
- D
- EIt is not possible.

**Q7: **

Consider the matrices Find and if possible.

- A,
- BIt is not possible.
- C,
- D,
- E,

**Q8: **

Consider the matrices

Find .

- A
- B
- C
- D
- E

Find .

- A
- B
- C
- D
- E

**Q9: **

Suppose

Find the product .

- A
- B
- C
- D
- E

Find the product .

- A
- B
- C
- D
- E

**Q10: **

Evaluate the matrix product

- A
- B
- C
- D
- E

**Q11: **

Consider the matrix product

What can you conclude about it?

- AFor a given matrix , there cannot be any matrix except the identity matrix for which .
- BFor a given matrix , there can be a matrix that is not the identity matrix for which .
- CFor a given matrix , there can be a matrix that is not the identity matrix for which .
- DFor a given matrix , there can be a matrix that is not the identity matrix for which .

Is it possible to find a matrix with the above property for every matrix ?

- Ano
- Byes

**Q12: **

Consider the matrices

Find and .

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

**Q14: **

Consider the matrices Find if possible.

- A
- B
- C
- D

**Q15: **

Given that and is the unit matrix of the same order, find for which .

**Q16: **

Given that find if possible.

- A
- B
- C
- D

**Q17: **

Given that and , find if possible.

- A
- B
- C
- D

**Q18: **

Consider the matrices Find , if possible.

- A
- B
- C
- D

**Q19: **

Given that determine if possible.

- A
- Bundefined
- C
- D

**Q20: **

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

- Ayes, ;
- Bno
- Cyes, ;

**Q21: **

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 ?

- Ayes, , , ; , , ; , ,
- Byes, , , ; , , ; , ,
- Cyes, , , ; , , ; , ,
- Dno
- Eyes, , , ; , , ; , ,

**Q22: **

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.

**Q24: **

Suppose Which of the following products is defined?

- A
- B
- C
- D
- E

**Q25: **

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