# Worksheet: Scalar Multiplication of Matrices

In this worksheet, we will practice multiplying a scalar by a matrix and identifying the properties of their multiplication.

**Q2: **

Find numbers , , and so that .

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

**Q3: **

Given that find the value of .

**Q4: **

Let be a matrix whose entries are all zero. If is any matrix, which of following is equivalent to ?

- A
- B
- C
- D
- E

**Q5: **

Given the matrix what is the greatest number for which no entry of is greater than 1?

- A
- B
- C
- D
- E

**Q6: **

If , what is ?

- A
- B
- C 6
- D
- E[9]

**Q7: **

Consider the matrix . Find .

- A
- B
- C
- D

**Q8: **

If , what is ?

- A
- B 0
- C
- D
- E

**Q9: **

Olivia has defined the notion of a 'prime matrix' as follows. A matrix is a prime matrix if the following two conditions hold:

- It is none zeros with integers entries.
- If , then or .

Which of the following matrices are prime according to Olivia's definition?

- A
- B
- C
- D
- E