# Worksheet: Scalar Multiplication of Matrices

In this worksheet, we will practice carrying out scalar multiplication of matrices.

**Q2: **

Given that , find .

- A
- B
- C
- D

**Q3: **

Using the properties of determinants, find the value of

**Q4: **

Find numbers , , and so that .

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

**Q5: **

Given that find the value of .

**Q6: **

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

- A
- B
- C
- D
- E

**Q7: **

Let and be the identity matrix. Find , , and their product , and then use this to express as a combination of and .

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

**Q8: **

Fill in the blank. Columns of an matrix are an orthonormal basis for , if and only if is a matrix.

- Asymmetric
- Bnormal
- Csquare
- Dunitary