In this worksheet, we will practice determining whether a matrix is orthogonal and finding unknown elements of a matrix to be an orthogonal matrix.

**Q1: **

Is the given matrix orthogonal?

- A yes
- B no

**Q2: **

Is the given matrix orthogonal?

- A yes
- B no

**Q3: **

Is the given matrix orthogonal?

- A no
- B yes

**Q4: **

Is the given matrix orthogonal?

- A yes
- B no

**Q5: **

Given that the matrix is orthogonal, find the values of , , , and .

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

**Q6: **

Given that the matrix is orthogonal, find the values of , , , and .

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

**Q7: **

Given that the matrix is orthogonal, find the values of , , , and .

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

**Q8: **

Fill in the missing entries to make the matrix orthogonal.

- A
- B
- C
- D
- E

**Q9: **

A matrix is said to be orthogonal if . Thus, the inverse of an orthogonal matrix is just its transpose. What are the possible values of if is an orthogonal matrix?

- A or
- B
- C
- D or
- E or

**Q10: **

True or false: the matrix is orthogonal?

- ATrue
- B False