In this worksheet, we will practice determining whether a matrix is symmetric or skew-symmetric and using their properties to solve problems.

**Q1: **

Which of the following matrices is skew-symmetric?

- A
- B
- C
- D

**Q3: **

Which of the following matrices is symmetric?

- A
- B
- C
- D

**Q4: **

Find the value of which makes the matrix symmetric.

**Q5: **

Suppose that and are symmetric matrices and that . Does it follow that is also a symmetric matrix?

- Ayes
- Bno

**Q6: **

If and are symmetric matrices, does it follow that is also symmetric?

- Ano
- Byes

**Q7: **

Given that the matrix is skew-symmetric, find the value of .

**Q8: **

The non-zero eigenvalues of a real, skew-symmetric matrix are .

- Apurely real
- Bnon-negative
- Cpurely imaginary

**Q9: **

Suppose is a real matrix. Which of the following is true about the matrix ?

- Ais always singular
- Bis always skew-symmetric
- Cis always nonsingular
- Dis always symmetric

**Q11: **

Which of the following matrices is skew-symmetric?

- A
- B
- C
- D

**Q12: **

Which of the following matrices is skew-symmetric?

- A
- B
- C
- D

**Q13: **

Given that the matrix is skew-symmetric, find the value of .

**Q14: **

Given that the matrix is skew-symmetric, find the value of .

**Q15: **

Find the value of which makes the matrix symmetric.

**Q16: **

Find the value of which makes the matrix symmetric.