**Q1: **

Calculate the eigenvalues of

- A1, degenerate
- B
- C
- D , degenerate

**Q2: **

Is it possible for a nonzero matrix to have 0 as its only eigenvalue?

- Ayes
- Bno

**Q3: **

Can a real matrix which has a nonreal eigenvalue be defective?

- Ano
- Byes

**Q4: **

Fill in the blanks.

Let be an matrix. Then ) equals and equals .

- A ;
- Bsum of the eigenvalues of ; negative of the sum of the eigenvalues of
- Cthe product of the eigenvalues of ; the sum of the eigenvalues of
- Dthe sum of the eigenvalues of ; the product of the eigenvalues of

**Q5: **

Suppose is a linear operator. Then is an eigenvalue of if and only if

- A is invertible.
- B is not injective.
- C is surjective.
- D is not injective.

**Q6: **

Suppose that , is an eigenpair of the invertible matrix . Then , is an eigenpair of which of the following matrices?

- A
- B
- C
- D