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Worksheet: Eigenvalues of a Matrix
Q1:
Can a real matrix which has a nonreal eigenvalue be defective?
- Ano
- Byes
Q2:
Suppose that , is an eigenpair of the invertible matrix . Then , is an eigenpair of which of the following matrices?
- A
- B
- C
- D
Q3:
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
Q4:
Is it possible for a nonzero matrix to have 0 as its only eigenvalue?
- Ayes
- Bno
Q5:
Calculate the eigenvalues of
- A1, degenerate
- B
- C
- D , degenerate
Q6:
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.