# Lesson Worksheet: Eigenvalues and Eigenvectors for Special Matrices Mathematics

In this worksheet, we will practice finding the eigenvalues and eigenvectors of special matrices such as upper triangular, lower triangular, and diagonal matrices.

**Q1: **

Let be a matrix, where is some real number. Suppose that the matrix has an eigenvalue 9.

Determine the value of .

- A5
- B9
- C
- D1

Does the matrix have eigenvalues other than 9?

- ANo
- BYes

**Q2: **

Find all corresponding eigenvectors for the matrix

- A
- B
- C
- D

**Q3: **

Find all corresponding eigenvectors for the matrix .

- A
- B
- C
- D

**Q4: **

Find all corresponding eigenvectors for the matrix

- A
- B
- C
- D

**Q5: **

Let be a matrix, where is some real number. Suppose that the matrix has an eigenvalue 8. Find all corresponding eigenvectors for the matrix .

- A
- B
- C
- D
- E

**Q6: **

Let be a matrix, where is some real number. Suppose that the matrix has an eigenvalue . Find all corresponding eigenvectors for the matrix .

- A
- B
- C
- D
- E

**Q7: **

Let the matrix

Find all the eigenvalues of the matrix .

- A
- B
- C
- D

Find all corresponding eigenvectors for the matrix .

- A
- B
- C
- D

**Q8: **

Let the matrix

Find all the eigenvalues of the matrix .

- A
- B
- C
- D

Find all corresponding eigenvectors for the matrix .

- A
- B
- C
- D

**Q9: **

Let matrix .

Find all the eigenvalues of matrix .

- A
- B
- C
- D

Find all the corresponding eigenvectors for matrix .

- A
- B
- C
- D

**Q10: **

Let be a matrix, where is some real number. Suppose that the matrix has an eigenvalue 1 . Find all corresponding eigenvectors for the matrix .

- A
- B
- C
- D
- E