# Worksheet: Eigenvalues and Eigenvectors for Special Matrices

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 . Find all corresponding eigenvectors for the matrix .

• A
• B
• C
• D
• E

Q2:

Find all corresponding eigenvectors for the matrix

• A
• B
• C
• D

Q3:

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

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:

Find all corresponding eigenvectors for the matrix

• A
• B
• C
• D

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