# 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