# Worksheet: The Power Method For Eigenvalues

In this worksheet, we will practice finding the largest absolute value for an eigenvalue of a 3-by-3 matrix using the power method for approximating eigenvalues.

Q1:

Consider the matrix Using the power method, determine, to the nearest integer, the eigenvalue of largest absolute value that has.

• AThe largest eigenvalue is approximately 6.
• BThe largest eigenvalue is approximately 5.
• CThe largest eigenvalue is approximately 4.
• DThe largest eigenvalue is approximately 7.
• EThe largest eigenvalue is approximately 8.

Q2:

Using the power method, find the eigenvalue with the largest absolute value for the following matrix

Q3:

Using the power method, find the eigenvalue with the largest absolute value for the following matrix

• AThe actual largest eigenvalue is 12.
• BThe actual largest eigenvalue is .
• CThe actual largest eigenvalue is 13.
• DThe actual largest eigenvalue is 5.
• EThe actual largest eigenvalue is 10.

Q4:

Using the power method, find the eigenvalue with the largest absolute value for the following matrix

• AThe actual largest eigenvalue is 8.
• BThe actual largest eigenvalue is .
• CThe actual largest eigenvalue is 9.
• DThe actual largest eigenvalue is 10.
• EThe actual largest eigenvalue is 7.