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 𝐴 has.

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

Q2:

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

  • A1
  • B32
  • C 2
  • D 1 6
  • E2

Q3:

Using the power method, find the eigenvalue with the largest absolute value for the following matrix Round your answer to one decimal place if necessary.

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

Q4:

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

  • AThe actual largest eigenvalue is 9.
  • BThe actual largest eigenvalue is 4 .
  • CThe actual largest eigenvalue is 10.
  • DThe actual largest eigenvalue is 8.
  • EThe actual largest eigenvalue is 7.

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