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Worksheet: Eigenvalues of a Matrix

In this worksheet, we will practice determining the eigenvalues of a nonzero square matrix by finding the scalar values that satisfy its characteristic equation.

Q1:

Calculate the eigenvalues of

  • A1, degenerate
  • B
  • C
  • D , degenerate

Q2:

Find the eigenvalues of

  • A
  • B
  • C
  • D

Q3:

Is it possible for a nonzero matrix to have 0 as its only eigenvalue?

  • Ayes
  • Bno

Q4:

Can a real matrix which has a nonreal eigenvalue be defective?

  • Ano
  • Byes

Q5:

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.

Q6:

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

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