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Mathematics · University

Eigenvalue from a known eigenvector

Verify the vector is nonzero. Distinct eigenvectors can have distinct eigenvalues.

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Method and conditions

Verify the vector is nonzero. Distinct eigenvectors can have distinct eigenvalues.

A(1,1)ᵀ = (a+b)(1,1)ᵀ for A=[[a,b],[b,a]]

Worked examples

For A = [[13,9],[9,13]], find the eigenvalue belonging to v = (1,1). Round the final result to 4 decimal places if needed.

Multiplication gives Av = (22,22) = (22)v.

22

For A = [[-8,4],[4,-8]], find the eigenvalue belonging to v = (1,1). Round the final result to 4 decimal places if needed.

Multiplication gives Av = (-4,-4) = (-4)v.

-4

Try it

  1. For A = [[18,20],[20,18]], find the eigenvalue belonging to v = (1,1). Round the final result to 4 decimal places if needed.

  2. For A = [[-4,11],[11,-4]], find the eigenvalue belonging to v = (1,1). Round the final result to 4 decimal places if needed.

Check your work

Answers and marking notes
  1. 38

    Multiplication gives Av = (38,38) = (38)v.

  2. 7

    Multiplication gives Av = (7,7) = (7)v.

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