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Exercise 5

Avg difficulty 2.5

For the following matrices, find the eigenvectors and associated eigenvalues by thinking geometrically about the corresponding matrix transformation.

  1. [3003]\left[\begin{array}{rr} 3 & 0 \\ 0 & 3 \\ \end{array}\right].

  2. [−2004]\left[\begin{array}{rr} -2 & 0 \\ 0 & 4 \\ \end{array}\right].

  3. What are the eigenvectors and associated eigenvalues of the identity matrix?

  4. What are the eigenvectors and associated eigenvalues of a diagonal matrix with distinct diagonal entries?

Austin, Understanding Linear Algebra, §4.1 An introduction to eigenvalues and eigenvectors, Exercise 5

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.