?When Shortcut Fails The eigenvector shortcut of may fail when b = 0, forcing a return
Chapter 5, Problem 18(choose chapter or problem)
When Shortcut Fails The eigenvector shortcut of Problem 17 may fail when b = 0, forcing a return to the definition \(A \bar{v}=\lambda \bar{v}\) to find the eigenvector(s). For each eigenvalue in the following matrices, find the eigenvector(s). Discuss how/why the shortcut fails and why the definition succeeds.
(a) \(\left[\begin{array}{ll} 3 & 0 \\ 5 & 3 \end{array}\right]\)
(b) \(\left[\begin{array}{ll} 3 & 0 \\ 5 & 2 \end{array}\right]\)
(c) \(\left[\begin{array}{ll} 3 & 0 \\ 0 & 3 \end{array}\right]\)
Equation Transcription:
Text Transcription:
A bar v = lambda bar v
[3 0 _ 5 3]
[3 0 _ 5 2]
[3 0 _ 0 3]
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