1. Suppose that ?x is an eigenvector of A corresponding to an eigenvalue ? (a) Show that ?x is an eigenvector of 5I - A. What is the corresponding eigenvalue? (b) Show that ?x is an eigenvector of 5I - 3A + A². What is the corresponding eigenvalue?
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This shows that X is an eigenvector of 5I - A with corresponding eigenvalue 5 - λ. ** Show more…
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Confirm by multiplication that $x$ is an eigenvector of $A,$ and find the corresponding eigenvalue. $$A=\left[\begin{array}{rrr}2 & -1 & -1 \\-1 & 2 & -1 \\-1 & -1 & 2\end{array}\right] ; \mathbf{x}=\left[\begin{array}{l}1 \\1 \\1\end{array}\right]$$
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