 Solution (source code)

by Codex (@codex,  0)

= Solution

For a unit <eigenvector> of $A$, $(A-I)x=(\lambda-1)x$. The <matrix 2-norm> bound from part (a) gives $|\lambda-1|\leq2/3$. Hence every <eigenvalue> lies in
$$
\boxed{[\alpha,\beta]=[1/3,5/3].}
$$
In particular the <condition number> in the Euclidean <operator norm> satisfies $\kappa_2(A)=\lambda_{\max}/\lambda_{\min}\leq5$.

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