Chapter 2.3, Problem 9E

(a) Find the condition number (in the infinity norm) of the matrix $A=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right]$ . (b) Let D be an $n\times n$ diagonal matrix with diagonal entries $d_1,d_2,\mathrm{...},d_n$

. Express the condition number (in the infinity norm) of D in terms of the $d_i$.