Chapter 7.6, Problem 7E

(a)

To determine

To show:if $\left|x_i\right|={\Vert x\Vert }_{\infty }$ , then ${\displaystyle \sum _{j=1}^n{a}_{ij}{x}_j=\lambda x_{\begin{array}{l}i\\ \end{array}}}$

(b)

To determine

To show: if $\left|x_i\right|={\Vert x\Vert }_{\infty }$ , then $\left|\lambda -a_{ii}\right|\le {\displaystyle \sum _{\begin{array}{l}j=1\\ j\ne i\end{array}}^n\left|a_{ij}\right|}$