a$)$ Create a Python function called SpectralRadius that finds the spectral radius of a matrix $T.$ Here $T$ will depend on a matrix $A,$ such that

$T=(D-L{)}^{-1}U,$

where

$A=([a_{11},a_{12},$cdots,$a_{1n}$

$a_{21},a_{22},$ddots,vdots

vdots,ddots,ddots,$a_{n-1,n}$

$a_{n1},$cdots,$a_{n,n-1},a_{}])$

$=D-L-U$

$=([a_{11},0,$cdots,$0$

$0,a_{22},$ddots,vdots

vdots,ddots,ddots,$0$

$0,$cdots,$0,a_{}])-([0,a_{12},$cdots,$0$

$-a_{21},0,$ddots,vdots

vdots,ddots,ddots,$0$

$-a_{n1},$cdots,$-a_{n,n-1},0])-([0,-a_{12},$cdots,$-a_{1n}$

$0,0,$ddots,vdots

vdots,ddots,ddots,$-a_{n-1,n}$

$0,$cdots,$0,0]).$

The function needs to:

accept a matrix $A$;

return the spectral radius of $T.$

Y def SpectralRadius$($A$)$:

$\text{'}$ 'Calculate the spectral radius of a matrix $T=(D-L{)}^{{?}^{{?}^{?}}}\{-1\}U,$ where $D$ is the main diagonal of $A,$

$L$ is the lower triangular matrix of A multiplied element$-$wise by minus $1,$ and $U$ is the upper

triangular matrix of A multiplied element$-$wise by minus $1.$

Parameters

A: nxn matrix

Returns

radius : spectral radius of $T$

Usage### YOUR CODE HERE ###

b$)$ Consider the linear system given by

$10x_1-x_2+2x_3=0$

$-x_1+11x_2-x_3+3x_4=1$

$2x_1-x_2+10x_3-x_4=1$

$3x_2-x_3+x_4=0.$

Jsing the two functions above, plot the spectral radius and number of iterations required for the cases $=\{4,5,6,7\}.$ Again, use a tolerance of ${10}^{-8}$ and a

naximum number of $30$ iterations.