In this problem we study the temperature distribution in a two$-$dimensional object, like a very thin metal plate. We can model

such an object as a grid of wires, as shown below. In the example, we assume that the temperature at the exterior grid points is

constant and known. Your job is to determine the temperature at the interior points in the thermal equilibrium.

When the temperature distribution in the grid is stable, the temperature at each interior point is the average of the

temperatures at the four adjacent points. For example,

$q,T_2=\frac{T_1+T_4+S_7+S_8}{4}.$

You are now given the vector $S=\left[\begin{array}{c}{S}_0\end{array}\right]$

vdots

$S_8.$ Compute $T=\left[\begin{array}{c}{T}_0\end{array}\right]$

vdots

$T_4$

The vector $S$ is stored as a $1-$d numpy array in $s.$ Use this to compute $T$ and store the vector in $T$ as a numpy array of the same

shape as S$.$

The setup code gives the following variables:

Your code snippet should define the following variables:

Note: The use of np$.$ linalg. solve$()$ is not permitted in this question, as you may not have access to it on the exam. How else

can you solve a system of equations?import numpy as np