Using the system of linear equations I have built, figure out the temperatures of the nodes and how many iterations using my python code of the conjugate gradient method. The linear equation I built was based of a thin plate. I have linked my linear equation and I need to use the computer program i have built based of the conjugate gradient method to solve the built linear equation.I also need to be using these variables to solve it: x$0=$ a matrix with height $9$ and with $1,$ and inside matrix its all $10.$ TOL$=0\mathrm{.}5.$ The question reads: what is your estimated solution $($three digits after the comma$)$ for the temperatures T$1,$ T$2,$ T$3,$ T$4,$ T$5,$ T$6,$ T$7,$ T$8$ and T$9?$ How many iterations were necessary?

The python code i made and that i will use:

import numpy as np

def conjgrad$($A$,$ b$,$ x$0)$:

x $=$ x$0$

r $=$ b $-$ np$.$dot$($A$,$ x$)$

p $=$ r

rsold $=$ np$.$dot$($np$.$transpose$($r$),$ r$)$

while np$.$sqrt$($rsold$)>1$e$-8$:

Ap $=$ np$.$dot$($A$,$ p$)$

alpha $=$ rsold $/$ np$.$dot$($np$.$transpose$($p$),$ Ap$)$

x $=$ x $+$ alpha $*$ p

s $=$ r $-$ alpha $*$ Ap

rsnew $=$ np$.$dot$($np$.$transpose$($s$),$ s$)$

beta $=$ rsnew $/$ rsold

p $=$ s $+$ beta $*$ p

r $=$ s

rsold $=$ rsnew

return x

# Define the matrix A and vector b

A $=$

# Initial guess for x

x$\_0=$

# Tolerance

TOL $=0\mathrm{.}5$

# Solve using conjugate gradient method

x $=$ conjgrad$($A$,$ b$,$ x$\_0)$

# Print the solution rounded to three digits after the comma

print$("$Estimated Temperatures:"$)$

for i$,$ temp in enumerate$($x$,$ start$=1)$:

print$($f$"$T$\{$i$\}$: $\{$temp:$\mathrm{.}3$f$\}")$

I have trouble understanding how to figure out what b is and how to put everything in to the code and what the answer to the question is$.$

Thank you