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 the linear equation question to get a better understanding on what the teperatures are and to solve it based of my code. Ihave pasted 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 linear equation i built.

IP$=$ Inner Point

IP:$1$: $32+17+T_2+T_4-4T_1=0=>4T_1-T_2-T_4=49$

IP $2$:$32+T_1+T_5+T_3-4T_2=0=>-T_1+4T_2-T_3-T_5=32$

IP $3$: $9+32+T_2+T_6-4T_3=0=>-T_2+4T_3-T_6=41$

IP$4$: $17+T_1+T_5+T_7-4T_4=0=>-T_1+4T_4-T_5-T_7=17$

IP$5$: $T_2+T_4+T_8+T_6-4T_5=0=>-T_2-T_4+4T_5-T_6-T_8=0$

IP$6$: $9+T_3+T_5+T_9-4T_6=0=>-T_3-T_5+4T_6-T_9=9$

IP$7$:$17+13+$T $T_8+T_4-4T_7=0=>-T_4+4T_7-T_8=30$

IP $8$: $13+T_7+T_5+T_9-4T_8=0=>-T_5-T_7+4T_8-T_9=13$

IP$9$: $9+13+T_8+T_6-4T_9=0=>-T_6-T_8+4T_9=22$

$[A][T]=[c]$

$[A]=\left[\begin{array}{ccccccccc}4& -1& 0& -1& 0& 0& 0& 0& 0\\ -1& 4& -1& 0& -1& 0& 0& 0& 0\\ 0& -1& 4& -1& 0& -1& 0& 0& 0\\ -1& 0& -1& 4& -1& 0& -1& 0& 0\\ 0& -1& 0& -1& 4& -1& 0& -1& 0\\ 0& 0& -1& 0& -1& 4& -1& 0& -1\\ 0& 0& 0& -1& 0& -1& 4& -1& 0\\ 0& 0& 0& 0& -1& 0& -1& 4& -1\\ 0& 0& 0& 0& 0& -1& 0& -1& 4\end{array}\right],[C]=\left[\begin{array}{c}49\\ 32\\ 41\\ 17\\ 0\\ 9\\ 30\\ 13\\ 22\end{array}\right]$

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