why is this code not working, I cannot figure out please help! import numpy as np

# Given values

x$1=2\mathrm{.}95$

x$2=1\mathrm{.}74$

x$3=-1\mathrm{.}45$

x$4=1\mathrm{.}32$

# Constructing matrix A

A $=$ np$.$array$([[1,0,0,0],$

$[0,1,0,0],$

$[0,0,1,0],$

$[0,0,0,1],$

$[1,-1,0,0],$

$[1,0,-1,0],$

$[1,0,0,-1],$

$[0,1,-1,0],$

$[0,1,0,-1],$

$[0,0,1,-1]])$

# Constructing vector b

b $=$ np$.$array$([$x$1,$ x$2,$ x$3,$ x$4,1\mathrm{.}23,4\mathrm{.}45,1\mathrm{.}61,3\mathrm{.}21,0\mathrm{.}45,-2\mathrm{.}75],$dtype$=$float$)$

def householder$($A$)$:

m$,$ n $=$ A$.$shape

Q $=$ np$.$eye$($m$)$

for k in range$($n$)$:

u $=$ A$[$k:$,$ k$].$copy$()$

u$[0]+=$ np$.$sign$($u$[0])*$ np$.$linalg.norm$($u$)$

u $/=$ np$.$linalg.norm$($u$),$

A$[$k:$,$ k:$]-=2\mathrm{.}0*$ np$.$outer$($u$,$ u$)$ @ A$[$k:$,$ k:$]$

Q$[$k:$,$ :$]-=2\mathrm{.}0*$ np$.$outer$($u$,$ u$)$ @ Q$[$k:$,$ :$]$

return Q

#Apply the Householder transformation to A

Q $=$ householder $($A$)$

R $=$ Q $\%$ A

#Implement the backward substitution

def backwardSubstitution$($A$,$ b$)$:

n $=$ A$.$shape$[1]$

x $=$ np$.$zeros$($n$)$

for i in range$($n $-1,-1,-1)$:

x$[$i$]=($b$[$i$]-$ np$.$dot$($A$[$i$,$ i $+1$:$],$ x$[$i $+1$:$]))/$ A$[$i$,$ i$]$

return x

#tep $5$: Solve for the best values of the altitudes using backward substitution.

x$\_$hat $=$ backwardSubstitution $($R$,$ Q$.$T @ b$)$

dx $=$ x$\_$hat $-$ np$.$array $([$x$1,$ x$2,$ x$3,$ x$4])$

#Step $7$: Print the required values

print$("$Matrix A:$")$

print$($A$)$

print$("$

Calculated Altitudes $($x$\_$hat$)$:$")$

print$($x$\_$hat$)$

print$("$

Differences $($dx$)$:$")$

print$($dx$)$