Do task $5,$ i also provided an example code of another problem here below:

# import numpy module

import numpy as np

import math

def g$0($x$)$:

$$ return np$.$log$($x$)$

def g$1($x$)$:

$$ return np$.$cos$($x$)$

def g$2($x$)$:

$$ return np$.$exp$($x$)$

x $=$ np$.$array$([[0\mathrm{.}24],[0\mathrm{.}65],[0\mathrm{.}95],[1\mathrm{.}24],[1\mathrm{.}73],[2\mathrm{.}01],[2\mathrm{.}23],[2\mathrm{.}52],[2\mathrm{.}77],[2\mathrm{.}99]])$

# create matrix A and vector y of the exervise on Slide $37$ of Topic $3\mathrm{.}3$

A $=$ np$.$zeros$((10,3))$

A$[$:$,0]=$ g$0($x$).$ravel$()$ # numpy.ravel$()$ functions returns $1$d array

A$[$:$,1]=$ g$1($x$).$ravel$()$

A$[$:$,2]=$ g$2($x$).$ravel$()$

y $=$ np$.$array$([[0\mathrm{.}23],[-0\mathrm{.}26],[-1\mathrm{.}10],[-0\mathrm{.}45],[0\mathrm{.}27],[0\mathrm{.}10],[-0\mathrm{.}29],[0\mathrm{.}24],[0\mathrm{.}56],[1\mathrm{.}00]])$

# compute A$\text{'}$A

ATA $=$ np$.$matmul$($np$.$transpose$($A$),$ A$)$

# compute inverse of A$\text{'}$A

inv$\_$ATA $=$ np$.$linalg.inv$($ATA$)$

# compute A$\text{'}$y

ATy $=$ np$.$matmul$($np$.$transpose$($A$),$ y$)$

# compute z $=$ inverse$($A$\text{'}$A$)*$A$\text{'}$y

z $=$ np$.$matmul$($inv$\_$ATA, ATy$)$

print$($z$)$