In this question we explore the differences between lists and numpy arrays.

First, you will create an $mn$ matrix $M$ filled with numbers $1,2,3,$dots,$mn$ in order, by

rows. For example, if $m=2$ and $n=3,$ then

if $m=1$ and $n=7,$ then

$M=\left[\begin{array}{ccccc}1& 2& 3& 5& 6\end{array}\right]$

$4$

$M=[1,2,3,4,5,6,7]$

$\left[\begin{array}{ccccccccccccc}1& 2& 3& 4& 5& 7& 8& 9& 10& 12& 13& 14& 15\end{array}\right]$

$11$

$6$

$1$

and $ifm=3$ and $n=5$

Parts $($a$)-($c$)$: Use commands for lists only $($no numpy arrays$)$

$($a$)[1]$ Write a function create$\_$matrix $(m,n)$ to create the $mn$ matrix $M$ as described above.

$($b$)[1]$ Write a function sum$\_$columns$($M$)$ to create a list whose entry under index $j$ is the

sum of all elements in the column $j$ of $M.$

$($c$)[1]$ Write a function sum$\_$rows $(M)$ to create a list whose entry under index $i$ is the sum

of all elements in the row $i$ of $M.$

Parts $($d$)-($f$)$: Use commands for numpy arrays only, such as np$.$arange, np$.$reshape,

$.$sum, etc., as well as slicing. Do not use commands for lists, such as $.$append.

$($d$)[1]$ Write a function np$\_$create$\_$matrix $(m,n)$ to create the $mn$ numpy array $M$ as de$-$

scribed above.

$($e$)[1]$ Write a function np$\_$sum$\_$columns$($M$)$ to create a numpy vector $($i$.$e$.,$ a one$-$dimensional

array$)$ whose entry under index $j$ is the sum of all elements in the column $j$ of $M.$

$($f$)[1]$ Write a function np$\_$sum$\_$rows$($M$)$ to create a a numpy vector $($i$.$e$.,$ a one$-$dimensional

array$)$ whose entry under index $i$ is the sum of all elements in the row $i$ of $M.$