import random

def matrix$\_$generate$($n$,$m$)$:

$"""$Receives the number of rows n and number of columns m

and generates a matrix of size n$-$by$-$m with entries choosen as

random values in the range $(0,10).$

The return matrix is stored as a list$-$of$-$lists"""

a $=[[$ random.randint$(0,10)$ for i in range$($m$)]$ for j in range$($n$)]$

return a

def matrix$\_$check$($a$)$:

$"""$Given a matrix a check if each row has the same elements.

If corrent return True, else return False."""

n$=$len$($a$)$

m$=$len$($a$[0])$

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

if len$($a$[$i$])!=$ m:

return False

return True

def matrix$\_$display$($a$)$:

$"""$Display the entries of a matrix as shown in the slides

This function has no return. It simply prints a

formatted view of the matrix. $"""$

n$=$len$($a$)$

m$=$len$($a$[0])$

out$=""$

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

out $+="["$

for j in range$($m$)$:

out $+=$ f$"\{$a$[$i$][$j$]$:$4\}"$

out $+="]$

$"$

print$($out$)$

def matrix$\_$sum$($a$,$b$)$:

$"""$ Given two matrices a and b$,$ check the size

of the matrices.

If the sizes match, calculate the sum of the matrices

and return the resulting matrix.

$"""$

###############################

# Implement this function

###############################

return

def matrix$\_$transpose$($a$)$:

$"""$ Given a matrix A of size nxm$,$

return the resulting matrix A$^$T of size mxn$.$

$"""$

###############################

# Implement this function

###############################

return

def matrix$\_$is$\_$symmetric$($a$)$:

$"""$Return True if the matrix is symmetric,

and False otherwise.

The matrix has to be square $($n$-$by$-$n$),$

and a$[$i$][$j$]$ has to be same as a$[$j$][$i$]$

$"""$

###############################

# Implement this function

##############################

return

if $"\_\_$main$\_\_"==\_\_$name$\_\_$:

#Let's create two $2-$by$-3$ matrices

n $=2$

m $=3$

A $=$ matrix$\_$generate$($n$,$m$)$

B $=$ matrix$\_$generate$($n$,$m$)$

#Display the matrices

print$("$Matrix A$")$

matrix$\_$display$($A$)$

print$("$Matrix B$")$

matrix$\_$display$($B$)$

#Check the size of the matrices

print$("$Is A a proper matrix?"$)$

print$($matrix$\_$check$($A$))$

print$("$Is B a proper matrix?"$)$

print$($matrix$\_$check$($B$))$

######################################################

#Display the sum of the matrices

######################################################

#Uncomment these lines after implementing matrix$\_$sum

#print$("$Matrix C $=$ A$+$B$")$

#C $=$ matrix$\_$sum$($A$,$B$)$

#matrix$\_$display$($C$)$

######################################################

#Uncomment these lines after implementing matrix$\_$transpose

#print$("$Matrix A$\text{'}$s transpose is:$")$

#C $=$ matrix$\_$transpose$($A$)$

#matrix$\_$display$($C$)$

######################################################

#Uncomment the two print lines below after implementing

#matrix$\_$is$\_$symmmetric function

#Let create a $3$x$3$ matrix

print$("$

Let's create a $3-$by$-3$ matrix and check if it is symmetric"$)$

n$=3$

A $=$ matrix$\_$generate$($n$,$n$)$

matrix$\_$display$($A$)$

print$("$Is this a symmetric matrix?"$)$

#print$($is$\_$symmetric$($A$))$

#Let's make the matrix symmetric

for i in range$(0,$n$)$:

for j in range$($i$+1,$n$)$:

A$[$i$][$j$]=$ A$[$j$][$i$]$

matrix$\_$display$($A$)$

print$("$Is this a symmetric matrix?"$)$

#print$($is$\_$symmetric$($A$))$