Use the functions you defined in the Problem $2$ to construct a single matrix which performs the following sequence of transformations $($in order$)$ when acting on an image.

Stretch the image vertically by a factor of $2.$

Rotate the image pi$/4$ radians clockwise.

Reflect the image over the line $2$y$=-3$x $.$

Stretch the image horizontally by a factor of $1/2.$

save the resulting $2$x$2$ matrix as comp$\_$matrix.

Funcitons defined in problem $2$:

# This function should take a matrix of coordinates, and output a matrix which corresponds to the image that has been stetched in the

# horizantal direction by a factor of a and in the verticle direction by a factor of b$.$

def stretch$($image$,$ a$,$ b$)$:

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

$[0,$ b$]])$

return np$.$dot$($A$,$ image$)$

# This function should take a matrix of coordinates, and output a matrix which corresponds to the image that has been sheared by a horizantal factor of a and

# a vertical factor of b

def shear$($image$,$ a$,$ b$)$:

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

$[$b$,1]])$

return np$.$dot$($A$,$ image$)$

# This function should take a matrix of coordinates, and output a matrix which corresponds to the image that has been reflected in the

# line spanned by the vector $[$a$,$b$]^$T

def reflect$($image$,$ a$,$ b$)$:

A $=$ np$.$array$([[$a$**2-$ b$**2,2*$a$*$b$],$

$[2*$a$*$b$,$ b$**2-$ a$**2]])/($a$**2+$ b$**2)$

return np$.$dot$($A$,$ image$)$

# This function should take a matrix of coordinates, and output a matrix which corresponds to the image that has been rotated in the

# counterclockwise direction by an angle of theta radians.

def rotate$($image$,$ theta$)$:

A $=$ np$.$array$([[$np$.$cos$($theta$),-$np$.$sin$($theta$)],$

$[$np$.$sin$($theta$),$ np$.$cos$($theta$)]])$

return np$.$dot$($A$,$ image$)$