$3\mathrm{.}1$ Grayscale Images

A grayscale image can be associated with a set of numbers representing the brightness of each pixel.

For example, the $2$ x $2$ pixel image below can be associated with the corresponding array of numbers, where the black squares represent pixels with intensity $0$ and the white squares represent pixels with intensity $16$:

$16$

$8$

$0$

$16$

Note that this interpretation gives us a way to think about multiplying an image by a constant and adding two images. For example, suppose we start with the three images $($A$,$ B$,$ and C$)$ below.

Then multiplying Image A by $0\mathrm{.}5$ results in Image $1$ below. Note that the maximum intensity is now half what it previously was, so the all pixels have become darker gray $($representing their lower intensity$).$ Adding Image $1$ to Image C results in Image $2$ below; so Image $2$ is created by doing arithmetic on Images A and C$.$

Exercise $1$: Write Image $3$ and Image $4$ using arithmetic operations of Images A$,$ B$,$ and C$.$