Vector Images

Learning Objectives: Use vectors to express data in real life examples.

The $\mathrm{.}16$a image format represents images as vectors! For any image that is $m$ by $n,$ it has a corresponding

stacked vector $v=\left[\begin{array}{c}{p}_0\\ \text{d}\text{o}\text{t}\text{s}\\ p_i\\ \text{d}\text{o}\text{t}\text{s}\\ p_{mn-1}\end{array}\right],$ where $p_i=\left[\begin{array}{c}{x}_r\\ x_g\\ x_b\end{array}\right]$ is a $3-$dimensional vector containing the RGB values of a

specific pixel $i.$ For a pixel in an $m$ by $n$ image, assume that the pixel at coordinate $(x,y)$ is defined by $p_{x*n+y}.$

Note that the image and the stacked vector are zero$-$indexed.

For the purposes of this question, you are allowed to refer to the pixel vectors $p_i$ as pixel subvectors.

$($a$)$ Given an image vector $z,$ describe the image of the reversed vector.

$($b$)$ Describe the vector of a purely blue image, of any shade.

$($c$)$ Describe a vector $x$ such that for any square $(n$ by $n)$ image $z,x^{TT}z$ is the sum of the entries in the pixel

vectors along the diagonal, from $(0,0)$ to $(n-1,n-1).$