Eigen Image: Given the following exemplar three$-$pixel images:

$f1=[100,20,75{]}^T$

$f2=[5,75,220{]}^T$

$f3=[150,255,10{]}^T$

f$4=[175,200,200{]}^T$

f$5=[100,110,120{]}^T$

a$)$ Solve the KV $=$ uV for the eigen images $($V$)$ and the eigenvalues $($u$)($show ALL work$)$

b$)$ Determine the principal eigen image and explain what makes this the principal eigen image

c$)$ What percentage of the total variance does the principal eigen image consider?