Q$2[20$ Marks$]$

$($a$)$ Consider the four $2-$dimensional data points:

$a$:$(6,6),b$:$(8,8),c$:$(5,9)$ and $d$:$(9,5)$

We can make use of PCA for dimensionality reduction. In dimensionality reduction, given an L$-$

dimensional data point, we want to transform this point to a $K-$dimensional data point where $L=2K=1K$ such

that the information loss during the transformation $is$ minimized.

Please illustrate with the above example when $L=2$ and $K=1.$ Please write the numbers $upto2$ decimal

places. You cannot use XLMiner $in$ this part.