Problem $1($Principle Component Analysis$)(0\mathrm{.}5\%)$

Given $10$ samples in $3$D:

$(1,2,3),(4,8,5),(3,12,9),(1,8,5),(5,14,2),(7,4,1),(9,8,9),(3,8,1),(11,5,6),(10,11,7)$

What are the principal axes? Please write down your derivation or provide your code of computation at HW$3$ math problems $($NTU COOL$)$ through "add another file".

Please compute the principal components for each sample and either write down your derivation or provide your code of computation in report.

What is the average reconstruction error if reduce dimension to $2$D$?$ Here the reconstruction error is defined as the squared loss.