$1\mathrm{.}4$ Problem: PCA $(12$ pts$.)$

Consider the following $10$ data points: $,(-1,1,3,2,-1),(1,0,1,-1,1),(2,3,-1,1,-2),(-2,3,-3,3,2),(-2,-2,2,3,-2),(-2,-3,1,-2,-3),(-3,2,0,-1,-2).$ Compute the unit$-$length principle components of $x$ and choose two of them for PCA, then calculate the projection of each data on these two principal components. You could use python or matlab to obtain eigenvectors and eigenvalues.