Consider the following design matrix, representing four sample points X; € R². X = [4 2 5 3 0 We want to represent the data in only one dimension, so we turn to principal components analysis (PCA). (1) Compute the unit-length principal component directions of X, and state which one the PCA algorithm would choose if you request just one principal component. Please provide an exact answer, without approximation. (You will

Consider the following design matrix, representing four sample points X; € R². X = [4 2 5 3 0 We want to represent the data in only one dimension, so we turn to principal components analysis (PCA). (1) Compute the unit-length principal component directions of X, and state which one the PCA algorithm would choose if you request just one principal component. Please provide an exact answer, without approximation. (You will