Q7. [18 pt] Consider the following design matrix_ representing four sample points X; R2. We want to represent the data in only one dimension, so we turn to principal components analysis (PCA). 4 1 2 3 X54. 10 (a) [6 pt] Compute the unit-length principal component directions of X, and state wlhich one the PCA algorithm would choose 1f you request just one principal component. Please provide an exact answer, without approximation. (You will need to use the square root symbol.) Show your work