3. PCA : Principal Component Analysis (a) (5 points) For each of the two data sets shown below, draw vectors that correspond to the rst and second principal components that would be produced by Principal Components Analysis (PCA). For each diagram, label which vector is the rst component, and which is the second. (b) Let 3 x N matrix X be a dataset with 3 variables and N samples. Now consider drawing the columns of X = [X 1, . . .,X N] from the given multivariate Gaussian distribution: 5 6 3 U XRNN a: 5 ,2: 3 6 U 10 U 0 10 o (5 points) What are the ordered variances 01,02,03 (high to low) for the ordered principal components? 0 (5 points) What are the ordered basis vectors 11,1 , 11,2, H3 E R3 for the ordered principal components? {You can use any software for calculating this)