(2) Consider 3 data points in the 2D space: (2,2), (0,0), (-2,-2). Please answer the following questions. a) Calculate the rst principal component by calculating the eigenvalue (non-zero) and eigenvector of the covariance matrix. You need to provide the actual vector of the rst principal component (with length=l). You can use the unbiased estimation of the covariance: N 1 _ WT'CX) = (Xn \" 1'02 \" n=1 Cov(X, Y) = zi': (X1,1 \" )(Yn F) b) If we project the three data points into the 1D subspace by the principal component obtained in (a), what are the new coordinates of the three data points in the ID subspace? What is the variance of the data after projection? c) What is the cumulative explained variance of the rst principal component? Is there any variance that is not captured by it