1. A dataset contains 5 two-dimensional samples: x, = [5 1]', x, = [4 2]', x, =[3 3], x, = [2 4] and x, = [1 5]. (a) Compute the sample covariance matrix of the dataset. (10 Marks) (b) Plot the five samples as 5 points in the data space x. (10 Marks) (c) Obtain the eigenvalues and the unit-length eigenvectors of the covariance matrix. (10 Marks) (d) Project the data into vectors [1 0] , [0 1] and the unit-length eigenvectors and compute the variances of the projected one-dimensional data along each of these 4 dimensions. (10 Marks) (e) Interpret the meanings of the eigenvalues and the eigenvector of a covariance matrix that support the results from (a), (b), (c) and (d). (10 Marks)