2. Given a dataset 331, . . . , mm where the dimension of each observation is 3. The sample mean and sample covariance matrix are 1 10.5 5 2.1 if: = 2 , S = 5 6.3 1.4 3 2.1 1.4 9.9 The spectral decomposition op S is S = H AH T, where 0.553 0.366 0.748 2.98 0 0 H = 0.833 0.243 0.497 , A = 0 8.67 0 0 0.898 0.440 0 0 15.06 (a) What is the percentage of the total variance by the rst, second and the third principal component? (b) Consider an observation 33g 2 (1,2,2)T, what are the scores for the rst and second principal component for are? (c) What is the reconstructed in: for are in (b) using both the rst and the second principal components? ((1) Find a 3 X 1 vector 'u, to minimize \"1%:\". What is the corresponding minimum value? Is this vector it. unique? Explain your answer. (e) denote y = (X1,X2,X3)T , where XLXQ, and X3 are the three variables in the random vector :8. Compute the sample covariance and the sample correlation matrix for y