2. (10 pts) The three-dimensional vector samples X1, ..., X,, taken from the distribution of three vari- ables (X1, X2, X3), yield the following the mean vector and the sample covariance matrix 10.5] 1 0.7 0 X = 5.2 , S= 0.7 1 0.3 4.8 0 0.3 1 1. Determine the sample principal components and their variances for these data. 2. Find the proportions of the total sample variance explained by the first two simple principal components , and 12