4 a) What does it mean for a covariance matrix to be full rank? In the context of PCA, why is a full-rank covariance matrix important? b) Why is it a common practice to neglect the later eigenvectors with smaller eigenvalues in PCA? In what situations might it be reasonable to consider or not consider these less signif- icant eigenvectors? c) Given a dataset with a total sum of eigenvalues equal to 50, and the first eigenvalues being 15, 12, 8, and 3, determine the proportion of variance explained by the first two principal components. What does this value suggest about the choice of components and how many of these should you choose