Please answer the question in the picture below:

1. Principal Components Analysis (PCA) and Linear Discriminant Analysis (LDA) have different purposes. The former operates on the total (unlabeled) dataset to find the directions that contain the maximum variance; the latter operates on labeled data to find the directions which are best at distinguishing the labeled classes. In general, the results (principal components and canonicals, respec- tively) will be quite different. However, for special examples of data the principal components and canonicals could be in the same directions. (1) Draw an example of two-class, two-dimensional data such that PCA and LDA find the same directions. (2) Draw an example of two-class, two-dimensional data such that PCA and LDA find totally different directions