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Suppose we have 4 points in 3-dimensional Euclidean space, namely (1, 0,0.5), (6, 14, 3), (11, 28, 5.5), and (7, 21, 3.5). (a) (3 points) Find the first principal direction. First, write down the data matrix and make sure you fill in numbers specific for this problem. Then explain how to find the first principal direction and what is the optimization problem you need to solve? Find the first principal direction either by calculation in hand, or using program or software - report the first principal direction you found. (a) (b) (b) (2 points) What are the first principle components, for each of the data points? (c) (2 points) When we reduce the dimensionality from 3 to 1 based on the principal direction you found in (a), what is the remaining variance in the data? (d) (3 points) You are given the following 2-D datasets, approximately draw the first and second principal directional on each plot