1. (5 points) Please prove the first principle component direction v corresponds to the largest eigenvector of the sample covariance matrix: m v = arg max w:| | w| 1 m i=1 You may use the proof steps in the lecture, but please write them logically and cohesively. 2. (5 points) Based on your answer to the question above, explain how to further find the second, and the third largest principle component directions