Recall that PCA finds a direction w in which the projected data has highest variance by solving the following program:

Now you are given a dataset of four points (2, 0), (2, 2), (6, 0) and (6, 2). Draw the four data points on the 2D plane. Given this dataset, what is the dimension of the covariance matrix in Eq. (1)? Also, explicitly write down the values of given the dataset.

maxw:w2=1wTw