Consider 3 data points in the 2-d space: (1, 1), (0, 0), (1, 1). 1. (8 points) What is the first principal component (write down the actual vector)? 2. (9 points) If we project the original data points into the 1-d subspace by the principal component you choose, what are their coordinates in the 1-d subspace? And what is the variance of the projected data? 3. (8 points) For the projected data you just obtained above, now if we represent them in the original 2-d space and consider them as the reconstruction of the original data points, what is the reconstruction error