PCA Plots In each plot below, some d-dimensional data is projected onto two unit vectors. The x-coordinate is the projection onto the first vector (written as v1), and the y-coordinate is the projection onto the second vector (written as h v2). Mathematically, we can say that we have some data matrix D = d 1 d 2 d n i where each d i Rd . We then project each d i onto the column space of the matrix V = h v1 v2 i and plot the projection coefficients below. We say that a plot is "valid" if v1 could be the first principal component. (HINT: Note that the mean or "center of mass" of the data points is the origin, (0, 0), in all of the plots. The procedure for this problem is very similar to the procedure in Discussion 14B, where you were similarly asked to judge the "validity" of scatterplots.)