9. The first principle direction is the direction in the input space along which the projections of the data points have the largest variance. We use W to denote the first principle direction (w has unit length i.e. L2 norm is 1), 2 to represent the first/largest eigenvalue of the covariance matrix, u to represent the sample mean, and x to represent a data point. The deviation of x from the mean is x . We do dimensionality reduction: y = PCA(x) with "whiten-True" in sk-learn, and the number of components/elements of y is less than the the number of components/elements of x (1) what is the vector-projection of x in the direction of w ? (2) what is the vector-projection of the deviation x - u in the direction of w? (3) what is the first component of y? (whiten=True: something divided by (4) assuming y only has one component, then we do inverse transform to recover/approximate the input x = PCA-(y) compute x using , y, and w: x = ??? (5) what is x x if x and y have the same number of elements?