You are given the following data set: -[4-[] = You would like to use PCA to find a 1-dimensional representation of the data. a. Plot the data set. b. Compute the feature covariance matrix S. c. You find that S has eigenvector [-11]T with eigenvalue 1 and eigenvector [11] with eigenvalue 3. What is the (normalized) basis vector u of your 1-dimensional representation? Add the basis vector u to your plot. d. Compute the coefficients Z1, Z2, Z3 where z = xu. Add the lower-dimensional representations Z, Z2U, Z3U to your plot. Based on your plot, what is the relationship between zu and x, with respect to the new basis? e. Based on your plot, what would happen if you chose the unused eigenvector to be your basis vector?