(a) (8 points) Suppose we have 5 data points in a 2-dimensional Euclidean space: x1= [12]T,x2=[7376]T,x3=[36]T,x4=[56512]T,x5=[320340]T. What are the first and second principal components? (Please do not use code to solve this sub-problem.) (b) (12 points) Consider a dataset of automobiles' information (file: automobile.csv 2 ), we will analyze it through PCA. Use these five feature columns: curb-weight, horsepower, city-mpg, highway-mpg, price to obtain a subdataset, and answer the following question: what are the first principal component and second principal component of this subdataset? If you want to use Python for this problem, please note that only standard Python library such as Numpy, Scikit-learn, Pandas are allowed. Your source code is required to be submitted and please make sure it is bug-free