(15 points) PCA. Considering the following data matrix, where your data sample is in two dimensional space. X=42511340 We want to represent the data in one dimensional space using PCA. (a) (5 points) Calculate the covariance matrix. Show your work. (b) (5 points) Assume the covariance matrix has eigenvector v1=[11]T with eigenvalue 1=16 and v2=[11]T with eigenvalue 2=4. Find the projection of x1=[41]T in the direction of maximum variance. (c) (5 points) Calculate the total variance of all the data sample in the direction of maximum variance