(a) Describe the curse of dimensionality. Why does it make learning hard in high dimensional space (b) Summarize main idea(s)in PCA and what is it used for? Is PCA a supervised or an unsupervised method? Why? (c) Assume that a three-dimensional (3D) feature space has the following covariance matrix. 0.681 -0.039 1.265 = 1 -0.039 0.187 -0.320 1.265 -0.32 3.092) Apply PCA to the 3D feature space vector x=[0.5,0.42,1.3] in order to project it onto the two-dimensional (2D) space. Show your work in detail.