Consider the data matrix X of size 3 x N, where N is the number of samples. The covariance matrix K, of size 3 x 3 has 3 eigenvectors vâ = [-0.99, 0.09, 0], v2 = = [0, 0, 1] and v3 = [-0.09, -0.99, 0] with eigenvalues Xâ = 0.98, Aâ = 0.5 and X3 = 1.98, respectively. Answer the following questions: 1. What linear transformation would you use to uncorrelate the data X? Provide a numerical solution and justify your answer. 2. Use Principal Component Analysis (PCA) to project the 3-dimensional space to a 2-dimensional space. Define the linear transformation (using a numerical answer). 3.What is the amount of explained variance of this 2-D projection? Show your work. 4. Let Y be the data (linear) transformation obtained by principal component transform of X onto a 2-dimensional space. What is resulting covariance matrix of transformed data Y? Use a numerical answer and justify your answer.