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Principal Component Analysis (PCA) and Optimization For all questions below, you need to show intermediate steps as well. You are NOT allowed to use programming/code and every computation should be done by hand unless instructed. 1. We will compute PCA with the data (data matrix X consists of x.- 6 R2, 1 S x,- S 6): x = ( 1 2 3 5 6 7 ) 0 0 0 8 8 8 (a) Compute covariance matrix from the data (b) Compute eigenvectors and eigenvalues of the computed covariance matrix in (a). (c) Create orthogonal base with the top eigenvector (so we project data to 1D). (d) Transform data by multiplying with the base in (c). (e) Visualize the original and transformed data by using 2D and 1D plot (i.e., 2D plane with x and y axes and 1D line with only x axis). You can use hand for visualization here