1. Question 1: Let XRNd denote the data matrix consisting of N examples each of dimension d. The principal components in the PCA analysis are computed by taking the eigen decomposition of X. True/False? 2. Question 2: When performing PCA from a 1000-dimensional space to a 2dimensional space, there will be a loss of information even if the data originally lies in a 2-dimensional space. True/False? 3. Question 3: PCA minimizes the variance of the data in the low-dimensional representation. True/False? 4. Question 4: To reduce the dimensionality of a new point using PCA, one must project the point onto the eigenvectors of the covariance matrix of the dataset. True/False? 5. Question 5: In implementing PCA using auto-encoders, the weight matrices of the encoder and decoder should be tied together, and they should be transposes of each other. True/False