In this problem yau will use Principal Components Analysis (PCA) ta analyze a simple data set. Do not use a PCA software but only the information provided below. You are free to use a calculator to aid your computations. Consider the following date set, X: The covariance matrix of X (and of centered X) is given by: The eigen vectors and the corresponding eigen values of the covariance matrix are given by: and 0.75 3.68 8.27 respectively. Apply PCA to the centered version of the data set showed above, using only the top principal component to embed data into a I-D latent space. Answer the following questions about the location of the data points in the latent space (rounded the second decimal): A: -0.17, 8: -2.89 G: -2.23, H: 3 25 G: -1.62, 211 a) d) 0.37, J: