1. In the code shown in Tab. 1, what is the size of matrix X? 2. In the code shown in Tab. 1, what is the size of matrix S? 3. In the code shown in Tab. 1, what is the size of matrix U? 4. In the code shown in Tab. 1, explain what the function svd does. 5. Consider u1 and u2 eigenvectors of matrix S wih respective eigenvalues 1 and 2 with 1>2. Defining u3=u1+u2, is u3 an eigenvector of S ? Explain. 6. PCA is computed on a set of vectors of dimension D=5 and the eigenvalues computed for the corresponding covariance matrix are 1=5,2=4,3=3,4=2 and 5=1. How many eigenvectors do we need to keep for reconstruction to get at least 90% of the variance explained? 7. Using the code shown in Tab. 2, what is the size of matrix X? 8. Using the code shown in Tab. 2, what is the size of matrix S ? 9. Using the code shown in Tab. 2, what is the value of the highest eigenvalue? 10. Using the code shown in Tab. 2, how many principal components do we need to keep for reconstruction to get at least 90% of the variance explained? Table 1: Matlab code for PCA on a dataset created in R2. Table 2: PCA with MNIST dataset