The full assignment is

8.3.2e

8.3.3 a, c

8.3.15 a, c, g

8.4.1 b,d

8.5.1 e

In 8.5.1 e I’d like you not just to find the singular values, but also the eigenvectors and Q matrices, and verify that Q Sigma Q^T = A where you use the appropriate Q matrix in the appropriate places. Also find the “compressed image” that results when you discard the smaller singular value and calculate Qcompressed Sigmacompressed Qcompressed^T; how does it compare to A? Find the pseudoinverse A^+ = Q Sigma^-1 Q^T, and calculate the products AA^+ and A^+A (one of which will be an identity matrix, I think). Then find the “compressed pseudoinverse” A^+compressed = Qcompressed Sigmacompressed^-1 Qcompressed^T. How does A times the compressed pseudoinverse look (whichever order gave I), compared to the identity?

That should be loads of fun!