Given the following text documents and assumed decomposition: (a) create matrix A by using term counts from the original documents;  (b) obtain rank 1, 2, and 3 approximations to the document...

Given the following text documents and assumed decomposition:

(a) create matrix A by using term counts from the original documents;

 (b) obtain rank 1, 2, and 3 approximations to the document representations;

 (c) calculate the variability preserved by rank 1, 2, and 3 approximations;

 (d) Manually cluster documents A, B, C, and D into two clusters.