It says under Motivation

Consider the most extreme case - reconstructing the matrix using an outer product of two vectors. Clearly, in most cases we won’t be able to reconstruct the matrix exactly.

Why would we not be able to reconstruct the matrix exactly? Are approximate matrix decomposition more common than exact decomposition?

Also the **Motivation** mentioned is the motivation for NMF, SVD, topic modeling with NMF and SVD or bag of words approach? I have re watched the first 30 minutes of the video on 5 different days but I am still not able to tell what the motivation part was referring to.