The document discusses the geometric effects of multiplying vectors by invertible matrices. It states that the geometric effect is a succession of shears, compressions, expansions, and reflections. It provides two examples: 1) a matrix representing a compression or expansion in the x- and y-directions, and 2) expressing a matrix as a product of elementary matrices to describe its geometric effect in terms of basic transformations. It also lists properties that are preserved under these transformations.