In Section 3.1, we studied the geometry of matrices by regarding them as functions, i.e., by considering the associated matrix transformations. We defined some vocabulary (domain, codomain, range), and asked a number of natural questions about a transformation. For a matrix transformation, these translate into questions about matrices, which we have many tools to answer.
In this section, we make a change in perspective. Suppose that we are given a transformation that we would like to study. If we can prove that our transformation is a matrix transformation, then we can use linear algebra to study it. This raises two important questions:
For example, we saw in this example in Section 3.1 that the matrix transformation