__Brief overview of the
development of the relationship between a linear transformation T and its
associated matrix M.__

__Assumptions:__

Vector spaces and bases have been discussed. In addition, the fact that a linear
transformation
is completely determined by its action on a basis has been covered.

__Sketch of the development:
__Let S = {

.

It follows by the linearity property for linear transformations that

.

Hence the m by n matrix **M**
associated with the linear transformation **T** is given by

.

Since **T**(**e _{j}**) is in R