ABSTRACT
In this chapter, the authors describe the analogues of the functions whose graphs are straight lines through the origin, the linear transformations. They define addition and scalar multiplication of linear transformations and matrices. The authors also relate these operations by showing that the matrix of the sum of two linear transformations is the sum of the matrices of the individual linear transformations. They show that the sum and scalar multiple of linear transformations are again linear transformations, it is reasonable to attempt to describe the matrices of these transformations in terms of the matrices of the original transformations. The authors explain the derivative of a real-valued function of one variable. This interpretation will form the basis for the definition of the derivative of a vector-valued function of several variables and will serve to motivate the material.
