ABSTRACT
We now begin to focus on answering the basic mapping questions for linear transformations; that is, for linear mappings
T : Rm → Rn
As we observed in Theorem 5.6, every linear transformation is represented by a matrix, via matrix/vector multiplication. Specifically, we have the formula
T (x) = Ax
where A is the matrix whose columns are given by the T (ej)’s. For this reason, we can usually reduce questions about the mapping T to calculations involving the matrix A .
