Alternative method to determine linear transformations

This work proposes to present some discussions about techniques for determining a linear transformation from an action in a basis of its domain. We will approach, in parallel to a well-known technique and widely used in the basic bibliography of Linear Algebra, another method of determination of a linear transformation once the images of the vectors of a basis of the domain are given. This method was tried, at first, in exercises from books usually used as references in the Linear Algebra discipline and based on practical experience, it was developed in a more descriptive and generalized way. Finally, we discuss compatibility between methods.