Abstract.  Lines and surfaces are boundary elements of objects and buildings: it is very important to give the students a mathematical approach to them. Elena Marchetti and Luisa Rossi Costa present linear algebra (by vectors and matrices) as an elegant and synthetic method, not only for the description but also for the virtual reconstruction of shapes.The aim of our activity is to facilitate—and, at the same time, to develop—the comprehension of crucial mathematical tools involved in the realization of forms and shapes in arts, architecture and industrial design and in computer graphics. Another important aspect of linear algebra to be pointed out to the students is its application in graphics software packages, which work with transformations that change the position, orientation and size of objects in a drawing