This second block is focused on the algebraic applications of the algorithm, which include: the problem of the membership of a vector to a cone and the intersection of two cones. The first of these is a complex problem because it involves nonnegative linear combinations, that is, systems of linear inequations, whose solutions are not usually known by students or studied in standard algebra courses. The use of the algorithm, explained in the previous block, allows to solve the problem in a very elegant way and avoid having to solve these systems. The intersection of cones is another problem of some complexity, since it also implies the systems of inequations, solving it in an ingenious way. It can also be resolved by realizing that such an intersection is the dual cone of the dual of one of them in the other, which directly suggests how to solve it.