The purpose of this paper is to explore the possibility of evaluating SPARQL queries containing probabilities using linear algebraic methods and techniques. This approach has many important advantages, such as simplicity, succinctness, elegance and greater familiarity to a wide base of practitioners. On the other hand, there are questions regarding its efficiency in view of the huge datasets of the current era. In this paper, we advocate that in the case of sparse RDF graphs we can resort to sparse matrices for computing complicated probabilistic queries. It is demonstrated that via probabilistic sparse matrices one can evaluate specific types of queries involving transitive predicates, which are of great practical importance. The algorithm and data structures that are currently available for handling sparse matrices promise improved performance in pragmatic situations, which constitutes this line of approach particularly promising.