A systematic method is developed for determining an output matrix C for a given matrix pair (A, B) such that the resulting linear system characterized by the matrix triple (A, B, C) has the pre-specified system structural properties, such as the finite and infinite zero structure and the invertibility structures. Since the matrix C describes the locations of the sensors, the procedure of choosing C is often referred to as sensor selection. The method developed in this paper for sensor selection can be applied to the dual problem of actuator selection, where, for a given matrix pair (A, C), a matrix B is to be determined such that the resulting matrix triple (A, B, C) has the pre-specified structural properties.