In the present study, an $(n+1)$-dimensional module over the local ring $\boldsymbol K=\boldsymbol M_{mm}(\mathbb R)$ is constructed. Further, an $n$-dimensional projective coordinate space over this module is constructed with the help of equivalence classes. The points and lines of this space are determined and the points are classified. Finally, for a 3-dimensional projective coordinate space, the incidence matrix for a line that goes through the given points and also all points of a line given with the incidence matrix are found by the use of Maple commands.