||A construction method is presented for a class of simple C*-algebras whose basic properties -including their real ranks- can be computed relatively easily, using linear algebra. A numerical invariant attached to the construction determines whether a given algebra has real rank 0 or 1 . Moreover, these algebras all have stable rank 1, and each nonzero hereditary sub-C*-algebra contains a nonzero projection, yet there are examples in which the linear span of the projections is not dense. (This phenomenon was first exhibited by Blackadar and Kumjian. ) The construction also produces easy examples of simple C*-algebras with real rank 0 and stable rank 1 for which Ko fails to be unperforated.