  A basic theory on the first order right and left linear quaternion
differential systems (LQDS) is given systematic in this paper. To proceed the
theory of LQDS we adopt the theory of column-row determinants recently
introduced by the author. In this paper, the algebraic structure of their
general solutions are established. Determinantal representations of solutions
of systems with constant coefficient matrices and sources vectors are obtained
in both cases when coefficient matrices are invertible and singular. In the
last case, we use determinantal representations of the quaternion Drazin
inverse within the framework of the theory of column-row determinants.
  Numerical examples to illustrate the main results are given.
