In each case determine how many solutions (and how many parameters) are possible for a homogeneous system

Question:

In each case determine how many solutions (and how many parameters) are possible for a homogeneous system of four linear equations in six variables with augmented matrix A. Assume that A has nonzero entries. Give all possibilities.
(a) Rank A = 2.
(b) Rank A = 1.
(c) A has a row of zeros.
(d) The row-echelon form of A has a row of zeros.