Which of the following subsets of the vector space r 3 are subspaces of r 3 ?

(i) the set of all vectors v =   x y z   with the property 2xyz = 0.

(ii) the set of all the solutions of the equation x − 5y + 2z = 0.

(iii) the set of all solutions for the system   2 3 2 5 2 8 −1 1 3     x y z   =   0 0 0  .

(iv) the set of all the solutions of the equation x + 3y = 2z + 1.