Prove if true otherwise give a counterexample when it is fal

Prove if true otherwise give a counterexample when it is false. The set w={(X1, 2, X3):X1 and X3 are real numbers} is a subspace of R^3 with the standard operations

Solution

(0,2,0) and (1,2,0) both belong to w. Not lets add the two elements.

(0,2,0)+(1,2,0)=(1,4,0)

which does not belong to w.

Hence , w is not a subspace.