Question 1182432
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Yes, W is a subspace in R^3.


You can easily check it on your own, that all axioms of a subspace are held.

It is a standard routine check (nothing special or interesting).



W is a subspace of the dimension 2 in R^3  (since one and only one linear equation determines this subspace).


Its basis are these two vectors of R^3 


     (3,1,0)  and  (0,0,1).
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If you have questions, let me know.


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What university are you from and what is your Algebra textbook / the problems book ?