SOLUTION: Let V=R^3 and let W={(x, y, z) ∈ R^3| x=3y} Is W a subspace of V? If it is, find a basis and dimension for this subspace

Question 1182432: Let V=R^3 and let W={(x, y, z) ∈ R^3| x=3y}
Is W a subspace of V?
If it is, find a basis and dimension for this subspace
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.


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).

If you have questions, let me know.

----------------

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

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