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(52775)   (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.
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What university are you from and what is your Algebra textbook / the problems book ?
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