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Let V be the set of all vectors of form $(a, b, c)$ where $a + 2b − c = 0$. Find a basis $B$ for $V$ and find $\dim(V)$.

I'm stuck on this one. I know it won't have dimension of 3 because it's easy to see that it won't span all of $\mathbb{R^3}$

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    $\begingroup$ Have you tried expressing one of $a$,$b$,$c$ in terms of the other two? $\endgroup$ – Michael M Nov 12 '14 at 0:36
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Hint: $(a,b,c) = (a,b,a+2b) = a(1,0,1) + b(0,1,2)$.

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  • $\begingroup$ oh, duh! thanks! $\endgroup$ – oliverjones Nov 12 '14 at 0:50

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