A subspace of $\displaystyle \mathbb{R}^3$ is given by:

$\displaystyle S=\lbrace (a,b,c)|a-10b+12c=0 \rbrace$

Determine two vectors X and Y such that {X, Y} forms a spanning set for S.

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Hmm...

Now I understand that I need to find two vectors such that set of all combinations:

$\displaystyle \lbrace aX + bY | a, b \in R \rbrace = S$

but I'm not sure how to proceed from here...