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How can I determine whether the span of a set of vectors (such as $\mathrm{span}\{(3, 1), (4,1), (0,1)\}$ contains the span of another set of vector?

EDIT: I realize that my original question was too vague. If A and B are sets of vectors in $\mathbb{R}^3$, how can you determine whether $\mathrm{span}\{A\}$ contains $\mathrm{span}\{B\}$?

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    Are there any additional steps involved? Is this sufficient for showing that the span of one set of vectors contains the span of another set of vectors?2012-06-03
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    @Ananda In general checking linear independence won't be good enough to answer this kind of question.2012-06-03
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    @Brett Frankel : I have to change the answer with the Edit.2012-06-03
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    BTW this question is closely related: [Linear Algebra: determine whether the sets span the same subspace](http://math.stackexchange.com/questions/47625/linear-algebra-determine-whether-the-sets-span-the-same-subspace)2012-06-03

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