Suppose you have two sets [itex]S_{1}[/itex] and [itex]S_{2}[/itex]. Suppose you also know that every vector in [itex]S_{1}[/itex] is expressible as a linear combination of the vectors in [itex]S_{2}[/itex]. Then can you conclude that the two sets span the same space?(adsbygoogle = window.adsbygoogle || []).push({});

If not, what if you further knew that every vector in [itex]S_{2}[/itex] is expressible as a linear combination of the vectors in [itex]S_{1}[/itex]?

I merely need an answer. I will work out the details (proof) for myself. Thanks!!

BiP

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# Do these sets span the same space?

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