If I want to show two orthogonal subsets S[itex]_{1}[/itex] and S[itex]_{2}[/itex] of ℝ[itex]^{n}[/itex] both span the same subspace W of ℝ[itex]^{n}[/itex] does it suffice to show that(adsbygoogle = window.adsbygoogle || []).push({});

S[itex]_{1}[/itex][itex]\subset[/itex]S[itex]_{2}[/itex] and that S[itex]_{2}[/itex][itex]\subset[/itex]S[itex]_{1}[/itex], thus showing S[itex]_{1}[/itex] = S[itex]_{2}[/itex]

[itex]\Rightarrow[/itex] they span the same space.

If theres a better method, I'd like to know.

Thanks!

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# Proving the subspaces are equal

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