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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!