A,B are subsets of$\displaystyle R^{n}$prove that if$\displaystyle A^{\perp}\subset B^{\perp}$then there is $\displaystyle v\epsilon A$ so v is not part of SpB

how i tryed to solve it:

$\displaystyle s\epsilon A^{\perp}$

$\displaystyle t\epsilon B^{\perp}$

if there is $\displaystyle v\epsilon A$ then $\displaystyle v\bullet s=0$ and because $\displaystyle A^{\perp}\subset B^{\perp}$ then $\displaystyle v\bullet t=0$

so because v is othogonal to $\displaystyle B^{\perp}$and to $\displaystyle A^{\perp}$so $\displaystyle

SpA\subseteq SpB

A^{\perp}=(SpA){}^{\perp}

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