Vector subspace as the space of solutions to matrix multiplication

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Given a subset W of a vector space V = F^n (for some field F), prove that W is the subspace of solutions of the matrix equation AX = 0 for some A.
 
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Why?

Seriously, this sounds like a homework problem so it should be in the homework section.

In any case, define the orthogonal complement of W and let A be the projection onto that complement.
 
I would just solve for A myself. :smile:
 

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