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Let W be some subspace of Rn, let WW consist of those vectors in Rn that are orthognoal to all vectors in W.

1) Show that WW is a subspace of Rn?

So for this part I'm thinking that because WW is a linear combination of W (maybe) then therefore it forms a subspace of Rn

2) If {v1, v2,...vt} is a basis for W, show that a vector X in Rn lies in WW if and only if x is orthogonal to each of the vectors v1, v2,...vt?

And for this one I'm really at a lose for where to start. Any help would be appreciated.

Thanks