Question: Suppose we know that u v = u w . Does it follow that v = w ? If it does, give a proof that

Suppose we know thatuv=uw.

Does it follow thatv=w?

If it does, give a proof that is valid inn; otherwise, give acounterexample

(i.e., aspecificset of vectorsu, v, andw for whichuv=uw butvw).

Which is the correct choice?

Yes.uv=uwimpliesu(vw) =0, which impliesv=w.

Yes.uv=uwimpliesuv = uw , which impliesv=w.

u u

No. Consideru=0,v= [1, 2], andw= [17, 12].

No. Consideru= [4, 2],v=0, andw=0.

No. Consideru= [5, 7],v= [1, 1], andw= [1,1].

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