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QUESTION Which of the following sets of vector are subspaces of
$\textbf{R}^3$? Give reasons.

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\item[(a)]
all vectors of the form $(v,0,0);$

\item[(b)]
all vectors of the form $(v,1,1);$

\item[(c)]
all vectors of the form $(u,v,w)$ where $v=u+w.$

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ANSWER
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\item[(a)]
Yes - both closure axioms hold.

\item[(b)]
No - the set is not closed under addition: $2(v,1,1)$ is not in
the set, for example. Alternatively $(0,0,0)$ is not in the set.

\item[(c)]
Yes.

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