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QUESTION Which of the following sets of vector are subspaces of
$\textbf{R}^3$? Give reasons.
\begin{description}
\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 $v=u+w.$
\end{description}
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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