quiz2.tex

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\Large
\rm{Math 221-AB1:  Quiz 2}
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\vspace{0.1in}
\begin{enumerate}

\item{ Consider the following set of vectors.
	
	\begin{displaymath}
	\left\{
	\left[ \begin{array}{r} 1 \\ 0 \\ 3  \end{array}\right],
	\left[ \begin{array}{r} 1 \\ -1  \\ 1 \end{array}\right],
	\left[ \begin{array}{r} 1 \\ -1  \\ 2 \end{array}\right]
	\right\}
	\end{displaymath}

\begin{enumerate}
	\item {(\emph{3 pts}) Find a linear combination of these vectors that equals the vector $x$.
		\begin{displaymath}
	x = \left[ \begin{array}{r} 2 \\ -3 \\ 1  \end{array}\right]
	\end{displaymath}}
	\vspace{2.5in}
	\item{(\emph{2 pts}) What is the dimension of the subspace spanned by this set of vectors.  Give a reason for your answer.}
\end{enumerate}
}



\vspace{2in}

\item{Let $W = \left\{\left[ \begin{array}{rrrr} a & b & 0 & b \end{array} \right]^T: a,b\in\mathbb{R}\right\}$
\begin{enumerate}
	\item {(\emph{3 pts}) Show that $W$ is a subspace of $\mathbb{R}^4$.}
	\item {(\emph{2 pts}) Give a basis for $W$.}
\end{enumerate} 

}

%
%\item{(\emph{3 pts}) 
%	\begin{displaymath}
%	{\bf B}= \left[ \begin{array}{rrrr} 1 & 0 &  0 & 4 \\ 0 & 0 & 1 & 3 \end{array} \right]
%	\end{displaymath}
%	Let $N = \{{\bf x} \in \mathbb{R}^4 \,|\, {\bf Bx} = {\bf 0}  \}$. 
%	Does $\left[\begin{array}{rrrr} -4 & 0 & -3 & 1 \end{array} \right]^T$ span $N$?  Explain.
%}

\end{enumerate}

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