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\begin{center}
{\bf Math 226.01: Differential Equations and Linear Algebra }
\\
{\bf Quiz 9}
\\
{\bf November 19, 1998}
\end{center}
\vspace*{.4cm}

\underline{{\bf Name:}\hspace*{10cm}}

(a) \hfill\begin{minipage}[t]{18cm}
(6 points) 
For the vectors given below determine whether 
$b\in\mbox{\rm span}\,\{v_1,\,v_2,\,v_3\}$ or not. 
If $b$ is in the span, find 
coefficients $\lambda_1,\,\lambda_2$, and $\lambda_3$, such that 
$b= \lambda_1 v_1+\lambda_2 v_2 +\lambda_3 v_3$. 
\[
   v_1=\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix},\quad
   v_2=\begin{pmatrix} -2 \\ -3 \\ -5 \end{pmatrix},\quad
   v_3=\begin{pmatrix} \ \;\,1 \\ -1 \\ \ \;\,2 \end{pmatrix},\quad
    b=\begin{pmatrix} 0 \\ 1 \\ 3 \end{pmatrix}.  
\]
\vspace*{8cm}

\end{minipage}

(b) \hfill\begin{minipage}[t]{18cm}
(2 points. No partial credit!)
Are the vectors $v_1,\,v_2,\,v_3$ linearly independent or dependent? 
\vspace*{2.5cm}

\end{minipage}

(c) \hfill\begin{minipage}[t]{18cm}
(2 points. No partial credit!)
Are the vectors $v_1,\,v_2,\,v_3,\,b$ linearly independent or dependent? 
\vspace*{2.5cm}

\end{minipage}


\vfill
%\underline{{\bf Answer:}\hspace*{10cm}}

Sign the pledge:
``On my honor, I have neither given nor received unauthorized aid on this Exam.''

\underline{{\bf Signature:}\mbox{\hspace*{10cm}}}






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