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{\bf Math 226.01: Differential Equations and Linear Algebra }
\\
{\bf Quiz 10}
\\
{\bf December 3, 1998}
\end{center}
\vspace*{.4cm}

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

(a) \hfill\begin{minipage}[t]{18cm}
Use the Gram-Schmidt-process to find an orthogonal set of vectors $w_1,\,w_2,\,w_3$
spanning the same space span$\{v_1,\,v_2,\,v_3\}$ as the vectors given below. 
\[
   v_1=(0,1,1,2),\quad 
   v_2=(0,2,0,2),\quad
   v_3=(5,-6,-8,1).
\]
\vspace*{9cm}

\end{minipage}

(b) \hfill\begin{minipage}[t]{18cm}
Build the $3\times4$-matrix 
$A=\begin{bmatrix} w_1\\w_2\\w_3\end{bmatrix}$ 
having as rows the vectors computed in (a). 
Calculate the matrix product $A A^{\mbox{\rm t}}$. 
\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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