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\headers{Math343}{Quiz 1}{Aug 29 2025}

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\noindent
\textbf{Directions:} Show all work.  No credit for answers without work.

\begin{enumerate}

\item\points{4} Solve the following linear system.
\[  \begin{array}{*{7}{r}}
	      & &   2x_2   &+&   x_3  &=&  1\\
   -2x_1  &+&  17x_2   &+& 16x_3  &=&  1\\
	 x_1  &-&   8x_2   &-&  8x_3  &=&  1
    \end{array}
\]
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\item\points{3} Give an example of an \textbf{inconsistent} linear system with two equations $\mathrm{Eq1}$ and $\mathrm{Eq2}$ such that each equation individually has infinitely many solutions.
\vspace{4cm}

\newpage

\item\points{3} The following augmented matrix represents a linear system.  Find all values for $h$ that make the system consistent.  (Hint: simplify the second and third rows as much as possible before involving $h$ in your computation.  Avoid fractions if possible.)
\[ 
\left[
	\begin{array}{*{3}{r}}
	-1 & h & 30\\
	5 & -2 & -24\\
	3 & 2 & 8
	\end{array}
\right]
\]


\end{enumerate}
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