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\begin{document}
\title{Worksheet \#3 -- Math 6310\\Fall 2017}
\author{Due Wednesday October 15th}
\maketitle
For each problem below, find a normal form of the given matrix over the given Euclidean domain.
\vskip 9pt
\noindent
{\bf 1.}  The Euclidean domain is $\bZ$.  The matrix is
\[
\left[ \begin{array}{ccc}  
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & -8 & 9
\end{array}  \right]
\]
\vskip 115pt
\noindent
{\bf 2.}  The Euclidean domain is $\bQ[x]$.  The matrix is
\[
\left[ \begin{array}{cc}
x & 0  \\
x & x^2  \\
1 & 1 
\end{array}  \right]
\]
\vskip 115pt
\noindent
{\bf 3.}  The Euclidean domain is $\bZ[i]$.  The matrix is
\[
\left[ \begin{array}{ccc}
2 & i & -1 \\
0 & 2i & 1+i \\
i & 1 & 2
\end{array}
\right]
\]
\end{document}

