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\newcommand{\ds}{\displaystyle}
\newcommand{\pl}{\partial}
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\begin{document}


{\bf Question}

Find the inverses of

\begin{description}
\item[(i)] $\ds \left( \begin{array}{ccc}2 &amp; 4 &amp; 1 \\ 1 &amp; 1 &amp; 1 \\ 2 &amp; 3 &amp; 1
 \end{array} \right)$

\item[(ii)]$\ds \left( \begin{array}{ccc} 5 &amp; 15 &amp; -10 \\ -2 &amp; -2 &amp; -4 \\ 3 &amp; 4 &amp; 1
\end{array} \right)$
\item[(iii)]$\ds \left( \begin{array}{cccc} 1 &amp; -2 &amp; 1 &amp; -5 \\ 3 &amp; -6 &amp; 4 &amp; -14 \\
-2 &amp; 4 &amp; -4 &amp; 9 \\ 4 &amp; -7 &amp; 5 &amp; -18 \end{array} \right) $
\end{description}

Check your answer by multiplication.

\vspace{.25in}

{\bf Answer}

\begin{description}
\item[(i)] Inverse $ = \left( \begin{array}{ccc} -2 &amp; -1 &amp; 3 \\ 1 &amp; 0 &amp; -1
\\ 1 &amp; 2 &amp; -2\end{array} \right)$
\item[(ii)] Inverse $\ds = \left( \begin{array}{ccc} \ds -\frac{7}{30} &amp;  \ds \frac{11}{12} &amp;  \ds \frac{4}{3}
\\ \\ \ds \frac{5}{30} &amp;  \ds -\frac{7}{12} &amp;  \ds -\frac{2}{2} \\ \\ \ds \frac{1}{30} &amp;
\ds -\frac{5}{12} &amp;  \ds -\frac{1}{3} \end{array} \right)$
\item[(iii)] Inverse $ = \left( \begin{array}{cccc} -14 &amp; 5 &amp; 4 &amp; 2 \\
3 &amp; -3 &amp; -1 &amp; 1 \\ 1 &amp; -1 &amp; -1 &amp; 0 \\ -4 &amp; 2 &amp; 1 &amp; 0 \end{array}
\right)$
\end{description}


\end{document}
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