<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\newcommand{\ds}{\displaystyle}
\newcommand{\pl}{\partial}
\parindent=0pt
\begin{document}


{\bf Question}

Evaluate the following determinants: $$\left| \begin{array}{cc} 15
&amp; 19 \\ 13 &amp; 16 \end{array} \right| \hspace{.5in} \left|
\begin{array}{ccc} 76 &amp; -23 &amp; 53 \\ 103 &amp; 199 &amp; 302 \\ 176 &amp; 177 &amp; 353
\end{array} \right|.$$

\vspace{.25in}

{\bf Answer}

\begin{eqnarray*}\left| \begin{array}{cc} 15 &amp; 19 \\ 13 &amp; 16
\end{array} \right| &amp; = &amp;  \left| \begin{array}{cc}2 &amp; 3 \\ 13 &amp; 16
\end{array} \right| \\ &amp; = &amp; \left| \begin{array}{cc} 2 &amp; 3 \\ 1 &amp;
-2\end{array} \right| \\ &amp; = &amp;  -7 \end{eqnarray*}


\begin{eqnarray*} \left| \begin{array}{ccc} 76 &amp; -23 &amp; 53 \\ 103 &amp; 199 &amp; 302
\\ 176 &amp; 177 &amp; 353 \end{array} \right| &amp; = &amp;  \left| \begin{array}{ccc}
76 &amp; -23 &amp; 53 \\ 103 &amp; 199 &amp; 302 \\ 100 &amp; 200&amp; 300
\end{array} \right| \\ &amp; = &amp; \left| \begin{array}{ccc} 76 &amp; -23 &amp; 53 \\
3 &amp; -1 &amp; 2 \\ 100 &amp; 200 &amp; 300 \end{array} \right|
\\ &amp; = &amp; 100 \left| \begin{array}{ccc} 76 &amp; -23 &amp; 53 \\ 3 &amp; -1 &amp; 2 \\ 1 &amp; 2 &amp; 3
\end{array} \right| \\ &amp; = &amp; 100 \left| \begin{array}{ccc} 1 &amp; 2 &amp; 3 \\
3&amp; -1 &amp; 2 \\ 1&amp; 2 &amp; 3\end{array} \right|\\ &amp; = &amp; 0\end{eqnarray*}


\end{document}
</pre></body></html>