Inverses and determinants for n x n matrices
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Find the determinant of \(\left[ {\begin{array}{*{20}{c}}8&1&2\\2&1&3\\1&2&3\end{array}} \right]\)
$$
\begin{aligned}
\begin{array}{|lll|}
8 & 1 & 2 \\
2 & 1 & 3 \\
1 & 2 & 3
\end{array}=& 8\begin{array}{|cc|}
1 & 3 \\
2 & 3
\end{array}-1\begin{array}{|ll|}
2 & 3 \\
1 & 3
\end{array}+2\begin{array}{|ll|}
2 & 1 \\
1 & 2
\end{array} \\
&=8(3-6)-1(6-3)+2(4-1) \\
&=8 \times-3-1 \times 3+2 \times 3 \\
&=-24-3+6 \\
&=-21
\end{aligned}
$$
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