Question
Evaluate the following $: \left|\begin{array}{ll} 2 & 1 \\ 3 & 2 \\ 1 & 1 \end{array}\right|\left|\begin{array}{ccc} 1 & -2 & 1 \\ 2 & 1 & 3 \end{array}\right| $
✓
Answer
$\begin{array}{l}\left|\begin{array}{cc}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right|_{3 \times 2}\left|\begin{array}{ccc}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right|_{2 \times 3} \end{array} $
$ =\left|\begin{array}{ccc}2+2 & -4+1 & 2+3 \\ 3+4 & -6+2 & 3+6 \\ 1+2 & -2+1 & 1+3\end{array}\right| $
$ =\left|\begin{array}{ccc}4 & -3 & 5 \\ 7 & -4 & 9 \\ 3 & -1 & 4\end{array}\right|_{3 \times 3}$
$ =\left|\begin{array}{ccc}2+2 & -4+1 & 2+3 \\ 3+4 & -6+2 & 3+6 \\ 1+2 & -2+1 & 1+3\end{array}\right| $
$ =\left|\begin{array}{ccc}4 & -3 & 5 \\ 7 & -4 & 9 \\ 3 & -1 & 4\end{array}\right|_{3 \times 3}$
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