Evaluate the following : | cc 0 & 1 -1 & 2 -2 & 0 | | ccc 0 & -4 … - Vidyadip

Question

Evaluate the following $: \left|\begin{array}{cc} 0 & 1 \\ -1 & 2 \\ -2 & 0 \end{array}\right|\left|\begin{array}{ccc} 0 & -4 & 0 \\ 3 & 0 & -1 \end{array}\right| $

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Answer

$\begin{array}{l}\left|\begin{array}{cc}0 & 1 \\ -1 & 2 \\ -2 & 0\end{array}\right|_{3 \times 2}\left|\begin{array}{ccc}0 & -4 & 0 \\ 3 & 0 & -1\end{array}\right|_{2 \times 3} \end{array} $
$ =\left|\begin{array}{ccc}0+3 & 0+0 & 0-1 \\ 0+6 & 4+0 & 0-2 \\ 0+0 & 8+0 & 0+0\end{array}\right| $
$ =\left|\begin{array}{ccc}3 & 0 & -1 \\ 6 & 4 & -2 \\ 0 & 8 & 0\end{array}\right|_{3 \times 3}$

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