Question
If $P=\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right|$ and $Q=\left|\begin{array}{ll}7 & 3 \\ 4 & 1\end{array}\right|$ find $2Q - P$
✓
Answer
$\begin{array}{l}=\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right|_{2 \times 2}, Q=\left|\begin{array}{ll}7 & 3 \\ 4 & 1\end{array}\right|_{2 \times 2} \end{array} $
$ 2 Q-P=\left|\begin{array}{cc}14 & 6 \\ 8 & 2\end{array}\right|-\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right| $
$ =\left|\begin{array}{cc}14-2 & 6-9 \\ 8-5 & 2-7\end{array}\right|$
$=\left|\begin{array}{c}12-3 \\ 3-5\end{array}\right|_{2 \times 2}$
$ 2 Q-P=\left|\begin{array}{cc}14 & 6 \\ 8 & 2\end{array}\right|-\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right| $
$ =\left|\begin{array}{cc}14-2 & 6-9 \\ 8-5 & 2-7\end{array}\right|$
$=\left|\begin{array}{c}12-3 \\ 3-5\end{array}\right|_{2 \times 2}$
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