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 $3 P - 2Q$
✓
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} $
$3 P-2 Q=\left|\begin{array}{cc}6 & 27 \\ 15 & 21\end{array}\right|-\left|\begin{array}{cc}14 & 6 \\ 8 & 2\end{array}\right| $
$ =\left|\begin{array}{cc}6-14 & 27-6 \\ 15-8 & 21-2\end{array}\right|$
$=\left|\begin{array}{cc}-8 & 21 \\ 7 & 19\end{array}\right|_{2 \times 2}$
$3 P-2 Q=\left|\begin{array}{cc}6 & 27 \\ 15 & 21\end{array}\right|-\left|\begin{array}{cc}14 & 6 \\ 8 & 2\end{array}\right| $
$ =\left|\begin{array}{cc}6-14 & 27-6 \\ 15-8 & 21-2\end{array}\right|$
$=\left|\begin{array}{cc}-8 & 21 \\ 7 & 19\end{array}\right|_{2 \times 2}$
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