Question
If $P=\left|\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right|, Q=\left|\begin{array}{ll}5 & 1 \\ 7 & 4\end{array}\right|$ and $R=\left|\begin{array}{ll}2 & 1 \\ 4 & 2\end{array}\right|$ find the value of $(R+Q) P$
✓
Answer
$\begin{array}{l}R+Q=\left|\begin{array}{ll}2 & 1 \\ 4 & 2\end{array}\right|+\left|\begin{array}{ll}5 & 1 \\ 7 & 4\end{array}\right| \end{array} $
$ =\left|\begin{array}{cc}7 & 2 \\ 11 & 6\end{array}\right|_{2 \times 2} $
$ (R+Q) P=\left|\begin{array}{cc}7 & 2 \\ 11 & 6\end{array}\right|\left|\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right| $
$ =\left|\begin{array}{cc}7+6 & 14+8 \\ 11+18 & 22+24\end{array}\right| $
$ =\left|\begin{array}{cc}13 & 22 \\ 29 & 46\end{array}\right|_{2 \times 2}$
$ =\left|\begin{array}{cc}7 & 2 \\ 11 & 6\end{array}\right|_{2 \times 2} $
$ (R+Q) P=\left|\begin{array}{cc}7 & 2 \\ 11 & 6\end{array}\right|\left|\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right| $
$ =\left|\begin{array}{cc}7+6 & 14+8 \\ 11+18 & 22+24\end{array}\right| $
$ =\left|\begin{array}{cc}13 & 22 \\ 29 & 46\end{array}\right|_{2 \times 2}$
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