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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices4 Marks
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 $P(Q+R)$
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Answer

$\begin{array}{l}P=\left|\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right|_{2 \times 2}, Q=\left|\begin{array}{ll}5 & 1 \\ 7 & 4\end{array}\right|_{2 \times 2} R=\left|\begin{array}{ll}2 & 1 \\ 4 & 2\end{array}\right|_{2 \times 2} \end{array} $
$ Q+R=\left|\begin{array}{ll}5 & 1 \\ 7 & 4\end{array}\right|+\left|\begin{array}{ll}2 & 1 \\ 4 & 2\end{array}\right| $
$ =\left|\begin{array}{ll}7 & 2 \\ 2 & 6\end{array}\right|  $
$ P(Q+R)=\left|\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right|\left|\begin{array}{ll}7 & 2 \\ 2 & 6\end{array}\right|  $
$ =\left|\begin{array}{ll}7+22 & 2+12 \\ 21+44 & 6+24\end{array}\right|  $
$ =\left|\begin{array}{ll}29 & 14 \\ 65 & 30\end{array}\right|_{2 \times 2}$

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