If P = | cc 14 & 17 13 & 1 | and Q = | cc 2 & 1 3 & -3 |, find ma… - Vidyadip

Question

If $P =\left|\begin{array}{cc}14 & 17 \\ 13 & 1\end{array}\right|$ and $Q =\left|\begin{array}{cc}2 & 1 \\ 3 & -3\end{array}\right|,$ find matrix $M$ such that $P - M =3 Q$

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Answer

$\begin{array}{l}P=\left|\begin{array}{cc}14 & 17 \\ 13 & 1\end{array}\right|_{2 \times 2}\end{array} $
$Q=\left|\begin{array}{cc}2 & 1 \\ 3 & -3\end{array}\right|_{2 \times 2} $
$ P-M=3 Q $
$ M=P-3 Q $
$ M=\left|\begin{array}{cc}14 & 17 \\ 13 & 1\end{array}\right|-\left|\begin{array}{cc}6 & 3 \\ 9 & -9\end{array}\right| $
$ =\left|\begin{array}{cc}14-6 & 17-3 \\ 13-9 & 1+9\end{array}\right| $
$ =\left|\begin{array}{ll}8 & 14 \\ 4 & 10\end{array}\right|_{2 \times 2}$

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