Question
If $A=\left|\begin{array}{ll}15 & 7 \\ 13 & 8\end{array}\right|$ and $B=\left|\begin{array}{ll}16 & 12 \\ 27 & 11\end{array}\right|$, find matrix $X$ such that $2 A-X=B$.
✓
Answer
$\begin{array}{l}A=\left|\begin{array}{ll}15 & 7 \\ 13 & 8\end{array}\right|_{2 \times 2}\end{array}, $
$B=\left|\begin{array}{ll}16 & 12 \\ 27 & 11\end{array}\right|_{2 \times 2} $
$ 2 A-X=B $
$ X=2 A-B $
$ X=\left|\begin{array}{ll}30 & 14 \\ 26 & 16\end{array}\right|-\left|\begin{array}{ll}16 & 12 \\ 27 & 11\end{array}\right| $
$ =\left|\begin{array}{ll}14 & 2 \\ -1 & 5\end{array}\right|_{2 \times 2}$
$B=\left|\begin{array}{ll}16 & 12 \\ 27 & 11\end{array}\right|_{2 \times 2} $
$ 2 A-X=B $
$ X=2 A-B $
$ X=\left|\begin{array}{ll}30 & 14 \\ 26 & 16\end{array}\right|-\left|\begin{array}{ll}16 & 12 \\ 27 & 11\end{array}\right| $
$ =\left|\begin{array}{ll}14 & 2 \\ -1 & 5\end{array}\right|_{2 \times 2}$
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