Question
Given $A=2\left[\begin{array}{ll}2 & 1 \\ 3 & 0\end{array}\right]-3\left[\begin{array}{ll}1 & 1 \\ 5 & 2\end{array}\right]+\left[\begin{array}{cc}-3 & -1 \\ 0 & 0\end{array}\right] :$ find $A + 2C – B$
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Answer
$A + 2C – B$
$\begin{array}{l}=\left[\begin{array}{ll}2 & 1 \\ 3 & 0\end{array}\right]+2\left[\begin{array}{cc}-3 & -1 \\ 0 & 0\end{array}\right]+\left[\begin{array}{ll}1 & 1 \\ 5 & 2\end{array}\right] \end{array} $
$ =\left[\begin{array}{ll}2 & 1 \\ 3 & 0\end{array}\right]+\left[\begin{array}{cc}-6 & -2 \\ 0 & 0\end{array}\right]-\left[\begin{array}{ll}1 & 1 \\ 5 & 2\end{array}\right] $
$ =\left[\begin{array}{ll}2-6-1 & 1-2-1 \\ 3+0-5 & 0+0-2\end{array}\right] $
$ =[-5-2] $
$ =[-2-2]$
$\begin{array}{l}=\left[\begin{array}{ll}2 & 1 \\ 3 & 0\end{array}\right]+2\left[\begin{array}{cc}-3 & -1 \\ 0 & 0\end{array}\right]+\left[\begin{array}{ll}1 & 1 \\ 5 & 2\end{array}\right] \end{array} $
$ =\left[\begin{array}{ll}2 & 1 \\ 3 & 0\end{array}\right]+\left[\begin{array}{cc}-6 & -2 \\ 0 & 0\end{array}\right]-\left[\begin{array}{ll}1 & 1 \\ 5 & 2\end{array}\right] $
$ =\left[\begin{array}{ll}2-6-1 & 1-2-1 \\ 3+0-5 & 0+0-2\end{array}\right] $
$ =[-5-2] $
$ =[-2-2]$
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