Question
Given$A=\left[\begin{array}{cc}-3 & 6 \\ 0 & -9\end{array}\right]$ and $A^t$ its transpose matrix. Find $2 A+3 A^t$
✓
Answer
$\begin{array}{l}A=\left[\begin{array}{cc}-3 & 6 \\ 0 & -9\end{array}\right] \end{array} $
$ A^t=\left[\begin{array}{cc}-3 & 0 \\ 6 & -9\end{array}\right] $
$2 A+3 A^t $
$ =2\left[\begin{array}{cc}-3 & 6 \\ 0 & -9\end{array}\right]+3\left[\begin{array}{cc}-3 & 0 \\ 6 & -9\end{array}\right] $
$ =\left[\begin{array}{cc}-6 & 12 \\ 0 & -18\end{array}\right]+\left[\begin{array}{cc}-9 & 0 \\ 18 & -27\end{array}\right] $
$ =\left[\begin{array}{cc}-15 & 12 \\ 18 & -45\end{array}\right]$
$ A^t=\left[\begin{array}{cc}-3 & 0 \\ 6 & -9\end{array}\right] $
$2 A+3 A^t $
$ =2\left[\begin{array}{cc}-3 & 6 \\ 0 & -9\end{array}\right]+3\left[\begin{array}{cc}-3 & 0 \\ 6 & -9\end{array}\right] $
$ =\left[\begin{array}{cc}-6 & 12 \\ 0 & -18\end{array}\right]+\left[\begin{array}{cc}-9 & 0 \\ 18 & -27\end{array}\right] $
$ =\left[\begin{array}{cc}-15 & 12 \\ 18 & -45\end{array}\right]$
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