Question
If $I$ is the unit matrix of order $2 \times 2$ Find the matrix $M$ such that $M-2 I=3\left[\begin{array}{cc}-1 & 0 \\ 4 & 1\end{array}\right]$
✓
Answer
$\begin{array}{l}M-2 I=3\left[\begin{array}{cc}-1 & 0 \\ 4 & 1\end{array}\right]\end{array} $
$ M=3\left[\begin{array}{cc}-1 & 0 \\ 4 & 1\end{array}\right]+2 I $
$ M=3\left[\begin{array}{cc}-1 & 0 \\ 4 & 1\end{array}\right]+2\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] $
$ M=\left[\begin{array}{cc}-3 & 0 \\ 12 & 3\end{array}\right]+\left[\begin{array}{ll}2 & 0 \\ 0 & 2\end{array}\right] $
$ M=\left[\begin{array}{cc}-1 & 0 \\ 12 & 5\end{array}\right]$
$ M=3\left[\begin{array}{cc}-1 & 0 \\ 4 & 1\end{array}\right]+2 I $
$ M=3\left[\begin{array}{cc}-1 & 0 \\ 4 & 1\end{array}\right]+2\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] $
$ M=\left[\begin{array}{cc}-3 & 0 \\ 12 & 3\end{array}\right]+\left[\begin{array}{ll}2 & 0 \\ 0 & 2\end{array}\right] $
$ M=\left[\begin{array}{cc}-1 & 0 \\ 12 & 5\end{array}\right]$
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