Question
Given $\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right] X =\left[\begin{array}{l}7 \\ 6\end{array}\right]$. the matrix $X.$
✓
Answer
Let $X =\left[\begin{array}{l}a \\ b\end{array}\right]$
$\begin{array}{l}\text { so }\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right]\left[\begin{array}{l}a \\ b\end{array}\right]=\left[\begin{array}{l}7 \\ 6\end{array}\right] \end{array} $
$ \Rightarrow\left[\begin{array}{c}2 a+b \\ -3 a+4 b\end{array}\right]=\left[\begin{array}{l}7 \\ 6\end{array}\right] $
$ \Rightarrow 2 a + b =7 \ldots(1) \\ -3 a +4 b =6 \ldots(2) \\ \text { From (1) and (2) } a =2, b =3$
$\Rightarrow X=\left[\begin{array}{l}2 \\ 3\end{array}\right]$.
$\begin{array}{l}\text { so }\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right]\left[\begin{array}{l}a \\ b\end{array}\right]=\left[\begin{array}{l}7 \\ 6\end{array}\right] \end{array} $
$ \Rightarrow\left[\begin{array}{c}2 a+b \\ -3 a+4 b\end{array}\right]=\left[\begin{array}{l}7 \\ 6\end{array}\right] $
$ \Rightarrow 2 a + b =7 \ldots(1) \\ -3 a +4 b =6 \ldots(2) \\ \text { From (1) and (2) } a =2, b =3$
$\Rightarrow X=\left[\begin{array}{l}2 \\ 3\end{array}\right]$.
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