If $A =\begin{bmatrix}3&7\\4&-2\end{bmatrix}],X=\begin{bmatrix}α\\-2\end{bmatrix},B=\begin{bmatrix}7\\32\end{bmatrix}$ and $AX = B$, then the value of the $α$ is

7

The correct answer is Option (1) → 7

$A=\begin{pmatrix}3&7\\4&-2\end{pmatrix},\; X=\begin{pmatrix}\alpha\\-2\end{pmatrix},\; B=\begin{pmatrix}7\\32\end{pmatrix}$

$AX=B$

$\begin{pmatrix}3&7\\4&-2\end{pmatrix} \begin{pmatrix}\alpha\\-2\end{pmatrix} =\begin{pmatrix}7\\32\end{pmatrix}$

First equation

$3\alpha+7(-2)=7$

$3\alpha-14=7$

$3\alpha=21$

$\alpha=7$

Second equation

$4\alpha-2(-2)=32$

$4\alpha+4=32$

$4\alpha=28$

$\alpha=7$

The value of $\alpha$ is $7$.