If $A=\left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right], X=\left[\begin{array}{l}n \\ 1\end{array}\right], B=\left[\begin{array}{c}8 \\ 11\end{array}\right]$ and $A X=B$, then the value of $n$ will be:

2

The correct answer is Option (3) → 2

Given

$A=\begin{bmatrix}2&4\\4&3\end{bmatrix},\; X=\begin{bmatrix}n\\1\end{bmatrix},\; B=\begin{bmatrix}8\\11\end{bmatrix}$

$AX=B$

$\begin{bmatrix}2&4\\4&3\end{bmatrix} \begin{bmatrix}n\\1\end{bmatrix} =\begin{bmatrix}8\\11\end{bmatrix}$

From first row

$2n+4=8$

$2n=4$

$n=2$

Check with second row

$4n+3=4(2)+3=11$ ✔

The value of $n$ is $2$.