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:
Answer & explanation
Correct answer: option 3
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 $2$.