If \(A=\begin{bmatrix}2 & 4\\4 & 3\end{bmatrix}, X=\begin{bmatrix}n\\1\end{bmatrix}, B=\begin{bmatrix}8\\11\end{bmatrix}\)
and AX = B, then the value of n will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
Multiplying out AX = B:
\( \displaystyle \begin{bmatrix}2 & 4\\4 & 3\end{bmatrix}\begin{bmatrix}n\\1\end{bmatrix} = \begin{bmatrix}2n+4\\4n+3\end{bmatrix} = \begin{bmatrix}8\\11\end{bmatrix} \)
Equal matrices have equal corresponding entries. From the first row:
\(2n + 4 = 8\)
\(n = 2\)
The second row agrees: \(4(2) + 3 = 11\).