Question

If \[A = \begin{bmatrix}2 & 4 \\ 4 & 3\end{bmatrix}, X = \binom{n}{1}, B = \binom{ 8}{11}\]  and AX = B, then find n.

Answer 1

Here,
\[\begin{bmatrix}2 & 4 \\ 4 & 3\end{bmatrix}\binom{n}{1} = \binom{8}{11}\]
\[ \Rightarrow \binom{2n + 4}{4n + 3} = \binom{8}{11}\]
\[ \Rightarrow 2n + 4 = 8 \]
\[ \Rightarrow 2n = 4\]
\[ \Rightarrow n = 2\]