Jambmaths question:
if $\left| \begin{matrix} 5 & 3 \\ x & 2 \\\end{matrix} \right|=\left| \begin{matrix} 3 & 5 \\ 4 & 5 \\\end{matrix} \right|$, find the value of x
Option A:
34
Option B:
4
Option C:
5
Option D:
7
Jamb Maths Solution:
$\begin{align} & Note:\text{ } \\ & \left| \begin{matrix} a & b \\ c & d \\\end{matrix} \right|=ad-cb\text{ }\!\!\{\!\!\text{ Definition of determinant 2}\times \text{2 }\!\!\}\!\!\text{ } \\ & \left| \begin{matrix} 5 & 3 \\ x & 2 \\\end{matrix} \right|=\left| \begin{matrix} 3 & 5 \\ 4 & 5 \\\end{matrix} \right| \\ & 10-3x=15-20 \\ & 10-3x=-5 \\ & -3x=-15 \\ & x=5 \\\end{align}$
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