Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 04 (a)/Statement

A model of love affairs is described by the following system of differential equations

${\begin{aligned}R'&=R+4J,\\J'&=-2R-3J,\end{aligned}}$

where $R(t)$ and $J(t)$ are, respectively, Romeo’s and Juliet’s amount of love for each other at time $t$.

(a) Express the system in matrix form ${\frac {d{\mathbf {x}}}{dt}}=A{\mathbf {x}}$, where ${\mathbf {x}}(t)={\begin{bmatrix}R(t)&J(t)\end{bmatrix}}^{T}$ .