Sketching Trajectories: Understanding Matrix System Dynamics

[simo1]

am studying a chapter on trajectories. when am given a syatem like
x^'=ax-bx²-cxy
y^'=py-qy²-rxy
and they say sketch the trajectories. i know how to do it. i look for my equilibruim points, sketch the graph and check what happens maybe at x'>0 etc

my problem comes when am given a matrix. how do i sketch a trajectory then say for this matrix

A=

1	0
0	2

 

[gtoguy97]

The first step is to convert the matrix into a system of equations. You can do this by multiplying it by a vector of variables (x and y). For example, A*[x;y] = [x';y'], where x' and y' are the derivatives of x and y respectively. Once you have the system of equations, you can proceed as usual. Look for equilibrium points, sketch the graph, and check what happens at certain conditions (e.g. x'>0).