Meaning of Matrices in Systems of Differential Equation

[daveyman]

Homework Statement

My question is a general question about the meaning of matrices, but I will narrow it down to a single problem.

The problems asks to draw a direction field and find the general solution for the following system:

$$x'=\left(<br /> \begin{array}{cc}<br /> 1 & 1 \\<br /> 4 & 1<br /> \end{array}<br /> \right)x$$

I don't quite understand what this matrix means in this context (I have not taken linear algebra yet). I know this represents a system of equations, but how could I rewrite this system in standard notation?

Homework Equations

N/A

The Attempt at a Solution

My only thought is that maybe it could be rewritten as:

$$x'=1x+1x$$ and $$x_2'=4x+1x$$. Is this correct?

 

[Dick]

Write a column vector of two functions, x=(x1,x2). Then x'=(x1',x2'). The system is x1'=x1+x2, x2'=4x1+x2.