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Meaning of Matrices in Systems of Differential Equation

  1. Nov 19, 2008 #1
    1. The problem statement, all variables and given/known data

    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:

    1 & 1 \\
    4 & 1

    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?

    2. Relevant equations

    3. The attempt at a solution

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

    [tex]x'=1x+1x[/tex] and [tex]x_2'=4x+1x[/tex]. Is this correct?
  2. jcsd
  3. Nov 19, 2008 #2


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    Science Advisor
    Homework Helper

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