I am getting stuck on the very beginning of these homework problems.(adsbygoogle = window.adsbygoogle || []).push({});

Solve the linear system to determine whether the critical point (0,0) is stable, asymtotically stable, or unstable.

[tex]dx/dt = -2x, dy/dt = -2y[/tex]

The book uses separation of variables, but the professor has instructed us to use matrices to do these homework problems.

[tex] x= \left(\begin{array}{c} -2 \ 0\\ 0 \ -2 \end{array}\right) [/tex]

[tex]\lambda_1 = 0, \lambda_2 = 4[/tex]

Is this the right matrix? When I use lambda = 0 in the eigenvalue method (A - (lambda)I)=0 on that matrix, the vector entries a and b both = 0 because it's just a diagonal matrix. I need to find a general solution such that

x = c1v1e^((lambda)t) + c2v2e^((lambda)t). Then determine the stability of x. But first I need to know how to set it up.

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# Setting up linear systems in a matrix

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