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## Homework Statement

the higher order equation y'' + y = 0 can be written as a first order system by introducing y' as another unknown besides y:

## Homework Equations

d[y y']

^{t}/dt = [y' y'']

^{t}= [y' -y]

^{t}

if this is du/dt = Au what is 2x2 matrix A?

## The Attempt at a Solution

I think it's

[0 1]

[-1 0]

but then I get complex eigenvalues so I am a bit suspicious... could someone verify or help me out?

thanks.