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**1. The problem statement, all variables and given/known data**

I'm doing an ODE for homework and I cant find the eigenvector for this matrix (sorry, I don't know how to make matrices on here. Consider these as one matrix.):

[ 2 0] [v[itex]_{1}[/itex]] = [0]

[ 1 1] [v[itex]_{2}[/itex]] = [0]

**2. Relevant equations**

The only way he has taught us to find eigenvectors seems mostly like guesswork to me.

**3. The attempt at a solution**

2v[itex]_{1}[/itex] + 0v[itex]_{2}[/itex] = 0

v[itex]_{1}[/itex] + v[itex]_{2}[/itex] = 0

So 2v[itex]_{1}[/itex] = 0 =====> v[itex]_{1}[/itex] = 0

But v[itex]_{1}[/itex] + v[itex]_{2}[/itex] = 0, so v[itex]_{2}[/itex] = 0 as well. But eigenvectors cannot consist of all zeros?