How to find eigenvector here

[stiff warren]

interpret it as a system of equations

x_1 is free and x_2 must be 0

so an eigenvector looks like [x_1,0] in span([1,0])

[stiff warren]

that's the 1st one, yes

so x_2=0

and the other is just 0=0.. so you dont have any requirements for what x_1 is

so x_1 parameterizes what the eigenvector is

no

an eigenvector will be [x_1,x_2]=[x_1,0]