Find the solution of the system

x (with a dot above it, dont know the Latex) = 2x - y

y (same, with dot) = 3x - 2y

so matrix A =;

[2 -1]

[3 -2]

satisfying x(0) = 2 and y(0) = -1.

Now i got the eigenvalues to be

so how to i calculate the eigenvectors given that;

for

we have A - I =;

[1 -1]

[3 -3]

and for

we have A - I =;

[3 -1]

[3 -1]

I cant seem to find any examples that actually explain hows its done, every example just seems to state the eigenvector straight after stating the matrices.

Any help? Cheers.