Solution
= Solution
The <characteristic polynomial> is $(1-\lambda)^2-4=(\lambda-3)(\lambda+1)$. For $\lambda=3$ the components are equal; for $\lambda=-1$ they are opposite. After normalization, the <eigenvalues> and associated <eigenvectors> are
$$
\boxed{\lambda_1=3,\quad\mathbf v_1=\frac{(1,1)}{\sqrt2};\qquad
\lambda_2=-1,\quad\mathbf v_2=\frac{(1,-1)}{\sqrt2}}.
$$
An overall sign change of either normalized <eigenvector> is equivalent.