The matrix $$A=\left[\begin{array}{cccc} 2 &0 &-2 &0\cr 2 &0 &0 &2\cr 0 &0 &0 &0\cr 0 &0 &2 &2 \end{array}\right]$$ has two distinct real eigenvalues $\lambda_1 < \lambda_2$. Find the eigenvalues and a basis for each eigenspace.

The smaller eigenvalue $\lambda_1$ is and a basis for its associated eigenspace is



The larger eigenvalue $\lambda_2$ is and a basis for its associated eigenspace is