9. (7 points) Let $A = \begin{bmatrix} 6 & 2 & 2 \\ -2 & 6 & 2 \end{bmatrix}$, and consider the singular value decomposition (SVD) $A = U\Sigma V^T$.

a. (3 points) Find $U$, $\Sigma$, and $V$.

b. (4 points) Find orthonormal bases for $C(A^T)$, $N(A)$, $C(A)$, and $N(A^T)$, respectively, from the results obtained from SVD.