For the Given Matrix A, Find a Basis for the Corresponding

Multiple Choice

For the given matrix A, find a basis for the corresponding eigenspace for the given eigenvalue.
- $$A = \left[ \begin{array} { r r r } 1 & 6 & 6 \\6 & 1 & - 6 \\- 6 & 6 & 13\end{array} \right] , \lambda = 7$$

A) $\left\{\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right],\left[\begin{array}{r}0 \\ 1 \\ -1\end{array}\right]\right\}$

B) $\left\{\left[\begin{array}{r}1 \\ 0 \\ -1\end{array}\right],\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}\right]\right\}$

C) $\left\{\left[\begin{array}{r}0 \\ 1 \\ -1\end{array}\right]\right\}$

D) $\left\{\left[\begin{array}{r}1 \\ 0 \\ -1\end{array}\right]\right\}$