$2\mathrm{.}6$ The stress tensor $T_{ij}=\left[\begin{array}{ccc}-2& 2& -3\\ 2& 1& -6\\ 1& -2& 0\end{array}\right].$ Show steps to receive full credit.

$(1)$ Decompose the tensor into its corresponding symmetric and asymmetric

tensors, $T_{ij}^{(S)}$ and $T_{ij}^{(A)},$ respectively.

Determine the Eigenvalues and corresponding Eigenvectors of the tensor.