10. For the given Tensor T, (a) Decompose the tensor into a symmetric and an antisymmetric part, (b) Find the dual vector for the antisymmetric part, (c) Verify $\mathbf{T}^A \cdot \vec{a} = \vec{t}^A \times \vec{a}$ for $\vec{a} = \hat{e}_1 + \hat{e}_3$.
Note: $^A$ represents antisymmetric, and $\vec{t}^A$ is the dual vector of antisymmetric tensor.