Topology. Elementary alternating tensors.

Let $\displaystyle x,y,z,w \in \mathbb{R}^5 $ Let

$\displaystyle T(x,y,z) = 2x_2 y_2 z_1 +x_1 y_5 z_4 $

$\displaystyle S(x,y) = x_1 y_3 + x_3 y_1 $

$\displaystyle R(w) = w_1-2w_3 $

(a) Write $\displaystyle Alt(T)$ and $\displaystyle Alt(S)$ in terms of elementary alternating tensors. (I think this is analogically to writing $\displaystyle T$ and $\displaystyle S$ in terms of

alternating tensors )

(b) Express $\displaystyle Alt(T) \wedge R $ in terms of elementary alternating tensors.

(c) Express $\displaystyle Alt(T)(x,y,z)$ as a FUNCTION.