## Topology. Elementary alternating tensors.

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

$T(x,y,z) = 2x_2 y_2 z_1 +x_1 y_5 z_4$
$S(x,y) = x_1 y_3 + x_3 y_1$
$R(w) = w_1-2w_3$

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

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

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