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**1. Homework Statement**

Let [tex]x_1,...,x_n: M \rightarrow R [/tex] be functions on a manifold which form a local coordinate system on some region. Show that every differential form on this region can be written uniquely in the form

[tex]w^k = \sum_{i_1<...<i_k} a_{i_1,...i_k}(\bf{x})dx_{1_i} \wedge .. \wedge dx_{1_k} [/tex]

Any ideas?

**2. Homework Equations**

**3. The Attempt at a Solution**