Elementary question on multilinearity of differential forms

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Have I got this notion of multilinearity right? Say I feed $k$ vectors to a differential $k$-form and out pops a number, 3, for example. If I triple the size of one of the vectors, will the number then be 9? And so on, so halving one of the vectors would give 1.5. Is that correct?

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That is indeed correct. There is little more to add to this answer due to the concise nature of the question!