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Jul 27, 2021 at 12:32 comment added Steven Gubkin I like this approach since it reinforces the definition. I also like the opportunity to point out that this system of equations is nonlinear, since it involves a product of the variables. It is, however, linear in each variable separately. The determinant is also a multilinear gadget, and this points the way to a connection.
Jul 27, 2021 at 4:41 history answered TomKern CC BY-SA 4.0