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I normally start with Gaussian Elimination, vectors and then matrices. I know a number of books which start with matrices and then go on to Gaussian Elimination and vectors. What is the most appropriate way to ensure most students are fully engaged with a linear algebra module?

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I'm not sure, but I think this may well depend on *which" students...in my Alma Mater we used to begin linear algebra with some review of the most usual fields (reals, complex, prime residues, etc.), then get into a little theory of vector spaces and then into linear systems, Gaussian elimination and stuff. I suppose this approach may be too heavy for non-mathematics students... –  DonAntonio May 30 '12 at 18:17

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