So the way it worked here before I arrived was that either in the intro to proofs class or the third quarter of honors calculus, you did a few weeks of basic linear algebra. Vector spaces, transformations, determinants, all that stuff. A bit came up in analysis when an eye toward multi, and then you'd really do it mostly in the second quarter of algebra. Not just as a special case of modules, like it used Curtis/Hoffman-Kunze for a good block, and did some multilinear algebra