Illustration
Sep. 3rd, 2019 06:09 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowToday in Linear Algebra, we began discussing matrix operations. Matrix addition is simple enough, even obvious, but matrix multiplication is an altogether different beast, and making it digestible to students is a perennial problem.
About half an hour before class, an idea struck me. When the time came to introduce multiplication, I asked if anyone in the class had ever played Skyrim. Only a few hands went up - perhaps half a dozen, out of a nominal thirty students - but I forged ahead, talking about the problem of building and furnishing a homestead, and the levels of complication - finding or buying the basic components, assembling them into furnishings, and installing the furnishings into rooms of the house. Representing these as matrices ("You need so many nails, so much lumber, and so many hinges to build a chest/desk/cabinet" and "A fully stocked storeroom includes this many chests, this many desks, this many cabinets", leading to "How many nails/boards/hinges do you need to furnish a storeroom?"), I showed that matrix multiplication arises naturally. I provided a couple of more mundane examples as well, but I hope the first one will stick in their minds and get them comfortable with the operation.
About half an hour before class, an idea struck me. When the time came to introduce multiplication, I asked if anyone in the class had ever played Skyrim. Only a few hands went up - perhaps half a dozen, out of a nominal thirty students - but I forged ahead, talking about the problem of building and furnishing a homestead, and the levels of complication - finding or buying the basic components, assembling them into furnishings, and installing the furnishings into rooms of the house. Representing these as matrices ("You need so many nails, so much lumber, and so many hinges to build a chest/desk/cabinet" and "A fully stocked storeroom includes this many chests, this many desks, this many cabinets", leading to "How many nails/boards/hinges do you need to furnish a storeroom?"), I showed that matrix multiplication arises naturally. I provided a couple of more mundane examples as well, but I hope the first one will stick in their minds and get them comfortable with the operation.
