Because in the dark ages we didn't have the nice, convenient linear algebra functions, so you had to know how to do it "manually". That's the point of most homework problems. For you to understand the concept so you know what it actually means, and the implementation so you know how to do it yourself.
Just like in the dark ages we didn't have Google, so we used these buildings called libraries. And you looked things up in these great big cabinets full of drawers that had hundreds of cards in them. And you had to know the Dewey Decimal system.
