From a university lecture in linear algebra, I expect that it carries me through as many important topics as possible while giving me the tools to form a good formal and intuitive understanding.
Sure and unless your goal is to do pure mathematics research, part of that is providing some motivation in terms of understanding applications. There's nothing wrong with a class on LA (or any other topic as far as that goes) spending some time motivating study of the topic by showing how it can be useful... even explaining how it might used to make millions or billions of dollars.