When studying linear algebra in mathematics (I mean, for the people studying mathematics) there are many ways of approaching it, depending of your needs, however supposedly every mathematician should have about the same basic concepts, which I think I have.
I've been asked to help this kid, who's studying engineering, and is having a lot of trouble with linear algebra, nonetheless I'm a little nervous because I don't know how to help him well. Some friends tell me that is practically the same as pure mathematics except without proofs and that is just doing excercices. But what does that mean? Getting really good with Gram–Schmidt without understanding where it came from? Do they study dual spaces? What is the best way to help without making a mess in his mind?