I don't think it was this way in 1820, but I agree with your point. Even though I also use Linear Algebra mostly computationally today, the origin of it is in

I don't think it was this way in 1820, but I agree with your point. Even though I also use Linear Algebra mostly computationally today, the origin of it is in the geometry and I think this connection should come first. Also, "number crunching" is a boring way to learn things. Though, "matrix way" can be good for engineers.