The fact that there is a precise analogy between how Ax + s = b works when A is a matrix and the other quantities are vectors, and how this works when everything is scalars or what have you, is a fundamental insight which is useful to notationally encode. It's good to be able to readily reason that in either case, x = A^(-1) (b - s) if A is invertible, and so on.

It's good to be able to think and talk in terms of abstractions that do not force viewing analogous situations in very different terms. This is much of what math is about.

Well, obviously they will be confused because you jumped from a square of numbers to a bunch of operations. They’d be equally confused if you presented those operations numerically. I am not sure what it is you want to prove with that example. I am also not sure that a child can actually understand what a matrix is if you just show them some numbers (i.e., will they actually understand that a matrix is a linear transformer of vectors and the properties it has just by showing them some numbers?)

> a bunch of operations.

Sorry, the notation is bit confusing. The 'A' here is a matrix.

I know it is a matrix, the notation is not confusing at all. I am saying that the concept of a matrix as a set of numbers arranged in a rectangles and the concept of operations on a matrix are very different things, the confusion will not come from notation.

You must be correct, because this interaction is completely devoid of any confusion between the two people attempting to communicate clearly.

I do not have any confusion with the notation, I am confused about what the argument you’re trying to convey with English words.

Ceci n'est pas une pipe.

This is funny. “Mathematics notation is confusing to me because I refuse to learn it. I refuse to learn it because mathematics notation is confusing to me.” Okay sure, be happy with yourself.

> This is so wrong it can only come from a place of inexperience and ignorance.

Thanks for the laughs :D

> Show a child a matrix numerically and they can understand it, show them Ax+s=b, and watch the confusion.

Show a HN misunderstood genius Riemann Zeta function as a Zeta() and they think they can figure out it's zeros. Show it as a Greek letter and they'll lament how impossible it is to understand.