I had three years of high school with a substantial amount of calculus; by contrast while I was introduced to matrices and Gaussian elimination at high school, the treatment of the algebraic side was almost completely superficial and focussed on solving systems of linear equations.

At university that changed, with a clear treatment of vector spaces and linear algebra as generally interesting topics. But still, they received far less time than calculus in my first year in a maths degree.

Now that was over 30 years ago and things might be a bit different today. But I have the impression that the more generally applicable subject of linear algebra gets less time unless students get interested in the applications that demand it be taught properly.

Yea, theorems like least square prove that A^T * A * X = A^T * B. but how exactly is this related to calculus though?

Derivatives are (derivations are the generalization so of course are but I would be surprised to see an undergrad class treat them)