[ojnabieoot]

I would not describe his approach as “the US approach” but it is a pretty standard approach to introducing linear algebra to engineers, which is the theme of the course.

I was also taught linear algebra this way, by an applied mathematician with a background in chemical engineering:

- start by solving Ax=b with row reduction

- develop theorems about linear independence and spanning sets of vectors based on these exercises

- introduce the determinant from the perspective of linear systems (rather than eg geometry or group theory)

- eigenvectors and eigenvalues

Later I switched from physics to math and TAed a more “algebraic” approach involving groups/rings/fields. But the matrix-first approach was more helpful for both my physics coursework and later courses in numerical linear algebra.