Why is linear Algebra so hard to understand?

they teach it at the same time as calculus where I'm from

Vectors is sometimes part of precalculus

It's hard if you are taught it the wrong way; same goes for any other subject.
Linear Algebra is taught wrongly way too often though, because they teach it by focusing on matrices rather than linear maps.
Rule of thumb for Linear Algebra is "Think with maps, compute with matrices".

Yes. Let f represent the left matrix and g represent the right matrix (given the usual base [math] \{e_i\} [/math] .
Then [math] g(e_i) [/math] is the i-th column of the right matrix.
The i-th column of [math] f \circ g [/math] is [math] f \circ g (e_i) = f(g(e_i)) = f( \text{ i-th column of the right matrix } ) [/math] .

Matrix multiplication is defined this way so that it if you have:
the matrix A of a linear map g under the bases u and v
and
the matrix B of a linear map f under the bases v and w,
then the matrix of f ο g under the bases u and w can be acquired by BA.

That's the only reason it is defined this way.

It's misguided to call linear algebra a subset of group theory. They really serve totally different purposes. The fact that a vector space forms an abelian group under addition doesn't mean you're doing group theory. In fact, abelian groups are really closer to being linear algebra than vice versa.

Welders don't need linear algebra you cuck

everything becomes easier when you understand that matrices are really just functions if they are on the left, and a group of column vectors that serve as arguments a function (matrix) if they are on the right

this guy got it

you cant be serious right?