Matrix × Vector
Rows dot the vector, one output per row.
Concept
A matrix is a function on vectors
To multiply a 2×2 matrix by a 2-vector, dot each row with the vector. The result is a new vector — the transformed point.
Equivalently, the output is a combination of the matrix's columns weighted by the vector's entries. That view explains almost everything later in the course.
[a b; c d]·[x, y] = [ax + by, cx + dy]