Vector span

It’s extending the unit vector idea.

Matrices Elimination

Matrices elimination (or solving system of linear equations) is the very first and fundamental skill throughout Linear Algebra. It's probably the first lesson of all sorts of courses.

Terminology

Change of basis

Changing basis of a vector, the vector’s length & direction remain the same, but the numbers represent the vector will change, since the meaning of the numbers have changed. 
Our goal is to calculate the New numbers in the vector in terms of the new basis.

Matrix Transformation

It’s a subset of Linear transformation, just with higher dimension rules & multiple points graph multiplying together.

YOU BREAK THE RULE IN TO DIFFERENT UNIT VECTORS i, j, k... AND BREAK THE GRAPH INTO DIFFERENT POINTS, AND APPLY EACH i, j, k RULES TO EACH POINT.

Vectors multiplication

Vector multiplication is FUNDAMENTAL skill to solve Matrices multiplication.

Determinant of Transformation

It’s quite easy to calculate, and not too hard to understand what’s behind it.

The Determinant of a transformation is How much the AREA of the new Graph scaled.

Matrix multiplication

IT IS A WHOLE NEW AREA ASIDE FROM MATRICES BASIC OPERATIONS.