Main Points.

Linear Combinations is the when there is vector addition and scalar multiplication done simultaneously. When given three vectors, there are multiple ways to determine what operation must be performed on the first two to equal the third. It can be done graphically, or algebraically where x and y represent the unknown, the multiples. 

A system of equations can be points interpreted where you determine at which point the two eqns intersect. In vector interpretation, you determine which multiples are needed to produce a certain vector from two others.

Vectors can be drawn in higher dimensions, with R^3 being 3-D. Matrices are boxes of numbers, with their own special notation, with dimensions m by n. 

The span of vectors are all vectors that can be produced from those vectors via linear combos.

Linear dependency is determined by whether any vectors from the span, is a span from any vectors from that same span.

All vectors in the span of a span or list make up a subpace. The subpace's dimension is the smallest amount of vectos needed to make a subspace.

Reflection.

I don't really understand matrices but they seem to be a much more efficient way of keeping track of and adding or multiplying points then always writing out the vectors. I believe they are important for coding where numbers are used to represent letters and the given multiplier serves as the "key" for the code.

Conflicts.

I don't get linear combos because scalers and vectors are tow different things. I don't understand multiplying the matrices, the numbers seemed to be coming out of nowhere.