11/18: Linear combinations, linear independence, span

1. Main Points
One can combine the two operations, adding multiples of two vectors. A sum of multiples is a
linear combination.
A system of equations for unknowns x and y
ax + by = e
cx + dy = f
Has two fundamental but different geometric interpretations: the points interpretation and the vector interpretation.
Linear combinations of vectors occur so frequently that a special notation has been developed
using matrices. This is defined as an m × n matrix which is a rectangular array of numbers, arranged in m rows and n columns.

2. Challenging
Linear combinations in higher dimensions was a little challenging to think about.

3. Intruiging
I can see how linear combinations can be applied in many areas of science!