Vectors and spaces videos

Vector intro for linear algebra

Multiplying a vector by a scalar

Real coordinate spaces

Adding vectors algebraically & graphically

Parametric representations of lines

Vector examples

Unit vectors intro

Linear combinations and span

More on linear independence

Introduction to linear independence

Span and linear independence example

Linear subspaces

Basis of a subspace

Vector dot product and vector length

Proving vector dot product properties

Defining the angle between vectors

Proof of the Cauchy-Schwarz inequality

Vector triangle inequality

Defining a plane in R3 with a point and normal vector

Cross product introduction

Proof: Relationship between cross product and sin of angle

Dot and cross product comparison/intuition

Normal vector from plane equation

Vector triple product expansion (very optional)

Distance between planes

Point distance to plane

Solving linear systems with matrices

Solving a system of 3 equations and 4 variables using matrix row-echelon form

Using matrix row-echelon form in order to show a linear system has no solutions

Null space 2: Calculating the null space of a matrix

Matrix vector products

Introduction to the null space of a matrix

Null space and column space basis

Null space 3: Relation to linear independence

Column space of a matrix

Visualizing a column space as a plane in R3

Dimension of the column space or rank

Proof: Any subspace basis has same number of elements

Dimension of the null space or nullity

Showing relation between basis cols and pivot cols