Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn’t a prereq) so don’t confuse this with regular high school algebra.

Course Curriculum

Introduction to matrices Details 11:51
Matrix multiplication (part 1) Details 13:41
Matrix multiplication (part 2) Details 14:37
Inverse Matrix (part 1) Details 14:15
Inverting matrices (part 2) Details 16:45
Inverting Matrices (part 3) Details 13:36
Matrices to solve a system of equations Details 16:33
Matrices to solve a vector combination problem Details 14:20
Singular Matrices Details 14:27
3-variable linear equations (part 1) Details 8:2
Solving 3 Equations with 3 Unknowns Details 15:26
Linear Algebra: Introduction to Vectors Details
Linear Algebra: Vector Examples Details 25:34
Linear Algebra: Parametric Representations of Lines Details 24:46
Linear Combinations and Span Details 20:35
Linear Algebra: Introduction to Linear Independence Details 15:46
More on linear independence Details 17:38
Span and Linear Independence Example Details 16:53
Linear Subspaces Details 23:29
Linear Algebra: Basis of a Subspace Details 0:19
Vector Dot Product and Vector Length Details 9:10
Proving Vector Dot Product Properties Details 10:46
Proof of the Cauchy-Schwarz Inequality Details 16:55
Linear Algebra: Vector Triangle Inequality Details 18:53
Defining the angle between vectors Details 25:11
Defining a plane in R3 with a point and normal vector Details 13:53
Linear Algebra: Cross Product Introduction Details 15:47
Proof: Relationship between cross product and sin of angle Details 18:9
Dot and Cross Product Comparison/Intuition Details 19:14
Matrices: Reduced Row Echelon Form 1 Details 17:43
Matrices: Reduced Row Echelon Form 2 Details 7:37
Matrices: Reduced Row Echelon Form 3 Details 12:8
Matrix Vector Products Details 21:10
Introduction to the Null Space of a Matrix Details 10:23
Null Space 2: Calculating the null space of a matrix Details 13:7
Null Space 3: Relation to Linear Independence Details 11:35
Column Space of a Matrix Details 10:40
Null Space and Column Space Basis Details 25:13
Visualizing a Column Space as a Plane in R3 Details 21:11
Proof: Any subspace basis has same number of elements Details 21:35
Dimension of the Null Space or Nullity Details 13:59
Dimension of the Column Space or Rank Details 12:48
Showing relation between basis cols and pivot cols Details 8:33
Showing that the candidate basis does span C(A) Details 13:40
A more formal understanding of functions Details 16:2
Vector Transformations Details 14:19
Linear Transformations Details 13:52
Matrix Vector Products as Linear Transformations Details 17:4
Linear Transformations as Matrix Vector Products Details 17:32
Image of a subset under a transformation Details 18:11

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