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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