Khan Academy Course , Prof. Salman Khan

**240**students enrolled

Khan Academy Course , Prof. Salman Khan

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.

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What a matrix is. How to add and subtract them.

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

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