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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.

Self-Study Content
  1. Introduction to matrices

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

  2. Matrix multiplication (part 1)

    More free lessons at: http://www.khanacademy.org/video?v=aKhhYguY0DQ Multiplying two 2x2 matrices.

  3. Matrix multiplication (part 2)

    More free lessons at: http://www.khanacademy.org/video?v=OAh573i_qn8 More on multiplying matrices.

  4. Inverse Matrix (part 1)

    More free lessons at: http://www.khanacademy.org/video?v=iUQR0enP7RQ Taking the inverse of a 2x2 ma

  5. Inverting matrices (part 2)

    More free lessons at: http://www.khanacademy.org/video?v=S4n-tQZnU6o Inverting a 3x3 matrix

  6. Inverting Matrices (part 3)

    More free lessons at: http://www.khanacademy.org/video?v=obts_JDS6_Q Using Gauss-Jordan elimination

  7. Matrices to solve a system of equations

    More free lessons at: http://www.khanacademy.org/video?v=AUqeb9Z3y3k Using the inverse of a matrix

  8. Matrices to solve a vector combination problem

    More free lessons at: http://www.khanacademy.org/video?v=gsNgdVdAT1o Using matrices to figure out i

  9. Singular Matrices

    More free lessons at: http://www.khanacademy.org/video?v=UqyN7-tRS00 When and why you can't invert

  10. 3-variable linear equations (part 1)

    Visual intuition of a 3-variable linear equation.

  11. Solving 3 Equations with 3 Unknowns

    Solving 3 equations with 3 unknowns (old video from July 2008)

  12. Linear Algebra: Vector Examples

    More free lessons at: http://www.khanacademy.org/video?v=r4bH66vYjss Visually understanding basic v

  13. Linear Algebra: Parametric Representations of Lines

    More free lessons at: http://www.khanacademy.org/video?v=hWhs2cIj7Cw Linear Algebra: Parametric Rep

  14. Linear Combinations and Span

    More free lessons at: http://www.khanacademy.org/video?v=Qm_OS-8COwU Understanding linear combinati

  15. Linear Algebra: Introduction to Linear Independence

    More free lessons at: http://www.khanacademy.org/video?v=CrV1xCWdY-g Linear Algebra: Introduction t

  16. More on linear independence

    More free lessons at: http://www.khanacademy.org/video?v=Alhcv5d_XOs More examples determining line

  17. Span and Linear Independence Example

    More free lessons at: http://www.khanacademy.org/video?v=9kW6zFK5E5c Determining whether 3 vectors

  18. Linear Subspaces

    More free lessons at: http://www.khanacademy.org/video?v=pMFv6liWK4M Introduction to linear subspac

  19. Linear Algebra: Basis of a Subspace

    More free lessons at: http://www.khanacademy.org/video?v=zntNi3-ybfQ Understanding the definition o

  20. Vector Dot Product and Vector Length

    More free lessons at: http://www.khanacademy.org/video?v=WNuIhXo39_k Definitions of the vector dot

  21. Proving Vector Dot Product Properties

    More free lessons at: http://www.khanacademy.org/video?v=rVQ3G9epCjw Proving the

  22. Proof of the Cauchy-Schwarz Inequality

    More free lessons at: http://www.khanacademy.org/video?v=r2PogGDl8_U Proof of the Cauchy-Schwarz In

  23. Linear Algebra: Vector Triangle Inequality

    More free lessons at: http://www.khanacademy.org/video?v=PsNidCBr5II Proving the triangle inequalit

  24. Defining the angle between vectors

    More free lessons at: http://www.khanacademy.org/video?v=5AWob_z74Ks Introducing the idea of an ang

  25. Defining a plane in R3 with a point and normal vector

    More free lessons at: http://www.khanacademy.org/video?v=UJxgcVaNTqY Determining the equation for a

  26. Linear Algebra: Cross Product Introduction

    More free lessons at: http://www.khanacademy.org/video?v=pJzmiywagfY Introduction to the cross prod

  27. Proof: Relationship between cross product and sin of angle

    More free lessons at: http://www.khanacademy.org/video?v=7MKA2QlKvHc Proof: Relationship between th

  28. Dot and Cross Product Comparison/Intuition

    More free lessons at: http://www.khanacademy.org/video?v=tdwFdzVqito Dot and Cross Product Comparis

  29. Matrices: Reduced Row Echelon Form 1

    More free lessons at: http://www.khanacademy.org/video?v=L0CmbneYETs Solving a system of linear equ

  30. Matrices: Reduced Row Echelon Form 2

    More free lessons at: http://www.khanacademy.org/video?v=lP1DGtZ8Wys Another example of solving a s

  31. Matrices: Reduced Row Echelon Form 3

    More free lessons at: http://www.khanacademy.org/video?v=JVDrlTdzxiI And another example of solving

  32. Matrix Vector Products

    More free lessons at: http://www.khanacademy.org/video?v=7Mo4S2wyMg4 Defining and understanding wha

  33. Introduction to the Null Space of a Matrix

    More free lessons at: http://www.khanacademy.org/video?v=jCwRV1QL_Xs Showing that the Null Space of

  34. Null Space 2: Calculating the null space of a matrix

    More free lessons at: http://www.khanacademy.org/video?v=qvyboGryeA8 Calculating the null space of

  35. Null Space 3: Relation to Linear Independence

    More free lessons at: http://www.khanacademy.org/video?v=vFctYRhK2M0 Understanding how the null spa

  36. Column Space of a Matrix

    More free lessons at: http://www.khanacademy.org/video?v=st6D5OdFV9M Introduction to the column spa

  37. Null Space and Column Space Basis

    More free lessons at: http://www.khanacademy.org/video?v=_uTAdf_AsfQ Figuring out the null space an

  38. Visualizing a Column Space as a Plane in R3

    More free lessons at: http://www.khanacademy.org/video?v=EGNlXtjYABw Determining the planar equatio

  39. Proof: Any subspace basis has same number of elements

    More free lessons at: http://www.khanacademy.org/video?v=Zn2K8UIT8r4 Proof: Any subspace basis has

  40. Dimension of the Null Space or Nullity

    More free lessons at: http://www.khanacademy.org/video?v=abYAUqs_n6I Dimension of the Null Space or

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