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.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using stateoftheart, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Precalculus channel:
www.youtube.com/channel/UCBeHztH...ion=1
Subscribe to Khan Academy: www.youtube.com/subscription_cen...ademy
Lessons 

1) Introduction to matricesWhat a matrix is. How to add and subtract them.596 views

2) Matrix multiplication (part 1)Multiplying two 2x2 matrices.533 views

3) Matrix multiplication (part 2)More on multiplying matrices.438 views

4) Idea behind inverting a 2x2 matrix  Matrices  PrecalculusWhat the inverse of a matrix is. Examples of inverting a 2x2 matrix. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ...505 views

5) Classic video on inverting a 3x3 matrix part 1  Matrices  PrecalculusInverting a 3x3 matrix Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ...539 views

6) Classic video on inverting a 3x3 matrix part 2  Matrices  PrecalculusUsing GaussJordan elimination to invert a 3x3 matrix. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ...576 views

7) Matrices to solve a system of equations  Matrices  PrecalculusUsing the inverse of a matrix to solve a system of equations.522 views

8) Matrices to solve a vector combination problem  Matrices  PrecalculusUsing matrices to figure out if some combination of 2 vectors can create a 3rd vector573 views

9) Singular matrices  Matrices  PrecalculusWhen and why you can't invert a matrix. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ...483 views

10) 3variable linear equations (part 1)Visual intuition of a 3variable linear equation.465 views

11) Solving 3 Equations with 3 UnknownsSolving 3 equations with 3 unknowns (old video from July 2008)523 views

12) Vector examples  Vectors and spaces  Linear AlgebraVisually understanding basic vector operations Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/linear ...527 views

13) Parametric representations of lines  Vectors and spaces  Linear AlgebraParametric Representations of Lines in R2 and R3426 views

14) Linear combinations and span  Vectors and spaces  Linear AlgebraUnderstanding linear combinations and spans of vectors480 views

15) Introduction to linear independence  Vectors and spaces  Linear AlgebraIntroduction to linear dependence and independence522 views

16) More on linear independence  Vectors and spaces  Linear AlgebraMore examples determining linear dependence or independence.541 views

17) Span and linear independence example  Vectors and spaces  Linear AlgebraDetermining whether 3 vectors are linearly independent and/or span R3470 views

18) Linear subspaces  Vectors and spaces  Linear AlgebraIntroduction to linear subspaces of Rn634 views

19) Basis of a subspace  Vectors and spaces  Linear AlgebraUnderstanding the definition of a basis of a subspace485 views

20) Vector dot product and vector length  Vectors and spaces  Linear AlgebraDefinitions of the vector dot product and vector length576 views

21) Proving vector dot product properties  Vectors and spaces  Linear AlgebraProving the "associative", "distributive" and "commutative" properties for vector dot products.531 views

22) Proof of the CauchySchwarz inequality  Vectors and spaces  Linear AlgebraProof of the CauchySchwarz Inequality746 views

23) Vector triangle inequality  Vectors and spaces  Linear AlgebraProving the triangle inequality for vectors in Rn494 views

24) Defining the angle between vectors  Vectors and spaces  Linear AlgebraIntroducing the idea of an angle between two vectors502 views

25) Defining a plane in R3 with a point and normal vector  Linear AlgebraDetermining the equation for a plane in R3 using a point on the plane and a normal vector600 views

26) Cross product introduction  Vectors and spaces  Linear AlgebraIntroduction to the cross product564 views

27) Proof: Relationship between cross product and sin of angle  Linear AlgebraProof: Relationship between the cross product and sin of angle between vectors570 views

28) Dot and cross product comparison/intuition  Vectors and spaces  Linear AlgebraDot and Cross Product Comparison/Intuition508 views

29) Matrices: Reduced row echelon form 1  Vectors and spaces  Linear AlgebraSolving a system of linear equations by putting an augmented matrix into reduced row echelon form554 views

30) Matrices: Reduced row echelon form 2  Vectors and spaces  Linear AlgebraAnother example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form684 views

31) Matrices: Reduced row echelon form 3  Vectors and spaces  Linear AlgebraAnd another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form550 views

32) Matrix vector products  Vectors and spaces  Linear AlgebraDefining and understanding what it means to take the product of a matrix and a vector518 views

33) Introduction to the null space of a matrix  Vectors and spaces  Linear AlgebraShowing that the Null Space of a Matrix is a valid Subspace627 views

34) Null space 2: Calculating the null space of a matrix  Linear AlgebraCalculating the null space of a matrix483 views

35) Null space 3: Relation to linear independence  Vectors and spaces  Linear AlgebraUnderstanding how the null space of a matrix relates to the linear independence of its column vectors472 views

36) Column space of a matrix  Vectors and spaces  Linear AlgebraIntroduction to the column space of a matrix499 views

37) Null space and column space basis  Vectors and spaces  Linear AlgebraFiguring out the null space and a basis of a column space for a matrix590 views

38) Visualizing a column space as a plane in R3  Vectors and spaces  Linear AlgebraDetermining the planar equation for a column space in R3497 views

39) Proof: Any subspace basis has same number of elements  Linear AlgebraProof: Any subspace basis has same number of elements509 views

40) Dimension of the null space or nullity  Vectors and spaces  Linear AlgebraDimension of the Null Space or Nullity508 views

41) Dimension of the column space or rank  Vectors and spaces  Linear AlgebraDimension of the Column Space or Rank578 views

42) Showing relation between basis cols and pivot cols  Linear AlgebraShowing that linear independence of pivot columns implies linear independence of the corresponding columns in the original equation584 views

43) Showing that the candidate basis does span C(A)  Vectors and spaces  Linear AlgebraShowing that just the columns of A associated with the pivot columns of rref(A) do indeed span C(A).580 views

44) A more formal understanding of functions  Matrix transformations  Linear AlgebraA more formal understanding of functions481 views

45) Vector transformations  Matrix transformations  Linear AlgebraIntroduction to the notion of vector transformations550 views

46) Linear transformations  Matrix transformations  Linear AlgebraIntroduction to linear transformations563 views

47) Matrix vector products as linear transformations  Linear AlgebraMatrix Vector Products as Linear Transformations508 views

48) Linear transformations as matrix vector products  Linear AlgebraShowing how ANY linear transformation can be represented as a matrix vector product483 views

49) Image of a subset under a transformation  Matrix transformations  Linear AlgebraExploring what happens to a subset of the domain under a transformation539 views

50) im(T): Image of a transformation  Matrix transformations  Linear AlgebraShowing that the image of a subspace under a transformation is also a subspace. Definition of the image of a Transformation.602 views

51) Preimage of a set  Matrix transformations  Linear AlgebraDefinition of preimage of a set485 views

52) Preimage and kernel example  Matrix transformations  Linear AlgebraExample involving the preimage of a set under a transformation. Definition of kernel of a transformation.516 views

53) Sums and scalar multiples of linear transformations  Linear AlgebraSums and Scalar Multiples of Linear Transformations. Definitions of matrix addition and scalar multiplication.501 views

54) More on matrix addition and scalar multiplication  Linear AlgebraMore on Matrix Addition and Scalar Multiplication602 views

55) Linear transformation examples: Scaling and reflections  Linear AlgebraCreating scaling and reflection transformation matrices (which are diagonal)559 views

56) Linear transformation examples: Rotations in R2  Linear AlgebraLinear Transformation Examples: Rotations in R2420 views

57) Rotation in R3 around the xaxis  Matrix transformations  Linear AlgebraConstruction a rotation transformation in R3509 views

58) Unit vectors  Matrix transformations  Linear AlgebraWhat unit vectors are and how to construct them442 views

59) Introduction to projections  Matrix transformations  Linear AlgebraDetermining the projection of a vector on s line448 views

60) Expressing a projection on to a line as a matrix vector prod  Linear AlgebraExpressing a Projection on to a line as a Matrix Vector prod469 views

61) Compositions of linear transformations 1  Matrix transformations  Linear AlgebraIntroduction to compositions of Linear Transformations577 views

62) Compositions of linear transformations 2  Matrix transformations  Linear AlgebraProviding the motivation for definition of matrix products470 views

63) Matrix product examples  Matrix transformations  Linear AlgebraExample of taking the product of two matrices522 views

64) Matrix product associativity  Matrix transformations  Linear AlgebraShowing that matrix products are associative555 views

65) Distributive property of matrix products  Matrix transformations  Linear AlgebraShowing that matrix products are associative407 views

66) Introduction to the inverse of a function  Matrix transformations  Linear AlgebraIntroduction to the inverse of a function438 views

67) Proof: Invertibility implies a unique solution to f(x)=y  Linear AlgebraProof: Invertibility implies a unique solution to f(x)=y for all y in codomain of f.473 views

68) Surjective (onto) and injective (onetoone) functions  Linear AlgebraIntroduction to surjective and injective functions501 views

69) Relating invertibility to being onto and onetoone  Linear AlgebraRelating invertibility to being onto (surjective) and onetoone (injective)549 views

70) Determining whether a transformation is onto  Linear AlgebraDetermining whether a transformation is onto580 views

71) Exploring the solution set of Ax = b  Matrix transformations  Linear AlgebraExploring the solution set of Ax=b (non homogeneous equations)604 views

72) Matrix condition for onetoone trans  Matrix transformations  Linear AlgebraShowing that the rank of the of an mxn transformation matrix has to be an for the transformation to be onetoone (injective)446 views

73) Simplifying conditions for invertibility  Matrix transformations  Linear AlgebraShowing that a transformation is invertible if and only if rref(A) is equal to the identity matrix441 views

74) Showing that inverses are linear  Matrix transformations  Linear AlgebraShowing that inverse transformations are also linear442 views

75) Deriving a method for determining inverses  Matrix transformations  Linear AlgebraDetermining a method for constructing inverse transformation matrices478 views

76) Example of finding matrix inverse  Matrix transformations  Linear AlgebraExample of calculating the inverse of a matrix470 views

77) Formula for 2x2 inverse  Matrix transformations  Linear AlgebraFiguring out the formula for a 2x2 matrix. Defining the determinant.441 views

78) 3 x 3 determinant  Matrix transformations  Linear AlgebraDeterminants: Finding the determinant of a 3x3 matrix533 views

79) n x n determinant  Matrix transformations  Linear AlgebraDefining the determinant for nxn matrices. An example of a 4x4 determinant.538 views

80) Determinants along other rows/cols  Matrix transformations  Linear AlgebraFinding the determinant by going along other rows or columns438 views

81) Rule of Sarrus of determinants  Matrix transformations  Linear AlgebraA alternative "short cut" for calculating 3x3 determinants (Rule of Sarrus)595 views

82) Determinant when row multiplied by scalar  Matrix transformations  Linear AlgebraThe determinant when a row is multiplied by a scalar667 views

83) (correction) scalar multiplication of row  Matrix transformations  Linear AlgebraCorrection of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant484 views

84) Determinant when row is added  Matrix transformations  Linear AlgebraThe determinant when one matrix has a row that is the sum of the rows of other matrices (and every other term is identical in the 3 matrices)569 views

85) Duplicate row determinant  Matrix transformations  Linear AlgebraDeterminant of a matrix with duplicate rows555 views

86) Determinant after row operations  Matrix transformations  Linear AlgebraWhat happens to the determinant when we perform a row operation506 views

87) Upper triangular determinant  Matrix transformations  Linear AlgebraThe determinant of an upper triangular matrix470 views

88) Simpler 4x4 determinant  Matrix transformations  Linear AlgebraCalculating a 4x4 determinant by putting in in upper triangular form first.469 views

89) Determinant and area of a parallelogram  Matrix transformations  Linear AlgebraRealizing that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix560 views

90) Determinant as scaling factor  Matrix transformations  Linear AlgebraViewing the determinant of the transformation matrix as a scaling factor of regions485 views

91) Transpose of a matrix  Matrix transformations  Linear AlgebraTranspose of a matrix570 views

92) Determinant of transpose  Matrix transformations  Linear AlgebraProof by induction that transposing a matrix does not change its determinant485 views

93) Transpose of a matrix product  Matrix transformations  Linear AlgebraTaking the transpose of the product of two matrices461 views

94) Transposes of sums and inverses  Matrix transformations  Linear AlgebraTransposes of sums and inverses462 views

95) Transpose of a vector  Matrix transformations  Linear AlgebraTranspose of a column vector. Matrixmatrix products using vectors513 views

96) Rowspace and left nullspace  Matrix transformations  Linear AlgebraRowspace and Left Nullspace602 views

97) Visualizations of left nullspace and rowspace  Linear AlgebraRelationship between left nullspace, rowspace, column space and nullspace.460 views

98) Orthogonal complements  Alternate coordinate systems (bases)  Linear AlgebraOrthogonal Complements as subspaces.508 views

99) rank(a) = rank(transpose of a)  Matrix transformations  Linear AlgebraRank(A) = Rank(transpose of A)414 views

100) dim(v) + dim(orthogonal complement of v) = n  Linear AlgebraShowing that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n458 views

Correlated course
3ds max ragdoll script FREE
This video demonstrates how to use the built in 3ds max Ragdoll script. the code is rctMakeRagdollUI () copy that into the Max script Listener and press enter or you can copy this max script i m
Intro to Theoretical Computer Science FREE
This class teaches you about basic concepts in theoretical computer science  such as NPcompleteness  and what they imply for solving tough algorithmic problems.At the end of this course, you will
Google Location Services on Android FREE
This course is deprecated. We recommend taking Advanced Android App Development instead.Vitally important for building the best possible mobile app, the Location and Context API allows your Android ap
Firebug editing and debugging CSS, PHP and Ajax applications FREE
The Firebug Firefox extension allows you to edit in real time your CSS code. Instead of having to make a change, reload, make a change, reload you can just edit it live to see the results. Using the
MIT SA+P Commercial Real Estate Analysis and Investment Paid Course
Gain the tools necessary to anticipate and guide any development decisions your clients may have to make.
Chemistry  Khan Academy FREE
Videos on chemistry (roughly covering a firstyear high school or college course).
Classification Models FREE
The Classification Models course provides students with the foundational knowledge to use classification models to create business insights. You will learn:How classification modeling differs from mod
Software Development Process FREE
This class is offered as CS6300 at Georgia Tech where it is a part of the Online Masters Degree (OMS). Taking this course here will not earn credit towards the OMS degree.In SDP, you will learn how to
Microsoft Power Platform Paid Course
Get your start in one of the fastest growing fields in technology.
TAG Cloud
Web Stats
Active courses: 74,474
Lessons: 2,066,701
Data: 74 GB
Online: 57 users