Linear Algebra
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19:53
Linear Algebra - Matrix Transformations
/ 573 viewsMatrix multiplication and linear algebra explained with 3D animations.
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47:36
Completing the square - Live algebra lesson
/ 619 viewsDo you need help with your algebra homework? Send photos of any problems you need help with to LiveStream@MathMeeting.com. Today I am focusing on solving quadratic equations by completing the square. I will help you live right here on this live stream :)
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15:34
Linear Algebra: Eigenvectors and Eigenspaces for a 3x3 matrix
/ 668 viewsEigenvectors and eigenspaces for a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=3Md5KCCQX-0
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14:08
Linear Algebra: Eigenvalues of a 3x3 matrix
/ 675 viewsDetermining the eigenvalues of a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=11dNghWC4HI
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14:34
Linear Algebra: Finding Eigenvectors and Eigenspaces example
/ 698 viewsFinding the eigenvectors and eigenspaces of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=3-xfmbdzkqc
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05:39
Linear Algebra: Example solving for the eigenvalues of a 2x2 matrix
/ 682 viewsExample solving for the eigenvalues of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=pZ6mMVEE89g
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09:19 Popular
Linear Algebra: Proof of formula for determining Eigenvalues
/ 706 viewsProof of formula for determining Eigenvalues More free lessons at: http://www.khanacademy.org/video?v=rfm0wQObxjk
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07:43
Linear Algebra: Introduction to Eigenvalues and Eigenvectors
/ 663 viewsWhat eigenvectors and eigenvalues are and why they are interesting More free lessons at: http://www.khanacademy.org/video?v=PhfbEr2btGQ
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13:57
Linear Algebra: Gram-Schmidt example with 3 basis vectors
/ 679 viewsGram-Schmidt example with 3 basis vectors More free lessons at: http://www.khanacademy.org/video?v=ZRRG386v6DI
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13:14
Linear Algebra: Gram-Schmidt Process Example
/ 635 viewsUsing Gram-Schmidt to find an orthonormal basis for a plane in R3 More free lessons at: http://www.khanacademy.org/video?v=tu1GPtfsQ7M
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19:24
Linear Algebra: The Gram-Schmidt Process
/ 647 viewsFinding an orthonormal basis for a subspace using the Gram-Schmidt Process More free lessons at: http://www.khanacademy.org/video?v=rHonltF77zI
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11:16 Popular
Lin Alg: Orthogonal matrices preserve angles and lengths
/ 751 viewsShowing that orthogonal matrices preserve angles and lengths More free lessons at: http://www.khanacademy.org/video?v=yDwIfYjKEeo
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27:04 Popular
Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix
/ 706 viewsExample using orthogonal change-of-basis matrix to find transformation matrix More free lessons at: http://www.khanacademy.org/video?v=gfVY7cW7VLQ
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06:42
Lin Alg: Finding projection onto subspace with orthonormal basis example
/ 655 viewsExample of finding the transformation matrix for the projection onto a subspace with an orthonormal basis More free lessons at: http://www.khanacademy.org/video?v=SUoqA9srY1Q
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16:14
Lin Alg: Projections onto subspaces with orthonormal bases
/ 658 viewsProjections onto subspaces with orthonormal bases More free lessons at: http://www.khanacademy.org/video?v=we829K4NOq8
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15:28 Popular
Linear Algebra: Coordinates with respect to orthonormal bases
/ 753 viewsSeeing that orthonormal bases make for good coordinate systems More free lessons at: http://www.khanacademy.org/video?v=SWbis2zWIvo
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11:16
Linear Algebra: Introduction to Orthonormal Bases
/ 651 viewsLooking at sets and bases that are orthonormal -- or where all the vectors have length 1 and are orthogonal to each other. More free lessons at: http://www.khanacademy.org/video?v=7BFx8pt2aTQ
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29:00 Popular
Lin Alg: Changing coordinate systems to help find a transformation matrix
/ 845 viewsChanging our coordinate system to find the transformation matrix with respect to standard coordinates More free lessons at: http://www.khanacademy.org/video?v=K_na_j1Msfg
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12:36 Popular
Lin Alg: Alternate Basis Tranformation Matrix Example Part 2
/ 911 viewsShowing that the transformation matrix with respect to basis B actually works. Brief point on why someone would want to operate in a different basis to begin with. More free lessons at: http://www.khanacademy.org/video?v=EyORbCPUAd4
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13:20 Popular
Lin Alg: Alternate Basis Tranformation Matrix Example
/ 802 viewsExample of finding the transformation matrix for an alternate basis More free lessons at: http://www.khanacademy.org/video?v=lCRGNykWqFI
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18:02
Lin Alg: Transformation Matrix with Respect to a Basis
/ 698 viewsFinding the transformation matrix with respect to a non-standard basis More free lessons at: http://www.khanacademy.org/video?v=PiuhTj0zCf4
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13:34
Lin Alg: Invertible Change of Basis Matrix
/ 636 viewsUsing an invertible change of basis matrix to go between different coordinate systems More free lessons at: http://www.khanacademy.org/video?v=meibWcbGqt4
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17:55 Popular
Linear Algebra: Change of Basis Matrix
/ 705 viewsUsing a change of basis matrix to get us from one coordinate system to another. More free lessons at: http://www.khanacademy.org/video?v=1j5WnqwMdCk
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16:08
Linear Algebra: Coordinates with Respect to a Basis
/ 644 viewsUnderstanding alternate coordinate systems More free lessons at: http://www.khanacademy.org/video?v=uvgru6FcyxU
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13:25 Popular
Linear Algebra: Another Least Squares Example
/ 721 viewsUsing least squares approximation to fit a line to points More free lessons at: http://www.khanacademy.org/video?v=QkepM8Vv3kw
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18:50
Linear Algebra: Least Squares Examples
/ 671 viewsAn example using the least squares solution to an unsolvable system More free lessons at: http://www.khanacademy.org/video?v=8mAZYv5wIcE
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15:32
Linear Algebra: Least Squares Approximation
/ 662 viewsThe least squares approximation for otherwise unsolvable equations More free lessons at: http://www.khanacademy.org/video?v=MC7l96tW8V8
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09:05 Popular
Linear Alg: Projection is closest vector in subspace
/ 703 viewsShowing that the projection of x onto a subspace is the closest vector in the subspace to x More free lessons at: http://www.khanacademy.org/video?v=b269qpILOpk
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21:36 Popular
Lin Alg: Another Example of a Projection Matrix
/ 1,151 viewsFiguring out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first More free lessons at: http://www.khanacademy.org/video?v=XhCSHu6dHb8
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13:04 Popular
Linear Algebra: Subspace Projection Matrix Example
/ 760 viewsExample of a transformation matrix for a projection onto a subspace More free lessons at: http://www.khanacademy.org/video?v=QTcSBB3uVP0
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16:16
Lin Alg: A Projection onto a Subspace is a Linear Transforma
/ 674 viewsShowing that a projection onto a subspace is a linear transformation More free lessons at: http://www.khanacademy.org/video?v=cTyNpXB92bQ
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09:28
Linear Alg: Visualizing a projection onto a plane
/ 648 viewsVisualizing a projection onto a plane. Showing that the old and new definitions of projections aren't that different. More free lessons at: http://www.khanacademy.org/video?v=uWbZlJURkfA
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17:26
Linear Algebra: Projections onto Subspaces
/ 677 viewsProjections onto subspaces More free lessons at: http://www.khanacademy.org/video?v=5B8XluiqdHM
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12:34
Lin Alg: Showing that A-transpose x A is invertible
/ 659 viewsShowing that (transpose of A)(A) is invertible if A has linearly independent columns More free lessons at: http://www.khanacademy.org/video?v=ESSMQH6Y5OA
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19:38
Linear Alg: Rowspace Solution to Ax=b example
/ 638 viewsVisualizing the rowspace solution to Ax=b More free lessons at: http://www.khanacademy.org/video?v=qdf2CuMGdKs
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19:12 Popular
Lin Alg: Unique rowspace solution to Ax=b
/ 707 viewsShowing that, for any b that is in the column space of A, there is a unique member of the row space that is the "smallest" solution to Ax=b More free lessons at: http://www.khanacademy.org/video?v=czIYvs9zj2g
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03:27 Popular
Lin Alg: Orthogonal Complement of the Nullspace
/ 718 viewsThe orthogonal complement of the nullspace and left nullspace. More free lessons at: http://www.khanacademy.org/video?v=LE_aQAur7nI
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12:18
Lin Alg: Orthogonal Complement of the Orthogonal Complement
/ 619 viewsFinding that the orthogonal complement of the orthogonal complement of V is V More free lessons at: http://www.khanacademy.org/video?v=zlI8mx8Hc8o
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27:01 Popular
Lin Alg: Representing vectors in Rn using subspace members
/ 1,081 viewsShowing that any member of Rn can be represented as a unique sum of a vector in subspace V and a vector in the orthogonal complement of V. More free lessons at: http://www.khanacademy.org/video?v=M6lFqkqvUgo
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09:27
Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n
/ 617 viewsShowing that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n More free lessons at: http://www.khanacademy.org/video?v=pGhBfkBqok0
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11:14
Linear Algebra: Rank(A) = Rank(transpose of A)
/ 689 viewsRank(A) = Rank(transpose of A) More free lessons at: http://www.khanacademy.org/video?v=tqqVOWm9YsU
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22:08
Linear Algebra: Orthogonal Complements
/ 653 viewsOrthogonal Complements as subspaces. More free lessons at: http://www.khanacademy.org/video?v=QOTjdgmNqlg
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19:50
Lin Alg: Visualizations of Left Nullspace and Rowspace
/ 628 viewsRelationship between left nullspace, rowspace, column space and nullspace. More free lessons at: http://www.khanacademy.org/video?v=GW8ZPjGlk24
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23:19
Linear Algebra: Rowspace and Left Nullspace
/ 632 viewsRowspace and Left Nullspace More free lessons at: http://www.khanacademy.org/video?v=qBfc57x_RSg
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12:07
Linear Algebra: Transpose of a Vector
/ 629 viewsTranspose of a column vector. Matrix-matrix products using vectors More free lessons at: http://www.khanacademy.org/video?v=lSoaMCNKfAg
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08:41
Linear Algebra: Transposes of sums and inverses
/ 659 viewsTransposes of sums and inverses More free lessons at: http://www.khanacademy.org/video?v=Br_8t58mdeI
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08:50
Linear Algebra: Transpose of a Matrix Product
/ 653 viewsTaking the transpose of the product of two matrices More free lessons at: http://www.khanacademy.org/video?v=UdHgWK13x5I
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14:10
Linear Algebra: Determinant of Transpose
/ 677 viewsProof by induction that transposing a matrix does not change its determinant More free lessons at: http://www.khanacademy.org/video?v=x-GV2v0dRNE
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08:37
Linear Algebra: Transpose of a Matrix
/ 624 viewsTranspose of a matrix More free lessons at: http://www.khanacademy.org/video?v=2t0003_sxtU
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20:10 Popular
Linear Algebra: Determinant as Scaling Factor
/ 736 viewsViewing the determinant of the transformation matrix as a scaling factor of regions More free lessons at: http://www.khanacademy.org/video?v=g3MqSdO5Ubc
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21:38 Popular
Linear Algebra: Determinant and area of a parallelogram
/ 1,248 viewsRealizing that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix More free lessons at: http://www.khanacademy.org/video?v=n-S63_goDFg
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09:13
Linear Algebra: Simpler 4x4 determinant
/ 694 viewsCalculating a 4x4 determinant by putting in in upper triangular form first. More free lessons at: http://www.khanacademy.org/video?v=QV0jsTiobU4
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08:07
Linear Algebra: Upper Triangular Determinant
/ 645 viewsThe determinant of an upper triangular matrix More free lessons at: http://www.khanacademy.org/video?v=VX7K8iqoiRc
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10:25
Linear Algebra: Determinant after row operations
/ 622 viewsWhat happens to the determinant when we perform a row operation More free lessons at: http://www.khanacademy.org/video?v=kpG7xySkivg
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08:19
Linear Algebra: Duplicate Row Determinant
/ 699 viewsDeterminant of a matrix with duplicate rows More free lessons at: http://www.khanacademy.org/video?v=gYv8sttBIqs
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16:55 Popular
Linear Algebra: Determinant when row is added
/ 902 viewsThe 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) More free lessons at: http://www.khanacademy.org/video?v=VrB3LaSD_uo
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02:52 Popular
Linear Algebra: (correction) scalar muliplication of row
/ 977 viewsCorrection of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant More free lessons at: http://www.khanacademy.org/video?v=WY6QG0mZ7uQ
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13:20
Linear Algebra: Determinant when row multiplied by scalar
/ 630 viewsThe determinant when a row is multiplied by a scalar More free lessons at: http://www.khanacademy.org/video?v=32rdijPB-rA
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07:18 Popular
Linear Algebra: Rule of Sarrus of Determinants
/ 708 viewsA alternative "short cut" for calculating 3x3 determinants (Rule of Sarrus) More free lessons at: http://www.khanacademy.org/video?v=4xFIi0JF2AM
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09:03
Linear Algebra: Determinants along other rows/cols
/ 652 viewsFinding the determinant by going along other rows or columns More free lessons at: http://www.khanacademy.org/video?v=nu87kfmwNfU
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18:40
Linear Algebra: nxn Determinant
/ 619 viewsDefining the determinant for nxn matrices. An exampled of a 4x4 determinant. More free lessons at: http://www.khanacademy.org/video?v=H9BWRYJNIv4
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10:01
Linear Algebra: 3x3 Determinant
/ 676 viewsDeterminants: Finding the determinant of a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=0c7dt2SQfLw
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18:20
Linear Algebra: Formula for 2x2 inverse
/ 657 viewsFiguring out the formula for a 2x2 matrix. Defining the determinant. More free lessons at: http://www.khanacademy.org/video?v=eEUK_ThrHuQ
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06:22
Linear Algebra: Example of Finding Matrix Inverse
/ 630 viewsExample of calculating the inverse of a matrix More free lessons at: http://www.khanacademy.org/video?v=r9aTLTN16V4
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18:00
Linear Algebra: Deriving a method for determining inverses
/ 617 viewsDetermining a method for constructing inverse transformation matrices More free lessons at: http://www.khanacademy.org/video?v=6DpzCKJBsz0
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21:25
Linear Algebra: Showing that Inverses are Linear
/ 599 viewsShowing that inverse transformations are also linear More free lessons at: http://www.khanacademy.org/video?v=mr9Tow8hpCg
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06:37
Linear Algebra: Simplifying conditions for invertibility
/ 630 viewsShowing that a transformation is invertible if and only if rref(A) is equal to the identity matrix More free lessons at: http://www.khanacademy.org/video?v=Yz2OosyMTmY
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20:00
Linear Algebra: Matrix condition for one-to-one trans
/ 677 viewsShowing that the rank of the of an mxn transformation matrix has to be an for the transformation to be one-to-one (injective) More free lessons at: http://www.khanacademy.org/video?v=M3FuL9qKTBs
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16:34 Popular
Linear Algebra: Exploring the solution set of Ax=b
/ 1,830 viewsExploring the solution set of Ax=b (non homogeneous equations) More free lessons at: http://www.khanacademy.org/video?v=1PsNIzUJPkc
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25:51
Determining whether a transformation is onto
/ 609 viewsDetermining whether a transformation is onto More free lessons at: http://www.khanacademy.org/video?v=eR8vEdJTvd0
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06:31
Relating invertibility to being onto and one-to-one
/ 627 viewsRelating invertibility to being onto (surjective) and one-to-one (injective) More free lessons at: http://www.khanacademy.org/video?v=QIU1daMN8fw
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09:32
Surjective (onto) and Injective (one-to-one) functions
/ 636 viewsIntroduction to surjective and injective functions More free lessons at: http://www.khanacademy.org/video?v=xKNX8BUWR0g
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22:41 Popular
Proof: Invertibility implies a unique solution to f(x)=y
/ 709 viewsProof: Invertibility implies a unique solution to f(x)=y for all y in co-domain of f. More free lessons at: http://www.khanacademy.org/video?v=7GEUgRcnfVE
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18:54
Linear Algebra: Introduction to the inverse of a function
/ 629 viewsIntroduction to the inverse of a function More free lessons at: http://www.khanacademy.org/video?v=-eAzhBZgq28
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09:52 Popular
Distributive Property of Matrix Products
/ 744 viewsShowing that matrix products exhibit the distributive property More free lessons at: http://www.khanacademy.org/video?v=oMWTMj78cwc
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11:59
Matrix Product Associativity
/ 697 viewsShowing that matrix products are associative More free lessons at: http://www.khanacademy.org/video?v=Hhc96U_HvQE
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18:14
Linear Algebra: Matrix Product Examples
/ 680 viewsExample of taking the product of two matrices More free lessons at: http://www.khanacademy.org/video?v=x1z0hOyjapU
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16:31
Compositions of Linear Transformations 2
/ 625 viewsProviding the motivation for definition of matrix products More free lessons at: http://www.khanacademy.org/video?v=BuqcKpe5ZQs
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12:21
Compositions of Linear Transformations 1
/ 642 viewsIntroduction to compositions of Linear Transformations More free lessons at: http://www.khanacademy.org/video?v=f_DTiXZpb8M
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16:41
Expressing a Projection on to a line as a Matrix Vector prod
/ 650 viewsExpressing a Projection on to a line as a Matrix Vector prod More free lessons at: http://www.khanacademy.org/video?v=JK-8XNIoAkI
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14:37
Introduction to Projections
/ 638 viewsDetermining the projection of a vector on s line More free lessons at: http://www.khanacademy.org/video?v=27vT-NWuw0M
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06:59
Unit Vectors
/ 668 viewsWhat unit vectors are and how to construct them More free lessons at: http://www.khanacademy.org/video?v=lQn7fksaDq0
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12:18
Rotation in R3 around the X-axis
/ 618 viewsConstruction a rotation transformation in R3 More free lessons at: http://www.khanacademy.org/video?v=gkyuLPzfDV0
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17:52
Linear Transformation Examples: Rotations in R2
/ 655 viewsLinear Transformation Examples: Rotations in R2 More free lessons at: http://www.khanacademy.org/video?v=lPWfIq5DzqI
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15:13
Linear Transformation Examples: Scaling and Reflections
/ 642 viewsCreating scaling and reflection transformation matrices (which are diagonal) More free lessons at: http://www.khanacademy.org/video?v=qkfODKmZ-x4
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10:42
More on Matrix Addition and Scalar Multiplication
/ 652 viewsMore on Matrix Addition and Scalar Multiplication More free lessons at: http://www.khanacademy.org/video?v=Z19-ObbmHJE
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15:09
Sums and Scalar Multiples of Linear Transformations
/ 626 viewsSums and Scalar Multiples of Linear Transformations. Definitions of matrix addition and scalar multiplication. More free lessons at: http://www.khanacademy.org/video?v=wHuY97vss18
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15:23
Preimage and Kernel Example
/ 686 viewsExample involving the preimage of a set under a transformation. Definition of kernel of a transformation. More free lessons at: http://www.khanacademy.org/video?v=6yrPU8rYOhs
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05:23 Popular
Preimage of a set
/ 801 viewsDefinition of preimage of a set More free lessons at: http://www.khanacademy.org/video?v=zVsGtU8lIWs
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16:37 Popular
im(T): Image of a Transformation
/ 720 viewsShowing that the image of a subspace under a transformation is also a subspace. Definition of the image of a Transformation. More free lessons at: http://www.khanacademy.org/video?v=hZ827mfh1Jo
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18:11
Image of a subset under a transformation
/ 648 viewsExploring what happens to a subset of the domain under a transformation More free lessons at: http://www.khanacademy.org/video?v=MIAmN5kgp3k
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17:32 Popular
Linear Transformations as Matrix Vector Products
/ 772 viewsShowing how ANY linear transformation can be represented as a matrix vector product More free lessons at: http://www.khanacademy.org/video?v=PErhLkQcpZ8
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17:04 Popular
Matrix Vector Products as Linear Transformations
/ 749 viewsMatrix Vector Products as Linear Transformations More free lessons at: http://www.khanacademy.org/video?v=ondmopWLiEg
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13:53
Linear Transformations
/ 623 viewsIntroduction to linear transformations More free lessons at: http://www.khanacademy.org/video?v=4PCktDZJH8E
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14:19
Vector Transformations
/ 583 viewsIntroduction to the notion of vector transformations More free lessons at: http://www.khanacademy.org/video?v=gAbadNuQEjI
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16:02 Popular
A more formal understanding of functions
/ 758 viewsA more formal understanding of functions More free lessons at: http://www.khanacademy.org/video?v=BQMyeQOLvpg
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13:40
Showing that the candidate basis does span C(A)
/ 618 viewsShowing that just the columns of A associated with the pivot columns of rref(A) do indeed span C(A). More free lessons at: http://www.khanacademy.org/video?v=CkQOCnLWPUA
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08:33
Showing relation between basis cols and pivot cols
/ 625 viewsShowing that linear independence of pivot columns implies linear independence of the corresponding columns in the original equation More free lessons at: http://www.khanacademy.org/video?v=BfVjTOjvI30
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12:48
Dimension of the Column Space or Rank
/ 632 viewsDimension of the Column Space or Rank More free lessons at: http://www.khanacademy.org/video?v=JUgrBkPteTg
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13:59 Popular
Dimension of the Null Space or Nullity
/ 786 viewsDimension of the Null Space or Nullity More free lessons at: http://www.khanacademy.org/video?v=abYAUqs_n6I
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21:35 Popular
Proof: Any subspace basis has same number of elements
/ 736 viewsProof: Any subspace basis has same number of elements More free lessons at: http://www.khanacademy.org/video?v=Zn2K8UIT8r4
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21:11
Visualizing a Column Space as a Plane in R3
/ 659 viewsDetermining the planar equation for a column space in R3 More free lessons at: http://www.khanacademy.org/video?v=EGNlXtjYABw
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25:13 Popular
Null Space and Column Space Basis
/ 852 viewsFiguring out the null space and a basis of a column space for a matrix More free lessons at: http://www.khanacademy.org/video?v=_uTAdf_AsfQ
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10:40
Column Space of a Matrix
/ 621 viewsIntroduction to the column space of a matrix More free lessons at: http://www.khanacademy.org/video?v=st6D5OdFV9M
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11:35
Null Space 3: Relation to Linear Independence
/ 657 viewsUnderstanding how the null space of a matrix relates to the linear independence of its column vectors More free lessons at: http://www.khanacademy.org/video?v=vFctYRhK2M0
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13:08
Null Space 2: Calculating the null space of a matrix
/ 684 viewsCalculating the null space of a matrix More free lessons at: http://www.khanacademy.org/video?v=qvyboGryeA8
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10:23
Introduction to the Null Space of a Matrix
/ 661 viewsShowing that the Null Space of a Matrix is a valid Subspace More free lessons at: http://www.khanacademy.org/video?v=jCwRV1QL_Xs
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21:10
Matrix Vector Products
/ 697 viewsDefining and understanding what it means to take the product of a matrix and a vector More free lessons at: http://www.khanacademy.org/video?v=7Mo4S2wyMg4
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12:08
Matrices: Reduced Row Echelon Form 3
/ 673 viewsAnd another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form More free lessons at: http://www.khanacademy.org/video?v=JVDrlTdzxiI
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07:37
Matrices: Reduced Row Echelon Form 2
/ 629 viewsAnother example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form More free lessons at: http://www.khanacademy.org/video?v=lP1DGtZ8Wys
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17:43
Matrices: Reduced Row Echelon Form 1
/ 619 viewsSolving a system of linear equations by putting an augmented matrix into reduced row echelon form More free lessons at: http://www.khanacademy.org/video?v=L0CmbneYETs
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19:14
Dot and Cross Product Comparison/Intuition
/ 597 viewsDot and Cross Product Comparison/Intuition More free lessons at: http://www.khanacademy.org/video?v=tdwFdzVqito
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18:09
Proof: Relationship between cross product and sin of angle
/ 669 viewsProof: Relationship between the cross product and sin of angle between vectors More free lessons at: http://www.khanacademy.org/video?v=7MKA2QlKvHc
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15:47
Linear Algebra: Cross Product Introduction
/ 562 viewsIntroduction to the cross product More free lessons at: http://www.khanacademy.org/video?v=pJzmiywagfY
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13:53
Defining a plane in R3 with a point and normal vector
/ 680 viewsDetermining the equation for a plane in R3 using a point on the plane and a normal vector More free lessons at: http://www.khanacademy.org/video?v=UJxgcVaNTqY
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25:11
Defining the angle between vectors
/ 685 viewsIntroducing the idea of an angle between two vectors More free lessons at: http://www.khanacademy.org/video?v=5AWob_z74Ks
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18:53
Linear Algebra: Vector Triangle Inequality
/ 595 viewsProving the triangle inequality for vectors in Rn More free lessons at: http://www.khanacademy.org/video?v=PsNidCBr5II
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16:56 Popular
Proof of the Cauchy-Schwarz Inequality
/ 722 viewsProof of the Cauchy-Schwarz Inequality More free lessons at: http://www.khanacademy.org/video?v=r2PogGDl8_U
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10:46
Proving Vector Dot Product Properties
/ 686 viewsProving the "associative", "distributive" and "commutative" properties for vector dot products. More free lessons at: http://www.khanacademy.org/video?v=rVQ3G9epCjw
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09:10
Vector Dot Product and Vector Length
/ 551 viewsDefinitions of the vector dot product and vector length More free lessons at: http://www.khanacademy.org/video?v=WNuIhXo39_k
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19:00
Linear Algebra: Basis of a Subspace
/ 571 viewsUnderstanding the definition of a basis of a subspace More free lessons at: http://www.khanacademy.org/video?v=zntNi3-ybfQ
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23:29
Linear Subspaces
/ 538 viewsIntroduction to linear subspaces of Rn More free lessons at: http://www.khanacademy.org/video?v=pMFv6liWK4M
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16:53
Span and Linear Independence Example
/ 525 viewsDetermining whether 3 vectors are linearly independent and/or span R3 More free lessons at: http://www.khanacademy.org/video?v=9kW6zFK5E5c
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17:38
More on linear independence
/ 546 viewsMore examples determining linear dependence or independence. More free lessons at: http://www.khanacademy.org/video?v=Alhcv5d_XOs
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15:46
Linear Algebra: Introduction to Linear Independence
/ 563 viewsLinear Algebra: Introduction to linear dependence and independence More free lessons at: http://www.khanacademy.org/video?v=CrV1xCWdY-g
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20:35
Linear Combinations and Span
/ 524 viewsUnderstanding linear combinations and spans of vectors More free lessons at: http://www.khanacademy.org/video?v=Qm_OS-8COwU
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24:47
Linear Algebra: Parametric Representations of Lines
/ 554 viewsLinear Algebra: Parametric Representations of Lines in R2 and R3 More free lessons at: http://www.khanacademy.org/video?v=hWhs2cIj7Cw
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25:34
Linear Algebra: Vector Examples
/ 552 viewsVisually understanding basic vector operations More free lessons at: http://www.khanacademy.org/video?v=r4bH66vYjss
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15:26
Solving 3 Equations with 3 Unknowns
/ 608 viewsSolving 3 equations with 3 unknowns (old video from July 2008)
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08:02 Popular
3-variable linear equations (part 1)
/ 705 viewsVisual intuition of a 3-variable linear equation.
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14:27
Singular Matrices
/ 686 viewsWhen and why you can't invert a matrix. More free lessons at: http://www.khanacademy.org/video?v=UqyN7-tRS00
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14:20
Matrices to solve a vector combination problem
/ 576 viewsUsing matrices to figure out if some combination of 2 vectors can create a 3rd vector More free lessons at: http://www.khanacademy.org/video?v=gsNgdVdAT1o
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16:33
Matrices to solve a system of equations
/ 573 viewsUsing the inverse of a matrix to solve a system of equations. More free lessons at: http://www.khanacademy.org/video?v=AUqeb9Z3y3k
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13:36
Inverting Matrices (part 3)
/ 664 viewsUsing Gauss-Jordan elimination to invert a 3x3 matrix. More free lessons at: http://www.khanacademy.org/video?v=obts_JDS6_Q
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16:45
Inverting matrices (part 2)
/ 502 viewsInverting a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=S4n-tQZnU6o
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14:15 Popular
Inverse Matrix (part 1)
/ 728 viewsTaking the inverse of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=iUQR0enP7RQ
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12:14
Using the Convolution Theorem to Solve an Initial Value Prob
/ 586 viewsUsing the Convolution Theorem to solve an initial value problem More free lessons at: http://www.khanacademy.org/video?v=rfyq32mHcYs
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13:46
The Convolution and the Laplace Transform
/ 589 viewsUnderstanding how the product of the Transforms of two functions relates to their convolution. More free lessons at: http://www.khanacademy.org/video?v=TJgBEI3drUc
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18:59
Introduction to the Convolution
/ 552 viewsIntroduction to the Convolution More free lessons at: http://www.khanacademy.org/video?v=IW4Reburjpc
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12:13
Laplace Transform of the Dirac Delta Function
/ 635 viewsFiguring out the Laplace Transform of the Dirac Delta Function More free lessons at: http://www.khanacademy.org/video?v=vhfjEpQWWeE
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17:48
Dirac Delta Function
/ 583 viewsIntroduction to the Dirac Delta Function More free lessons at: http://www.khanacademy.org/video?v=4qfdCwys2ew
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19:12 Popular
Laplace/Step Function Differential Equation
/ 732 viewsHairy differential equation involving a step function that we use the Laplace Transform to solve. More free lessons at: http://www.khanacademy.org/video?v=R0JY8oWsuOY
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19:15
Inverse Laplace Examples
/ 563 viewsUsing our toolkit to take some inverse Laplace Transforms More free lessons at: http://www.khanacademy.org/video?v=BbqbvSig6Mc
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24:16 Popular
Laplace Transform of the Unit Step Function
/ 776 viewsIntroduction to the unit step function and its Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=4Mr7aEHQr8E
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10:16
Laplace Transform of t^n: L{t^n}
/ 529 viewsLaplace Transform of t^n: L{t^n} More free lessons at: http://www.khanacademy.org/video?v=pZIaUx3UQoA
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09:07
Laplace Transform of : L{t}
/ 574 viewsDetermining the Laplace Transform of t More free lessons at: http://www.khanacademy.org/video?v=qhKJ1DG9kYY
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18:48
Using the Laplace Transform to solve a nonhomogenous eq
/ 481 viewsSolving a non-homogeneous differential equation using the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=nlUG4OKN1IY
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11:17
More Laplace Transform tools
/ 639 viewsA grab bag of things to know about the Laplace Transform. More free lessons at: http://www.khanacademy.org/video?v=_X_QwpXsdOs
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10:46
Laplace Transform solves an equation 2
/ 527 viewsSecond part of using the Laplace Transform to solve a differential equation. More free lessons at: http://www.khanacademy.org/video?v=EdQ7Q9VoF44
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10:52
Laplace Transform to solve an equation
/ 582 viewsUsing the Laplace Transform to solve an equation we already knew how to solve. More free lessons at: http://www.khanacademy.org/video?v=3uYb-RhM7lU
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09:46
Laplace Transform 6
/ 565 viewsLaplace transform of cosine and polynomials! More free lessons at: http://www.khanacademy.org/video?v=fyJkXBvcA2Q
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11:37 Popular
Laplace Transform 5
/ 711 viewsUseful properties of the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=E2VxbufzuWQ
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09:14
Laplace Transform 4
/ 533 viewsPart 2 of getting the Laplace transform of sin(at) More free lessons at: http://www.khanacademy.org/video?v=-cApVwKR1Ps
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10:45
Laplace Transform 3 (L{sin(at)})
/ 584 viewsLaplace Transform of sin(at) (part 1) More free lessons at: http://www.khanacademy.org/video?v=gMcs6RF_LrQ
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07:35
Laplace Transform 2
/ 562 viewsLaplace transform of e^at More free lessons at: http://www.khanacademy.org/video?v=33TYoybjqPg
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08:02
Laplace Transform 1
/ 528 viewsIntroduction to the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=OiNh2DswFt4
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05:55
Undetermined Coefficients 4
/ 543 viewsPutting it all together! More free lessons at: http://www.khanacademy.org/video?v=vAepSNDLZRM
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08:10
Undetermined Coefficients 3
/ 543 viewsAnother example where the nonhomogeneous part is a polynomial More free lessons at: http://www.khanacademy.org/video?v=I3vIAzMcm4Y
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11:01
Undetermined Coefficients 2
/ 485 viewsAnother example using undetermined coefficients. More free lessons at: http://www.khanacademy.org/video?v=hbJ2o9EUmJ0
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10:11
Undetermined Coefficients 1
/ 565 viewsUsing the method of undetermined coefficients to solve nonhomogeneous linear differential equations. More free lessons at: http://www.khanacademy.org/video?v=znE4Nq9NJCQ
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08:52
Repeated roots of the characterisitic equations part 2
/ 520 viewsAn example where we use initial conditions to solve a repeated-roots differential equation. More free lessons at: http://www.khanacademy.org/video?v=YezsgIlcb68
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11:58
Repeated roots of the characteristic equation
/ 485 viewsWhat happens when the characteristic equation only has 1 repeated root? More free lessons at: http://www.khanacademy.org/video?v=NW9JfMvIsxw
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10:12
Complex roots of the characteristic equations 3
/ 528 viewsLets do an example with initial conditions! More free lessons at: http://www.khanacademy.org/video?v=rGaM6pwqhB0
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10:24
Complex roots of the characteristic equations 2
/ 585 viewsWhat happens when the characteristic equation has complex roots? More free lessons at: http://www.khanacademy.org/video?v=jJyRrIZ595c
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10:28
Complex roots of the characteristic equations 1
/ 566 viewsWhat happens when the characteristic equations has complex roots?! More free lessons at: http://www.khanacademy.org/video?v=6xEO4BeawzA
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09:11
2nd Order Linear Homogeneous Differential Equations 4
/ 623 viewsAnother example with initial conditions! More free lessons at: http://www.khanacademy.org/video?v=3uO_uPb9H8w
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05:59
2nd Order Linear Homogeneous Differential Equations 3
/ 565 viewsLet's use some initial conditions to solve for the particular solution More free lessons at: http://www.khanacademy.org/video?v=UyCwAFQt4v0
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08:28
2nd Order Linear Homogeneous Differential Equations 2
/ 582 viewsLet's find the general solution! More free lessons at: http://www.khanacademy.org/video?v=SPVqgkOZMAc
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09:45
2nd Order Linear Homogeneous Differential Equations 1
/ 574 viewsIntroduction to 2nd order, linear, homogeneous differential equations with constant coefficients. More free lessons at: http://www.khanacademy.org/video?v=UFWAu8Ptth0
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08:23
First order homogenous equations 2
/ 563 viewsAnother example of using substitution to solve a first order homogeneous differential equations. More free lessons at: http://www.khanacademy.org/video?v=6YRGEsQWZzY
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07:22
First order homegenous equations
/ 594 viewsIntroduction to first order homogenous equations. More free lessons at: http://www.khanacademy.org/video?v=9Wfn-WWV1aY
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08:26
Integrating factors 2
/ 488 viewsNow that we've made the equation exact, let's solve it! More free lessons at: http://www.khanacademy.org/video?v=0NyeDUhKwBE
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10:17
Integrating factors 1
/ 541 viewsUsing an integrating factor to make a differential equation exact More free lessons at: http://www.khanacademy.org/video?v=j511hg7Hlbg
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09:59
Exact Equations Example 3
/ 536 viewsOne more exact equation example More free lessons at: http://www.khanacademy.org/video?v=eu_GFuU7tLI
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08:01
Exact Equations Example 2
/ 546 viewsSome more exact equation examples More free lessons at: http://www.khanacademy.org/video?v=utQi1ZhF__Q
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12:10
Exact Equations Example 1
/ 547 viewsFirst example of solving an exact differential equation. More free lessons at: http://www.khanacademy.org/video?v=Pb04ntcDJcQ
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10:51
Exact Equations Intuition 2 (proofy)
/ 556 viewsMore intuitive building blocks for exact equations. More free lessons at: http://www.khanacademy.org/video?v=a7wYAtMjORQ
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09:54
Exact Equations Intuition 1 (proofy)
/ 692 viewsChain rule using partial derivatives (not a proof; more intuition). More free lessons at: http://www.khanacademy.org/video?v=iEpqcdaJNTQ
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05:38
Separable differential equations 2
/ 611 viewsAnother separable differential equation example. More free lessons at: http://www.khanacademy.org/video?v=xVWCfMe97ws
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12:01
Separable Differential Equations
/ 572 viewsIntroduction to separable differential equations. More free lessons at: http://www.khanacademy.org/video?v=C5-lz0hcqsE
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11:03
What is a differential equation
/ 580 viewsWhat a differential equation is and some terminology.