Linear Algebra

04:30
Identifying Non Equivalent Systems
Added 102 Views / 0 LikesIdentifying non equivalent systems

15:34
Linear Algebra: Eigenvectors and Eigenspaces for a 3x3 matrix
Added 153 Views / 0 LikesEigenvectors and eigenspaces for a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=3Md5KCCQX0

14:08
Linear Algebra: Eigenvalues of a 3x3 matrix
Added 161 Views / 0 LikesDetermining the eigenvalues of a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=11dNghWC4HI

14:34
Linear Algebra: Finding Eigenvectors and Eigenspaces example
Added 177 Views / 0 LikesFinding the eigenvectors and eigenspaces of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=3xfmbdzkqc

05:39
Linear Algebra: Example solving for the eigenvalues of a 2x2 matrix
Added 181 Views / 0 LikesExample solving for the eigenvalues of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=pZ6mMVEE89g

09:19
Linear Algebra: Proof of formula for determining Eigenvalues
Added 174 Views / 0 LikesProof of formula for determining Eigenvalues More free lessons at: http://www.khanacademy.org/video?v=rfm0wQObxjk

07:43
Linear Algebra: Introduction to Eigenvalues and Eigenvectors
Added 147 Views / 0 LikesWhat eigenvectors and eigenvalues are and why they are interesting More free lessons at: http://www.khanacademy.org/video?v=PhfbEr2btGQ

13:57
Linear Algebra: GramSchmidt example with 3 basis vectors
Added 156 Views / 0 LikesGramSchmidt example with 3 basis vectors More free lessons at: http://www.khanacademy.org/video?v=ZRRG386v6DI

13:14
Linear Algebra: GramSchmidt Process Example
Added 157 Views / 0 LikesUsing GramSchmidt to find an orthonormal basis for a plane in R3 More free lessons at: http://www.khanacademy.org/video?v=tu1GPtfsQ7M

19:24
Linear Algebra: The GramSchmidt Process
Added 148 Views / 0 LikesFinding an orthonormal basis for a subspace using the GramSchmidt Process More free lessons at: http://www.khanacademy.org/video?v=rHonltF77zI

11:16
Lin Alg: Orthogonal matrices preserve angles and lengths
Added 150 Views / 0 LikesShowing that orthogonal matrices preserve angles and lengths More free lessons at: http://www.khanacademy.org/video?v=yDwIfYjKEeo

27:04
Lin Alg: Example using orthogonal changeofbasis matrix to find transformation matrix
Added 157 Views / 0 LikesExample using orthogonal changeofbasis matrix to find transformation matrix More free lessons at: http://www.khanacademy.org/video?v=gfVY7cW7VLQ

06:42
Lin Alg: Finding projection onto subspace with orthonormal basis example
Added 176 Views / 0 LikesExample 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

16:14
Lin Alg: Projections onto subspaces with orthonormal bases
Added 147 Views / 0 LikesProjections onto subspaces with orthonormal bases More free lessons at: http://www.khanacademy.org/video?v=we829K4NOq8

15:28
Linear Algebra: Coordinates with respect to orthonormal bases
Added 158 Views / 0 LikesSeeing that orthonormal bases make for good coordinate systems More free lessons at: http://www.khanacademy.org/video?v=SWbis2zWIvo

11:16
Linear Algebra: Introduction to Orthonormal Bases
Added 149 Views / 0 LikesLooking 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

29:00
Lin Alg: Changing coordinate systems to help find a transformation matrix
Added 217 Views / 0 LikesChanging 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

12:36
Lin Alg: Alternate Basis Tranformation Matrix Example Part 2
Added 161 Views / 0 LikesShowing 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

13:20
Lin Alg: Alternate Basis Tranformation Matrix Example
Added 169 Views / 0 LikesExample of finding the transformation matrix for an alternate basis More free lessons at: http://www.khanacademy.org/video?v=lCRGNykWqFI

18:02
Lin Alg: Transformation Matrix with Respect to a Basis
Added 171 Views / 0 LikesFinding the transformation matrix with respect to a nonstandard basis More free lessons at: http://www.khanacademy.org/video?v=PiuhTj0zCf4

13:34
Lin Alg: Invertible Change of Basis Matrix
Added 157 Views / 0 LikesUsing an invertible change of basis matrix to go between different coordinate systems More free lessons at: http://www.khanacademy.org/video?v=meibWcbGqt4

17:55
Linear Algebra: Change of Basis Matrix
Added 185 Views / 0 LikesUsing 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

16:08
Linear Algebra: Coordinates with Respect to a Basis
Added 161 Views / 0 LikesUnderstanding alternate coordinate systems More free lessons at: http://www.khanacademy.org/video?v=uvgru6FcyxU

13:25
Linear Algebra: Another Least Squares Example
Added 154 Views / 0 LikesUsing least squares approximation to fit a line to points More free lessons at: http://www.khanacademy.org/video?v=QkepM8Vv3kw

18:50
Linear Algebra: Least Squares Examples
Added 158 Views / 0 LikesAn example using the least squares solution to an unsolvable system More free lessons at: http://www.khanacademy.org/video?v=8mAZYv5wIcE

15:32
Linear Algebra: Least Squares Approximation
Added 159 Views / 0 LikesThe least squares approximation for otherwise unsolvable equations More free lessons at: http://www.khanacademy.org/video?v=MC7l96tW8V8

09:05
Linear Alg: Projection is closest vector in subspace
Added 183 Views / 0 LikesShowing 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

21:36
Lin Alg: Another Example of a Projection Matrix
Added 161 Views / 0 LikesFiguring 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

13:04
Linear Algebra: Subspace Projection Matrix Example
Added 233 Views / 0 LikesExample of a transformation matrix for a projection onto a subspace More free lessons at: http://www.khanacademy.org/video?v=QTcSBB3uVP0

16:16
Lin Alg: A Projection onto a Subspace is a Linear Transforma
Added 182 Views / 0 LikesShowing that a projection onto a subspace is a linear transformation More free lessons at: http://www.khanacademy.org/video?v=cTyNpXB92bQ

09:28
Linear Alg: Visualizing a projection onto a plane
Added 156 Views / 0 LikesVisualizing 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

17:26
Linear Algebra: Projections onto Subspaces
Added 162 Views / 0 LikesProjections onto subspaces More free lessons at: http://www.khanacademy.org/video?v=5B8XluiqdHM

12:34
Lin Alg: Showing that Atranspose x A is invertible
Added 198 Views / 0 LikesShowing that (transpose of A)(A) is invertible if A has linearly independent columns More free lessons at: http://www.khanacademy.org/video?v=ESSMQH6Y5OA

19:38
Linear Alg: Rowspace Solution to Ax=b example
Added 152 Views / 0 LikesVisualizing the rowspace solution to Ax=b More free lessons at: http://www.khanacademy.org/video?v=qdf2CuMGdKs

19:12
Lin Alg: Unique rowspace solution to Ax=b
Added 177 Views / 0 LikesShowing 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

03:27
Lin Alg: Orthogonal Complement of the Nullspace
Added 161 Views / 0 LikesThe orthogonal complement of the nullspace and left nullspace. More free lessons at: http://www.khanacademy.org/video?v=LE_aQAur7nI

12:18
Lin Alg: Orthogonal Complement of the Orthogonal Complement
Added 164 Views / 0 LikesFinding that the orthogonal complement of the orthogonal complement of V is V More free lessons at: http://www.khanacademy.org/video?v=zlI8mx8Hc8o

27:01
Lin Alg: Representing vectors in Rn using subspace members
Added 148 Views / 0 LikesShowing 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

09:27
Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n
Added 160 Views / 0 LikesShowing 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

11:14
Linear Algebra: Rank(A) = Rank(transpose of A)
Added 179 Views / 0 LikesRank(A) = Rank(transpose of A) More free lessons at: http://www.khanacademy.org/video?v=tqqVOWm9YsU

22:08
Linear Algebra: Orthogonal Complements
Added 154 Views / 0 LikesOrthogonal Complements as subspaces. More free lessons at: http://www.khanacademy.org/video?v=QOTjdgmNqlg

19:50
Lin Alg: Visualizations of Left Nullspace and Rowspace
Added 153 Views / 0 LikesRelationship between left nullspace, rowspace, column space and nullspace. More free lessons at: http://www.khanacademy.org/video?v=GW8ZPjGlk24

23:19
Linear Algebra: Rowspace and Left Nullspace
Added 167 Views / 0 LikesRowspace and Left Nullspace More free lessons at: http://www.khanacademy.org/video?v=qBfc57x_RSg

12:07
Linear Algebra: Transpose of a Vector
Added 135 Views / 0 LikesTranspose of a column vector. Matrixmatrix products using vectors More free lessons at: http://www.khanacademy.org/video?v=lSoaMCNKfAg

08:41
Linear Algebra: Transposes of sums and inverses
Added 143 Views / 0 LikesTransposes of sums and inverses More free lessons at: http://www.khanacademy.org/video?v=Br_8t58mdeI

08:50
Linear Algebra: Transpose of a Matrix Product
Added 149 Views / 0 LikesTaking the transpose of the product of two matrices More free lessons at: http://www.khanacademy.org/video?v=UdHgWK13x5I

14:10
Linear Algebra: Determinant of Transpose
Added 161 Views / 0 LikesProof by induction that transposing a matrix does not change its determinant More free lessons at: http://www.khanacademy.org/video?v=xGV2v0dRNE

08:37
Linear Algebra: Transpose of a Matrix
Added 156 Views / 0 LikesTranspose of a matrix More free lessons at: http://www.khanacademy.org/video?v=2t0003_sxtU

20:10
Linear Algebra: Determinant as Scaling Factor
Added 165 Views / 0 LikesViewing the determinant of the transformation matrix as a scaling factor of regions More free lessons at: http://www.khanacademy.org/video?v=g3MqSdO5Ubc

21:38
Linear Algebra: Determinant and area of a parallelogram
Added 202 Views / 0 LikesRealizing 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=nS63_goDFg

09:13
Linear Algebra: Simpler 4x4 determinant
Added 148 Views / 0 LikesCalculating a 4x4 determinant by putting in in upper triangular form first. More free lessons at: http://www.khanacademy.org/video?v=QV0jsTiobU4

08:07
Linear Algebra: Upper Triangular Determinant
Added 150 Views / 0 LikesThe determinant of an upper triangular matrix More free lessons at: http://www.khanacademy.org/video?v=VX7K8iqoiRc

10:25
Linear Algebra: Determinant after row operations
Added 150 Views / 0 LikesWhat happens to the determinant when we perform a row operation More free lessons at: http://www.khanacademy.org/video?v=kpG7xySkivg

08:19
Linear Algebra: Duplicate Row Determinant
Added 161 Views / 0 LikesDeterminant of a matrix with duplicate rows More free lessons at: http://www.khanacademy.org/video?v=gYv8sttBIqs

16:55
Linear Algebra: Determinant when row is added
Added 148 Views / 0 LikesThe 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

02:52
Linear Algebra: (correction) scalar muliplication of row
Added 141 Views / 0 LikesCorrection 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

13:20
Linear Algebra: Determinant when row multiplied by scalar
Added 149 Views / 0 LikesThe determinant when a row is multiplied by a scalar More free lessons at: http://www.khanacademy.org/video?v=32rdijPBrA

07:18
Linear Algebra: Rule of Sarrus of Determinants
Added 155 Views / 0 LikesA alternative "short cut" for calculating 3x3 determinants (Rule of Sarrus) More free lessons at: http://www.khanacademy.org/video?v=4xFIi0JF2AM

09:03
Linear Algebra: Determinants along other rows/cols
Added 135 Views / 0 LikesFinding the determinant by going along other rows or columns More free lessons at: http://www.khanacademy.org/video?v=nu87kfmwNfU

18:40
Linear Algebra: nxn Determinant
Added 150 Views / 0 LikesDefining the determinant for nxn matrices. An exampled of a 4x4 determinant. More free lessons at: http://www.khanacademy.org/video?v=H9BWRYJNIv4

10:01
Linear Algebra: 3x3 Determinant
Added 140 Views / 0 LikesDeterminants: Finding the determinant of a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=0c7dt2SQfLw

18:20
Linear Algebra: Formula for 2x2 inverse
Added 152 Views / 0 LikesFiguring out the formula for a 2x2 matrix. Defining the determinant. More free lessons at: http://www.khanacademy.org/video?v=eEUK_ThrHuQ

06:22
Linear Algebra: Example of Finding Matrix Inverse
Added 143 Views / 0 LikesExample of calculating the inverse of a matrix More free lessons at: http://www.khanacademy.org/video?v=r9aTLTN16V4

18:00
Linear Algebra: Deriving a method for determining inverses
Added 146 Views / 0 LikesDetermining a method for constructing inverse transformation matrices More free lessons at: http://www.khanacademy.org/video?v=6DpzCKJBsz0

21:25
Linear Algebra: Showing that Inverses are Linear
Added 142 Views / 0 LikesShowing that inverse transformations are also linear More free lessons at: http://www.khanacademy.org/video?v=mr9Tow8hpCg

06:37
Linear Algebra: Simplifying conditions for invertibility
Added 133 Views / 0 LikesShowing 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

20:00
Linear Algebra: Matrix condition for onetoone trans
Added 156 Views / 0 LikesShowing that the rank of the of an mxn transformation matrix has to be an for the transformation to be onetoone (injective) More free lessons at: http://www.khanacademy.org/video?v=M3FuL9qKTBs

16:34
Linear Algebra: Exploring the solution set of Ax=b
Added 148 Views / 0 LikesExploring the solution set of Ax=b (non homogeneous equations) More free lessons at: http://www.khanacademy.org/video?v=1PsNIzUJPkc

25:51
Determining whether a transformation is onto
Added 159 Views / 0 LikesDetermining whether a transformation is onto More free lessons at: http://www.khanacademy.org/video?v=eR8vEdJTvd0

06:31
Relating invertibility to being onto and onetoone
Added 141 Views / 0 LikesRelating invertibility to being onto (surjective) and onetoone (injective) More free lessons at: http://www.khanacademy.org/video?v=QIU1daMN8fw

09:32
Surjective (onto) and Injective (onetoone) functions
Added 149 Views / 0 LikesIntroduction to surjective and injective functions More free lessons at: http://www.khanacademy.org/video?v=xKNX8BUWR0g

22:41
Proof: Invertibility implies a unique solution to f(x)=y
Added 155 Views / 0 LikesProof: Invertibility implies a unique solution to f(x)=y for all y in codomain of f. More free lessons at: http://www.khanacademy.org/video?v=7GEUgRcnfVE

18:54
Linear Algebra: Introduction to the inverse of a function
Added 155 Views / 0 LikesIntroduction to the inverse of a function More free lessons at: http://www.khanacademy.org/video?v=eAzhBZgq28

09:52
Distributive Property of Matrix Products
Added 153 Views / 0 LikesShowing that matrix products exhibit the distributive property More free lessons at: http://www.khanacademy.org/video?v=oMWTMj78cwc

11:59
Matrix Product Associativity
Added 163 Views / 0 LikesShowing that matrix products are associative More free lessons at: http://www.khanacademy.org/video?v=Hhc96U_HvQE

18:14
Linear Algebra: Matrix Product Examples
Added 147 Views / 0 LikesExample of taking the product of two matrices More free lessons at: http://www.khanacademy.org/video?v=x1z0hOyjapU

16:31
Compositions of Linear Transformations 2
Added 145 Views / 0 LikesProviding the motivation for definition of matrix products More free lessons at: http://www.khanacademy.org/video?v=BuqcKpe5ZQs

12:21
Compositions of Linear Transformations 1
Added 149 Views / 0 LikesIntroduction to compositions of Linear Transformations More free lessons at: http://www.khanacademy.org/video?v=f_DTiXZpb8M

16:41
Expressing a Projection on to a line as a Matrix Vector prod
Added 159 Views / 0 LikesExpressing a Projection on to a line as a Matrix Vector prod More free lessons at: http://www.khanacademy.org/video?v=JK8XNIoAkI

14:37
Introduction to Projections
Added 146 Views / 0 LikesDetermining the projection of a vector on s line More free lessons at: http://www.khanacademy.org/video?v=27vTNWuw0M

06:59
Unit Vectors
Added 153 Views / 0 LikesWhat unit vectors are and how to construct them More free lessons at: http://www.khanacademy.org/video?v=lQn7fksaDq0

12:18
Rotation in R3 around the Xaxis
Added 144 Views / 0 LikesConstruction a rotation transformation in R3 More free lessons at: http://www.khanacademy.org/video?v=gkyuLPzfDV0

17:52
Linear Transformation Examples: Rotations in R2
Added 146 Views / 0 LikesLinear Transformation Examples: Rotations in R2 More free lessons at: http://www.khanacademy.org/video?v=lPWfIq5DzqI

15:13
Linear Transformation Examples: Scaling and Reflections
Added 154 Views / 0 LikesCreating scaling and reflection transformation matrices (which are diagonal) More free lessons at: http://www.khanacademy.org/video?v=qkfODKmZx4

10:42
More on Matrix Addition and Scalar Multiplication
Added 144 Views / 0 LikesMore on Matrix Addition and Scalar Multiplication More free lessons at: http://www.khanacademy.org/video?v=Z19ObbmHJE

15:09
Sums and Scalar Multiples of Linear Transformations
Added 151 Views / 0 LikesSums and Scalar Multiples of Linear Transformations. Definitions of matrix addition and scalar multiplication. More free lessons at: http://www.khanacademy.org/video?v=wHuY97vss18

15:23
Preimage and Kernel Example
Added 141 Views / 0 LikesExample 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

05:23
Preimage of a set
Added 148 Views / 0 LikesDefinition of preimage of a set More free lessons at: http://www.khanacademy.org/video?v=zVsGtU8lIWs

16:37
im(T): Image of a Transformation
Added 154 Views / 0 LikesShowing 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

18:11
Image of a subset under a transformation
Added 143 Views / 0 LikesExploring what happens to a subset of the domain under a transformation More free lessons at: http://www.khanacademy.org/video?v=MIAmN5kgp3k

17:32
Linear Transformations as Matrix Vector Products
Added 154 Views / 0 LikesShowing how ANY linear transformation can be represented as a matrix vector product More free lessons at: http://www.khanacademy.org/video?v=PErhLkQcpZ8

17:04
Matrix Vector Products as Linear Transformations
Added 155 Views / 0 LikesMatrix Vector Products as Linear Transformations More free lessons at: http://www.khanacademy.org/video?v=ondmopWLiEg

13:53
Linear Transformations
Added 138 Views / 0 LikesIntroduction to linear transformations More free lessons at: http://www.khanacademy.org/video?v=4PCktDZJH8E

14:19
Vector Transformations
Added 138 Views / 0 LikesIntroduction to the notion of vector transformations More free lessons at: http://www.khanacademy.org/video?v=gAbadNuQEjI

16:02
A more formal understanding of functions
Added 163 Views / 0 LikesA more formal understanding of functions More free lessons at: http://www.khanacademy.org/video?v=BQMyeQOLvpg

13:40
Showing that the candidate basis does span C(A)
Added 158 Views / 0 LikesShowing 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

08:33
Showing relation between basis cols and pivot cols
Added 148 Views / 0 LikesShowing 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

12:48
Dimension of the Column Space or Rank
Added 147 Views / 0 LikesDimension of the Column Space or Rank More free lessons at: http://www.khanacademy.org/video?v=JUgrBkPteTg

13:59
Dimension of the Null Space or Nullity
Added 160 Views / 0 LikesDimension of the Null Space or Nullity More free lessons at: http://www.khanacademy.org/video?v=abYAUqs_n6I

21:35
Proof: Any subspace basis has same number of elements
Added 183 Views / 0 LikesProof: Any subspace basis has same number of elements More free lessons at: http://www.khanacademy.org/video?v=Zn2K8UIT8r4

21:11
Visualizing a Column Space as a Plane in R3
Added 156 Views / 0 LikesDetermining the planar equation for a column space in R3 More free lessons at: http://www.khanacademy.org/video?v=EGNlXtjYABw

25:13
Null Space and Column Space Basis
Added 174 Views / 0 LikesFiguring 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

10:40
Column Space of a Matrix
Added 145 Views / 0 LikesIntroduction to the column space of a matrix More free lessons at: http://www.khanacademy.org/video?v=st6D5OdFV9M

11:35
Null Space 3: Relation to Linear Independence
Added 74 Views / 0 LikesUnderstanding 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

13:08
Null Space 2: Calculating the null space of a matrix
Added 99 Views / 0 LikesCalculating the null space of a matrix More free lessons at: http://www.khanacademy.org/video?v=qvyboGryeA8

10:23
Introduction to the Null Space of a Matrix
Added 84 Views / 0 LikesShowing that the Null Space of a Matrix is a valid Subspace More free lessons at: http://www.khanacademy.org/video?v=jCwRV1QL_Xs

21:10
Matrix Vector Products
Added 92 Views / 0 LikesDefining 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

12:08
Matrices: Reduced Row Echelon Form 3
Added 90 Views / 0 LikesAnd 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

07:37
Matrices: Reduced Row Echelon Form 2
Added 76 Views / 0 LikesAnother 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

17:43
Matrices: Reduced Row Echelon Form 1
Added 79 Views / 0 LikesSolving 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

19:14
Dot and Cross Product Comparison/Intuition
Added 90 Views / 0 LikesDot and Cross Product Comparison/Intuition More free lessons at: http://www.khanacademy.org/video?v=tdwFdzVqito

18:09
Proof: Relationship between cross product and sin of angle
Added 119 Views / 0 LikesProof: Relationship between the cross product and sin of angle between vectors More free lessons at: http://www.khanacademy.org/video?v=7MKA2QlKvHc

15:47
Linear Algebra: Cross Product Introduction
Added 72 Views / 0 LikesIntroduction to the cross product More free lessons at: http://www.khanacademy.org/video?v=pJzmiywagfY

13:53
Defining a plane in R3 with a point and normal vector
Added 146 Views / 0 LikesDetermining 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

25:11
Defining the angle between vectors
Added 81 Views / 0 LikesIntroducing the idea of an angle between two vectors More free lessons at: http://www.khanacademy.org/video?v=5AWob_z74Ks

18:53
Linear Algebra: Vector Triangle Inequality
Added 89 Views / 0 LikesProving the triangle inequality for vectors in Rn More free lessons at: http://www.khanacademy.org/video?v=PsNidCBr5II

16:56
Proof of the CauchySchwarz Inequality
Added 131 Views / 0 LikesProof of the CauchySchwarz Inequality More free lessons at: http://www.khanacademy.org/video?v=r2PogGDl8_U

10:46
Proving Vector Dot Product Properties
Added 78 Views / 0 LikesProving the "associative", "distributive" and "commutative" properties for vector dot products. More free lessons at: http://www.khanacademy.org/video?v=rVQ3G9epCjw

09:10
Vector Dot Product and Vector Length
Added 71 Views / 0 LikesDefinitions of the vector dot product and vector length More free lessons at: http://www.khanacademy.org/video?v=WNuIhXo39_k

19:00
Linear Algebra: Basis of a Subspace
Added 91 Views / 0 LikesUnderstanding the definition of a basis of a subspace More free lessons at: http://www.khanacademy.org/video?v=zntNi3ybfQ

23:29
Linear Subspaces
Added 73 Views / 0 LikesIntroduction to linear subspaces of Rn More free lessons at: http://www.khanacademy.org/video?v=pMFv6liWK4M

16:53
Span and Linear Independence Example
Added 66 Views / 0 LikesDetermining whether 3 vectors are linearly independent and/or span R3 More free lessons at: http://www.khanacademy.org/video?v=9kW6zFK5E5c

17:38
More on linear independence
Added 70 Views / 0 LikesMore examples determining linear dependence or independence. More free lessons at: http://www.khanacademy.org/video?v=Alhcv5d_XOs

15:46
Linear Algebra: Introduction to Linear Independence
Added 77 Views / 0 LikesLinear Algebra: Introduction to linear dependence and independence More free lessons at: http://www.khanacademy.org/video?v=CrV1xCWdYg

20:35
Linear Combinations and Span
Added 66 Views / 0 LikesUnderstanding linear combinations and spans of vectors More free lessons at: http://www.khanacademy.org/video?v=Qm_OS8COwU

24:47
Linear Algebra: Parametric Representations of Lines
Added 85 Views / 0 LikesLinear Algebra: Parametric Representations of Lines in R2 and R3 More free lessons at: http://www.khanacademy.org/video?v=hWhs2cIj7Cw

25:34
Linear Algebra: Vector Examples
Added 85 Views / 0 LikesVisually understanding basic vector operations More free lessons at: http://www.khanacademy.org/video?v=r4bH66vYjss

15:26
Solving 3 Equations with 3 Unknowns
Added 92 Views / 0 LikesSolving 3 equations with 3 unknowns (old video from July 2008)

08:02
3variable linear equations (part 1)
Added 67 Views / 0 LikesVisual intuition of a 3variable linear equation.

14:27
Singular Matrices
Added 86 Views / 0 LikesWhen and why you can't invert a matrix. More free lessons at: http://www.khanacademy.org/video?v=UqyN7tRS00

14:20
Matrices to solve a vector combination problem
Added 77 Views / 0 LikesUsing 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

16:33
Matrices to solve a system of equations
Added 70 Views / 0 LikesUsing the inverse of a matrix to solve a system of equations. More free lessons at: http://www.khanacademy.org/video?v=AUqeb9Z3y3k

13:36
Inverting Matrices (part 3)
Added 78 Views / 0 LikesUsing GaussJordan elimination to invert a 3x3 matrix. More free lessons at: http://www.khanacademy.org/video?v=obts_JDS6_Q

16:45
Inverting matrices (part 2)
Added 72 Views / 0 LikesInverting a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=S4ntQZnU6o

14:15
Inverse Matrix (part 1)
Added 90 Views / 0 LikesTaking the inverse of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=iUQR0enP7RQ

11:51
Introduction to matrices
Added 68 Views / 0 LikesWhat a matrix is. How to add and subtract them.

12:14
Using the Convolution Theorem to Solve an Initial Value Prob
Added 72 Views / 0 LikesUsing the Convolution Theorem to solve an initial value problem More free lessons at: http://www.khanacademy.org/video?v=rfyq32mHcYs

13:46
The Convolution and the Laplace Transform
Added 77 Views / 0 LikesUnderstanding how the product of the Transforms of two functions relates to their convolution. More free lessons at: http://www.khanacademy.org/video?v=TJgBEI3drUc

18:59
Introduction to the Convolution
Added 83 Views / 0 LikesIntroduction to the Convolution More free lessons at: http://www.khanacademy.org/video?v=IW4Reburjpc

12:13
Laplace Transform of the Dirac Delta Function
Added 84 Views / 0 LikesFiguring out the Laplace Transform of the Dirac Delta Function More free lessons at: http://www.khanacademy.org/video?v=vhfjEpQWWeE

17:48
Dirac Delta Function
Added 64 Views / 0 LikesIntroduction to the Dirac Delta Function More free lessons at: http://www.khanacademy.org/video?v=4qfdCwys2ew

19:12
Laplace/Step Function Differential Equation
Added 88 Views / 0 LikesHairy 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

19:15
Inverse Laplace Examples
Added 69 Views / 0 LikesUsing our toolkit to take some inverse Laplace Transforms More free lessons at: http://www.khanacademy.org/video?v=BbqbvSig6Mc

24:16
Laplace Transform of the Unit Step Function
Added 107 Views / 0 LikesIntroduction to the unit step function and its Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=4Mr7aEHQr8E

10:16
Laplace Transform of t^n: L{t^n}
Added 77 Views / 0 LikesLaplace Transform of t^n: L{t^n} More free lessons at: http://www.khanacademy.org/video?v=pZIaUx3UQoA

09:07
Laplace Transform of : L{t}
Added 85 Views / 0 LikesDetermining the Laplace Transform of t More free lessons at: http://www.khanacademy.org/video?v=qhKJ1DG9kYY

18:48
Using the Laplace Transform to solve a nonhomogenous eq
Added 80 Views / 0 LikesSolving a nonhomogeneous differential equation using the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=nlUG4OKN1IY

11:17
More Laplace Transform tools
Added 84 Views / 0 LikesA grab bag of things to know about the Laplace Transform. More free lessons at: http://www.khanacademy.org/video?v=_X_QwpXsdOs

10:46
Laplace Transform solves an equation 2
Added 84 Views / 0 LikesSecond part of using the Laplace Transform to solve a differential equation. More free lessons at: http://www.khanacademy.org/video?v=EdQ7Q9VoF44

10:52
Laplace Transform to solve an equation
Added 71 Views / 0 LikesUsing the Laplace Transform to solve an equation we already knew how to solve. More free lessons at: http://www.khanacademy.org/video?v=3uYbRhM7lU

09:46
Laplace Transform 6
Added 72 Views / 0 LikesLaplace transform of cosine and polynomials! More free lessons at: http://www.khanacademy.org/video?v=fyJkXBvcA2Q

11:37
Laplace Transform 5
Added 74 Views / 0 LikesUseful properties of the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=E2VxbufzuWQ

09:14
Laplace Transform 4
Added 70 Views / 0 LikesPart 2 of getting the Laplace transform of sin(at) More free lessons at: http://www.khanacademy.org/video?v=cApVwKR1Ps

10:45
Laplace Transform 3 (L{sin(at)})
Added 69 Views / 0 LikesLaplace Transform of sin(at) (part 1) More free lessons at: http://www.khanacademy.org/video?v=gMcs6RF_LrQ

07:35
Laplace Transform 2
Added 63 Views / 0 LikesLaplace transform of e^at More free lessons at: http://www.khanacademy.org/video?v=33TYoybjqPg

08:02
Laplace Transform 1
Added 71 Views / 0 LikesIntroduction to the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=OiNh2DswFt4

05:55
Undetermined Coefficients 4
Added 73 Views / 0 LikesPutting it all together! More free lessons at: http://www.khanacademy.org/video?v=vAepSNDLZRM

08:10
Undetermined Coefficients 3
Added 58 Views / 0 LikesAnother example where the nonhomogeneous part is a polynomial More free lessons at: http://www.khanacademy.org/video?v=I3vIAzMcm4Y

11:01
Undetermined Coefficients 2
Added 63 Views / 0 LikesAnother example using undetermined coefficients. More free lessons at: http://www.khanacademy.org/video?v=hbJ2o9EUmJ0

10:11
Undetermined Coefficients 1
Added 79 Views / 0 LikesUsing the method of undetermined coefficients to solve nonhomogeneous linear differential equations. More free lessons at: http://www.khanacademy.org/video?v=znE4Nq9NJCQ

08:52
Repeated roots of the characterisitic equations part 2
Added 70 Views / 0 LikesAn example where we use initial conditions to solve a repeatedroots differential equation. More free lessons at: http://www.khanacademy.org/video?v=YezsgIlcb68

11:58
Repeated roots of the characteristic equation
Added 68 Views / 0 LikesWhat happens when the characteristic equation only has 1 repeated root? More free lessons at: http://www.khanacademy.org/video?v=NW9JfMvIsxw

10:12
Complex roots of the characteristic equations 3
Added 62 Views / 0 LikesLets do an example with initial conditions! More free lessons at: http://www.khanacademy.org/video?v=rGaM6pwqhB0

10:24
Complex roots of the characteristic equations 2
Added 57 Views / 0 LikesWhat happens when the characteristic equation has complex roots? More free lessons at: http://www.khanacademy.org/video?v=jJyRrIZ595c

10:28
Complex roots of the characteristic equations 1
Added 80 Views / 0 LikesWhat happens when the characteristic equations has complex roots?! More free lessons at: http://www.khanacademy.org/video?v=6xEO4BeawzA

09:11
2nd Order Linear Homogeneous Differential Equations 4
Added 127 Views / 0 LikesAnother example with initial conditions! More free lessons at: http://www.khanacademy.org/video?v=3uO_uPb9H8w

05:59
2nd Order Linear Homogeneous Differential Equations 3
Added 88 Views / 0 LikesLet's use some initial conditions to solve for the particular solution More free lessons at: http://www.khanacademy.org/video?v=UyCwAFQt4v0

08:28
2nd Order Linear Homogeneous Differential Equations 2
Added 75 Views / 0 LikesLet's find the general solution! More free lessons at: http://www.khanacademy.org/video?v=SPVqgkOZMAc

09:45
2nd Order Linear Homogeneous Differential Equations 1
Added 87 Views / 0 LikesIntroduction to 2nd order, linear, homogeneous differential equations with constant coefficients. More free lessons at: http://www.khanacademy.org/video?v=UFWAu8Ptth0

08:23
First order homogenous equations 2
Added 87 Views / 0 LikesAnother example of using substitution to solve a first order homogeneous differential equations. More free lessons at: http://www.khanacademy.org/video?v=6YRGEsQWZzY

07:22
First order homegenous equations
Added 79 Views / 0 LikesIntroduction to first order homogenous equations. More free lessons at: http://www.khanacademy.org/video?v=9WfnWWV1aY

08:26
Integrating factors 2
Added 68 Views / 0 LikesNow that we've made the equation exact, let's solve it! More free lessons at: http://www.khanacademy.org/video?v=0NyeDUhKwBE

10:17
Integrating factors 1
Added 81 Views / 0 LikesUsing an integrating factor to make a differential equation exact More free lessons at: http://www.khanacademy.org/video?v=j511hg7Hlbg

09:59
Exact Equations Example 3
Added 67 Views / 0 LikesOne more exact equation example More free lessons at: http://www.khanacademy.org/video?v=eu_GFuU7tLI

08:01
Exact Equations Example 2
Added 73 Views / 0 LikesSome more exact equation examples More free lessons at: http://www.khanacademy.org/video?v=utQi1ZhF__Q

12:10
Exact Equations Example 1
Added 81 Views / 0 LikesFirst example of solving an exact differential equation. More free lessons at: http://www.khanacademy.org/video?v=Pb04ntcDJcQ

10:51
Exact Equations Intuition 2 (proofy)
Added 75 Views / 0 LikesMore intuitive building blocks for exact equations. More free lessons at: http://www.khanacademy.org/video?v=a7wYAtMjORQ

09:54
Exact Equations Intuition 1 (proofy)
Added 81 Views / 0 LikesChain rule using partial derivatives (not a proof; more intuition). More free lessons at: http://www.khanacademy.org/video?v=iEpqcdaJNTQ

05:38
Separable differential equations 2
Added 151 Views / 0 LikesAnother separable differential equation example. More free lessons at: http://www.khanacademy.org/video?v=xVWCfMe97ws

12:01
Separable Differential Equations
Added 103 Views / 0 LikesIntroduction to separable differential equations. More free lessons at: http://www.khanacademy.org/video?v=C5lz0hcqsE

11:03
What is a differential equation
Added 70 Views / 0 LikesWhat a differential equation is and some terminology.