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# Linear Algebra

• 19:53

### Linear Algebra - Matrix Transformations

/ 387 views

Matrix multiplication and linear algebra explained with 3D animations.

• 47:36

### Completing the square - Live algebra lesson

/ 530 views

Do 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 :)

• 04:30

### Identifying Non Equivalent Systems

/ 585 views

Identifying non equivalent systems

• 05:31

### Identifying Equivalent Systems

/ 658 views

Identifying equivalent systems

• 15:34

### Linear Algebra: Eigenvectors and Eigenspaces for a 3x3 matrix

/ 590 views

Eigenvectors and eigenspaces for a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=3Md5KCCQX-0

• 14:08

### Linear Algebra: Eigenvalues of a 3x3 matrix

/ 592 views

Determining 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

/ 626 views

Finding the eigenvectors and eigenspaces of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=3-xfmbdzkqc

• 05:39

### Linear Algebra: Example solving for the eigenvalues of a 2x2 matrix

/ 611 views

Example 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

/ 621 views

Proof 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

/ 585 views

What eigenvectors and eigenvalues are and why they are interesting More free lessons at: http://www.khanacademy.org/video?v=PhfbEr2btGQ

• 13:57

### Linear Algebra: Gram-Schmidt example with 3 basis vectors

/ 617 views

Gram-Schmidt example with 3 basis vectors More free lessons at: http://www.khanacademy.org/video?v=ZRRG386v6DI

• 13:14

### Linear Algebra: Gram-Schmidt Process Example

/ 561 views

Using Gram-Schmidt 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 Gram-Schmidt Process

/ 573 views

Finding an orthonormal basis for a subspace using the Gram-Schmidt Process More free lessons at: http://www.khanacademy.org/video?v=rHonltF77zI

• 11:16

### Lin Alg: Orthogonal matrices preserve angles and lengths

/ 667 views

Showing 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 change-of-basis matrix to find transformation matrix

/ 612 views

Example using orthogonal change-of-basis 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

/ 588 views

Example 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

/ 579 views

Projections 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

/ 689 views

Seeing 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

/ 577 views

Looking 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 Popular

### Lin Alg: Changing coordinate systems to help find a transformation matrix

/ 765 views

Changing 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 Popular

### Lin Alg: Alternate Basis Tranformation Matrix Example Part 2

/ 749 views

Showing 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 Popular

### Lin Alg: Alternate Basis Tranformation Matrix Example

/ 715 views

Example 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

/ 622 views

Finding the transformation matrix with respect to a non-standard basis More free lessons at: http://www.khanacademy.org/video?v=PiuhTj0zCf4

• 13:34

### Lin Alg: Invertible Change of Basis Matrix

/ 559 views

Using 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

/ 613 views

Using 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

/ 572 views

Understanding alternate coordinate systems More free lessons at: http://www.khanacademy.org/video?v=uvgru6FcyxU

• 13:25

### Linear Algebra: Another Least Squares Example

/ 631 views

Using 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

/ 592 views

An 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

/ 574 views

The 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

/ 599 views

Showing 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 Popular

### Lin Alg: Another Example of a Projection Matrix

/ 989 views

Figuring 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

/ 683 views

Example 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

/ 601 views

Showing 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

/ 579 views

Visualizing 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

/ 597 views

Projections onto subspaces More free lessons at: http://www.khanacademy.org/video?v=5B8XluiqdHM

• 12:34

### Lin Alg: Showing that A-transpose x A is invertible

/ 597 views

Showing 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

/ 564 views

Visualizing 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

/ 626 views

Showing 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

/ 643 views

The 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

/ 553 views

Finding 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 Popular

### Lin Alg: Representing vectors in Rn using subspace members

/ 935 views

Showing 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

/ 537 views

Showing 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)

/ 616 views

Rank(A) = Rank(transpose of A) More free lessons at: http://www.khanacademy.org/video?v=tqqVOWm9YsU

• 22:08

### Linear Algebra: Orthogonal Complements

/ 576 views

Orthogonal Complements as subspaces. More free lessons at: http://www.khanacademy.org/video?v=QOTjdgmNqlg

• 19:50

### Lin Alg: Visualizations of Left Nullspace and Rowspace

/ 550 views

Relationship 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

/ 559 views

Rowspace and Left Nullspace More free lessons at: http://www.khanacademy.org/video?v=qBfc57x_RSg

• 12:07

### Linear Algebra: Transpose of a Vector

/ 553 views

Transpose of a column vector. Matrix-matrix products using vectors More free lessons at: http://www.khanacademy.org/video?v=lSoaMCNKfAg

• 08:41

### Linear Algebra: Transposes of sums and inverses

/ 587 views

Transposes 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

/ 581 views

Taking 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

/ 605 views

Proof by induction that transposing a matrix does not change its determinant More free lessons at: http://www.khanacademy.org/video?v=x-GV2v0dRNE

• 08:37

### Linear Algebra: Transpose of a Matrix

/ 549 views

Transpose of a matrix More free lessons at: http://www.khanacademy.org/video?v=2t0003_sxtU

• 20:10

### Linear Algebra: Determinant as Scaling Factor

/ 656 views

Viewing 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 Popular

### Linear Algebra: Determinant and area of a parallelogram

/ 1,090 views

Realizing 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

• 09:13

### Linear Algebra: Simpler 4x4 determinant

/ 622 views

Calculating 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

/ 574 views

The 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

/ 554 views

What 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

/ 622 views

Determinant of a matrix with duplicate rows More free lessons at: http://www.khanacademy.org/video?v=gYv8sttBIqs

• 16:55 Popular

### Linear Algebra: Determinant when row is added

/ 744 views

The 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 Popular

### Linear Algebra: (correction) scalar muliplication of row

/ 897 views

Correction 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

/ 565 views

The determinant when a row is multiplied by a scalar More free lessons at: http://www.khanacademy.org/video?v=32rdijPB-rA

• 07:18

### Linear Algebra: Rule of Sarrus of Determinants

/ 634 views

A 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

/ 570 views

Finding 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

/ 547 views

Defining 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

/ 580 views

Determinants: 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

/ 564 views

Figuring 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

/ 560 views

Example 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

/ 545 views

Determining 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

/ 521 views

Showing 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

/ 553 views

Showing 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 one-to-one trans

/ 612 views

Showing 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

• 16:34 Popular

### Linear Algebra: Exploring the solution set of Ax=b

/ 1,744 views

Exploring 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

/ 536 views

Determining whether a transformation is onto More free lessons at: http://www.khanacademy.org/video?v=eR8vEdJTvd0

• 06:31

### Relating invertibility to being onto and one-to-one

/ 568 views

Relating invertibility to being onto (surjective) and one-to-one (injective) More free lessons at: http://www.khanacademy.org/video?v=QIU1daMN8fw

• 09:32

### Surjective (onto) and Injective (one-to-one) functions

/ 563 views

Introduction 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

/ 610 views

Proof: 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

• 18:54

### Linear Algebra: Introduction to the inverse of a function

/ 548 views

Introduction to the inverse of a function More free lessons at: http://www.khanacademy.org/video?v=-eAzhBZgq28

• 09:52

### Distributive Property of Matrix Products

/ 662 views

Showing that matrix products exhibit the distributive property More free lessons at: http://www.khanacademy.org/video?v=oMWTMj78cwc

• 11:59

### Matrix Product Associativity

/ 598 views

Showing that matrix products are associative More free lessons at: http://www.khanacademy.org/video?v=Hhc96U_HvQE

• 18:14

### Linear Algebra: Matrix Product Examples

/ 591 views

Example 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

/ 562 views

Providing 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

/ 569 views

Introduction 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

/ 581 views

Expressing a Projection on to a line as a Matrix Vector prod More free lessons at: http://www.khanacademy.org/video?v=JK-8XNIoAkI

• 14:37

### Introduction to Projections

/ 552 views

Determining the projection of a vector on s line More free lessons at: http://www.khanacademy.org/video?v=27vT-NWuw0M

• 06:59

### Unit Vectors

/ 603 views

What 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 X-axis

/ 549 views

Construction a rotation transformation in R3 More free lessons at: http://www.khanacademy.org/video?v=gkyuLPzfDV0

• 17:52

### Linear Transformation Examples: Rotations in R2

/ 563 views

Linear Transformation Examples: Rotations in R2 More free lessons at: http://www.khanacademy.org/video?v=lPWfIq5DzqI

• 15:13

### Linear Transformation Examples: Scaling and Reflections

/ 570 views

Creating scaling and reflection transformation matrices (which are diagonal) More free lessons at: http://www.khanacademy.org/video?v=qkfODKmZ-x4

• 10:42

### More on Matrix Addition and Scalar Multiplication

/ 580 views

More on Matrix Addition and Scalar Multiplication More free lessons at: http://www.khanacademy.org/video?v=Z19-ObbmHJE

• 15:09

### Sums and Scalar Multiples of Linear Transformations

/ 556 views

Sums 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

/ 618 views

Example 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 Popular

### Preimage of a set

/ 724 views

Definition of preimage of a set More free lessons at: http://www.khanacademy.org/video?v=zVsGtU8lIWs

• 16:37

### im(T): Image of a Transformation

/ 643 views

Showing 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

/ 573 views

Exploring 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

/ 693 views

Showing 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

/ 679 views

Matrix Vector Products as Linear Transformations More free lessons at: http://www.khanacademy.org/video?v=ondmopWLiEg

• 13:53

### Linear Transformations

/ 544 views

Introduction to linear transformations More free lessons at: http://www.khanacademy.org/video?v=4PCktDZJH8E

• 14:19

### Vector Transformations

/ 511 views

Introduction 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

/ 680 views

A 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)

/ 550 views

Showing 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

/ 551 views

Showing 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

/ 545 views

Dimension 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

/ 684 views

Dimension 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

/ 648 views

Proof: 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

/ 590 views

Determining the planar equation for a column space in R3 More free lessons at: http://www.khanacademy.org/video?v=EGNlXtjYABw

• 25:13 Popular

### Null Space and Column Space Basis

/ 756 views

Figuring 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

/ 551 views

Introduction 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

/ 587 views

Understanding 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

/ 606 views

Calculating 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

/ 571 views

Showing 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

/ 628 views

Defining 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

/ 571 views

And 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

/ 536 views

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=lP1DGtZ8Wys

• 17:43

### Matrices: Reduced Row Echelon Form 1

/ 526 views

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=L0CmbneYETs

• 19:14

### Dot and Cross Product Comparison/Intuition

/ 522 views

Dot 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

/ 583 views

Proof: 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

/ 479 views

Introduction 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

/ 608 views

Determining 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

/ 608 views

Introducing 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

/ 518 views

Proving the triangle inequality for vectors in Rn More free lessons at: http://www.khanacademy.org/video?v=PsNidCBr5II

• 16:56

### Proof of the Cauchy-Schwarz Inequality

/ 640 views

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

• 10:46

### Proving Vector Dot Product Properties

/ 603 views

Proving 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

/ 484 views

Definitions 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

/ 487 views

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

• 23:29

### Linear Subspaces

/ 471 views

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

• 16:53

### Span and Linear Independence Example

/ 454 views

Determining 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

/ 465 views

More 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

/ 477 views

Linear Algebra: Introduction to linear dependence and independence More free lessons at: http://www.khanacademy.org/video?v=CrV1xCWdY-g

• 20:35

### Linear Combinations and Span

/ 454 views

Understanding linear combinations and spans of vectors More free lessons at: http://www.khanacademy.org/video?v=Qm_OS-8COwU

• 24:47

### Linear Algebra: Parametric Representations of Lines

/ 483 views

Linear 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

/ 483 views

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

• 15:26

### Solving 3 Equations with 3 Unknowns

/ 511 views

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

• 08:02

### 3-variable linear equations (part 1)

/ 611 views

Visual intuition of a 3-variable linear equation.

• 14:27

### Singular Matrices

/ 527 views

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

• 14:20

### Matrices to solve a vector combination problem

/ 498 views

Using 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

/ 498 views

Using 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)

/ 596 views

Using Gauss-Jordan 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)

/ 439 views

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

• 14:15

### Inverse Matrix (part 1)

/ 662 views

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

• 14:37

### Matrix multiplication (part 2)

/ 457 views

More on multiplying matrices.

• 13:41

### Matrix multiplication (part 1)

/ 621 views

Multiplying two 2x2 matrices.

• 11:51

### Introduction to matrices

/ 456 views

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

• 12:14

### Using the Convolution Theorem to Solve an Initial Value Prob

/ 507 views

Using 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

/ 514 views

Understanding 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

/ 470 views

Introduction to the Convolution More free lessons at: http://www.khanacademy.org/video?v=IW4Reburjpc

• 12:13

### Laplace Transform of the Dirac Delta Function

/ 521 views

Figuring 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

/ 506 views

Introduction to the Dirac Delta Function More free lessons at: http://www.khanacademy.org/video?v=4qfdCwys2ew

• 19:12

### Laplace/Step Function Differential Equation

/ 652 views

Hairy 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

/ 488 views

Using 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

/ 681 views

Introduction 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}

/ 453 views

Laplace 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}

/ 499 views

Determining 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

/ 429 views

Solving a non-homogeneous differential equation using the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=nlUG4OKN1IY

• 11:17

### More Laplace Transform tools

/ 571 views

A 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

/ 456 views

Second 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

/ 490 views

Using 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

• 09:46

### Laplace Transform 6

/ 480 views

Laplace transform of cosine and polynomials! More free lessons at: http://www.khanacademy.org/video?v=fyJkXBvcA2Q

• 11:37

### Laplace Transform 5

/ 631 views

Useful properties of the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=E2VxbufzuWQ

• 09:14

### Laplace Transform 4

/ 466 views

Part 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)})

/ 510 views

Laplace Transform of sin(at) (part 1) More free lessons at: http://www.khanacademy.org/video?v=gMcs6RF_LrQ

• 07:35

### Laplace Transform 2

/ 489 views

Laplace transform of e^at More free lessons at: http://www.khanacademy.org/video?v=33TYoybjqPg

• 08:02

### Laplace Transform 1

/ 452 views

Introduction to the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=OiNh2DswFt4

• 05:55

### Undetermined Coefficients 4

/ 479 views

Putting it all together! More free lessons at: http://www.khanacademy.org/video?v=vAepSNDLZRM

• 08:10

### Undetermined Coefficients 3

/ 481 views

Another example where the nonhomogeneous part is a polynomial More free lessons at: http://www.khanacademy.org/video?v=I3vIAzMcm4Y

• 11:01

### Undetermined Coefficients 2

/ 435 views

Another example using undetermined coefficients. More free lessons at: http://www.khanacademy.org/video?v=hbJ2o9EUmJ0

• 10:11

### Undetermined Coefficients 1

/ 503 views

Using 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

/ 454 views

An example where we use initial conditions to solve a repeated-roots differential equation. More free lessons at: http://www.khanacademy.org/video?v=YezsgIlcb68

• 11:58

### Repeated roots of the characteristic equation

/ 413 views

What 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

/ 446 views

Lets 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

/ 488 views

What 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

/ 480 views

What 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

/ 531 views

Another 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

/ 477 views

Let'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

/ 515 views

Let'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

/ 491 views

Introduction 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

/ 501 views

Another 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

/ 522 views

Introduction to first order homogenous equations. More free lessons at: http://www.khanacademy.org/video?v=9Wfn-WWV1aY

• 08:26

### Integrating factors 2

/ 426 views

Now 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

/ 464 views

Using 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

/ 466 views

One more exact equation example More free lessons at: http://www.khanacademy.org/video?v=eu_GFuU7tLI

• 08:01

### Exact Equations Example 2

/ 473 views

Some more exact equation examples More free lessons at: http://www.khanacademy.org/video?v=utQi1ZhF__Q

• 12:10

### Exact Equations Example 1

/ 471 views

First 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)

/ 470 views

More intuitive building blocks for exact equations. More free lessons at: http://www.khanacademy.org/video?v=a7wYAtMjORQ

• 09:54

### Exact Equations Intuition 1 (proofy)

/ 610 views

Chain 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

/ 541 views

Another separable differential equation example. More free lessons at: http://www.khanacademy.org/video?v=xVWCfMe97ws

• 12:01

### Separable Differential Equations

/ 497 views

Introduction to separable differential equations. More free lessons at: http://www.khanacademy.org/video?v=C5-lz0hcqsE

• 11:03

### What is a differential equation

/ 488 views

What a differential equation is and some terminology.