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# Linear Algebra

• ### Linear Algebra - Matrix Transformations

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Matrix multiplication and linear algebra explained with 3D animations.

• ### Completing the square - Live algebra lesson

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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 :)

• ### Identifying Non Equivalent Systems

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Identifying non equivalent systems

• ### Identifying Equivalent Systems

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Identifying equivalent systems

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

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

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

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Determining the eigenvalues of a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=11dNghWC4HI

• ### Linear Algebra: Finding Eigenvectors and Eigenspaces example

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

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

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Example solving for the eigenvalues of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=pZ6mMVEE89g

• ### Linear Algebra: Proof of formula for determining Eigenvalues

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Proof of formula for determining Eigenvalues More free lessons at: http://www.khanacademy.org/video?v=rfm0wQObxjk

• ### Linear Algebra: Introduction to Eigenvalues and Eigenvectors

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

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

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

• ### Linear Algebra: Gram-Schmidt Process Example

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Using Gram-Schmidt to find an orthonormal basis for a plane in R3 More free lessons at: http://www.khanacademy.org/video?v=tu1GPtfsQ7M

• ### Linear Algebra: The Gram-Schmidt Process

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

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

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Showing that orthogonal matrices preserve angles and lengths More free lessons at: http://www.khanacademy.org/video?v=yDwIfYjKEeo

• ### Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix

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Example using orthogonal change-of-basis matrix to find transformation matrix More free lessons at: http://www.khanacademy.org/video?v=gfVY7cW7VLQ

• ### Lin Alg: Finding projection onto subspace with orthonormal basis example

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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

• ### Lin Alg: Projections onto subspaces with orthonormal bases

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Projections onto subspaces with orthonormal bases More free lessons at: http://www.khanacademy.org/video?v=we829K4NOq8

• ### Linear Algebra: Coordinates with respect to orthonormal bases

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Seeing that orthonormal bases make for good coordinate systems More free lessons at: http://www.khanacademy.org/video?v=SWbis2zWIvo

• ### Linear Algebra: Introduction to Orthonormal Bases

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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

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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

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

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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

• ### Lin Alg: Alternate Basis Tranformation Matrix Example

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Example of finding the transformation matrix for an alternate basis More free lessons at: http://www.khanacademy.org/video?v=lCRGNykWqFI

• ### Lin Alg: Transformation Matrix with Respect to a Basis

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

• ### Lin Alg: Invertible Change of Basis Matrix

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Using an invertible change of basis matrix to go between different coordinate systems More free lessons at: http://www.khanacademy.org/video?v=meibWcbGqt4

• ### Linear Algebra: Change of Basis Matrix

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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

• ### Linear Algebra: Coordinates with Respect to a Basis

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

• ### Linear Algebra: Another Least Squares Example

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Using least squares approximation to fit a line to points More free lessons at: http://www.khanacademy.org/video?v=QkepM8Vv3kw

• ### Linear Algebra: Least Squares Examples

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An example using the least squares solution to an unsolvable system More free lessons at: http://www.khanacademy.org/video?v=8mAZYv5wIcE

• ### Linear Algebra: Least Squares Approximation

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The least squares approximation for otherwise unsolvable equations More free lessons at: http://www.khanacademy.org/video?v=MC7l96tW8V8

• ### Linear Alg: Projection is closest vector in subspace

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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

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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

• ### Linear Algebra: Subspace Projection Matrix Example

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Example of a transformation matrix for a projection onto a subspace More free lessons at: http://www.khanacademy.org/video?v=QTcSBB3uVP0

• ### Lin Alg: A Projection onto a Subspace is a Linear Transforma

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Showing that a projection onto a subspace is a linear transformation More free lessons at: http://www.khanacademy.org/video?v=cTyNpXB92bQ

• ### Linear Alg: Visualizing a projection onto a plane

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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

• ### Linear Algebra: Projections onto Subspaces

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

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

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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

• ### Linear Alg: Rowspace Solution to Ax=b example

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Visualizing the rowspace solution to Ax=b More free lessons at: http://www.khanacademy.org/video?v=qdf2CuMGdKs

• ### Lin Alg: Unique rowspace solution to Ax=b

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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

• ### Lin Alg: Orthogonal Complement of the Nullspace

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The orthogonal complement of the nullspace and left nullspace. More free lessons at: http://www.khanacademy.org/video?v=LE_aQAur7nI

• ### Lin Alg: Orthogonal Complement of the Orthogonal Complement

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Finding that the orthogonal complement of the orthogonal complement of V is V More free lessons at: http://www.khanacademy.org/video?v=zlI8mx8Hc8o

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

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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

• ### Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n

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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

• ### Linear Algebra: Rank(A) = Rank(transpose of A)

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

• ### Linear Algebra: Orthogonal Complements

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

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

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Relationship between left nullspace, rowspace, column space and nullspace. More free lessons at: http://www.khanacademy.org/video?v=GW8ZPjGlk24

• ### Linear Algebra: Rowspace and Left Nullspace

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

• ### Linear Algebra: Transpose of a Vector

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

• ### Linear Algebra: Transposes of sums and inverses

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Transposes of sums and inverses More free lessons at: http://www.khanacademy.org/video?v=Br_8t58mdeI

• ### Linear Algebra: Transpose of a Matrix Product

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Taking the transpose of the product of two matrices More free lessons at: http://www.khanacademy.org/video?v=UdHgWK13x5I

• ### Linear Algebra: Determinant of Transpose

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

• ### Linear Algebra: Transpose of a Matrix

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

• ### Linear Algebra: Determinant as Scaling Factor

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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

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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

• ### Linear Algebra: Simpler 4x4 determinant

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Calculating a 4x4 determinant by putting in in upper triangular form first. More free lessons at: http://www.khanacademy.org/video?v=QV0jsTiobU4

• ### Linear Algebra: Upper Triangular Determinant

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The determinant of an upper triangular matrix More free lessons at: http://www.khanacademy.org/video?v=VX7K8iqoiRc

• ### Linear Algebra: Determinant after row operations

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What happens to the determinant when we perform a row operation More free lessons at: http://www.khanacademy.org/video?v=kpG7xySkivg

• ### Linear Algebra: Duplicate Row Determinant

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

• ### Linear Algebra: Determinant when row is added

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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

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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

• ### Linear Algebra: Determinant when row multiplied by scalar

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

• ### Linear Algebra: Rule of Sarrus of Determinants

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A alternative "short cut" for calculating 3x3 determinants (Rule of Sarrus) More free lessons at: http://www.khanacademy.org/video?v=4xFIi0JF2AM

• ### Linear Algebra: Determinants along other rows/cols

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Finding the determinant by going along other rows or columns More free lessons at: http://www.khanacademy.org/video?v=nu87kfmwNfU

• ### Linear Algebra: nxn Determinant

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Defining the determinant for nxn matrices. An exampled of a 4x4 determinant. More free lessons at: http://www.khanacademy.org/video?v=H9BWRYJNIv4

• ### Linear Algebra: 3x3 Determinant

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Determinants: Finding the determinant of a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=0c7dt2SQfLw

• ### Linear Algebra: Formula for 2x2 inverse

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Figuring out the formula for a 2x2 matrix. Defining the determinant. More free lessons at: http://www.khanacademy.org/video?v=eEUK_ThrHuQ

• ### Linear Algebra: Example of Finding Matrix Inverse

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Example of calculating the inverse of a matrix More free lessons at: http://www.khanacademy.org/video?v=r9aTLTN16V4

• ### Linear Algebra: Deriving a method for determining inverses

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Determining a method for constructing inverse transformation matrices More free lessons at: http://www.khanacademy.org/video?v=6DpzCKJBsz0

• ### Linear Algebra: Showing that Inverses are Linear

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Showing that inverse transformations are also linear More free lessons at: http://www.khanacademy.org/video?v=mr9Tow8hpCg

• ### Linear Algebra: Simplifying conditions for invertibility

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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

• ### Linear Algebra: Matrix condition for one-to-one trans

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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

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Exploring the solution set of Ax=b (non homogeneous equations) More free lessons at: http://www.khanacademy.org/video?v=1PsNIzUJPkc

• ### Determining whether a transformation is onto

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

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

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

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

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Introduction to surjective and injective functions More free lessons at: http://www.khanacademy.org/video?v=xKNX8BUWR0g

• ### Proof: Invertibility implies a unique solution to f(x)=y

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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

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

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

• ### Distributive Property of Matrix Products

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

• ### Matrix Product Associativity

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

• ### Linear Algebra: Matrix Product Examples

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Example of taking the product of two matrices More free lessons at: http://www.khanacademy.org/video?v=x1z0hOyjapU

• ### Compositions of Linear Transformations 2

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Providing the motivation for definition of matrix products More free lessons at: http://www.khanacademy.org/video?v=BuqcKpe5ZQs

• ### Compositions of Linear Transformations 1

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Introduction to compositions of Linear Transformations More free lessons at: http://www.khanacademy.org/video?v=f_DTiXZpb8M

• ### Expressing a Projection on to a line as a Matrix Vector prod

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

• ### Introduction to Projections

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

• ### Unit Vectors

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What unit vectors are and how to construct them More free lessons at: http://www.khanacademy.org/video?v=lQn7fksaDq0

• ### Rotation in R3 around the X-axis

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

• ### Linear Transformation Examples: Rotations in R2

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

• ### Linear Transformation Examples: Scaling and Reflections

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

• ### More on Matrix Addition and Scalar Multiplication

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

• ### Sums and Scalar Multiples of Linear Transformations

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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

• ### Preimage and Kernel Example

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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

• ### Preimage of a set

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

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

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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

• ### Image of a subset under a transformation

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Exploring what happens to a subset of the domain under a transformation More free lessons at: http://www.khanacademy.org/video?v=MIAmN5kgp3k

• ### Linear Transformations as Matrix Vector Products

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Showing how ANY linear transformation can be represented as a matrix vector product More free lessons at: http://www.khanacademy.org/video?v=PErhLkQcpZ8

• ### Matrix Vector Products as Linear Transformations

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

• ### Linear Transformations

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

• ### Vector Transformations

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Introduction to the notion of vector transformations More free lessons at: http://www.khanacademy.org/video?v=gAbadNuQEjI

• ### A more formal understanding of functions

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A more formal understanding of functions More free lessons at: http://www.khanacademy.org/video?v=BQMyeQOLvpg

• ### Showing that the candidate basis does span C(A)

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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

• ### Showing relation between basis cols and pivot cols

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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

• ### Dimension of the Column Space or Rank

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

• ### Dimension of the Null Space or Nullity

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

• ### Proof: Any subspace basis has same number of elements

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

• ### Visualizing a Column Space as a Plane in R3

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

• ### Null Space and Column Space Basis

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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

• ### Column Space of a Matrix

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

• ### Null Space 3: Relation to Linear Independence

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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

• ### Null Space 2: Calculating the null space of a matrix

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

• ### Introduction to the Null Space of a Matrix

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

• ### Matrix Vector Products

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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

• ### Matrices: Reduced Row Echelon Form 3

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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

• ### Matrices: Reduced Row Echelon Form 2

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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

• ### Matrices: Reduced Row Echelon Form 1

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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

• ### Dot and Cross Product Comparison/Intuition

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

• ### Proof: Relationship between cross product and sin of angle

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

• ### Linear Algebra: Cross Product Introduction

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

• ### Defining a plane in R3 with a point and normal vector

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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

• ### Defining the angle between vectors

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

• ### Linear Algebra: Vector Triangle Inequality

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

• ### Proof of the Cauchy-Schwarz Inequality

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

• ### Proving Vector Dot Product Properties

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Proving the "associative", "distributive" and "commutative" properties for vector dot products. More free lessons at: http://www.khanacademy.org/video?v=rVQ3G9epCjw

• ### Vector Dot Product and Vector Length

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

• ### Linear Algebra: Basis of a Subspace

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

• ### Linear Subspaces

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

• ### Span and Linear Independence Example

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Determining whether 3 vectors are linearly independent and/or span R3 More free lessons at: http://www.khanacademy.org/video?v=9kW6zFK5E5c

• ### More on linear independence

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More examples determining linear dependence or independence. More free lessons at: http://www.khanacademy.org/video?v=Alhcv5d_XOs

• ### Linear Algebra: Introduction to Linear Independence

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

• ### Linear Combinations and Span

/ 382 views

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

• ### Linear Algebra: Parametric Representations of Lines

/ 427 views

Linear Algebra: Parametric Representations of Lines in R2 and R3 More free lessons at: http://www.khanacademy.org/video?v=hWhs2cIj7Cw

• ### Linear Algebra: Vector Examples

/ 432 views

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

• ### Solving 3 Equations with 3 Unknowns

/ 461 views

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

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

/ 541 views

Visual intuition of a 3-variable linear equation.

• ### Singular Matrices

/ 428 views

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

• ### Matrices to solve a vector combination problem

/ 445 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

• ### Matrices to solve a system of equations

/ 454 views

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

• ### Inverting Matrices (part 3)

/ 541 views

Using Gauss-Jordan elimination to invert a 3x3 matrix. More free lessons at: http://www.khanacademy.org/video?v=obts_JDS6_Q

• ### Inverting matrices (part 2)

/ 392 views

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

• ### Inverse Matrix (part 1)

/ 581 views

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

• ### Matrix multiplication (part 2)

/ 407 views

More on multiplying matrices.

• ### Matrix multiplication (part 1)

/ 569 views

Multiplying two 2x2 matrices.

• ### Introduction to matrices

/ 405 views

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

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

/ 456 views

Using the Convolution Theorem to solve an initial value problem More free lessons at: http://www.khanacademy.org/video?v=rfyq32mHcYs

• ### The Convolution and the Laplace Transform

/ 470 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

• ### Introduction to the Convolution

/ 416 views

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

• ### Laplace Transform of the Dirac Delta Function

/ 455 views

Figuring out the Laplace Transform of the Dirac Delta Function More free lessons at: http://www.khanacademy.org/video?v=vhfjEpQWWeE

• ### Dirac Delta Function

/ 444 views

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

• ### Laplace/Step Function Differential Equation

/ 589 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

• ### Inverse Laplace Examples

/ 435 views

Using our toolkit to take some inverse Laplace Transforms More free lessons at: http://www.khanacademy.org/video?v=BbqbvSig6Mc

• ### Laplace Transform of the Unit Step Function

/ 614 views

Introduction to the unit step function and its Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=4Mr7aEHQr8E

• ### Laplace Transform of t^n: L{t^n}

/ 401 views

Laplace Transform of t^n: L{t^n} More free lessons at: http://www.khanacademy.org/video?v=pZIaUx3UQoA

• ### Laplace Transform of : L{t}

/ 447 views

Determining the Laplace Transform of t More free lessons at: http://www.khanacademy.org/video?v=qhKJ1DG9kYY

• ### Using the Laplace Transform to solve a nonhomogenous eq

/ 380 views

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

• ### More Laplace Transform tools

/ 520 views

A grab bag of things to know about the Laplace Transform. More free lessons at: http://www.khanacademy.org/video?v=_X_QwpXsdOs

• ### Laplace Transform solves an equation 2

/ 404 views

Second part of using the Laplace Transform to solve a differential equation. More free lessons at: http://www.khanacademy.org/video?v=EdQ7Q9VoF44

• ### Laplace Transform to solve an equation

/ 435 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

• ### Laplace Transform 6

/ 423 views

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

• ### Laplace Transform 5

/ 572 views

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

• ### Laplace Transform 4

/ 419 views

Part 2 of getting the Laplace transform of sin(at) More free lessons at: http://www.khanacademy.org/video?v=-cApVwKR1Ps

• ### Laplace Transform 3 (L{sin(at)})

/ 446 views

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

• ### Laplace Transform 2

/ 432 views

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

• ### Laplace Transform 1

/ 392 views

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

• ### Undetermined Coefficients 4

/ 406 views

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

• ### Undetermined Coefficients 3

/ 408 views

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

• ### Undetermined Coefficients 2

/ 382 views

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

• ### Undetermined Coefficients 1

/ 423 views

Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations. More free lessons at: http://www.khanacademy.org/video?v=znE4Nq9NJCQ

• ### Repeated roots of the characterisitic equations part 2

/ 400 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

• ### Repeated roots of the characteristic equation

/ 362 views

What happens when the characteristic equation only has 1 repeated root? More free lessons at: http://www.khanacademy.org/video?v=NW9JfMvIsxw

• ### Complex roots of the characteristic equations 3

/ 391 views

Lets do an example with initial conditions! More free lessons at: http://www.khanacademy.org/video?v=rGaM6pwqhB0

• ### Complex roots of the characteristic equations 2

/ 430 views

What happens when the characteristic equation has complex roots? More free lessons at: http://www.khanacademy.org/video?v=jJyRrIZ595c

• ### Complex roots of the characteristic equations 1

/ 425 views

What happens when the characteristic equations has complex roots?! More free lessons at: http://www.khanacademy.org/video?v=6xEO4BeawzA

• ### 2nd Order Linear Homogeneous Differential Equations 4

/ 484 views

Another example with initial conditions! More free lessons at: http://www.khanacademy.org/video?v=3uO_uPb9H8w

• ### 2nd Order Linear Homogeneous Differential Equations 3

/ 429 views

Let's use some initial conditions to solve for the particular solution More free lessons at: http://www.khanacademy.org/video?v=UyCwAFQt4v0

• ### 2nd Order Linear Homogeneous Differential Equations 2

/ 447 views

Let's find the general solution! More free lessons at: http://www.khanacademy.org/video?v=SPVqgkOZMAc

• ### 2nd Order Linear Homogeneous Differential Equations 1

/ 434 views

Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients. More free lessons at: http://www.khanacademy.org/video?v=UFWAu8Ptth0

• ### First order homogenous equations 2

/ 450 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

• ### First order homegenous equations

/ 476 views

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

• ### Integrating factors 2

/ 376 views

Now that we've made the equation exact, let's solve it! More free lessons at: http://www.khanacademy.org/video?v=0NyeDUhKwBE

• ### Integrating factors 1

/ 413 views

Using an integrating factor to make a differential equation exact More free lessons at: http://www.khanacademy.org/video?v=j511hg7Hlbg

• ### Exact Equations Example 3

/ 407 views

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

• ### Exact Equations Example 2

/ 418 views

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

• ### Exact Equations Example 1

/ 420 views

First example of solving an exact differential equation. More free lessons at: http://www.khanacademy.org/video?v=Pb04ntcDJcQ

• ### Exact Equations Intuition 2 (proofy)

/ 411 views

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

• ### Exact Equations Intuition 1 (proofy)

/ 555 views

Chain rule using partial derivatives (not a proof; more intuition). More free lessons at: http://www.khanacademy.org/video?v=iEpqcdaJNTQ

• ### Separable differential equations 2

/ 493 views

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

• ### Separable Differential Equations

/ 453 views

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

• ### What is a differential equation

/ 433 views

What a differential equation is and some terminology. #### Categories           