Linear Algebra

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Linear Algebra - Matrix Transformations

6 years ago / 694 views

Matrix multiplication and linear algebra explained with 3D animations.
47:36 Popular
Completing the square - Live algebra lesson

7 years ago / 749 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 Popular
Identifying Non Equivalent Systems

9 years ago / 776 views

Identifying non equivalent systems
05:31 Popular
Identifying Equivalent Systems

9 years ago / 870 views

Identifying equivalent systems
15:34 Popular
Linear Algebra: Eigenvectors and Eigenspaces for a 3x3 matrix

9 years ago / 763 views

Eigenvectors and eigenspaces for a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=3Md5KCCQX-0
14:08 Popular
Linear Algebra: Eigenvalues of a 3x3 matrix

9 years ago / 792 views

Determining the eigenvalues of a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=11dNghWC4HI
14:34 Popular
Linear Algebra: Finding Eigenvectors and Eigenspaces example

9 years ago / 839 views

Finding the eigenvectors and eigenspaces of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=3-xfmbdzkqc
05:39 Popular
Linear Algebra: Example solving for the eigenvalues of a 2x2 matrix

9 years ago / 820 views

Example solving for the eigenvalues of a 2x2 matrix More free lessons at: http://www.khanacademy.org/video?v=pZ6mMVEE89g
09:19 Popular
Linear Algebra: Proof of formula for determining Eigenvalues

9 years ago / 812 views

Proof of formula for determining Eigenvalues More free lessons at: http://www.khanacademy.org/video?v=rfm0wQObxjk
07:43 Popular
Linear Algebra: Introduction to Eigenvalues and Eigenvectors

9 years ago / 787 views

What eigenvectors and eigenvalues are and why they are interesting More free lessons at: http://www.khanacademy.org/video?v=PhfbEr2btGQ
13:57 Popular
Linear Algebra: Gram-Schmidt example with 3 basis vectors

9 years ago / 800 views

Gram-Schmidt example with 3 basis vectors More free lessons at: http://www.khanacademy.org/video?v=ZRRG386v6DI
13:14 Popular
Linear Algebra: Gram-Schmidt Process Example

9 years ago / 756 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 Popular
Linear Algebra: The Gram-Schmidt Process

9 years ago / 772 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 Popular
Lin Alg: Orthogonal matrices preserve angles and lengths

9 years ago / 851 views

Showing that orthogonal matrices preserve angles and lengths More free lessons at: http://www.khanacademy.org/video?v=yDwIfYjKEeo
27:04 Popular
Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix

9 years ago / 813 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 Popular
Lin Alg: Finding projection onto subspace with orthonormal basis example

9 years ago / 740 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 Popular
Lin Alg: Projections onto subspaces with orthonormal bases

9 years ago / 781 views

Projections onto subspaces with orthonormal bases More free lessons at: http://www.khanacademy.org/video?v=we829K4NOq8
15:28 Popular
Linear Algebra: Coordinates with respect to orthonormal bases

9 years ago / 862 views

Seeing that orthonormal bases make for good coordinate systems More free lessons at: http://www.khanacademy.org/video?v=SWbis2zWIvo
11:16 Popular
Linear Algebra: Introduction to Orthonormal Bases

9 years ago / 765 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

9 years ago / 980 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

9 years ago / 1,017 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

9 years ago / 929 views

Example of finding the transformation matrix for an alternate basis More free lessons at: http://www.khanacademy.org/video?v=lCRGNykWqFI
18:02 Popular
Lin Alg: Transformation Matrix with Respect to a Basis

9 years ago / 788 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 Popular
Lin Alg: Invertible Change of Basis Matrix

9 years ago / 734 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 Popular
Linear Algebra: Change of Basis Matrix

9 years ago / 816 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 Popular
Linear Algebra: Coordinates with Respect to a Basis

9 years ago / 754 views

Understanding alternate coordinate systems More free lessons at: http://www.khanacademy.org/video?v=uvgru6FcyxU
13:25 Popular
Linear Algebra: Another Least Squares Example

9 years ago / 823 views

Using least squares approximation to fit a line to points More free lessons at: http://www.khanacademy.org/video?v=QkepM8Vv3kw
18:50 Popular
Linear Algebra: Least Squares Examples

9 years ago / 797 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 Popular
Linear Algebra: Least Squares Approximation

9 years ago / 762 views

The least squares approximation for otherwise unsolvable equations More free lessons at: http://www.khanacademy.org/video?v=MC7l96tW8V8
09:05 Popular
Linear Alg: Projection is closest vector in subspace

9 years ago / 796 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

9 years ago / 1,280 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 Popular
Linear Algebra: Subspace Projection Matrix Example

9 years ago / 898 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 Popular
Lin Alg: A Projection onto a Subspace is a Linear Transforma

9 years ago / 779 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 Popular
Linear Alg: Visualizing a projection onto a plane

9 years ago / 747 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 Popular
Linear Algebra: Projections onto Subspaces

9 years ago / 771 views

Projections onto subspaces More free lessons at: http://www.khanacademy.org/video?v=5B8XluiqdHM
12:34 Popular
Lin Alg: Showing that A-transpose x A is invertible

9 years ago / 751 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 Popular
Linear Alg: Rowspace Solution to Ax=b example

9 years ago / 735 views

Visualizing the rowspace solution to Ax=b More free lessons at: http://www.khanacademy.org/video?v=qdf2CuMGdKs
19:12 Popular
Lin Alg: Unique rowspace solution to Ax=b

9 years ago / 818 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 Popular
Lin Alg: Orthogonal Complement of the Nullspace

9 years ago / 808 views

The orthogonal complement of the nullspace and left nullspace. More free lessons at: http://www.khanacademy.org/video?v=LE_aQAur7nI
12:18 Popular
Lin Alg: Orthogonal Complement of the Orthogonal Complement

9 years ago / 729 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

9 years ago / 1,201 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 Popular
Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n

9 years ago / 732 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 Popular
Linear Algebra: Rank(A) = Rank(transpose of A)

9 years ago / 799 views

Rank(A) = Rank(transpose of A) More free lessons at: http://www.khanacademy.org/video?v=tqqVOWm9YsU
22:08 Popular
Linear Algebra: Orthogonal Complements

9 years ago / 749 views

Orthogonal Complements as subspaces. More free lessons at: http://www.khanacademy.org/video?v=QOTjdgmNqlg
19:50 Popular
Lin Alg: Visualizations of Left Nullspace and Rowspace

9 years ago / 726 views

Relationship between left nullspace, rowspace, column space and nullspace. More free lessons at: http://www.khanacademy.org/video?v=GW8ZPjGlk24
23:19 Popular
Linear Algebra: Rowspace and Left Nullspace

9 years ago / 761 views

Rowspace and Left Nullspace More free lessons at: http://www.khanacademy.org/video?v=qBfc57x_RSg
12:07 Popular
Linear Algebra: Transpose of a Vector

9 years ago / 749 views

Transpose of a column vector. Matrix-matrix products using vectors More free lessons at: http://www.khanacademy.org/video?v=lSoaMCNKfAg
08:41 Popular
Linear Algebra: Transposes of sums and inverses

9 years ago / 763 views

Transposes of sums and inverses More free lessons at: http://www.khanacademy.org/video?v=Br_8t58mdeI
08:50 Popular
Linear Algebra: Transpose of a Matrix Product

9 years ago / 767 views

Taking the transpose of the product of two matrices More free lessons at: http://www.khanacademy.org/video?v=UdHgWK13x5I
14:10 Popular
Linear Algebra: Determinant of Transpose

9 years ago / 787 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 Popular
Linear Algebra: Transpose of a Matrix

9 years ago / 732 views

Transpose of a matrix More free lessons at: http://www.khanacademy.org/video?v=2t0003_sxtU
20:10 Popular
Linear Algebra: Determinant as Scaling Factor

9 years ago / 851 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

9 years ago / 1,362 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 Popular
Linear Algebra: Simpler 4x4 determinant

9 years ago / 780 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 Popular
Linear Algebra: Upper Triangular Determinant

9 years ago / 761 views

The determinant of an upper triangular matrix More free lessons at: http://www.khanacademy.org/video?v=VX7K8iqoiRc
10:25 Popular
Linear Algebra: Determinant after row operations

9 years ago / 766 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 Popular
Linear Algebra: Duplicate Row Determinant

9 years ago / 803 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

9 years ago / 1,039 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

9 years ago / 1,081 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 Popular
Linear Algebra: Determinant when row multiplied by scalar

9 years ago / 732 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 Popular
Linear Algebra: Rule of Sarrus of Determinants

9 years ago / 839 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 Popular
Linear Algebra: Determinants along other rows/cols

9 years ago / 738 views

Finding the determinant by going along other rows or columns More free lessons at: http://www.khanacademy.org/video?v=nu87kfmwNfU
18:40 Popular
Linear Algebra: nxn Determinant

9 years ago / 744 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 Popular
Linear Algebra: 3x3 Determinant

9 years ago / 803 views

Determinants: Finding the determinant of a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=0c7dt2SQfLw
18:20 Popular
Linear Algebra: Formula for 2x2 inverse

9 years ago / 780 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 Popular
Linear Algebra: Example of Finding Matrix Inverse

9 years ago / 775 views

Example of calculating the inverse of a matrix More free lessons at: http://www.khanacademy.org/video?v=r9aTLTN16V4
18:00 Popular
Linear Algebra: Deriving a method for determining inverses

9 years ago / 705 views

Determining a method for constructing inverse transformation matrices More free lessons at: http://www.khanacademy.org/video?v=6DpzCKJBsz0
21:25 Popular
Linear Algebra: Showing that Inverses are Linear

9 years ago / 710 views

Showing that inverse transformations are also linear More free lessons at: http://www.khanacademy.org/video?v=mr9Tow8hpCg
06:37 Popular
Linear Algebra: Simplifying conditions for invertibility

9 years ago / 733 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 Popular
Linear Algebra: Matrix condition for one-to-one trans

9 years ago / 781 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

9 years ago / 1,991 views

Exploring the solution set of Ax=b (non homogeneous equations) More free lessons at: http://www.khanacademy.org/video?v=1PsNIzUJPkc
25:51 Popular
Determining whether a transformation is onto

9 years ago / 712 views

Determining whether a transformation is onto More free lessons at: http://www.khanacademy.org/video?v=eR8vEdJTvd0
06:31 Popular
Relating invertibility to being onto and one-to-one

9 years ago / 712 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 Popular
Surjective (onto) and Injective (one-to-one) functions

9 years ago / 782 views

Introduction to surjective and injective functions More free lessons at: http://www.khanacademy.org/video?v=xKNX8BUWR0g
22:41 Popular
Proof: Invertibility implies a unique solution to f(x)=y

9 years ago / 832 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 Popular
Linear Algebra: Introduction to the inverse of a function

9 years ago / 744 views

Introduction to the inverse of a function More free lessons at: http://www.khanacademy.org/video?v=-eAzhBZgq28
09:52 Popular
Distributive Property of Matrix Products

9 years ago / 864 views

Showing that matrix products exhibit the distributive property More free lessons at: http://www.khanacademy.org/video?v=oMWTMj78cwc
11:59 Popular
Matrix Product Associativity

9 years ago / 803 views

Showing that matrix products are associative More free lessons at: http://www.khanacademy.org/video?v=Hhc96U_HvQE
18:14 Popular
Linear Algebra: Matrix Product Examples

9 years ago / 786 views

Example of taking the product of two matrices More free lessons at: http://www.khanacademy.org/video?v=x1z0hOyjapU
16:31 Popular
Compositions of Linear Transformations 2

9 years ago / 727 views

Providing the motivation for definition of matrix products More free lessons at: http://www.khanacademy.org/video?v=BuqcKpe5ZQs
12:21 Popular
Compositions of Linear Transformations 1

9 years ago / 746 views

Introduction to compositions of Linear Transformations More free lessons at: http://www.khanacademy.org/video?v=f_DTiXZpb8M
16:41 Popular
Expressing a Projection on to a line as a Matrix Vector prod

9 years ago / 773 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 Popular
Introduction to Projections

9 years ago / 788 views

Determining the projection of a vector on s line More free lessons at: http://www.khanacademy.org/video?v=27vT-NWuw0M
06:59 Popular
Unit Vectors

9 years ago / 759 views

What unit vectors are and how to construct them More free lessons at: http://www.khanacademy.org/video?v=lQn7fksaDq0
12:18 Popular
Rotation in R3 around the X-axis

9 years ago / 722 views

Construction a rotation transformation in R3 More free lessons at: http://www.khanacademy.org/video?v=gkyuLPzfDV0
17:52 Popular
Linear Transformation Examples: Rotations in R2

9 years ago / 782 views

Linear Transformation Examples: Rotations in R2 More free lessons at: http://www.khanacademy.org/video?v=lPWfIq5DzqI
15:13 Popular
Linear Transformation Examples: Scaling and Reflections

9 years ago / 753 views

Creating scaling and reflection transformation matrices (which are diagonal) More free lessons at: http://www.khanacademy.org/video?v=qkfODKmZ-x4
10:42 Popular
More on Matrix Addition and Scalar Multiplication

9 years ago / 759 views

More on Matrix Addition and Scalar Multiplication More free lessons at: http://www.khanacademy.org/video?v=Z19-ObbmHJE
15:09 Popular
Sums and Scalar Multiples of Linear Transformations

9 years ago / 739 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 Popular
Preimage and Kernel Example

9 years ago / 807 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

9 years ago / 903 views

Definition of preimage of a set More free lessons at: http://www.khanacademy.org/video?v=zVsGtU8lIWs
16:37 Popular
im(T): Image of a Transformation

9 years ago / 830 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 Popular
Image of a subset under a transformation

9 years ago / 766 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 Popular
Linear Transformations as Matrix Vector Products

9 years ago / 904 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 Popular
Matrix Vector Products as Linear Transformations

9 years ago / 872 views

Matrix Vector Products as Linear Transformations More free lessons at: http://www.khanacademy.org/video?v=ondmopWLiEg
13:53 Popular
Linear Transformations

9 years ago / 718 views

Introduction to linear transformations More free lessons at: http://www.khanacademy.org/video?v=4PCktDZJH8E
14:19
Vector Transformations

9 years ago / 677 views

Introduction to the notion of vector transformations More free lessons at: http://www.khanacademy.org/video?v=gAbadNuQEjI
16:02 Popular
A more formal understanding of functions

9 years ago / 867 views

A more formal understanding of functions More free lessons at: http://www.khanacademy.org/video?v=BQMyeQOLvpg
13:40 Popular
Showing that the candidate basis does span C(A)

9 years ago / 715 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 Popular
Showing relation between basis cols and pivot cols

9 years ago / 728 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 Popular
Dimension of the Column Space or Rank

9 years ago / 757 views

Dimension of the Column Space or Rank More free lessons at: http://www.khanacademy.org/video?v=JUgrBkPteTg
13:59 Popular
Dimension of the Null Space or Nullity

9 years ago / 927 views

Dimension of the Null Space or Nullity More free lessons at: http://www.khanacademy.org/video?v=abYAUqs_n6I
21:35 Popular
Proof: Any subspace basis has same number of elements

9 years ago / 843 views

Proof: Any subspace basis has same number of elements More free lessons at: http://www.khanacademy.org/video?v=Zn2K8UIT8r4
21:11 Popular
Visualizing a Column Space as a Plane in R3

9 years ago / 806 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

9 years ago / 982 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 Popular
Column Space of a Matrix

9 years ago / 723 views

Introduction to the column space of a matrix More free lessons at: http://www.khanacademy.org/video?v=st6D5OdFV9M
11:35 Popular
Null Space 3: Relation to Linear Independence

9 years ago / 749 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 Popular
Null Space 2: Calculating the null space of a matrix

9 years ago / 800 views

Calculating the null space of a matrix More free lessons at: http://www.khanacademy.org/video?v=qvyboGryeA8
10:23 Popular
Introduction to the Null Space of a Matrix

9 years ago / 772 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 Popular
Matrix Vector Products

9 years ago / 795 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 Popular
Matrices: Reduced Row Echelon Form 3

9 years ago / 822 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 Popular
Matrices: Reduced Row Echelon Form 2

9 years ago / 754 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 Popular
Matrices: Reduced Row Echelon Form 1

9 years ago / 757 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 Popular
Dot and Cross Product Comparison/Intuition

9 years ago / 707 views

Dot and Cross Product Comparison/Intuition More free lessons at: http://www.khanacademy.org/video?v=tdwFdzVqito
18:09 Popular
Proof: Relationship between cross product and sin of angle

9 years ago / 790 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

9 years ago / 650 views

Introduction to the cross product More free lessons at: http://www.khanacademy.org/video?v=pJzmiywagfY
13:53 Popular
Defining a plane in R3 with a point and normal vector

9 years ago / 769 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 Popular
Defining the angle between vectors

9 years ago / 841 views

Introducing the idea of an angle between two vectors More free lessons at: http://www.khanacademy.org/video?v=5AWob_z74Ks
18:53 Popular
Linear Algebra: Vector Triangle Inequality

9 years ago / 737 views

Proving the triangle inequality for vectors in Rn More free lessons at: http://www.khanacademy.org/video?v=PsNidCBr5II
16:56 Popular
Proof of the Cauchy-Schwarz Inequality

9 years ago / 856 views

Proof of the Cauchy-Schwarz Inequality More free lessons at: http://www.khanacademy.org/video?v=r2PogGDl8_U
10:46 Popular
Proving Vector Dot Product Properties

9 years ago / 792 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

9 years ago / 655 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

9 years ago / 680 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

9 years ago / 610 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

9 years ago / 612 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

9 years ago / 650 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

9 years ago / 664 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

9 years ago / 636 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

9 years ago / 645 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

9 years ago / 642 views

Visually understanding basic vector operations More free lessons at: http://www.khanacademy.org/video?v=r4bH66vYjss
15:26 Popular
Solving 3 Equations with 3 Unknowns

9 years ago / 714 views

Solving 3 equations with 3 unknowns (old video from July 2008)
08:02 Popular
3-variable linear equations (part 1)

9 years ago / 821 views

Visual intuition of a 3-variable linear equation.
14:27 Popular
Singular Matrices

9 years ago / 815 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

9 years ago / 673 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

9 years ago / 682 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 Popular
Inverting Matrices (part 3)

9 years ago / 792 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)

9 years ago / 606 views

Inverting a 3x3 matrix More free lessons at: http://www.khanacademy.org/video?v=S4n-tQZnU6o
14:15 Popular
Inverse Matrix (part 1)

9 years ago / 826 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)

9 years ago / 621 views

More on multiplying matrices.
13:41 Popular
Matrix multiplication (part 1)

9 years ago / 824 views

Multiplying two 2x2 matrices.
11:51
Introduction to matrices

9 years ago / 626 views

What a matrix is. How to add and subtract them.
12:14 Popular
Using the Convolution Theorem to Solve an Initial Value Prob

9 years ago / 703 views

Using the Convolution Theorem to solve an initial value problem More free lessons at: http://www.khanacademy.org/video?v=rfyq32mHcYs
13:46 Popular
The Convolution and the Laplace Transform

9 years ago / 712 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

9 years ago / 629 views

Introduction to the Convolution More free lessons at: http://www.khanacademy.org/video?v=IW4Reburjpc
12:13 Popular
Laplace Transform of the Dirac Delta Function

9 years ago / 776 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

9 years ago / 683 views

Introduction to the Dirac Delta Function More free lessons at: http://www.khanacademy.org/video?v=4qfdCwys2ew
19:12 Popular
Laplace/Step Function Differential Equation

9 years ago / 850 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

9 years ago / 643 views

Using our toolkit to take some inverse Laplace Transforms More free lessons at: http://www.khanacademy.org/video?v=BbqbvSig6Mc
24:16 Popular
Laplace Transform of the Unit Step Function

9 years ago / 910 views

Introduction to the unit step function and its Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=4Mr7aEHQr8E
10:16 $Laplace Transform of t^n: L{t^n}$
Laplace Transform of t^n: L{t^n}

9 years ago / 623 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}

9 years ago / 658 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

9 years ago / 587 views

Solving a non-homogeneous differential equation using the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=nlUG4OKN1IY
11:17 Popular
More Laplace Transform tools

9 years ago / 739 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

9 years ago / 622 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

9 years ago / 667 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

9 years ago / 689 views

Laplace transform of cosine and polynomials! More free lessons at: http://www.khanacademy.org/video?v=fyJkXBvcA2Q
11:37 Popular
Laplace Transform 5

9 years ago / 822 views

Useful properties of the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=E2VxbufzuWQ
09:14
Laplace Transform 4

9 years ago / 623 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)})

9 years ago / 685 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

9 years ago / 654 views

Laplace transform of e^at More free lessons at: http://www.khanacademy.org/video?v=33TYoybjqPg
08:02
Laplace Transform 1

9 years ago / 634 views

Introduction to the Laplace Transform More free lessons at: http://www.khanacademy.org/video?v=OiNh2DswFt4
05:55
Undetermined Coefficients 4

9 years ago / 632 views

Putting it all together! More free lessons at: http://www.khanacademy.org/video?v=vAepSNDLZRM
08:10
Undetermined Coefficients 3

9 years ago / 627 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

9 years ago / 564 views

Another example using undetermined coefficients. More free lessons at: http://www.khanacademy.org/video?v=hbJ2o9EUmJ0
10:11
Undetermined Coefficients 1

9 years ago / 665 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

9 years ago / 620 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

9 years ago / 594 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

9 years ago / 649 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

9 years ago / 672 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

9 years ago / 689 views

What happens when the characteristic equations has complex roots?! More free lessons at: http://www.khanacademy.org/video?v=6xEO4BeawzA
09:11 Popular
2nd Order Linear Homogeneous Differential Equations 4

9 years ago / 701 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

9 years ago / 682 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 Popular
2nd Order Linear Homogeneous Differential Equations 2

9 years ago / 704 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

9 years ago / 676 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

9 years ago / 657 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

9 years ago / 693 views

Introduction to first order homogenous equations. More free lessons at: http://www.khanacademy.org/video?v=9Wfn-WWV1aY
08:26
Integrating factors 2

9 years ago / 568 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

9 years ago / 625 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

9 years ago / 630 views

One more exact equation example More free lessons at: http://www.khanacademy.org/video?v=eu_GFuU7tLI
08:01
Exact Equations Example 2

9 years ago / 635 views

Some more exact equation examples More free lessons at: http://www.khanacademy.org/video?v=utQi1ZhF__Q
12:10
Exact Equations Example 1

9 years ago / 637 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)

9 years ago / 659 views

More intuitive building blocks for exact equations. More free lessons at: http://www.khanacademy.org/video?v=a7wYAtMjORQ
09:54 Popular
Exact Equations Intuition 1 (proofy)

9 years ago / 803 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

9 years ago / 699 views

Another separable differential equation example. More free lessons at: http://www.khanacademy.org/video?v=xVWCfMe97ws
12:01
Separable Differential Equations

9 years ago / 677 views

Introduction to separable differential equations. More free lessons at: http://www.khanacademy.org/video?v=C5-lz0hcqsE
11:03 Popular
What is a differential equation

9 years ago / 702 views

What a differential equation is and some terminology.