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• 18:14

### 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

• 08:50

### Linear Algebra: Transpose of a Matrix Product

347 views / 0 likes - added

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

• 19:53

### Linear Algebra - Matrix Transformations

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Matrix multiplication and linear algebra explained with 3D animations.

• 08:37

### Linear Algebra: Transpose of a Matrix

341 views / 0 likes - added

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

• 06:22

### Linear Algebra: Example of Finding Matrix Inverse

339 views / 0 likes - added

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

• 14:08

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

359 views / 0 likes - added

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

• 13:04

### Linear Algebra: Subspace Projection Matrix Example

436 views / 0 likes - added

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

• 17:55

### Linear Algebra: Change of Basis Matrix

379 views / 0 likes - added

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

• 20:00

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

375 views / 0 likes - added

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

• 05:39

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

385 views / 0 likes - added

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

• 15:34

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

345 views / 0 likes - added

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

• 15:47

### 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

• 17:32

### Linear Transformations as Matrix Vector Products

416 views / 0 likes - added

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

• 15:46

### Linear Algebra: Introduction to Linear Independence

257 views / 0 likes - added

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

• 17:04

### Matrix Vector Products as Linear Transformations

422 views / 0 likes - added

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

• 25:34

### Linear Algebra: Vector Examples

270 views / 0 likes - added

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

• 18:50

### Linear Algebra: Least Squares Examples

357 views / 0 likes - added

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

• 11:59

### 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

• 17:52

### 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

• 08:52

### Linear Models Example 1 | Algebra I | Khan Academy

342 views / 0 likes - added

• 08:23

### Constructing Linear Functions Example 2 | Algebra I | Khan Academy

245 views / 0 likes - added

Linear model for painting Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/linear-functions-modeling/e/constructing-linear-functions-word-problems?utm_sour

• 06:35

### Constructing Linear Functions Example 1 | Algebra I | Khan Academy

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Linear model for ice sheet thickness Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/linear-functions-modeling/e/constructing-linear-functions-word-proble

• 05:37

### Linear Models Example 2 | Algebra I | Khan Academy

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Marbles and water in tank Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/linear-functions-modeling/e/constructing-and-interpreting-linear-functions?utm_s

• 03:12

### Graphing Linear Functions Example 2 | Algebra I | Khan Academy

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Graphing equation for filling pool Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/linear-functions-modeling/e/graphing-linear-functions-word-problems?utm

• 02:40

### Interpreting Linear Formulas Example 1 | Algebra I | Khan Academy

333 views / 0 likes - added

Interpreting a linear formula Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/interpreting_linear_functions/e/interpreting-features-of-linear-functions?ut

• 05:30

### Graphing Linear Functions Example 1 | Algebra I | Khan Academy

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Learn how graph a linear function. This video gives an example of graphing fuel consumption as a function of distance. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-

• 02:35

### Interpreting Linear Formulas Example 2 | Algebra I | Khan Academy

258 views / 0 likes - added

Linear equation for file transfer Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/interpreting_linear_functions/e/interpreting-features-of-linear-function

• 07:11

### Graphing Solutions To Two-variable Linear Equations Example 2 | Algebra I | Khan Academy

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Graphing solutions to 2 variable linear equations Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/solutions-to-two-var-linear-equations/e/graphing-solutio

• 08:21

### Two-variable Linear Equations And Their Graphs | Algebra I | Khan Academy

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Introduction to 2-variable linear equations and their graphs Watch the next lesson: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/solutions-to-two-var-linear-equations/v/checking-ordered-pair-solutions-to-equatio

• 24:47

### Linear Algebra: Parametric Representations of Lines

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

• 07:08

### Early Train Word Problem | Linear Equations | Algebra I | Khan Academy

351 views / 0 likes - added

Fun word problem that is almost a brain teaser. Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/More-equation-practice/v/patterns-in-sequences-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

• 12:07

### Linear Algebra: Transpose of a Vector

322 views / 0 likes - added

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

• 12:49

### Scientific Notation Examples | Pre-Algebra | Khan Academy

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• 21:25

### Linear Algebra: Showing that Inverses are Linear

319 views / 0 likes - added

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

• 21:38

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

454 views / 0 likes - added

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

• 27:04

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

384 views / 0 likes - added

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

• 07:18

### Origins Of Algebra | Introduction To Algebra | Algebra I | Khan Academy

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Where did the word "Algebra" and its underlying ideas come from? Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-algebra/overview_hist_alg/v/abstract-ness?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Algebra I on Kha

• 10:01

### Linear Algebra: 3x3 Determinant

360 views / 0 likes - added

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

• 14:10

### Linear Algebra: Determinant of Transpose

365 views / 0 likes - added

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

• 06:45

### Algebra: Linear Equations 3

206 views / 0 likes - added

Linear equations with multiple variable and constant terms More free lessons at: http://www.khanacademy.org/video?v=Zn-GbH2S0Dk

• 08:19

### Linear Algebra: Duplicate Row Determinant

388 views / 0 likes - added

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

• 08:07

### Linear Algebra: Upper Triangular Determinant

368 views / 0 likes - added

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

• 14:34

### Linear Algebra: Finding Eigenvectors and Eigenspaces example

397 views / 0 likes - added

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

• 18:20

### Linear Algebra: Formula for 2x2 inverse

352 views / 0 likes - added

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

• 06:37

### Linear Algebra: Simplifying conditions for invertibility

324 views / 0 likes - added

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

• 20:10

### Linear Algebra: Determinant as Scaling Factor

394 views / 0 likes - added

Viewing the determinant of the transformation matrix as a scaling factor of regions More free lessons at: http://www.khanacademy.org/video?v=g3MqSdO5Ubc

• 04:08

### Cross Product and Dot Product: Visual explanation

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Visual interpretation of the cross product and the dot product of two vectors. My Patreon page: https://www.patreon.com/EugeneK

• 16:55

### Linear Algebra: Determinant when row is added

353 views / 0 likes - added

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

• 07:00

### Abstract-ness | Introduction To Algebra | Algebra I | Khan Academy

272 views / 0 likes - added

The general idea behind the word 'abstract' Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-algebra/overview_hist_alg/v/the-beauty-of-algebra?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Missed the previous lesson? h

• 06:55

### What Are Variables, Expressions, And Equations? | Introduction To Algebra | Algebra I | Khan Academy

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Learn what variables, expressions, and equations really are. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/introduction-to-algebra/feel-for-equations-and-inequalit/e/dependent-and-independent-variable

• 15:13

### Linear Transformation Examples: Scaling and Reflections

348 views / 0 likes - added

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

• 21:10

### Matrix Vector Products

360 views / 0 likes - added

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

• 12:07

### Algebra Basics: What Is Algebra? - Math Antics

408 views / 0 likes - added

The first video in the Algebra Basics Series: https://www.youtube.com/watch?v=NybHckSEQBI&list=PLUPEBWbAHUszT_GebJK23JHdd_Bss1N-G Next video: https://youtu.be/l3XzepN03KQ This video gives an overview of Algebra and introduces the concepts of unknown value

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• 07:28

### Algebra: Linear Equations 1

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equations of the form AX=B More free lessons at: http://www.khanacademy.org/video?v=bAerID24QJ0

• 06:07

### Algebra: Linear Equations 2

216 views / 0 likes - added

solving equations of the form AX+B=C More free lessons at: http://www.khanacademy.org/video?v=DopnmxeMt-s

• 13:25

### Linear Algebra: Another Least Squares Example

361 views / 0 likes - added

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

• 18:40

### Linear Algebra: nxn Determinant

341 views / 0 likes - added

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

• 22:08

### Linear Algebra: Orthogonal Complements

363 views / 0 likes - added

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

• 17:26

### Linear Algebra: Projections onto Subspaces

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

• 19:00

### Linear Algebra: Basis of a Subspace

295 views / 0 likes - added

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

• 15:32

### Linear Algebra: Least Squares Approximation

362 views / 0 likes - added

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

• 21:36

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

345 views / 0 likes - added

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

• 08:41

### Linear Algebra: Transposes of sums and inverses

349 views / 0 likes - added

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

• 16:08

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

351 views / 0 likes - added

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

• 09:03

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

339 views / 0 likes - added

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

• 23:19

### Linear Algebra: Rowspace and Left Nullspace

350 views / 0 likes - added

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

• 07:18

### Linear Algebra: Rule of Sarrus of Determinants

359 views / 0 likes - added

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

• 11:16

### Linear Algebra: Introduction to Orthonormal Bases

366 views / 0 likes - added

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

• 18:54

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

340 views / 0 likes - added

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

• 10:25

### Linear Algebra: Determinant after row operations

337 views / 0 likes - added

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

• 09:13

### Linear Algebra: Simpler 4x4 determinant

370 views / 0 likes - added

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

• 19:24

### Linear Algebra: The Gram-Schmidt Process

348 views / 0 likes - added

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

• 13:14

### Linear Algebra: Gram-Schmidt Process Example

357 views / 0 likes - added

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

• 18:53

### Linear Algebra: Vector Triangle Inequality

289 views / 0 likes - added

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

• 07:43

### Linear Algebra: Introduction to Eigenvalues and Eigenvectors

365 views / 0 likes - added

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

• 02:35

### Checking Ordered Pair Solutions To Equations Example 1 | Algebra I | Khan Academy

329 views / 0 likes - added

Checking ordered pair solutions to equations Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/solutions-to-two-var-linear-equations/e/plugging_in_values?ut

• 11:35

### Null Space 3: Relation to Linear Independence

312 views / 0 likes - added

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

• 02:27

### Checking Ordered Pair Solutions To Equations Example 2 | Algebra I | Khan Academy

274 views / 0 likes - added

Second example of ordered pair solutions Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/solutions-to-two-var-linear-equations/e/plugging_in_values?utm_so

• 17:38

### More on linear independence

264 views / 0 likes - added

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

• 13:20

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

342 views / 0 likes - added

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

• 02:52

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

427 views / 0 likes - added

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

• 15:28

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

439 views / 0 likes - added

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

• 16:34

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

343 views / 0 likes - added

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

• 18:00

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

346 views / 0 likes - added

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

• 13:57

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

390 views / 0 likes - added

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

• 09:19

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

386 views / 0 likes - added

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

• 15:09

### Sums and Scalar Multiples of Linear Transformations

339 views / 0 likes - added

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

• 13:09

### Linear Algebra: Showing that an eigenbasis makes for good coordinate systems

359 views / 0 likes - added

Showing that an eigenbasis makes for good coordinate systems More free lessons at: http://www.khanacademy.org/video?v=C2PC9185gIw

• 05:02

### Positive And Negative Slope | Algebra I | Khan Academy

324 views / 0 likes - added

Positive and negative slope Watch the next lesson: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/slope/v/similar-triangles-to-prove-that-the-slope-is-constant-for-a-line?utm_source=YT&utm_medium=Desc&utm_campaign

• 05:09

### Converting From Slope-intercept To Standard Form | Algebra I | Khan Academy

371 views / 0 likes - added

Converting from slope-intercept to standard form Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/standard-form/e/converting_between_slope_intercept_and_st

• 06:54

### Extracellular Matrix

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Overview of how cells relate to the extracellular matrix.

• 03:04

### How To Create A Function From An Equation (example) | Functions | Algebra I | Khan Academy

259 views / 0 likes - added

Sal find the formula of a function that, given an input value "b," outputs a value "a" that satisfies the equation 4a+7b=-52. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/algebra-functions/functions-

• 01:40

### How To Match Function Input To Output Given The Formula (example) | Algebra I | Khan Academy

247 views / 0 likes - added

Sal finds the input value for which f(t)=13, given that f(t)=-2t+5. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/algebra-functions/function-inputs-and-outputs/e/functions_matching_inputs_outputs?utm_

• 01:07

### How To Match Function Input To Output Given The Graph (example) | Algebra I | Khan Academy

270 views / 0 likes - added

Sal finds the input value for which g(x)=-2 given the graph of g. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/algebra-functions/function-inputs-and-outputs/e/functions_matching_inputs_outputs?utm_so

• 02:34

### Converting From Standard Form To Slope-intercept Form | Algebra I | Khan Academy

391 views / 0 likes - added

Standard form to slope-intercept form Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/standard-form/e/slope-from-an-equation-in-standard-form?utm_source=Y

• 03:24

### How To Interpret An Expression With Function Notation | Functions | Algebra I | Khan Academy

263 views / 0 likes - added

Sal interprets the expression M(30)-M(0)=100 where M models an account balance over time. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/algebra-functions/interpreting-function-notation/e/function-nota

• 02:36

### How To Interpret An Expression With Function Notation | Functions | Algebra I | Khan Academy

330 views / 0 likes - added

Sal interprets the expression P(5) minor P(9) where P models the number of people at the beach over time. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/algebra-functions/interpreting-function-notation

• 10:40

### Column Space of a Matrix

341 views / 0 likes - added

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

• 14:15

### Inverse Matrix (part 1)

355 views / 0 likes - added

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

• 10:42

### More on Matrix Addition and Scalar Multiplication

343 views / 0 likes - added

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

• 10:23

### Introduction to the Null Space of a Matrix

306 views / 0 likes - added

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

• 09:52

### Distributive Property of Matrix Products

385 views / 0 likes - added

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

• 13:20

### Lin Alg: Alternate Basis Tranformation Matrix Example

452 views / 0 likes - added

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

• 13:34

### 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

• 18:02

### 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

• 16:41

### 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

• 09:27

### 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

• 12:14

### Algebra Basics: Exponents In Algebra - Math Antics

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Part of the Algebra Basics Series: https://www.youtube.com/watch?v=NybHckSEQBI&list=PLUPEBWbAHUszT_GebJK23JHdd_Bss1N-G Previous video: https://youtu.be/K6ewhnaL4KQ This video shows how exponents can be used more generally with variables. It explains why x

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### AMAZING~Once in a Lifetime AMMONITES & MATRIX FOUND..!!

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Arrowhead Hunting Mississippi....Two once in a lifetime.,65 million year old Ammonites and matrix found prospecting a new creek for Arrowheads...This beast measures 16 inches in diameter and weighs 36 lbs....Thanks for watching

• 01:42

### Factoring As Product Of Binomials

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Factoring as product of binomials

• 06:37

### Equivalent Vectors Examples

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Equivalent vectors examples

• 05:16

278 views / 0 likes - added

• 29:00

### 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

• 11:14

### 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

• 12:36

### 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

• 10:03

### Cross product 1

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Introduction to the cross product More free lessons at: http://www.khanacademy.org/video?v=zA0fvwtvgvA

• 10:53

### Cross Product 2

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A little more intuition on the cross product. More free lessons at: http://www.khanacademy.org/video?v=o_puKe_lTKk

• 10:33

### The dot product

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Introduction to the vector dot product. More free lessons at: http://www.khanacademy.org/video?v=KDHuWxy53uM

• 07:14

### Examples Of Finding The Domain Of A Function

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Examples of finding the domain of a function

• 05:42

### Examples of null and alternative hypotheses

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Examples of null and alternative hypotheses

• 04:24

### Examples Evaluating Piecewise Functions

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Examples evaluating piecewise functions

• 06:58

### Arc Measure With Equations Examples

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Arc measure with equations examples

• 04:37

### Tangents Of Circles Exercise Examples

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Tangents of circles exercise examples

• 07:21

### Correlation Coefficient Intuition Examples

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Correlation coefficient intuition examples

• 06:42

### More Examples Finding Vector Angles

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More examples finding vector angles

• 08:59

### More Organic Chemistry Naming Examples 1

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More Organic Chemistry Naming Examples 1

• 09:58

### Two more examples of solving rational equations

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Two more examples of solving rational equations

• 07:48

### Organic Chemistry Naming Examples 4

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Organic Chemistry Naming Examples 4

• 11:02

### Chiral Examples 1

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Chiral Examples 1 More free lessons at: http://www.khanacademy.org/video?v=0XSSPow5oAc

• 10:19

### Chiral Examples 2

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Chiral Examples 2 More free lessons at: http://www.khanacademy.org/video?v=QQMZ1ljepWg

• 10:01

### Cross Product and Torque

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The cross product and the direction of torque. More free lessons at: http://www.khanacademy.org/video?v=s38l6nmTrvM

• 07:32

### Examples Interpreting Graphs Of Proportional Relationships

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Examples interpreting graphs of proportional relationships

• 05:55

### Worked Examples From Solving Systems Graphically

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Worked examples from solving systems graphically

• 04:53

### Examples From Understanding Scalar Multiplication Exercise

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Examples from understanding scalar multiplication exercise

• 07:22

### More Exponential Decay Examples

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A few more examples of exponential decay. More free lessons at: http://www.khanacademy.org/video?v=Hqzakjo_dYg

• 08:27

### Naming Alkenes Examples

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Naming Alkenes Examples More free lessons at: http://www.khanacademy.org/video?v=KWv5PaoHwPA

• 10:44

### Snell's Law Examples 1

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Snell's Law Examples 1 More free lessons at: http://www.khanacademy.org/video?v=HahjsBApxLE

• 09:36

### Convex Lens Examples

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Convex Lens Examples More free lessons at: http://www.khanacademy.org/video?v=xxF_mdoZom0

• 07:15

### Product Rule for derivatives: Visualized with 3D animations

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Visual representation of the product rule for derivatives in Calculus.

• 04:28

### Product rule - Logarithm derivatives example

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Learn calculus with this product rule Derivative example with logarithms and exponential functions. This complete calculus derivatives tutorial explains why and how to use the product rule. To see all my calculus videos check out my website http://MathMee

• 03:00

### Product of Functions

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u17_l3_t1_we3 Product of Functions More free lessons at: http://www.khanacademy.org/video?v=JKvmAexeMgY Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

• 10:04

### Organic Chemistry Naming Examples 5

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Organic Chemistry Naming Examples 5 More free lessons at: http://www.khanacademy.org/video?v=6BR0Q5e74bs

• 10:26

### Organic Chemistry Naming Examples 2

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Organic Chemistry Naming Examples 2 More free lessons at: http://www.khanacademy.org/video?v=CJRQ8gOjq4E

• 19:14

### 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

• 14:25

### Vector Triple Product Expansion (very optional)

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A shortcut for having to evaluate the cross product of three vectors More free lessons at: http://www.khanacademy.org/video?v=b7JTVLc_aMk

• 08:11

### Organic Chemistry Naming Examples 3

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Organic Chemistry Naming Examples 3 More free lessons at: http://www.khanacademy.org/video?v=Se-ekDNhCDk

• 04:01

### Product rule - Calculus derivatives tutorial

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Learn how to take the derivative of a function using the product rule. This complete calculus derivatives tutorial explains why and how to use the product rule. To see all my calculus videos check out my website http://MathMeeting.com My name is Chris and

• 06:32

### Examples Analyzing Clusters, Gaps, Peaks And Outliers For Distributions

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Examples analyzing clusters, gaps, peaks and outliers for distributions

• 09:56

### Probability 1 Module Examples

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Basic probability examples (the type seen in the probability 1 module) More free lessons at: http://www.khanacademy.org/video?v=mLE-SlOZToc

• 18:09

### 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

• 06:04

### Entgegen-Zusammen Naming Scheme for Alkenes Examples

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Entgegen-Zusammen Naming Scheme for Alkenes Examples More free lessons at: http://www.khanacademy.org/video?v=GFiizJ-jGVw

• 05:05

### Solving Ratio Problems With Tables Example 1 | Pre-Algebra | Khan Academy

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We're displaying ratios in a table format here, and then asking: given a ratio, solve for equivalent ratios. Here are a few examples to practice on. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/r

• 12:14

### Using a Linear Model

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Using a Linear Model

• 04:16

### Least Common Multiple Exercise | Factors And Multiples | Pre-Algebra | Khan Academy

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We're practicing finding the least common multiple in these example exercises. We'll teach you the prime factorization approach which is a pretty nifty way to find the lcm (least common multiple). Practice this lesson yourself on KhanAcademy.org right now

• 11:46

### Predicting with Linear Models

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Predicting with Linear Models

• 08:52

### Systems of Linear Inequalities

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Systems of Linear Inequalities

• 04:59

### Interpreting Visual Linear Inequality

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Interpreting visual linear inequality

• 03:42

### Understanding Linear Inequality With Two Variables

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Understanding linear inequality with two variables

• 02:22

### Setting Up A Linear Inequality In Two Variables

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Setting up a linear inequality in two variables

• 04:20

### Analyzing Two Variable Linear Inequality

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Analyzing two variable linear inequality

• 08:07

### Standard Form For Linear Equations

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Standard form for linear equations

• 08:15

### Linear, Quadratic, and Exponential Models

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• 08:02

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

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Visual intuition of a 3-variable linear equation.

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### 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

• 07:25

### Domain And Range For Piecewise Linear Function

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Domain and range for piecewise linear function

• 04:12

### Constraining Solutions To Two Variable Linear Inequalities

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Constraining solutions to two variable linear inequalities

• 04:33

### Multiplying Negative And Positive Fractions | Fractions | Pre-Algebra | Khan Academy

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See examples of multiplying and dividing fractions with negative numbers. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/multiplying-fractions-pre-alg/e/multiplying_fractions?utm_

• 13:53

### Linear Transformations

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

• 23:29

### Linear Subspaces

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

• 11:49

### Linear Function Graphs

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Linear Function Graphs More free lessons at: http://www.khanacademy.org/video?v=EmTvdKkAUtE

• 12:21

### 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

• 02:42

### Basic Linear Function

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U03_L2_T4_we1 : Basic Linear Function Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

• 02:42

### Graphing linear inequalities in two variables 2 (old and redone in newer video)

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U05_L2_T1_we2 : Graphing linear inequalities in two variables

• 20:35

### Linear Combinations and Span

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

• 03:55

### How to name a product, from the man behind Swiffer and BlackBerry

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Have you ever wondered how products get their names? Swiffer, BlackBerry, Febreze, Dibs, Dasani– all these brands have one thing in common. They are products named by a small firm in Sausalito, California, called Lexicon Branding. The firm, founded by Dav

• 10:09

### Linear Equations in Standard Form

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Linear Equations in Standard Form More free lessons at: http://www.khanacademy.org/video?v=BaQXFstxCMo

• 08:30

### Solving Linear Systems by Graphing

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Solving Linear Systems by Graphing More free lessons at: http://www.khanacademy.org/video?v=5a6zpfl50go

• 09:21

### Solving Linear Systems by Substitution

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Solving Linear Systems by Substitution More free lessons at: http://www.khanacademy.org/video?v=V7H1oUHXPkg

• 15:18 Popular

### Special Types of Linear Systems

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Special Types of Linear Systems More free lessons at: http://www.khanacademy.org/video?v=5qkyuHIE2GM

• 02:38

### Graphing Linear Equations — Harder Example | Math | New SAT | Khan Academy

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Watch Sal work through a harder Graphing linear equations problem. Watch the next lesson: https://www.khanacademy.org/test-prep/new-sat/new-sat-math/new-sat-heart-of-algebra/v/sat-math-h3-easier?utm_source=YT&utm_medium=Desc&utm_campaign=NewSAT Missed the

• 14:58

### Linear Equations in Slope Intercept Form

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Linear Equations in Slope Intercept Form More free lessons at: http://www.khanacademy.org/video?v=5fkh01mClLU

• 09:39

### Linear Equations in Point Slope Form

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Linear Equations in Point Slope Form More free lessons at: http://www.khanacademy.org/video?v=zqCokP2vDGo

• 02:55

### Linear Equation Word Problems — Basic Example | Math | New SAT | Khan Academy

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Watch Sal work through a basic Linear equations word problem. Watch the next lesson: https://www.khanacademy.org/test-prep/new-sat/new-sat-math/new-sat-heart-of-algebra/v/sat-math-h2-easier?utm_source=YT&utm_medium=Desc&utm_campaign=NewSAT Missed the prev

• 16:16

### 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

• 05:26

### Factors And Divisibility In Algebra

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Factors and divisibility in algebra

• 10:29

### Algebra Basics: Solving 2-Step Equations - Math Antics

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There was a confusing example in the original video. This is the updated version. This video shows students how to solve 2-step Algebra equations involving one addition or subtraction and one multiplication or division. Part of the Algebra Basics Series:

• 11:59

### Generalized Linear Consumption Function

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Generalizing a linear consumption function as a function of aggregate income More free lessons at: http://www.khanacademy.org/video?v=N44RZtJ4jj4

• 02:51

### The Horse Horseshoe Boots Viral Algebra Problem - The Correct Answer Explained

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A lot of people are arguing over the correct answer to this algebra problem involving horses, horseshoes, and boots. A Facebook post with this problem has over 500,000 comments. Can you figure it out? In this video I explain the correct answer. Blog post:

• 06:17

### Solving Percent Problems | Decimals | Pre-Algebra | Khan Academy

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We'll use algebra to solve this percent problem. Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-word-probs-pre-alg/v/solving-percent-problems-2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra Missed the

• 03:03

### Introduction To Exponents | Pre-Algebra | Khan Academy

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Taking an exponent is basically the act of repeated multiplication. You know how to multiply, right? If so, understanding exponents is completely within your grasp! Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/ma

• 03:21

### Introduction To Perimeter | Measurement | Pre-Algebra | Khan Academy

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Find perimeter by adding side-lengths of various figures. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/measurement/perimeter/e/perimeter_1?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra Wa

• 09:45

### 2nd Order Linear Homogeneous Differential Equations 1

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

• 05:27

### Converting Directly From Binary To Hexadecimal | Pre-Algebra | Khan Academy

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• 04:58

### Exploring linear relationships

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U03_L2_T4_we2 : Exploring linear relationships More free lessons at: http://www.khanacademy.org/video?v=qPx7i1jwXX4 Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

• 04:01

### Recognizing Linear Functions

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U03_L2_T5_we1 : Recognizing Linear Functions More free lessons at: http://www.khanacademy.org/video?v=AZroE4fJqtQ Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

• 05:45

### Non-Linear Systems of Equations 1

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U10_L2_T2_we1 Non-Linear Systems of Equations 1 More free lessons at: http://www.khanacademy.org/video?v=hjigR_rHKDI Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

• 08:22

### Non-Linear Systems of Equations 2

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U10_L2_T2_we2 Non-Linear Systems of Equations 2 More free lessons at: http://www.khanacademy.org/video?v=XPf8LMu7QSw Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

• 06:57

### Non-Linear Systems of Equations 3

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U10_L2_T2_we3 Non-Linear Systems of Equations 3 More free lessons at: http://www.khanacademy.org/video?v=FksgVpM_iXs Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

• 20:48

### Introduction To Scientific Notation | Pre-Algebra | Khan Academy

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Introduction to scientific notation. An in-depth discussion about why and how scientific notation is used. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/exponents-radicals/scientific-notation/e/sc

• 09:17

### Unit Conversion Within The Metric System | Pre-Algebra | Khan Academy

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Metric unit conversion Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/metric-system-tutorial/v/converting-within-the-metric-system?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra Missed the previous lesson? http

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### 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

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### Algebra Basics: Solving Basic Equations Part 2 - Math Antics

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Part of the Algebra Basics Series: https://www.youtube.com/watch?v=NybHckSEQBI&list=PLUPEBWbAHUszT_GebJK23JHdd_Bss1N-G Previous video: https://youtu.be/l3XzepN03KQ Next video: Coming Soon This video shows students how to solve simple 1-step Algebra equati

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