This 12-minute video lesson provides another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 32 of 143]
This 10-minute video lesson shows how to figure out a normal vector to a plane from its equation. [Linear Algebra playlist: Lesson 141 of 143]
This 13-minute video lesson shows how to calculate the null space of a matrix. [Linear Algebra playlist: Lesson 35 of 143]
This 12-minute video lesson discusses how to understand how the null space of a matrix relates to the linear independence of its column vectors. [Linear Algebra playlist: Lesson 36 of 143]
This 12-minute video lesson finds that the orthogonal complement of the orthogonal complement of V is V. [Linear Algebra playlist: Lesson 103 of 143]
This 11-minute video lesson shows that orthogonal matrices preserve angles and lengths. [Linear Algebra playlist: Lesson 129 of 143]
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.
This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.
This 23-minute video lesson looks at Rowspace and Left Nullspace. [Linear Algebra playlist: Lesson 97 of 143]
This 9-minute video lesson provides definitions of the vector dot product and vector length.
This 19-minute video lesson proves the triangle inequality for vectors in Rn.
This 20-minute video lesson looks at the relationship between left nullspace, rowspace, column space and nullspace. [Linear Algebra playlist: Lesson 98 of 143]
This 14-minute video lesson provides an Introduction to linear transformations.
Linear velocity from the radius and angular velocity for two pumpkin catapults with different arm lengths.
Linkage institutions: elections, media, interest groups and political parties.
Thinking about how real GDP can drive real interest rates. Created by Sal Khan.
How do savers and borrowers find each other? In the market for loanable funds! In this video, learn how the demand of loanable funds and the supply of loanable funds interact to determine real interest rates.
Logistic growth versus exponential growth (for familiarity with AP Biology formula sheet).
We claim that aggregate supply is not responsive to changes in the price level in the long run, leading to a vertical long-run aggregate supply (LRAS) curve, but why? In this video we explore why aggregate supply may not be influenced by prices in the long-run. Created by Sal Khan.
In this video we explore the long run average total cost curve and how average costs vary when all inputs can be adjusted.