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.
Showing that matrix products are associative. Created by Sal Khan.
This lesson discusses how to identify sets of numbers as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
To plot an inequality, such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in. Finally, draw a line going from the circle in the direction of the numbers that make the inequality true.
This 15-minute video lesson gives an example involving the preimage of a set under a transformation. It also gives a definition of kernel of a transformation.
Examples finding probabilities from probability distributions for continuous random variables.
The addition rule for probability is explained using Venn Diagrams. [Probability playlist: Lesson 3 of 29]
This lesson introduces basic probability. [Probability playlist: Lesson 1 of 29]
This lesson is a birthday problem that determines the probability that at least 2 people in a room of 30 share the same birthday. [Probability playlist: Lesson 17 of 29]
This lesson presents an example of dependent probability. [Probability playlist: Lesson 10 of 29]
This lesson presents an example of dependent probability. [Probability playlist: Lesson 11 of 29]
This lesson begins a six part series of basic probabiltiy using module examples. [Probability playlist: Lesson 4 of 29]
This lesson demonstrates probability using combinations and shows the probability of getting exatly 3 heads in 8 flips of a fair coin. [Probability playlist: Lesson 14 of 29]
This lesson is another demonstration of probability and combinations to determine the probability of making at least 3 out of 5 basketball free throws. [Probability playlist: Lesson 15 of 29]
This lesson uses playing cards and Venn Diagrams to explain the idea of probability [Probability playlist: Lesson 2 of 29]