Khan Academy: Dependent Probability: Introduction to Dependent Probability

Video explains what linearly dependent vectors and linearly independent vectors are. Shows visual representations to help explain the concept and relates it to the span of the linear combination of the vectors. [15:46]

Video reviews how to use vectors to define a line. Gives an intuitive sense of what a projection is, then explains step-by-step where the formula for projections comes from. Shows an example of calculating a vector projection. [14:37]

Video defining an orthonormal set as a set of vectors that all have the length of 1 and are orthogonal to each other. Using proof by contradiction, the set is proven to be linearly independent and can be considered an orthonormal basis....

Video first reviews what a function is. Explains what the identity function is and uses it to define what makes a function invertible. Shows that the inverse will be unique. This video also appears in the strand Algebra: Functions. [18:53]

Video first reviews the criteria for a subspace and then goes through the steps to show the null space meets the criteria and is a a subspace. This video also appears in the strand Algebra: Matrices. [10:21]

Video defining eigenvectors as scaled vectors and eigenvalues as their scale value and explaining their significance. Video references the example from a previous video about changing coordinate systems to make finding the transformation...

Instructional video explaining the concept of a limit. Does not provide a formal definition of limit. Includes graphical and numerical examples using both a virtual chalkboard and virtual graphing calculator. Includes link to practice...

A video exploring the concept of compound interest by introducing the idea that interest can be compounded at different intervals, i.e. annually, monthly, daily, continuously, etc. The instructor uses a concrete example to show what...

An instructional video explaining the concept of function inverses. A linear function is given and a diagram is drawn to show the mapping of some elements of the domain to the corresponding elements in the range. The inverse of the...

Find dependent probabilities like P(A | B) or P(B | A) for a variety of contexts. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.