Practice communication skills and solidify a linear algebra concept as you create a short real-time video aimed at your classmates that focuses on one example. Here, real-time communication includes real-time handwriting on a board or paper and real-time audio and video. Your face, voice, and handwriting must be present in the video all at the same time, at all times, although you may begin with some writing already there.

Start by introducing yourself and listing the topic you chose. The rest is up to you but you should focus on one specific example as you explain it and discuss the related concepts in your own words. Creativity is encouraged, but keep it professional. Explaining concepts to others is one of the best ways to learn yourself.

Pretend you are presenting to the class in real time, but these can be more polished since you can plan, re-record and make revisions if needed.

Here is a 3-minute sample video for a different class at a different school. Please keep your video to 5 minutes or less.

Recording from a phone, computer, or tablet is the method I would expect many to use. Another option is the library tech desk, which allows you to check out digital equipment, including camcorders like the GoPro Hero. The library also has private studyrooms with whiteboards that you can book and record in. Taping up paper and writing on that with a marker is another option. I can also help you film during office hours--for example we could set up my laptop to record you in front of my board.

Upload your video to your school YouTube channel as follows:

First be sure that you are logged in to your school gmail account.

Then upload your video.

Change the privacy setting to

Then send me the video link in the private forum on ASULearn. I'll respond there if I recommend any changes. When it is ready I'll approve your video and will add it to a page on ASULearn designed to add to the class resources and build community.

This will be worth 1 point on the problem set and will be graded on a scale of 0, 1, 2 (out of 30 points on problem set 3). So it is possible to obtain extra credit on the problem set by obtaining a 2 here.

The full-credit video

A score of 1 is given for a good faith effort but not quite ready for prime time if it is mostly error free and complete, but may have some minor issues. You can revise your video by using my feedback to improve it.

The choice of topic is first-come, first-served on ASULearn.

- by-hand Gaussian and solutions of a 2x3 with a generic
*k* - by-hand Gaussian of a 3x4 with full pivots
- by-hand Gaussian of a 3x4 with no solutions
- back-substitution of a 3x4 matrix in Gaussian but not Gauss-Jordan with 1 solution
- parametric vector form of infinite solutions from a 2x4 already in Gaussian
- an overdetermined system with a solution
- an underdetermined system with no solutions
- recognizing when there are no solutions
- pivots and pivot columns
- backward phase starting from Gaussian 3x4 and going to Gauss-Jordan
- intersection of 3 planes
- linear combination and weights
- span a line in R^3
- span a plane in R^3
- span all of R^3
- a mix that is a linear combination of vectors but that cannot be physically produced
- a vector outside a span
- multiply a matrix and a vector using linear combinations
- multiply a matrix and a vector using dot product
- Theorem 4 in 1.4 via an example
- The negation of Theorem 4 in 1.4 via a counterexample
- vectors ending on the line through p parallel to v
- diagonal of a parallelogram
- linearly independent in R^3
- 3 vectors not linearly independent in R^3 but no 2 on the same line
- converting between a vector equation and matrix equation for linearly independence
- linearly independent but not span
- span but not linearly independent
- multiply two matrices
- matrix multiplication is not commutative
- 2 non-zero matrices that multiply to yield a zero matrix
- transpose of a matrix
- inverse of a 2x2 matrix
- applying the inverse of a matrix to Ax=b
- 2x2 elementary matrix for replacement and its inverse matrix
- associativity
- distributivity
- addition (of linear objects: equations, vectors, matrices)
- scalar multiplication (of linear objects: equations, vectors, matrices)