Linear algebra is the first kind of algebra that a student is introduced to.

We recognise linear equations because each term is either a constant or the product of a constant and a variable. Note that there are no squares or other powers, an no xy terms or anything like that. These equations can have one or more variables but we are limited to one variable per term.

Although the study of linear equations is extensive and can enter many dimensions, and can involve complex numbers (for example), I am mostly going to restrict myself to work that would be covered in high school (and the first year or so of college/university).

I have been watching your “Integration technique” videos with high expectation and excitement. They never fail to give me a lot of joy and much pleasure. You must have been one hell of teacher at your time! … just continue making highly enjoyable and intellectually stimulating videos. … Unfortunately, what you learn at the university, you hardly ever see again in your office job. That is why I try to repeat some thing I learned: to enjoy it a bit more, to marvel upon beauty, and to keep my brain sharp. There is where your videos come in perfectly: interesting, amusing and thought provoking problems neatly presented. … You do your best to share your passion, knowledge and experience. The least I can do is to say an honest “Thank you!” As I said, your videos give me much pleasure. You may freely let other people know that. … Rest assured that I shall be watching your videos in the future. With joy and excitement. And I shall comment on them from time to time. You just continue making them.

Zoran V (in private correspondence via YouTube, quoted with permission)

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