What is a Solution to a Linear System? Intro

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We kick off our course by establishing the core problem of Linear Algebra. This video introduces the algebraic side of Linear Systems (the next will address the geometric side). In particular, we will be able to:
*Identify when an equation is linear
*Define what a system of linear equations is
*Verify that a list of values is a solution to a system of linear equations
*Use a_ij notation to express generic linear systems
*Use the terminology of coefficients, constants, and variables.

Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master math means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

This video is part of a Linear Algebra course taught by Dr. Trefor Bazett at the University of Cincinnati.

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What I really like about your teaching style is the fact that you don’t gloss over the most basic ideas. Your teaching method makes it dummy proof — allowing the initiating student to connect with the very spirit and the motives behind the development of the subject matter. In fact, we could be fairly certain that this is the way in which the ancient scholars themselves arrived at their discoveries; by trying to make sense of, and working through, the most basic ideas and assumptions. Without seeing the underlying motives, having an idea of the global picture, and getting a feel for the possible applications, it is much more difficult for students to make headway into the mathematical fields of study.

NothingMaster

So great how excited he is about math. Wonderful teacher. I took linear algebra at university many years ago, don't remember much. But this intro make me inspired to learn again.

ramyhuber

Hi, Mr. Bazett. Thanks for the video. I have studied linear algebra earlier but your way of teaching is so cool (I couldn't find a better word) that I want to take this course again. It's always as if you and I are having this engaging conversation about a Math concept. I am eagerly waiting for your next video. Love, from India.

prateeksenapati

Dear Dr. Trefor Bazett, you are the math hero of planet earth. Thank you so much, lots of love from Turkey

selindoga

Congrats again for this great video series. I'm learning ML, so I'm watching this course to get some details about linear algebra. :)

cicerohen

This is great you are explaining terms. This playlist is a great introduction to linear algebra. I am everyday exploring branches of mathematics, writing down jargons onto little notebook, deciphering symbols/notations, etc. It is like learning new languages.

pinklady

ho gosh, you made linear algebra so much easier for me for now, I hope this way you teaching continues to the end of the course 😁

heydyvex

You are a wonderful teacher. I'm glad I found you here. Just getting started here, but I think I can follow you. Again, thank you for your efforts here. REally appreciate it!

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