What is a Solution to a Linear System? **Intro**

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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