Introducing Linear Combinations & Span

We saw Vector Addition & Scalar Multiplication in 1.3 Part I. Now we take arbitrary combinations of those two arbitrations, called Linear Combinations. We can compute this algebraically and visualize it geometrically. The set of ALL linear combinations is called the span. In some cases this is set is everything, sometimes just a line, sometimes even just the single zero vector! Two vectors are particularly nice, called the standard basis vectors whose span is immediately able to be determined.

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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Видео Introducing Linear Combinations & Span канала Dr. Trefor Bazett