What does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the span of the linear combinations of vectors. The presentation provides both 2-D and 3-D examples of the definitions.

Concepts

linear algebra, vectors, linear combinations, 2-d, 3-d, coordinate plane

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Additional Tags

math

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Instructional Ideas

• Stop the video at 1:53 and have the class discuss possible answers to the question before moving on
• Before getting to the section on 3-D space at the 6:00 timestamp, ask class members what it would take to be able to span all of 3-D space

Classroom Considerations

• Individuals should know how to represent a vector

• This video is hosted on YouTube

Pros

• Makes it easier to envision the span of two and three vectors
• Includes a question at the end to ponder about two different definitions for linearly independent
• The video is closed captioned to help with note taking if needed

Cons

• None

Common Core

HSN-VM.B.4.a HSN-VM.B.5.a MP2 MP4