Linear Combinations, Span, and Basis Vectors | Essence of Linear Algebra, Chapter 2

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.

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CCSS: Adaptable
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

  • 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

  • None