Instructional Video

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

Curated and Reviewed by Lesson Planet

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
Additional Tags
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
  • 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