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Exercise 22

Avg difficulty 3.0

For Corollary 1.17,

  • fill in the induction for the proof;

  • give an alternate proof that starts with the empty set and builds a sequence of linearly independent subsets of the given finite set until one appears with the same span as the given set.

Hefferon, Linear Algebra, Vector Spaces, Definition and Examples, Exercise 22

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.