Week 4: October 2-6, 2017

  • The front row seat, right next to the center aisle, will from now on be reserved for one of your classmates who needs this arrangement.
  • Required reading: Chapters 1.3, 1.4, 1.5.
  • Vector spaces: Basic properties, subspaces, intersections and sums of subspaces, linear combinations, linear dependence and independence.
  • Homework #3 is due 11pm on Friday, October 6
  • Additional homework (not to be handed in):
  • Just for fun: A famous linear algebra puzzle (clever but not easy): In a town with $n$ inhabitants, there are $N$ clubs. Each club has an odd number of members, and for any two distinct clubs there is an even number of common members. Prove that $n\ge N$. Hint: Work with the field $\mathbb{Z}_2$, and use facts about bases and dimension.