HW3, due Wed Feb 1, 2017

In class on January 25, we went over a large number of exercises.  You will not be asked to submit solutions on February 1.  Instead, read all of the exercises from Sections 2.1 (17 problems), 2.2 (14 problems), and 2.3 (26 problems).


Submit a sheet of paper stating for each problem which category each problem falls into:

  • (Solved) You have solved the problem.
  • (Understand)  You have not solved the problem, but you are convinced that you understand exactly how to solve the problem.
  • (Unsolved) You are not convinced you understand how to solve the problem.


HW2, due Wed Jan 25, 2017

  • DF Sec 1.3 #5, #8, #14
  • DF Sec 1.6 #9, #17, #23,
  • DF Sec 1.7 #17
  • (wording updated on Jan 23.) Let F be a field.  Let V=F^n, viewed as an n-dimensional vector space over the field F.  Show the following:
    • The group G=GL(n,F) acts on V by linear transformations.
    • If B=(e_1,\ldots,e_n) is  the standard ordered basis of V and if g \in G, then g B = (g e_1,\ldots,g e_n)  is an ordered basis of V.
    • There is a 1-1 correspondence between elements of GL(n,F) and bases of V.