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.

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