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.