- 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 , 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 is the standard ordered basis of V and if , then is an ordered basis of V.
- There is a 1-1 correspondence between elements of GL(n,F) and bases of V.