|Additions to this web site no longer count towards good deed points.
||Notes and Links
||About This Class, Tuesday, Thursday
||HW1, Tuesday, Thursday, HW1 Solutions
||HW2, Tuesday, Class Photo, Thursday
||HW3, Tuesday, Thursday
||HW4, Tuesday, Thursday
||HW5, Tuesday, Term Test was on Thursday. HW5 Solutions
||Why LinAlg?, HW6, Tuesday, Thursday, Nov 4 is the last day to drop this class
||Monday-Tuesday is UofT November break, HW7, Thursday
||HW9, Tuesday , Thursday
||Tuesday UofT Fall Semester ends Wednesday
||The Final Exam (time, place, style, office hours times)
|Register of Good Deeds
Add your name / see who's in!
||Dror's notes above / Students' notes below
1. If G generates, |G| n and G contains a basis, |G|=n then G is a basis
2. If L is linearly independent, |L| n and L can be extended to be a basis. |L|=n => L is a basis.
3.W V a subspace then W is finite dimensioned and dim W dim V
If dim W = dim V, then V = W
If dim W < dim V, then any basis of W can be extended to be a basis of V
Proof of W is finite dimensioned:
Let L be a linearly independent subset of W which is of maximal size.
Fact about N
- Every subset A of N, which is:
1. Non empty
2. Bounded : N N, a A, a N
has a maximal element: an element m A, a A, a m ( m + 1 A )