Additions to this web site no longer count towards good deed points.

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Week of...

Notes and Links

1

Sep 10

About This Class, Tuesday, Thursday

2

Sep 17

HW1, Tuesday, Thursday, HW1 Solutions

3

Sep 24

HW2, Tuesday, Class Photo, Thursday

4

Oct 1

HW3, Tuesday, Thursday

5

Oct 8

HW4, Tuesday, Thursday

6

Oct 15

Tuesday, Thursday

7

Oct 22

HW5, Tuesday, Term Test was on Thursday. HW5 Solutions

8

Oct 29

Why LinAlg?, HW6, Tuesday, Thursday, Nov 4 is the last day to drop this class

9

Nov 5

Tuesday, Thursday

10

Nov 12

MondayTuesday is UofT November break, HW7, Thursday

11

Nov 19

HW8, Tuesday,Thursday

12

Nov 26

HW9, Tuesday , Thursday

13

Dec 3

Tuesday UofT Fall Semester ends Wednesday

F

Dec 10

The Final Exam (time, place, style, office hours times)

Register of Good Deeds

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Dror's notes above / Students' notes below


Theorems
1. If G generates, G $\geq \!\,$ n and G contains a basis, G=n then G is a basis
2. If L is linearly independent, L $\leq \!\,$ n and L can be extended to be a basis. L=n => L is a basis.
3.W $\subset \!\,$ V a subspace then W is finite dimensioned and dim W $\leq \!\,$ 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 : $\exists \!\,$ N $\in \!\,$ N, $\forall \!\,$ a $\in \!\,$ A, a $\leq \!\,$ N
has a maximal element: an element m $\in \!\,$ A, $\forall \!\,$ a $\in \!\,$ A, a $\leq \!\,$ m ( m + 1 $\notin \!\,$ A )
class note