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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)

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Riddle Along
Four cars drive in the Sahara desert at constant speeds and with constant directions. A meets B, C, D; B meets C, D. Do C and D meet?
Goals
1. compute Rank T over A
2. Compute $T^{1}$ over $A^{1}$
3. Solve systems of linear equations
Theorems
1. Given V' > V > W > W' (where the linear transformations are Q, T, P respectively)
such that P and Q are invertible (i.e. Q is surjective and P is injective)
then rank T = rank PTQ
2. if T: V > W, V with basis $\beta$ and W with basis $\gamma$
rank $[T]_{\beta }^{\gamma }$ = rank T
3. if P and Q are invertible matrices, A is some other matrix, rank A = rank PAQ
Definitions
if A = $M_{(}m\times n)$, then it is linear transformation $T_{A}:F^{n}>F^{m}$