Welcome to Math 240! (additions to this web site no longer count towards good deed points)

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Week of...

Notes and Links

1

Sep 8

About This Class, What is this class about? (PDF, HTML), Monday, Wednesday

2

Sep 15

HW1, Monday, Wednesday, TheComplexField.pdf,HW1_solutions.pdf

3

Sep 22

HW2, Class Photo, Monday, Wednesday, HW2_solutions.pdf

4

Sep 29

HW3, Wednesday, Tutorial, HW3_solutions.pdf

5

Oct 6

HW4, Monday, Wednesday, Tutorial, HW4_solutions.pdf

6

Oct 13

No Monday class (Thanksgiving), Wednesday, Tutorial

7

Oct 20

HW5, Term Test at tutorials on Tuesday, Wednesday

8

Oct 27

HW6, Monday, Why LinAlg?, Wednesday, Tutorial

9

Nov 3

Monday is the last day to drop this class, HW7, Monday, Wednesday, Tutorial

10

Nov 10

HW8, Monday, Tutorial

11

Nov 17

MondayTuesday is UofT November break

12

Nov 24

HW9

13

Dec 1

Wednesday is a "makeup Monday"! EndofCourse Schedule, Tutorial

F

Dec 8

The Final Exam

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Boris
Theorem
Let be a matrix and be the matrix with two rows interchanged. Then . Boris decided to prove the following lemma first:
Lemma 1
Let be a matrix and be the matrix with two adjacent rows interchanged. Then .
All we need to show is that . Assume that is the matrix with rows of interchanged. Since the determinant of a matrix with two identical rows is , then:


 .
Since the determinant is linear in each row, then we continue where we left off:


 .
Then and . The proof of the lemma is complete.
For the proof of the theorem, assume that is the matrix with rows of interchanged and . By Lemma 1, we have the following:




 .
Then the proof of the theorem is complete.
Nikita
Scanned Tutorial Notes by Boyang.wu
File:Tut.pdf