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Welcome to Math 240! (additions to this web site no longer count towards good deed points)
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Week of...
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Notes and Links
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1
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Sep 8
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About This Class, What is this class about? (PDF, HTML), Monday, Wednesday
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2
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Sep 15
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HW1, Monday, Wednesday, TheComplexField.pdf,HW1_solutions.pdf
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3
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Sep 22
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HW2, Class Photo, Monday, Wednesday, HW2_solutions.pdf
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4
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Sep 29
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HW3, Wednesday, Tutorial, HW3_solutions.pdf
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5
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Oct 6
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HW4, Monday, Wednesday, Tutorial, HW4_solutions.pdf
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6
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Oct 13
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No Monday class (Thanksgiving), Wednesday, Tutorial
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7
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Oct 20
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HW5, Term Test at tutorials on Tuesday, Wednesday
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8
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Oct 27
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HW6, Monday, Why LinAlg?, Wednesday, Tutorial
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9
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Nov 3
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Monday is the last day to drop this class, HW7, Monday, Wednesday, Tutorial
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10
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Nov 10
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HW8, Monday, Tutorial
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11
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Nov 17
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Monday-Tuesday is UofT November break
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12
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Nov 24
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HW9
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13
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Dec 1
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Wednesday is a "makeup Monday"! End-of-Course Schedule, Tutorial
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F
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Dec 8
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The Final Exam
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Register of Good Deeds
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Add your name / see who's in!
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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