|Welcome to Math 240!|
(additions to this web site no longer count towards good deed points)
||Notes and Links
||About This Class, What is this class about? (PDF, HTML), Monday, Wednesday
||HW1, Monday, Wednesday, TheComplexField.pdf,HW1_solutions.pdf
||HW2, Class Photo, Monday, Wednesday, HW2_solutions.pdf
||HW3, Wednesday, Tutorial, HW3_solutions.pdf
||HW4, Monday, Wednesday, Tutorial, HW4_solutions.pdf
||No Monday class (Thanksgiving), Wednesday, Tutorial
||HW5, Term Test at tutorials on Tuesday, Wednesday
||HW6, Monday, Why LinAlg?, Wednesday, Tutorial
||Monday is the last day to drop this class, HW7, Monday, Wednesday, Tutorial
||HW8, Monday, Tutorial
||Monday-Tuesday is UofT November break
||Wednesday is a "makeup Monday"! End-of-Course Schedule, Tutorial
||The Final Exam
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Let be a matrix and be the matrix with two rows interchanged. Then . Boris decided to prove the following lemma first:
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.
Scanned Tutorial Notes by Boyang.wu