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Week of...
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Notes and Links
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1
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Sep 7
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Tue, About, Thu
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2
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Sep 14
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Tue, HW1, HW1 Solution, Thu
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3
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Sep 21
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Tue, HW2, HW2 Solution, Thu, Photo
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4
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Sep 28
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Tue, HW3, HW3 Solution, Thu
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5
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Oct 5
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Tue, HW4, HW4 Solution, Thu,
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6
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Oct 12
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Tue, Thu
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7
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Oct 19
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Tue, HW5, HW5 Solution, Term Test on Thu
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8
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Oct 26
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Tue, Why LinAlg?, HW6, HW6 Solution, Thu
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9
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Nov 2
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Tue, MIT LinAlg, Thu
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10
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Nov 9
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Tue, HW7, HW7 Solution Thu
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11
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Nov 16
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Tue, HW8, HW8 Solution, Thu
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12
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Nov 23
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Tue, HW9, HW9 Solution, Thu
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13
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Nov 30
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Tue, On the final, Thu
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S
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Dec 7
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Office Hours
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F
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Dec 14
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Final on Dec 16
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To Do List
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The Algebra Song!
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Register of Good Deeds
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Misplaced Material
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Add your name / see who's in!
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A complete set of the December 1st lecture notes given by Professor Dror Bar-Natan for the Fall Session of MAT240 at the University of Toronto.
~In the above gallery, there is a complete copy of notes for the lecture given on December 1st by Professor Natan (in PDF format).
--- Wiki Format ---
MAT240 – December 1st
Basic Properties of :
(Note that det(EA) = det(E)·det(A) and that det(A) may be written as |A|.)
0.
1.
- Exchanging two rows flips the sign.
2.
- These are "enough"!
3.
- Adding a multiple of one row to another does not change the determinant.
The determinant of any matrix can be calculated using the properties above.
Theorem:
If satisfies properties 0-3 above, then
Philosophical remark: Why not begin our inquiry with the properties above?
We must find an implied need for their use; thus, we must know whether a function exists first.