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* <math>VS_4 : \forall x \in V, \exists y \in V, x + y = 0</math>. |
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* <math>VS_4 : \forall x \in V, \exists y \in V, x + y = 0</math>. |
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* <math>VS_5 : \forall x \in V, 1 \times x = x</math>. |
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* <math>VS_5 : \forall x \in V, 1 \times x = x</math>. |
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http://drorbn.net/skins/common/images/icons/fileicon-pdf.png |
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* <math>VS_6 : \forall a, b \in F, \forall x \in V, a(bx) = (ab)x</math>. |
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* <math>VS_6 : \forall a, b \in F, \forall x \in V, a(bx) = (ab)x</math>. |
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* <math>VS_7 : \forall a \in F, \forall x, y \in V, a(x + y) = ax + ay</math>. |
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* <math>VS_7 : \forall a \in F, \forall x, y \in V, a(x + y) = ax + ay</math>. |
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* <math>VS_8 : \forall a, b \in F, \forall x \in V, (a + b)x = ax + bx</math>. |
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* <math>VS_8 : \forall a, b \in F, \forall x \in V, (a + b)x = ax + bx</math>. |
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http://drorbn.net/images/f/f0/MAT240_Sept_22%2C14_%281_of_2%29.pdf |
Revision as of 08:49, 25 September 2014
Welcome to Math 240! (additions to this web site no longer count towards good deed points)
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#
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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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![Class Photo](/images/thumb/6/6b/14-240-ClassPhoto.jpg/310px-14-240-ClassPhoto.jpg) Add your name / see who's in!
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Polar coordinates:
![{\displaystyle r\times e^{i\theta }=r\times cos\theta +i\times rsin\theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/bb3fe12b7abc1bc87939455defa0f886e9a426ae)
![{\displaystyle r_{1}\times e^{i\theta _{2}}=r_{1}\times (cos\theta +sin\theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/468b17fbb162ee9c6fa30873a69a4883723a5743)
The Fundamantal Theorem of Algebra:
where
and
has a soluion
In particular,
has a solution.
- Forces can multiple by a "scalar"(number).
No "multiplication" of forces.
Definition of Vector Space:
A "Vector Space" over a field F is a set V with a special element
and two binary operations:
![{\displaystyle +:V\times V->V}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d5969788edd165631a0c7c5fbc249dce78e5206)
![{\displaystyle \times :V\times V->V}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b2747ffcfd962547656ac0ca993731463f2b5da)
s.t.
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http://drorbn.net/images/f/f0/MAT240_Sept_22%2C14_%281_of_2%29.pdf