12-240/Classnotes for Thursday November 8

DBN: Classes: 2012-13: 12-240 / Navigation Additions to this web site no longer count towards good deed points. # Week of... Notes and Links 1 Sep 10 About This Class, Tuesday, Thursday 2 Sep 17 HW1, Tuesday, Thursday, HW1 Solutions 3 Sep 24 HW2, Tuesday, Class Photo, Thursday 4 Oct 1 HW3, Tuesday, Thursday 5 Oct 8 HW4, Tuesday, Thursday 6 Oct 15 Tuesday, Thursday 7 Oct 22 HW5, Tuesday, Term Test was on Thursday. HW5 Solutions 8 Oct 29 Why LinAlg?, HW6, Tuesday, Thursday, Nov 4 is the last day to drop this class 9 Nov 5 Tuesday, Thursday 10 Nov 12 Monday-Tuesday is UofT November break, HW7, Thursday 11 Nov 19 HW8, Tuesday,Thursday 12 Nov 26 HW9, Tuesday , Thursday 13 Dec 3 Tuesday UofT Fall Semester ends Wednesday F Dec 10 The Final Exam (time, place, style, office hours times) Register of Good Deeds Add your name / see who's in!

Riddle Along

Four cars drive in the Sahara desert at constant speeds and with constant directions. A meets B, C, D; B meets C, D. Do C and D meet?

Goals

1. compute Rank T over A
2. Compute $T^{-1}$ over $A^{-1}$
3. Solve systems of linear equations

Theorems

1. Given V' -> V -> W -> W' (where the linear transformations are Q, T, P respectively)
such that P and Q are invertible (i.e. Q is surjective and P is injective) then rank T = rank PTQ

2. if T: V -> W, V with basis $\beta$ and W with basis $\gamma$ rank $[T]_{\beta }^{\gamma }$ = rank T

3. if P and Q are invertible matrices, A is some other matrix, rank A = rank PAQ

Definitions

if A = $M_{(}m\times n)$, then it is linear transformation $T_{A}:F^{n}->F^{m}$

Lecture notes upload by yaaleni.vijay

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