12-240/Classnotes for Thursday November 8 - Revision history

Grace.zhu at 06:15, 4 December 2012

2012-12-04T06:15:46Z

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	== Riddle Along ==		== 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?		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?
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Grace.zhu: /* Goals */

2012-12-03T21:51:16Z

Goals

← Older revision		Revision as of 17:51, 3 December 2012
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	== Goals ==		== Goals ==
	1. compute Rank T over A		1. compute Rank T over A<br>
	2. Compute <math>T^(-1)</math> over <math>A^(-1)</math>		2. Compute <math>T^{-1}</math> over <math>A^{-1}</math><br>
	3. Solve systems of linear equations		3. Solve systems of linear equations

Grace.zhu at 21:50, 3 December 2012

2012-12-03T21:50:02Z

← Older revision		Revision as of 17:50, 3 December 2012
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			== 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 <math>T^(-1)</math> over <math>A^(-1)</math>
			3. Solve systems of linear equations

			== Theorems ==
			1. Given V' -> V -> W -> W' (where the linear transformations are Q, T, P respectively)<br>
			such that P and Q are invertible (i.e. Q is surjective and P is injective)
			then rank T = rank PTQ<br>
			<br>
			2. if T: V -> W, V with basis <math>\beta</math> and W with basis <math>\gamma</math>
			rank <math>[T]_\beta^\gamma</math> = rank T<br>
			<br>
			3. if P and Q are invertible matrices, A is some other matrix, rank A = rank PAQ

			== Definitions ==
			if A = <math>M_(m \times n)</math>, then it is linear transformation <math>T_A : F^n -> F^m</math>

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Yaaleni.vijay: /* Lecture notes upload by yaaleni.vijay */

2012-11-23T03:31:32Z

Lecture notes upload by yaaleni.vijay

← Older revision		Revision as of 23:31, 22 November 2012
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Yaaleni.vijay at 22:55, 22 November 2012

2012-11-22T22:55:15Z

New page

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