Linear Algebra 9c: Why Gaussian Elimination Works

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I have wondered this all time! Now i become clear Thx

meonjiworld
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I laughed out loud when you proposed a question to keep some of us busy.

kakaoo
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Recalling the first lectures that emphasized the geometric interpretation of "travelling" to villages.  Say going from village A to village B.  It seems to me that the NULL space are all the non repeating detours that allow me to travel to the same village. In the context of a taxi driver, it would be all the different scenic routes and still arrive at our destination.  The later analogy breaks down a little because I would like to pay the same fare all the time and I do not believe the taxi drive would be too happy. 

alanburns
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Okay so regarding column spaces, I can see that by adding a multiple of one row to another, columns are getting sheared. I know that shearing won't change dimensions. So the column space's dimensions would remain the same but the column space might change.

YouShallKnowNothingByRea-ytbw
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BTW - I truly enjoy your explanations.  Thank you!

alanburns
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8:00 What if we permuted rows 1 and 3? I supposed we have to change the column space for [0 1 1]. Is that correct?

Thank you for all your great videos you made! I look forward to watch them all and I definitely promote your channel on the web.

swalscha
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At this stage, I've forgot what the null space is and am having trouble juxtaposing / recalling the idea of column VS row 'space' -> god I'm dumb.

Hythloday