Linear Algebra 9c: Why Gaussian Elimination Works

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lem.ma/LA - Linear Algebra on Lemma
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[@MathTheBeautiful]

Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

[@meonjiworld]

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

[@kaka0o0o]

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

[@alanburns819]

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.

[@MathTheBeautiful]

Actually, your intuition corresponds to a very specific and important application of the null space. Check out this lecture by Professor Strang: czcams.com/video/6-wh6yvk6uc/video.html
Also, I really like how you capitalize NULL. After years of C development, when I type "null" I think I'll get a syntax error.

[@supplementaluniversity8094]

You're a legend

[@YouShallKnowNothingByRea-yt4bw]

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.

[@MathTheBeautiful]

Yes, most likely the column space will chaning (while preserving its dimension)

[@PyMoondra]

Great job.

[@alanburns819]

BTW - I truly enjoy your explanations. Thank you!

[@swalscha]

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.

[@Hythloday71]

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.

[@MathTheBeautiful]

See if this is helpful: czcams.com/video/KT3NOmOOcmE/video.html

[@Hythloday71]

thank you.

[@electric_sand]

@@Hythloday71 Can you still remember? 😂