Linear Algebra 9c: Why Gaussian Elimination Works

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  • Опубликовано: 16 янв 2025

Комментарии • 15

  • @MathTheBeautiful
    @MathTheBeautiful  4 года назад +4

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

  • @meonjiworld
    @meonjiworld 3 года назад +3

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

  • @PyMoondra
    @PyMoondra 5 лет назад +2

    Great job.

  • @kaka0o0o
    @kaka0o0o 5 лет назад +1

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

  • @supplementaluniversity8094
    @supplementaluniversity8094 7 лет назад +4

    You're a legend

  • @swalscha
    @swalscha 7 лет назад

    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.

  • @alanburns819
    @alanburns819 10 лет назад +2

    BTW - I truly enjoy your explanations. Thank you!

  • @alanburns819
    @alanburns819 10 лет назад +4

    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
      @MathTheBeautiful  10 лет назад +3

      Actually, your intuition corresponds to a very specific and important application of the null space. Check out this lecture by Professor Strang: ruclips.net/video/6-wh6yvk6uc/видео.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.

  • @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
      @MathTheBeautiful  Год назад

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

  • @Hythloday71
    @Hythloday71 10 лет назад


    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
      @MathTheBeautiful  10 лет назад +2

      See if this is helpful: ruclips.net/video/KT3NOmOOcmE/видео.html

    • @Hythloday71
      @Hythloday71 10 лет назад +1

      thank you.

    • @electric_sand
      @electric_sand Год назад

      @@Hythloday71 Can you still remember? 😂