Linear Algebra 1.1.2 Solve Systems of Linear Equations in Augmented Matrices Using Row Operations

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  • เผยแพร่เมื่อ 27 ธ.ค. 2024

ความคิดเห็น • 88

  • @superioritymelee
    @superioritymelee ปีที่แล้ว +41

    I thought something was wrong with me as everyone else just breezes through these in my class but it was all about no one tried to explain it this way. I just couldn't make the connection between what we are doing and what we actually try to achieve by the row operations. I understand it much better now. Thank you for the great content!

  • @mbulelogumede6903
    @mbulelogumede6903 2 ปีที่แล้ว +22

    Kimberly, you're my best teacher so far in linear algebra.

  • @azucenarebolloso2099
    @azucenarebolloso2099 ปีที่แล้ว +9

    I'm sure i speak for everyone when I say I wish you were my professor for all my math classes! As a math major, I get upset that a lot of these professors always say, "you should know this already" instead of teaching it in class to make sure everyone is on the same page.

  • @j.j.3759
    @j.j.3759 2 ปีที่แล้ว +44

    Thank you for these videos. :) I was trying to do the freecodecamp Linear Algebra class (in preparation for my actual class this semester) and the professor said he was going to explain everything, but then kept saying, "everyone knows how to do this" seemingly every 3 minutes and then not actually explaining things. Your videos are much clearer.

    • @opufy
      @opufy 2 ปีที่แล้ว +8

      I was gonna watch it, but I guess I'll stay here lol I'm also taking linear and my teacher has a youtube channel where we take notes for class but I find these are done better.

  • @simpleandminimalmaybe
    @simpleandminimalmaybe ปีที่แล้ว +6

    i passed my discreet maths because of your course. thank you, once the money starts rolling in i will send a special $Thanks$

  • @afgaesthetics
    @afgaesthetics 2 ปีที่แล้ว +45

    I was absent the whole semester and tomorrow i have a linear Algebra final exam, your linear Algebra lessons saved me, thank you

    • @SawFinMath
      @SawFinMath  2 ปีที่แล้ว +8

      Glad I could help!

    • @ifeanyiogbennaya7773
      @ifeanyiogbennaya7773 ปีที่แล้ว +1

      Did u pass?

    • @afgaesthetics
      @afgaesthetics ปีที่แล้ว +20

      @@ifeanyiogbennaya7773 I did

    • @css2165
      @css2165 ปีที่แล้ว +7

      And millions of people are in debt right now for this education that you can get anywhere online for free. Way to go, America!

    • @ibruhem
      @ibruhem 10 หลายเดือนก่อน +2

      Relatable

  • @tsaikuo-wei3111
    @tsaikuo-wei3111 19 วันที่ผ่านมา

    This is the very best linear algebra course I ever got.

  • @faresobaid6223
    @faresobaid6223 4 ปีที่แล้ว +25

    4:41 hhhhh it's makes my laugh . I'm the one who make this video lol ... thanks any way

  • @bingfenggoh3885
    @bingfenggoh3885 23 ชั่วโมงที่ผ่านมา

    I have been using substitution method for all my life, and this is like a eureka moment. It just solves a 3 variable equation very quickly.

  • @bleachonacob4060
    @bleachonacob4060 ปีที่แล้ว +5

    One of the best teachers of TH-cam University!

    • @mujtaba135
      @mujtaba135 ปีที่แล้ว +1

      Lol, youtube is literally a university of everything

  • @marianagastelum1891
    @marianagastelum1891 5 ปีที่แล้ว +47

    I think you made a mistake in notation @14:20, you took half of your row 1 to be your new row 1 but you put row 2 in the notation (1/2R1-->R2 instead of 1/2R1-->R1). Also, thank you so much for these videos! I really appreciate the extra help! :D

    • @SawFinMath
      @SawFinMath  4 ปีที่แล้ว +21

      You are absolutely correct. Thanks for letting me know!

    • @yobro7837
      @yobro7837 7 หลายเดือนก่อน

      ​@@SawFinMath 13:30 Hi There,Can't We Interchange Row 1 with Row 3....If Not Then Kindly Brief It.

  • @HoagMinh
    @HoagMinh 3 หลายเดือนก่อน +1

    "but for now, you'll just do the way I want to do about it because I'm the one who make the video", fair enough LOL

  • @sarkersaadahmed
    @sarkersaadahmed 3 หลายเดือนก่อน +1

    I FINALLY UNDERSTOOD
    for anyone confused, try comparing elimination with augmented matrix honestyly and you will see the change
    DIAGONAL BECAUSE WE WANT TO FIND VALUES OF X1 X2 X3

  • @donovanrao5164
    @donovanrao5164 4 หลายเดือนก่อน +2

    The Professor Leonard of linear algebra! (Anyone studying pre-calc -> calc 3 needs Professor Leonard, he is the reason I love math so much, I made A's all the way through calc 3, thank me later!)

    • @SawFinMath
      @SawFinMath  4 หลายเดือนก่อน

      @@donovanrao5164 I haven’t heard of professor Leonard, but I also have a calc I and calc II series

    • @donovanrao5164
      @donovanrao5164 4 หลายเดือนก่อน

      @@SawFinMath everything in () was aimed at other students. However, you seem to be very interested in teaching. I highly recommend you watch his lectures for tips on how to teach topics in calc that you find students struggle with. He explains the fundamentals so well it's like the concepts just stick bc the "logical" nature of the math stands out in bright red! Also, it's probably has to do with how I learn best, I learn by understanding concepts, not memorization. Anyway, he does not have a course on linear algebra, so I'm here, thank you so much! 😁

  • @TumeloCarson
    @TumeloCarson ปีที่แล้ว +2

    Thank you for this video! All the other videos I watched prior to this one didn't explain why we were manipulating the matrix to achieve 1s and 0s, they assumed we knew why- which was frustrating.

    • @SawFinMath
      @SawFinMath  ปีที่แล้ว

      Agreed. I always try to focus on the ‘why’!

  • @halowiz1000
    @halowiz1000 2 ปีที่แล้ว +5

    These are incredible videos, being an engineering student taking pre-professional courses I have found myself behind in my linear class. So thank you, truly for your work. I did have a question about the Replacement part of Row Operations. You had put -2R2 + R1 = R2. Should it have been -2R2 + R1 = R1? This was at 1:23 in the video. Thank you again.

    • @halowiz1000
      @halowiz1000 2 ปีที่แล้ว

      Note: I have also adopted your style/color schematic of your note-taking. The way you represent the notes is incredible and super visually pleasing. Keep up the great work.

    • @ismaeeelxd
      @ismaeeelxd 10 หลายเดือนก่อน

      a year late but I think so yes.

  • @chimdiebubeokoro6218
    @chimdiebubeokoro6218 7 หลายเดือนก่อน +1

    20:07 Instead of Row 2 - Row 3 to be the new Row 3, I did half of Row 1 + Row 3 to be the new Row 3 and at 20:43 instead of a third of Row 3 to be the new Row 3, I did -2 multiplied by Row 3 to be the new Row 3.
    In the end, my solution was (22, 12, 2) but the main matrix was the same as yours and all my other steps were the same. What did I do wrong please?

  • @rudrajoshi8963
    @rudrajoshi8963 2 ปีที่แล้ว +1

    your videos are so deep i love them

  • @gerardtavares45
    @gerardtavares45 7 หลายเดือนก่อน

    This is a good math to practice during the summer 😊 thanks for the video

  • @EtreNameless
    @EtreNameless ปีที่แล้ว

    Better than my in person professor.

  • @xo_vallee
    @xo_vallee 3 ปีที่แล้ว +5

    Great explanation

  • @rd5991
    @rd5991 ปีที่แล้ว +2

    At 3:18, your equations and the matrix don't match up for row 3. You have to change the 3rd equation to -> -4x,1 + 5x,2 +9x,3 = -9. Otherwise, when you substitute the points (x,y,z) -> (29,16,3) back in, it won't make sense.

  • @tankieag1117
    @tankieag1117 3 หลายเดือนก่อน

    by the definition written for replacement "replace one row by the sum of itself and multiple of another row" right? so it should be R1 = R1 + (-2)R2 where the first R1 on the right hand side is the sum of itself and (-2)R2 is the multiple of another row. It wouldn't change the answer but I just wanna know if the other way around is correct as well.

  • @quinquintero6966
    @quinquintero6966 7 หลายเดือนก่อน

    Is scaling the only method in which we multiply the constant to the value (right side of augmented matrix)?

  • @yobro7837
    @yobro7837 7 หลายเดือนก่อน

    ​ @SawFinMath 13:30 Hi There,Can't We Interchange Row 1 with Row 3....If Not Then Kindly Brief It.

  • @DragonFire-tt7ly
    @DragonFire-tt7ly ปีที่แล้ว +1

    How did you get -4 5 and 9 on row 3?

  • @aframeunice5701
    @aframeunice5701 3 ปีที่แล้ว +2

    God bless you. You are very good

  • @altheebqatar
    @altheebqatar 7 หลายเดือนก่อน

    In the pr ties question why did u make the the number above the rectangle 0 is it nessary ?

  • @yonteelskywolf3886
    @yonteelskywolf3886 9 หลายเดือนก่อน

    Am wondering for the practice question how come when i do -1/10 r3->r3 to save a step my x3 become -3/5? Do I have a calculation error or is there a rule im breaking?

  • @aryamantrinity4687
    @aryamantrinity4687 3 หลายเดือนก่อน

    i love u... thank u for this playlist

  • @albertd.bangura3794
    @albertd.bangura3794 3 ปีที่แล้ว +2

    You are great! Thank you mam!

  • @_atif_
    @_atif_ 2 ปีที่แล้ว +1

    shouldnt the coefficient of X3 at R3 be -5 at 20:32 and not -3?

    • @sandhyaganesh5178
      @sandhyaganesh5178 2 ปีที่แล้ว

      The operation was -4-(-1) so it would be -3

  • @aboodhoms6662
    @aboodhoms6662 ปีที่แล้ว +2

    the answers are ( -1,0,-1) you have missed the -4 when you multiply it by 2, it is -8 not 8. correct me if im wrong thx.

  • @VolkColopatrion
    @VolkColopatrion 6 หลายเดือนก่อน

    what do you mean sum of itself and a multiple of another row?

  • @syedzaidi9642
    @syedzaidi9642 4 หลายเดือนก่อน

    I want to point out a small mistake, on the first example the matrix doesn't match the linear equations( missing 5 and 9 on the third eqn). Any ways Thank you very much for these videos! You are great

  • @bluevalley82
    @bluevalley82 2 ปีที่แล้ว

    4:39 why there is -1,5,9 in the matrices?

  • @paddygthatsme
    @paddygthatsme 2 ปีที่แล้ว +1

    Very helpful, cheers!

  • @aqibriaz5975
    @aqibriaz5975 3 ปีที่แล้ว +1

    really help full thanks

  • @bjjohnson5695
    @bjjohnson5695 ปีที่แล้ว

    Do you have a book recommendation that goes along with this course?

    • @SawFinMath
      @SawFinMath  ปีที่แล้ว +2

      I used David Lay’s Linear Algebra and applications 5e, though if I redo this series I will likely use the new Larson text. Much better development of topics.

  • @Ariobarzanes113
    @Ariobarzanes113 11 หลายเดือนก่อน +1

    Thanks a lot !

  • @manasacharya3653
    @manasacharya3653 6 หลายเดือนก่อน

    hey do you use a book for these topics?

    • @SawFinMath
      @SawFinMath  6 หลายเดือนก่อน

      This series uses Lay's text

  • @hyperplasma7005
    @hyperplasma7005 ปีที่แล้ว

    Could I just do -7 + 8 = 1 and -4 + 4 = 0 on the last step since it’s faster?

  • @AyushVikramSingh-fj6sv
    @AyushVikramSingh-fj6sv 2 ปีที่แล้ว +1

    thank you very much mam

  • @ifeanyichukwuchinwuko
    @ifeanyichukwuchinwuko 3 หลายเดือนก่อน

    Sorry but i don't really understand how you got (1,0,-1) cause i stopped at (0,4,-1)
    Do we really need to solve further or can we leave our answers this way

  • @oladapoajayi5685
    @oladapoajayi5685 ปีที่แล้ว

    Good day professor
    I believe there's a mistake in 4:13
    X3 has a coefficient of 1 but its 9 in the augmented matrix

  • @davidmurphy563
    @davidmurphy563 ปีที่แล้ว

    I'm struggling to picture the replacement row operation geometrically. I'm interpreting the matrix as a row basis which we're looking to transform into an orthonormal identity matrix basis.
    So we've got a vector plotted with the starting weird arbitrary basis. So we want to see where that vector lands plotted on standard x, y z unit vectors.
    So scaling a row is obviously valid as long as you replot the vector. Swapping rows doesn't change the space, it's just a change in our representation of it. Ie a rotation.
    Now substitution is obviously an operation on a R2 plane within R3.
    But it's not clear to me why this preserves the latent space...
    Oh wait, it's a shear! You're just straightening it up so it's at right angles. Right, got it.
    Rotation, scale and shear on a row basis matrix to make it an orthonormal basis matrix. And then you just shift the vector along with it.
    Really, you should have said that. It's confusing just doing the operation without knowing why.

  • @moth36
    @moth36 4 ปีที่แล้ว

    Millions of likes and thanks

  • @AbdurRehman-bo9bo
    @AbdurRehman-bo9bo ปีที่แล้ว

    you didnt mentioned about when the solution is unique?

  • @ticketpirates
    @ticketpirates 4 ปีที่แล้ว +2

    thank you

    • @SawFinMath
      @SawFinMath  4 ปีที่แล้ว +1

      You're welcome

  • @rennaafi_
    @rennaafi_ 2 ปีที่แล้ว

    nuhun pisann teh kimberly

    • @SawFinMath
      @SawFinMath  2 ปีที่แล้ว

      You are welcome!

  • @jewel_throne2950
    @jewel_throne2950 3 ปีที่แล้ว +1

    Splendid

    • @SawFinMath
      @SawFinMath  3 ปีที่แล้ว

      I appreciate it!

  • @pendarghasemi
    @pendarghasemi ปีที่แล้ว

    Thank you!

  • @flawlessnay773
    @flawlessnay773 3 ปีที่แล้ว

    I think you made a mistake @22:46 it’s supposed to be 8 not 0

  • @bryanproa628
    @bryanproa628 4 ปีที่แล้ว

    these help so much

    • @SawFinMath
      @SawFinMath  4 ปีที่แล้ว

      I'm so glad they helped!

  • @dylankapustka8895
    @dylankapustka8895 5 ปีที่แล้ว +2

    thank you! ^.^

  • @kazimnaqvi-uo5cw
    @kazimnaqvi-uo5cw ปีที่แล้ว

    from which book you teach

    • @kazimnaqvi-uo5cw
      @kazimnaqvi-uo5cw ปีที่แล้ว

      if you don't mind can u share a name and author name please

  • @kardelenkartal9989
    @kardelenkartal9989 3 หลายเดือนก่อน

    I do not understand how is this more practical , it takes longer to calculate

  • @xbz24
    @xbz24 ปีที่แล้ว +1

    exam tomorrow lets go

  • @zuko803
    @zuko803 3 หลายเดือนก่อน

    why my math teacher not taught this details when i was in high school...

  • @Rahul-yu3ro
    @Rahul-yu3ro 10 หลายเดือนก่อน

    11:44 - timestamp for me

  • @ball_like_bill
    @ball_like_bill 7 หลายเดือนก่อน +1

    4:41 Yes, ma'am 🫡 Take the lead 😄

  • @feilongish
    @feilongish 2 ปีที่แล้ว

    7: