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!
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.
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.
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.
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
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.
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
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 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! 😁
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.
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.
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
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.
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?
Your approach (1/2 Row 1 + Row 3 -> Row 3) doesn't change the answer, but in following the rest of the steps, it undoes much of the previous elimination. In the end, the solution is the same. I would repeat the steps you took to see if your arithmetic matches the steps described.
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.
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.
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?
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.
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
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!
Kimberly, you're my best teacher so far in linear algebra.
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.
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.
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.
I was absent the whole semester and tomorrow i have a linear Algebra final exam, your linear Algebra lessons saved me, thank you
Glad I could help!
Did u pass?
@@ifeanyiogbennaya7773 I did
And millions of people are in debt right now for this education that you can get anywhere online for free. Way to go, America!
Relatable
i passed my discreet maths because of your course. thank you, once the money starts rolling in i will send a special $Thanks$
4:41 hhhhh it's makes my laugh . I'm the one who make this video lol ... thanks any way
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
You are absolutely correct. Thanks for letting me know!
@@SawFinMath 13:30 Hi There,Can't We Interchange Row 1 with Row 3....If Not Then Kindly Brief It.
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.
This is the very best linear algebra course I ever got.
One of the best teachers of UA-cam University!
Lol, youtube is literally a university of everything
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.
Agreed. I always try to focus on the ‘why’!
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
Thank you for the great explanation, single handedly saving my grades fr
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!)
@@donovanrao5164 I haven’t heard of professor Leonard, but I also have a calc I and calc II series
@@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! 😁
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.
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.
a year late but I think so yes.
"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
your videos are so deep i love them
Thanks a lot I really understand things I wouldn't imagine to understand ^_^
This is a good math to practice during the summer 😊 thanks for the video
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
Better than my in person professor.
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.
Great explanation
God bless you. You are very good
Thanks so much!
i love u... thank u for this playlist
You are great! Thank you mam!
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?
Your approach (1/2 Row 1 + Row 3 -> Row 3) doesn't change the answer, but in following the rest of the steps, it undoes much of the previous elimination. In the end, the solution is the same. I would repeat the steps you took to see if your arithmetic matches the steps described.
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
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.
I think you mixed it up with the -4 next to it, but that column has a +4 for row 2, which makes 2 x +4 = +8
@SawFinMath 13:30 Hi There,Can't We Interchange Row 1 with Row 3....If Not Then Kindly Brief It.
Thanks a lot !
really help full thanks
Very helpful, cheers!
Is scaling the only method in which we multiply the constant to the value (right side of augmented matrix)?
thank you very much mam
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.
11:44 - timestamp for me
can you please tell me which book to use to solve questions?
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.
shouldnt the coefficient of X3 at R3 be -5 at 20:32 and not -3?
The operation was -4-(-1) so it would be -3
How did you get -4 5 and 9 on row 3?
thank you
You're welcome
Thank you!
In the pr ties question why did u make the the number above the rectangle 0 is it nessary ?
nuhun pisann teh kimberly
You are welcome!
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?
what do you mean sum of itself and a multiple of another row?
Splendid
I appreciate it!
4:39 why there is -1,5,9 in the matrices?
I think you made a mistake @22:46 it’s supposed to be 8 not 0
Do you have a book recommendation that goes along with this course?
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.
Millions of likes and thanks
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
thank you! ^.^
these help so much
I'm so glad they helped!
Could I just do -7 + 8 = 1 and -4 + 4 = 0 on the last step since it’s faster?
I do not understand how is this more practical , it takes longer to calculate
hey do you use a book for these topics?
This series uses Lay's text
you didnt mentioned about when the solution is unique?
why my math teacher not taught this details when i was in high school...
from which book you teach
if you don't mind can u share a name and author name please
exam tomorrow lets go
7:
4:41 Yes, ma'am 🫡 Take the lead 😄