There's no greater feeling than clicking on a video and having all your doubts and questions washed away in one sitting. Thank you, this was extremely helpful!
There's no greater feeling than clicking on a video and having all your doubts and questions washed away in one sitting. Thank you, this was extremely helpful! Thank you sir!
I am watching this again and again.It is masterpiece,you explained everything in 20 munite that my prof. couldnt explain to me in 3 weeks.Thank you so much,Sir
Thank you so much! This video cleared the confusing I was having. My professor just threw the formula for rank nullity theorem and I couldnt understand why it was like that. This video explained it nicely and added a gag to it too. Wish I had you as my professor!
thank you for such a clear video! You explained it really well and have a passion for the subject that is hard to not follow! thanks again, all the best!
What a life saver! I wish i saw this video earlier,, I have my la exam tomorrow and i was still having hard time understanding all those concepts,, and this single video untangled everything in my brain:) You r not even explaining in my mother tongue but you got me better than my own professor who speaks the same language as me hahaha Thank u so much!!!!
If you imagine 2x1 matrix, the transformation takes 2D space to 1D space, meaning there exists a line in the 2D space that goes to origin after the transformation, meaning that it's the null space of the matrix. Since column space is the output span, and null space is in a sense number of dimensions lost, the N (original number of dimensions) becomes the sum of column space and null space.
One question I encountered In case of equations Ax=0. Suppose that we consider row vectors instead of column vectors. Essentially the dot product of row vectors is 0 with x, which means that the x is perpendicular to all the row vectors. Why is x perpendicular to all the row vectors? I do understand that dot product being 0 means perpendicularity. I want to draw an insight here somehow.
4:17 - since those are 3 linearly independant vectors in R³, their span should be all of R³, so wouldn't the columns of the identity matrix also serve as a sufficient basis?
@@drpeyam and what about the 3 L.I. vectors of the row-reduced matrix? Shouldn't they span R3 as well? I didn't understand the "span non-preservation property" between the L.I. vectors in the original matrix vs the L.I. vectors in the row-reduced matrix
Hi Dr Peyam! If you have time, I was wondering if you could help me prove two things regarding column spaces and null spaces. I’m supposed to prove Nul(B) ⊂ Nul(AB). Here’s my attempt at the proof: Nul(B) contains all the vectors x that make the homogeneous Bx=0. We are allowed to left-multiply both sides by the matrix A. ABx = A0 ABx = 0 So I think we can say that if Bx=0, then ABx=0. If x makes Bx = 0 true, then x makes ABx=0 true. If x belongs to the null space of B, then x belongs to the null space of AB. Thus, we have proven that Nul(B) ⊂ Nul(AB). Is this reasoning correct or flawed? I’m also supposed to prove Col(AB) ⊂ Col(A). This one is trickier for me. Col(AB) contains all the output vectors y such that (AB)x = y. By the property of associative matrix multiplication, we are allowed to shift the parenthesis to say A(Bx) = y. If (AB)x = y then A(Bx) = y. So I’m seeing that if we can use AB to obtain the image vector y, then we can use A to obtain the same image vector y. But does this demonstrate that Col(AB) is a subset of Col(A)? I’ve been so confused by this for a long time and was wondering if you would be able to help clear up the confusion for me. Thank you so much!
I like how two seemingly parallel lines in this video seem to intersect somewhere off screen to the right. Do the top and bottom of the whiteboard form a basis of the column space of the whiteboard from this angle?
4:04 Row reduction destroys span? Why, columns 1, 3 and 5 are Linear independent and span R3 just like before row reduction Is the span of the matrix all 5 columns?
Thanks Dr Peyam, is there anyway you and your team will do a real analysis for those struggling in undergrad schools and introductions of proofs. Thanks as always, and it is a pleasure to watch your output.
Thanks, I am taking my linear algebra exam within an hour. I don’t want to say this video is helpful, but this video is super helpful!
Hahaha
I hope you already passed your LA exam years ago lol.
i m surprised that u could find time to take linear algebra despite ur busy schedule
wait, I thought you were a university professor? Why are you taking Linear Algebra ??
I actually have the exam in three hours 💀
There's no greater feeling than clicking on a video and having all your doubts and questions washed away in one sitting. Thank you, this was extremely helpful!
exactly
There's no greater feeling than clicking on a video and having all your doubts and questions washed away in one sitting. Thank you, this was extremely helpful!
Thank you sir!
Happy to help!
"every answer in linear algebra is row reduction"
Exactly what I was thinking! Thank you sir for making cramming fun and effective 👏
I am watching this again and again.It is masterpiece,you explained everything in 20 munite that my prof. couldnt explain to me in 3 weeks.Thank you so much,Sir
ı am here before the every linear algebra exam😂😂
Thank you so much! This video cleared the confusing I was having. My professor just threw the formula for rank nullity theorem and I couldnt understand why it was like that. This video explained it nicely and added a gag to it too. Wish I had you as my professor!
thank you for such a clear video! You explained it really well and have a passion for the subject that is hard to not follow! thanks again, all the best!
Honestly! This is so much helpful...I have my LA exam in an hour and with no preparation, I just watched this video now and gosh it felt good...
😂😂😂 the way he began am literally two hours away from my exam
I actually do have an linear algebra exam in an hour and needed this video so badly !
Bro you’re too good at teaching this concept… I’m crystal clear now, thx a lot!
Thank you :3
What a life saver! I wish i saw this video earlier,, I have my la exam tomorrow and i was still having hard time understanding all those concepts,, and this single video untangled everything in my brain:) You r not even explaining in my mother tongue but you got me better than my own professor who speaks the same language as me hahaha
Thank u so much!!!!
I liked the M and N acronyms rule. Thank you very much for this lecture.
thank you so much, you saved my life.
Thank you so much! I love your energy and enthusiasm for math!
+ Respect
Need more enthusiastic teachers/lecturers/professors like you
May Lord Shiva Bless you.
meat(A) + fat(A) = steak(A)
Thanks for posting this! I have a linear algebra final next week and I was stressing over this topic. Thank you!
What a top G. Huge respect for you brother
you are the goat mate thank you so much your teaching is incredible
You're very welcome! 😊
I don't know why his way of teaching makes me happy ...Anyways thanks for clear explanation of concepts .
Thank you so much, sir! You clarified my confusion hell out of me!
Thanks for the amazing video ! I found hope in linear algebra again !
You are welcome!
Your way of teaching is so good👍
Thankyou Sir, crystal clear explanation
Thanks! explaining everything in very simple way
You're welcome!
This channel is soo underrated
Thank you!!!
Thank you for this video😄This video make me pass the exam in linear algebra 😄I like it
Ooh I loved this algebra craziness ❤
Realy i like linear algebra because your explain is very very good thank y so much
u make maths so interesting. thanks Sir. it was so clear
Brilliant!! Absolutely Brilliant!
thank you so much, this was an eye opener.
So helpful sir. Thank you so much
your energyyyyy wake me up!!
You are so sweet...
You explained very easily, the most confusing topic for me in linear algebra.
OMG a lot of very useful things with only one example Thank you so much
Thanks so much...I am going to watch through all your videos
Thank you for the video Dr. Peyam
Thank you very much for the video!
من طرف الدكتور عيسى قيقية , كل الدعم❤❤😘
hey sir thanks a lot you cleared any of my doubts
Ok, This was actually a Great video THANK A lot sir!!!!!
Great Examples
Wow, thanks for the video, your explanations helped me a lot.
well done and thank you. extremely clear information and process
Thank you!!!
Thank you for this video!
You Made my day ❤
If you imagine 2x1 matrix, the transformation takes 2D space to 1D space, meaning there exists a line in the 2D space that goes to origin after the transformation, meaning that it's the null space of the matrix. Since column space is the output span, and null space is in a sense number of dimensions lost, the N (original number of dimensions) becomes the sum of column space and null space.
THANK YOU SO MUCH! God bless you sir!
One question I encountered
In case of equations Ax=0.
Suppose that we consider row vectors instead of column vectors.
Essentially the dot product of row vectors is 0 with x, which means that the x is perpendicular to all the row vectors.
Why is x perpendicular to all the row vectors?
I do understand that dot product being 0 means perpendicularity. I want to draw an insight here somehow.
Thank you! Explained very well
I have exactly one hour 2 minutes to take my linear algebra exam 😭
You are a fantastic teacher :)
Thank you so much!
thank you sir...its really helpful 😊
Amazing video. Thank you!
4:17 - since those are 3 linearly independant vectors in R³, their span should be all of R³, so wouldn't the columns of the identity matrix also serve as a sufficient basis?
Or any other set of 3 independant vectors
Yes, of course!
@@drpeyam and what about the 3 L.I. vectors of the row-reduced matrix? Shouldn't they span R3 as well? I didn't understand the "span non-preservation property" between the L.I. vectors in the original matrix vs the L.I. vectors in the row-reduced matrix
Awww we just learned rank recently, vector system's rank, rank of a linear function and ofc matrix rank. Also the Kronecker rank theorem and so on ^_^
you are the best ever.
Wonderful video Professor.
you are a great man
Thank you so much sir
super informative thank you!!
THANK YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! so helpful!!!!
It's more than super helpful 🙂
Amazing sir..... thankyou 👍
Is there any video that explains these concepts and why row reduction works geometrically ?
You can check out the playlist!!
Thank you, you are excellent!
00:13 I have the exam in an hour 😂😂
sir , why didnt you wrote the simplified matrix in row space span ? u said it preserves the span .
Tell you what. This video saved my test 2😂. Took something of 2 weeks into 20 minutes 😂
Very helpful thanks!
You’re welcome!
Hi Dr Peyam!
If you have time, I was wondering if you could help me prove two things regarding column spaces and null spaces.
I’m supposed to prove Nul(B) ⊂ Nul(AB).
Here’s my attempt at the proof:
Nul(B) contains all the vectors x that make the homogeneous Bx=0.
We are allowed to left-multiply both sides by the matrix A.
ABx = A0
ABx = 0
So I think we can say that if Bx=0, then ABx=0.
If x makes Bx = 0 true, then x makes ABx=0 true.
If x belongs to the null space of B, then x belongs to the null space of AB.
Thus, we have proven that Nul(B) ⊂ Nul(AB).
Is this reasoning correct or flawed?
I’m also supposed to prove Col(AB) ⊂ Col(A).
This one is trickier for me.
Col(AB) contains all the output vectors y such that (AB)x = y.
By the property of associative matrix multiplication, we are allowed to shift the parenthesis to say A(Bx) = y.
If (AB)x = y then A(Bx) = y.
So I’m seeing that if we can use AB to obtain the image vector y, then we can use A to obtain the same image vector y.
But does this demonstrate that Col(AB) is a subset of Col(A)?
I’ve been so confused by this for a long time and was wondering if you would be able to help clear up the confusion for me.
Thank you so much!
I like how two seemingly parallel lines in this video seem to intersect somewhere off screen to the right. Do the top and bottom of the whiteboard form a basis of the column space of the whiteboard from this angle?
thank you
Thanks sir
How are you teaching sooo good sir
Awwwww thank you!!!
Many thanks!!!
thank you very much
THank you for this vedio.... :)
4:04 Row reduction destroys span? Why, columns 1, 3 and 5 are Linear independent and span R3 just like before row reduction
Is the span of the matrix all 5 columns?
Yeah but this example is just a coincidence
Thanku sir
lot of thanks🥰🥰
Dr. Peyam should get waves 🌊
very nice!
First thanks it was very useful second I got headache for camera’s angle
I was watching etc etc n etc then found it now I regret why didn't I found it earlier.
RoWs and nOse
Columns Schmolumns 😂
when you are finding the Col(A) can you use the RREF or do you have to use REF
REF is enough
@@drpeyam but can you do rref and the answer be the same?
Yes, since the pivots are still at the same positions
for the colspace of A. I think you needed to out "span" of such 3 vectors
yea the video is super super good
Thanks so much!
The negative nine and positive two... Shouldn't that be positive nine ? Kindly inquiring
I think so, see comments
I bet that when you play Super Smash Bros, you always go for linear combos.
These are the best ones :P
Hahaha, of course 😂
Heck, within 30 seconds I feel so called out lol
valeu paee
Thanks Dr Peyam, is there anyway you and your team will do a real analysis for those struggling in undergrad schools and introductions of proofs. Thanks as always, and it is a pleasure to watch your output.
Real Analysis ua-cam.com/play/PLJb1qAQIrmmDs56gwp6yeytyy0wxWLac8.html
Bro he is hacker 😮 🔥
“maybe you have an exam in an hour”
Me: 😳 he caught me
Row space and column space be like: I am inevitable.
Dr peyam: and I am......🤏 🤏Dr peyam.
Thanks for helping me sir.