This is beyond useful. My professor never answers questions if you don't ask them in the exact presice mathematical terms and linear algebra is super abstract. I have been having a really hard time trying to understand all the terms. This video expresses the terms in easy and memorable ways. You have earned a subscriber!
Really useful stuff on TH-cam that I have found is Prime Newtons classes. Very good explanation sir 👍👍 Your students are really blessed to have you as their Mathematics Teacher. Keep rocking sir 👍👍
I'm doing Linear Algebra next semester, and the course has a 20% pass rate, I have watched all your videos before entering the danger zone. Thank you!!
10:20 Okay!!!! Basically the column space is set of all possible linear combinations made by the columns of original matrix. When we determine this set, a vector which could be written as the linear combination of vectors in the same set must be removed, since it is just extra information, and the column space won't be affected since the vector removed is itself made of the 'important' (basis) vectors we kept.
This is why the linearly independent vectors in the set are called basis!! Since they are the building blocks that define the vector space, and by removing any of them, we destroy the vector space/ make it represent another new vector space!! Basis = base that builds vector space/important vectors for the space.
Null space tells us what can be removed out of the column space, since it will contains the linearly dependent vectors (which we remove from the column space at the end). We call it null space because it ckntains all the columns that end up as 'zero columns' once we reduce matrix to rref. We do this proceudre to determine what is linearly dependent and what is not. So by the end of rref, we get: 1) the columns that can be deleted/ set to null through row operations, 2) the columns that are actually linearly indepenet and make up the span of col space. We use rank nullity theorm to determin which of our ve
I understood the concept really well, Thank you so much. The issue I faced was that the reduced row echelon form for the matrix given was wrong so I tripped on that for a while
Nice video!!! Your explanations are detailed and with examples. You explained definition as well as the intuition. Your voice is clear while your speaking speed is not too fast which gives me time to think and follow. And your handwriting is excellent!!!
Bro i subscribed your channel, as literally says you make these topics really easy. Hats off to your efforts and really grateful for all these type of videos.
I would say the column Space is a plane also the span of all linear independent columns of A (two columns on this example)and the null Space is a line also the span of all linear dependent columns of A (just one on this example)
at 11.18, you mentioned using column vectors in the REF for the column space. I think you can't do that as the row operations had affected the column vectors. Only the column vectors of the original matrix can form the column space.
thanks for your videos very clear and understandable. i have a question at the end of the video you told that R^n n is the number of rows. isn't it the number of columns? thanks again
![Rank & Nullity; How to Find a Basis for Null Space and Column Space [Passing Linear Algebra]](/img/n.gif)
This is the most underrated LA tutorial I ever seen.
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This is beyond useful. My professor never answers questions if you don't ask them in the exact presice mathematical terms and linear algebra is super abstract. I have been having a really hard time trying to understand all the terms. This video expresses the terms in easy and memorable ways. You have earned a subscriber!
Been watching Prime Newtons' videos for the past 3 months now. They really make the best lectures.
Prime Newtons does another brilliant job of tying concepts together. Well done, sir! And with your usual gusto! 🎉😊
I'm glad that you explained my confusion in matrix.God bless you brother.
i never took him for serious but now the tutor has won my heart, now i can see beyond
thank you prime newtons
i really couldn't find easy explanations for linear algebra and I'm so thankful to have found your channel
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Glad you found it helpful.
Really useful stuff on TH-cam that I have found is Prime Newtons classes. Very good explanation sir 👍👍
Your students are really blessed to have you as their Mathematics Teacher.
Keep rocking sir 👍👍
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the way you manage to explain stuff in an intuitive way is great
I'm so gland I found your chanel. I just started learning linear algebra, calculus and analytic geometry so I'm pretty lost half the time.
I'm doing Linear Algebra next semester, and the course has a 20% pass rate, I have watched all your videos before entering the danger zone.
Thank you!!
I'll make more soon
Same tomorrow is my exam
How did it go ?@@prabalmohanta138
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The analogies are enough to watch even if you know every single term. Really good video.
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10:20 Okay!!!! Basically the column space is set of all possible linear combinations made by the columns of original matrix. When we determine this set, a vector which could be written as the linear combination of vectors in the same set must be removed, since it is just extra information, and the column space won't be affected since the vector removed is itself made of the 'important' (basis) vectors we kept.
This is why the linearly independent vectors in the set are called basis!! Since they are the building blocks that define the vector space, and by removing any of them, we destroy the vector space/ make it represent another new vector space!! Basis = base that builds vector space/important vectors for the space.
Null space tells us what can be removed out of the column space, since it will contains the linearly dependent vectors (which we remove from the column space at the end).
We call it null space because it ckntains all the columns that end up as 'zero columns' once we reduce matrix to rref. We do this proceudre to determine what is linearly dependent and what is not. So by the end of rref, we get: 1) the columns that can be deleted/ set to null through row operations, 2) the columns that are actually linearly indepenet and make up the span of col space.
We use rank nullity theorm to determin which of our ve
20 minutes away from my final exam and I FINALLY understand this, thank you so much
You're the best! We love you. Thank you🙏
great sir,the way you make us understand was fantastic,learnt so many things from this vid.
easy way of learning linear algebra i ever found sir.easy understanding
Explained better than my professor did in 3 lectures...
Really well explained, crisp and to the point! Thank you!!
I understood the concept really well, Thank you so much. The issue I faced was that the reduced row echelon form for the matrix given was wrong so I tripped on that for a while
This was fun and quite helpful I must say! Cracked me up yet learnt so much. Thank youuuu
Nice video!!! Your explanations are detailed and with examples. You explained definition as well as the intuition. Your voice is clear while your speaking speed is not too fast which gives me time to think and follow. And your handwriting is excellent!!!
You teach very well so that every healthy gentle person will understand 😂
Prime Newtons you did it again!!!!!!!!!!💯
Good 👍
Thank you for making this easier ❤
So well done thank you for your time
Bro i subscribed your channel, as literally says you make these topics really easy. Hats off to your efforts and really grateful for all these type of videos.
Thanks and welcome
Hello, I really enjoyed this! Very exciting to learn new things, always🙋🙏
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Glad to find you , Professor!
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AWESOME EXPLANATION SIR 🔥
This is greater than great sir.
Thank you from South Korea
Great explanation that can benefit every mathematics students with difficulty. Keep up!!
Holy crap this finally clicked. Thank you so much!
Amazing sir this video is really help me
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Bangladesh
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very nice and clear explanations, thank you!
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Thank you Sir and keep teaching us 😁.
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This was so helpful, thank you!
13:37 i TOOK [1,-1,4] as one vector in null space. Then do multiply with matrix , it is not giving 0...plz recheck
I need a help from you sir on how to find the determinant of the upper triangular matrix if the first leading element is greater than 1
Thanks a lot, for clarifying a lot of concept
You didnt add row space explanation, would love that also. thanks
Awsome Video! Thanks a lot
Bro is majestic
I would say the column Space is a plane also the span of all linear independent columns of A (two columns on this example)and the null Space is a line also the span of all linear dependent columns of A (just one on this example)
god bless you sir thank you
I love your tshirt
at 11.18, you mentioned using column vectors in the REF for the column space. I think you can't do that as the row operations had affected the column vectors. Only the column vectors of the original matrix can form the column space.
Thank you. It would be great if you could make a video about RREF
That was incredible
thanks for your videos very clear and understandable. i have a question at the end of the video you told that R^n n is the number of rows. isn't it the number of columns? thanks again
Wow!
This is helpful.
Must I always have my matrix in RREF before finding the Null space?
Great
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This nice n easy...
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Good
thank you!
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Span of (1 -1 4)^T and the span of (1 -3 0)^T can't be the same. Hence the null space is not the span of (1 - 3 0)^T
thank you, but i think the RREF of A is {1 0 -1,0 1 1,0 0 0}
Prof are you sure if you did the RREF
correctly on A13 where it is '0' is it not supposed to be '-1'?
I am having a difficulty computing how that RREF became like that from the REF. It appears that the last column cannot all be equal to 0. 😢
Where my row space at? We would take the transpose to get the row space right for the rows that don’t contain all zeros?
underrted goaat
Thanks
👍
absolute G
Please can you do a video for a determinant question that is recursive
It is a matrix with unknown size and we have to find the determinant
Coming in clutch 5 mins before a final
thank you
Hi sir, Just a doubt when I tried to reduce the given matrix to RREF form, I got -1,1,0 in 3rd column, could anyone explain this
thanks sir.
Isnt the rref wrong tho? You can’t get top right 0 from the ref??
YOU ARE HIM
I think the rref entry for the first row third column should be -1 not 0. Help please.